Abstract
Comets have three known reservoirs: the roughly spherical Oort Cloud (for long-period comets), the flattened Kuiper Belt (for ecliptic comets), and, surprisingly, the asteroid belt (for main-belt comets). Comets in the Oort Cloud were thought to have formed in the region of the giant planets and then placed in quasi-stable orbits at distances of thousands or tens of thousands of AU through the gravitational effects of the planets and the Galaxy. The planets were long assumed to have formed in place. However, the giant planets may have undergone two episodes of migration. The first would have taken place in the first few million years of the Solar System, during or shortly after the formation of the giant planets, when gas was still present in the protoplanetary disk around the Sun. The Grand Tack (Walsh et al. in Nature 475:206–209, 2011) models how this stage of migration could explain the low mass of Mars and deplete, then repopulate the asteroid belt, with outer-belt asteroids originating between, and outside of, the orbits of the giant planets. The second stage of migration would have occurred later (possibly hundreds of millions of years later) due to interactions with a remnant disk of planetesimals, i.e., a massive ancestor of the Kuiper Belt. Safronov (Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets, 1969) and Fernández and Ip (Icarus 58:109–120, 1984) proposed that the giant planets would have migrated as they interacted with leftover planetesimals; Jupiter would have moved slightly inward, while Saturn and (especially) Uranus and Neptune would have moved outward from the Sun. Malhotra (Nature 365:819–821, 1993) showed that Pluto’s orbit in the 3:2 resonance with Neptune was a natural outcome if Neptune captured Pluto into resonance while it migrated outward. Building on this work, Tsiganis et al. (Nature 435:459–461, 2005) proposed the Nice model, in which the giant planets formed closer together than they are now, and underwent a dynamical instability that led to a flood of comets and asteroids throughout the Solar System (Gomes et al. in Nature 435:466–469, 2005b). In this scenario, it is somewhat a matter of luck whether an icy planetesimal ends up in the Kuiper Belt or Oort Cloud (Brasser and Morbidelli in Icarus 225:40–49, 2013), as a Trojan asteroid (Morbidelli et al. in Nature 435:462–465, 2005; Nesvorný and Vokrouhlický in Astron. J. 137:5003–5011, 2009; Nesvorný et al. in Astrophys. J. 768:45, 2013), or as a distant “irregular” satellite of a giant planet (Nesvorný et al. in Astron. J. 133:1962–1976, 2007). Comets could even have been captured into the asteroid belt (Levison et al. in Nature 460:364–366, 2009). The remarkable finding of two “inner Oort Cloud” bodies, Sedna and 2012 \(\mbox{VP}_{113}\), with perihelion distances of 76 and 81 AU, respectively (Brown et al. in Astrophys. J. 617:645–649, 2004; Trujillo and Sheppard in Nature 507:471–474, 2014), along with the discovery of other likely inner Oort Cloud bodies (Chen et al. in Astrophys. J. Lett. 775:8, 2013; Brasser and Schwamb in Mon. Not. R. Astron. Soc. 446:3788–3796, 2015), suggests that the Sun formed in a denser environment, i.e., in a star cluster (Brasser et al. in Icarus 184:59–82, 2006, 191:413–433, 2007, 217:1–19, 2012b; Kaib and Quinn in Icarus 197:221–238, 2008). The Sun may have orbited closer or further from the center of the Galaxy than it does now, with implications for the structure of the Oort Cloud (Kaib et al. in Icarus 215:491–507, 2011).
We focus on the formation of cometary nuclei; the orbital properties of the cometary reservoirs; physical properties of comets; planetary migration; the formation of the Oort Cloud in various environments; the formation and evolution of the Kuiper Belt and Scattered Disk; and the populations and size distributions of the cometary reservoirs. We close with a brief discussion of cometary analogs around other stars and a summary.
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Notes
We generally use the term “Kuiper Belt Objects” in a broad sense to mean small bodies with semi-major axes outside of Neptune’s orbit, excepting inner Oort Cloud bodies like Sedna. “KBOs” thus include classical and resonant KBOs and Scattered Disk Objects. In most cases we follow the terminology of Gladman et al. (2008), except that they refer to bodies beyond Neptune as Trans-Neptunian Objects (TNOs). See Bierhaus and Dones (2015) for a summary of different types of KBOs and Sect. 6.1 for a comparison of dynamical classification schemes.
The term “pebble accretion” is used in studies of planet formation that assume planetesimals have already formed (e.g., Morbidelli et al. 2015; Bitsch et al. 2015). If “pebbles” are present in the solar nebula, the planetesimals may be able to grow rapidly into planetary “embryos,” the cores of the giant planets, or the terrestrial planets. The planetesimals, in turn, might consist of pebbles that clumped together through the streaming instability or other mechanisms that concentrate particles (Wahlberg Jansson and Johansen 2014). Within low-mass planetesimals, pebbles will collide at low speeds, so fragmentation will not occur and the planetesimal will remain a low-density “pebble pile” (Wahlberg Jansson and Johansen 2014; Hopkins 2014). Jacobson and Walsh (2015) define a pebble as a particle with Stokes number between 0.01 and 1. (These Stokes numbers correspond to particle radii \(r\approx0.8~\mbox{cm--}80~\mbox{cm}\) in the asteroid belt and 0.07–7 cm at 30 AU (Carrera et al. 2015), so the astrophysical use of the word “pebble” differs from its geological meaning.) The Stokes number of a particle in a flow, \(\mathit{St}\), is a measure of the particle’s “stopping time” \(\tau_{s}\) due to its interaction with the gas, relative to the particle’s orbital period. Specifically, \(\mathit{St} = \varOmega\tau_{s}\), where \(\varOmega\) is the particle’s orbital frequency and \(\varOmega= 2 \pi/T\), where \(T\) is the particle’s orbital period. When \(\mathit{St} \ll1\), the particle follows the flow, while for \(\mathit{St} \gg1\), the particle does not “feel” the gas. Carrera et al. (2015) find that the streaming instability can operate for \(0.003 \le \mathit{St}\leq0.3\), with the range depending on the solid-to-gas ratio in the disk. The biggest particles inferred in protoplanetary disks or seen to coagulate in experiments are only mm–cm sized. Carrera et al. (2015) therefore focus on formation of planetesimals from chondrules (typically \(r \approx0.3~\mbox{mm}\)), since half or more of the mass in many types of chondritic meteorites is in the form of chondrules. Johansen et al. (2015a) consider the growth of asteroids, Kuiper Belt Objects, and planetary embryos by accretion of chondrules.
We think an anonymous referee for calling our attention to the fascinating history of ideas about comets in the 17th century.
The “hyperbolic” comets were almost certainly on highly eccentric elliptical (“near-parabolic”) orbits. See Sect. 2.1 for discussion.
For a comet or asteroid with semi-major axis \(a\), eccentricity \(e\), and inclination \(i\) with respect to the orbital plane of a planet with semi-major axis \(a_{P}\), the Tisserand parameter \(T = a_{P}/a + 2 \sqrt{a(1 - e^{2})/a_{P}} \cos i\). We consider the Tisserand parameter of comets with respect to Jupiter, for which \(a_{P} \sim5.2~\mbox{AU}\). The Tisserand parameter is an approximation to the Jacobi integral, which is a constant of motion for the circular restricted three-body problem (Carusi et al. 1995).
Johnston explains his total as follows (W.R. Johnston, personal communication, 2015): “The comet numbers are my attempt to count all known comets, whether or not they have received IAUC/MPC designations. The categories include:
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Numbered comets—those periodic comets with permanent numbers, excluding Chiron and Echeclus which are counted among Centaurs.
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Provisional designations—those with official designations other than permanent numbers, old or new style, both long- and short-period, and including 15 letter-designated fragments of numbered comets.
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Without designations—known or suspected comets without IAUC designations, includes: SOHO/STEREO comets; distinct ancient/historical comets identified by Gary Kronk in the Cometography volumes but not identified with numbered/provisional comets; and “X” comets. Of those without designations, 456 are ones listed by Kronk from pre-modern observations, most of the remainder are SOHO comets.
Given that a number of SOHO comets have made identified returns, I do not delete sungrazers that are suspected but not proven to have disintegrated on perihelion passage (though …many, possibly most, have). Similarly, some comets given “D” designations have been rediscovered so I don’t automatically exclude these. I do exclude those known to have collided with Jupiter (25 Shoemaker-Levy 9 fragments) or the Sun (the latter based on a calculated perihelion below the Sun’s surface).”
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The term “inner Oort Cloud” is now used for bodies like Sedna with perihelion distances outside the orbits of the planets and semi-major axes of hundreds of AU (as opposed to thousands of AU for the inner cloud discussed by Hills 1981). The existence of “Sednas” is not expected in models in which the Sun formed as an isolated star. See Sects. 5 and 6 for further discussion.
Todorovic-Juchnicwicz (1981) found that the orbit of a long-period comet can be approximated well by a barycentric orbit neglecting planetary perturbations beyond distances of 150 to 200 AU from the Sun. The Polish group therefore tabulates orbital elements before and after a comet traverses the planetary region at a distance of 250 AU.
The activity of an individual Centaur may bear no clear relationship to its distance (\(r\)) from the Sun. A coma around Chiron was first detected in 1989 when Chiron was inbound at \(r \sim12~\mbox{AU}\). Activity decreased through perihelion at 8.5 AU in 1996 until 1999, and then increased in 2000 and 2001 when Chiron was 10–11 AU from the Sun (Duffard et al. 2002). Chiron appears to have been more active when it was near aphelion at 19 AU in the early 1970s (Bus et al. 2001). Many comets, including Centaurs such as Chiron and 29P/Schwassmann-Wachmann 1, undergo outbursts in which they brighten by several magnitudes or more (Gronkowski and Wesołowski 2015). Chiron probably was in outburst near its last aphelion passage (Prialnik et al. 2004).
Motivated by a model for the formation of super-Earths, Izidoro et al. (2014) proposed that the surface mass density of solids could have declined very rapidly with distance in the region of the terrestrial planets and the asteroid belt. This model explains the small mass of Mars, but predicts asteroid eccentricities and, particularly, inclinations that are smaller than the observed values (Izidoro et al. 2015). Levison et al. (2015b) have proposed yet another model, a variant of their “viscous stirred pebble accretion” idea (Levison et al. 2015), to explain the small mass of Mars and the asteroid belt.
Deienno et al. (2011) find that the uranian satellites out to Oberon, the outermost regular moon, would likely survive encounters with another ice giant and massive planetesimals during the Nice model, but hypothetical moons only a bit further from Uranus would have been destabilized. Gomes et al. (2012) find that if Neptune had a close encounter with Jupiter, Triton would have a 65 % chance of remaining bound to Neptune. If Uranus had a close encounter with Jupiter, all of the regular satellites would remain bound to Uranus about 60 % of the time. The orbital properties of the giant planet satellite systems can be used to constrain the nature of the planetary encounters that took place in the Nice model and its progeny such as the “jumping Jupiter” model (Deienno et al. 2014; Nesvorný et al. 2014; Cloutier et al. 2015).
Reyes-Ruiz et al. (2015) find shorter instability timescales (\({<} 70~\mbox{Myr}\)) using a different code (Mercury 6.5) to investigate this problem.
Shannon et al. (2015b) simulate the formation of the Oort Cloud with the planets in their present-day orbits and the Sun in its current galactic environment. They estimate that some 4 % of the bodies in the Oort Cloud should be “asteroids,” i.e., bodies that formed within 2.5 AU of the Sun.
For an isotropic distribution, \(\cos i\) is uniformly distributed between −1 and 1, so the median value of \(\cos i = 0\), corresponding to \(i = 90^{\circ}\), and \(e^{2}\) is uniformly distributed between 0 and 1, so the median value of \(e^{2}\) is \(\frac{1}{2}\) and the median value of \(e = 1/\sqrt{2}\) (Jeans 1919).
There is no consensus on the direction or amount of the Sun’s migration. For instance, Martínez-Barbosa et al. (2015) find that the Sun has probably undergone little migration, but if it has done so, it was probably born further out, near 11 kpc, while Halle et al. (2015) find that stars in the solar neighborhood “may have experienced very limited churning from the inner disc.” Hayden et al. (2015) find that “about 30 % of the stars in our Galaxy have traveled a long way from the orbits in which they were born” (http://www.sdss3.org/press/20150730.farfromhome.php).
An animation by Alex Parker showing the rough relative sizes and true orbital motion of all trans-Neptunian objects with semi-major axes greater than Neptune’s as of 2014 can be seen at https://vimeo.com/96874127. See http://www.alexharrisonparker.com/datavisualization/ for other visualizations by Parker.
See http://www.icq.eps.harvard.edu/kb.html for a discussion of how Kuiper never predicted the present-day existence of the belt that bears his name, while others, such as Leonard, Whipple, and Cameron, came closer to doing so.
Oort (1950) found that, relative to the number of comets in the spike, fewer “returning” comets than expected were seen. Fitting the energy distribution of long-period comets required Oort to assume that “new or almost new” comets were unusually bright and that comets had a \({\approx}1~\%\) chance of being disrupted during each perihelion passage. This “fading” problem persists even now. Wiegert and Tremaine (1999) define fading as “all factors that reduce the intrinsic brightness of the comet near perihelion, and includes splitting into two or more large pieces, disruption into many small pieces, the depletion of volatiles, and the formation of insulating crusts of refractory materials.” Wiegert and Tremaine (1999) investigate fading in great detail, and find they can match the observed orbit distribution of long-period comets if the fraction of comets remaining observable after \(m\) apparitions \(\propto m^{0.6\pm0.1}\) or if \({\approx}95~\%\) of comets survive for only \({\approx}6\) returns and the rest last indefinitely.
The absolute magnitude derived for a comet depends both on the aperture of the telescope used to observe it (since comets are extended sources) and the assumed value of the photometric index \(\nu\), which is not always stated. Even though both studies assumed \(\nu= 4\), Kresák and Kresáková (1989) derived absolute magnitudes that differed, on average, from those of Vsekhsvyatskij (1958) by 1.9 magnitudes, with a standard deviation of 1.5 magnitudes. For instance, Kresák and Kresáková (1989) derive a mean absolute magnitude for 1P/Halley of 2.8 from its 1835, 1910, and 1986 apparitions, while Hughes (1988), who uses Vsekhsvyatskij’s magnitudes, states that “during its last 30 apparitions, [Halley’s] \(H_{10}\) value has remained sensibly constant at \(5.5 \pm0.7\).”
Using the traditional definition of a new comet as one with an original semi-major axis \({>} 10{,}000~\mbox{AU}\), Wiegert and Tremaine (1999) assume one long-period comet in three is dynamically new, while Fernández and Sosa (2012) find that new comets are \(30 \pm10~\%\) of long-period comets with perihelia \({<}1.3~\mbox{AU}\).
Kaib and Quinn (2009) estimate that the fraction of Oort Cloud comets reaching orbits with \(q < 5~\mbox{AU}\) per year is \(1.4 \times10^{-11}\) and \(0.9 \times10^{-11}\) for comets from the outer (\(a >20{,}000~\mbox{AU}\)) and inner (\(a <20{,}000~\mbox{AU}\)) clouds, respectively.
One dimming event reduced the star’s light by 20 %. Wright et al. (2015) state that the light curve is “consistent with a ‘swarm’ of megastructures,” i.e., a Dyson sphere. The SETI Institute is observing KIC 8462852 with the Allen Telescope Array to investigate this possibility (http://www.seti.org/seti-institute/mysterious-star-kic-8462852).
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Acknowledgements
We thank Bob Johnston for discussions about his database of comets; my tweeps Alessondra Springmann, Sarah Hörst, Chris Granade, Brian Wolven, and especially Andy Kass for help fixing a last-minute BibTeX disaster; Bill Bottke, Robert Jedicke, and Mikael Granvik for data on the size distribution of asteroids; Paul Weissman for sharing his work in advance of publication; Alfred McEwen and Alan Delamere for information on HiRISE observations of comet C/2013 A1; Scott Sheppard, Meg Schwamb, Lucie Maquet, Kevin Walsh, Konstantin Batygin, and Cory Shankman for providing figures; David Nesvorný for discussions about the Kuiper Belt and the Late Heavy Bombardment; the referees for helpful comments; and Nirmala Kumar at Springer and the editors, especially Kathy Mandt, for their patience. The Astrophysics Data System Abstract Service and the arXiv were of great value in searching the literature. We thank Iggy Confidential for motivation during the revisions.
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We thank the NASA Cassini Data Analysis Program for support of some of the work described here.
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Dones, L., Brasser, R., Kaib, N. et al. Origin and Evolution of the Cometary Reservoirs. Space Sci Rev 197, 191–269 (2015). https://doi.org/10.1007/s11214-015-0223-2
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DOI: https://doi.org/10.1007/s11214-015-0223-2