Hill sphere

About: Hill sphere is a research topic. Over the lifetime, 277 publications have been published within this topic receiving 8234 citations. The topic is also known as: Roche sphere.

Disk Accretion onto High-Mass Planets

Abstract: We analyze the nonlinear, two-dimensional response of a gaseous, viscous protoplanetary disk to the presence of a planet of one Jupiter mass (1 MJ) and greater that orbits a 1 M☉ star by using the ZEUS hydrodynamics code with high resolution near the planet's Roche lobe. The planet is assumed to be in a circular orbit around the central star and is not allowed to migrate. A gap is formed about the orbit of the planet, but there is a nonaxisymmetric flow through the gap and onto the planet. The gap partitions the disk into an inner (outer) disk that extends inside (outside) the planet's orbit. For a 1 MJ planet and typical disk parameters, the accretion through the gap onto the planet is highly efficient. That is, the rate is comparable to the accretion rate toward the central star that would occur in the absence of the planet (at the location of the planet). For typical disk parameters, the mass-doubling timescale is less than 105 yr, considerably shorter than the disk lifetime. Following shocks near the L1 and L2 Lagrangian points, disk material enters the Roche lobe in the form of two gas streams. Shocks occur within the Roche lobe as the gas streams collide, and shocks lead to rapid inflow toward the planet within much of planet's Roche lobe. Shocks also propagate in the inner and outer disks that orbit the star. For higher mass planets (of order 6 MJ), the flow rate onto the planet is considerably reduced, which suggests an upper mass limit to planets in the range of 10 MJ. This rate reduction is related to the fact that the gap width increases relative to the Roche (Hill sphere) radius with increasing planetary mass. The flow in the gap affects planetary migration. For the 1 MJ planet case, mass can penetrate from the outer disk to the inner disk, so that the inner disk is not depleted. The results suggest that most of the mass in gas giant planets is acquired by flows through gaps.

Formation of Kuiper-belt binaries by dynamical friction and three-body encounters

Abstract: The Kuiper belt is a disk of icy bodies that orbit the Sun beyond Neptune; the largest known members are Pluto and its companion Charon. A few per cent of Kuiper-belt bodies have recently been found to be binaries with wide separations and mass ratios of the order of unity. Collisions were too infrequent to account for the observed number of binaries, implying that these binaries formed through collisionless interactions mediated by gravity. These interactions are likely to have been most effective during the period of runaway accretion, early in the Solar System's history. Here we show that a transient binary forms when two large bodies penetrate one another's Hill sphere (the region where their mutual forces are larger than the tidal force of the Sun). The loss of energy needed to stabilize the binary orbit can then occur either through dynamical friction from surrounding small bodies, or through the gravitational scattering of a third large body. Our estimates slightly favour the former mechanism. We predict that five per cent of Kuiper-belt objects are binaries with apparent separations greater than 0.2 arcsec, and that most are in tighter binaries or systems of higher multiplicity.

Orbital and Collisional Evolution of the Irregular Satellites

Abstract: The irregular moons of the Jovian planets are a puzzling part of the solar system inventory. Unlike regular satellites, the irregular moons revolve around planets at large distances in tilted and eccentric orbits. Their origin, which is intimately linked with the origin of the planets themselves, is yet to be explained. Here we report a study of the orbital and collisional evolution of the irregular satellites from times after their formation to the present epoch. The purpose of this study is to find out the features of the observed irregular moons that can be attributed to this evolution and separate them from signatures of the formation process. We numerically integrated ≈60,000 test satellite orbits to map orbital locations that are stable on long time intervals. We found that the orbits highly inclined to the ecliptic are unstable due to the effect of the Kozai resonance, which radially stretches them so that satellites either escape from the Hill sphere, collide with massive inner moons, or impact the parent planet. We also found that prograde satellite orbits with large semimajor axes are unstable due to the effect of the evection resonance, which locks the orbit's apocenter to the apparent motion of the Sun around the parent planet. In such a resonance, the effect of solar tides on a resonant moon accumulates at each apocenter passage of the moon, which causes a radially outward drift of its orbital apocenter; once close to the Hill sphere, the moon escapes. By contrast, retrograde moons with large orbital semimajor axes are long-lived. We have developed an analytic model of the distant satellite orbits and used it to explain the results of our numerical experiments. In particular, we analytically studied the effect of the Kozai resonance. We numerically integrated the orbits of the 50 irregular moons (known by 2002 August 16) for 108 yr. All orbits were stable on this time interval and did not show any macroscopic variations that would indicate instabilities operating on longer time spans. The average orbits calculated from this experiment were then used to probe the collisional evolution of the irregular satellite systems. We found that (1) the large irregular moons must have collisionally eliminated many small irregular moons, thus shaping their population to the currently observed structures; (2) some dynamical families of satellites could have been formed by catastrophic collisions among the irregular moons; and (3) Phoebe's surface must have been heavily cratered by impacts from an extinct population of Saturnian irregular moons, much larger than the present one. We therefore suggest that the Cassini imaging of Phoebe in 2004 can be used to determine the primordial population of small irregular moons of Saturn. In such a case, we will also better understand the overall efficiency of the formation process of the irregular satellites and the physical conditions that existed during planetary formation. We discovered two dynamical families of tightly clustered orbits within the Jovian retrograde group. We believe that these two clusters may be the remnants of two collisionally disrupted bodies. We found that the entire Jovian retrograde group and the Saturnian inclination groups were not produced by single breakups, because the ejection velocities derived from the orbital structures of these groups greatly exceed values calculated by modern numerical models of collisional breakups. Taken together, the evidence presented here suggests that many properties of the irregular moons previously assigned to their formation process may have resulted from their later dynamical and collisional evolution. Finally, we have found that several irregular moons, namely, Pasiphae, Sinope, S/2001 J10, S/2000 S5, S/2000 S6, and S/2000 S3, have orbits characterized by secular resonances. The orbits of some of these moons apparently evolved by some slow dissipative process in the past and became captured in tiny resonant volumes.

Planet Migration and Gap Formation by Tidally Induced Shocks

Abstract: Gap formation in a gas disk triggered by disk-planet tidal interaction is considered. Density waves launched by the planet are assumed to be damped as a result of their nonlinear evolution leading to shock formation and its subsequent dissipation. As a consequence, wave angular momentum is transferred to the disk, leading to evolution of its surface density. Planetary migration is an important ingredient of the theory; effects of the planet-induced surface density perturbations on the migration speed are considered. A gap is assumed to form when a stationary solution for the surface density profile is no longer possible in the frame of reference migrating with the planet. An analytical limit on the planetary mass necessary to open a gap in an inviscid disk is derived. The critical mass turns out to be smaller than the mass M1 for which the planetary Hill radius equals the disk scale height by a factor of at least Q5/7 (Q is the Toomre stability parameter), depending on the strength of the migration feedback. In viscous disks the critical planetary mass could vary from ~0.2M1 to M1, depending on the disk viscosity. This implies that a gap could be formed by a planet with mass of 2-15 M⊕, depending on the disk aspect ratio, viscosity, and the planet's location in the nebula.