Near Field Cosmology: The Origin of the Galaxy and the Local Group

Abstract

The Galaxy has built up through a process of accretion and merging over billions of years which continues to this day. Astronomers are now embarking on a new era of massive stellar surveys over the coming decade.

Appendices

Appendix A: The Discovery of Dark Matter in Galaxies

In the past year, there have been excellent reviews that revisit how we got to where we are today. Who discovered that the Universe is expanding (Peacock 2013)? Who came up with Big Bang cosmology (Belenkiy 2012)? and so forth. Speakers introduce topics with a compressed narrative that tends to write out important contributions through the process of oversimplification. This is certainly the case for who discovered dark matter in galaxies.

One of the cornerstones of modern astrophysics is the cold dark matter paradigm. We know today that essentially all galaxies are encompassed by dark matter haloes that are an order of magnitude larger in diameter than what we observe with our telescopes. While the nature of “dark matter” remains a mystery, it is widely believed to be made up of one or more unidentified sub-atomic particles.

A question of more than historical interest is to ask how the existence of dark matter in galaxies was firmly established. Dark matter drives the large-scale dynamics of matter in the Universe and is the scaffolding on which individual galaxies are built. The role of dark matter in individual galaxies was finally recognized in the 1970s, as we discuss. We find that the history of this discovery is chequered with early hints, followed by definitive demonstrations, and ultimately a more complete understanding of its implications. In this respect, it is not easy to attribute the discovery of dark matter in galaxies to specific astronomers. The roll call includes Zwicky, Smith, Kahn and Woltjer for the discovery of dark matter in groups and clusters, followed by Freeman, Ostriker, Rubin and Bosma for the discovery of dark matter in galaxies. (These astronomers mostly published their results in multi-author papers, but credit is given to those that carried their arguments forward in later papers.)

The presence of some kind of “unseen matter” was first inferred by Zwicky (1933) in the Coma cluster, and by Smith (1936) in the Virgo cluster. Two decades on, Kahn and Woltjer (1959) showed that the total mass of the Local Group greatly exceeds the sum of the stellar masses of M31 and the Milky Way. In these early papers, it was not possible to establish how the unseen matter was distributed.

There were alternative interpretations that galaxy clusters were “birth sites” caught in the act of flying apart (Ambartsumian 1958; Neyman et al. 1961). But the problem with these ideas is that the core of the Coma cluster, for example, is 250 kpc in diameter, its 3D velocity dispersion is 1500 km s$^{-1}$ and hence its dispersal time is $\sim$10$^8$ yrs. The stellar populations, however, are obviously much older. (At about this time, tidal arms in interacting galaxies were being argued as an ejection phenomenon, an interpretation that was dismissed for the same reasons.) On the basis of more reliable velocity data, Peebles (1970) and Rood et al. (1972) both derived M/L values for Coma which exceeded those for any known stellar population.

Tremaine (1999) notes that deriving galaxy masses was a thriving industry in the 1960s, but these studies vastly underestimated the true masses due to their limited radial extent and because the connection to unseen matter in clusters had not been made. Ostriker et al. (1974) and Einasto et al. (1974) were some of the first to state clearly (cf. Freeman 1970; Roberts and Rots 1973) that unseen matter in clusters is probably distributed in extensive halos around individual galaxies. This made any interpretation of “dark matter” rather colder than, say, an invisible medium permeating clusters.

Ostriker in particular had fully understood the early signs from galaxian H${\scriptstyle \mathrm I}$ rotation curves that were more flat than Keplerian, and was therefore guided by this result, at least in part. It took several decades to establish the reality of super-Keplerian rotation. The effect was already clear in Babcock’s (1939) early observations confirmed decades later with more extensive observations by Roberts (1967). In hindsight, we can say that this was a necessary but not a sufficient condition because the rotation curves did not extend far enough in radius. Flat or slowly declining rotation over the inner 6 or so scale lengths is easily accounted for in terms of disk components (e.g. van Albada et al. 1985). Kalnajs (1983) questioned evidence for DM for some of the optical rotation curves presented by Rubin at the Besancon conference, where he found the stellar components alone could explain the raised rotation curves.

Throughout the 1970s, few were thinking of unseen haloes in terms of elementary particles (cf. Tremaine and Gunn 1979). Essentially all papers discussed unseen haloes in terms of baryons, especially low mass stars extending down to brown dwarfs (e.g. Roberts 1975; White and Rees 1978). For example, a string of influential papers on galaxy formation considered how gas accretes and cools within a gravitating potential well (Rees and Ostriker 1977; Binney 1977; Silk 1977). Gunn (1977) and White and Rees (1978) argued that the inferred dark haloes formed naturally from the infall of collisionless dark matter onto bound structures in an expanding universe. Interestingly, at the same time, Searle and Zinn (1978) realized that the Galactic system of globular clusters must have accreted onto the halo over billions of years, rather than in the rapid collapse envisioned by Eggen et al. (1962). As far as one can determine, these papers implicitly assumed that the gravitating haloes were baryonic in nature, to the extent that galaxy haloes were discussed by them.

Flat rotation curves. Flat rotation curves in individual galaxies, with their small velocity scales, provide some of the most compelling evidence we have for the existence of (cold) dark matter haloes. In her history of the discovery of dark matter, Trimble (1987) notes that “Freeman (1970) was among the first to notice that such non-Keplerian rotation curves were a widespread phenomenon and to deduce that there might be considerable gravitating mass outside the observed region.” This observation is in connection to his comment in his Appendix A that:

For NGC 300 and M33, the 21 cm data give turnover points near the photometric outer edges of these systems. These data have relatively low spatial resolution; if they are correct, then there must be in these galaxies additional matter which is undetected, either optically or at 21 cm. Its mass must be at least as large as the mass of the detected galaxy, and its distribution must be quite different from the exponential distribution which holds for the optical galaxy.

In the centennial issue of the Astrophysical Journal, Tremaine (1999) comments on the importance of the Ostriker et al. (1974) paper but notes that “the first clear statement that rotation curves demand dark matter” is Freeman’s (1970) statement above. This point is made again in van Albada et al.’s (1985) classic study of NGC 3198.

An influential paper in the same year as Freeman’s classic work was Rubin and Ford’s (1970) optical study of M31. They show the galaxy has a non-Keplerian (although declining) rotation curve to a radius of 20 kpc. No definitive conclusions were drawn from their careful study about unseen matter because their disk models were able to produce some of the slow decline in rotation over the inner disk. They state that “it does not appear possible, from the presently available data, to infer anything about the mass beyond 24 kpc in M31.”

In a published Research Note, on the basis of three extended rotation curves (M81, M101, and Rubin’s data for M31), Roberts and Rots (1973) noted that extended rotation curves indicate “a significant amount of matter at these large distances and imply that spiral galaxies are larger than found from photometric measurements.” These authors discussed the possible role of mass to light variations in galaxies and between galaxies. In a published Comment, Roberts (1976) drew attention to the striking phenomenon of flat rotation curves (see also Roberts 1975).

In the mid 1970s, there was some discussion that the few extended H${\scriptstyle \mathrm I}$ rotation curves that existed (e.g. M81, M31, M33) are possibly affected by dynamical interactions with neighbours (e.g. conference discussions by Sancisi, van der Kruit, van Albada, Allen). Another point of discussion was the contribution of poorly calibrated side lobes (Salpeter) and beam smearing arising from the Arecibo observations.

But the critical study that put the role of galaxian dark matter beyond doubt was Bosma’s (1978) PhD thesis which included 21 cm rotation curves for a large sample of galaxies, including about 20 disk galaxies to unprecedented radial scales. This thesis was widely circulated at the time and remains the 2nd most cited PhD in the history of astronomy. Bosma concludes “The mass models indicate that in the outer parts of a spiral the mass-to-light ratio is higher than in the inner parts. Perhaps a substantial fraction of the mass is not distributed in a disk at all.”

From 1978 to 1985, Rubin and collaborators wrote influential papers presenting a large sample of optical rotation curves, many of which exhibit flat rotation on radial scales comparable to Bosma’s H${\scriptstyle \mathrm I}$ data and consistent with dark matter (cf. Kalnajs 1983). Rubin considered both disk and spherical models and recognized the possible implication of massive halos around spirals to large radius, an insight that they credit to the Einasto and Ostriker papers. In the same year as Bosma’s thesis, Rubin et al. (1978) state:

These results take on added importance in conjunction with the suggestion of Einasto et al. (1974) and Ostriker et al. (1974) that galaxies contain massive halos extending to large radius. Such models imply that the galaxy mass increases significantly with increasing radius which in turn requires that rotational velocities remain high for large radius. The observations presented here are thus a necessary but not sufficient condition for massive halos. The developments of the 1970s, in large part because of the phenomenon of flat rotation curves, paved the way for the cold dark matter paradigm in the following decade.

Today, the nature of dark matter remains unclear although one or more sub-atomic particles appear to be the most likely candidates. Examples include the hypothetical axion, neutralino, or a weakly interacting massive particle (WIMP), perhaps 100 times the mass of the proton, predicted by extensions of the Standard Model. WIMPs may be their own antiparticles and therefore capable of mutual annihilation, an effect that can be searched for with gamma ray satellites. The most recent $\varLambda$CDM simulations involving as many as 1010 particles reveal that dark haloes are likely to be highly structured and clumpy. Recent experiments with the Fermi gamma ray satellite to search for decaying dark matter (assuming a decay channel involving photons) has drawn a blank. A recent review by Abbasi et al. (2012) puts stringent limits on all dark matter candidates to date.

In summary, Ostriker was arguably the most persistent champion of dark haloes in the early 1970s. While no single result was compelling, taken together, the case for dark haloes appeared to be strong, as discussed in his 1974 paper. Most but not all of the arguments have held up with the passage of time (Tremaine 1999). For example, Turner’s (1976a, b) arguments based on binary galaxies were undermined by White (1981, 1983): the derived masses are plagued by uncertain orbits, contamination, selection effects and so on. In the same vein, Ostriker and Peebles (1973)¹⁴ wrote an influential paper on the stabilizing influence of dark haloes against bar modes. They fully understood that a disk could be stabilized by its internal velocity dispersion (e.g. Hohl 1970) but the Q parameter required is much larger than observed. Bars are not a solution either: the stable barred galaxies that they found were again much hotter than observed bar galaxies. (What could conceivably undermine their result is a rotation curve with a sharp bend near the centre, i.e. with a very small uniformly rotating core. This was demonstrated by Toomre and Sellwood in the 1980s.) Today we know that bars occur in a high fraction of disk galaxies (Eskridge et al. 2000) so it seems unlikely that dark haloes are successful in stabilizing disks against bar modes.

Appendix B: Stellar Data: Sources and Techniques

1.1.1 B.1 Data Needed for Galactic Archaeology

Our goal is to use relic or fossil information to evaluate the state of the Galaxy and understand how it got to be in this state. We want to answer questions such as

• What were the major formation events?

• How important was the role of mergers?

• What was the infall history and the star formation history?

• What were the major dynamical and chemical evolution processes?

To answer these questions, we need stellar data to compare with theoretical predictions and to guide the theory. The basic stellar data that we need are the magnitudes and colours of the stars, their distances, motions and chemical properties, and their ages. We will look first at which each kind of data can do for us, and then at the techniques for acquiring the data.

1.1.1.1 B.1.1 Stellar Photometry: Magnitudes and Colours of Stars

Photometric catalogues are essential input data for stellar observational programs. They give magnitudes and colours for up to billions of stars over the whole sky or large fractions of the sky. The catalogues typically have stellar coordinates and photometry in two or more optical or near-IR bands, at different levels of accuracy.

Fig. 1.32

Distribution of metallicity in the Galaxy from SDSS photometry (from Ivezic et al. 2008)

They can be used to make preliminary estimates of stellar parameters like temperature and chemical abundance and distance for vast numbers of stars. From photometric catalogues alone, it is possible to derive useful information about the structure of the Galaxy. For example, the 5-band ${ ugriz}$ photometry from the Sloan Digital Sky Survey has been used to derive the distribution of stars and their overall chemical abundances in the Galaxy. Ivezic et al. (2008) estimated photometric distances and [Fe/H] abundance for $2.5$ million FG stars from the SDSS to derive the distribution of abundance and of positions $(R,z)$ out to distances of about $8$ kpc from the Sun. Their map (Fig. 1.32) nicely shows the planar stratification of [Fe/H] in the Galaxy, decreasing with height above the Galactic plane. The Monoceros concentration of relatively metal-poor stars at a Galactocentric distance of about 16 kpc can also been seen in their data.

1.1.1.2 B.1.2 Stellar Distances: Where Do Stars Lie

We need stellar distances to

• measure transverse velocities of stars from their proper motions

• map substructure in the halo and disk

• calibrate the luminosities of different kinds of stars

• measure the structure and dynamics of the Galactic components.

1.1.1.3 B.1.3 Stellar Motions

The basic data are the stellar radial velocities and proper motions. With an estimate of distance, it is possible to calculate the 3D space motions. The motions of stars are used to

• measure how energetic the orbits of particular kinds of stars are, and how far they are from circular motion

• measure the sense of their angular momentum: prograde or retrograde

• see how stellar orbits have evolved: how do the orbital properties correlate with age and metallicity

• detect kinematic substructure, such as moving stellar groups

• compute stellar orbits to learn about the dynamical structure of the Galaxy.

• measure the properties of the Galactic potential from their spatial and kinematic distributions. In this way, the dark matter content of the Galaxy can be measured from the kinematics and distribution of distant halo stars, and the total density of luminous and dark matter near the sun can be estimated from the properties of nearer disk stars.

Fig. 1.33

The Lindblad diagram shows orbital energy and angular momentum for Galactic disk and halo stars. Very energetic halo stars lie towards the top of the diagram; some halo stars are in retrograde orbits ($L_z < 0$). Disk stars lie near the prograde circular orbit locus (the black curve on the right). The sun is located near the “8” on the prograde circular orbit locus. The energy $E$ and angular momentum component $L_z$ are both integrals of the motion in a steady-state axisymmetric galaxy (from Morrison et al. 2009)

Fig. 1.34

The Toomre diagram for nearby stars of the thin (open symbols) and thick (filled symbols) disk. The $V$ component of the stellar velocity represents the stellar angular momentum and has an asymmetric distribution with a negative mean: this asymmetric drift increases with velocity dispersion and is a useful diagnostic. The $U$ and $W$ components have more or less symmetric distributions about zero mean, so their combination is a measure of the orbital energy (from Bensby et al. 2005)

Fig. 1.35

A typical stellar orbit in an axisymmetric potential (adapted from Binney and Tremaine 2008)

Figure 1.33 shows the Lindblad diagram (orbital energy against angular momentum) for a sample of halo and disk stars. This diagram can be constructed for stars with known motions, and is a very useful diagnostic of the dynamical properties of different stellar populations. It is immediately clear if stars are in near-circular orbits, retrograde orbits, or highly energetic orbits. The Toomre diagram (Fig. 1.34) is another diagram derived from stellar kinematics and is much used to identify to which Galactic component (thin disk, thick disk, halo) a star belongs. Here $(U,V,W)$ are components of the star’s motion relative to the Local Standard of Rest: $U$ is in the Galactic radial direction (towards $l = 0^\circ$ or $180^\circ$ depending on the convention), $V$ in the direction of rotation (towards $l = 90^\circ$) and $W$ in the vertical direction towards the North Galactic Pole. Stars of the thin disk are clustered towards low velocities, while the stars of the thin disk are hotter kinematically.

If we know the 3D location and velocity for a star, and have a reliable model for the Galactic gravitational potential, then we can compute the Galactic orbit of the star. Figure 1.35 shows the plane and edge-on view of a typical stellar orbit. Stars from the inner and outer Galaxy can pass through the solar neighborhood. Knowing the orbit is not always very useful for Galactic archaeology. There is no guarantee that the dynamical properties of a star have remained unchanged throughout the life of the star. The Galactic potential has evolved as the Galaxy’s mass has gradually increased by accretion of baryonic and dark matter. Stellar orbits can be disturbed as the star interacts with spiral structure and giant molecular clouds, and resonances with the central bar and the spiral structure can flip a star from one near-circular orbit to another.

Fig. 1.36

The cosmic abundance distribution, showing structure due to the major chemical evolution processes

1.1.1.4 B.1.4 Stellar Element Abundances

The cosmic abundance distribution in Fig. 1.36 shows the outcome (in the solar neighborhood) of the chemical evolution of our Galaxy. The element abundances of stars come initially from the abundances in the gas from which they formed. This gas has been enriched by previous generations of evolving and dying stars. Different element groups come from different progenitors.

• the Fe-peak elements come mainly from type Ia SN

• the $\alpha$-elements (e.g. Mg, Si, Ca, Ti) and r-process elements come mainly from the more massive type II SN

• the s-process elements come mainly from thermally pulsing AGB stars

For most of the heavier elements, stars remember the abundances with which they are born. The abundances of different element groups in stars can tell us a lot about the star formation history which led to the formation of these particular stars. For example, $\alpha$-enrichment relative to Fe indicates that SNII were important for the chemical evolution and the star formation history was fairly rapid, on a timescale of order $1$ Gyr: Fe-enrichment from SNIa (which take $\sim$1 Gyr to evolve) was less prominent.

Different components of the Galaxy (halo, bulge, thick disk, thin disk) each have different characteristic chemical properties. For example, the halo stars are mostly metal poor ($-1 >$ [Fe/H] $> -5$), while the thick disk stars are more metal rich ($-0.2 >$ [Fe/H] $> -2$). The halo and thick disk stars are both enriched in $\alpha$-elements (Mg, Si, Ca, Ti). The [Fe/H] range of the thin and thick disks overlap; the thick disk stars have higher [$\alpha$/Fe] ratios than thin disk stars of the with similar [Fe/H] abundances, indicating that the chemical evolution of the thick disk proceeded more rapidly.

Groups of stars born together, like open star clusters, usually have almost identical abundances, reflecting the abundances of the gas from which they formed (e.g. De Silva et al. 2009). This is true also for most of the globular clusters: a few have heavy element variations from star to star, and many show correlated variations of lighter elements such as C, N, O, Na, Mg, Al, the origin of which are not full understood yet. Chemical signatures may allow us to recognize groups of stars which were born together but have dispersed and drifted apart . This technique is known as chemical tagging and will be used for analysing the products of large high resolution spectroscopic surveys like the HERMES survey on the AAT and the APOGEE near-IR survey with the Sloan telescope. Although it is readily possible to measure abundances of more than 30 elements, these elements do not all vary independently. The number of independently varying elements is 8–9 (Ting et al. 2012): this is the dimensionality of the space defined by the abundances of the chemical elements.

1.1.1.5 B.1.5 Stellar Ages

Stellar ages let us evaluate when events occurred in the evolution of the Galaxy. They are important for measuring the star formation history and for understanding how the metallicity and dynamics of different groups of stars have evolved. For example, how has the star formation rate in the disk of the Galaxy evolved since the disk began to form? The star formation rate is believed to have been roughly constant over time near the sun, with episodic star bursts over the past 10 Gyr (e.g. Rocha-Pinto et al. 2000) but this remains uncertain because of uncertain ages. How have the kinematics and the metallicity of the thin disk near the sun changed from 10 Gyr ago to the present time under the effects of dynamical and chemical evolution? Again, the kinematics and metallicities are not difficult to measure, but the derivation of stellar ages remains problematic. Because stellar ages are still difficult to measure, there remains much uncertainty about the evolution of the Galaxy. Measuring stellar ages is one of the most important goals for Galactic evolution for the future.

1.1.2 B.2 Sources of Data

Now we turn to the sources of the various kinds of data needed for Galactic archaeology.

1.1.2.1 B.2.1 Photometric Catalogs

Here is an incomplete list of some of the major photometric catalogs.

2MASS is a relatively shallow all-sky near-IR (JHK) survey and includes a point source catalog. This catalog is notable for its excellent astrometry and is an invaluable source of stars for brighter spectroscopic surveys. The UKIDSS survey (${ YJHK}$) is a deeper survey of 7500 square degrees of northern sky. The VISTA VHS survey (JK) is still in progress and will also go significantly deeper.

The Sloan Digital Sky Survey (SDSS) covers about 8000 square degrees, mainly in the northern sky. It uses a 5-filter system (${ ugriz}$) which has become a standard system. The Pan-STARRS project will survey about 30,000 square degrees, again mainly in the northern sky, using ${ grizy}$ filters. In the future, the LSST will provide a very deep survey of the whole southern sky with ${ ugrizy}$ filters. In the meantime, the SkyMapper survey will cover the southern sky several times, using a six-filter system (${ uvgriz}$), reaching somewhat deeper than the SDSS.

1.1.2.2 B.2.2 Techniques for Measuring Distances

Trigonometric parallaxes. The stellar distance scale (and the extragalactic distance scale) are based on fundamental trigonometric parallaxes. Stellar positions are measured from the extremes of the earth’s orbit around the sun (see Fig. 1.37). Because this technique is used for relatively nearby stars, it is usually necessary to continue the observation for several seasons, in order to separate out the shifts in position due to parallax from the shifts due to the star’s transverse or proper motion. From the ground, parallax errors of a few milli-arcseconds (mas) can be achieved, giving distances with 10 % errors out to about 30 pc from the sun.

Fig. 1.37

Geometry of parallax measurement

From space, higher precision is possible. The Hipparcos mission provided parallaxes with errors of about 1 mas. The Gaia mission, due for launch in 2013, will give parallax errors of about 10 $\upmu$ as at a $V$-magnitude of about 14. Parallaxes with this level of accuracy will be useful out to distances of about $10$ kpc. For turnoff stars with $V \sim 14$, the distances will be known to within about 1 %. The Gaia parallax errors are larger for fainter stars.

Photometric and spectroscopic parallaxes. Theoretical or empirical isochrones are used to estimate the absolute magnitude and hence the distance of the star. To make this work well, one needs to know the abundance [Fe/H] of the star, and an estimate of its effective temperature and surface gravity or luminosity. These can all be derived from multi-filter photometry or spectroscopy. An assumption of the star’s age is needed if the star has evolved from the main sequence.

The more one knows, the better this works. If only broad-band colors are known, the distance errors can be very large. In the best cases, when the errors are $\sim$0.1 in [Fe/H], $100$ K in temperature and $0.1$ in $\log g$, distance errors of about $15$ % can be achieved. For stars on the steep giant branch, the distance estimates are usually less accurate.

For some kinds of stars, like the He-core burning RR Lyrae stars, blue horizontal branch stars and red giant branch clump (RGBC) stars, accurate absolute magnitudes are known or can be estimated from periods and colors, and the errors in their photometric distances can be $<$10 %. RR Lyr and BHB stars are usually found in more metal-poor populations like the Galactic halo and thick disk. RGBC stars are particularly useful for studies of galactic structure in the more metal-rich populations because they are so common and it is easy to measure their element abundances.

For star clusters, one can fit theoretical isochrones to their color-magnitude diagrams to derive ages and distances if their metallicities are known. Globular clusters mostly have horizontal branch stars or RR Lyr stars from which accurate distances can be derived.

Interstellar reddening and extinction are a problem for photometric parallaxes. This problem is less significant in the near-infrared. Multicolor photometry can give independent stellar reddening estimates if the wavelength dependence of reddening is known. For individual stars, the diffuse interstellar bands can be used to estimate the reddening directly (e.g. Munari et al. 2008). The reddening can also be derived from reddening maps of the Galaxy, like the Schlegel et al. (1998) maps derived from the COBE/DIRBE near-IR mapping of the Milky Way. These maps give the total reddening along each line of sight. For stars that are located within the reddening layer, correction is needed via models of the reddening distribution along the line of sight.

1.1.2.3 B.2.3 Techniques for Measuring Stellar Velocities

Radial (line of sight) velocities are measured spectroscopically via the Doppler shift. Proper (transverse) motions are measured astrometrically from the shift of a star’s position with time relative to a set of reference stars, and are usually measured from wide field photographic or CCD images.

Some large stellar radial velocity surveys are in progress for Doppler planet searches and for Galactic structure and dynamics. The fiber spectrograph surveys SEGUE , and RAVE surveys are observing several $\times 10^5$ stars for Galactic structure and chemical evolution. The LAMOST survey is one or two orders of magnitude larger. Radial velocities have typical accuracies ranging from about $1$ m s$^{-1}$ with special techniques at spectroscopic resolution $R = \lambda /\varDelta \lambda \sim$ 50,000 to $1$ km s$^{-1}$ at $R \sim 7000$ (RAVE) and $5$ km s$^{-1}$ at $R \sim 2000$ (SEGUE, LAMOST). For most Galactic programs, $5$ km s$^{-1}$ is good enough. For some programs, like finding the kinematically cold debris of tidally disrupting star clusters, an accuracy of $1$ km s$^{-1}$ can be very useful. Spectra acquired for radial velocities can also give useful estimates of the stellar parameters $T_\mathrm{eff}, \log g$ and [Fe/H].

From the ground, the proper motion accuracy can be a few mas yr$^{-1} ~( \sim \!20$ km s$^{-1}$ at a distance of $1$ kpc). Very large samples of proper motions ($10^5$ to $10^9$ stars) come from many ground-based surveys, such as USNO, UCAC2, SPM, SDSS, 2MASS, GSC, PM2000, PPMXL ...with more to come from the large imaging surveys Pan-STARRS, SkyMapper and LSST.

From space, the Hipparcos/Tycho mission provided proper motions of about $2$ million stars, with an accuracy of about $1$ mas yr$^{-1}$. The Gaia mission will give proper motions for about a billion stars: the accuracy depends on the brightness and color of the star, and is about $10\,\upmu$ as yr$^{-1}$ at $V = 14$ (i.e. about $0.7$ km s$^{-1}$ for a bright giant at a distance of $15$ kpc). Gaia will really change Galactic astrophysics, with vast numbers of very precise parallaxes and proper motions. We should be prepared to get the most from this resource (launch is due in 2013). The JASMINE missions are smaller near-IR astrometric space projects, aimed particularly at the Galactic plane and bulge.

1.1.2.4 B.2.4 Techniques for Measuring Chemical Abundances

Intermediate and broad band photometry, such as the Strömgren photometry and the SDSS/SkyMapper photometry, can give estimates of stellar temperature, gravity and metallicity. The typical metallicity errors are about $0.2$ dex but can be smaller. Figure 1.38 shows how the passbands of the $uvgr$ filters of the SkyMapper and SDSS systems align with features in FGK stars. Examples of photometric surveys that have generated large samples of stellar abundances are the Geneva-Copenhagen survey (GCS) of about 14,000 nearby FG dwarfs using Strömgren photometry complemented with Hipparcos astrometry and precise groundbased radial velocities (Nordström et al. 2004), and the large study of the Galactic abundance distribution by Ivezic et al. (2008) using DSS data.

Medium resolution spectroscopy ($R \sim$ 2000–10,000) uses the strengths of spectral features to estimate stellar parameters, including [Fe/H] and sometimes [$\alpha$/Fe] and a few other elements. Recent examples are the RAVE and SEGUE surveys of several $\times \!10^5$ stars. Various techniques are used to measure the stellar parameters, including empirical calibration of individual line strengths and $\chi ^2$ matching of the spectra to grids of synthetic spectra. The [Fe/H] errors are typically about $0.15$ dex. Several of the medium resolution spectroscopy facilities can acquire spectra of many stars at once. For example, the AAOmega spectrometer on the AAT is fed by optical fibers and can measure medium resolution spectra of up to about 400 stars simultaneously in a 2$^{\circ }$ diameter field.

High resolution spectroscopy ($R >$ 20,000) allows measurement of abundances for many elements, including the important neutron-capture elements. Many of these elements have relatively weak lines which are difficult to measure at lower resolutions. It is also possible to measure isotopic abundances for some elements, and these can be good diagnostics of nuclear processes. From high resolution spectra with high signal-to-noise ratios, it is possible to measure differential abundances with an error as low as 0.02 dex in the element abundance ratios [X/Fe] when comparing stars of similar temperatures and gravities. Techniques include analysis of equivalent widths of individual spectral lines and matching synthetic spectra in detail to the observed spectra. The newly developed MATISSE method (Recio-Blanco et al. 2006) involves projection of the spectra onto basis vectors to derive the individual parameters.

High resolution spectrographs are usually echelle spectrographs, some with a few hundred fibers for multi-object capability. Existing systems include Hectochelle on the MMT, MIKE and MIKE-fibers on Magellan, and the FLAMES/GIRAFFE/UVES system on the VLT. HERMES on AAT and APOGEE on the Sloan telescope are coming soon and will be used for large high-resolution spectroscopic surveys of $10^5$ to $10^6$ stars at resolutions of 20,000 (APOGEE, in the NIR H-band) to 30,000 (HERMES in optical bands). HERMES will also have a $R=$ 48,000 multi-object capability. The analysis of high resolution spectra is currently laborious, but this will change as pipelines are developed for the coming high-resolution surveys of large samples of stars.

Fig. 1.38

The filter passbands of the SkyMapper and SDSS filter system are aligned with the spectrum of a cooler star to show how the passbands are located relative to features in the spectrum of the star

Currently available compilations of high resolution abundance data for nearby stars include those by Venn et al. (2004: 781 stars) and Soubiran and Girard (2005: 743 stars).

For large optical high-resolution surveys, FGK stars with $T_\mathrm{eff}=$ 4000–6500 K are usually selected. These stars are cool enough to have plenty of lines and warm enough for analysis to be relatively straightforward. Hotter stars have mostly weaker metallic lines and are often younger and rotating which broadens the lines and makes weak lines difficult to measure. Cooler stars have complex atmospheres with molecules: they are more difficult to analyse from optical spectra, and are better studied in the near-IR, which is also much less affected by interstellar extinction. The infrared is not so good for neutron capture elements.

This is a very brief overview of high resolution spectroscopy and has not attempted to address the many issues involved in abundance analysis related to the physics of energy transfer in stellar atmospheres. The study of hotter and cooler stars are each major specialties in astrophysics.

1.1.2.5 B.2.5 Techniques for Measuring Stellar Ages

Measuring ages for individual stars remains difficult; see Soderblom (2010) for a comprehensive review.

Nuclear cosmochronology is a fundamental technique for estimating ages: the observed ratios of radioactive and stable species (e.g ratio of Th to U) are compared to the expected production ratios from nucleosynthesis theory. The technique has been used on a few stars. The expected production ratios from theory are somewhat uncertain.

Asteroseismology uses the spectrum of stellar oscillations to estimate the stellar age. The frequency spectrum depends on the structure of the stellar interior, which changes as the star ages. Accurate photometry at the $\mu$mag level is needed and is usually done from space. The asteroseismology space missions (CoRoT, Kepler) promise to derive stellar ages with 5–10 % errors. The technique works for main sequence and giant stars for which it is otherwise difficult to determine reliable ages.

Stellar activity and rotation are useful estimators of stellar age. Stars spin down as they age, with rotation periods that typically increase roughly as (age)$^{1/2}$. The rotation periods are measured photometrically or spectroscopically, and the relation between rotation period and age is calibrated empirically on star clusters and the Sun (see Barnes 2007). Chromospheric activity (usually measured from Ca K emission) is associated with rotation and decreases with age. It was much used in the past but is believed to be less accurate for older stars. Figure 1.17 compares rotational (gyro) ages and chromospheric ages for a sample of well studied stars.

If the stellar temperature, metallicity and luminosity (or surface gravity) are known, it is possible to estimate the age of a star from isochrones. In its most direct form, the trigonometric parallax gives the absolute magnitude and hence the stellar luminosity $L$ after bolometric correction. Photometry or spectroscopy gives the temperature $T_\mathrm{eff}$ and the metallicity. One then compares the location of the star in the $L-T_\mathrm{eff}$ plane with theoretical isochrones for the appropriate metallicity. This works if the star is in a region of the $L-T_\mathrm{eff}$ plane where the luminosity and temperature depend on age, so it does not work on the unevolved main sequence and not well on the upper giant branch. It can be used for evolved stars which are still close to the main sequence, but accurate temperatures are needed. As seen in Fig. 1.39, one needs to beware of regions near the turnoff where the isochrones cross and the estimated ages can be multi-valued. Subgiants are well suited to isochrone aging because the isochrones are well separated on the subgiant branch: see Fig. 1.39. The Gaia mission will provide a huge increase in the numbers of stars for which accurate luminosities are known, and for which accurate isochrone ages can be derived. Recall that the Gaia distance errors will be about 1 % at $V = 14$.

Fig. 1.39

Isochrones from Bertelli et al. (1994) for stars of near-solar abundance and a range of ages from 1.6 to 16 Gyr. The isochrones can overlap near the turnoff are well separated in the subgiant region

If parallaxes are not available, isochrone ages can be measured by using the isochrones in the surface gravity—temperature plane. The gravity $g$ is related to the luminosity, mass and temperature by $L = 4 \pi G M a T_\mathrm{eff}^4/g$ where $a$ is the Stefan-Boltzmann constant and $M$ the stellar mass. The gravity can be measured spectroscopically with a typical error in $\log g$ of about $0.3$ for medium resolution spectra and 0.1–0.2 for high resolution spectroscopy. Age errors of about 25 % can be achieved in this way.

Large biases can occur in isochrone ages if the errors in $L$ or $\log g$, temperature and abundance are significant. These occur because the underlying distributions of stellar mass and abundance are not uniform. They reflect the stellar initial mass function, Galactic density distribution and metallicity distribution function. Bayesian techniques can include these underlying mass distributions as priors: see Pont and Eyer (2004).

For populations of stars, such as white dwarfs of the disk, and for clusters of stars, other techniques can be used. The luminosity function of a population of white dwarfs can be used to estimate its age; as the white dwarfs cool and fade, their luminosity function evolves in a predictable way. At the faint end, the white dwarf luminosity function drops rapidly, and the luminosity at which it drops is a measure of the age of the white dwarf population. For example, Leggett et al. (1998) use the luminosity function of white dwarfs in the disk to estimate that the oldest disk stars are about $9$ Gyr old. For open and globular clusters, the color-magnitude diagram defines an empirical isochrone which can be dated by comparison with theoretical isochrones of the same metallicity.

1.1.3 B.3 Sources of Models

In this section we will briefly discuss stellar atmosphere models, theoretical isochrones and Galactic models which are important tools for Galactic archaeology.

1.1.3.1 B.3.1 Stellar Atmosphere Models

Model atmospheres and synthetic spectra are used for deriving element abundances and other stellar parameters from medium and high resolution spectra by comparison with observed spectra. The most widely used synthetic spectra come either from the Kurucz models (e.g. Munari et al. 2005) or the MARCS models (marcs.astro.uu.se). The models available at this time are one-dimensional local thermodynamic equilibrium (LTE) models, giving flux vs wavelength at various spectral resolutions for a wide range of stellar parameters. For example, the RAVE pipeline works by fitting the observed spectra ($R \sim 7000$, SNR $\sim 40$) in the Ca triplet region (840–880 nm) to a grid of such models. The internal accuracy of these fits is about $0.1$ in [M/H], 0.2 in $\log g$ and $135$ K in $T_\mathrm{eff}$.

1.1.3.2 B.3.2 Isochrone Models

Isochrones are derived from stellar evolution models. Some of the widely used isochrone libraries come from the Padova, Dartmouth, Victoria-Regina, BaSTI, Geneva and Yale-Yonsei models. They can be found on the www and give isochrones of chosen age metallicity and sometimes [$\alpha$/Fe], typically tabulating the stellar mass, bolometric luminosity, temperature, gravity, absolute magnitude in various photometric systems, and sometimes useful derived quantities such as the number of stars per solar mass of system at each step along the isochrone.

1.1.3.3 B.3.3 Galactic Models

Galactic models are constructed to represent the stellar density distribution, kinematics and reddening of the various components of the Galaxy. They are used to simulate observations such as star counts and kinematics and are very useful for planning large surveys. Widely used examples include the Besançon model (Robin et al. 2003), the TRILEGAL model (Girardi et al. 2005) and the Galaxia model (Sharma et al. 2011). Stellar evolution models are part of these Galactic models.

Generating a synthetic catalog of stars in accordance with a given model of galaxy formation has a number of uses. First, it helps to interpret the observational data. Secondly, it can be used to test the theories upon which the models are based. Moreover synthetic catalogs can be used to test the capabilities of different instruments, check for systematics and device strategies to reduce measurement errors. This is well understood by the architects of galaxy redshift surveys who rely heavily on $\varLambda$CDM simulations to remove artefacts imposed by the observing strategy (e.g. Colless et al. 2001).

Given the widespread use of synthetic catalogs, a need for faster and accurate methods to generate such synthetic catalogs has recently arisen due to the advent of large scale surveys in astronomy, e.g., future surveys like LSST and GAIA have plans to measure over 1 billion stars. In order to generate a synthetic catalog, one first needs to have a model of the Milky Way. While we are far from a dynamically consistent model, a working framework is fundamental to progress. Inevitably, this will require approximations or assumptions that may not be mutually consistent. Cosmologists already accept such compromises when they relate the observed galaxies to the dark-matter test particles that emerge from cosmological simulations.

There have been various attempts over the past few decades to create a Galaxy model that is constrained by observations. The earliest such attempt was by Bahcall and Soneira (1984) where they assumed an exponential disc with magnitude dependent scale heights. An evolutionary model using population synthesis techniques was presented by Robin and Creze (1986). Given a star formation rate (SFR) and an initial mass function (IMF), one calculates the resulting stellar populations using theoretical evolutionary tracks. Local observations were then used to constrain the SFR and IMF. Bienayme et al. (1987) later introduced dynamical self consistency to constrain the disc scale height (cf. Bertelli et al. 1995).

The present state of the art is described in Robin et al. (2003) and is known as the Besançon model. Here the disc is constructed from a set of isothermal populations that are assumed to be in equilibrium. Analytic functions for density distributions, the age/metallicity relation and the IMF are provided for each population. A similar scheme is also used by the photometric code Trilegal by Girardi et al. (2005).

In spite of its popularity, the current Besançon model has important shortcomings. A web interface exists to generate synthetic catalogs from the model but it has limited applicability for generating wide area surveys and the output is not drawn correctly from a statistical distribution. Discrete step sizes for radial, and angular coordinates-ordinates need to be specified by the user and results might differ depending upon the chosen step size. The scale height and the velocity dispersion of the disc are in reality a function of age but, due to computational complexity, the disc is modeled as a finite set of isothermal discs of different ages. Increasing the number of discs enhances the smoothness of the model but at the price of computational cost (Girardi et al. 2005).

In addition to the disc components, one also needs a model of the stellar halo. Under the hierarchical structure formation paradigm, the stellar halo is thought to have been produced by numerous accretion events and signatures for which should be visible as substructures in the stellar halo. Missions like GAIA, LSST and PanSTARRS are being planned which will enable us to detect substructures in the stellar halo.

A smooth analytic stellar halo as in the Besançon model is inadequate for testing schemes of substructure detection. Furthermore, such a halo does not accomodate known structures like the Sagittarius dwarf stream which may constitute a large fraction of the present halo (Ibata et al. 1995; Chou et al. 2010). Substructures have complex shapes and hence to model them we cannot use the approach of analytic density distributions as discussed earlier. However, N-body models are ideally suited for this task. Brown et al. (2005) attempted to combine a smooth galaxy model with some simulated N-body models of disrupting satellites, but the stellar halo was not simulated in a proper cosmological context.

Recently, using hybrid N-body techniques, Bullock and Johnston (2005) have produced high resolution N-body models of the stellar halo which are simulated within a cosmological context; see also Cooper et al. (2009) and (De Lucia and Helmi 2008) for a similar approach. These can be used to make accurate predictions of the substructures in the stellar halo and also test the $\varLambda$CDM paradigm. However, as highlighted by Brown et al. (2005) there are several unresolved issues related to sampling of an N-body model which has prevented their widespread use.

The new Galaxia code (Sharma et al. 2011) allows for fast and accurate methods to convert analytic and N-body models of a galaxy into a synthetic catalog of stars. This relieves the burden of generating catalogs from modelers on one hand and on the other hand allow the testing of models generated by different groups. This is a new scheme for sampling the analytical models which enables the user to generate continuous values of the variables like position and age of stars. Instead of a set of discs at specified ages, our methodology allows us to generate a disc which is continuous in age.

As a concrete example, Sharma et al. (2011) demonstrate the Besançon analytical model for the disc. To model the disc kinematics more accurately, Galaxia employs the Shu (1969) distribution function that describes the non-circular motion in the plane of the disc. This function has now been generalised for a range of rotation curves (Sharma and Bland-Hawthorn 2013). For the stellar halo, Galaxia uses the simulated N-body models of Bullock and Johnston (2005) which can reproduce the substructure in the halo. We show a scheme for sampling the N-body particles such that the sampled stars preserve the underlying phase space density of N-body particles.

Another powerful aspect of Galaxia is the use of Markov Chain Monte (MCMC) Carlo methods that allow the determination of many parameters from model fitting applied to a large stellar survey. For the first time, we find that two very different, large stellar surveys (GCS, RAVE) yield the same kinematic parameters for the local disk (Sharma et al. 2013). Moreover, the more spatially extended RAVE data demand the use of a Shu distribution function to yield meaningful results. This has strong parallels with MCMC analysis of galaxy redshift surveys in the context of $\varLambda$CDM simulations. In time, it will be possible to apply MCMC model fitting of the most detailed Galaxy simulations to stellar surveys which of course reinforces the remarkable complementarity between near-field and far-field cosmology.

Finally, we would like to commend the ESA-ESO Working Group Report 4: Galactic Populations, Chemistry and Dynamics (Turon and Primas 2008). This is a very useful compendium of the major problems in Galactic astronomy, ways to attack them, and major surveys past, present and future.