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As the Galactic tide acts to decouple bodies from the scattered disk it creates a spiral structure in physical space that is roughly 15,000 au in length. The spiral is long-lived and persists in the inner Oort cloud to the present time. Here we discuss dynamics underlying the Oort spiral and (feeble) prospects for its observational detection., Comment: ApJ, in press

So-called 'dark comets' are small, morphologically inactive near-Earth objects (NEOs) that exhibit nongravitational accelerations inconsistent with radiative effects. These objects exhibit short rotational periods (minutes to hours), where measured. We find that the strengths required to prevent catastrophic disintegration are consistent with those measured in cometary nuclei and expected in rubble pile objects. We hypothesize that these dark comets are the end result of a rotational fragmentation cascade, which is consistent with their measured physical properties. We calculate the predicted size-frequency distribution for objects evolving under this model. Using dynamical simulations, we further demonstrate that the majority of these bodies originated from the $\nu_6$ resonance, implying the existence of volatiles in the current inner main belt. Moreover, one of the dark comets, (523599) 2003 RM, likely originated from the outer main belt, although a JFC origin is also plausible. These results provide strong evidence that volatiles from a reservoir in the inner main belt are present in the near-Earth environment., Comment: 17 pages, 7 figures, 12 supplementary figures & pages. Accepted for publication in Icarus

Context: Increasingly, Oort Cloud comets are being discovered at great distances from the Sun and tracked over ever wider ranges of heliocentric distances as observational equipment improves. Aims: To investigate in detail how the original semimajor axis for near-parabolic comets depends on the selected data arc and the assumed form of the non-gravitational (NG) acceleration. Methods: Among currently known Oort Cloud comets with large perihelion distances ($q > 3$ au), we selected 32 objects observed over the widest ranges of heliocentric distances in orbital legs before and after perihelion. For each of them, we determined a series of orbits using at least three basic types of data sets selected from available positional data (pre- and post-perihelion data and the entire data set), and a few forms of NG acceleration representing water ice or CO sublimation. Results: We found that the motion of comets is often measurably affected by NG forces at heliocentric distances beyond 5 au from the Sun. The most spectacular example is C/2010 U3 (Boattini), whose perihelion distance is 8.44 au. NG effects are detectable for 19 of the 32 comets within the positional data. For five comets, we found asymmetric effects of NG forces - in three cases significantly greater before perihelion than afterward (C/2017 M4, C/2000 SV$_{75}$, and C/2015 O1), and in two others the opposite (C/1997 BA$_6$ and C/2006 S3). We also find that the well-known systematic effect of finding more tightly bound original orbits when including the NG acceleration than in purely gravitational solutions may be related to the specific form of the standard $g(r)$ function describing the sublimation of ices., Comment: 22 pages, 11 tables, 10 figures. Astronomy & Astrophysics, in press

Previous studies of cometary impacts in the outer Solar System used the spatial distribution of ecliptic comets (ECs) from dynamical models that assumed ECs began on low-inclination orbits (<5 deg) in the Kuiper belt. In reality, the source population of ECs - the trans-Neptunian scattered disk - has orbital inclinations reaching up to ~30 deg. In Nesvorny et al. (2017), we developed a new dynamical model of ECs by following comets as they evolved from the scattered disk to the inner Solar System. The model was absolutely calibrated from the population of Centaurs and active ECs. Here we use our EC model to determine the steady-state impact flux of cometary/Centaur impactors on Jupiter, Saturn, Uranus, and their moons. Relative to previous work (Zahnle et al. 2003), we find slightly higher impact probabilities on the outer moons and lower impact probabilities on the inner moons. The impact probabilities are smaller when comet disruption is accounted for. The results provide a modern framework for the interpretation of the cratering record in the outer Solar System., Comment: PSJ, in press

The tumultuous early era of outer solar system evolution culminated when Neptune migrated across the primordial Kuiper belt (PKB) and triggered a dynamical instability among the giant planets. This event led to the ejection of approximately 99.9\% of the PKB (here called the destabilized population), heavy bombardment of the giant planet satellites, and the capture of Jupiter's Trojans. While this scenario has been widely tested using dynamical models, there have been fewer investigations into how the PKB, its destabilized population, and the Trojans experienced collisional evolution. Here we examined this issue for all three populations with the code Boulder. Our constraints included the size-frequency distributions (SFDs) of the Trojan asteroids and craters on the giant planet satellites. Using this combination, we solved for the unknown disruption law affecting bodies in these populations. The weakest ones, from an impact energy per mass perspective, were 20 m in diameter. Overall, collisional evolution produces a power-law-like shape for multikilometer Trojans and a wavy-shaped SFD in the PKB and destabilized populations. The latter can explain (i) the shapes of the ancient and younger crater SFDs observed on the giant planet satellites, (ii) the shapes of the Jupiter family and long-period comet SFDs, which experienced different degrees of collision evolution, and (iii) the present-day impact frequency of superbolides on Jupiter and smaller projectiles on Saturn's rings. Our model results also indicate that many observed comets, most which are smaller than 10 km in diameter, are likely to be gravitational aggregates formed by large-scale collision events., Comment: 95 pages, 19 figures. Accepted for publication in PSJ

Kuiper Belt Objects, or more generally Trans-Neptunian Objects (TNOs), are planetesimals found beyond the orbit of Neptune. Some TNOs evolve onto Neptune-crossing orbits and become Centaurs. Many Centaurs, in turn, reach Jupiter-crossing orbits and become Jupiter-family comets (JFCs). TNOs are the main source of the JFCs. TNOs offer a different window than the JFCs, of more primordial bodies and over a different size and temperature range. It is in that context that this chapter is written. Here we discuss the dynamical pathways taken from the trans-Neptunian region to the JFCs, and the most important properties of TNOs that relate to the JFC population, including considerations of their origins, compositions, morphologies, and size distributions. We relate these properties to the JFCs whenever possible. We reflect on a few key outstanding issues regarding our incomplete knowledge of TNOs as they pertain to the Centaurs and JFC populations. We finish with a short discussion of notable new and upcoming facilities and the impacts they will have regarding these outstanding questions., Comment: 32 pages, 2 tables, 15 figures. Accepted for publication

We develop an evolutionary model of the long-period comet (LPC) population, starting from their birthplace in a massive trans-Neptunian disk that was dispersed by migrating giant planets. Most comets that remain bound to the Solar system are stored in the Oort cloud. Galactic tides and passing stars make some of these bodies evolve into observable comets in the inner Solar system. Our approach models each step in a full-fledged numerical framework. Subsequent analysis consists of applying plausible fading models and computing the original orbits to compare with observations. Our results match the observed semimajor axis distribution of LPCs when Whipple's power-law fading scheme with an exponent $\kappa= 0.6^{+0.1}_{-0.2}$ is adopted. The cumulative perihelion ($q$) distribution is fit well by a linear increase plus a weak quadratic term. Beyond $q = 15$~au, however, the population increases steeply and the isotropy of LPC orbital planes breaks. We find tentative evidence from the perihelion distribution of LPCs that the returning comets are depleted in supervolatiles and become active due to water ice sublimation for $q\leq 3$ au. Using an independent calibration of the population of the initial disk, our predicted LPC flux is smaller than observations suggest by a factor of $\simeq 2$. Current data only characterize comets from the outer Oort cloud (semimajor axes $\gtrsim 10^4$~au). A true boost in understanding the Oort cloud's structure should result from future surveys when they detect LPCs with perihelia beyond $15$~au. Our results provide observational predictions of what can be expected from these new data., Comment: 35 pages, 22 figures, AAS journals in press

Using numerical integrations, we find that the orbital eccentricity of Saturn's moon Iapetus undergoes prominent multi-Myr oscillations. We identify the responsible resonant argument to be $\varpi-\varpi_{g5}+\Omega-\Omega_{eq}$, with the terms being the longitudes of pericenter of Iapetus and planetary secular mode $g_5$, Iapetus's longitude of the node and Saturn's equinox. We find that this argument currently (on a $10^7$~yr timescale) appears to librate with a very large amplitude. On longer timescales, the behavior of this resonant angle is strongly dependent on the resonant interaction between Saturn's spin axis and the planetary mode $f_8$, with long-term secular resonance being possible if Saturn's equinox is librating relative to the node of the $f_8$ eigenmode. We present analytical estimates of the dependence of the resonant argument on the orbital elements of Iapetus. We find that this Iapetus-$g_5$ secular resonance could have been established only after the passage of Iapetus through the 5:1 mean-motion resonance with Titan, possibly in the last Gyr. Using numerical simulations, we show that the capture into the secular resonance appears to be a low-probability event. While the Iapetus-$g_5$ secular resonance can potentially help us put new constraints on the past dynamics of the Saturnian system, uncertainties in both the spin axis dynamics of Saturn and the tidal evolution rate of Titan make it impossible to make any firm conclusions about the resonance's longevity and origin., Comment: Accepted for MNRAS

Future remote sensing of exoplanets will be enhanced by a thorough investigation of our solar system Ice Giants (Neptune-size planets). What can the configuration of the magnetic field tell us (remotely) about the interior, and what implications does that field have for the structure of the magnetosphere; energy input into the atmosphere, and surface geophysics (for example surface weathering of satellites that might harbour sub-surface oceans). How can monitoring of auroral emission help inform future remote observations of emission from exoplanets? Our Solar System provides the only laboratory in which we can perform in-situ experiments to understand exoplanet formation, dynamos, systems and magnetospheres., Comment: Exoplanet Science Strategy White Paper, submitted to the National Academies of Sciences, Engineering and Medicine, Space Studies Board, 9 March 2018

We explore the past evolution of Saturn's moons using direct numerical integrations. We find that the past Tethys-Dione 3:2 orbital resonance predicted in standard models likely did not occur, implying that the system is less evolved than previously thought. On the other hand, the orbital inclinations of Tethys, Dione and Rhea suggest that the system did cross the Dione-Rhea 5:3 resonance, which is closely followed by a Tethys-Dione secular resonance. A clear implication is that either the moons are significantly younger than the planet, or that their tidal evolution must be extremely slow (Q > 80,000). As an extremely slow-evolving system is incompatible with intense tidal heating of Enceladus, we conclude that the moons interior to Titan are not primordial, and we present a plausible scenario for the system's recent formation. We propose that the mid-sized moons re-accreted from a disk about 100 Myr ago, during which time Titan acquired its significant orbital eccentricity. We speculate that this disk has formed through orbital instability and massive collisions involving the previous generation of Saturn's mid-sized moons. We identify the solar evection resonance perturbing a pair of mid-sized moons as the most likely trigger of such an instability. This scenario implies that most craters on the moons interior to Titan must have been formed by planetocentric impactors., Comment: To appear in The Astrophysical Journal on March 24, 2016

Reflected light curves observed for exoplanets indicate bright clouds at some of them. We estimate how the light curve and total stellar heating of a planet depend on forward and backward scattering in the clouds based on Pioneer and Cassini spacecraft images of Jupiter and Saturn. We fit analytical functions to the local reflected brightnesses of Jupiter and Saturn depending on the planet's phase. These observations cover broad bands at 0.59-0.72 and 0.39-0.5 {\mu}m, and narrow bands at 0.938 (atmospheric window), 0.889 (CH4 absorption band), and 0.24-0.28 {\mu}m. We simulate the images of the planets with a ray-tracing model, and disk-integrate them to produce the full-orbit light curves. For Jupiter, we also fit the modeled light curves to the observed full-disk brightness. We derive spherical albedos for Jupiter, Saturn, and for planets with Lambertian and Rayleigh-scattering atmospheres. Jupiter-like atmospheres can produce light curves that are a factor of two fainter at half-phase than the Lambertian planet, given the same geometric albedo at transit. The spherical albedo is typically lower than for a Lambertian planet by up to a factor of 1.5. The Lambertian assumption will underestimate the absorption of the stellar light and the equilibrium temperature of the planetary atmosphere. We also compare our light curves with the light curves of solid bodies: the moons Enceladus and Callisto. Their strong backscattering peak within a few degrees of opposition (secondary eclipse) can lead to an even stronger underestimate of the stellar heating., Comment: 21 pages, 4 figures

Lainey et al. (2012), by re-analyzing long-baseline astrometry of Saturn's moons, have found that the moons' tidal evolution is much faster than previously thought, implying an order of magnitude stronger tidal dissipation within Saturn. This result is controversial and implies recent formation of at least some of the mid-sized icy moons of Saturn. Here we show that this more intensive tidal dissipation is in full agreement with the evolved state of the Titan-Hyperion resonance. This resonance was previously thought to be non-tidal in origin, as the amount of tidal evolution required for its assembly is beyond what is possible in models that assume that all the major moons are primordial. We find that the survival of the Titan-Hyperion resonance is in agreement with a past Titan-Iapetus 5:1 resonance, but not with unbroken tidal evolution of Rhea from the rings to its current distance., Comment: Submitted to ApJL

The origin of Saturn's inner mid-sized moons (Mimas, Enceladus, Tethys, Dione and Rhea) and Saturn's rings is debated. Charnoz et al. (2010) introduced the idea that the smallest inner moons could form from the spreading of the rings' edge while Salmon et al. (2010) showed that the rings could have been initially massive, and so was the ring's progenitor itself. One may wonder if the mid-sized moons may have formed also from the debris of a massive ring progenitor, as also suggested in Canup (2010). However, the process driving mid-sized moons accretion from the icy debris disks has not been investigated in details. In particular, this process does not seem able to explain the varying silicate contents of the mid-sized moons (from 6% to 57% in mass). Here, we explore the formation of large objects from a massive ice-rich ring (a few times Rhea's mass) and describe the fundamental properties and implications of this new process. Using a hybrid computer model, we show that accretion within massive icy rings can form all mid-sized moons from Mimas to Rhea. However in order to explain their current locations, intense dissipation within Saturn (with Qp<2000) would be required. Our results are consistent with a satellite origin tied to the rings formation at least 2.5 Gy ago, both compatible with either a formation concurrent to Saturn or during the Late Heavy Bombardment. Tidal heating related to high-eccentricity post-accretional episodes may induce early geological activity. If some massive irregular chunks of silicates were initially present within the rings, they would be present today inside the satellites' cores which would have accreted icy shells while being tidally expelled from the rings (via a heterogeneous accretion process)while those still present in the rings are interpreted as today Saturn's rings' propellers and ring-moons (like Pan or Daphnis)., Comment: 41 pages, 14 figures. Accepted in ICARUS

We find evidence that crater ejecta play an important role in the small crater populations on the Saturnian satellites, and more broadly, on cratered surfaces throughout the Solar System. We measure crater populations in Cassini images of Enceladus, Rhea, and Mimas, focusing on image data with scales less than 500 m/pixel. We use recent updates to crater scaling laws and their constants to estimate the amount of mass ejected in three different velocity ranges: (i) greater than escape velocity, (ii) less than escape velocity and faster than the minimum velocity required to make a secondary crater (v_min), and (iii) velocities less than v_min. Although the vast majority of mass on each satellite is ejected at speeds less than v_min, our calculations demonstrate that the differences in mass available in the other two categories should lead to observable differences in the small crater populations; the predictions are borne out by the measurements we have made to date. Rhea, Tethys, and Dione have sufficient surface gravities to retain ejecta moving fast enough to make secondary crater populations. The smaller satellites, such as Enceladus but especially Mimas, are expected to have little or no traditional secondary populations because their escape velocities are near the threshold velocity necessary to make a secondary crater. Our work clarifies why the Galilean satellites have extensive secondary crater populations relative to the Saturnian satellites. The presence, extent, and sizes of sesquinary craters (craters formed by ejecta that escape into temporary orbits around Saturn before re-impacting the surface) is not yet well understood. Finally, our work provides further evidence for a "shallow" size-frequency distribution (slope index of ~2 for a differential power-law) for comets a few km diameter and smaller. [slightly abbreviated], Comment: Submitted to Icarus. 77 double-spaced pages, including 25 figures and 5 tables

The origin and long-term evolution of Saturn's rings is still an unsolved problem in modern planetary science. In this chapter we review the current state of our knowledge on this long-standing question for the main rings (A, Cassini Division, B, C), the F Ring, and the diffuse rings (E and G). During the Voyager era, models of evolutionary processes affecting the rings on long time scales (erosion, viscous spreading, accretion, ballistic transport, etc.) had suggested that Saturn's rings are not older than 100 My. In addition, Saturn's large system of diffuse rings has been thought to be the result of material loss from one or more of Saturn's satellites. In the Cassini era, high spatial and spectral resolution data have allowed progress to be made on some of these questions. Discoveries such as the ''propellers'' in the A ring, the shape of ring-embedded moonlets, the clumps in the F Ring, and Enceladus' plume provide new constraints on evolutionary processes in Saturn's rings. At the same time, advances in numerical simulations over the last 20 years have opened the way to realistic models of the rings's fine scale structure, and progress in our understanding of the formation of the Solar System provides a better-defined historical context in which to understand ring formation. All these elements have important implications for the origin and long-term evolution of Saturn's rings. They strengthen the idea that Saturn's rings are very dynamical and rapidly evolving, while new arguments suggest that the rings could be older than previously believed, provided that they are regularly renewed. Key evolutionary processes, timescales and possible scenarios for the rings's origin are reviewed in the light of t, Comment: Chapter 17 of the book ''Saturn After Cassini-Huygens'' Saturn from Cassini-Huygens, Dougherty, M.K.; Esposito, L.W.; Krimigis, S.M. (Ed.) (2009) 537-575

By examining the absolute magnitude (H) distributions (hereafter HD) of the cold and hot populations in the Kuiper belt and of the Trojans of Jupiter, we find evidence that the Trojans have been captured from the outer part of the primordial trans-Neptunian planetesimal disk. We develop a sketch model of the HDs in the inner and outer parts of the disk that is consistent with the observed distributions and with the dynamical evolution scenario known as the `Nice model'. This leads us to predict that the HD of hot population should have the same slope of the HD of the cold population for 6.5 < H < 9, both as steep as the slope of the Trojans' HD. Current data partially support this prediction, but future observations are needed to clarify this issue. Because the HD of the Trojans rolls over at H~9 to a collisional equilibrium slope that should have been acquired when the Trojans were still embedded in the primordial trans-Neptunian disk, our model implies that the same roll-over should characterize the HDs of the Kuiper belt populations, in agreement with the results of Bernstein et al. (2004) and Fuentes and Holman (2008). Finally, we show that the constraint on the total mass of the primordial trans-Neptunian disk imposed by the Nice model implies that it is unlikely that the cold population formed beyond 35 AU., Comment: Icarus (2009) in press

In this paper, we characterize the morphology of the disk-integrated phase functions of satellites and rings around the giant planets of our Solar System. We find that the shape of the phase function is accurately represented by a logarithmic model (Bobrov, 1970, in Surfaces and Interiors of Planets and Satellites, Academic, edited by A. Dollfus). For practical purposes, we also parametrize the phase curves by a linear-exponential model (Kaasalainen et al., 2001, Journal of Quantitative Spectroscopy and Radiative Transfer, 70, 529-543) and a simple linear-by-parts model (Lumme and Irvine, 1976, Astronomical Journal, 81, 865-893), which provides three morphological parameters : the amplitude A and the Half-Width at Half-Maximum (HWHM) of the opposition surge, and the slope S of the linear part of the phase function at larger phase angles. Our analysis demonstrates that all of these morphological parameters are correlated with the single scattering albedos of the surfaces. By taking more accurately into consideration the finite angular size of the Sun, we find that the Galilean, Saturnian, Uranian and Neptunian satellites have similar HWHMs (0.5 degrees), whereas they have a wide range of amplitudes A. The Moon has the largest HWHM (2 degrees). We interpret that as a consequence of the solar size bias, via the finite size of the Sun which varies dramatically from the Earth to Neptune. By applying a new method that attempts to morphologically deconvolve the phase function to the solar angular size, we find that icy and young surfaces, with active resurfacing, have the smallest values of A and HWHM, whereas dark objects (and perhaps older surfaces) such as the Moon, Nereid and Saturn C ring have the largest A and HWHM., Comment: 5 tables, 10 figures, submitted to PSS

The Cassini cameras have captured the opposition effect in Saturn rings with a high radial resolution at phase angles down to 0.01o in the entire main ring system. We derive phase functions from 0.01 to 25 degrees of phase angle in the Wide-Angle Camera clear filters with a central wavelength of 0.611microns and phase functions from 0.001 to 25 degrees of phase angle in the Narrow-Angle and Wide-Angle Cameras color filters (from the blue 0.451 microns to the near infrared 0.752 microns). We characterize the morphology of the phase functions of different features in the main rings. We find that the shape of the phase function is accurately represented by a logarithmic model (Bobrov 1970, in Surfaces and Interiors of Planets and Satellites, Academic, edited by A. Dollfus). For practical purposes, we also parametrize the phase curves by a simple linear-by-part model (Lumme and Irvine 1976, Astronomical Journal, 81, p865), which provides three morphological parameters : the amplitude and the Half-Width at Half-Maximum (HWHM) of the surge, and the slope S of the linear-part of the phase function at larger phase angles. Our analysis demonstrates that all of these parameters show trends with the optical depth of the rings. These trends imply that the optical depth is a key-element determining the physical properties which act on the opposition effect. Wavelength variations of the morphological parameters of the surge show important trends with the optical depth in the green filter (0.568 microns), which implies that grain size effects are maximum in this wavelength., Comment: 5 tables and 13 figures

The origin of Saturn\' s massive ring system is still unknown. Two popular scenarios - the tidal splitting of passing comets and the collisional destruction of a satellite - rely on a high cometary flux in the past. In the present paper we attempt to quantify the cometary flux during the Late Heavy Bombardment (LHB) to assess the likelihood of both scenarios. Our analysis relies on the so-called Nice model of the origin of the LHB (Tsiganis et al., 2005; Morbidelli et al., 2005; Gomes et al., 2005) and on the size distribution of the primordial trans-Neptunian planetesimals constrained in Charnoz & Morbidelli (2007). We find that the cometary flux on Saturn during the LHB was so high that both scenarios for the formation of Saturn rings are viable in principle. However, a more detailed study shows that the comet tidal disruption scenario implies that all four giant planets should have comparable ring systems whereas the destroyed satellite scenario would work only for Saturn, and perhaps Jupiter. This is because in Saturn\'s system, the synchronous orbit is interior to the Roche Limit, which is a necessary condition for maintaining a satellite in the Roche zone up to the time of the LHB. We also discuss the apparent elimination of silicates from the ring parent body implied by the purity of the ice in Saturn \' s rings. The LHB has also strong implications for the survival of the Saturnian satellites: all satellites smaller than Mimas would have been destroyed during the LHB, whereas Enceladus would have had from 40% to 70% chance of survival depending on the disruption model. In conclusion, these results suggest that the LHB is the sweet moment for the formation of a massive ring system around Saturn., Comment: 39 pages, 9 figures, 3 tables. Accepted for publication in ICARUS. New version with figures included in the text

We predict how a remote observer would see the brightness variations of giant planets similar to Jupiter and Saturn as they orbit their central stars. We model the geometry of Jupiter, Saturn and Saturn's rings for varying orbital and viewing parameters. Scattering properties for the planets and rings at wavelenghts 0.6-0.7 microns follow Pioneer and Voyager observations, namely, planets are forward scattering and rings are backward scattering. Images of the planet with or without rings are simulated and used to calculate the disk-averaged luminosity varying along the orbit, that is, a light curve is generated. We find that the different scattering properties of Jupiter and Saturn (without rings) make a substantial difference in the shape of their light curves. Saturn-size rings increase the apparent luminosity of the planet by a factor of 2-3 for a wide range of geometries. Rings produce asymmetric light curves that are distinct from the light curve of the planet without rings. If radial velocity data are available for the planet, the effect of the ring on the light curve can be distinguished from effects due to orbital eccentricity. Non-ringed planets on eccentric orbits produce light curves with maxima shifted relative to the position of the maximum planet's phase. Given radial velocity data, the amount of the shift restricts the planet's unknown orbital inclination and therefore its mass. Combination of radial velocity data and a light curve for a non-ringed planet on an eccentric orbit can also be used to constrain the surface scattering properties of the planet. To summarize our results for the detectability of exoplanets in reflected light, we present a chart of light curve amplitudes of non-ringed planets for different eccentricities, inclinations, and the viewing azimuthal angles of the observer., Comment: 40 pages, 13 figures, submitted to Ap.J