Binary and Millisecond Pulsars

An Earlier Version of this article was published on 09 November 2005

The Original Version of this article was published on 25 September 1998


We review the main properties, demographics and applications of binary and millisecond radio pulsars. Our knowledge of these exciting objects has greatly increased in recent years, mainly due to successful surveys which have brought the known pulsar population to over 1800. There are now 83 binary and millisecond pulsars associated with the disk of our Galaxy, and a further 140 pulsars in 26 of the Galactic globular clusters. Recent highlights include the discovery of the young relativistic binary system PSR J1906+0746, a rejuvination in globular cluster pulsar research including growing numbers of pulsars with masses in excess of 1.5 M, a precise measurement of relativistic spin precession in the double pulsar system and a Galactic millisecond pulsar in an eccentric (e = 0.44) orbit around an unevolved companion.


Pulsars — rapidly rotating highly magnetised neutron stars — have many applications in physics and astronomy. Striking examples include the confirmation of the existence of gravitational radiation [366, 367, 368], the first extra-solar planetary system [404, 293] and the first detection of gas in a globular cluster [116]. The diverse zoo of radio pulsars currently known is summarized in Figure 1.

Figure 1

Venn diagram showing the numbers and locations of the various types of radio pulsars known as of September 2008. The large and small Magellanic clouds are denoted by LMC and SMC.

Pulsar research has proceeded at a rapid pace during the first three versions of this article [218, 219, 221]. Surveys with the Parkes radio telescope [308], at Green Bank [278], Arecibo [274] and the Giant Metre Wave Radio Telescope [277] have more than doubled the number of pulsars known a decade ago. With new instrumentation coming online, and new telescopes planned [105, 186, 154], these are exciting times for pulsar astronomy.

The aims of this review are to introduce the reader to the field and to focus on some of the many applications of pulsar research in relativistic astrophysics. We begin in Section 2 with an overview of the pulsar phenomenon, a review of the key observed population properties, the origin and evolution of pulsars and the main search strategies. In Section 3, we review present understanding in pulsar demography, discussing selection effects and their correction techniques. This leads to empirical estimates of the total number of normal and millisecond pulsars (see Section 3.3) and relativistic binaries (see Section 3.4) in the Galaxy and has implications for the detection of gravitational radiation by current and planned telescopes. Our review of pulsar timing in Section 4 covers the basic techniques (see Section 4.2), timing stability (see Section 4.3), binary pulsars (see Section 4.4), and using pulsars as sensitive detectors of long-period gravitational waves (see Section 4.7). We conclude with a brief outlook to the future in Section 5. Up-to-date tables of parameters of binary and millisecond pulsars are included in Appendix A.

Pulsar Phenomenology

Most of the basic observational facts about radio pulsars were established shortly after their discovery [141] in 1967. Although there are still many open questions, the basic model has long been established beyond all reasonable doubt, i.e. pulsars are rapidly rotating, highly magnetised neutron stars formed during the supernova explosions of massive stars.

The lighthouse model

Figure 2 shows an animation depicting the rotating neutron star, also known as the “lighthouse” model. As the neutron star spins, charged particles are accelerated along magnetic field lines forming a beam (depicted by the gold cones). The accelerating particles emit electromagnetic radiation, most readily detected at radio frequencies as a sequence of observed pulses. Each pulse is produced as the magnetic axis (and hence the radiation beam) crosses the observer’s line of sight each rotation. The repetition period of the pulses is therefore simply the rotation period of the neutron star. The moving “tracker ball” on the pulse profile in the animation shows the relationship between observed intensity and rotational phase of the neutron star.

Figure 2

gif-Movie (861 KB) Still from a movie showing The rotating neutron star (or “lighthouse”) model for pulsar emission. Animation designed by Michael Kramer. (For video see appendix)

Neutron stars are essentially large celestial flywheels with moments of inertia ∼1038 kg m2. The rotating neutron star model [290, 122] predicts a gradual slowdown and hence an increase in the pulse period as the outgoing radiation carries away rotational kinetic energy. This idea gained strong support when a period increase of 36.5 ns per day was measured for the pulsar B0531+21Footnote 1 in the Crab nebula [321], which implied that a rotating neutron star with a large magnetic field must be the dominant energy supply for the nebula [123].

Pulse periods and slowdown rates

The pulsar catalogue [248, 12] contains up-to-date parameters for 1775 pulsars. Most of these are “normal” with pulse periods P ∼ 0.5 s which increase secularly at rates ∼ 10−15 s/s. A growing fraction are “millisecond pulsars”, with 1.4 ms ≲ P ≲ 30 ms and ≲ 10−19 s/s. As shown in the “P diagram” in Figure 3, normal and millisecond pulsars are distinct populations.

Figure 3

The P−Ṗ diagram showing the current sample of radio pulsars. Binary pulsars are highlighted by open circles. Lines of constant magnetic field (dashed), characteristic age (dash-dotted) and spin-down energy loss rate (dotted) are also shown.

The differences in P and imply fundamentally different magnetic field strengths and ages. Treating the pulsar as a rotating magnetic dipole, one may show [226] that the surface magnetic field strength B ∝ (PṖ)1/2 and the characteristic age τc = P/(2). Lines of constant B and τc are drawn on Figure 3, from which we infer typical values of 1012 G and 107 yr for the normal pulsars and 108 G and 109 yr for the millisecond pulsars. For the rate of loss of kinetic energy, sometimes called the spin-down luminosity, we have ĖṖ/P3. The lines of constant Ė shown on Figure 3 indicate that the most energetic objects are the very young normal pulsars and the most rapidly spinning millisecond pulsars.

The most rapidly rotating neutron star currently known, J1748−2446ad,with a spin rate of 716 Hz, resides in the globular cluster Terzan 5 [140]. As discussed by Lattimer & Prakash [206], the limiting (non-rotating) radius of a 1.4 M neutron star with this period is 14.3 km. If a precise measurement for the pulsar mass can be made through future timing measurements (Section 4), then this pulsar could be a very useful probe of the equation of state of super dense matter.

While the hunt for more rapidly rotating pulsars and even “sub-millisecond pulsars” continues, and most neutron star equations of state allow higher spin rates than 716 Hz, it has been suggested [38] that the dearth of pulsars with P < 1.5 ms is caused by gravitational wave emission from Rossby-mode instabilities [5]. The most rapidly rotating pulsars [140] are predominantly members of eclipsing binary systems which could hamper their detection in radio surveys. Independent constraints on the limiting spin frequencies of neutron stars come from studies of millisecond X-ray binaries [66] which are not thought to be selection-effect limited [67]. This analysis does not predict a significant population of neutron stars with spin rates in excess of 730 Hz.

Pulse profiles

Pulsars are weak radio sources. Measured intensities at 1.4 GHz vary between 5μJy and 1 Jy (1 Jy ≡ 10−26 W m−2 Hz−1). As a result, even with a large radio telescope, the coherent addition of many hundreds or even thousands of pulses is usually required in order to produce a detectable “integrated profile”. Remarkably, although the individual pulses vary dramatically, the integrated profile at a given observing frequency is very stable and can be thought of as a fingerprint of the neutron star’s emission beam. Profile stability is of key importance in pulsar timing measurements discussed in Section 4.

The selection of integrated profiles in Figure 4 shows a rich diversity in morphology including two examples of “interpulses” — a secondary pulse separated by about 180 degrees from the main pulse. One interpretation for this phenomenon is that the two pulses originate from opposite magnetic poles of the neutron star (see however [249]). Since this is an unlikely viewing angle, we would expect interpulses to be a rare phenomenon. Indeed, the fraction of known pulsars in which interpulses are observed in their pulse profiles is only a few percent [194]. Recent work [392] on the statistics of interpulses among the known population show that the interpulse fraction depends inversely on pulse period. The origin of this effect could be due to alignment between the spin and magnetic axis of neutron stars on timescales of order 107 yr [392]. If we take this result at face value, and assume that all millisecond pulsars descend from normal pulsars (Section 2.6), then the implication is that millisecond pulsars should be preferentially aligned rotators. However, their appears to be no strong evidence in favour of this expectation based on the pulse profile morphology of millisecond pulsars [203].

Figure 4

A variety of integrated pulse profiles taken from the available literature. References: Panels a, b, d, f [124], Panel c [23], Panels e, g, i [203], Panel h [31]. Each profile represents 360 degrees of rotational phase. These profiles are freely available from an online database [378].

Two contrasting phenomenological models have been proposed to explain the observed pulse shapes. The “core and cone” model [310] depicts the beam as a core surrounded by a series of nested cones. Alternatively, the “patchy beam” model [243, 128] has the beam populated by a series of randomly-distributed emitting regions. Recent work suggests that the observational data can be better explained by a hybrid empirical model depicted in Figure 5 which employs patchy beams in a core and cone structure [179].

Figure 5

A recent phenomenological model for pulse shape morphology. The neutron star is depicted by the grey sphere and only a single magnetic pole is shown for clarity. Left: a young pulsar with emission from a patchy conal ring at high altitudes from the surface of the neutron star. Right: an older pulsar in which emission emanates from a series of patchy rings over a range of altitudes. Centre: schematic representation of the change in emission height with pulsar age. Figure designed by Aris Karastergiou and Simon Johnston [179].

A key feature of this new model is that the emission height of young pulsars is radically different from that of the older population. Monte Carlo simulations [179] using this phenomenological model appear to be very successful at explaining the rich diversity of pulse shapes. Further work in this area is necessary to understand the origin of this model, and improve our understanding of the shape and evolution of pulsar beams and fraction of sky they cover. This is of key importance to the results of population studies reviewed in Section 3.2.

The pulsar distance scale

Quantitative estimates of the distance to each pulsar can be made from the measurement of pulse dispersion — the delay in pulse arrival times across a finite bandwidth. Dispersion occurs because the group velocity of the pulsed radiation through the ionised component of the interstellar medium is frequency dependent. As shown in Figure 6, pulses emitted at lower radio frequencies travel slower through the interstellar medium, arriving later than those emitted at higher frequencies.

Figure 6

Pulse dispersion shown in this Parkes observation of the 128 ms pulsar B1356–60. The dispersion measure is 295 cm−3 pc. The quadratic frequency dependence of the dispersion delay is clearly visible. Figure provided by Andrew Lyne.

Quantitatively, the delay Δt in arrival times between a high frequency νhi and a low frequency νlo pulse can be shown [226] to be

$$\Delta t = 4.15\;{\rm{ms}} \times \left[ {{{\left({{{{\nu _{{\rm{lo}}}}} \over {{\rm{GHz}}}}} \right)}^{- 2}} - {{\left({{{{\nu _{{\rm{hi}}}}} \over {{\rm{GHz}}}}} \right)}^{- 2}}} \right] \times \left({{{{\rm{DM}}} \over {{\rm{c}}{{\rm{m}}^{{\rm{- 3}}}}{\rm{pc}}}}} \right),$$

where the dispersion measure

$${\rm{DM =}}\int\nolimits_0^d {{n_{\rm{e}}}dl,}$$

is the integrated column density of electrons, ne, out to the pulsar at a distance d. This equation may be solved for d given a measurement of DM and a model of the free electron distribution calibrated from the 100 or so pulsars with independent distance estimates and measurements of scattering for lines of sight towards various Galactic and extragalactic sources [364, 390]. A recent model of this kind, known as NE2001 [84, 85], provides distance estimates with an average uncertainty of ∼ 30%.

Because the electron density models are only as good as the scope of their input data allow, one should be mindful of systematic uncertainties. For example, studies of the Parkes multibeam pulsar distribution [199, 224] suggest that the NE2001 model underestimates the distances of pulsars close to the Galactic plane. This suspicion has been dramatically confirmed recently by an extensive analysis [120] of pulsar DMs and measurements of Galactic Hα emission. This work shows that the distribution of Galactic free electrons to be exponential in form with a scale height of \(1830_{- 250}^{+ 120}{\rm{pc}}\). This value is a factor of two higher than previously thought. A revised version of the NE2001 model which takes into account these and other developments is currently in preparation [79].

Pulsars in binary systems

As can be inferred from Figure 1, only a few percent of all known pulsars in the Galactic disk are members of binary systems. Timing measurements (see Section 4) place useful constraints on the masses of the companions which, often supplemented by observations at other wavelengths, tell us a great deal about their nature. The present sample of orbiting companions are either white dwarfs, main sequence stars or other neutron stars. Two notable hybrid systems are the “planet pulsars” B1257+12 and B1620−26. PSR B1257+12 is a 6.2-ms pulsar accompanied by at least three terrestrial-mass bodies [404, 293, 403] while B1620−26, an 11-ms pulsar in the globular cluster M4, is part of a triple system with a 1–2 MJupiter planet [370, 16, 369, 338] orbiting a neutron star—white dwarf stellar binary system. The current limits from pulsar timing favour a roughly 45-yr mildly-eccentric (e ∼ 0.16) orbit with semi-major axis ∼ 25 AU. Despite several tentative claims over the years, no other convincing cases for planetary companions to pulsars exist. Orbiting companions are much more common around millisecond pulsars (∼ 80% of the observed sample) than around the normal pulsars (≲ 1%). In general, binary systems with low-mass companions (≲ 0.7 M — predominantly white dwarfs) have essentially circular orbits: 10−5e ≲ 0.01. Binary pulsars with high-mass companions (≳ 1 M — massive white dwarfs, other neutron stars or main sequence stars) tend to have more eccentric orbits, 0.15 ≲ e ≲ 0.9.

Evolution of normal and millisecond pulsars

A simplified version of the presently favoured model [39, 110, 339, 2] to explain the formation of the various types of systems observed is shown in Figure 7. Starting with a binary star system, a neutron star is formed during the supernova explosion of the initially more massive star. From the virial theorem, in the absence of any other factors, the binary will be disrupted if more than half the total pre-supernova mass is ejected from the system during the (assumed symmetric) explosion [142, 36]. In practice, the fraction of surviving binaries is also affected by the magnitude and direction of any impulsive “kick” velocity the neutron star receives at birth from a slightly asymmetric explosion [142, 19]. Binaries that disrupt produce a high-velocity isolated neutron star and an OB runaway star [40]. The high probability of disruption explains qualitatively why so few normal pulsars have companions. Those that survive will likely have high orbital eccentricities due to the violent conditions in the supernova explosion. There are currently four known normal radio pulsars with massive main sequence companions in eccentric orbits which are examples of binary systems which survived the supernova explosion [169, 182, 348, 349, 236]. Over the next 107–8 yr after the explosion, the neutron star may be observable as a normal radio pulsar spinning down to a period ≳ several seconds. After this time, the energy output of the star diminishes to a point where it no longer produces significant amounts of radio emission.

Figure 7

Cartoon showing various evolutionary scenarios involving binary pulsars.

For those few binaries that remain bound, and in which the companion is sufficiently massive to evolve into a giant and overflow its Roche lobe, the old spun-down neutron star can gain a new lease of life as a pulsar by accreting matter and angular momentum at the expense of the orbital angular momentum of the binary system [2]. The term “recycled pulsar” is often used to describe such objects. During this accretion phase, the X-rays produced by the frictional heating of the infalling matter onto the neutron star mean that such a system is expected to be visible as an X-ray binary. Two classes of X-ray binaries relevant to binary and millisecond pulsars exist: neutron stars with high-mass or low-mass companions. Detailed reviews of the X-ray binary population, including systems likely to contain black holes, can be found elsewhere [36, 320].

High-mass systems

In a high-mass X-ray binary, the companion is massive enough that it also explodes as a supernova, producing a second neutron star. If the binary system is lucky enough to survive the explosion, the result is a double neutron star binary. Nine such systems are now known, the original example being PSR B1913+16 [150] — a 59-ms radio pulsar which orbits its companion every 7.75 hr [366, 367]. In this formation scenario, PSR B1913+16 is an example of the older, first-born, neutron star that has subsequently accreted matter from its companion.

For many years, no clear example was known where the second-born neutron star was observed as a pulsar. The discovery of the double pulsar J0737-3039 [48, 239], where a 22.7-ms recycled pulsar “A” orbits a 2.77-s normal pulsar “B” every 2.4 hr, has now provided a dramatic confirmation of this evolutionary model in which we identify A and B as the first and second-born neutron stars respectively. Just how many more observable double pulsar systems exist in our Galaxy is not clear. While the population of double neutron star systems in general is reasonably well understood (see Section 3.4.1), a number of effects conspire to reduce the detectability of double pulsar systems. First, the lifetime of the second born pulsar cannot be prolonged by accretion and spin-up and hence is likely to be less than one tenth that of the recycled pulsar. Second, the radio beam of the longer period second-born pulsar is likely to be much smaller than its spun-up partner making it harder to detect (see Section 3.2.3). Finally, as discussed in Section 4.4, the PSR J0737−3039 system is viewed almost perfectly edge-on to the line of sight and there is strong evidence [258] that the wind of the more rapidly spinning A pulsar is impinging on B’s magnetosphere which affects its radio emission. In summary, the prospects of ever finding more than a few 0737-like systems appears to be rather low.

A notable recent addition to the sample of double neutron star binaries is PSR J1906+0746, a 144-ms pulsar in a highly relativistic 4-hr orbit with an eccentricity of 0.085 [232]. Timing observations show the pulsar to be young with a characteristic age of only 105 yr. Measurements of the relativistic periastron advance and gravitational redshift (see Section 4.4) constrain the masses of the pulsar and its companion to be 1.25 M and 1.37 M respectively [180]. We note, however, that the pulsar exhibits significant amounts of timing noise (see Section 4.3), making the analysis of the system far from trivial. Taken at face value, these parameters suggest that the companion is also a neutron star, and the system appears to be a younger version of the double pulsar. Despite intensive searches, no pulsations from the companion star (expected to be a recycled radio pulsar) have so far been observed [232]. This could be due to unfavourable beaming and/or intrinsic radio faintness. Continued searches for radio pulsations from these companions are strongly encouraged, however, as geodetic precession may make their radio beams visible in future years.

Low-mass systems

The companion in a low-mass X-ray binary evolves and transfers matter onto the neutron star on a much longer timescale, spinning it up to periods as short as a few ms [2]. Tidal forces during the accretion process serve to circularize the orbit. At the end of the spin-up phase, the secondary sheds its outer layers to become a white dwarf in orbit around a rapidly spinning millisecond pulsar. This model has gained strong support in recent years from the discoveries of quasi-periodic kHz oscillations in a number of low-mass X-ray binaries [396], as well as Doppler-shifted 2.49-ms X-ray pulsations from the transient X-ray burster SAX J1808.4-3658 [398, 65]. Seven other “X-ray millisecond pulsars” are now known with spin rates and orbital periods ranging between 185–600 Hz and 40 min −4.3 hr respectively [397, 263, 173, 204].

Numerous examples of these systems in their post X-ray phase are now seen as the millisecond pulsar—white dwarf binary systems. Presently, 20 of these systems have compelling optical identifications of the white dwarf companion, and upper limits or tentative detections have been found in about 30 others [384]. Comparisons between the cooling ages of the white dwarfs and the millisecond pulsars confirm the age of these systems and suggest that the accretion rate during the spin-up phase was well below the Eddington limit [132].

Further support for the above evolutionary scenarios comes from two correlations in the observed sample of low-mass binary pulsars. Firstly, as seen in Figure 8, there is a strong correlation between orbital period and eccentricity. The data are in very good agreement with a theoretical relationship which predicts a relic orbital eccentricity due to convective eddy currents in the accretion process [298]. Secondly, as shown in Panel b of Figure 9, where companion masses have been measured accurately, through radio timing (see Section 4.4) and/or through optical observations [384], they are in good agreement with a relation between companion mass and orbital period predicted by binary evolution theory [361]. A word of caution is required in using these models to make predictions, however. When confronted with a larger ensemble of binary pulsars using statistical arguments to constrain the companion masses (see Panel a of Figure 9), current models have problems in explaining the full range of orbital periods on this diagram [347].

Figure 8

Eccentricity versus orbital period for a sample of 21 low-mass binary pulsars which are not in globular clusters, with the triangles denoting three recently discovered systems [347]. The solid line shows the median of the predicted relationship between orbital period and eccentricity [298]. Dashed lines show 95% the confidence limit about this relationship. The dotted line shows Pbe2. Figure provided by Ingrid Stairs [347] using an adaptation of the orbital period-eccentricity relationship tabulated by Fernando Camilo.

Figure 9

Orbital period versus companion mass for binary pulsars showing the whole sample where, in the absence of mass determinations, statistical arguments based on a random distribution of orbital inclination angles (see Section 4.4) have been used to constrain the masses as shown (Panel a), and only those with well determined companion masses (Panel b). The dashed lines show the uncertainties in the predicted relation [361]. This relationship indicates that as these systems finished a period of stable mass transfer due to Roche-lobe overflow, the size and hence period of the orbit was determined by the mass of the evolved secondary star. Figure provided by Marten van Kerkwijk [384].

Intermediate mass binary pulsars

The range of white dwarf masses observed is becoming broader. Since this article originally appeared [218], the number of “intermediate-mass binary pulsars” [53] has grown significantly [57]. These systems are distinct to the millisecond pulsar-white dwarf binaries in several ways:

  1. 1.

    The spin period of the radio pulsar is generally longer (9 — 200 ms).

  2. 2.

    The mass of the white dwarf is larger (typically ≳ 0.5 M).

  3. 3.

    The orbit, while still essentially circular, is often significantly more eccentric (e ≳ 10−3).

  4. 4.

    The binary parameters do not necessarily follow the mass—period or eccentricity—period relationships.

It is not presently clear whether these systems originated from low- or high-mass X-ray binaries. It was suggested by van den Heuvel [382] that they have more in common with high-mass systems. Subsequently, Li proposed [210] that a thermal-viscous instability in the accretion disk of a low-mass X-ray binary could truncate the accretion phase and produce a more slowly spinning neutron star.

Isolated recycled pulsars

The scenarios outlined qualitatively above represent a reasonable understanding of binary evolution. There are, however, a number of pulsars with spin properties that suggest a phase of recycling took place but have no orbiting companions. While the existence of such systems in globular clusters are more readily explained by the high probability of stellar interactions compared to the disk [337], it is somewhat surprising to find them in the Galactic disk. Out of a total of 72 Galactic millisecond pulsars, 16 are isolated (see Table 2). Although it has been proposed that these millisecond pulsars have ablated their companion via their strong relativistic winds [192] as may be happening in the PSR B1957+20 system [119], it is not clear whether the energetics or timescales for this process are feasible [208].

There are four further “anomalous” isolated pulsars with periods in the range 28–60 ms [58, 229]. When placed on the P diagram, these objects populate the region occupied by the double neutron star binaries. The most natural explanation for their existence, therefore, is that they are “failed double neutron star binaries” which disrupted during the supernova explosion of the secondary [58]. A simple calculation [229], suggested that for every double neutron star we should see of order ten such isolated objects. Recent work [29] has investigated why so few are observed. Using the most recent population synthesis models to follow the evolution of binary systems [28], it appears that the discrepancy may not be as significant as previously supposed. In particular, the space velocity distribution of surviving binary systems is narrower than for the isolated objects that were during the second supernova explosion. The isolated systems occupy a larger volume of the Galaxy than the surviving binaries and are harder to detect. When this selection effect is accounted for [29], the relative sample sizes appear to be consistent with the disruption hypothesis.

A new class of millisecond pulsars?

One of the most remarkable recent discoveries is the binary pulsar J1903+0327 [70]. Found in an on-going multibeam survey with the Arecibo telescope [275, 82], this 2.15-ms pulsar is distinct from all other millisecond pulsars in that its 95-day orbit has an eccentricity of 0.43! In addition, timing measurements of the relativistic periastron advance and Shapiro delay in this system (see Section 4.4), show the mass of the pulsar to be 1.74 ± 0.04M and the companion star to be 1.051 ± 0.015M. Optical observations show a possible counterpart which is consistent with a 1 M star. While similar systems have been observed in globular clusters (e.g. PSR J0514−4002A in NGC 1851[117]), presumably a result of exchange interactions, the standard recycling hypothesis outlined in Section 2.6 cannot account for pulsars like J1903+0327 in the Galactic disk.

How could such an eccentric binary millisecond pulsar system form? One possibility is that the binary system was produced in an exchange interaction in a globular cluster and subsequently ejected, or the cluster has since disrupted. Statistical estimates [70] of the likelihood of both these channels are in the range 1–10%, implying that a globular cluster origin cannot be ruled out.

Another possibility is that the pulsar is a member of an hierarchical triple system with a one solar mass white dwarf in the 95-day orbit, and a main sequence star in a much wider and highly inclined orbit which has so far not been revealed by timing. The origin of the high eccentricity is through perturbations from the outer star, the so-called Kozai mechanism [197]. Formation estimates based on observational data on stellar multiplicity [304] find that around 4% of all binary millisecond pulsars are expected to be triple systems [70]. The existence of a single triple system among the current sample of millisecond pulsars appears to be consistent with this hypothesis.

If future observations of the proposed optical counterpart confirm it as the binary companion through spectral line measurements of orbital Doppler shifts, the above triple-system scenario will be ruled out. Such an observation would favour a hybrid scenario suggested by van den Heuvel [383] in which the white dwarf and pulsar merge due to gravitational radiation losses. Tidal disruption of the white dwarf in the inspiral would produce an accretion disk and induce an eccentricity in the orbit of the outer star leaving behind an eccentric binary system. This idea could naturally account for the high pulsar mass observed in this system which could arise from accretion of a white-dwarf debris disk following coalescence. Alternatively, as suggested by Champion et al. [70], the millisecond pulsar might have ablated the white dwarf companion in a triple system leaving only the unevolved companion in an elliptical orbit.

Pulsar velocities

Pulsars have long been known to have space velocities at least an order of magnitude larger than those of their main sequence progenitors, which have typical values between 10 and 50 km s−1. Proper motions for over 250 pulsars have now been measured largely by radio timing and interferometric techniques [237, 24, 111, 133, 144, 406]. These data imply a broad velocity spectrum ranging from 0 to over 1000 km s−1 [242], with the current record holder being PSR B1508+55 [72], with a proper motion and parallax measurement implying a transverse velocity of \(1083_{- 90}^{+ 103}{\rm{km}}\,{{\rm{s}}^{- 1}}\). As Figure 10 illustrates, high-velocity pulsars born close to the Galactic plane quickly migrate to higher Galactic latitudes. Given such a broad velocity spectrum, as many as half of all pulsars will eventually escape the Galactic gravitational potential [242, 81].

Figure 10

gif-Movie (213 KB) Still from a movie showing A simulation following the motion of 100 pulsars in a model gravitational potential of our Galaxy for 200 Myr. The view is edge-on, i.e. the horizontal axis represents the Galactic plane (30 kpc across) while the vertical axis represents ±10 kpc from the plane. This snapshot shows the initial configuration of young neutron stars. (For video see appendix)

Such large velocities are perhaps not surprising, given the violent conditions under which neutron stars are formed. If the explosion is only slightly asymmetric, an impulsive “kick” velocity of up to 1000 km s−1 can be imparted to the neutron star [336]. In addition, if the neutron star progenitor was a member of a binary system prior to the explosion, the pre-supernova orbital velocity will also contribute to the resulting speed of the newly-formed pulsar. The relative contributions of these two factors to the overall pulsar birth velocity distribution is currently not well understood.

The distribution of pulsar velocities has a high velocity component due to the normal pulsars [242, 144, 106], and a lower velocity component from binary and millisecond pulsars [217, 80, 244, 144]. One reason for this dichotomy appears to be that, in order to survive and subsequently form recycled pulsars through the accretion process outlined above, the binary systems contain only those neutron stars with lower birth velocities. In addition, the surviving neutron star has to pull the companion along with it, thus slowing the system down.

Further insights into pulsar kicks from analyses of proper motion and polarization data [165, 166, 311] find strong evidence for an alignment between the spin axis and the velocity vector at birth. These data have recently been combined with modeling of pulsar-wind nebulae [281], where strong evidence is found for a model in which the natal impulse is provided by an anisotropic flux of neutrinos from the proto-neutron star on timescales of a few seconds.

Pulsar searches

The radio sky is being repeatedly searched for new pulsars in a variety of ways. In the following, we outline the major search strategies that are optimized for binary and millisecond pulsars.

All-sky searches

The oldest radio pulsars form a relaxed population of stars oscillating in the Galactic gravitational potential [131]. The scale height for such a population is at least 500 pc [221], about 10 times that of the massive stars which populate the Galactic plane. Since the typical ages of millisecond pulsars are several Gyr or more, we expect, from our vantage point in the Galaxy, to be in the middle of an essentially isotropic population of nearby sources. All-sky searches for millisecond pulsars at high Galactic latitudes have been very effective in probing this population.

Motivated by the discovery of two recycled pulsars at high latitudes with the Arecibo telescope [401, 404], surveys carried out at Arecibo, Parkes, Jodrell Bank and Green Bank by others in the 1990s [58, 59, 60, 251, 244] discovered around 30 further objects. Although further searching of this kind has been carried out at Arecibo in the past decade [233], much of the recent efforts have been concentrated along the plane of our Galaxy and in globular clusters discussed below. Very recently, however, 12,000 square degrees of sky was surveyed using a new 350-MHz receiver on the Green Bank Telescope [393, 43]. Processing of these data is currently underway, with two millisecond pulsars found with around 10% of the dataset analysed.

Searches close to the plane of our Galaxy

Young pulsars are most likely to be found near to their places of birth close to the Galactic plane. This was the target region of the main Parkes multibeam survey and has so far resulted in the discovery of 783 pulsars [250, 264, 199, 145, 108, 224, 187, 49], almost half the number currently known! Such a large haul inevitably results in a number of interesting individual objects such as the relativistic binary pulsar J1141−6545 [183, 288, 25, 148, 35], a young pulsar orbiting an ∼ 11M star (probably a main sequence B-star [348, 349]), a young pulsar in a ∼ 5 yr-eccentric orbit (e = 0.955; the most eccentric found so far) around a 10 —20 M companion [236, 224], several intermediate-mass binary pulsars [57], and two double neutron star binaries [240, 107]. Further analyses of this rich data set are now in progress and will ensure yet more discoveries in the near future.

Motivated by the successes at Parkes, a multibeam survey is now in progress with the Arecibo telescope [275] and the Effelsberg radio telescope. The Arecibo survey has so far discovered 46 pulsars [275, 82] with notable finds including a highly relativistic binary [232] and an eccentric millisecond pulsar binary [70]. Hundreds more pulsars could be found in this survey over the next five years. A significant fraction of this yield are expected to be distant millisecond pulsars in the disk of our Galaxy. With the advent of sensitive low-noise receivers at lower observing frequencies, surveys of the Galactic plane are being carried out with the GMRT [171], Green Bank [138] and Westerbork [326]. At the time of writing, no new millisecond pulsars have been found in these searches, though significant amounts of data remain to be fully processed.

Searches at intermediate and high Galactic latitudes

To probe more deeply into the population of millisecond and recycled pulsars than possible at high Galactic latitudes, the Parkes multibeam system was also used to survey intermediate latitudes [102, 100]. Among the 69 new pulsars found in the survey, 8 are relatively distant recycled objects. Two of the new recycled pulsars from this survey [100] are mildly relativistic neutron star-white dwarf binaries. An analysis of the full results from this survey should significantly improve our knowledge on the Galaxy-wide population and birth-rate of millisecond pulsars. Arecibo surveys at intermediate latitudes also continue to find new pulsars, such as the long-period binaries J2016+1948 and J0407+1607 [279, 233], and the likely double neutron star system J1829+2456 [68].

Although the density of pulsars decreases with increasing Galactic latitude, discoveries away from the plane provide strong constraints on the scale height of the millisecond pulsar population. Two recent surveys with the Parkes multibeam system [49, 156] have resulted in a number of interesting discoveries. Pulsars at high latitudes are especially important for the millisecond pulsar timing array (Section 4.7.3) which benefits from widely separated pulsars on the sky to search for correlations in the cosmic gravitational wave background on a variety of angular scales.

Targeted searches of globular clusters

Globular clusters have long been known to be breeding grounds for millisecond and binary pulsars [63]. The main reason for this is the high stellar density and consequently high rate of stellar interaction in globular clusters relative to most of the rest of the Galaxy. As a result, low-mass X-ray binaries are almost 10 times more abundant in clusters than in the Galactic disk. In addition, exchange interactions between binary and multiple systems in the cluster can result in the formation of exotic binary systems [337]. To date, searches have revealed 140 pulsars in 26 globular clusters [276]. Early highlights include the double neutron star binary in M15 [305] and a low-mass binary system with a 95-min orbital period in 47 Tucanae [56], one of 23 millisecond pulsars currently known in this cluster alone [56, 223].

On-going surveys of clusters continue to yield new surprises [316, 89], with no less than 70 discoveries in the past five years [314]. Among these is the most eccentric binary pulsar in a globular cluster so far — J0514−4002 is a 4.99 ms pulsar in a highly eccentric (e = 0.89) binary system in the globular cluster NGC 1851 [114]. The cluster with the most pulsars is now Terzan 5 which boasts 33 [317, 276], 30 of which were found with the Green Bank Telescope [278]. The spin periods and orbital parameters of the new pulsars reveal that, as a population, they are significantly different to the pulsars of 47 Tucanae which have periods in the range 2–8 ms [223]. The spin periods of the new pulsars span a much broader range (1.4–80 ms) including the first, third and fourth shortest spin periods of all pulsars currently known. The binary pulsars include six systems with eccentric orbits and likely white dwarf companions. No such systems are known in 47 Tucanae. The difference between the two pulsar populations may reflect the different evolutionary states and physical conditions of the two clusters. In particular, the central stellar density of Terzan 5 is about twice that of 47 Tucanae, suggesting that the increased rate of stellar interactions might disrupt the recycling process for the neutron stars in some binary systems and induce larger eccentricities in others.

Targeted searches of other regions

While globular clusters are the richest targets for finding millisecond pulsars, other regions of interest have been searched. Recently, a search of error boxes from unidentified sources from the Energetic Gamma-Ray Experiment Telescope (EGRET) revealed three new binary pulsars J1614−2318, J1614−2230 and J1744−3922 [139, 88, 313]. None of these pulsars is likely to be energetic enough to be associated with their target EGRET sources [139]. While convincing EGRET associations with several young pulsars are now known [199], it is not clear whether millisecond pulsars are relevant to the energetics of these enigmatic sources [69]. Despite this lack of success, it is quite possible that the recent launches of the AGILE [152] and GLAST [271] gamma-ray observatories will provide further opportunities for follow-up.

Other targets of interest are X-ray point sources found with the Chandra [270] and XMM-Newton [103] observatories and TeV sources found with HESS [255]. The X-ray sources have been particularly fruitful targets for young pulsars, with a number of discoveries of extremely faint objects [54]. Although not directly relevant to the topic of this review, these searches are revolutionizing our picture of the young neutron star population and should provide valuable insights into the beaming fraction and birthrate of these pulsars.

Extragalactic searches

The only radio pulsars known outside of the Galactic field and its globular cluster systems are the 19 currently known in the Large and Small Magellanic Clouds [256, 87, 247]. The lack of millisecond pulsars in the sample so far is most likely due to the limited sensitivity of the searches and large distance to the clouds. Further surveys in the Magellanic clouds are warranted. Surveys of more distant galaxies have so far been fruitless. Current instrumentation is only sensitive to giant isolated pulsars of the kind observed from the Crab [130] and the millisecond pulsars [193]. While surveys for such events are on-going [195], detections of weaker periodic sources are likely to require the enhanced sensitivity of the next generation radio telescopes.

Surveys with new telescopes

All surveys that have so far been conducted, or will be carried out in the next few years, will ultimately be surpassed by the next generation of radio telescopes. The Allen Telescope Array in California [334] is now beginning operations and could allow large-area coverage of the 1–10 GHz sky for pulsars and transients. In Europe, the low-frequency array [212, 104] is set to discover hundreds of faint nearby pulsars [387] in the next five years. While the Square Kilometre Array [154] is not expected to be completed until 2020, a number of pathfinder instruments are now under development. In China, the Five hundred meter Aperture Spherical Telescope [105] is scheduled for completion in 2013 and will provide significant advances for pulsar research [266]. The Australian Square Kilometre Array Pathfinder, will have some applications as a pulsar instrument [164]. Very exciting wide-field search capabilities will be offered by the South African MeerKAT array of 80 dishes set to begin operations in 2012 [186].

Going further

Two books, Pulsar Astronomy [241] and Handbook of Pulsar Astronomy [226], cover the literature and techniques and provide excellent further reading. The morphological properties of pulsars have recently been comprehensively discussed in recent reviews [340, 333]. Those seeking a more theoretical viewpoint are advised to read The Theory of Neutron Star Magnetospheres [261] and The Physics of the Pulsar Magnetosphere [34]. Our summary of evolutionary aspects serves merely as a primer to the vast body of literature available. Further insights can be found from more detailed reviews [36, 300, 345].

Pulsar resources available on the Internet are continually becoming more extensive and useful. A good starting point for pulsar-surfers is the Handbook of Pulsar Astronomy website [227], as well as the Pulsar Astronomy wiki [307] and the Cool Pulsars site [375].

Pulsar Statistics and Demography

The observed pulsar sample is heavily biased towards the brighter objects that are the easiest to detect. What we observe represents only the tip of the iceberg of a much larger underlying population [127]. The bias is well demonstrated by the projection of pulsars onto the Galactic plane shown in Figure 11. The clustering of sources around the Sun seen in the left panel is clearly at variance with the distribution of other stellar populations which show a radial distribution symmetric about the Galactic centre. Also shown in Figure 11 is the cumulative number of pulsars as a function of the projected distance from the Sun compared to the expected distribution for a simple model population with no selection effects. The observed number distribution becomes strongly deficient beyond a few kpc.

Figure 11

Left panel: The current sample of all known radio pulsars projected onto the Galactic plane. The Galactic centre is at the origin and the Sun is at (0, 8.5) kpc. Note the spiral-arm structure seen in the distribution which is now required by the most recent Galactic electron density model [84, 85]. Right panel: Cumulative number of pulsars as a function of projected distance from the Sun. The solid line shows the observed sample while the dotted line shows a model population free from selection effects.

Selection effects in pulsar searches

The inverse square law and survey thresholds

The most prominent selection effect is the inverse square law, i.e. for a given intrinsic luminosityFootnote 2, the observed flux density varies inversely with the distance squared. This results in the observed sample being dominated by nearby and/or high luminosity objects. Beyond distances of a few kpc from the Sun, the apparent flux density falls below the detection thresholds Smin of most surveys. Following [98], we express this threshold as follows:

$${S_{\min}} = {{{\rm{S}}/{{\rm{N}}_{\min}}} \over {\eta \sqrt {{n_{{\rm{pol}}}}}}}\left({{{{T_{{\rm{rec}}}} + {T_{{\rm{sky}}}}} \over K}} \right){\left({{G \over {{\rm{K}}\;{\rm{J}}{{\rm{y}}^{-1}}}}} \right)^{- 1}}{\left({{{\Delta \nu} \over {{\rm{MHz}}}}} \right)^{- 1/2}}{\left({{{{t_{{\mathop{\rm int}}}}} \over {\rm{s}}}} \right)^{- 1/2}}{\left({{W \over {P - W}}} \right)^{1/2}}{\rm{mJy,}}$$

where S/Nmin is the threshold signal-to-noise ratio, η is a generic fudge factor (≲ 1) which accounts for losses in sensitivity (e.g., due to sampling and digitization noise), npol is the number of polarizations recorded (either 1 or 2), Trec and Tsky are the receiver and sky noise temperatures, G is the gain of the antenna, Δν is the observing bandwidth, tint is the integration time, W is the detected pulse width and P is the pulse period.

Interstellar pulse dispersion and multipath scattering

It follows from Equation (3) that the minimum flux density increases as W/(PW) and hence W increases. Also note that if WP, the pulsed signal is smeared into the background emission and is no longer detectable, regardless of how luminous the source may be. The detected pulse width W may be broader than the intrinsic value largely as a result of pulse dispersion and multipath scattering by free electrons in the interstellar medium. The dispersive smearing scales as Δν/ν3, where ν is the observing frequency. This can largely be removed by dividing the pass-band into a number of channels and applying successively longer time delays to higher frequency channels before summing over all channels to produce a sharp profile. This process is known as incoherent dedispersion.

The smearing across the individual frequency channels, however, still remains and becomes significant at high dispersions when searching for short-period pulsars. Multipath scattering from electron density irregularities results in a one-sided broadening of the pulse profile due to the delay in arrival times. A simple scattering model is shown in Figure 12 in which the scattering electrons are assumed to lie in a thin screen between the pulsar and the observer [331]. The timescale of this effect varies roughly as ν−4, which can not currently be removed by instrumental means.

Figure 12

Left panel: Pulse scattering caused by irregularities in the interstellar medium. The different path lengths and travel times of the scattered rays result in a “scattering tail” in the observed pulse profile which lowers its signal-to-noise ratio. Right panel: A simulation showing the percentage of Galactic pulsars that are likely to be undetectable due to scattering as a function of observing frequency. Low-frequency (≲ 1 GHz) surveys clearly miss a large percentage of the population due to this effect.

Dispersion and scattering are most severe for distant pulsars in the inner Galaxy where the number of free electrons along the line of sight becomes large. The strong frequency dependence of both effects means that they are considerably less of a problem for surveys at observing frequencies ≳ 1.4 GHz [76, 168] compared to the 400-MHz search frequency used in early surveys. An added bonus for such observations is the reduction in Tsky which scales with frequency as approximately ν−2.8 [207]. Pulsar intensities also have an inverse frequency dependence, with the average scaling being ν−1.6 [234], so that flux densities are roughly an order of magnitude lower at 1.4 GHz compared to 400 MHz. Fortunately, this can be at least partially compensated for by the use of larger receiver bandwidths at higher radio frequencies. For example, the 1.4-GHz system at Parkes has a bandwidth of 288 MHz [240] compared to the 430-MHz system, where nominally 32 MHz is available [251].

Orbital acceleration

Standard pulsar searches use Fourier techniques [226] to search for a priori unknown periodic signals and usually assume that the apparent pulse period remains constant throughout the observation. For searches with integration times much greater than a few minutes, this assumption is only valid for solitary pulsars or binary systems with orbital periods longer than about a day. For shorter-period binary systems, the Doppler-shifting of the period results in a spreading of the signal power over a number of frequency bins in the Fourier domain, leading to a reduction in S/N [162]. An observer will perceive the frequency of a pulsar to shift by an amount aT/(Pc), where a is the (assumed constant) line-of-sight acceleration during the observation of length T, P is the (constant) pulsar period in its rest frame and c is the speed of light. Given that the width of a frequency bin in the Fourier domain is 1/T, we see that the signal will drift into more than one spectral bin if aT2/(Pc) > 1. Survey sensitivities to rapidly-spinning pulsars in tight orbits are therefore significantly compromised when the integration times are large.

As an example of this effect, as seen in the time domain, Figure 13 shows a 22.5-min search mode observation of the binary pulsar B1913+16 [150, 366, 367]. Although this observation covers only about 5% of the orbit (7.75 hr), the severe effects of the Doppler smearing on the pulse signal are very apparent. While the standard search code nominally detects the pulsar with S/N = 9.5 for this observation, it is clear that this value is significantly reduced due to the Doppler shifting of the pulse period seen in the individual sub-integrations.

Figure 13

Left panel: A 22.5-min Arecibo observation of the binary pulsar B1913+16. The assumption that the pulsar has a constant period during this time is clearly inappropriate given the quadratic drifting in phase of the pulse during the observation (linear grey scale plot). Right panel: The same observation after applying an acceleration search. This shows the effective recovery of the pulse shape and a significant improvement in the signal-to-noise ratio.

It is clearly desirable to employ a technique to recover the loss in sensitivity due to Doppler smearing. One such technique, the so-called “acceleration search” [262], assumes the pulsar has a constant acceleration during the observation. Each time series can then be re-sampled to refer it to the frame of an inertial observer using the Doppler formula to relate a time interval τ in the pulsar frame to that in the observed frame at time t, as τ(t) ∝ (1 + at/c). Searching over a range of accelerations is desirable to find the time series for which the trial acceleration most closely matches the true value. In the ideal case, a time series is produced with a signal of constant period for which full sensitivity is recovered (see right panel of Figure 13). This technique was first used to find PSR B2127+11C [4], a double neutron star binary in M15 which has parameters similar to B1913+16. Its application to 47 Tucanae [56] resulted in the discovery of nine binary millisecond pulsars, including one in a 96-min orbit around a low-mass (0.15 M) companion. This is currently the shortest binary period for any known radio pulsar. The majority of binary millisecond pulsars with orbital periods less than a day found in recent globular cluster searches would not have been discovered without the use of acceleration searches.

For intermediate orbital periods, in the range 30 min — several hours, another promising technique is the dynamic power spectrum search shown in Figure 14. Here the time series is split into a number of smaller contiguous segments which are Fourier-transformed separately. The individual spectra are displayed as a two-dimensional (frequency versus time) image. Orbitally modulated pulsar signals appear as sinusoidal signals in this plane as shown in Figure 14.

Figure 14

Dynamic power spectra showing two recent pulsar discoveries in the globular cluster M62 showing fluctuation frequency as a function of time. Figure provided by Adam Chandler.

This technique has been used by various groups where spectra are inspected visually [245]. Much of the human intervention can be removed using a hierarchical scheme for selecting significant events [71]. This approach was recently applied to a search of the globular cluster M62 resulting in the discovery of three new pulsars. One of the new discoveries — M62F, a faint 2.3-ms pulsar in a 4.8-hr orbit — was detectable only using the dynamic power spectrum technique.

For the shortest orbital periods, the assumption of a constant acceleration during the observation clearly breaks down. In this case, a particularly efficient algorithm has been developed [78, 312, 172, 315] which is optimised to finding binaries with periods so short that many orbits can take place during an observation. This “phase modulation” technique exploits the fact that the Fourier components are modulated by the orbit to create a family of periodic sidebands around the nominal spin frequency of the pulsar. While this technique has so far not resulted in any new discoveries, the existence of short period binaries in 47 Tucanae [56], Terzan 5 [317] and the 11-min X-ray binary X1820−303 in NGC 6624 [354], suggests that there are more ultra-compact radio binary pulsars that await discovery.

Correcting the observed pulsar sample

In the following, we review common techniques to account for many of the aforementioned selection effects and form a less biased picture of the true pulsar population.

Scale factor determination

A very useful approach [299, 389], is to define a scaling factor ξ as the ratio of the total Galactic volume weighted by pulsar density to the volume in which a pulsar is detectable:

$$\xi (P,L) = {{\int {\int\nolimits_{\rm{G}} {\Sigma (R,z)RdRdz}}} \over {\int {\int\nolimits_{P,L} {\Sigma (R,z)RdRdz}}}}.$$

Here, Σ(R, z) is the assumed pulsar space density distribution in terms of galactocentric radius R and height above the Galactic plane z. Note that ξ is primarily a function of period P and luminosity L such that short-period/low-luminosity pulsars have smaller detectable volumes and therefore higher ξ values than their long-period/high-luminosity counterparts.

In practice, ξ is calculated for each pulsar separately using a Monte Carlo simulation to model the volume of the Galaxy probed by the major surveys [268]. For a sample of Nobs observed pulsars above a minimum luminosity Lmin, the total number of pulsars in the Galaxy

$${N_{\rm{G}}} = \sum\limits_{i = 1}^{{N_{{\rm{obs}}}}} {{{{\xi _i}} \over {{f_i}}},}$$

where f is the model-dependent “beaming fraction” discussed below in Section 3.2.3. Note that this estimate applies to those pulsars with luminosities ≳ Lmin. Monte Carlo simulations have shown this method to be reliable, as long as Nobs is reasonably large [222].

The small-number bias

For small samples of observationally-selected objects, the detected sources are likely to be those with larger-than-average luminosities. The sum of the scale factors (5), therefore, will tend to underestimate the true size of the population. This “small-number bias” was first pointed out [174, 178] for the sample of double neutron star binaries where we know of only five systems relevant for calculations of the merging rate (see Section 3.4.1). Only when Nobs ≳ 10 does the sum of the scale factors become a good indicator of the true population size.

Despite a limited sample size, it has been demonstrated [190] that rigorous confidence intervals of NG can be derived using Bayesian techniques. Monte Carlo simulations verify that the simulated number of detected objects Ndetected closely follows a Poisson distribution and that Ndetected = αNG, where α is a constant. By varying the value of NG in the simulations, the mean of this Poisson distribution can be measured. The Bayesian analysis [190] finds, for a single object, the probability density function of the total population is

$$P({N_{\rm{G}}}) = {\alpha ^2}{N_{\rm{G}}}\exp (- \alpha {N_{\rm{G}}}).$$

Adopting the necessary assumptions required in the Monte Carlo population about the underlying pulsar distribution, this technique can be used to place interesting constraints on the size and, as we shall see later, birth rate of the underlying population.

Figure 15

Small-number bias of the scale factor estimates derived from a synthetic population of sources where the true number of sources is known. Left panel: An edge-on view of a model Galactic source population. Right panel: The thick line shows NG, the true number of objects in the model Galaxy, plotted against Nobserved, the number detected by a flux-limited survey. The thin solid line shows Nest, the median sum of the scale factors, as a function of Nobs from a large number of Monte Carlo trials. Dashed lines show 25 and 75% percentiles of the Nest distribution.

The beaming correction

The “beaming fraction” f in Equation (5) is the fraction of 4π steradians swept out by a pulsar’s radio beam during one rotation. Thus f is the probability that the beam cuts the line-of-sight of an arbitrarily positioned observer. A naïve estimate for f of roughly 20% assumes a circular beam of width ∼ 10° and a randomly distributed inclination angle between the spin and magnetic axes [365]. Observational evidence summarised in Figure 16 suggests that shorter period pulsars have wider beams and therefore larger beaming fractions than their long-period counterparts [269, 243, 37, 360].

Figure 16

Beaming fraction plotted against pulse period for four different beaming models: Narayan & Vivekanand 1983 (NV83) [269], Lyne & Manchester 1988 (LM88) [243], Biggs 1990 (JDB90) [37] and Tauris & Manchester 1998 (TM98) [360].

When most of these beaming models were originally proposed, the sample of millisecond pulsars was ≲ 5 and hence their predictions about the beaming fractions of short-period pulsars relied largely on extrapolations from the normal pulsars. An analysis of a large sample of millisecond pulsar profiles [203] suggests that their beaming fraction lies between 50 and 100%. Independent constraints on f for millisecond pulsars come from deep Chandra observations of the globular cluster 47 Tucanae [126] and radio pulsar surveys [56] which suggest that f > 0.4 and likely close to unity [135]. The large beaming fraction and narrow pulses often observed strongly suggests a fan beam model for millisecond pulsars [261].

The population of normal and millisecond pulsars

Luminosity distributions and local number estimates

Based on a number of all-sky surveys carried out in the 1990s, the scale factor approach has been used to derive the characteristics of the true normal and millisecond pulsar populations and is based on the sample of pulsars within 1.5 kpc of the Sun [244]. Within this region, the selection effects are well understood and easier to quantify than in the rest of the Galaxy. These calculations should therefore give a reliable local pulsar population estimate.

The 430-MHz luminosity distributions obtained from this analysis are shown in Figure 17. For the normal pulsars, integrating the corrected distribution above 1 mJy kpc2 and dividing by π × (1.5)2 kpc2 yields a local surface density, assuming a beaming model [37], of 156±31pulsars kpc−2 for 430-MHz luminosities above 1 mJy kpc2. The same analysis for the millisecond pulsars, assuming a mean beaming fraction of 75% [203], leads to a local surface density of 38 ± 16 pulsars kpc−2 also for 430-MHz luminosities above 1 mJy kpc2.

Figure 17

Left panel: The corrected luminosity distribution (solid histogram with error bars) for normal pulsars. The corrected distribution before the beaming model has been applied is shown by the dot-dashed line. Right panel: The corresponding distribution for millisecond pulsars. In both cases, the observed distribution is shown by the dashed line and the thick solid line is a power law with a slope of −1. The difference between the observed and corrected distributions highlights the severe under-sampling of low-luminosity pulsars.

Galactic population and birth-rates

Integrating the local surface densities of pulsars over the whole Galaxy requires a knowledge of the presently rather uncertain Galactocentric radial distribution [163, 220]. One approach is to assume that pulsars have a radial distribution similar to that of other stellar populations and to scale the local number density with this distribution in order to estimate the total Galactic population. The corresponding local-to-Galactic scaling is 1000±250 kpc2 [318]. This implies a population of ∼ 160,000 active normal pulsars and ∼ 40,000 millisecond pulsars in the Galaxy.

Based on these estimates, we are in a position to deduce the corresponding rate of formation or birth-rate required to sustain the observed population. From the P diagram in Figure 3, we infer a typical lifetime for normal pulsars of ∼ 107 yr, corresponding to a Galactic birth rate of ∼ 1 per 60 yr — consistent with the rate of supernovae [381]. As noted in Section 2.2, the millisecond pulsars are much older, with ages close to that of the Universe τu (we assume here τu = 13.8 Gyr [405]). Taking the maximum age of the millisecond pulsars to be τu, we infer a mean birth rate of at least 1 per 345,000 yr. This is consistent, within the uncertainties, of other studies of the millisecond pulsar population [109, 357] and with the birth-rate of low-mass X-ray binaries [231, 188].

The population of relativistic binaries

Although no radio pulsar has so far been observed in orbit around a black hole companion, we now know of several double neutron star and neutron star-white dwarf binaries which will merge due to gravitational wave emission within a reasonable timescale. The current sample of objects is shown as a function of orbital period and eccentricity in Figure 18. Isochrones showing various coalescence times τg are calculated using the expression

$${\tau _{\rm{g}}} \simeq 9.83 \times {10^6}{\rm{yr}}{\left({{{{P_{\rm{b}}}} \over {{\rm{hr}}}}} \right)^{8/3}}{\left({{{{m_1} + {m_2}} \over {{M_ \odot}}}} \right)^{- 2/3}}{\left({{\mu \over {{M_ \odot}}}} \right)^{- 1}}{(1 - {e^2})^{7/2}},$$

where m1 and m2 are the masses of the two stars, μ = m1m2/(m1+ m2) is the “reduced mass”, Pb is the binary period and e is the eccentricity. This formula is a good analytic approximation (within a few percent) to the numerical solution of the exact equations for τg [294, 295].

Figure 18

The relativistic binary merging plane. Top: Orbital eccentricity versus period for eccentric binary systems involving neutron stars. Bottom: Orbital period distribution for the massive white dwarf-pulsar binaries. Isocrones show coalescence times assuming neutron stars of 1.4M and white dwarfs of 0.3 M.

In addition to tests of strong-field gravity through observations of relativistic binary systems (see Section 4.4), estimates of their Galactic population and merger rate are of great interest as one of the prime sources for current gravitational wave detectors such as GEO600 [265], LIGO [51], VIRGO [153] and TAMA [273]. In the following, we review empirical determinations of the population sizes and merging rates of binaries where at least one component is visible as a radio pulsar.

Double neutron star binaries

As discussed in Section 2.2, double neutron star (DNS) binaries are expected to be rare. This is certainly the case; as summarized in Table 1, only around ten DNS binaries are currently known. Although we only see both neutron stars as pulsars in J0737−3039 [239], we are “certain” of the identification in five other systems from precise component mass measurements from pulsar timing observations (see Section 4.4). The other systems listed in Table 1 have eccentric orbits, mass functions and periastron advance measurements that are consistent with a DNS identification, but for which there is presently not sufficient component mass information to confirm their nature. One further DNS candidate, the 95-ms pulsar J1753−2243 (see Table 3), has recently been discovered [187]. Although the mass function for this pulsar is lower than the DNS systems listed in Table 1, a neutron star companion cannot be ruled out in this case. Further observations should soon clarify the nature of this system. We note, however, that the 13.6-day orbital period of this system means that it will not contribute to gravitational wave inspiral rate calculations discussed below.

Table 1 Known and likely DNS binaries. Listed are the pulse period P, orbital period Pb, orbital eccentricity e, characteristic age τc, and expected binary coalescence timescale τg due to gravitational wave emission calculated from Equation (7). To distinguish between definite and candidate DNS systems, we also list whether the masses of both components have been determined via the measurement of two or more post-Keplerian parameters as described in Section 4.4.

Despite the uncertainties in identifying DNS binaries, for the purposes of determining the Galactic merger rate, the systems for which τg is less than τu (i.e. PSRs J0737−3039, B1534+12, J1756−2251, J1906+0746, B1913+16 and B2127+11C) are primarily of interest. Of these PSR B2127+11C is in the process of being ejected from the globular cluster M15 [305, 301] and is thought to make only a negligible contribution to the merger rate [297]. The general approach with the remaining systems is to derive scale factors for each object, construct the probability density function of their total population (as outlined in Section 3.2.1) and then divide these by a reasonable estimate for the lifetime. Getting such estimates is, however, difficult. It has been proposed [178] that the observable lifetimes for these systems are determined by the timescale on which the current orbital period is reduced by a factor of two [7]. Below this point, the orbital smearing selection effect discussed in Section 3.1.3 will render the binary undetectable by current surveys. More recent work [73] has suggested that a significant population of highly eccentric binary systems could easily evade detection due to their short lifetimes before gravitational wave inspiral. If this selection effect is significant, then the merger rate estimates quoted below could easily be underestimated by a factor of a few.

The results of the most recent DNS merger rate estimates of this kind [189] are summarised in the left panel of Figure 19. The combined Galactic merger rate, dominated by the double pulsar and J1906+0746 is found to be \(118_{- 79}^{+ 174}\,{\rm{My}}{{\rm{r}}^{- 1}}\), where the uncertainties reflect the 95% confidence level using the techniques summarised in Section 3.2.2. Extrapolating this number to include DNS binaries detectable by LIGO in other galaxies [297], the expected event rate is \(49_{- 33}^{+ 73} \times {10^{- 3}}\,{\rm{y}}{{\rm{r}}^{- 1}}\) for initial LIGO and \(265_{- 178}^{+ 390}\,{\rm{y}}{{\rm{r}}^{- 1}}\) for advanced LIGO. Future prospects for detecting gravitational wave emission from binary neutron star inspirals are therefore very encouraging, especially if the population of highly eccentric systems is significant [73]. Since much of the uncertainty in the rate estimates is due to our ignorance of the underlying distribution of double neutron star systems, future gravitational wave detection could ultimately constrain the properties of this exciting binary species.

Figure 19

The current best empirical estimates of the coalescence rates of relativistic binaries involving neutron stars. The individual contributions from each known binary system are shown as dashed lines, while the solid line shows the total probability density function on a logarithmic and (inset) linear scale. The left panel shows the most recent analysis for DNS binaries [189], while the right panel shows the equivalent results for NS-WD binaries [191]. Figures provided by Chunglee Kim.

Although the double pulsar system J0737−3039 will not be important for ground-based detectors until its final coalescence in another 85 Myr, it may be a useful calibration source for the future space-based detector LISA [272]. It is calculated [175] that a 1-yr observation with LISA would detect (albeit with S/N ∼ 2) the continuous emission at a frequency of 0.2 mHz based on the current orbital parameters. Although there is the prospect of using LISA to detect similar systems through their continuous emission, current calculations [175] suggest that significant (S/N > 5) detections are not likely. Despite these limitations, it is likely that LISA observations will be able to place independent constraints on the Galactic DNS binary population after several years of operation.

White dwarf—neutron star binaries

Although the population of white dwarf-neutron star (WDNS) binaries in general is substantial, the fraction which will merge due to gravitational wave emission is small. Like the DNS binaries, the observed WDNS sample suffers from small-number statistics. From Figure 18, we note that only three WDNS systems are currently known that will merge within τu, PSRs J0751+1807 [235], J1757−5322 [100] and J1141−6545 [183]. Applying the same techniques as used for the DNS population, the merging rate contributions of the three systems can be calculated [191] and are shown in Figure 19. The combined Galactic coalescence rate is \(4_{- 3}^{+ 5}\,{\rm{My}}{{\rm{r}}^{- 1}}\) (at 68% confidence interval). This result is not corrected for beaming and therefore should be regarded as a lower limit on the total event rate. Although the orbital frequencies of these objects at coalescence are too low to be detected by LIGO, they do fall within the band planned for LISA [272]. Unfortunately, an extrapolation of the Galactic event rate out to distances at which such events would be detectable by LISA does not suggest that these systems will be a major source of detection [191]. Similar conclusions were reached by considering the statistics of low-mass X-ray binaries [77].

Going further

Good starting points for further reading can be found in other review articles [300, 189]. Our coverage of compact object coalescence rates has concentrated on empirical methods. Two software packages are freely available which allow the user to synthesize and search radio pulsar populations [287, 394, 322]. An alternative approach is to undertake a full-blown Monte Carlo simulation of the most likely evolutionary scenarios described in Section 2.6. In this scheme, a population of primordial binaries is synthesized with a number of underlying distribution functions: primary mass, binary mass ratio, orbital period distribution etc. The evolution of both stars is then followed to give a predicted sample of binary systems of all the various types. Although selection effects are not always taken into account in this approach, the final census is usually normalized to the star formation rate.

Numerous population syntheses (most often to populations of binaries where one or both members are NSs) can be found in the literature [96, 324, 374, 303, 211, 27, 28]. A group in Moscow has made a web interface to their code [355]. Although extremely instructive, the uncertain assumptions about initial conditions, the physics of mass transfer and the kicks applied to the compact object at birth result in a wide range of predicted event rates which are currently broader than the empirical methods [176, 191, 177]. Ultimately, the detection statistics from the gravitational wave detectors could provide far tighter constraints on the DNS merging rate than the pulsar surveys from which these predictions are made. Very recently [289] the results from empirical population constraints and full-blown binary population synthesis codes have been combined to constrain a variety of input parameters and physical conditions. The results of this work are promising, with stringent constraints being placed on the kick distributions, mass-loss fraction during mass transfer and common envelope assumptions.

Principles and Applications of Pulsar Timing

Pulsars are excellent celestial clocks. The period of the first pulsar [141] was found to be stable to one part in 107 over a few months. Following the discovery of the millisecond pulsar B1937+21 [18] it was demonstrated that its period could be measured to one part in 1013 or better [94]. This unrivaled stability leads to a host of applications including uses as time keepers, probes of relativistic gravity and natural gravitational wave detectors.

Observing basics

Each pulsar is typically observed at least once or twice per month over the course of a year to establish its basic properties. Figure 20 summarises the essential steps involved in a “time-of-arrival” (TOA) measurement. Pulses from the neutron star traverse the interstellar medium before being received at the radio telescope where they are dedispersed and added to form a mean pulse profile.

Figure 20

Schematic showing the main stages involved in pulsar timing observations.

During the observation, the data regularly receive a time stamp, usually based on a caesium time standard or hydrogen maser at the observatory plus a signal from the Global Positioning System of satellites (GPS; see [93]). The TOA is defined as the arrival time of some fiducial point on the integrated profile with respect to either the start or the midpoint of the observation. Since the profile has a stable form at any given observing frequency (see Section 2.3), the TOA can be accurately determined by cross-correlation of the observed profile with a high S/N “template” profile obtained from the addition of many observations at the particular observing frequency.

Successful pulsar timing requires optimal TOA precision which largely depends on the signal-to-noise ratio (S/N) of the pulse profile. Since the TOA uncertainty ∊TOA is roughly the pulse width divided by the S/N, using Equation (3) we may write the fractional error as

$${{{\epsilon _{{\rm{TOA}}}}} \over P} \simeq {\left({{{{S_{{\rm{psr}}}}} \over {{\rm{mJy}}}}} \right)^{- 1}}\left({{{{T_{{\rm{rec}}}} + {T_{{\rm{sky}}}}} \over K}} \right){\left({{G \over {{\rm{K}}\;{\rm{J}}{{\rm{y}}^{\rm{1}}}}}} \right)^{- 1}}{\left({{{\Delta \nu} \over {{\rm{MHz}}}}} \right)^{- 1/2}}{\left({{{{t_{{\mathop{\rm int}}}}} \over {\rm{s}}}} \right)^{- 1/2}}{\left({{W \over P}} \right)^{3/2}}.$$

Here, Spsr is the flux density of the pulsar, Trec and Tsky are the receiver and sky noise temperatures, G is the antenna gain, Δν is the observing bandwidth, tint is the integration time, W is the pulse width and P is the pulse period (we assume WP). Optimal results are thus obtained for observations of short period pulsars with large flux densities and small duty cycles (i.e. small W/P) using large telescopes with low-noise receivers and large observing bandwidths.

One of the main problems of employing large bandwidths is pulse dispersion. As discussed in Section 2.4, pulses emitted at lower radio frequencies travel slower and arrive later than those emitted at higher frequencies. This process has the effect of “stretching” the pulse across a finite receiver bandwidth, increasing W and therefore increasing TOA. For normal pulsars, dispersion can largely be compensated for by the incoherent dedispersion process outlined in Section 3.1.

The short periods of millisecond pulsars offer the ultimate in timing precision. In order to fully exploit this, a better method of dispersion removal is required. Technical difficulties in building devices with very narrow channel bandwidths require another dispersion removal technique. In the process of coherent dedispersion [129, 226] the incoming signals are dedispersed over the whole bandwidth using a filter which has the inverse transfer function to that of the interstellar medium. The signal processing can be done online either using high speed devices such as field programmable gate arrays [64, 291] or completely in software [343, 350]. Off-line data reduction, while disk-space limited, allows for more flexible analysis schemes [20].

The maximum time resolution obtainable via coherent dedispersion is the inverse of the total receiver bandwidth. The current state of the art is the detection [130] of features on nanosecond timescales in pulses from the 33-ms pulsar B0531+21 in the Crab nebula shown in Figure 21. Simple light travel-time arguments can be made to show that, in the absence of relativistic beaming effects [121], these incredibly bright bursts originate from regions less than 1 m in size.

Figure 21

A 120 µs window centred on a coherently-dedispersed giant pulse from the Crab pulsar showing high-intensity nanosecond bursts. Figure provided by Tim Hankins [130].

The timing model

To model the rotational behaviour of the neutron star we ideally require TOAs measured by an inertial observer. An observatory located on Earth experiences accelerations with respect to the neutron star due to the Earth’s rotation and orbital motion around the Sun and is therefore not in an inertial frame. To a very good approximation, the solar system centre-of-mass (barycentre) can be regarded as an inertial frame. It is now standard practice [151] to transform the observed TOAs to this frame using a planetary ephemeris such as the JPL DE405 [352]. The transformation between barycentric (T) and observed (t) takes the form

$${\mathcal T} - t = {{\underline{r} . \underline {\hat s}} \over c} + {{{{({\underline{r} . \underline {\hat s}})}^2} - \vert \underline{r} {\vert ^2}} \over {2cd}} + \Delta {t_{{\rm{rel}}}} - \Delta {t_{{\rm{DM}}}}.$$

Here r is the position of the observatory with respect to the barycentre, \(\underline {\hat s}\) is a unit vector in the direction of the pulsar at a distance d and c is the speed of light. The first term on the right hand side of Equation (9) is the light travel time from the observatory to the solar system barycentre. Incoming pulses from all but the nearest pulsars can be approximated by plane wavefronts. The second term, which represents the delay due to spherical wavefronts, yields the parallax and hence d. This has so far only been measured for five nearby millisecond pulsars [329, 373, 213, 342, 215]. The term Δtrel represents the Einstein and Shapiro corrections due to general relativistic time delays in the solar system [17]. Since measurements can be carried out at different observing frequencies with different dispersive delays, TOAs are generally referred to the equivalent time that would be observed at infinite frequency. This transformation is the term ΔtDM (see also Equation (1)).

Following the accumulation of a number of TOAs, a surprisingly simple model is usually sufficient to account for the TOAs during the time span of the observations and to predict the arrival times of subsequent pulses. The model is a Taylor expansion of the rotational frequency Ω = 2π/P about a model value Ω0 at some reference epoch T0. The model pulse phase

$$\phi ({\mathcal T}) = {\phi _0} + ({\mathcal T} - {{\mathcal T}_0}){\Omega _0} + {1 \over 2}{({\mathcal T} - {{\mathcal T}_0})^2}{\dot \Omega _0} + \ldots ,$$

where T is the barycentric time and ϕ0 is the pulse phase at T0. Based on this simple model, and using initial estimates of the position, dispersion measure and pulse period, a “timing residual” is calculated for each TOA as the difference between the observed and predicted pulse phases.

A set of timing residuals for the nearby pulsar B1133+16 spanning almost 10 years is shown in Figure 22. Ideally, the residuals should have a zero mean and be free from any systematic trends (see Panel a of Figure 22). To reach this point, however, the model needs to be refined in a bootstrap fashion. Early sets of residuals will exhibit a number of trends indicating a systematic error in one or more of the model parameters, or a parameter not incorporated into the model.

Figure 22

Timing model residuals for PSR B1133+16. Panel a: Residuals obtained from the best-fitting model which includes period, period derivative, position and proper motion. Panel b: Residuals obtained when the period derivative term is set to zero. Panel c: Residuals showing the effect of a 1-arcmin position error. Panel d: Residuals obtained neglecting the proper motion. The lines in Panels b–d show the expected behaviour in the timing residuals for each effect. Data provided by Andrew Lyne.

From Equation (10), an error in the assumed Ω0 results in a linear slope with time. A parabolic trend results from an error in \({{\dot \Omega}_0}\) (see Panel b of Figure 22). Additional effects will arise if the assumed position of the pulsar (the unit vector \(\underline {\hat s}\) in Equation (9)) used in the barycentric time calculation is incorrect. A position error results in an annual sinusoid (see Panel c of Figure 22). A proper motion produces an annual sinusoid of linearly increasing magnitude (see Panel d of Figure 22).

After a number of iterations, and with the benefit of a modicum of experience, it is possible to identify and account for each of these various effects to produce a “timing solution” which is phase coherent over the whole data span. The resulting model parameters provide spin and astrometric information with a precision which improves as the length of the data span increases. For example, timing observations of the original millisecond pulsar B1937+21, spanning almost 9 years (exactly 165,711,423,279 rotations!), measure a period of 1.5578064688197945±0.0000000000000004 ms [185, 181] defined at midnight UT on December 5, 1988! Measurements of other parameters are no less impressive, with astrometric errors of ∼ 3 μarcsec being presently possible for the bright millisecond pulsar J0437−4715 [388].

Timing stability

Ideally, after correctly applying a timing model, we would expect a set of uncorrelated timing residuals with a zero mean and a Gaussian scatter with a standard deviation consistent with the measurement uncertainties. As can be seen in Figure 23, this is not always the case; the residuals of many pulsars exhibit a quasi-periodic wandering with time.

Figure 23

Examples of timing residuals for a number of normal pulsars. Note the varying scale on the ordinate axis, the pulsars being ranked in increasing order of timing “activity”. Data taken from the Jodrell Bank timing program [335, 146]. Figure provided by Andrew Lyne.

Such “timing noise” is most prominent in the youngest of the normal pulsars [253, 83] and present at a lower level in the much older millisecond pulsars [185, 9]. While the physical processes of this phenomenon are not well understood, it seems likely that they may be connected to super-fluid processes and temperature changes in the interior of the neutron star [3], or to processes in the magnetosphere [75, 74].

The relative dearth of timing noise for the older pulsars is a very important finding. It implies that the measurement precision presently depends primarily on the particular hardware constraints of the observing system. Consequently, a large effort in hardware development is now being made to improve the precision of these observations using, in particular, coherent dedispersion outlined in Section 4.1. Much progress in this area has been made by groups at Princeton [306], Berkeley [377], Jodrell Bank [379], UBC [376], Swinburne [359] and ATNF [13]. From high quality observations spanning over a decade [327, 328, 185], these groups have demonstrated that the timing stability of millisecond pulsars over such timescales is comparable to terrestrial atomic clocks.

This phenomenal stability is demonstrated in Figure 24 which shows σz [254, 380], a parameter closely resembling the Allan variance used by the clock community to estimate the stability of atomic clocks [362, 1]. Both PSRs B1937+21 and B1855+09 seem to be limited by a power law component which produces a minimum in σz after 2 yr and 5 yr respectively. This is most likely a result of a small amount of intrinsic timing noise [185]. The σz based on timing observations [388] of the bright millisecond pulsar J0437−4715 is now 1–2 orders of magnitude smaller than the other two pulsars or the atomic clock!

Figure 24

The fractional stability of three millisecond pulsars compared to an atomic clock. Both PSRs B1855+09 and B1937+21 are comparable, or just slightly worse than, the atomic clock behaviour over timescales of a few years [254]. More recent timing of the millisecond pulsar J0437−4715 [388] indicates that it is inherently a very stable clock. Data for the latter pulsar provided by Joris Verbiest.

Timing binary pulsars

For binary pulsars, the timing model introduced in Section 4.2 needs to be extended to incorporate the additional motion of the pulsar as it orbits the common centre-of-mass of the binary system. Describing the binary orbit using Kepler’s laws to refer the TOAs to the binary barycentre requires five additional model parameters: the orbital period Pb, projected semi-major orbital axis x, orbital eccentricity e, longitude of periastron ω and the epoch of periastron passage T0. This description, using five “Keplerian parameters”, is identical to that used for spectroscopic binary stars. Analogous to the radial velocity curve in a spectroscopic binary, for binary pulsars the orbit is described by the apparent pulse period against time. An example of this is shown in Panel a of Figure 25. Alternatively, when radial accelerations can be measured, the orbit can also be visualised in a plot of acceleration versus period as shown in Panel b of Figure 25. This method is particularly useful for determining binary pulsar orbits from sparsely sampled data [115].

Figure 25

Panel a: Keplerian orbital fit to the 669-day binary pulsar J0407+1607 [233]. Panel b: Orbital fit in the period-acceleration plane for the globular cluster pulsar 47 Tuc S [115].

Constraints on the masses of the pulsar mp and the orbiting companion mc can be placed by combining x and Pb to obtain the mass function

$${f_{{\rm{mass}}}} = {{4{\pi ^2}} \over G}{{{x^3}} \over {P_{\rm{b}}^2}} = {{{{({m_{\rm{c}}}\sin i)}^3}} \over {{{({m_{\rm{p}}} + {m_{\rm{c}}})}^2}}},$$

where G is Newton’s gravitational constant and i is the (initially unknown) angle between the orbital plane and the plane of the sky (i.e. an orbit viewed edge-on corresponds to i = 90°). In the absence of further information, the standard practice is to consider a random distribution of inclination angles. Since the probability that i is less than some value i0 is p(< i0) = 1 − cos(i0), the 90% confidence interval for i is 26° < i < 90°. For an assumed pulsar mass, the 90% confidence interval for mc can be obtained by solving Equation (11) for i = 26° and 90°.

Although most of the presently known binary pulsar systems can be adequately timed using Kepler’s laws, there are a number which require an additional set of “post-Keplerian” (PK) parameters which have a distinct functional form for a given relativistic theory of gravity [92]. In general relativity (GR) the PK formalism gives the relativistic advance of periastron

$$\dot \omega = 3{\left({{{{P_{\rm{b}}}} \over {2\pi}}} \right)^{- 5/3}}{({T_ \odot}M)^{2/3}}{(1 - {e^2})^{- 1}},$$

the time dilation and gravitational redshift parameter

$$\gamma = e{\left({{{{P_{\rm{b}}}} \over {2\pi}}} \right)^{1/3}}T_ \odot ^{2/3}{M^{- 4/3}}{m_{\rm{c}}}({m_{\rm{p}}} + 2{m_{\rm{c}}}),$$

the rate of orbital decay due to gravitational radiation

$${\dot{P}_{\rm{b}}} = - {{192\pi} \over 5}{\left({{{{P_{\rm{b}}}} \over {2\pi}}} \right)^{- 5/3}}\left({1 + {{73} \over {24}}{e^2} + {{37} \over {96}}{e^4}} \right){(1 - {e^2})^{- 7/2}}T_ \odot ^{5/3}{m_{\rm{p}}}{m_{\rm{c}}}{M^{- 1/3}}$$

and the two Shapiro delay parameters

$$r = {T_\odot}{m_{\rm{c}}}$$


$$s = x{\left({{{{P_{\rm{b}}}} \over {2\pi}}} \right)^{- 2/3}}T_ \odot ^{- 1/3}{M^{2/3}}m_{\rm{c}}^{- 1}$$

which describe the delay in the pulses around superior conjunction where the pulsar radiation traverses the gravitational well of its companion. In the above expressions, all masses are in solar units, Mmp + mc, xap sin i/c, s ≡ sin i and TGM/c3 = 4.925490947 μs. Some combinations, or all, of the PK parameters have now been measured for a number of binary pulsar systems. Further PK parameters due to aberration and relativistic deformation [90] are not listed here but may soon be important for the double pulsar [201].

Testing general relativity

The key point in the PK definitions introduced in the previous section is that, given the precisely measured Keplerian parameters, the only two unknowns are the masses of the pulsar and its companion, mp and mc. Hence, from a measurement of just two PK parameters (e.g., \({\dot \omega}\) and γ) one can solve for the two masses and, using Equation (11), find the orbital inclination angle i. If three (or more) PK parameters are measured, the system is “overdetermined” and can be used to test GR (or, more generally, any other theory of gravity) by comparing the third PK parameter with the predicted value based on the masses determined from the other two.

The first binary pulsar used to test GR in this way was PSR B1913+16 discovered by Hulse & Taylor in 1974 [150]. Measurements of three PK parameters (\({\dot \omega}\), γ and b) were obtained from long-term timing observations at Arecibo [366, 367, 391]. The measurement of orbital decay, which corresponds to a shrinkage of about 3.2 mm per orbit, is seen most dramatically as the gradually increasing shift in orbital phase for periastron passages with respect to a non-decaying orbit shown in Figure 26. This figure includes recent Arecibo data taken since the upgrade of the telescope in the mid 1990s.

Figure 26

Orbital decay in the binary pulsar B1913+16 system demonstrated as an increasing orbital phase shift for periastron passages with time. The GR prediction due entirely to the emission of gravitational radiation is shown by the parabola. Figure provided by Joel Weisberg.

The measurement of orbital decay in the B1913+16 system, obtained from observations spanning a 30-yr baseline [391], is within 0.2% of the GR prediction and provided the first indirect evidence for the existence of gravitational waves. Hulse and Taylor were awarded the 1993 Nobel Physics prize [368, 149, 363] in recognition of their discovery of this remarkable laboratory for testing GR. A similar, though less precise, test of GR from this combination of PK parameters has recently been performed in the double neutron star binary PSR B2127+11C in the globular cluster M15 [158]. For this system, the measurement uncertainties permit a test of GR to 3% precision which is unlikely to improve due to various kinematic contaminations including the acceleration of the binary system in the cluster’s gravitational potential.

Five PK parameters have been measured for the double pulsar discussed in detail below and for the double neutron star system PSR B1534+12 [351] where the test of GR comes from measurements of \({\dot \omega}\), γ and s. In this system, the agreement between theory and observation is within 0.7% [351]. This test will improve in the future as the timing baseline extends and a more significant measurement of r can be made.

Currently the best binary pulsar system for testing GR in the strong-field regime is the double pulsar J0737−3039. In this system, where two independent pulsar clocks can be timed, five PK parameters of the 22.7-ms pulsar “A” have been measured as well as two additional constraints from the measured mass function and projected semi-major axis of the 2.7-s pulsar “B”. A useful means of summarising the limits so far is Figure 27 which shows the allowed regions of parameter space in terms of the masses of the two pulsars. The shaded regions are excluded by the requirement that sin i < 1. Further constraints are shown as pairs of lines enclosing permitted regions as predicted by GR. The measurement [201] of \(\dot \omega = 16.899 \pm 0.001\,\deg \,{\rm{y}}{{\rm{r}}^{- 1}}\) gives the total system mass M = 2.5871 ± 0.0002 M.

Figure 27

‘Mass—mass’ diagram showing the observational constraints on the masses of the neutron stars in the double pulsar system J0737−3039. Inset is an enlarged view of the small square encompassing the intersection of the tightest constraints. Figure provided by René Breton [44].

The measurement of the projected semi-major axes of both orbits gives the mass ratio R = 1.071 ± 0.001. The mass ratio measurement is unique to the double pulsar system and rests on the basic assumption that momentum is conserved. This constraint should apply to any reasonable theory of gravity. The intersection between the lines for \({\dot \omega}\) and R yield the masses of A and B as mA = 1.3381 ± 0.007 M and mB = 1.2489 ± 0.0007 M. From these values, using Equations (13–16) the expected values of γ, b, r and s may be calculated and compared with the observed values. These four tests of GR all agree with the theory to within the uncertainties. Currently the tightest constraint is the Shapiro delay parameter s where the observed value is in agreement with GR at the 0.05% level [201].

Another unique feature of the double pulsar system is the interactions between the two pulsars’ radiation beams. Specifically, the signal from A is eclipsed for 30 s each orbit by the magnetosphere of B [239, 184, 260] and the radio pulses from B are modulated by the relativistic wind from A during two phases of the orbit [258]. These provide unique insights into plasma physics [125] and, as shown shown in Figure 27, a measurement of relativistic spin-orbit coupling in the binary system and, hence, another constraint on GR. By careful modeling of the change in eclipse profiles of A over a four-year baseline, Breton et al. [44] have been able to fit a remarkably simple modelFootnote 3 and determine the precession of B’s spin axis about the orbital angular momentum vector. This remarkable measurement agrees, within the 13% measurement uncertainty, to the GR prediction.

It took only two years for the double pulsar system to surpass the tests of GR possible from three decades of monitoring PSR B1913+16 and over a decade of timing PSR B1534+12. Ongoing precision timing measurements of the double pulsar system should soon provide even more stringent and new tests of GR. Crucial to these measurements will be the timing of the 2.7-s pulsar B, where the observed profile is significantly affected by A’s relativistic wind [239, 258]. A careful decoupling of these profile variations is required to accurately measure TOAs for this pulsar and determine the extent to which the theory-independent mass ratio R can be measured. This task is compounded by the fact that pulsar B’s signal is now [44] significantly weaker compared to the discovery observations five years ago [239]. This appears to be a direct result of its beam precessing out of our line of sight.

The relativistic effects observed in the double pulsar system are so large that corrections to higher post-Newtonian order may soon need to be considered. For example, \(\dot \omega\) may be measured precisely enough to require terms of second post-Newtonian order to be included in the computations [91]. In addition, in contrast to Newtonian physics, GR predicts that the spins of the neutron stars affect their orbital motion via spin-orbit coupling. This effect would most clearly be visible as a contribution to the observed \({\dot \omega}\) in a secular [26] and periodic fashion [395]. For the J0737−3039 system, the expected contribution is about an order of magnitude larger than for PSR B1913+16 [239]. As the exact value depends on the pulsars’ moment of inertia, a potential measurement of this effect would allow the moment of inertia of a neutron star to be determined for the first time [91]. Such a measurement would be invaluable for studies of the neutron star equation of state and our understanding of matter at extreme pressure and densities [206].

Finally, in the neutron star-white dwarf binary J1141−6545, the measurement of b, \({\dot \omega}\), γ and s permit a 6% test of GR [35]. Despite this being nominally only a relatively weak constraint for GR, the significantly different self gravities of the neutron star and white dwarf permits constraints on two coupling parameters between matter and the scalar gravitational field. These parameters are non-existent in GR, which describes gravity in terms of a tensor field, but are predicted by some alternative theories of gravity which consider tensor and scalar field components. The constraints provided by PSR J1141−6545 for the strongly non-linear coupling parameter are currently the most stringent to date and are set to improve dramatically over the next five years of timing observations.

Pulsar timing and neutron star masses

Multiple PK parameters have now been measured for a number of binary pulsars which provide very precise measurements of the neutron star masses [371, 345]. Figure 28 shows the distribution of masses following updates to a recent compilation [345]. While the young pulsars and the double neutron star binaries are consistent with, or just below, the canonical 1.4 M, we note that the millisecond pulsars in binary systems have, on average, significantly larger masses. This provides strong support for their formation through an extended period of accretion in the past, as discussed in Section 2.6.

Figure 28

Distribution of neutron star masses as inferred from timing observations of binary pulsars and X-ray binary systems. Figure adapted from an original version provided by Ingrid stairs. Additional information on globular cluster pulsar mass constraints provided by Paulo Freire. Error bars show one-sigma uncertainties on each mass determination.

Also shown on this diagram are several eccentric binary systems in globular clusters which have their masses constrained from measurements of the relativistic advance of periastron and the Keplerian mass function. In these cases, the condition sin i < 1 sets a lower limit on the companion mass mc > (fmassM2)1/3 and a corresponding upper limit on the pulsar mass. Probability density functions for both mp and mc can also be estimated in a statistical sense by assuming a random distribution of orbital inclination angles. An example of this is shown in Figure 29 for the eccentric binary millisecond pulsar in M5 [118] where the nominal pulsar mass is 2.08 ± 0.19 M! This is a potentially outstanding result. If confirmed by the measurement of other relativistic parameters, these supermassive neutron stars will have important constraints on the equation of state of superdense matter.

Figure 29

Pulsar mass versus companion mass diagram showing mass constraints for the eccentric binary millisecond pulsar B1516+02B [118]. The allowed parameter space is bounded by the dashed lines which show the uncertainty on the total mass from the measurement of the relativistic advance of periastron. Masses within the hatched region are disallowed by the Keplerian mass function and the constraint that sin i < 1. Assuming a random distribution of orbital inclination angles allows the probability density functions of the pulsar and companion mass to be derived, as shown by the top and right hand panels. Figure provided by Paulo Freire.

Currently the largest measurement of a radio pulsar mass through multiple PK parameters is the eccentric millisecond pulsar binary system J1903+0327 [70] (see also Section 2.9). Thus, in addition to challenging models of millisecond pulsar formation, this new discovery has important implications for fundamental physics. When placed on the mass-radius diagram for neutron stars [206], this 1.74 M pulsar appears to be incompatible with at least four equations of state for superdense matter. Future timing measurements are required to consolidate and verify this potentially very exciting result.

Pulsar timing and gravitational wave detection

We have seen in the Section 4.4 how pulsar timing can be used to provide indirect evidence for the existence of gravitational waves from coalescing stellar-mass binaries. In this final section, we look at how pulsar timing might soon be used to detect gravitational radiation directly. The idea to use pulsars as natural gravitational wave detectors was first explored in the late 1970s [330, 95]. The basic concept is to treat the solar system barycentre and a distant pulsar as opposite ends of an imaginary arm in space. The pulsar acts as the reference clock at one end of the arm sending out regular signals which are monitored by an observer on the Earth over some timescale T. The effect of a passing gravitational wave would be to perturb the local spacetime metric and cause a change in the observed rotational frequency of the pulsar. For regular pulsar timing observations with typical TOA uncertainties of ϵTOA, this “detector” would be sensitive to waves with dimensionless amplitudes h ≲ ∊TOA/T and frequencies f ∼ 1/T [33, 41].

Probing the gravitational wave background

Many cosmological models predict that the Universe is presently filled with a low-frequency stochastic gravitational wave background (GWB) produced during the big bang era [292]. A significant component [309, 159] is the gravitational radiation from the inspiral prior to supermassive black hole mergers. In the ideal case, the change in the observed frequency caused by the GWB should be detectable in the set of timing residuals after the application of an appropriate model for the rotational, astrometric and, where necessary, binary parameters of the pulsar. As discussed in Section 4.2, all other effects being negligible, the rms scatter of these residuals σ would be due to the measurement uncertainties and intrinsic timing noise from the neutron star.

For a GWB with a flat energy spectrum in the frequency band f ± f/2 there is an additional contribution to the timing residuals σg [95]. When fT ≫ 1, the corresponding wave energy density is

$${\rho _{\rm{g}}} = {{243{\pi ^3}{f^4}\sigma _{\rm{g}}^2} \over {208G}}.$$

An upper limit to ρg can be obtained from a set of timing residuals by assuming the rms scatter is entirely due to this effect (σ = σg). These limits are commonly expressed as a fraction of the energy density required to close the Universe

$${\rho _{\rm{c}}} = {{3H_{\rm{0}}^2} \over {8\pi G}} \simeq 2 \times {10^{- 29}}{h^2}\;{\rm{g}}\;{\rm{cm}}^{{- 3}},$$

where the Hubble constant H0 = 100 h km s−1 Mpc.

This technique was first applied [325] to a set of TOAs for PSR B1237+25 obtained from regular observations over a period of 11 years as part of the JPL pulsar timing programme [99]. This pulsar was chosen on the basis of its relatively low level of timing activity by comparison with the youngest pulsars, whose residuals are ultimately plagued by timing noise (see Section 4.3). By ascribing the rms scatter in the residuals (σ = 240 ms) to the GWB, the limit is ρg/ρc ≲ 4 × 10−3h−2 for a centre frequency f = 7 nHz.

This limit, already well below the energy density required to close the Universe, was further reduced following the long-term timing measurements of millisecond pulsars at Arecibo (see Section 4.3). In the intervening period, more elaborate techniques had been devised [33, 41, 356] to look for the likely signature of a GWB in the frequency spectrum of the timing residuals and to address the possibility of “fitting out” the signal in the TOAs. Following [33] it is convenient to define

$${\Omega _{\rm{g}}} = {1 \over {{\rho _{\rm{c}}}}}{{{\rm{d}}\;{\rm{log}}\;{\rho _{\rm{g}}}} \over {{\rm{d}}\;{\rm{log}}\;f}},$$

i.e. the energy density of the GWB per logarithmic frequency interval relative to ρc. With this definition, the power spectrum of the GWB [147, 41] is

$${\mathcal P}(f) = {{G{\rho _{\rm{g}}}} \over {3{\pi ^3}{f^4}}} = {{H_0^2{\Omega _{\rm{g}}}} \over {8{\pi ^4}{f^5}}} = 1.34 \times {10^4}{\Omega _{\rm{g}}}{h^2}f_{{\rm{y}}{{\rm{r}}^{- 1}}}^{- 5}\mu {{\rm{s}}^{\rm{2}}}{\rm{yr,}}$$

where \({f_{{\rm{y}}{{\rm{r}}^{- 1}}}}\) is frequency in cycles per year. The long-term timing stability of B1937+21, discussed in Section 4.3, limits its use for periods ≳ 2 yr. Using the more stable residuals for PSR B1855+09, Kaspi et al. [185] placed an upper limit of Ωgh2 < 1.1 × 10−7. This limit is difficult to reconcile with most cosmic string models for galaxy formation [50, 372].

For binary pulsars, the orbital period provides an additional clock for measuring the effects of gravitational waves. In this case, the range of frequencies is not limited by the time span of the observations, allowing the detection of waves with periods as large as the light travel time to the binary system [33]. The most stringent results presently available are based on the B1855+09 limit Ωgh2 < 2.7 × 10−4 in the frequency range 10−11 < f < 4.4 × 10−9 Hz [196].

Constraints on massive black hole binaries

In addition to probing the GWB, pulsar timing is beginning to place interesting constraints on the existence of massive black hole binaries. Arecibo data for PSRs B1937+21 and J1713+0747 already make the existence of an equal-mass black hole binary in Sagittarius A* unlikely [214]. More recently, timing data from B1855+09 have been used to virtually rule out the existence of a proposed supermassive black hole as the explanation for the periodic motion seen at the centre of the radio galaxy 3C66B [358].

A simulation of the expected modulations of the timing residuals for the putative binary system, with a total mass of 5.4 × 1010 M, is shown along with the observed timing residuals in Figure 30. Although the exact signature depends on the orientation and eccentricity of the binary system, Monte Carlo simulations show that the existence of such a massive black hole binary is ruled out with at least 95% confidence [161].

Figure 30

Top panel: Observed timing residuals for PSR B1855+09. Bottom panel: Simulated timing residuals induced from a putative black hole binary in 3C66B. Figure provided by Rick Jenet [161].

A millisecond pulsar timing array

A natural extension of the single-arm detector concept discussed above is the idea of using timing data for a number of pulsars distributed over the whole sky to detect gravitational waves [137]. Such a “timing array” would have the advantage over a single arm in that, through a cross-correlation analysis of the residuals for pairs of pulsars distributed over the sky, it should be possible to separate the timing noise of each pulsar from the signature of the GWB common to all pulsars in the array. To illustrate this, consider the fractional frequency shift of the ith pulsar in an array

$${{\delta {\nu _i}} \over {{\nu _i}}} = {\alpha _i}{\mathcal A}(t) + {{\mathcal N}_i}(t),$$

where αi is a geometric factor dependent on the line-of-sight direction to the pulsar and the propagation and polarisation vectors of the gravitational wave of dimensionless amplitude A. The timing noise intrinsic to the pulsar is characterised by the function \({{\mathcal N}_i}\). The result of a cross-correlation between pulsars i and j is then

$${\alpha _i}{\alpha _j}\langle {{\mathcal A}^2}\rangle + {\alpha _i}\langle {\mathcal A}{{\mathcal N}_j}\rangle + {\alpha _j}\langle {\mathcal A}{{\mathcal N}_i}\rangle + \langle {{\mathcal N}_i}{{\mathcal N}_j}\rangle ,$$

where the bracketed terms indicate cross-correlations. Since the wave function and the noise contributions from the two pulsars are independent, the cross correlation tends to \({\alpha _i}{\alpha _j}\langle {{\mathcal A}^2}\rangle\) as the number of residuals becomes large. Summing the cross-correlation functions over a large number of pulsar pairs provides additional information on this term as a function of the angle on the sky [136] and allows the separation of the effects of clock and ephemeris errors from the GWB [112].

A recent analysis [160] applying the timing array concept to data for seven millisecond pulsars has reduced the energy density limit to Ωgh2 < 1.9 × 10−8 for a background of supermassive black hole sources. The corresponding limits on the background of relic gravitational waves and cosmic strings are 2.0 × 10−8 and 1.9 × 10−8 respectively. These limits can be used to constrain the merger rate of supermassive black hole binaries at high redshift, investigate inflationary parameters and place limits on the tension of currently proposed cosmic string scenarios.

The region of the gravitational wave energy density spectrum probed by the current pulsar timing array is shown in Figure 31 where it can be seen that the pulsar timing regime is complementary to the higher frequency bands of LISA and LIGO.

Figure 31

Summary of the gravitational wave spectrum showing the location in phase space of the pulsar timing array (PTA) and its extension with the Square Kilometre Array (SKA). Figure updated by Michael Kramer [198] from an original design by Richard Battye.

A number of long-term timing projects are now underway to make a large-scale pulsar timing array a reality. The Parkes pulsar timing array [11, 143] observes twenty millisecond pulsars twice a month. The European Pulsar Timing Array [10] uses the Lovell, Westerbork, Effelsberg and Nancay radio telescopes to regularly observe a similar number. Finally, at Arecibo and Green Bank, regular timing of a dozen or more millisecond pulsars is carried out by a North American consortium [267]. It is expected that a combined analysis of all these efforts could reach a limits of Ωgh2 < 10−10 before 2010 [143]. Looking further ahead, the increase in sensitivity provided by the Square Kilometre Array [154, 198] should further improve the limits of the spectrum probed by pulsar timing. As Figure 31 shows, the SKA could provide up to two orders of magnitude improvement over current capabilities.

Going further

For further details on the techniques and prospects of pulsar timing, a number of excellent reviews are available [17, 362, 30, 344, 226]. Two audio files and slides from lectures at the centennial meeting of the American Physical Society are also available on-line [15, 399]. The tests of general relativity discussed in Section 4.4, along with further effects, are reviewed elsewhere in this journal by Will [400] and Stairs [344]. A recent review by Kramer & Stairs [200] provides a detailed account of the double pulsar. Further discussions on the realities of using pulsars as gravity wave detectors can be found in other review articles [323, 14, 143].

Summary and Future Prospects

The main aim of this article was to review some of the many astrophysical applications provided by the present sample of binary and millisecond radio pulsars that are relevant to gravitational physics. The topics covered here, along with the bibliography and associated tables of observational parameters, should be useful to those wishing to delve deeper into the vast body of literature that exists.

Through an understanding of the Galactic population of radio pulsars summarised in Section 3 it is possible to predict the detection statistics of terrestrial gravitational wave detectors to nearby rapidly spinning neutron stars (see Section 3.3), as well as coalescing relativistic binaries at cosmic distances (see Section 3.4). Continued improvements in gravitational wave detector sensitivities should result in a number of interesting developments and contributions in this area. These developments and contributions might include the detection of presently known radio pulsars, as well as a population of coalescing binary systems which have not yet been detected as radio pulsars.

The phenomenal timing stability of radio pulsars leads naturally to a large number of applications, including their use as laboratories for relativistic gravity (see Section 4.5), constraining the equation of state of superdense matter (see Section 4.6) and as natural detectors of gravitational radiation (see Section 4.7). Long-term timing experiments of the present sample of millisecond and binary pulsars currently underway appear to have tremendous potential in these areas and may detect the gravitational wave background (if it exists) within the next decade.

These applications will benefit greatly from the continuing discovery of new systems by the present generation of radio pulsar searches which continue to probe new areas of parameter space. Based on the results presented in Section 3.3, it is clear that we are aware of only a few per cent of the total active pulsar population in our Galaxy. In all likelihood, then, we have not seen all of the pulsar zoo. The current and futures surveys described in Section 2.11 will ultimately provide a far more complete census of the Galactic pulsar population. Three possible “holy grails” of pulsar astronomy which could soon be found are:

  • An X-ray/radio millisecond pulsar While the link between millisecond pulsars and X-ray binaries appears to be compelling, despite intensive searches [47], no radio pulsations have been detected in these binaries. This could be a result of free-free absorption of any radio waves by the thick accretion disk, or perhaps quenching of the accelerating potential in the neutron star magnetosphere by infalling matter. The recent discovery of radio pulsations from two magnetars [62, 61] demonstrates that radio emission can be found in seemingly unlikely sites. A millisecond pulsar in transition between an X-ray and radio phase would be another such remarkable discovery.

  • A pulsar—black hole binary system: Following the wide variety of science possible from the new double pulsar J0737−3039 (see Sections 2.6, 3.4.1 and 4.4), a radio pulsar with a black-hole companion would without doubt be a fantastic gravitational laboratory. Excellent places to look for such systems are globular clusters and the Galactic centre [296].

  • A sub-millisecond pulsar: The most rapidly spinning radio pulsar currently known is the 1.39-ms PSR J1748−2446ad in Terzan 5 [140]. Do neutron stars with kHz spin rates exist? Searches now have sensitivity to such objects [46] and a discovery of even one would constrain the equation of state of matter at high densities. As mentioned in Section 2.2, the R-mode instability may prevent neutron stars from reaching such high spin rates [38, 66]. Of course, this does not stop observers from looking for such objects! The current generation of surveys summarized in Section 2.11 continues to be more and more sensitive to this putative source population.

The discovery of the eccentric millisecond binary pulsar J1903+0327 [70] (see Sections 2.9 and 4.6) was completely unprecedented within the framework of our theories for binary pulsar formation. It therefore serves as a stark reminder that we should “expect the unexpected” ! Even though the study of radio pulsars is now 40 years old, these experiences tell us that many exciting discoveries lie ahead of us.

Pulsar astronomy remains an extremely active area of modern astrophysics and the next decade will undoubtedly continue to produce new results from currently known objects as well as new surprises. Although it is often stated that we are bound by available computational resources, in my opinion, pulsar research is currently limited by a shortage of researchers, and not necessarily computational resources. Keen students more than ever are needed to help shape the future of this exciting and continually evolving field.


  1. 1.

    Like most astronomical sources, pulsars are named after their position in the sky. Those pulsars discovered prior to the mid 1990s are named based on the Besselian equatorial coordinate system (B1950) and have a B prefix followed by their right ascension and declination. More recently discovered pulsars follow the Julian (J2000) epoch. Pulsars in globular clusters, where the positional designation is not unique, have additional characters to distinguish them. For example PSR J1748-2446ad in the globular cluster Terzan 5 [140].

  2. 2.

    Pulsar astronomers usually define the luminosity LSd2, where S is the mean flux density at 400 MHz (a standard observing frequency) and d is the distance derived from the DM (see Section 2.4). Since this ignores any assumptions about beaming or geometrical factors, it is sometimes referred to as a “pseudoluminosity” [6].

  3. 3.

    The reader is encouraged to view the beautiful movies explaining the eclipse model [257]


  1. [1]

    Allan, D.W., “The Allan Variance”, personal homepage, Allan’s Time Interval Metrology Enterprises. URL (cited on 7 December 2000):

  2. [2]

    Alpar, M.A., Cheng, A.F., Ruderman, M.A., and Shaham, J., “A new class of radio pulsars”, Nature, 300, 728–730, (1982).

    ADS  Google Scholar 

  3. [3]

    Alpar, M.A., Nandkumar, R., and Pines, D., “Vortex Creep and the Internal Temperature of Neutron Stars: Timing Noise of Pulsars”, Astrophys. J., 311, 197–213, (1986).

    ADS  Google Scholar 

  4. [4]

    Anderson, S.B., Gorham, P.W., Kulkarni, S.R., Prince, T.A., and Wolszczan, A., “Discovery of two radio pulsars in the globular cluster M15”, Nature, 346, 42–44, (1990).

    ADS  Google Scholar 

  5. [5]

    Andersson, N., Jones, D.I., Kokkotas, K.D., and Stergioulas, N., “r-Mode runaway and rapidly rotating neutron stars”, Astrophys. J. Lett., 534, L75–L78, (2000). ADS:

    ADS  Google Scholar 

  6. [6]

    Arzoumanian, Z., Chernoff, D.F., and Cordes, J.M., “The Velocity Distribution of Isolated Radio Pulsars”, Astrophys. J., 568, 289–301, (2002).

    ADS  Google Scholar 

  7. [7]

    Arzoumanian, Z., Cordes, J.M., and Wasserman, I., “Pulsar Spin Evolution, Kinematics, and the Birthrate of Neutron Star Binaries”, Astrophys. J., 520, 696–705, (1999).

    ADS  Google Scholar 

  8. [8]

    Arzoumanian, Z., Fruchter, A.S., and Taylor, J.H., “Orbital Variability in the Eclipsing Pulsar Binary PSR B1957+20”, Astrophys. J. Lett., 426, L85–L88, (1994).

    ADS  Google Scholar 

  9. [9]

    Arzoumanian, Z., Nice, D.J., Taylor, J.H., and Thorsett, S.E., “Timing Behavior of 96 Radio Pulsars”, Astrophys. J., 422, 671–680, (1994). ADS:

    ADS  Google Scholar 

  10. [10]

    ASTRON, “The European Pulsar Timing Array”, project homepage. URL (cited on 24 June 2008):∼stappers/epta/.

  11. [11]

    ATNF, “The Parkes Pulsar Timing Array”, project homepage. URL (cited on 24 June 2008):

  12. [12]

    ATNF/CSIRO, “ATNF Pulsar Catalogue”, web interface to database. URL (cited on 23 May 2008):

  13. [13]

    Australia Telescope National Facility, “ATNF Pulsar Group”, project homepage. URL (cited on 22 January 2005):

  14. [14]

    Backer, D.C., “Timing of Millisecond Pulsars”, in van Paradijs, J., van del Heuvel, E.P.J., and Kuulkers, E., eds., Compact Stars in Binaries (IAU Symposium 165), Proceedings of the 165th Symposium of the International Astronomical Union, held in the Hague, The Netherlands, August 15–19, 1994, pp. 197–211, (Kluwer, Dordrecht, Netherlands; Boston, U.S.A., 1996).

    Google Scholar 

  15. [15]

    Backer, D.C., “Pulsars — Nature’s Best Clocks”, lecture notes, American Physical Society, (1999). URL (cited on 8 December 2000):

    Google Scholar 

  16. [16]

    Backer, D.C., Foster, R.F., and Sallmen, S., “A second companion of the millisecond pulsar 1620–26”, Nature, 365, 817–819, (1993).

    ADS  Google Scholar 

  17. [17]

    Backer, D.C., and Hellings, R.W., “Pulsar Timing and General Relativity”, Annu. Rev. Astron. Astrophys., 24, 537–575, (1986).

    ADS  Google Scholar 

  18. [18]

    Backer, D.C., Kulkarni, S.R., Heiles, C., Davis, M.M., and Goss, W.M., “A millisecond pulsar”, Nature, 300, 615–618, (1982).

    ADS  Google Scholar 

  19. [19]

    Bailes, M., “The Origin of pulsar velocities and the velocity-magnetic moment correlation.”, Astrophys. J., 342, 917–927, (1989).

    ADS  Google Scholar 

  20. [20]

    Bailes, M., “Precision timing at the Parkes 64-m radio telescope”, in Bailes, M., Nice, D.J., and Thorsett, S.E., eds., Radio Pulsars, Proceedings of a meeting held at Mediterranean Agonomic Institute of Chania, Crete, Greece, 26–29 August 2002, ASP Conference Series, vol. 302, pp. 57–64, (Astronomical Society of the Pacific, San Fransisco, U.S.A., 2003).

    Google Scholar 

  21. [21]

    Bailes, M., “Latest timing results for PSR J1618−3921”, personal communication, (2008).

  22. [22]

    Bailes, M., Harrison, P.A., Lorimer, D.R., Johnston, S., Lyne, A.G., Manchester, R.N., D’Amico, N., Nicastro, L., Tauris, T.M., and Robinson, C., “Discovery of Three Galactic Binary Millisecond Pulsars”, Astrophys. J. Lett., 425, L41–L44, (1994).

    ADS  Google Scholar 

  23. [23]

    Bailes, M., Johnston, S., Bell, J.F., Lorimer, D.R., Stappers, B.W., Manchester, R.N., Lyne, A.G., D’Amico, N., and Gaensler, B.M., “Discovery of four isolated millisecond pulsars”, Astrophys. J., 481, 386–391, (1997).

    ADS  Google Scholar 

  24. [24]

    Bailes, M., Manchester, R.N., Kesteven, M.J., Norris, R.P., and Reynolds, J.E., “The proper motion of six southern radio pulsars”, Mon. Not. R. Astron. Soc., 247, 322–326, (1990).

    ADS  Google Scholar 

  25. [25]

    Bailes, M., Ord, S.M., Knight, H.S., and Hotan, A.W., “Self-consistency of relativistic observables with general relativity in the white dwarf-neutron star binary PSR J1141-6545”, Astrophys. J. Lett., 595, L49–L52, (2003).

    ADS  Google Scholar 

  26. [26]

    Barker, B.M., and O’Connell, R.F., “Gravitational two-body problem with arbitrary masses, spins, and quadrupole moments”, Phys. Rev. D, 12, 329–335, (1975).

    ADS  Google Scholar 

  27. [27]

    Belczynski, K., Kalogera, V., and Bulik, T., “A Comprehensive Study of Binary Compact Objects as Gravitational Wave Sources: Evolutionary Channels, Rates, and Physical Properties”, Astrophys. J., 572, 407–431, (2002).

    ADS  Google Scholar 

  28. [28]

    Belczynski, K., Kalogera, V., Rasio, F.A., Taam, R.E., Zezas, A., Bulik, T., Maccarone, T.J., and Ivanova, N., “Compact Object Modeling with the StarTrack Population Synthesis Code”, Astrophys. J., 174, 223–260, (2008).

    ADS  Google Scholar 

  29. [29]

    Belczynski, K., Lorimer, D.R., and Ridley, J.P., Mon. Not. R. Astron. Soc., in preparation, (2008).

  30. [30]

    Bell, J.F., “Radio Pulsar Timing”, Adv. Space Res., 21, 131–147, (1998).

    ADS  Google Scholar 

  31. [31]

    Bell, J.F., Bailes, M., Manchester, R.N., Lyne, A.G., Camilo, F., and Sandhu, J.S., “Timing measurements and their implications for four binary millisecond pulsars”, Mon. Not. R. Astron. Soc., 286, 463–469, (1997).

    ADS  Google Scholar 

  32. [32]

    Bell, J.F., Bessell, M.S., Stappers, B.W., Bailes, M., and Kaspi, V.M., “PSR J0045-7319: A dual-line binary radio pulsar”, Astrophys. J. Lett., 447, L117–L119, (1995).

    ADS  Google Scholar 

  33. [33]

    Bertotti, B., Carr, B.J., and Rees, M.J., “Limits from the timing of pulsars on the cosmic gravitational wave background”, Mon. Not. R. Astron. Soc., 203, 945–954, (1983).

    ADS  Google Scholar 

  34. [34]

    Beskin, V.S., Gurevich, A.V., and Istomin, Y.N., Physics of the Pulsar Magnetosphere, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1993).

    MATH  Google Scholar 

  35. [35]

    Bhat, N.D.R., Bailes, M., and Verbiest, J.P.W., “Gravitational-radiation losses from the pulsar-white-dwarf binary PSR J1141−6545”, Phys. Rev. D, 77(12), 124017, (2008). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  36. [36]

    Bhattacharya, D., and van den Heuvel, E.P.J., “Formation and evolution of binary and millisecond radio pulsars”, Phys. Rep., 203, 1–124, (1991).

    ADS  Google Scholar 

  37. [37]

    Biggs, J.D., “Meridional compression of radio pulsar beams”, Mon. Not. R. Astron. Soc., 245, 514–521, (1990).

    ADS  Google Scholar 

  38. [38]

    Bildsten, L., “Gravitational radiation and rotation of accreting neutron stars”, Astrophys. J. Lett., 501, L89–L93, (1998).

    ADS  Google Scholar 

  39. [39]

    Bisnovatyi-Kogan, G.S., and Komberg, B.V., “Pulsars and close binary systems”, Sov. Astron., 18, 217–221, (1974).

    ADS  Google Scholar 

  40. [40]

    Blaauw, A., “On the origin of the O- and B-type stars with high velocities (the ‘run-away’ stars), and some related problems”, Bull. Astron. Inst. Neth., 15, 265–290, (1961).

    ADS  Google Scholar 

  41. [41]

    Blandford, R.D., Narayan, R., and Romani, R.W., “Arrival-time analysis for a millisecond pulsar”, J. Astrophys. Astron., 5, 369–388, (1984).

    ADS  Google Scholar 

  42. [42]

    Boriakoff, V., Buccheri, R., and Fauci, F., “Discovery of a 6.1-ms binary pulsar, PSR 1953+29”, Nature, 304, 417–419, (1983).

    ADS  Google Scholar 

  43. [43]

    Boyles, J., “Initial Findings of the GBT 350-MHz Drift Scan Pulsar Survey”, 212th AAS Meeting, St. Louis, MO, 1–5 June 2008, conference paper, (2008). ADS:

  44. [44]

    Breton, R.P., Kaspi, V.M., Kramer, M., McLaughlin, M.A., Lyutikov, M., Ransom, S.M., Stairs, I.H., Ferdman, R.D., and Camilo, F., “Using the Double Pulsar Eclipses to Probe Fundamental Physics”, in Bassa, C.G., Wang, Z., Cumming, A., and Kaspi, V.M., eds., 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More, McGill University, Montréal, Canada, 12–17 August 2007, AIP Conference Proceedings, vol. 983, pp. 469–473, (American Institute of Physics, Melville, U.S.A., 2008).

    Google Scholar 

  45. [45]

    Breton, R.P., Roberts, M.S.E., Ransom, S.M., Kaspi, V.M., Durant, M., Bergeron, P., and Faulkner, A.J., “The Unusual Binary Pulsar PSR J1744−3922: Radio Flux Variability, Near-Infrared Observation, and Evolution”, Astrophys. J., 661, 1073–1083, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  46. [46]

    Burderi, L., and D’Amico, N., “Probing the Equation of State of Ultradense Matter with a Submillisecond Pulsar Search Experiment”, Astrophys. J., 490, 343–352, (1997).

    ADS  Google Scholar 

  47. [47]

    Burgay, M., Burderi, L., Possenti, A., D’Amico, N., Manchester, R.N., Lyne, A.G., Camilo, F., and Campana, S., “A Search for Pulsars in Quiescent Soft X-Ray Transients. I.”, Astrophys. J., 589, 902–910, (2003).

    ADS  Google Scholar 

  48. [48]

    Burgay, M., D’Amico, N., Possenti, A., Manchester, R.N., Lyne, A.G., Joshi, B.C., McLaughlin, M.A., Kramer, M., Sarkissian, J.M., Camilo, F., Kalogera, V., Kim, C., and Lorimer, D.R., “An increased estimate of the merger rate of double neutron stars from observations of a highly relativistic system”, Nature, 426, 531–533, (2003).

    ADS  Google Scholar 

  49. [49]

    Burgay, M., Joshi, B.C., D’Amico, N., Possenti, A., Lyne, A.G., Manchester, R.N., McLaughlin, M.A., Kramer, M., Camilo, F., and Freire, P.C.C., “The Parkes High-Latitude pulsar survey”, Mon. Not. R. Astron. Soc., 368, 283–292, (2006).

    ADS  Google Scholar 

  50. [50]

    Caldwell, R.R., and Allen, B., “Cosmological constraints on cosmic-string gravitational radiation”, Phys. Rev. D, 45, 3447–3468, (1992).

    ADS  Google Scholar 

  51. [51]

    California Institute of Technology, “Laser Interferometric Gravitational Wave Observatory”, project homepage. URL (cited on 29 January 2005):

  52. [52]

    Camilo, F., A Search for Millisecond Pulsars, Ph.D. Thesis, (Princeton University, Princeton, U.S.A., 1995).

    Google Scholar 

  53. [53]

    Camilo, F., “Intermediate-Mass Binary Pulsars: a New Class of Objects?”, in Johnston, S., Walker, M.A., and Bailes, M., eds., Pulsars: Problems and Progress (IAU Colloquium 160), Proceedings of the 160th Colloquium of the IAU, held at the Research Centre for Theoretical Astrophysics, University of Sydney, Australia, 8–12 January 1996, ASP Conference Series, vol. 105, pp. 539–540, (Astronomical Society of the Pacific, San Francisco, U.S.A., 1996).

    Google Scholar 

  54. [54]

    Camilo, F., “Deep Searches for Young Pulsars”, in Bailes, M., Nice, D.J., and Thorsett, S.E., eds., Radio Pulsars: In Celebration of the Contributions of Andrew Lyne, Dick Manchester and Joe Taylor — a Festschrift Honoring Their 60th Birthdays, ASP Conference Series, vol. 302, p. 145, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2003).

    Google Scholar 

  55. [55]

    Camilo, F., Foster, R.S., and Wolszczan, A., “High-precision timing of PSR J1713+0747: Shapiro delay”, Astrophys. J. Lett., 437, L39–L42, (1994).

    ADS  Google Scholar 

  56. [56]

    Camilo, F., Lorimer, D.R., Freire, P.C.C., Lyne, A.G., and Manchester, R.N., “Observations of 20 millisecond pulsars in 47 Tucanae at 20 centimeters”, Astrophys. J., 535, 975–990, (2000).

    ADS  Google Scholar 

  57. [57]

    Camilo, F., Lyne, A.G., Manchester, R.N., Bell, J.F., Stairs, I.H., D’Amico, N., Kaspi, V.M., Possenti, A., Crawford, F., and McKay, N.P.F., “Discovery of five binary radio pulsars”, Astrophys. J. Lett., 548, L187–L191, (2001).

    ADS  Google Scholar 

  58. [58]

    Camilo, F., Nice, D.J., and Taylor, J.H., “Discovery of two fast-rotating pulsars”, Astrophys. J. Lett., 412, L37–L40, (1993).

    ADS  Google Scholar 

  59. [59]

    Camilo, F., Nice, D.J., and Taylor, J.H., “A search for millisecond pulsars at galactic latitudes −50° < b < −20°”, Astrophys. J., 461, 812–819, (1996).

    ADS  Google Scholar 

  60. [60]

    Camilo, F., Nice, D.J., Taylor, J.H., and Shrauner, J.A., “Princeton-Arecibo Declination-Strip Survey for Millisecond Pulsars. I.”, Astrophys. J., 469, 819–827, (1996).

    ADS  Google Scholar 

  61. [61]

    Camilo, F., Ransom, S.M., Halpern, J.P., and Reynolds, J., “1E 1547.0-5408: A Radioemitting Magnetar with a Rotation Period of 2 Seconds”, Astrophys. J. Lett., 666, L93–L96, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  62. [62]

    Camilo, F., Ransom, S.M., Halpern, J.P., Reynolds, J., Helfand, D.J., Zimmerman, N., and Sarkissian, J., “Transient pulsed radio emission from a magnetar”, Nature, 442, 892–895, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  63. [63]

    Camilo, F., and Rasio, F.A., “Pulsars in Globular Clusters”, in Rasio, F.A., and Stairs, I.H., eds., Binary Radio Pulsars, Proceedings of a meeting held at the Aspen Center for Physics, USA, 12–16 January 2004, ASP Conference Series, vol. 328, pp. 147–169, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2005).

    Google Scholar 

  64. [64]

    CASPER, “Center for Astronomy Signal Processing and Electronics Research”, project homepage. URL (cited on 24 June 2008):

  65. [65]

    Chakrabarty, D., and Morgan, E.H., “The 2 hour orbit of a binary millisecond X-ray pulsar”, Nature, 394, 346–348, (1998).

    ADS  Google Scholar 

  66. [66]

    Chakrabarty, D., Morgan, E.H., Muno, M.P., Galloway, D.K., Wijnands, R., van der Klis, M., and Markwardt, C.B., “Nuclear-powered millisecond pulsars and the maximum spin frequency of neutron stars”, Nature, 424, 42–44, (2003).

    ADS  Google Scholar 

  67. [67]

    Champion, D.J., “Latest timing results for PSR J1829+2456”, personal communication, (2005).

  68. [68]

    Champion, D.J., Lorimer, D.R., McLaughlin, M.A., Arzoumanian, Z., Cordes, J.M., Weisberg, J., and Taylor, J.H., “PSR J1829+2456: a new relativistic binary system”, Mon. Not. R. Astron. Soc., 350, L61–L65, (2004).

    ADS  Google Scholar 

  69. [69]

    Champion, D.J., McLaughlin, M.A., and Lorimer, D.R., “A survey for pulsars in EGRET error boxes”, Mon. Not. R. Astron. Soc., 364, 1011–1014, (2005). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  70. [70]

    Champion, D.J., Ransom, S.M., Lazarus, P., Camilo, F., Bassa, C., Kaspi, V.M., Nice, D.J., Freire, P.C.C., Stairs, I.H., van Leeuwen, J., Stappers, B.W., Cordes, J.M., Hessels, J.W.T., Lorimer, D.R., Arzoumanian, Z., Backer, D.C., Bhat, N.D.R., Chatterjee, S., Cognard, I., Deneva, J.S., Faucher-Giguère, C.-A., Gaensler, B.M., Han, J.L., Jenet, F.A., Kasian, L., Kondratiev, V.I., Kramer, M., Lazio, T.J.W., McLaughlin, M.A., Venkataraman, A., and Vlemmings, W., “An Eccentric Binary Millisecond Pulsar in the Galactic Plane”, Science, 805, (2008). Related online version (cited on 28 October 2008):

  71. [71]

    Chandler, A.M., Pulsar Searches: From Radio to Gamma-Rays, Ph.D. Thesis, (California Institute of Technology, Pasadena, U.S.A., 2003).

    Google Scholar 

  72. [72]

    Chatterjee, S., Vlemmings, W.H.T., Brisken, W.F., Lazio, T.J.W., Cordes, J.M., Goss, W.M., Thorsett, S.E., Fomalont, E.B., Lyne, A.G., and Kramer, M., “Getting Its Kicks: A VLBA Parallax for the Hyperfast Pulsar B1508+55”, Astrophys. J. Lett., 630, L61–L64, (2005). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  73. [73]

    Chaurasia, H.K., and Bailes, M., “On the Eccentricities and Merger Rates of Double Neutron Star Binaries and the Creation of ‘Double Supernovae’”, Astrophys. J., 632, 1054–1059, (2005). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  74. [74]

    Cheng, K.S., “Could Glitches Inducing Magnetospheric Fluctuations Produce Low Frequency Timing Noise?”, Astrophys. J., 321, 805–812, (1987).

    ADS  Google Scholar 

  75. [75]

    Cheng, K.S., “Outer Magnetospheric Fluctuations and Pulsar Timing Noise”, Astrophys. J., 321, 799–804, (1987).

    ADS  Google Scholar 

  76. [76]

    Clifton, T.R., Lyne, A.G., Jones, A.W., McKenna, J., and Ashworth, M., “A high frequency survey of the Galactic plane for young and distant pulsars”, Mon. Not. R. Astron. Soc., 254, 177–184, (1992).

    ADS  Google Scholar 

  77. [77]

    Cooray, A., “Gravitational-wave background of neutron star-white dwarf binaries”, Mon. Not. R. Astron. Soc., 354, 25–30, (2004).

    ADS  Google Scholar 

  78. [78]

    Cordes, J.M., “Sideband analysis: a method for detecting fast binary pulsars”, unknown status, (1995).

  79. [79]

    Cordes, J.M., “New model of NE2001 in preparation”, personal communication, (2008).

  80. [80]

    Cordes, J.M., and Chernoff, D.F., “Neutron Star Population Dynamics. I. Millisecond Pulsars”, Astrophys. J., 482, 971–992, (1997).

    ADS  Google Scholar 

  81. [81]

    Cordes, J.M., and Chernoff, D.F., “Neutron Star Population Dynamics. II. Three-dimensional Space Velocities of Young Pulsars”, Astrophys. J., 505, 315–338, (1998).

    ADS  Google Scholar 

  82. [82]

    Cordes, J.M., Freire, P.C.C., Lorimer, D.R., Camilo, F., Champion, D.J., Nice, D.J., Ramachandran, R., Hessels, J.W.T., Vlemmings, W., van Leeuwen, J., Ransom, S.M., Bhat, N.D.R., Arzoumanian, Z., McLaughlin, M.A., Kaspi, V.M., Kasian, L., Deneva, J.S., Reid, B., Chatterjee, S., Han, J.L., Backer, D.C., Stairs, I.H., Deshpande, A.A., and Faucher-Giguère, C.-A., “Arecibo Pulsar Survey Using ALFA. I. Survey Strategy and First Discoveries”, Astrophys. J., 637, 446–455, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  83. [83]

    Cordes, J.M., and Helfand, D.J., “Pulsar timing III. Timing Noise of 50 Pulsars”, Astrophys. J. Lett., 239, 640–650, (1980).

    ADS  Google Scholar 

  84. [84]

    Cordes, J.M., and Lazio, T.J.W., “NE2001. I. A New Model for the Galactic Distribution of Free Electrons and its Fluctuations”, (2002). URL (cited on 22 January 2005):

  85. [85]

    Cordes, J.M., and Lazio, T.J.W., “NE2001. II. Using Radio Propagation Data to Construct a Model for the Galactic Distribution of Free Electrons”, (2003). URL (cited on 22 January 2005):

  86. [86]

    Cornell University, “ e-Print archive”, web interface to database. URL (cited on 19 March 2001):

  87. [87]

    Crawford, F., Kaspi, V.M., Manchester, R.N., Lyne, A.G., Camilo, F., and D’Amico, N., “Radio Pulsars in the Magellanic Clouds”, Astrophys. J., 553, 367–374, (2001). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  88. [88]

    Crawford, F., Roberts, M.S.E., Hessels, J.W.T., Ransom, S.M., Livingstone, M., Tam, C.R., and Kaspi, V.M., “A Survey of 56 Midlatitude EGRET Error Boxes for Radio Pulsars”, Astrophys. J., 652, 1499–1507, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  89. [89]

    D’Amico, N., Lyne, A.G., Manchester, R.N., Possenti, A., and Camilo, F., “Discovery of short-period binary millisecond pulsars in four globular clusters”, Astrophys. J. Lett., 548, L171–L174, (2001).

    ADS  Google Scholar 

  90. [90]

    Damour, T., and Deruelle, N., “General Relativistic Celestial Mechanics of Binary Systems. II. The Post-Newtonian Timing Formula”, Ann. Inst. Henri Poincare A, 44, 263–292, (1986).

    MathSciNet  MATH  Google Scholar 

  91. [91]

    Damour, T., and Schäfer, G., “Higher order relativistic periastron advances in binary pulsars”, Nuovo Cimento B, 101, 127, (1988).

    ADS  Google Scholar 

  92. [92]

    Damour, T., and Taylor, J.H., “Strong-field tests of relativistic gravity and binary pulsars”, Phys. Rev. D, 45, 1840–1868, (1992).

    ADS  Google Scholar 

  93. [93]

    Dana, P.H., “The Global Positioning System”, project homepage, Department of Geography, University of Colorado at Boulder. URL (cited on 19 March 2001):

  94. [94]

    Davis, M.M., Taylor, J.H., Weisberg, J.M., and Backer, D.C., “High-precision timing observations of the millisecond pulsar PSR 1937+21”, Nature, 315, 547–550, (1985).

    ADS  Google Scholar 

  95. [95]

    Detweiler, S.L., “Pulsar timing measurements and the search for gravitational waves”, Astrophys. J., 234, 1100–1104, (1979).

    ADS  Google Scholar 

  96. [96]

    Dewey, R.J., and Cordes, J.M., “Monte Carlo simulations of radio pulsars and their progenitors”, Astrophys. J., 321, 780–798, (1987).

    ADS  Google Scholar 

  97. [97]

    Dewey, R.J., Maguire, C.M., Rawley, L.A., Stokes, G.H., and Taylor, J.H., “Binary pulsar with a very small mass function”, Nature, 322, 712–714, (1986).

    ADS  Google Scholar 

  98. [98]

    Dewey, R.J., Stokes, G.H., Segelstein, D.J., Taylor, J.H., and Weisberg, J.M., “The Period Distribution of Pulsars”, in Reynolds, S.P., and Stinebring, D.R., eds., Birth and Evolution of Neutron Stars: Issues Raised by Millisecond Pulsars, Proceedings of a workshop, held at the National Radio Astronomy Observatory, Green Bank, West Virginia, June 6–8, 1984, NRAO Workshop, vol. 8, pp. 234–240, (National Radio Astronomy Observatory, Green Bank, U.S.A., 1984).

    Google Scholar 

  99. [99]

    Downs, G.S., and Reichley, P.E., “JPL pulsar timing observations. II. Geocentric arrival times”, Astrophys. J. Suppl. Ser., 53, 169–240, (1983).

    ADS  Google Scholar 

  100. [100]

    Edwards, R., and Bailes, M., “Discovery of two relativistic neutron star-white dwarf binaries”, Astrophys. J. Lett., 547, L37–L40, (2001).

    ADS  Google Scholar 

  101. [101]

    Edwards, R., and Bailes, M., “Recycled Pulsars Discovered at High Radio Frequency”, Astrophys. J., 553, 801–808, (2001).

    ADS  Google Scholar 

  102. [102]

    Edwards, R.T., “Discovery of Eight Recycled Pulsars — The Swinburne Intermediate Latitude Pulsar Survey”, in Kramer, M., Wex, N., and Wielebinski, R., eds., Pulsar Astronomy: 2000 and Beyond (IAU Colloquium 177), Proceedings of the 177th Colloquium of the IAU, held at the Max-Planck-Institut für Radioastronomie, Bonn, Germany, 30 August–3 September 1999, ASP Conference Series, vol. 202, pp. 33–34, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2000).

    Google Scholar 

  103. [103]

    ESA, “XMM-Newton homepage”, project homepage. URL (cited on 24 June 2008):

  104. [104]

    Falcke, H.D., van Haarlem, M.P., de Bruyn, A.G., Braun, R., Röttgering, H.J.A., Stappers, B.W., Boland, W.H.W.M., Butcher, H.R., de Geus, E.J., Koopmans, L.V., Fender, R.P., Kuijpers, H.J.M.E., Miley, G.K., Schilizzi, R.T., Vogt, C., Wijers, R.A.M.J., Wise, M.W., Brouw, W.N., Hamaker, J.P., Noordam, J.E., Oosterloo, T., Bähren, L., Brentjens, M.A., Wijnholds, S.J., Bregman, J.D., van Cappellen, W.A., Gunst, A.W., Kant, G.W., Reitsma, J., van der Schaaf, K., and de Vos, C.M., “A very brief description of LOFAR — the Low Frequency Array”, Proc. IAU, 2, 386–387, (2006). Related online version (cited on 12 July 2008):

    Google Scholar 

  105. [105]

    FAST, “Five hundred meter Aperture Spherical Telescope”, project homepage. URL (cited on 24 June 2008):

  106. [106]

    Faucher-Giguère, C.-A., and Kaspi, V.M., “Birth and Evolution of Isolated Radio Pulsars”, Astrophys. J., 643, 332–355, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  107. [107]

    Faulkner, A.J., Kramer, M., Lyne, A.G., Manchester, R.N., McLaughlin, M.A., Stairs, I.H., Hobbs, G., Possenti, A., Lorimer, D.R., D’Amico, N., Camilo, F., and Burgay, M., “PSR J1756−2251: A New Relativistic Double Neutron Star System”, Astrophys. J. Lett., 618, L119–L122, (2005).

    ADS  Google Scholar 

  108. [108]

    Faulkner, A.J., Stairs, I.H., Kramer, M., Lyne, A.G., Hobbs, G., Possenti, A., Lorimer, D.R., Manchester, R.N., McLaughlin, M.A., D’Amico, N., Camilo, F., and Burgay, M., “The Parkes Multibeam Pulsar Survey — V. Finding binary and millisecond pulsars”, Mon. Not. R. Astron. Soc., 355, 147–158, (2004).

    ADS  Google Scholar 

  109. [109]

    Ferrario, L., and Wickramasinghe, D., “The birth properties of Galactic millisecond radio pulsars”, Mon. Not. R. Astron. Soc., 375, 1009–1016, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  110. [110]

    Flannery, B.P., and van den Heuvel, E.P.J., “On the origin of the binary pulsar PSR 1913+16”, Astron. Astrophys., 39, 61–67, (1975).

    ADS  Google Scholar 

  111. [111]

    Fomalont, E.B., Goss, W.M., Lyne, A.G., Manchester, R.N., and Justtanont, K., “Positions and Proper Motions of Pulsars”, Mon. Not. R. Astron. Soc., 258, 497–510, (1992).

    ADS  Google Scholar 

  112. [112]

    Foster, R.S., and Backer, D.C., “Constructing a Pulsar Timing Array”, Astrophys. J., 361, 300–308, (1990).

    ADS  Google Scholar 

  113. [113]

    Foster, R.S., Wolszczan, A., and Camilo, F., “A new binary millisecond pulsar”, Astrophys. J. Lett., 410, L91–L94, (1993). ADS:

    ADS  Google Scholar 

  114. [114]

    Freire, P.C.C., Gupta, Y., Ransom, S.M., and Ishwara-Chandra, C.H., “Giant Metrewave Radio Telescope discovery of a millisecond pulsar in a very eccentric binary system”, Astrophys. J. Lett., 606, L53–L56, (2004).

    ADS  Google Scholar 

  115. [115]

    Freire, P.C.C., Kramer, M., and Lyne, A.G., “Determination of the orbital parameters of binary pulsars”, Mon. Not. R. Astron. Soc., 322, 885, (2001). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  116. [116]

    Freire, P.C.C., Kramer, M., Lyne, A.G., Camilo, F., Manchester, R.N., and D’Amico, N., “Detection of ionized gas in the globular cluster 47 Tucanae”, Astrophys. J. Lett., 557, L105–L108, (2001). ADS:

    ADS  Google Scholar 

  117. [117]

    Freire, P.C.C., Ransom, S.M., and Gupta, Y., “Timing the Eccentric Binary Millisecond Pulsar in NGC 1851”, Astrophys. J., 662, 1177–1182, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  118. [118]

    Freire, P.C.C., Wolszczan, A., van den Berg, M., and Hessels, J.W.T., “A Massive Neutron Star in the Globular Cluster M5”, Astrophys. J., 679, 1433–1442, (2008). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  119. [119]

    Fruchter, A.S., Stinebring, D.R., and Taylor, J.H., “A millisecond pulsar in an eclipsing binary”, Nature, 333, 237–239, (1988).

    ADS  Google Scholar 

  120. [120]

    Gaensler, B.M., Madsen, G.J., Chatterjee, S., and Mao, S.A., “The Vertical Structure of Warm Ionised Gas in the Milky Way”, Publ. Astron. Soc. Australia, submitted, (2008). Related online version (cited on 27 October 2008):

  121. [121]

    Gil, J., and Melikidze, G.I., “On the Giant Nano-subpulses in the Crab Pulsar”, in Camilo, F., and Gaensler, B.M., eds., Young neutron stars and their environments, Proceedings of an IAU Symposium on 14–17 July 2003 in Sydney, Australia, ASP Conference Series, vol. 218, p. 321, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2004).

    Google Scholar 

  122. [122]

    Gold, T., “Rotating neutron stars as the origin of the pulsating radio sources”, Nature, 218, 731–732, (1968).

    ADS  Google Scholar 

  123. [123]

    Gold, T., “Rotating neutron stars and the nature of pulsars”, Nature, 221, 25–27, (1969).

    ADS  Google Scholar 

  124. [124]

    Gould, D.M., and Lyne, A.G., “Multifrequency polarimetry of 300 radio pulsars”, Mon. Not. R. Astron. Soc., 301, 235–260, (1998).

    ADS  Google Scholar 

  125. [125]

    Graham-Smith, F., and McLaughlin, M.A., “A magnetopause in the double-pulsar binary system”, Astron. Geophys., 46(1), 1.23–1.25, (2005).

    ADS  Google Scholar 

  126. [126]

    Grindlay, J.E., Camilo, F., Heinke, C.O., Edmonds, P.D., Cohn, H., and Lugger, P., “Chandra Study of a Complete Sample of Millisecond Pulsars in 47 Tucanae and NGC 6397”, Astrophys. J., 581, 470–484, (2002). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  127. [127]

    Gunn, J.E., and Ostriker, J.P., “On the Nature of Pulsars. III. Analysis of Observations”, Astrophys. J., 160, 979–1002, (1970).

    ADS  Google Scholar 

  128. [128]

    Han, J.L., and Manchester, R.N., “The shape of radio pulsar beams”, Mon. Not. R. Astron. Soc., 320, L35–L40, (2001). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  129. [129]

    Hankins, T.H., “Microsecond Intensity Variation in the Radio Emission from CP 0950”, Astrophys. J., 169, 487–494, (1971).

    ADS  Google Scholar 

  130. [130]

    Hankins, T.H., Kern, J.S., Weatherall, J.C., and Eilek, J.A., “Nanosecond radio bursts from strong plasma turbulence in the Crab pulsar”, Nature, 422, 141–143, (2003).

    ADS  Google Scholar 

  131. [131]

    Hansen, B., and Phinney, E.S., “The pulsar kick velocity distribution”, Mon. Not. R. Astron. Soc., 291, 569–577, (1997).

    ADS  Google Scholar 

  132. [132]

    Hansen, B., and Phinney, E.S., “Stellar forensics — II. Millisecond pulsar binaries”, Mon. Not. R. Astron. Soc., 294, 569–581, (1998).

    ADS  Google Scholar 

  133. [133]

    Harrison, P.A., Lyne, A.G., and Anderson, B., “New Determinations of the Proper Motions of 44 Pulsars”, Mon. Not. R. Astron. Soc., 261, 113–124, (1993).

    ADS  Google Scholar 

  134. [134]

    Harvard-Smithsonian Center for Astrophysics, “The NASA Astrophysics Data System”, web interface to database. URL (cited on 19 March 2001):

  135. [135]

    Heinke, C.O., Grindlay, J.E., Edmonds, P.D., Cohn, H.N., Lugger, P.M., Camilo, F., Bogdanov, S., and Freire, P.C.C., “A Deep Chandra Survey of the Globular Cluster 47 Tucanae: Catalog of Point Sources”, Astrophys. J., 625, 796–824, (2005). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  136. [136]

    Hellings, R.W., “Thoughts on Detecting a Gravitational Wave Background with Pulsar Data”, in Backer, D.C., ed., Impact of Pulsar Timing on Relativity and Cosmology, Proceedings of the workshop, held at Berkeley, June 7–9, 1990, p. k1, (Center for Particle Astrophysics, Berkeley, U.S.A., 1990).

    Google Scholar 

  137. [137]

    Hellings, R.W., and Downs, G.S., “Upper limits on the isotropic gravitational radiation background from pulsar timing analysis”, Astrophys. J. Lett., 265, L39–L42, (1983).

    ADS  Google Scholar 

  138. [138]

    Hessels, J.W.T., Ransom, S.M., Kaspi, V.M., Roberts, M.S.E., Champion, D.J., and Stappers, B.W., “The GBT350 Survey of the Northern Galactic Plane for Radio Pulsars and Transients”, in Bassa, C.G., Wang, Z., Cumming, A., and Kaspi, V.M., eds., 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More, McGill University, Montréal, Canada, 12–17 August 2007, AIP Conference Proceedings, vol. 983, pp. 613–615, (American Institute of Physics, Melville, U.S.A., 2008).

    Google Scholar 

  139. [139]

    Hessels, J.W.T., Ransom, S.M., Roberts, M., Kaspi, V.M., Livingstone, M., Tam, C., and Crawford, F., “Three New Binary Pulsars Discovered With Parkes”, in Rasio, F.A., and Stairs, I.H., eds., Binary Radio Pulsars, Proceedings of the conference held 11–17 January 2004, Aspen, Colorado, USA, ASP Conference Series, vol. 328, p. 395, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2005). ADS:

    Google Scholar 

  140. [140]

    Hessels, J.W.T., Ransom, S.M., Stairs, I.H., Freire, P.C.C., Kaspi, V.M., and Camilo, F., “A Radio Pulsar Spinning at 716 Hz”, Science, 311, 1901–1904, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  141. [141]

    Hewish, A., Bell, S.J., Pilkington, J.D.H., Scott, P.F., and Collins, R.A., “Observation of a rapidly pulsating radio source”, Nature, 217, 709–713, (1968).

    ADS  Google Scholar 

  142. [142]

    Hills, J.G., “The effects of Sudden Mass loss and a random kick velocity produced in a supernova explosion on the Dynamics of a binary star of an Arbitrary orbital Eccentricity”, Astrophys. J., 267, 322–333, (1983).

    ADS  Google Scholar 

  143. [143]

    Hobbs, G., “Pulsars and Gravitational Wave Detection”, (2005). URL (cited on 22 January 2005):

  144. [144]

    Hobbs, G., Lorimer, D.R., Lyne, A.G., and Kramer, M., “A statistical study of 233 pulsar proper motions”, Mon. Not. R. Astron. Soc., 360, 974–992, (2005).

    ADS  Google Scholar 

  145. [145]

    Hobbs, G.B., Faulkner, A., Stairs, I.H., Camilo, F., Manchester, R.N., Lyne, A.G., Kramer, M., D’Amico, N., Kaspi, V.M., Possenti, A., McLaughlin, M.A., Lorimer, D.R., Burgay, M., Joshi, B.C., and Crawford, F., “The Parkes multibeam pulsar survey: IV. Discovery of 176 pulsars and parameters for 248 previously known pulsars”, Mon. Not. R. Astron. Soc., 352, 1439–1472, (2004).

    ADS  Google Scholar 

  146. [146]

    Hobbs, G.B., Lyne, A.G., Kramer, M., Martin, C.E., and Jordan, C., “Long-Term Timing Observations of 374 Pulsars”, Mon. Not. R. Astron. Soc., 353, 1311–1344, (2004).

    ADS  Google Scholar 

  147. [147]

    Hogan, C.J., and Rees, M.J., “Gravitational interactions of cosmic strings”, Nature, 311, 109–114, (1984).

    ADS  Google Scholar 

  148. [148]

    Hotan, A.W., Bailes, M., and Ord, S.M., “Geodetic Precession in PSR J1141−6545”, Astrophys. J., 624, 906–913, (2005).

    ADS  Google Scholar 

  149. [149]

    Hulse, R.A., “The discovery of the binary pulsar”, Rev. Mod. Phys., 66, 699–710, (1994).

    ADS  Google Scholar 

  150. [150]

    Hulse, R.A., and Taylor, J.H., “Discovery of a pulsar in a binary system”, Astrophys. J. Lett., 195, L51–L53, (1975).

    ADS  Google Scholar 

  151. [151]

    Hunt, G.C., “The rate of change of period of the pulsars”, Mon. Not. R. Astron. Soc., 153, 119–131, (1971).

    ADS  Google Scholar 

  152. [152]

    IASF, “AGILE: Astro-rivelatore Gamma a Immagini LEggero”, project homepage. URL (cited on 24 June 2008):

  153. [153]

    INFN, “The Virgo Project”, project homepage. URL (cited on 29 January 2005):

  154. [154]

    International SKA Project Office, “The Square Kilometre Array”, project homepage. URL (cited on 23 January 2005):

  155. [155]

    Jacoby, B.A., Recycled Pulsars, Ph.D. Thesis, (Calfornia Institute of Technology, Pasadena, U.S.A., 2004). Related online version (cited on 27 October 2008):

    Google Scholar 

  156. [156]

    Jacoby, B.A., Bailes, M., Ord, S.M., Knight, H.S., and Hotan, A.W., “Discovery of Five Recycled Pulsars in a High Galactic Latitude Survey”, Astrophys. J., 656, 408–413, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  157. [157]

    Jacoby, B.A., Bailes, M., van Kerkwijk, M.H., Ord, S., Hotan, A., Kulkarni, S.R., and Anderson, S.B., “PSR J1909-3744: A Binary Millisecond Pulsar with a Very Small Duty Cycle”, Astrophys. J. Lett., 599, L99–L102, (2003). ADS:

    ADS  Google Scholar 

  158. [158]

    Jacoby, B.A., Cameron, P.B., Jenet, F.A., Anderson, S.B., Murty, R.N., and Kulkarni, S.R., “Measurement of Orbital Decay in the Double Neutron Star Binary PSR B2127+11C”, Astrophys. J. Lett., 644, L113–L116, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  159. [159]

    Jaffe, A.H., and Backer, D.C., “Gravitational Waves Probe the Coalescence Rate of Massive Black Hole Binaries”, Astrophys. J., 583, 616–631, (2003).

    ADS  Google Scholar 

  160. [160]

    Jenet, F.A., Hobbs, G.B., van Straten, W., Manchester, R.N., Bailes, M., Verbiest, J.P.W., Edwards, R.T., Hotan, A.W., Sarkissian, J.M., and Ord, S.M., “Upper Bounds on the Low-Frequency Stochastic Gravitational Wave Background from Pulsar Timing Observations: Current Limits and Future Prospects”, Astrophys. J., 653, 1571–1576, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  161. [161]

    Jenet, F.A., Lommen, A.N., Larson, S.L., and Wen, L., “Constraining the properties fo supermassive black hole systems using pulsar timing: Application to 3C 66B”, Astrophys. J., 606, 799–803, (2004).

    ADS  Google Scholar 

  162. [162]

    Johnston, H.M., and Kulkarni, S.R., “On the detectability of pulsars in close binary systems”, Astrophys. J., 368, 504–514, (1991).

    ADS  Google Scholar 

  163. [163]

    Johnston, S., “Evidence for a deficit of pulsars in the inner Galaxy”, Mon. Not. R. Astron. Soc., 268, 595–601, (1994).

    ADS  Google Scholar 

  164. [164]

    Johnston, S., Bailes, M., Bartel, N., Baugh, C., Bietenholz, M., Blake, C., Braun, R., Brown, J., Chatterjee, S., Darling, J., Deller, A., Dodson, R., Edwards, P.G., Ekers, R., Ellingsen, S., Feain, I., Gaensler, B.M., Haverkorn, M., Hobbs, G., Hopkins, A., Jackson, C., James, C., Joncas, G., Kaspi, V.M., Kilborn, V., Koribalski, B., Kothes, R., Landecker, T.L., Lenc, E., Lovell, J., Macquart, J.-P., Manchester, R.N., Matthews, D., McClure-Griffiths, N.M., Norris, R., Pen, U.-L., Phillips, C., Power, C., Protheroe, R., Sadler, E., Schmidt, B., Stairs, I.H., Staveley-Smith, L., Stil, J., Taylor, R., Tingay, S., Tzioumis, A., Walker, M., Wall, J., and Wolleben, M., “Science with the Australian Square Kilometre Array Pathfinder”, Publ. Astron. Soc. Australia, 24, 174–188, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  165. [165]

    Johnston, S., Hobbs, G., Vigeland, S., Kramer, M., Weisberg, J.M., and Lyne, A.G., “Evidence for alignment of the rotation and velocity vectors in pulsars”, Mon. Not. R. Astron. Soc., 364, 1397–1412, (2005). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  166. [166]

    Johnston, S., Kramer, M., Karastergiou, A., Hobbs, G., Ord, S., and Wallman, J., “Evidence for alignment of the rotation and velocity vectors in pulsars — II. Further data and emission heights”, Mon. Not. R. Astron. Soc., 381, 1625–1637, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  167. [167]

    Johnston, S., Lorimer, D.R., Harrison, P.A., Bailes, M., Lyne, A.G., Bell, J.F., Kaspi, V.M., Manchester, R.N., D’Amico, N., Nicastro, L., and Shengzhen, J., “Discovery of a very bright, nearby binary millisecond pulsar”, Nature, 361, 613–615, (1993).

    ADS  Google Scholar 

  168. [168]

    Johnston, S., Lyne, A.G., Manchester, R.N., Kniffen, D.A., D’Amico, N., Lim, J., and Ashworth, M., “A High Frequency Survey of the Southern Galactic Plane for Pulsars”, Mon. Not. R. Astron. Soc., 255, 401–411, (1992).

    ADS  Google Scholar 

  169. [169]

    Johnston, S., Manchester, R.N., Lyne, A.G., Bailes, M., Kaspi, V.M., Qiao, G., and D’Amico, N., “PSR 1259−63: A binary radio pulsar with a Be star companion”, Astrophys. J. Lett., 387, L37–L41, (1992).

    ADS  Google Scholar 

  170. [170]

    Jones, A.W., and Lyne, A.G., “Timing Observations of the Binary Pulsar PSR 0655+64”, Mon. Not. R. Astron. Soc., 232, 473, (1988).

    ADS  Google Scholar 

  171. [171]

    Joshi, B.C., McLaughlin, M.A., Kramer, M., Lyne, A.G., Lorimer, D.R., Ludovici, D.A., Davies, M., and Faulkner, A.J., “A 610-MHz Galactic Plane Pulsar Search with the Giant Meterwave Radio Telescope”, in Bassa, C.G., Wang, Z., Cumming, A., and Kaspi, V.M., eds., 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More, McGill University, Montréal, Canada, 12–17 August 2007, AIP Conference Proceedings, vol. 983, pp. 616–617, (American Institute of Physics, Melville, U.S.A., 2008).

    Google Scholar 

  172. [172]

    Jouteux, S., Ramachandran, R., Stappers, B.W., Jonker, P.G., and van der Klis, M., “Searching for pulsars in close circular binary systems”, Astron. Astrophys., 384, 532–544, (2002).

    ADS  Google Scholar 

  173. [173]

    Kaaret, P., Morgan, E., and Vanderspek, R., “Orbital parameters of HETE J1900.1-2455”, Astron. Telegram, 2005(538), (2005). URL (cited on 19 July 2005):

  174. [174]

    Kalogera, V., “Close Binaries with Two Compact Objects”, in Kramer, M., Wex, N., and Wielebinski, R., eds., Pulsar Astronomy: 2000 and Beyond (IAU Colloquium 177), Proceedings of the 177th Colloquium of the IAU, held at the Max-Planck-Institut für Radioastronomie, Bonn, Germany, 30 August–3 September 1999, ASP Conference Series, pp. 579–584, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2000).

    Google Scholar 

  175. [175]

    Kalogera, V., “The Strongly Relativistic Double Pulsar and LISA”, lecture notes, Northwestern University, (2004). URL (cited on 19 July 2005): Invited talk at the 5th International LISA Symposium, ESTEC, Noordwijk, The Netherlands, July 12–15, 2004.

    Google Scholar 

  176. [176]

    Kalogera, V., Kim, C., Lorimer, D.R., Burgay, M., D’Amico, N., Possenti, A., Manchester, R.N., Lyne, A.G., Joshi, B.C., McLaughlin, M.A., Kramer, M., Sarkissian, J.M., and Camilo, F., “Erratum: The Cosmic Coalescence Rates for Double Neutron Star Binaries”, Astrophys. J. Lett., 614, L137–L138, (2004).

    ADS  Google Scholar 

  177. [177]

    Kalogera, V., Kim, C., Lorimer, D.R., Ihm, M., and Belczynski, K., “The Galactic Formation Rate of Eccentric Neutron Star — White Dwarf Binaries”, in Rasio, F.A., and Stairs, I.H., eds., Binary Radio Pulsars, Proceedings of a meeting held at the Aspen Center for Physics, USA, 12–16 January 2004, ASP Conference Series, vol. 328, pp. 261–267, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2005).

    Google Scholar 

  178. [178]

    Kalogera, V., Narayan, R., Spergel, D.N., and Taylor, J.H., “The Coalescence Rate of Double Neutron Star Systems”, Astrophys. J., 556, 340–356, (2001). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  179. [179]

    Karastergiou, A., and Johnston, S., “An empirical model for the beams of radio pulsars”, Mon. Not. R. Astron. Soc., 380, 1678–1684, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  180. [180]

    Kasian, L., “Timing and Precession of the Young, Relativistic Binary Pulsar PSR J1906+0746”, in Bassa, C., Wang, Z., Cumming, A., and Kaspi, V.M., eds., 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More, McGill University, Montréal, Canada, 12–17 August 2007, AIP Conference Proceeedings, vol. 983, pp. 485–487, (American Institute of Physics, Melville, U.S.A., 2008).

    Google Scholar 

  181. [181]

    Kaspi, V.M., Applications of Pulsar Timing, Ph.D. Thesis, (Princeton University, Princeton, U.S.A., 1994).

    Google Scholar 

  182. [182]

    Kaspi, V.M., Johnston, S., Bell, J.F., Manchester, R.N., Bailes, M., Bessell, M., Lyne, A.G., and D’Amico, N., “A massive radio pulsar binary in the Small Magellanic Cloud”, Astrophys. J. Lett., 423, L43–L45, (1994).

    ADS  Google Scholar 

  183. [183]

    Kaspi, V.M., Lyne, A.G., Manchester, R.N., Crawford, F., Camilo, F., Bell, J.F., D’Amico, N., Stairs, I.H., McKay, N.P.F., Morris, D.J., and Possenti, A., “Discovery of a young radio pulsar in a relativistic binary orbit”, Astrophys. J., 534, 321–327, (2000).

    ADS  Google Scholar 

  184. [184]

    Kaspi, V.M., Ransom, S.M., Backer, D.C., Ramachandran, R., Demorest, P., Arons, J., and Spitkovsky, A., “Green Bank Telescope Observations of the Eclipse of Pulsar “A” in the Double Pulsar Binary PSR J0737-3039”, Astrophys. J. Lett., 613, L137–L140, (2004). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  185. [185]

    Kaspi, V.M., Taylor, J.H., and Ryba, M.F., “High-precision timing of millisecond pulsars. III. Long-term monitoring of PSRs B1855+09 and B1937+21”, Astrophys. J., 428, 713–728, (1994).

    ADS  Google Scholar 

  186. [186]

    KAT, “The Karoo Array Telescope”, project homepage. URL (cited on 24 June 2008):

  187. [187]

    Keith, M., Towards a pulsar virtual observatory, Ph.D. Thesis, (University of Manchester, Manchester, U.K., 2008).

    Google Scholar 

  188. [188]

    Kiel, P.D., and Hurley, J.R., “Populating the Galaxy with low-mass X-ray binaries”, Mon. Not. R. Astron. Soc., 369, 1152–1166, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  189. [189]

    Kim, C., “Galactic Pulsar Population: Current Understanding and Future Prospects”, in Bassa, C.G., Wang, Z., Cumming, A., and Kaspi, V.M., eds., 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More, McGill University, Montréal, Canada, 12–17 August 2007, AIP Conference Proceedings, vol. 983, pp. 576–583, (American Institute of Physics, Melville, U.S.A., 2008).

    Google Scholar 

  190. [190]

    Kim, C., Kalogera, V., and Lorimer, D.R., “The Probability Distribution of Binary Pulsar Coalescence Rates. I. Double Neutron Star Systems in the Galactic Field”, Astrophys. J., 584, 985–995, (2003).

    ADS  Google Scholar 

  191. [191]

    Kim, C., Kalogera, V., Lorimer, D.R., and White, T., “The Probability Distribution Of Binary Pulsar Coalescence Rates. II. Neutron Star-White Dwarf Binaries”, Astrophys. J., 616, 1109–1117, (2004).

    ADS  Google Scholar 

  192. [192]

    Kluzniak, W., Ruderman, M., Shaham, J., and Tavani, M., “Nature and evolution of the eclipsing millisecond binary pulsar PSR 1957+20”, Nature, 334, 225–227, (1988).

    ADS  Google Scholar 

  193. [193]

    Knight, H.S., Bailes, M., Manchester, R.N., and Ord, S.M., “A Study of Giant Pulses from PSR J1824-2452A”, Astrophys. J., 653, 580–586, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  194. [194]

    Kolonko, M., Gil, J., and Maciesiak, K., “On the pulse-width statistics in radio pulsars”, Astron. Astrophys., 428, 943–951, (2005).

    ADS  Google Scholar 

  195. [195]

    Kondratiev, V.I., Lorimer, D.R., McLaughlin, M.A., and Ransom, S.M., “A pulsar census of the local group”, Astrophys. J., in preparation.

  196. [196]

    Kopeikin, S.M., “Binary pulsars as detectors of ultralow-frequency gravitational waves”, Phys. Rev. D, 56, 4455–4469, (1997).

    ADS  Google Scholar 

  197. [197]

    Kozai, Y., “Secular perturbations of asteroids with high inclination and eccentricity”, Astron. J., 67, 591–598, (1962). ADS:

    ADS  MathSciNet  Google Scholar 

  198. [198]

    Kramer, M., Backer, D.C., Cordes, J.M., Lazio, T.J.W., Stappers, B.W., and Johnston, S., “Strong-field tests of gravity using pulsars and black holes”, New Astron. Rev., 48, 993–1002, (2004).

    ADS  Google Scholar 

  199. [199]

    Kramer, M., Bell, J.F., Manchester, R.N., Lyne, A.G., Camilo, F., Stairs, I.H., D’Amico, N., Kaspi, V.M., Hobbs, G., Morris, D.J., Crawford, F., Possenti, A., Joshi, B.C., McLaughlin, M.A., Lorimer, D.R., and Faulkner, A.J., “The Parkes Multibeam Pulsar Survey — III. Young pulsars and the discovery and timing of 200 pulsars”, Mon. Not. R. Astron. Soc., 342, 1299–1324, (2003).

    ADS  Google Scholar 

  200. [200]

    Kramer, M., and Stairs, I.H., “The Double Pulsar”, Annu. Rev. Astron. Astrophys., 46, 541–572, (2008). ADS:

    ADS  Google Scholar 

  201. [201]

    Kramer, M., Stairs, I.H., Manchester, R.N., McLaughlin, M.A., Lyne, A.G., Ferdman, R.D., Burgay, M., Lorimer, D.R., Possenti, A., D’Amico, N., Sarkissian, J.M., Hobbs, G.B., Reynolds, J.E., Freire, P.C.C., and Camilo, F., “Tests of General Relativity from Timing the Double Pulsar”, Science, 314, 97–102, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  202. [202]

    Kramer, M., Xilouris, K.M., Camilo, F., Nice, D.J., Backer, D.C., Lorimer, D.R., Doroshenko, O.V., Lange, C., and Sallmen, S., “Profile Instabilities of the Millisecond Pulsar J1022+1001”, Astrophys. J., 520, 324–334, (1999).

    ADS  Google Scholar 

  203. [203]

    Kramer, M., Xilouris, K.M., Lorimer, D.R., Doroshenko, O.V., Jessner, A., Wielebinski, R., Wolszczan, A., and Camilo, F., “The characteristics of millisecond pulsar emission: I. Spectra, pulse shapes and the beaming fraction”, Astrophys. J., 501, 270–285, (1998).

    ADS  Google Scholar 

  204. [204]

    Krimm, H.A., Markwardt, C.B., Deloye, C.J., Romano, P., Chakrabarty, D., Campana, S., Cummings, J.R., Galloway, D.K., Gehrels, N., Hartman, J.M., Kaaret, P., Morgan, E.H., and Tueller, J., “Discovery of the Accretion-powered Millisecond Pulsar SWIFT J1756.9-2508 with a Low-Mass Companion”, Astrophys. J. Lett., 668, L147–L150, (2007). Related online version (cited on 12 July 2008): 2.6.2

    ADS  Google Scholar 

  205. [205]

    Lange, C., Camilo, F., Wex, N., Kramer, M., Backer, D.C., Lyne, A.G., and Doroshenko, O.V., “Precision timing measurements of PSR J1012+5307”, Mon. Not. R. Astron. Soc. 326, 274–282, (2001). 4

    ADS  Google Scholar 

  206. [206]

    Lattimer, J.M., and Prakash, M., “Neutron star observations: Prognosis for equation of state constraints”, Phys. Rep., 442, 109–165, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  207. [207]

    Lawson, K.D., Mayer, C.J., Osborne, J.L., and Parkinson, M.L., “Variations in the Spectral Index of the Galactic Radio Continuum Emission in the Northern Hemisphere”, Mon. Not. R. Astron. Soc., 225, 307–327, (1987). 3.1.2

    ADS  Google Scholar 

  208. [208]

    Levinson, A., and Eichler, D., “Can neutron stars ablate their companions?”, Astrophys. J., 379, 359–365, (1991). ADS:

    ADS  Google Scholar 

  209. [209]

    Lewandowski, W., Wolszczan, A., Feiler, G., Konacki, M., and Soltysinski, T., “Arecibo timing and single-pulse observations of eighteen pulsars”, Astrophys. J., 600, 905–913, (2004). ADS:

    ADS  Google Scholar 

  210. [210]

    Li, X., “Formation of Mildly Recycled Low-Mass Binary Pulsars from Intermediate-Mass X-Ray Binaries”, Astrophys. J., 564, 930–934, (2002).

    ADS  Google Scholar 

  211. [211]

    Lipunov, V.M., Postnov, K.A., and Prokhorov, M.E., “The Scenario Machine: Binary Star Population Synthesis”, Astrophys. Space Phys. Rev., 9, 1–178, (1996). Related online version (cited on 12 July 2008):∼mystery/articles/review/.

    Google Scholar 

  212. [212]

    LOFAR, “The Low Frequency Array”, project homepage. URL (cited on 24 June 2008):

  213. [213]

    Löhmer, O., Kramer, M., Driebe, T., Jessner, A., Mitra, D., and Lyne, A.G., “The parallax, mass and age of the PSR J2145-0750 binary system”, Astron. Astrophys., 426, 631–640, (2004).

    ADS  Google Scholar 

  214. [214]

    Lommen, A.N., and Backer, D.C., “Using Pulsars to Detect Massive Black Hole Binaries via Gravitational Radiation: Sagittarius A* and Nearby Galaxies”, Astrophys. J., 562, 297–302, (2001).

    ADS  Google Scholar 

  215. [215]

    Lommen, A.N., Kipphorn, R.A., Nice, D.J., Splaver, E.M., Stairs, I.H., and Backer, D.C., “The Parallax and Proper Motion of PSR J0030+0451”, Astrophys. J., 642, 1012–1017, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  216. [216]

    Lommen, A.N., Zepka, A.F., Backer, D.C., McLaughlin, M.A., Cordes, J.M., Arzoumanian, Z., and Xilouris, K.M., “New Pulsars from an Arecibo Drift Scan Search”, Astrophys. J., 545, 1007–1014, (2001).

    ADS  Google Scholar 

  217. [217]

    Lorimer, D.R., “Pulsar statistics — II. The local low-mass binary pulsar population”, Mon. Not. R. Astron. Soc., 274, 300–304, (1995).

    ADS  Google Scholar 

  218. [218]

    Lorimer, D.R., “Binary and Millisecond Pulsars”, Living Rev. Relativity, 1, lrr-1998-10, (1998). URL (cited on 19 March 2001):

  219. [219]

    Lorimer, D.R., “Binary and Millisecond Pulsars”, Living Rev. Relativity, 4, lrr-2001-5, (2001). URL (cited on 22 January 2005):

  220. [220]

    Lorimer, D.R., “The Galactic Population and Birth Rate of Radio Pulsars”, in Camilo, F., and Gaensler, B.M., eds., Young Neutron Stars and their Environments, Proceedings of the 218th symposium of the International Astronomical Union held during the IAU General Assembly XXV, Sydney, Australia, 14–17 July 2003, ASP Conference Series, vol. 218, p. 105, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2004).

    Google Scholar 

  221. [221]

    Lorimer, D.R., “Binary and Millisecond Pulsars”, Living Rev. Relativity, 8, lrr-2005-7, (2005). URL (cited on 23 May 2008):

  222. [222]

    Lorimer, D.R., Bailes, M., Dewey, R.J., and Harrison, P.A., “Pulsar statistics: the birthrate and initial spin periods of radio pulsars”, Mon. Not. R. Astron. Soc., 263, 403–415, (1993).

    ADS  Google Scholar 

  223. [223]

    Lorimer, D.R., Camilo, F., Freire, P.C.C., Kramer, M., Lyne, A.G., Manchester, R.N., and D’Amico, N., “Millisecond radio pulsars in 47 Tucanae”, in Bailes, M., Nice, D.J., and Thorsett, S.E., eds., Radio Pulsars, Proceedings of a meeting held at Mediterranean Agonomic Institute of Chania, Crete, Greece, 26–29 August 2002, ASP Conference Series, vol. 302, pp. 363–366, (Astronomical Society of the Pacific, San Fransisco, U.S.A., 2003).

    Google Scholar 

  224. [224]

    Lorimer, D.R., Faulkner, A.J., Lyne, A.G., Manchester, R.N., Kramer, M., McLaughlin, M.A., Hobbs, G., Possenti, A., Stairs, I.H., Camilo, F., Burgay, M., D’Amico, N., Corongiu, A., and Crawford, F., “The Parkes Multibeam Pulsar Survey — VI. Discovery and timing of 142 pulsars and a Galactic population analysis”, Mon. Not. R. Astron. Soc., 372, 777–800, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  225. [225]

    Lorimer, D.R., and Freire, P.C.C., “Long-period binaries and the strong equivalence principle”, in Rasio, F.A., and Stairs, I.H., eds., Binary Radio Pulsars, Proceedings of a meeting held at the Aspen Center for Physics, USA, 12–16 January 2004, ASP Conference Series, vol. 328, pp. 19–24, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2005).

    Google Scholar 

  226. [226]

    Lorimer, D.R., and Kramer, M., Handbook of Pulsar Astronomy, Cambridge Observing Handbooks for Research Astronomers, vol. 4, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 2005), 1st edition.

    Google Scholar 

  227. [227]

    Lorimer, D.R., and Kramer, M., Handbook of Pulsar Astronomy, Cambridge Observing Handbooks for Research Astronomers, vol. 4, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 2005). Related online version (cited on 12 July 2008):

    Google Scholar 

  228. [228]

    Lorimer, D.R., Lyne, A.G., Bailes, M., Manchester, R.N., D’Amico, N., Stappers, B.W., Johnston, S., and Camilo, F., “Discovery of four binary millisecond pulsars”, Mon. Not. R. Astron. Soc., 283, 1383–1387, (1996).

    ADS  Google Scholar 

  229. [229]

    Lorimer, D.R., McLaughlin, M.A., Arzoumanian, Z., Xilouris, K.M., Cordes, J.M., Lommen, A.N., Fruchter, A.S., Chandler, A.M., and Backer, D.C., “PSR J0609+2130: a disrupted binary pulsar?”, Mon. Not. R. Astron. Soc., 347, L21–L25, (2004).

    ADS  Google Scholar 

  230. [230]

    Lorimer, D.R., McLaughlin, M.A., Champion, D.J., and Stairs, I.H., “PSR J1453+1902 and the radio luminosities of solitary versus binary millisecond pulsars”, Mon. Not. R. Astron. Soc., 379, 282–288, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  231. [231]

    Lorimer, D.R., Nicastro, L., Lyne, A.G., Bailes, M., Manchester, R.N., Johnston, S., Bell, J.F., D’Amico, N., and Harrison, P.A., “Four new millisecond pulsars in the Galactic disk”, Astrophys. J., 439, 933–938, (1995).

    ADS  Google Scholar 

  232. [232]

    Lorimer, D.R., Stairs, I.H., Freire, P.C.C., Cordes, J.M., Camilo, F., Faulkner, A.J., Lyne, A.G., Nice, D.J., Ransom, S.M., Arzoumanian, Z., Manchester, R.N., Champion, D.J., van Leeuwen, J., McLaughlin, M.A., Ramachandran, R., Hessels, J.W.T., Vlemmings, W.H.T., Deshpande, A.A., Bhat, N.D.R., Chatterjee, S., Han, J.L., Gaensler, B.M., Kasian, L., Deneva, J.S., Reid, B., Lazio, T.J.W., Kaspi, V.M., Crawford, F., Lommen, A.N., Backer, D.C., Kramer, M., Stappers, B.W., Hobbs, G.B., Possenti, A., D’Amico, N., and Burgay, M., “Arecibo Pulsar Survey Using ALFA. II. The Young, Highly Relativistic Binary Pulsar J1906+0746”, Astrophys. J., 640, 428–434, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  233. [233]

    Lorimer, D.R., Xilouris, K.M., Fruchter, A.S., Stairs, I.H., Camilo, F., McLaughlin, M.A., Vazquez, A.M., Eder, J.E., Roberts, M.S.E., Hessels, J.W.T., and Ransom, S.M., “Discovery of 10 pulsars in an Arecibo drift-scan survey”, Mon. Not. R. Astron. Soc., 359, 1524–1530, (2005). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  234. [234]

    Lorimer, D.R., Yates, J.A., Lyne, A.G., and Gould, D.M., “Multifrequency Flux density measurements of 280 pulsars”, Mon. Not. R. Astron. Soc., 273, 411–421, (1995). 3.1.2

    ADS  Google Scholar 

  235. [235]

    Lundgren, S.C., Zepka, A.F., and Cordes, J.M., “A millisecond pulsar in a six hour orbit: PSR J0751+1807”, Astrophys. J., 453, 419–423, (1995).

    ADS  Google Scholar 

  236. [236]

    Lyne, A.G., “Binary Pulsar Discoveries in the Parkes Multibeam Survey”, in Rasio, F.A., and Stairs, I.H., eds., Binary Radio Pulsars, Proceedings of a meeting held at the Aspen Center for Physics, USA, 12–16 January 2004, ASP Conference Series, vol. 328, pp. 37–41, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2005).

    Google Scholar 

  237. [237]

    Lyne, A.G., Anderson, B., and Salter, M.J., “The Proper Motions of 26 Pulsars”, Mon. Not. R. Astron. Soc., 201, 503–520, (1982).

    ADS  Google Scholar 

  238. [238]

    Lyne, A.G., and Bailes, M., “The mass of the PSR 2303+46 system”, Mon. Not. R. Astron. Soc., 246, 15P–17P, (1990).

    ADS  Google Scholar 

  239. [239]

    Lyne, A.G., Burgay, M., Kramer, M., Possenti, A., Manchester, R.N., Camilo, F., McLaughlin, M.A., Lorimer, D.R., D’Amico, N., Joshi, B.C., Reynolds, J., and Freire, P.C.C., “A Double-Pulsar System: A Rare Laboratory for Relativistic Gravity and Plasma Physics”, Science, 303, 1153–1157, (2004).

    ADS  Google Scholar 

  240. [240]

    Lyne, A.G., Camilo, F., Manchester, R.N., Bell, J.F., Kaspi, V.M., D’Amico, N., McKay, N.P.F., Crawford, F., Morris, D.J., Sheppard, D.C., and Stairs, I.H., “The Parkes Multibeam Pulsar Survey: PSR J1811−1736, a pulsar in a highly eccentric binary system”, Mon. Not. R. Astron. Soc., 312, 698–702, (2000).

    ADS  Google Scholar 

  241. [241]

    Lyne, A.G., and Graham-Smith, F., Pulsar Astronomy, Cambridge Astrophysics Series, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 2006), 3rd edition. in press.

    Google Scholar 

  242. [242]

    Lyne, A.G., and Lorimer, D.R., “High Birth Velocities of Radio Pulsars”, Nature, 369, 127–129, (1994).

    ADS  Google Scholar 

  243. [243]

    Lyne, A.G., and Manchester, R.N., “The shape of pulsar radio beams”, Mon. Not. R. Astron. Soc., 234, 477–508, (1988).

    ADS  Google Scholar 

  244. [244]

    Lyne, A.G., Manchester, R.N., Lorimer, D.R., Bailes, M., D’Amico, N., Tauris, T.M., Johnston, S., Bell, J.F., and Nicastro, L., “The Parkes Southern Pulsar Survey — II. Final Results and Population Analysis”, Mon. Not. R. Astron. Soc., 295, 743–755, (1998).

    ADS  Google Scholar 

  245. [245]

    Lyne, A.G., Mankelow, S.H., Bell, J.F., and Manchester, R.N., “Radio pulsars in Terzan 5”, Mon. Not. R. Astron. Soc., 316, 491–493, (2000).

    ADS  Google Scholar 

  246. [246]

    Lyne, A.G., and McKenna, J., “PSR 1820–11: a binary pulsar in a wide and highly eccentric orbit”, Nature, 340, 367–369, (1989).

    ADS  Google Scholar 

  247. [247]

    Manchester, R.N., Fan, G., Lyne, A.G., Kaspi, V.M., and Crawford, F., “Discovery of 14 Radio Pulsars in a Survey of the Magellanic Clouds”, Astrophys. J., 649, 235–242, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  248. [248]

    Manchester, R.N., Hobbs, G.B., Teoh, A., and Hobbs, M., “The ATNF Pulsar Catalogue”, (2004). URL (cited on 22 January 2005):

  249. [249]

    Manchester, R.N., and Lyne, A.G., “Pulsar Interpulses — two poles or one?”, Mon. Not. R. Astron. Soc., 181, 761–767, (1977).

    ADS  Google Scholar 

  250. [250]

    Manchester, R.N., Lyne, A.G., Camilo, F., Bell, J.F., Kaspi, V.M., D’Amico, N., McKay, N.P.F., Crawford, F., Stairs, I.H., Possenti, A., Kramer, M., and Sheppard, D.C., “The Parkes multi-beam pulsar survey — I. Observing and data analysis systems, discovery and timing of 100 pulsars”, Mon. Not. R. Astron. Soc., 328, 17–35, (2001).

    ADS  Google Scholar 

  251. [251]

    Manchester, R.N., Lyne, A.G., D’Amico, N., Bailes, M., Johnston, S., Lorimer, D.R., Harrison, P.A., Nicastro, L., and Bell, J.F., “The Parkes Southern Pulsar Survey I. Observing and data analysis systems and initial results”, Mon. Not. R. Astron. Soc., 279, 1235–1250, (1996).

    ADS  Google Scholar 

  252. [252]

    Manchester, R.N., Newton, L.M., Cooke, D.J., and Lyne, A.G., “Detection of a pulsar in a long-period binary system”, Astrophys. J. Lett., 236, L25–L27, (1980).

    ADS  Google Scholar 

  253. [253]

    Manchester, R.N., and Taylor, J.H., “Period irregularities in pulsars”, Astrophys. J. Lett., 191, L63–L65, (1974).

    ADS  Google Scholar 

  254. [254]

    Matsakis, D.N., Taylor, J.H., Eubanks, T.M., and Marshall, T., “A statistic for describing pulsar and clock stabilities”, Astron. Astrophys., 326, 924–928, (1997).

    ADS  Google Scholar 

  255. [255]

    Max Planck Society, “The HESS project”, project homepage. URL (cited on 24 June 2008):

  256. [256]

    McCulloch, P.M., Hamilton, P.A., Ables, J.G., and Hunt, A.J., “A radio pulsar in the Large Magellanic Cloud”, Nature, 303, 307, (1983).

    ADS  Google Scholar 

  257. [257]

    McGill University, “René Breton’s Double Pulsar Page”, personal homepage. URL (cited on 7 July 2008):∼bretonr/doublepulsar.

  258. [258]

    McLaughlin, M.A., Kramer, M., Lyne, A.G., Lorimer, D.R., Stairs, I.H., Possenti, A., Manchester, R.N., Freire, P.C.C., Joshi, B.C., Burgay, M., Camilo, F., and D’Amico, N., “The double pulsar system J0737-3039: Modulation of the radio emission from B by the radiation from A”, Astrophys. J. Lett., 613, L57–L60, (2004). ADS:

    ADS  Google Scholar 

  259. [259]

    McLaughlin, M.A., Lorimer, D.R., Champion, D.J., Arzoumanian, Z., Backer, D.C., Cordes, J.M., Fruchter, A.S., Lommen, A.N., and Xilouris, K.M., “New Binary and Millisecond Pulsars from Arecibo Drift-Scan Searches”, in Rasio, F.A., and Stairs, I.H., eds., Binary Radio Pulsars, Proceedings of a meeting held at the Aspen Center for Physics, USA, 12–16 January 2004, ASP Conference Series, vol. 328, pp. 43–49, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2005).

    Google Scholar 

  260. [260]

    McLaughlin, M.A., Lyne, A.G., Lorimer, D.R., Possenti, A., Manchester, R.N., Camilo, F., Stairs, I.H., Kramer, M., Burgay, M., D’Amico, N., Freire, P.C.C., Joshi, B.C., and Bhat, N.D.R., “The Double Pulsar System J0737-3039: Modulation of A by B at Eclipse”, Astrophys. J., 616, L131–L134, (2004). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  261. [261]

    Michel, F.C., Theory of Neutron Star Magnetospheres, Theoretical Astrophysics, (University of Chicago Press, Chicago, U.S.A., 1991).

    Google Scholar 

  262. [262]

    Middleditch, J., and Kristian, J., “A search for young, luminous optical pulsars in extra-galactic supernova remnants”, Astrophys. J., 279, 157–161, (1984).

    ADS  Google Scholar 

  263. [263]

    Morgan, E., Kaaret, P., and Vanderspek, R., “HETE J1900.1-2455 is a millisecond pulsar”, Astron. Telegram, 2005(523), (2005). URL (cited on 19 July 2005):

  264. [264]

    Morris, D.J., Hobbs, G., Lyne, A.G., Stairs, I.H., Camilo, F., Manchester, R.N., Possenti, A., Bell, J.F., Kaspi, V.M., D’Amico, N., McKay, N.P.F., Crawford, F., and Kramer, M., “The Parkes Multibeam Pulsar Survey — II. Discovery and timing of 120 pulsars”, Mon. Not. R. Astron. Soc., 335, 275–290, (2002).

    ADS  Google Scholar 

  265. [265]

    MPI for Gravitational Physics (Albert Einstein Institute), “GEO600: The German-British Gravitational Wave Detector”, project homepage. URL (cited on 29 January 2005):

  266. [266]

    Nan, R.-D., Wang, Q.-M., Zhu, L.-C., Zhu, W.-B., Jin, C.-J., and Gan, H.-Q., “Pulsar Observations with Radio Telescope FAST”, Chin. J. Astron. Astrophys. Suppl., 6(2), 304–310, (2006).

    Google Scholar 

  267. [267]

    NANOGRAV, “The North American Nano-Hz Gravitational Wave Observatory”, project homepage. URL (cited on 24 June 2008):

  268. [268]

    Narayan, R., “The birthrate and initial spin period of single radio pulsars”, Astrophys. J., 319, 162–179, (1987).

    ADS  Google Scholar 

  269. [269]

    Narayan, R., and Vivekanand, M., “Evidence for evolving elongated Pulsar Beams”, Astron. Astrophys., 122, 45–53, (1983).

    ADS  Google Scholar 

  270. [270]

    NASA, “Chandra homepage”, project homepage. URL (cited on 24 June 2008):

  271. [271]

    NASA, “GLAST homepage”, project homepage. URL (cited on 24 June 2008):

  272. [272]

    NASA/ESA, “LISA: Laser Interferometer Space Antenna”, project homepage. URL (cited on 24 January 2005):

  273. [273]

    National Astronomical Observatory, “TAMA300: The 300m Laser Interferometer Gravitational Wave Antenna”, project homepage. URL (cited on 29 January 2005):

  274. [274]

    National Astronomy and Ionosphere Center, “The Arecibo Observatory”, project homepage. URL (cited on 29 January 2005):

  275. [275]

    National Astronomy and Ionosphere Center, “Preliminary PALFA survey”, project homepage. URL (cited on 23 January 2005):∼palfa.

  276. [276]

    National Astronomy and Ionospheric Center, “Pulsars in globular clusters”, personal homepage. URL (cited on 18 January 2005):∼pfreire/GCpsr.html.

  277. [277]

    National Centre for Radio Astonomy, “The Giant Metre Wave Radio Telescope”, project homepage. URL (cited on 23 January 2005):

  278. [278]

    National Radio Astronomy Observatory, “The Green Bank Telescope”, project homepage. URL (cited on 23 January 2005):

  279. [279]

    Navarro, J., Anderson, S.B., and Freire, P.C.C., “The Arecibo 430 MHz Intermediate Galactic Latitude Survey: Discovery of Nine Radio Pulsars”, Astrophys. J., 594, 943–951, (2003).

    ADS  Google Scholar 

  280. [280]

    Navarro, J., de Bruyn, A.G., Frail, D.A., Kulkarni, S.R., and Lyne, A.G., “A very luminous binary millisecond pulsar”, Astrophys. J. Lett., 455, L55–L58, (1995). ADS:

    ADS  Google Scholar 

  281. [281]

    Ng, C.-Y., and Romani, R.W., “Birth Kick Distributions and the Spin-Kick Correlation of Young Pulsars”, Astrophys. J., 660, 1357–1374, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  282. [282]

    Nicastro, L., Lyne, A.G., Lorimer, D.R., Harrison, P.A., Bailes, M., and Skidmore, B.D., “PSR J1012+5307: a 5.26-ms pulsar in a 14.5-h binary system”, Mon. Not. R. Astron. Soc. 273, L68–L70, (1995).

    ADS  Google Scholar 

  283. [283]

    Nice, D.J., Sayer, R.W., and Taylor, J.H., “PSR J1518+4904: A Mildly Relativistic Binary Pulsar System”, Astrophys. J. Lett., 466, L87–L90, (1996). 3

    ADS  Google Scholar 

  284. [284]

    Nice, D.J., Sayer, R.W., and Taylor, J.H., “Timing Observations of the J1518+4904 Double Neutron Star System”, in Arzoumanian, Z., van der Hooft, F., and van den Heuvel, E.P.J., eds., Pulsar Timing, General Relativity, and the Internal Structure of Neutron Stars, Proceedings of the colloquium, Amsterdam, 24–27 September 1996, pp. 79–83, (Royal Netherlands Academy of Arts and Sciences, Amsterdam, Netherlands, 1999).

    Google Scholar 

  285. [285]

    Nice, D.J., Splaver, E.M., and Stairs, I.H., “On the Mass and Inclination of the PSR J2019+2425 Binary System”, Astrophys. J., 549, 516–521, (2001).

    ADS  Google Scholar 

  286. [286]

    Nice, D.J., and Taylor, J.H., “PSRs J2019+2425 and J2322+2057 and the Proper Motions of Millisecond Pulsars”, Astrophys. J., 441, 429–435, (1995).

    ADS  Google Scholar 

  287. [287]

    Northwestern University, “Galactic Pulsar Population Generator”, project homepage. URL (cited on 24 June 2008):∼ciel/gppg_main.html.

  288. [288]

    Ord, S.M., Bailes, M., and van Straten, W., “The Scintillation Velocity of the Relativistic Binary Pulsar PSR J1141-6545”, Astrophys. J. Lett., 574, L75–L78, (2002).

    ADS  Google Scholar 

  289. [289]

    O’Shaughnessy, R., Kim, C., Kalogera, V., and Belczynski, K., “Constraining Population Synthesis Models via Empirical Binary Compact Object Merger and Supernova Rates”, Astrophys. J., 672, 479–488, (2008).

    ADS  Google Scholar 

  290. [290]

    Pacini, F., “Rotating neutron stars, pulsars, and supernova remnants”, Nature, 219, 145–146, (1968).

    ADS  Google Scholar 

  291. [291]

    Parsons, A., Backer, D.C., Chang, C., Chapman, D., Chen, H., Droz, P., de Jesus, C., MacMahon, D., Siemion, A., Werthimer, D., and Wright, M., “A New Approach to Radio Astronomy Signal Processing: Packet Switched, FPGA-based, Upgradeable, Modular Hardware and Reusable, Platform-Independent Signal Processing Libraries”, XXVIIIth URSI General Assembly, New Delhi, India, 23 to 29 October 2005, conference paper, (2005). Related online version (cited on 12 July 2008):

  292. [292]

    Peebles, P.J.E., Principles of Physical Cosmology, Princeton Series in Physics, (Princeton University Press, Princeton, U.S.A., 1993).

    MATH  Google Scholar 

  293. [293]

    Penn State University, “Pulsar Planets”, personal homepage. URL (cited on 19 March 2001):

  294. [294]

    Peters, P.C., “Gravitational Radiation and the Motion of Two Point Masses”, Phys. Rev., 136, B1224–B1232, (1964).

    ADS  MATH  Google Scholar 

  295. [295]

    Peters, P.C., and Mathews, J., “Gravitational Radiation from Point Masses in a Keplerian Orbit”, Phys. Rev., 131, 435–440, (1963).

    ADS  MathSciNet  MATH  Google Scholar 

  296. [296]

    Pfahl, E., and Loeb, A., “Probing the Spacetime Around Sgr A* with Radio Pulsars”, Astrophys. J., 615, 253–258, (2004). ADS:

    ADS  Google Scholar 

  297. [297]

    Phinney, E.S., “The rate of neutron star binary mergers in the universe: Minimal predictions for gravity wave detectors”, Astrophys. J. Lett., 380, L17–L21, (1991).

    ADS  Google Scholar 

  298. [298]

    Phinney, E.S., “Pulsars as Probes of Newtonian Dynamical Systems”, Philos. Trans. R. Soc. London, 341, 39–75, (1992).

    ADS  Google Scholar 

  299. [299]

    Phinney, E.S., and Blandford, R.D., “Analysis of the Pulsar P−Ṗ distribution”, Mon. Not. R. Astron. Soc., 194, 137–148, (1981).

    ADS  Google Scholar 

  300. [300]

    Phinney, E.S., and Kulkarni, S.R., “Binary and millisecond pulsars”, Annu. Rev. Astron. Astrophys., 32, 591–639, (1994).

    ADS  Google Scholar 

  301. [301]

    Phinney, E.S., and Sigurdsson, S., “Ejection of pulsars and binaries to the outskirts of globular clusters”, Nature, 349, 220–223, (1991).

    ADS  Google Scholar 

  302. [302]

    Phinney, E.S., and Verbunt, F., “Binary pulsars before spin-up and PSR 1820-11”, Mon. Not. R. Astron. Soc., 248, 21P–23P, (1991).

    ADS  Google Scholar 

  303. [303]

    Portegies Zwart, S.F., and Verbunt, F., “Population synthesis of high-mass binaries”, Astron. Astrophys., 309, 179–196, (1996).

    ADS  Google Scholar 

  304. [304]

    Preibisch, T., Balega, Y., Hofmann, K.-H., Weigelt, G., and Zinnecker, H., “Multiplicity of the massive stars in the Orion Nebula cluster”, New Astronomy, 4, 531–542, (1999).

    ADS  Google Scholar 

  305. [305]

    Prince, T.A., Anderson, S.B., Kulkarni, S.R., and Wolszczan, A., “Timing observations of the 8 hour binary pulsar 2127+11C in the globular cluster M15”, Astrophys. J. Lett., 374, L41–L44, (1991).

    ADS  Google Scholar 

  306. [306]

    Princeton University, “Princeton Pulsar Group”, project homepage. URL (cited on 20 March 2001):

  307. [307]

    Pulsar Astronomy Network, “Pulsar astronomy wiki”, online resource. URL (cited on 24 June 2008):

  308. [308]

    Pulsar Group of the Australia Telescope National Facility (ATNF), “Parkes Multibeam Pulsar Survey”, project homepage. URL (cited on 2 December 2000):

  309. [309]

    Rajagopal, M., and Romani, R.W., “Ultra-Low-Frequency Gravitational Radiation from Massive Black Hole Binaries”, Astrophys. J., 446, 543–549, (1995).

    ADS  Google Scholar 

  310. [310]

    Rankin, J.M., “Toward an empirical theory of pulsar emission. I. Morphological taxonomy”, Astrophys. J., 274, 333–358, (1983).

    ADS  Google Scholar 

  311. [311]

    Rankin, J.M., “Further Evidence for Alignment of the Rotation and Velocity Vectors in Pulsars”, Astrophys. J., 664, 443–447, (2007).

    ADS  Google Scholar 

  312. [312]

    Ransom, S.M., New search techniques for binary pulsars, Ph.D. Thesis, (Harvard University, Harvard, U.S.A., 2001).

    Google Scholar 

  313. [313]

    Ransom, S.M., “Latest timing results for PSRs J1614−2230 and J1614−2318”, personal communication, (2008).

  314. [314]

    Ransom, S.M., “Twenty Years of Searching for (and Finding) Globular Cluster Pulsars”, in Bassa, C.G., Wang, Z., Cumming, A., and Kaspi, V.M., eds., 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More, McGill University, Montréal, Canada, 12–17 August 2007, AIP Conference Proceedings, vol. 983, pp. 415–423, (American Institute of Physics, Melville, U.S.A., 2008).

    Google Scholar 

  315. [315]

    Ransom, S.M., Cordes, J.M., and Eikenberry, S.S., “A New Search Technique for Short Orbital Period Binary Pulsars”, Astrophys. J. Lett., 589, 911–920, (2003).

    ADS  Google Scholar 

  316. [316]

    Ransom, S.M., Greenhill, L.J., Herrnstein, J.R., Manchester, R.N., Camilo, F., Eikenberry, S.S., and Lyne, A.G., “A binary millisecond pulsar in globular cluster NGC 6544”, Astrophys. J. Lett., 546, L25–L28, (2001).

    ADS  Google Scholar 

  317. [317]

    Ransom, S.M., Hessels, J.W.T., Stairs, I.H., Freire, P.C.C., Camilo, F., Kaspi, V.M., and Kaplan, D.L., “Twenty-one millisecond pulsars in Terzan 5 using the Green Bank Telescope”, Science, 307(5711), 892–896, (2005).

    ADS  Google Scholar 

  318. [318]

    Ratnatunga, K.U., and van den Bergh, S., “The rate of stellar collapses in the galaxy”, Astrophys. J., 343, 713–717, (1989).

    ADS  Google Scholar 

  319. [319]

    Ray, P.S., Thorsett, S.E., Jenet, F.A., van Kerkwijk, M.H., Kulkarni, S.R., Prince, T.A., Sandhu, J.S., and Nice, D.J., “A Survey for Millisecond Pulsars”, Astrophys. J., 470, 1103–1110, (1996).

    ADS  Google Scholar 

  320. [320]

    Remillard, R.A., and McClintock, J.E., “X-Ray Properties of Black-Hole Binaries”, Annu. Rev. Astron. Astrophys., 44, 49–92, (2006). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  321. [321]

    Richards, D.W., and Comella, J.M., “The period of pulsar NP 0532”, Nature, 222, 551–552, (1969).

    ADS  Google Scholar 

  322. [322]

    Ridley, J., and Lorimer, D.R., “Pulsar Demographics”, 212th AAS Meeting, St. Louis, MO, 1–5 June 2008, conference paper, (2008). ADS:

  323. [323]

    Romani, R.W., “Timing a millisecond pulsar array”, in Ogelman, H., and van den Heuvel, E.P.J., eds., Timing Neutron Stars, Proceedings of the NATO Advanced Study Institute on Timing Neutron Stars, Çesme, Izmir, Turkey, 4–15 April 1988, NATO ASI Series, Series C, vol. 262, pp. 113–117, (Kluwer, Dordrecht, Netherlands; Boston, U.S.A., 1989).

    Google Scholar 

  324. [324]

    Romani, R.W., “Populations of low-mass black hole binaries”, Astrophys. J., 399, 621–626, (1992).

    ADS  Google Scholar 

  325. [325]

    Romani, R.W., and Taylor, J.H., “An Upper Limit on the Stochastic Background of Ultralow-Frequency Gravitational Waves”, Astrophys. J. Lett., 265, L35–L37, (1983).

    ADS  Google Scholar 

  326. [326]

    Rubio-Herrera, E., Braun, R., Janssen, G., van Leeuwen, J., and Stappers, B.W., “The 8gr8 Cygnus Survey for New Pulsars and RRATs”, in Becker, W., and Huang, H.H., eds., Proceedings of the 363. WE-Heraeus Seminar on Neutron Stars and Pulsars: 40 years after the discovery (Posters and contributed talks), Physikzentrum Bad Honnef, Germany, May 14–19, 2006, MPE Report, vol. 291, pp. 56–59, (Max Planck Institute for Extraterrestrial Physics, Garching, Germany, 2007). Related online version (cited on 16 July 2008):

    Google Scholar 

  327. [327]

    Ryba, M.F., and Taylor, J.H., “High Precision Timing of Millisecond Pulsars. I. Astrometry and Masses of the PSR 1855+09 System”, Astrophys. J., 371, 739–748, (1991).

    ADS  Google Scholar 

  328. [328]

    Ryba, M.F., and Taylor, J.H., “High Precision Timing of Millisecond Pulsars. II. Astrometry, Orbital Evolution, and Eclipses of PSR 1957+20”, Astrophys. J., 380, 557–563, (1991).

    ADS  Google Scholar 

  329. [329]

    Sandhu, J.S., Bailes, M., Manchester, R.N., Navarro, J., Kulkarni, S.R., and Anderson, S.B., “The Proper Motion and Parallax of PSR J0437-4715”, Astrophys. J. Lett., 478, L95–L98, (1997).

    ADS  Google Scholar 

  330. [330]

    Sazhin, M.V., “Opportunities for detecting ultralong gravitational waves”, Sov. Astron., 22, 36–38, (1978).

    ADS  Google Scholar 

  331. [331]

    Scheuer, P.A.G., “Amplitude variations of pulsed radio sources”, Nature, 218, 920–922, (1968).

    ADS  Google Scholar 

  332. [332]

    Segelstein, D.J., Rawley, L.A., Stinebring, D.R., Fruchter, A.S., and Taylor, J.H., “New millisecond pulsar in a binary system”, Nature, 322, 714–717, (1986).

    ADS  Google Scholar 

  333. [333]

    Seiradakis, J.H., and Wielebinski, R., “Morphology and characteristics of radio pulsars”, Astron. Astrophys. Rev., 12, 239–271, (2004).

    ADS  Google Scholar 

  334. [334]

    SETI, “The Allen Telescope Array”, project homepage. URL (cited on 24 June 2008):

  335. [335]

    Shemar, S.L., and Lyne, A.G., “Observations of pulsar glitches”, Mon. Not. R. Astron. Soc. 282, 677–690, (1996).

    ADS  Google Scholar 

  336. [336]

    Shklovskii, I.S., “Possible causes of the secular increase in pulsar periods”, Sov. Astron., 13, 562–565, (1970).

    ADS  Google Scholar 

  337. [337]

    Sigurdsson, S., and Phinney, E.S., “Dynamics and interactions of binaries and neutron stars in globular clusters”, Astrophys. J. Suppl. Ser., 99, 609–635, (1995).

    ADS  Google Scholar 

  338. [338]

    Sigurdsson, S., Richer, H.B., Hansen, B.M., Stairs, I.H., and Thorsett, S.E., “A Young White Dwarf Companion to Pulsar B1620-26: Evidence for Early Planet Formation”, Science, 301, 193–196, (2003).

    ADS  Google Scholar 

  339. [339]

    Smarr, L.L., and Blandford, R.D., “The binary pulsar: Physical processes, possible companions and evolutionary histories”, Astrophys. J., 207, 574–588, (1976).

    ADS  Google Scholar 

  340. [340]

    Smith, F.G., “The radio emission from pulsars”, Rep. Prog. Phys., 66, 173–238, (2003).

    ADS  Google Scholar 

  341. [341]

    Splaver, E.M., Nice, D.J., Arzoumanian, Z., Camilo, F., Lyne, A.G., and Stairs, I.H., “Probing the Masses of the PSR J0621+1002 Binary System through Relativistic Apsidal Motion”, Astrophys. J., 581, 509–518, (2002). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  342. [342]

    Splaver, E.M., Nice, D.J., Stairs, I.H., Lommen, A.N., and Backer, D.C., “Masses, Parallax, and Relativistic Timing of the PSR J1713+0747 Binary System”, Astrophys. J., 620, 405–415, (2005).

    ADS  Google Scholar 

  343. [343]

    Stairs, I.H., Observations of Binary and Millisecond Pulsars with a Baseband Recording System, Ph.D. Thesis, (Princeton University, Princeton, U.S.A., 1998).

    Google Scholar 

  344. [344]

    Stairs, I.H., “Testing General Relativity with Pulsar Timing”, Living Rev. Relativity, 6, lrr-2003-5, (2003). URL (cited on 22 January 2005):

  345. [345]

    Stairs, I.H., “Pulsars in Binary Systems: Probing Binary Stellar Evolution and General Relativity”, Science, 304, 547–552, (2004).

    ADS  Google Scholar 

  346. [346]

    Stairs, I.H., Arzoumanian, Z., Camilo, F., Lyne, A.G., Nice, D.J., Taylor, J.H., Thorsett, S.E., and Wolszczan, A., “Measurement of Relativistic Orbital Decay in the PSR B1534+12 Binary System”, Astrophys. J., 505, 352–357, (1998).

    ADS  Google Scholar 

  347. [347]

    Stairs, I.H., Faulkner, A.J., Lyne, A.G., Kramer, M., Lorimer, D.R., McLaughlin, M.A., Manchester, R.N., Hobbs, G.B., Camilo, F., Possenti, A., Burgay, M., D’Amico, N., Freire, P.C.C., and Gregory, P.C., “Discovery of three wide-orbit binary pulsars: Implications for Binary Evolution and Equivalence Principles”, Astrophys. J., 632, 1060–1068, (2005). Related online version (cited on 24 October 2008):

    ADS  Google Scholar 

  348. [348]

    Stairs, I.H., Manchester, R.N., Lyne, A.G., Kaspi, V.M., Camilo, F., Bell, J.F., D’Amico, N., Kramer, M., Crawford, F., Morris, D.J., McKay, N.P.F., Lumsden, S.L., Tacconi-Garman, L.E., Cannon, R.D., Hambly, N.C., and Wood, P.R., “PSR J1740-3052: a pulsar with a massive companion”, Mon. Not. R. Astron. Soc., 325, 979–988, (2001).

    ADS  Google Scholar 

  349. [349]

    Stairs, I.H., Manchester, R.N., Lyne, A.G., Kramer, M., Kaspi, V.M., Camilo, F., and D’Amico, N., “The massive binary pulsar J1740-3052”, in Bailes, M., Nice, D.J., and Thorsett, S.E., eds., Radio Pulsars, Proceedings of a meeting held at Mediterranean Agonomic Institute of Chania, Crete, Greece, 26–29 August 2002, ASP Conference Series, vol. 302, pp. 85–88, (Astronomical Society of the Pacific, San Fransisco, U.S.A., 2003).

    Google Scholar 

  350. [350]

    Stairs, I.H., Splaver, E.M., Thorsett, S.E., Nice, D.J., and Taylor, J.H., “A Baseband Recorder for Radio Pulsar Observations”, Mon. Not. R. Astron. Soc., 314, 459–467, (2000). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  351. [351]

    Stairs, I.H., Thorsett, S.E., Taylor, J.H., and Wolszczan, A., “Studies of the Relativistic Binary Pulsar PSR B1534+12. I. Timing Analysis”, Astrophys. J., 581, 501–508, (2002).

    ADS  Google Scholar 

  352. [352]

    Standish, E.M., and Newhall, X.X., “New accuracy levels for solar system ephemerides. (Lecture)”, in Ferraz-Mello, S., Morando, B., and Arlot, J.-E., eds., Dynamics, Ephemerides, and Astrometry of the Solar System, Proceedings of the 172nd Symposium of the International Astronomical Union, held in Paris, France, 3–8 July, 1995, p. 29, (Kluwer, Dordrecht, Netherlands; Boston, U.S.A., 1996).

    Google Scholar 

  353. [353]

    Stappers, B.W., Bailes, M., Lyne, A.G., Manchester, R.N., D’Amico, N., Tauris, T.M., Lorimer, D.R., Johnston, S., and Sandhu, J.S., “Probing the Eclipse Region of a Binary Millisecond Pulsar”, Astrophys. J. Lett., 465, L119–L122, (1996).

    ADS  Google Scholar 

  354. [354]

    Stella, L., Priedhorsky, W., and White, N.E., “The discovery of a 685 second orbital period from the X-ray source 4U 1820–30 in the globular cluster NGC 6624”, Astrophys. J. Lett. 312, L17–L21, (1987).

    ADS  Google Scholar 

  355. [355]

    Sternberg Astronomical Institute, Moscow State University, “Scenario Machine Engine”, project homepage. URL (cited on 19 March 2001):

  356. [356]

    Stinebring, D.R., Ryba, M.F., Taylor, J.H., and Romani, R.W., “Cosmic Gravitational-Wave Background: Limits from Millisecond Pulsar Timing”, Phys. Rev. Lett., 65, 285–288, (1990).

    ADS  Google Scholar 

  357. [357]

    Story, S.A., Gonthier, P.L., and Harding, A.K., “Population Synthesis of Radio and γ-Ray Millisecond Pulsars from the Galactic Disk”, Astrophys. J., 671, 713–726, (2007). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  358. [358]

    Sudou, H., Iguchi, S., Murata, Y., and Taniguchi, Y., “Orbital Motion in the Radio Galaxy 3C 66B: Evidence for a Supermassive Black Hole Binary”, Science, 300, 1263–1265, (2003).

    ADS  Google Scholar 

  359. [359]

    Swinburne University of Technology, “Centre for Astrophysics and Supercomputing”, institutional homepage. URL (cited on 8 December 2000):

  360. [360]

    Tauris, T.M., and Manchester, R.N., “On the evolution of pulsar beams”, Mon. Not. R. Astron. Soc., 298, 625–636, (1998).

    ADS  Google Scholar 

  361. [361]

    Tauris, T.M., and Savonije, G.J., “Formation of millisecond pulsars. I. Evolution of low-mass X-ray binaries with Porb > 2 days”, Astron. Astrophys., 350, 928–944, (1999).

    ADS  Google Scholar 

  362. [362]

    Taylor, J.H., “Millisecond Pulsars: Nature’s Most Stable Clocks”, Proc. IEEE, 79, 1054–1062, (1991).

    ADS  Google Scholar 

  363. [363]

    Taylor, J.H., “Binary Pulsars and Relativistic Gravity”, Rev. Mod. Phys., 66, 711–719, (1994).

    ADS  Google Scholar 

  364. [364]

    Taylor, J.H., and Cordes, J.M., “Pulsar Distances and the Galactic Distribution of Free Electrons”, Astrophys. J., 411, 674–684, (1993).

    ADS  Google Scholar 

  365. [365]

    Taylor, J.H., and Manchester, R.N., “Galactic distribution and evolution of pulsars”, Astrophys. J., 215, 885–896, (1977).

    ADS  Google Scholar 

  366. [366]

    Taylor, J.H., and Weisberg, J.M., “A New Test of General Relativity: Gravitational Radiation and the Binary Pulsar PSR 1913+16”, Astrophys. J., 253, 908–920, (1982).

    ADS  Google Scholar 

  367. [367]

    Taylor, J.H., and Weisberg, J.M., “Further experimental tests of relativistic gravity using the binary pulsar PSR 1913+16”, Astrophys. J., 345, 434–450, (1989).

    ADS  Google Scholar 

  368. [368]

    The Nobel Foundation, “The Nobel Prize in Physics 1993”, institutional homepage. URL (cited on 19 March 2001):

  369. [369]

    Thorsett, S.E., Arzoumanian, Z., Camilo, F., and Lyne, A.G., “The Triple Pulsar System PSR B1620−26 in M4”, Astrophys. J., 523, 763–770, (1999).

    ADS  Google Scholar 

  370. [370]

    Thorsett, S.E., Arzoumanian, Z., and Taylor, J.H., “PSR B1620-26: A binary radio pulsar with a planetary companion?”, Astrophys. J. Lett., 412, L33–L36, (1993).

    ADS  Google Scholar 

  371. [371]

    Thorsett, S.E., and Chakrabarty, D., “Neutron Star Mass Measurements. I. Radio Pulsars”, Astrophys. J., 512, 288–299, (1999).

    ADS  Google Scholar 

  372. [372]

    Thorsett, S.E., and Dewey, R.J., “Pulsar Timing Limits on Very Low Frequency Stochastic Gravitational Radiation”, Phys. Rev. D, 53, 3468, (1996).

    ADS  Google Scholar 

  373. [373]

    Toscano, M., Sandhu, J.S., Bailes, M., Manchester, R.N., Britton, M.C., Kulkarni, S.R., Anderson, S.B., and Stappers, B.W., “Millisecond pulsar velocities”, Mon. Not. R. Astron. Soc., 307, 925–933, (1999).

    ADS  Google Scholar 

  374. [374]

    Tutukov, A.V., and Yungelson, L.R., “The merger rate of neutron star and black hole binaries”, Mon. Not. R. Astron. Soc., 260, 675–678, (1993).

    ADS  Google Scholar 

  375. [375]

    University of British Columbia, “Cool Pulsars Encyclopedia”, online resource. URL (cited on 24 June 2008):

  376. [376]

    University of British Columbia, “Ingrid Stairs / UBC Pulsar Group”, personal homepage. URL (cited on 22 January 2005):

  377. [377]

    University of California Berkeley Astronomy Department, “Berkeley Pulsar Group”, project homepage. URL (cited on 20 March 2001):∼mpulsar/.

  378. [378]

    University of Manchester, “The European Pulsar Network Data Archive”, web interface to database. URL (cited on 17 January 2005):∼pulsar/Resources/epn.

  379. [379]

    University of Manchester, “Jodrell Bank Observatory Pulsar Group”, project homepage. URL (cited on 20 March 2001):∼pulsar.

  380. [380]

    US Naval Observatory, “Sigma z”, project homepage. URL (cited on 24 June 2008):

  381. [381]

    van den Bergh, S., and Tammann, G.A., “Galactic and Extragalactic Supernova Rates”, Annu. Rev. Astron. Astrophys., 29, 363–407, (1991).

    ADS  Google Scholar 

  382. [382]

    van den Heuvel, E.P.J., “The binary pulsar PSR J2145−0750: a system originating from a ow or intermediate mass X-ray binary with a donor star on the asymptotic giant branch?”, Astron. Astrophys., 291, L39–L42, (1994).

    ADS  Google Scholar 

  383. [383]

    van den Heuvel, P.J., “An Eccentric Pulsar: Result of a Threesome?”, Science, 320, 1298–1299, (2008).

    Google Scholar 

  384. [384]

    van Kerkwijk, M.H., Bassa, C.G., Jacoby, B.A., and Jonker, P.G., “Optical studies of companions to millisecond pulsars”, in Rasio, F.A., and Stairs, I.H., eds., Binary Radio Pulsars, Proceedings of a meeting held at the Aspen Center for Physics, USA, 12–16 January 2004, ASP Conference Series, vol. 328, pp. 357–369, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2005).

    Google Scholar 

  385. [385]

    van Kerkwijk, M.H., and Kulkarni, S.R., “Spectroscopy of the white-dwarf companions of PSR B 0655+64 and 0820+02”, Astrophys. J. Lett., 454, L141–L144, (1995).

    ADS  Google Scholar 

  386. [386]

    van Kerkwijk, M.H., and Kulkarni, S.R., “A Massive White Dwarf Companion to the Eccentric Binary Pulsar System PSR B2303+46”, Astrophys. J. Lett., 516, L25–L28, (1999).

    ADS  Google Scholar 

  387. [387]

    van Leeuwen, J., and Stappers, B.W., “Finding pulsars with LOFAR”, in Bassa, C.G., Wang, Z., Cumming, A., and Kaspi, V.M., eds., 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More, McGill University, Montréal, Canada, 12–17 August 2007, AIP Conference Proceedings, vol. 983, pp. 598–600, (American Institute of Physics, Melville, U.S.A., 2008).

    Google Scholar 

  388. [388]

    Verbiest, J.P.W., Bailes, M., van Straten, W., Hobbs, G.B., Edwards, R.T., Manchester, R.N., Bhat, N.D.R., Sarkissian, J.M., Jacoby, B.A., and Kulkarni, S.R., “Precision Timing of PSR J0437-4715: An Accurate Pulsar Distance, a High Pulsar Mass, and a Limit on the Variation of Newton’s Gravitational Constant”, Astrophys. J., 679, 675–680, (2008). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  389. [389]

    Vivekanand, M., and Narayan, R., “A New Look at Pulsar Statistics — Birthrate and Evidence for Injection”, J. Astrophys. Astron., 2, 315–337, (1981).

    ADS  Google Scholar 

  390. [390]

    Weisberg, J.M., “The Galactic Electron Density Distribution”, in Johnston, S., Walker, M.A., and Bailes, M., eds., Pulsars: Problems and Progress (IAU Colloquium 160), Proceedings of the 160th Colloquium of the IAU, held at the Research Centre for Theoretical Astrophysics, University of Sydney, Australia, 8–12 January 1996, ASP Conference Series, vol. 105, pp. 447–454, (Astronomical Society of the Pacific, San Francisco, U.S.A., 1996).

    Google Scholar 

  391. [391]

    Weisberg, J.M., and Taylor, J.H., “The relativistic binary pulsar B1913+16: Thirty years of observations and analysis”, in Rasio, F.A., and Stairs, I.H., eds., Binary Radio Pulsars, Proceedings of the 2004 Aspen Winter Conference, held 11–17 January, 2004 at Aspen Center for Physics, Aspen, Colorado, USA, ASP Conference Series, vol. 328, pp. 25–32, (Astronomical Society of the Pacific, San Francisco, U.S.A., 2005).

    Google Scholar 

  392. [392]

    Weltevrede, P., and Johnston, S., “The population of pulsars with interpulses and the implications for beam evolution”, Mon. Not. R. Astron. Soc., 387, 1755–1760, (2008). Related online version (cited on 12 July 2008):

    ADS  Google Scholar 

  393. [393]

    West Virginia University, “350-MHz GBT drift scan pulsar survey”, project homepage. URL (cited on 24 June 2008):∼pulsar/GBTdrift350.

  394. [394]

    West Virginia University, “Pulsar population synthesis code”, project homepage. URL (cited on 24 June 2008):

  395. [395]

    Wex, N., “The second post-Newtonian motion of compact binary-star systems with spin”, Class. Quantum Grav., 12, 983–1005, (1995).

    ADS  MathSciNet  MATH  Google Scholar 

  396. [396]

    White, N.E., and Zhang, W., “Millisecond X-Ray Pulsars in Low-mass X-ray Binaries”, Astrophys. J. Lett., 490, L87–L90, (1997).

    ADS  Google Scholar 

  397. [397]

    Wijnands, R., “Accretion-Driven Millisecond X-ray Pulsars”, in Lowry, J.A., ed., Trends in Pulsar Research, (Nova Science, Hauppauge, U.S.A., 2005). Related online version (cited on 12 July 2008): in press.

    Google Scholar 

  398. [398]

    Wijnands, R., and van der Klis, M., “A millisecond pulsar in an X-ray binary system”, Nature, 394, 344–346, (1998).

    ADS  Google Scholar 

  399. [399]

    Will, C.M., “Einstein’s Relativity Put to Nature’s Test: A Centennial Perspective”, lecture notes, American Physical Society, (1999). URL (cited on 8 December 2000):

    Google Scholar 

  400. [400]

    Will, C.M., “The Confrontation between General Relativity and Experiment”, Living Rev. Relativity, 9, lrr-2006-3, (2006). URL (cited on 12 July 2008):

  401. [401]

    Wolszczan, A., “A nearby 37.9 ms radio pulsar in a relativistic binary system”, Nature, 350, 688–690, (1991).

    ADS  Google Scholar 

  402. [402]

    Wolszczan, A., “Confirmation of Earth-mass planets orbiting the millisecond pulsar PSR 1257+12”, Science, 264, 538–542, (1994).

    ADS  Google Scholar 

  403. [403]

    Wolszczan, A., Doroshenko, O.V., Konacki, M., Kramer, M., Jessner, A., Wielebinski, R., Camilo, F., Nice, D.J., and Taylor, J.H., “Timing Observations of Four Millisecond Pulsars with the Arecibo and Effelsberg Radio Telescopes”, Astrophys. J., 528, 907–912, (2000).

    ADS  Google Scholar 

  404. [404]

    Wolszczan, A., and Frail, D.A., “A planetary system around the millisecond pulsar PSR 1257+12”, Nature, 355, 145–147, (1992).

    ADS  Google Scholar 

  405. [405]

    York, T., Jackson, N., Browne, I.W.A., Wucknitz