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Harold F. Levison

Publications and source records attributed to Harold F. Levison.

36 records · Page 2Linked to original sources
arXiv2009

Constructing the secular architecture of the solar system I: The giant planets

Using numerical simulations, we show that smooth migration of the giant planets through a planetesimal disk leads to an orbital architecture that is inconsistent with the current one: the resulting eccentricities and inclinations of their orbits are too small. The crossing of mutual mean motion resonances by the planets would excite their orbital eccentricities but not their orbital inclinations. Moreover, the amplitudes of the eigenmodes characterising the current secular evolution of the eccentricities of Jupiter and Saturn would not be reproduced correctly; only one eigenmode is excited by resonance-crossing. We show that, at the very least, encounters between Saturn and one of the ice giants (Uranus or Neptune) need to have occurred, in order to reproduce the current secular properties of the giant planets, in particular the amplitude of the two strongest eigenmodes in the eccentricities of Jupiter and Saturn.

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arXiv2009

Constructing the secular architecture of the solar system II: The terrestrial planets

We investigate the dynamical evolution of the terrestrial planets during the planetesimal-driven migration of the giant planets. A basic assumption of this work is that giant planet migration occurred after the completion of terrestrial planet formation, such as in the models that link the former to the origin of the Late Heavy Bombardment. The divergent migration of Jupiter and Saturn causes the g5 eigenfrequency to cross resonances of the form g5=gk with k ranging from 1 to 4. Consequently these secular resonances cause large-amplitude responses in the eccentricities of the terrestrial planets. We show that the resonances g5=g_4 and g5=g3 do not pose a problem if Jupiter and Saturn have a fast approach and departure from their mutual 2:1 mean motion resonance. On the other hand, the resonance crossings g5=g2 and g5=g1 are more of a concern as they tend to yield a terrestrial system incompatible with the current one. We offer two solutions to this problem. The first uses the fact that a secular resonance crossing can also damp the amplitude of a Fourier mode if the latter is large originally. A second scenario involves a 'jumping Jupiter' in which encounters between an ice giant and Jupiter, without ejection of the former, cause the latter to migrate away from Saturn much faster than if migration is driven solely by encounters with planetesimals. In this case, the g5=g2 and g5=g1 resonances can be jumped over, or occur very briefly.

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arXiv2009

Asteroids Were Born Big

How big were the first planetesimals? We attempt to answer this question by conducting coagulation simulations in which the planetesimals grow by mutual collisions and form larger bodies and planetary embryos. The size frequency distribution (SFD) of the initial planetesimals is considered a free parameter in these simulations, and we search for the one that produces at the end objects with a SFD that is consistent with asteroid belt constraints. We find that, if the initial planetesimals were small (e.g. km-sized), the final SFD fails to fulfill these constraints. In particular, reproducing the bump observed at diameter D~100km in the current SFD of the asteroids requires that the minimal size of the initial planetesimals was also ~100km. This supports the idea that planetesimals formed big, namely that the size of solids in the proto-planetary disk ``jumped'' from sub-meter scale to multi-kilometer scale, without passing through intermediate values. Moreover, we find evidence that the initial planetesimals had to have sizes ranging from 100 to several 100km, probably even 1,000km, and that their SFD had to have a slope over this interval that was similar to the one characterizing the current asteroids in the same size-range. This result sets a new constraint on planetesimal formation models and opens new perspectives for the investigation of the collisional evolution in the asteroid and Kuiper belts as well as of the accretion of the cores of the giant planets.

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arXiv2009

The History of the Solar System's Debris Disc: Observable Properties of the Kuiper Belt

The Nice model of Gomes et al. (2005) suggests that the migration of the giant planets caused a planetesimal clearing event which led to the Late Heavy Bombardment (LHB) at 880 Myr. Here we investigate the IR emission from the Kuiper belt during the history of the Solar System as described by the Nice model. We describe a method for easily converting the results of n-body planetesimal simulations into observational properties (assuming black-body grains and a single size distribution) and further modify this method to improve its realism (using realistic grain properties and a three-phase size distribution). We compare our results with observed debris discs and evaluate the plausibility of detecting an LHB-like process in extrasolar systems. Recent surveys have shown that 4% of stars exhibit 24 um excess and 16% exhibit 70 um excess. We show that the Solar System would have been amongst the brightest of these systems before the LHB at both 24 and 70 um. We find a significant increase in 24 um emission during the LHB, which rapidly drops off and becomes undetectable within 30 Myr, whereas the 70 um emission remains detectable until 360 Myr after the LHB. Comparison with the statistics of debris disc evolution shows that such depletion events must be rare occurring around less than 12% of Sun-like stars and with this level of incidence we would expect approximately 1 of the 413 Sun-like, field stars so far detected to have a 24 um excess to be currently going through an LHB. We also find that collisional processes are important in the Solar System before the LHB and that parameters for weak Kuiper belt objects are inconsistent with the Nice model interpretation of the LHB.

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arXiv2009

Considerations on the magnitude distributions of the Kuiper belt and of the Jupiter Trojans

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.

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arXiv2009

A Search for Multi-Planet Systems Using the Hobby-Eberly Telescope

Extrasolar multiple-planet systems provide valuable opportunities for testing theories of planet formation and evolution. The architectures of the known multiple-planet systems demonstrate a fascinating level of diversity, which motivates the search for additional examples of such systems in order to better constrain their formation and dynamical histories. Here we describe a comprehensive investigation of 22 planetary systems in an effort to answer three questions: 1) Are there additional planets? 2) Where could additional planets reside in stable orbits? and 3) What limits can these observations place on such objects? We find no evidence for additional bodies in any of these systems; indeed, these new data do not support three previously announced planets (HD 20367b: Udry et al. 2003, HD 74156d: Bean et al. 2008, and 47 UMa c: Fischer et al. 2002). The dynamical simulations show that nearly all of the 22 systems have large regions in which additional planets could exist in stable orbits. The detection-limit computations indicate that this study is sensitive to close-in Neptune-mass planets for most of the systems targeted. We conclude with a discussion on the implications of these non-detections.

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arXiv2008

On a Scattered-Disk Origin for the 2003 El61 Collisional Family - an Example of the Importance of Collisions on the Dynamics of Small Bodies

The recent discovery of the 2003EL61 collisional family in the Kuiper belt (Brown et al., 2007) is surprising because the formation of such a family is a highly improbable event in today's belt. Assuming Brown et al.'s estimate of the size of progenitors, we find that the probability that a Kuiper belt object was involved in such a collision since primordial times is less than roughly 0.001. In addition, it is not possible for the collision to have occurred in a massive primordial Kuiper belt because the dynamical coherence of the family would not have survived whatever event produced the currently observed orbital excitation. Here we suggest that the family is the result of a collision between two scattered disk objects. We show that the probability that a collision occurred between two such objects with sizes similar to those advocated in Brown et al. (2007) and that the center of mass of the resulting family is on an orbit typical of the Kuiper belt can be as large as 47%. Given the large uncertainties involved in this estimate, this result is consistent with the existence of one such family. If true, this result has implications far beyond the origin of a single collisional family, because it shows that collisions played an important role in shaping the dynamical structure of the small body populations that we see today.

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arXiv2008

Evidence for Two Populations of Classical Transneptunian Objects: The Strong Inclination Dependence of Classical Binaries

We have searched 101 Classical transneptunian objects for companions with the Hubble Space Telescope. Of these, at least 21 are binary. The heliocentric inclinations of the objects we observed range from 0.6-34 degrees. We find a very strong anticorrelation of binaries with inclination. Of the 58 targets that have inclinations of less than 5.5 degrees, 17 are binary, a binary fraction of 29 +7/-6%. All 17 are similar-brightness systems. On the contrary, only 4 of the 42 objects with inclinations greater than 5.5 degrees have satellites and only 1 of these is a similar-brightness binary. This striking dichotomy appears to agree with other indications that the low eccentricity, non-resonant Classical transneptunian objects include two overlapping populations with significantly different physical properties and dynamical histories.

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arXiv2007

Origin of the Structure of the Kuiper Belt during a Dynamical Instability in the Orbits of Uranus and Neptune

We explore the origin and orbital evolution of the Kuiper belt in the framework of a recent model of the dynamical evolution of the giant planets, sometimes known as the Nice model. This model is characterized by a short, but violent, instability phase, during which the planets were on large eccentricity orbits. One characteristic of this model is that the proto-planetary disk must have been truncated at roughly 30 to 35 AU so that Neptune would stop migrating at its currently observed location. As a result, the Kuiper belt would have initially been empty. In this paper we present a new dynamical mechanism which can deliver objects from the region interior to ~35 AU to the Kuiper belt without excessive inclination excitation. Assuming that the last encounter with Uranus delivered Neptune onto a low-inclination orbit with a semi-major axis of ~27 AU and an eccentricity of ~0.3, and that subsequently Neptune's eccentricity damped in ~1 My, our simulations reproduce the main observed properties of the Kuiper belt at an unprecedented level.

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arXiv2007

Dynamics of the giant planets of the solar system in the gaseous proto-planetary disk and relationship to the current orbital architecture

We study the orbital evolution of the 4 giant planets of our solar system in a gas disk. Our investigation extends the previous works by Masset and Snellgrove (2001) and Morbidelli and Crida (2007, MC07), which focussed on the dynamics of the Jupiter-Saturn system. The only systems that we found to reach a steady state are those in which the planets are locked in a quadruple mean motion resonance (i.e. each planet is in resonance with its neighbor). In total we found 6 such configurations. For the gas disk parameters found in MC07, these configurations are characterized by a negligible migration rate. After the disappearance of the gas, and in absence of planetesimals, only two of these six configurations (the least compact ones) are stable for a time of hundreds of millions of years or more. The others become unstable on a timescale of a few My. Our preliminary simulations show that, when a planetesimal disk is added beyond the orbit of the outermost planet, the planets can evolve from the most stable of these configurations to their current orbits in a fashion qualitatively similar to that described in Tsiganis et al. (2005).

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arXiv2007

Dynamical and Observational Constraints on Additional Planets in Highly Eccentric Planetary Systems

Long time coverage and high radial velocity precision have allowed for the discovery of additional objects in known planetary systems. Many of the extrasolar planets detected have highly eccentric orbits, which raises the question of how likely those systems are to host additional planets. We investigate six systems which contain a very eccentric (e>0.6) planet: HD 3651, HD 37605, HD 45350, HD 80606, HD 89744, and 16 Cyg B. We present updated radial-velocity observations and orbital solutions, search for additional planets, and perform test particle simulations to find regions of dynamical stability. The dynamical simulations show that short-period planets could exist in the HD 45350 and 16 Cyg B systems, and we use the observational data to set tight detection limits, which rule out additional planets down to a few Neptune masses in the HD 3651, HD 45350, and 16 Cyg B systems.

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arXiv2007

Models of the Collisional Damping Scenario for Ice Giant Planets and Kuiper Belt Formatio

Chiang et al. 2006, hereafter C06 have recently proposed that the observed structure of the Kuiper belt could be the result of a dynamical instability of a system of ~5 primordial ice giant planets in the outer Solar System. According to this scenario, before the instability occurred, these giants were growing in a highly collisionally damped environment according to the arguments in Goldreich et al. (2004a,b, hereafter G04). Here we test this hypothesis with a series of numerical simulations using a new code designed to incorporate the dynamical effects of collisions. We find that we cannot reproduce the observed Solar System. In particular, G04 and C06 argue that during the instability, all but two of the ice giants would be ejected from the Solar System by Jupiter and Saturn, leaving Uranus and Neptune behind. We find that ejections are actually rare and that instead the systems spread outward. This always leads to a configuration with too many planets that are too far from the Sun. Thus, we conclude that both G04's scheme for the formation of Uranus and Neptune and C06's Kuiper belt formation scenario are not viable in their current forms.

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arXiv2003

Oligarchic growth of giant planets

Runaway growth ends when the largest protoplanets dominate the dynamics of the planetesimal disk; the subsequent self-limiting accretion mode is referred to as ``oligarchic growth.'' Here, we begin by expanding on the existing analytic model of the oligarchic growth regime. From this, we derive global estimates of the planet formation rate throughout a protoplanetary disk. We find that a relatively high-mass protoplanetary disk ($\sim$ 10$\times$ minimum-mass) is required to produce giant planet core-sized bodies ($\sim$ 10 M$_{\oplus}$) within the lifetime of the nebular gas ($\la$ 10 million years). However, an implausibly massive disk is needed to produce even an Earth mass at the orbit of Uranus by 10 Myrs. Subsequent accretion without the dissipational effect of gas is even slower and less efficient. In the limit of non-interacting planetesimals, a reasonable-mass disk is unable to produce bodies the size of the Solar System's two outer giant planets at their current locations on {\it any} timescale; if collisional damping of planetesimal random velocities is sufficiently effective, though, it may be possible for a Uranus/Neptune to form in situ in less than the age of the Solar System. We perform numerical simulations of oligarchic growth with gas, and find that protoplanet growth rates agree reasonably well with the analytic model as long as protoplanet masses are well below their estimated final masses. However, accretion stalls earlier than predicted, so that the largest final protoplanet masses are smaller than those given by the model. Thus the oligarchic growth model, in the form developed here, appears to provide an upper limit for the efficiency of giant planet formation.

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arXiv2001

The formation of Uranus and Neptune among Jupiter and Saturn

The outer giant planets, Uranus and Neptune, pose a challenge to theories of planet formation. They exist in a region of the Solar System where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies ($\sim$ 15 and 17 times as massive as the Earth, respectively) very difficult. Previously, we proposed a model which addresses this problem: Instead of forming in the trans-Saturnian region, Uranus and Neptune underwent most of their growth among proto-Jupiter and -Saturn, were scattered outward when Jupiter acquired its massive gas envelope, and subsequently evolved toward their present orbits. We present the results of additional numerical simulations, which further demonstrate that the model readily produces analogues to our Solar System for a wide range of initial conditions. We also find that this mechanism may partly account for the high orbital inclinations observed in the Kuiper belt.

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arXiv1998

The Calibration of the HST Kuiper Belt Object Search: Setting the Record Straight

The limiting magnitude of the HST data set used by Cochran et al. (1995) to detect small objects in the Kuiper belt is reevaluated, and the methods used are described in detail. It is shown, by implanting artificial objects in the original HST images, and re-reducing the images using our original algorithm, that the limiting magnitude of our images (as defined by the 50% detectability limit) is $V=28.4$. This value is statistically the same as the value found in the original analysis. We find that $\sim50%$ of the moving Kuiper belt objects with $V=27.9$ are detected when trailing losses are included. In the same data in which these faint objects are detected, we find that the number of false detections brighter than $V=28.8$ is less than one per WFPC2 image. We show that, primarily due to a zero-point calibration error, but partly due to inadequacies in modeling the HST'S data noise characteristics and Cochran et al.'s reduction techniques, Brown et al. 1997 underestimate the SNR of objects in the HST dataset by over a factor of 2, and their conclusions are therefore invalid.

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arXiv1997

Variable Timestep Integrators for Long-Term Orbital Integrations

Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations in timescale, it is desirable to use a variable timestep. However, naively varying the timestep destroys the desirable properties of symplectic integrators. We discuss briefly the idea that choosing the timestep in a time symmetric manner can improve the performance of variable timestep integrators. Then we present a symplectic integrator which is based on decomposing the force into components and applying the component forces with different timesteps. This multiple timescale symplectic integrator has all the desirable properties of the constant timestep symplectic integrators.

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arXiv1995

The Discovery of Halley-sized Kuiper Belt Objects Using HST

We report the statistical detection (at the >99% confidence level) of a population of 28th magnitude objects exhibiting proper motions of ~1 arcsecond per hour at quadrature in deep HST/WFPC2 images. The drift directions imply a preponderance of objects on prograde orbits concentrated near the ecliptic plane. We interpret this as the detection of objects which reside in the Kuiper belt near or beyond the orbit of Neptune, comparable in size to comet 1P/Halley (radii ~10 km for an albedo of 4%). Our observations imply a population of ~2.5x10^4 objects deg^-2 with V<28.6. This must be viewed as a lower limit until our search of parameter space is complete. Our observations imply that there are >2x10^8 objects of this size in the Kuiper belt with inclinations <12 degrees and within ~40 AU of the Sun.

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