arXiv subjects

Rodney Gomes

Publications and source records attributed to Rodney Gomes.

15 recordsLinked to original sources

arXiv2026

Neptune's obliquity was likely engendered by Triton's tidal evolution

Neptune's present axial tilt of approximately 28 deg. with respect to its orbital plane can be explained by collisions that its primordial core may have experienced with surrounding planetary embryos during the final stages of its formation. Alternatively, Neptune could have attained its present mass solely through pebble accretion, without the formation of nearby planetary embryos. The embryo-collision scenario has the advantage of naturally explaining the large axial tilts observed in the ice giants. To account for these tilts without invoking late-stage catastrophic collisions, an alternative mechanism must be considered. In this work, I propose that Neptune's current axial tilt could result from the interaction between Triton's tidally evolving orbit and Neptune's spin axis, causing it to resonate with the solar system eigenfrequency s_8. Starting from a Triton-mass satellite captured via the binary planetesimal disruption mechanism, I show that orbital evolutions bringing the satellite near Triton's present orbit can induce a spin-s_8 resonance capable of producing a significant axial tilt of Neptune's spin axis. I develop a model for planetary spin-axis evolution using Euler's equations for a rigid body, which is incorporated into classical numerical integrations of the Newtonian equations of motion. I also include a tidal model to account for the satellite's semimajor-axis decay and orbital circularization. Several numerical simulations are performed with this model, including Neptune as the central body, the newly captured satellite, the Sun and the three other giant planets. Increases in Neptune's obliquity are observed, exceeding 50 deg. in some cases. An obliquity above 20 deg. is obtained for roughly 1/3 of the cases. If Neptune initially had a near-zero obliquity, its current value could therefore have been naturally engendered by the tidal evolution of Triton.

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arXiv2022

Dynamical origin of the Dwarf Planet Ceres

The Dwarf Planet Ceres revealed the presence of ammonia and other unique properties compared to other asteroids in the main belt which suggests that it was not formed in situ. We model the early dynamical evolution of the outer Solar System to study possible dynamical mechanisms to implant a Ceres-sized planetesimal in the asteroid belt from the trans-Saturnian region. We calculate that the fraction of the population of Ceres-sized planetesimals that are captured in the asteroid belt is in the range of 2.8e-5 to 1.2e-3 depending on the initial location in the outer planetesimal disk. The captured bodies have a 70% probability to have a semimajor axis between 2.5 and 3 au, a 33% probability to have an eccentricity smaller than 0.2 and a 45% probability to have an orbital inclination smaller than 10 degrees. Assuming the existence of 3,600 Ceres-size planetesimals in the inner part of the trans-Saturnian disk, consistent with the estimate of Nesvorny & Vokrouhlicky (2016) for the trans-Neptunian disk, our estimated capture probability and a final 80% depletion of the asteroid belt during the subsequent giant planet instability, lead to capture 1 Ceres in the asteroid belt, with a probability of 15%, 34%, and 51% to be located in the inner, middle and outer belt respectively.

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arXiv2020

The Formation of the Cold Classical Kuiper Belt by a Short Range Transport Mechanism

The Classical Kuiper Belt is populated by a group of objects with low inclination orbits, reddish colors and usually belonging to a binary system. This so called Cold Classical Kuiper Belt is considered to have been formed in situ from primordial ice pebbles that coagulated into planetesimals hundreds of kilometers in diameter. According to this scenario, the accretion of pebbles into large planetesimals would have occurred through the streaming instability mechanism that would be effective in the primordial Solar System disk of gas and solids. Nevertheless other objects with the same color characteristics as those found in the Cold Classical Kuiper Belt can be encountered also past the 2:1 mean motion resonance with Neptune as scattered or detached objects. Here I propose a mechanism that can account for both the cold Classical Kuiper Belt objects and other reddish objects outside the Classical Kuiper Belt. According to the proposed scenario, reddish objects were primordially in the outer portion of the planetesimal disk which was however truncated somewhere below 42 au. In this manner the cold Classical Kuiper Belt and its scattered / detached counterpart were respectively transported outwards by a short range or slightly scattered to their present locations. Resonant objects were also formed by the same process. This mechanism is aimed at explaining the distribution of all objects that share the same color characteristics as coming from a common origin in the outer borders of the primordial planetesimal disk. According to the scenario here proposed the Cold Classical Kuiper Belt would have been formed around 4 au inside its present location with a total mass 20 to 100 times as large as its present value.

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arXiv2019

Dynamical evidence for an early giant planet instability

The dynamical structure of the Solar System can be explained by a period of orbital instability experienced by the giant planets. While a late instability was originally proposed to explain the Late Heavy Bombardment, recent work favors an early instability. We model the early dynamical evolution of the outer Solar System to self-consistently constrain the most likely timing of the instability. We first simulate the dynamical sculpting of the primordial outer planetesimal disk during the accretion of Uranus and Neptune from migrating planetary embryos during the gas disk phase, and determine the separation between Neptune and the inner edge of the planetesimal disk. We performed simulations with a range of migration histories for Jupiter. We find that, unless Jupiter migrated inwards by 10 AU or more, the instability almost certainly happened within 100 Myr of the start of Solar System formation. There are two distinct possible instability triggers. The first is an instability that is triggered by the planets themselves, with no appreciable influence from the planetesimal disk. Of those, the median instability time is $\sim4$Myr. Among self-stable systems -- where the planets are locked in a resonant chain that remains stable in the absence of a planetesimal's disk-- our self-consistently sculpted planetesimal disks nonetheless trigger a giant planet instability with a median instability time of 37-62 Myr for a reasonable range of migration histories of Jupiter. The simulations that give the latest instability times are those that invoked long-range inward migration of Jupiter from 15 AU or beyond; however these simulations over-excited the inclinations of Kuiper belt objects and are inconsistent with the present-day Solar System. We conclude on dynamical grounds that the giant planet instability is likely to have occurred early in Solar System history.

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arXiv2018

Astrometry and Occultation predictions to Trans-Neptunian and Centaur Objects observed within the Dark Energy Survey

Transneptunian objects (TNOs) are a source of invaluable information to access the history and evolution of the outer solar system. However, observing these faint objects is a difficult task. As a consequence, important properties such as size and albedo are known for only a small fraction of them. Now, with the results from deep sky surveys and the Gaia space mission, a new exciting era is within reach as accurate predictions of stellar occultations by numerous distant small solar system bodies become available. From them, diameters with kilometer accuracies can be determined. Albedos, in turn, can be obtained from diameters and absolute magnitudes. We use observations from the Dark Energy Survey (DES) from November 2012 until February 2016, amounting to 4292847 CCD frames. We searched them for all known small solar system bodies and recovered a total of 202 TNOs and Centaurs, 63 of which have been discovered by the DES collaboration until the date of this writing. Their positions were determined using the Gaia Data Release 2 as reference and their orbits were refined. Stellar occultations were then predicted using these refined orbits plus stellar positions from Gaia. These predictions are maintained, and updated, in a dedicated web service. The techniques developed here are also part of an ambitious preparation to use the data from the Large Synoptic Survey Telescope (LSST), that expects to obtain accurate positions and multifilter photometry for tens of thousands of TNOs.

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arXiv2018

Dynamical effects on the classical Kuiper Belt during the excited-Neptune model

The link between the dynamical evolution of the giant planets and the Kuiper Belt orbital structure can provide clues and insight about the dynamical history of the Solar System. The classical region of the Kuiper Belt has two populations (the cold and hot populations) with completely different physical and dynamical properties. These properties have been explained in the framework of a subset of the simulations of the Nice Model, in which Neptune remained on a low-eccentricity orbit (Neptune's eccentricity is never larger than 0.1) throughout the giant planet instability. However, recent simulations have showed that the remaining Nice model simulations, in which Neptune temporarily acquires a large-eccentricity orbit (larger than 0.1), are also consistent with the preservation of the cold population (inclination smaller than 4 degrees), if the latter formed in situ. However, the resulting a cold population showed in many of the simulations eccentricities larger than those observed for the real population. We focus on a short period of time which is characterized by Neptune's large eccentricity and a slow precession of Neptune's perihelion. We show that if self-gravity is considered in the disk, the precession rate of the particles longitude of perihelion is slowed down. This, combined with the effect of mutual scattering among the bodies, which spreads all orbital elements, allows some objects to return to low eccentricities. However, we show that if the cold population originally had a small total mass, this effect is negligible. Thus, we conclude that the only possibilities to keep at low eccentricity some cold-population objects during a high-eccentricity phase of Neptune are that (i) either Neptune's precession was rapid, as suggested by Batygin et al. (2011) or (ii) Neptune's slow precession phase was long enough to allow some particles to experience a full secular cycle.

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arXiv2018

The Influence of Planet 9 on the Orbits of Distant TNOs: The Case for a Low Perihelion Planet

The hypothesis of an additional planet in the outer Solar System has gained new support as a result of the confinement noted in the angular orbital elements of distant trans-Neptunian objects. Orbital parameters proposed for the external perturber suggest semimajor axes between 500 and 1000 au, perihelion distances between 200 and 400 au for masses between 10 and 20 $M_{\oplus}$. In this paper we study the possibility that lower perihelion distances for the additional planet can lead to angular confinements as observed in the population of objects with semimajor axes greater than 250 au and perihelion distances higher than 40 au. We performed numerical integrations of a set of particles subjected to the influence of the known planets and the putative perturber during the age of the Solar System and compared our outputs with the observed population through a statistical analysis. Our investigations showed that lower perihelion distances from the outer planet usually lead to more substantial confinements than higher ones, while retaining the Classical Kuiper Belt as well as the ratio of the number of detached with perihelion distances higher than 42 au to scattering objects in the range of semimajor axes from 100 au to 200 au.

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arXiv2017

Checking the Compatibility of the Cold Kuiper Belt with a Planetary Instability Migration Model

The origin of the orbital structure of the cold component of the Kuiper belt is still a hot subject of investigation. Several features of the solar system suggest that the giant planets underwent a phase of global dynamical instability, but the actual dynamical evolution of the planets during the instability is still debated. To explain the structure of the cold Kuiper belt, Nesvorny (2015, AJ 150,68) argued for a soft instability, during which Neptune never achieved a very eccentric orbit. Here we investigate the possibility of a more violent instability, from an initially more compact fully resonant configuration of 5 giant planets. We show that the orbital structure of the cold Kuiper belt can be reproduced quite well provided that the cold population formed in situ, with an outer edge between 44 and 45 au and never had a large mass.

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arXiv2016

The inclination of the planetary system relative to the solar equator may be explained by the presence of Planet 9

We evaluate the effects of a distant planet, commonly known as planet 9, on the dynamics of the giant planets of the Solar System. We find that, given the large distance of planet 9, the dynamics of the inner giant planets can be decomposed into a classic Lagrange-Laplace dynamics relative to their own invariant plane (the plane orthogonal to their total angular momentum vector) and a slow precession of said plane relative to the total angular momentum vector of the Solar System, including planet 9. Under some specific configurations for planet 9, this precession can explain the current tilt of approximately 6 degrees between the invariant plane of the giant planets and the solar equator. An analytical model is developed to map the evolution of the inclination of the inner giant planets' invariant plane as a function of the planet 9's mass, inclination, eccentricity and semimajor axis, and some numerical simulations of the equations of motion of the giant planets and planet 9 are performed to validate our analytical approach. The longitude of the ascending node of planet 9 is found to be linked to the longitude of the ascending node of the giant planets' invariant plane, which also constrain the longitude of the node of planet 9 on the ecliptic. Some of the planet 9 configurations that allow explaining the current solar tilt are compatible with those proposed to explain the orbital confinement of the most distant Kuiper belt objects. Thus, this work on the one hand gives an elegant explanation for the current tilt between the invariant plane of the inner giant planets and the solar equator and, on the other hand, adds new constraints to the orbital elements of planet 9.

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arXiv2012

NOTE: Explaining why the Uranian satellites have equatorial prograde orbits despite the large planetary obliquity

We show that the existence of prograde equatorial satellites is consistent with a collisional tilting scenario for Uranus. In fact, if the planet was surrounded by a proto-satellite disk at the time of the tilting and a massive ring of material was temporarily placed inside the Roche radius of the planet by the collision, the proto-satellite disk would have started to precess incoherently around the equator of the planet, up to a distance greater than that of Oberon. Collisional damping would then have collapsed it into a thin equatorial disk, from which the satellites eventually formed. The fact that the orbits of the satellites are prograde requires Uranus to have had a non-negligible initial obliquity (comparable to that of Neptune) before it was finally tilted to 98 degrees.

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arXiv2010

Evidence from the asteroid belt for a violent past evolution of Jupiter's orbit

We use the current orbital structure of large (>50km) asteroids in the main asteroid belt to constrain the evolution of the giant planets when they migrated from their primordial orbits to their current ones. Minton & Malhotra (2009) showed that the orbital distribution of large asteroids in the main belt can be reproduced by an exponentially-decaying migration of the giant planets on a time scale of tau ~ 0.5My. However, self-consistent numerical simulations show that the planetesimal-driven migration of the giant planets is inconsistent with an exponential change in their semi major axes on such a short time scale (Hahn & Malhotra, 1999). In fact, the typical time scale is tau > 5My. When giant planet migration on this time scale is applied to the asteroid belt, the resulting orbital distribution is incompatible with the observed one. However, the planet migration can be significantly sped up by planet-planet encounters. Consider an evolution where both Jupiter and Saturn have close encounters with a Neptune-mass planet (presumably Uranus or Neptune themselves) and where this third planet, after being scattered inwards by Saturn, is scattered outwards by Jupiter. This scenario leads to a very rapid increase in the orbital separation between Jupiter and Saturn that we show here to have only mild effects on the structure of asteroid belt. This type of evolution is called a jumping-Jupiter case. Our results suggest that the total mass and dynamical excitation of the asteroid belt before migration were comparable to those currently observed. Moreover, they imply that, before migration, the orbits of Jupiter and Saturn were much less eccentric than the current ones.

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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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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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