Statistical Study of the Early Solar System's Instability with 4, 5 and 6 Giant Planets

Several properties of the Solar System, including the wide radial spacing and orbital eccentricities of giant planets, can be explained if the early Solar System evolved through a dynamical instability followed by migration of planets in the planetesimal disk. Here we report the results of a statistical study, in which we performed nearly 10^4 numerical simulations of planetary instability starting from hundreds of different initial conditions. We found that the dynamical evolution is typically too violent, if Jupiter and Saturn start in the 3:2 resonance, leading to ejection of at least one ice giant from the Solar System. Planet ejection can be avoided if the mass of the transplanetary disk of planetesimals was large (M_disk>50 M_Earth), but we found that a massive disk would lead to excessive dynamical damping (e.g., final e_55 < 0.01 compared to present e_55=0.044, where e_55 is the amplitude of the fifth eccentric mode in the Jupiter's orbit), and to smooth migration that violates constraints from the survival of the terrestrial planets. Better results were obtained when the Solar System was assumed to have five giant planets initially and one ice giant, with the mass comparable to that of Uranus and Neptune, was ejected into interstellar space by Jupiter. The best results were obtained when the ejected planet was placed into the external 3:2 or 4:3 resonance with Saturn and M_disk ~ 20 M_Earth. The range of possible outcomes is rather broad in this case, indicating that the present Solar System is neither a typical nor expected result for a given initial state, and occurs, in best cases, with only a ~5% probability (as defined by the success criteria described in the main text). The case with six giant planets shows interesting dynamics but does offer significant advantages relative to the five planet case.Comment: To appear in The Astronomical Journa

Fast Inversion Method for Determination of Planetary Parameters from Transit Timing Variations

The Transit Timing Variation (TTV) method relies on monitoring changes in timing of transits of known exoplanets. Non-transiting planets in the system can be inferred from TTVs by their gravitational interaction with the transiting planet. The TTV method is sensitive to low-mass planets that cannot be detected by other means. Here we describe a fast algorithm that can be used to determine the mass and orbit of the non-transiting planets from the TTV data. We apply our code, ttvim.f, to a wide variety of planetary systems to test the uniqueness of the TTV inversion problem and its dependence on the precision of TTV observations. We find that planetary parameters, including the mass and mutual orbital inclination of planets, can be determined from the TTV datasets that should become available in near future. Unlike the radial velocity technique, the TTV method can therefore be used to characterize the inclination distribution of multi-planet systems

Dynamics, Origin, and Activation of Main Belt Comets

The discovery of Main Belt Comets (MBCs) has raised many questions regarding the origin and activation mechanism of these objects. Results of a study of the dynamics of these bodies suggest that MBCs were formed in-situ as the remnants of the break-up of large icy asteroids. Simulations show that similar to the asteroids in the main belt, MBCs with orbital eccentricities smaller than 0.2 and inclinations lower than 25 degrees have stable orbits implying that many MBCs with initially larger eccentricities and inclinations might have been scattered to other regions of the asteroid belt. Among scattered MBCs, approximately 20 percent reach the region of terrestrial planets where they might have contributed to the accumulation of water on Earth. Simulations also show that collisions among MBCs and small objects could have played an important role in triggering the cometary activity of these bodies. Such collisions might have exposed sub-surface water ice which sublimated and created thin atmospheres and tails around MBCs. This paper discusses the results of numerical studies of the dynamics of MBCs and their implications for the origin of these objects. The results of a large numerical modeling of the collisions of m-sized bodies with km-sized asteroids in the outer part of the asteroid belt are also presented and the viability of the collision-triggering activation scenario is discussed.Comment: 9 pages, 4 figures, to appear in the proceedings of IAU Symposium 263: Icy Bodies of the Solar System (Eds. D. Lazzaro, D. Prialnik, o. Schulz and J.A. Fernandez), Cambridge Univ. Pres

A Region Void of Irregular Satellites Around Jupiter

An interesting feature of the giant planets of our solar system is the existence of regions around these objects where no irregular satellites are observed. Surveys have shown that, around Jupiter, such a region extends from the outermost regular satellite Callisto, to the vicinity of Themisto, the innermost irregular satellite. To understand the reason for the existence of such a satellite-void region, we have studied the dynamical evolution of Jovian irregulars by numerically integrating the orbits of several hundred test particles, distributed in a region between 30 and 80 Jupiter-radii, for different values of their semimajor axes, orbital eccentricities, and inclinations. As expected, our simulations indicate that objects in or close to the influence zones of the Galilean satellites become unstable because of interactions with Ganymede and Callisto. However, these perturbations cannot account for the lack of irregular satellites in the entire region between Callisto and Themisto. It is suggested that at distances between 60 and 80 Jupiter-radii, Ganymede and Callisto may have long-term perturbative effects, which may require the integrations to be extended to times much longer than 10 Myr. The interactions of irregular satellites with protosatellites of Jupiter at the time of the formation of Jovian regulars may also be a destabilizing mechanism in this region. We present the results of our numerical simulations and discuss their applicability to similar satellite void-regions around other giant planets.Comment: 21 pages, 9 figures, 2 tables, accepted for publication in the Astronomical Journa

Binary YORP and Evolution of Binary Asteroids

The rotation states of kilometer sized near earth asteroids are known to be affected by the YORP effect. In a related effect, Binary YORP (BYORP) the orbital properties of a binary asteroid evolves under a radiation effect mostly acting on a tidally locked secondary. The BYORP effect can alter the orbital elements in $\sim 10^{4-5}$ years for a $D_{p}=2\;km$ primary with a $D_{s}=0.4\; km$ secondary at $1\; AU$. It can either separate the binary components or cause them to collide. In this paper we devise a simple approach to calculate the YORP effect on asteroids and BYORP effect on binaries including $J_2$ effects due to primary oblateness and the sun. We apply this to asteroids with known shapes as well as a set of randomly generated bodies with various degrees of smoothness. We find a strong correlation between the strengths of an asteroid's YORP and BYORP effects. Therefore, a statistical knowledge on one, could be used to estimate the effect of the other. We show that the action of BYORP preferentially shrinks rather than expands the binary orbit and that YORP preferentially slows down asteroids. This conclusion holds for the two extremes of thermal conductivities studied in this work and assuming the asteroid reaches a stable point, but may break down for moderate thermal conductivity. The YORP and BYORP effects are shown to be smaller than what could be naively expected due to near cancellation of the effects on small scales. Taking this near cancellation into account, a simple order of magnitude estimate of the YORP and BYORP effects as function of the sizes and smoothness of the bodies is calculated. Finally, we provide a simple proof showing that there is no secular effect due to absorption of radiation in BYORP.Comment: Accepted to Astronomical Journa