Interaction between massive planets on inclined orbits and circumstellar discs

Abstract

We study the interaction between massive planets and a gas disc with a mass in the range expected for protoplanetary discs. We use SPH simulations to study the orbital evolution of a massive planet as well as the dynamical response of the disc for planet masses between 1 and 6 M J and the full range of initial relative orbital inclinations.We find that gap formation can occur for planets in inclined orbits as well as for coplanar orbits as expected. For given planet mass, a threshold relative orbital inclination exists under which a gap forms. This threshold increases with planet mass. Orbital migration manifest through a decreasing semi-major axis is seen in all cases.At high relative inclinations, the inclination decay rate increases for increasing planet mass and decreasing initial relative inclination as is expected from estimates based on dynamical friction between planet and disc. For an initial semi-major axis of 5 AU and relative inclination of i 0 = 80 • , the times required for the inclination to decay by 10 • is ∼ 10 6 yr and ∼ 10 5 yr for 1 M J and 6 M J respectively, these times scaling in the usual way for larger initial orbits. For retrograde planets, the inclination always evolves towards coplanarity with the disc, with the rate of evolution being fastest for orbits with i 0 → 180 • . The indication is thus that, without taking account of subsequent operation of phenomena such as the Lidov-Kozai effect, planets with mass 1 M J initiated in circular orbits with semi-major axis ∼ 5 AU and i 0 ∼ 90 • might only just become coplanar, as a result of frictional effects, within the disc lifetime. In other cases highly inclined orbits will survive only if they are formed after the disc has mostly dispersed.Planets on inclined orbits warp the disc by an extent that is negligible for 1 M J but increases with increasing mass becoming quite significant for a planet of mass 6 M J . In that case, the disc can gain a total inclination of up to 15 • together with a warped inner structure with an inclination of up to ∼ 20 • relative to the outer part. We also find a solid body precession of both the total disc angular momentum vector and the planet orbital momentum vector about the total angular momentum vector, with the angular velocity of precession decreasing with increasing relative inclination as expected in that case.Our results illustrate that the influence of an inclined massive planet on a protoplanetary disc can lead to significant changes of the disc structure and orientation which can in turn affect the orbital evolution of the planet significantly. A threedimensional treatment of the disc is then essential in order to capture all relevant dynamical processes in the composite system.

Gap formation by inclined massive planets in locally isothermal three-dimensional discs

“…In 100 orbits, the semimajor axis decays from 5.2 AU to 4.8 AU and the inclination from 20 to 13 deg, resulting in di/dt = −0.07 deg/orbit and dR p /dt = −4 × 10 −3 AU/orbit. These rates of inclination damping and radial migration are consistent with those found in previous studies (Marzari & Nelson 2009;Xiang-Gruess & Papaloizou 2013). For instance, for a planet with i 0 = 20 • , Σ 0 = 76, and q = 10 −3 , Xiang-Gruess & Papaloizou (2013) find that di/dt = −0.028 deg/orbit and dR p /dt = −0.9 × 10 −3 AU/orbit.…”

“…We assume the disc to be pressure-less, so that it consists of test particles, and calculate the disc and planet exchange of angular momentum as a result of the gravitational interaction of the particles with the planet. Treating the disc particles as being pressure-less is adequate as long as the velocity of the planet relative to the disc particles is supersonic (e.g., Cantó et al 2013;Xiang-Gruess & Papaloizou 2013). This condition is valid for planetary inclinations larger than the disc's aspect ratio 1 .…”

“…It was found that 40% of the massive planets observed have a non-zero tilt angle (Triaud et al 2010;Albrecht et al 2012). Different hypothesis have been suggested to explain how planets can have misaligned orbits (e.g., Xiang-Gruess & Papaloizou 2013;Picogna & Marzari 2015).…”

The Occurrence and Architecture of Exoplanetary Systems

“…The eccentricities are low because the streamlines within the disk are nearly circular; this is a consequence of viscous dissipation. Furthermore, even if an object managed to acquire a moderate eccentricity or inclination, gravitational and hydrodynamical interactions with the disk would coplanarize and circularize its orbit (Cresswell et al 2007, Xiang-Gruess & Papaloizou 2013. The theory also predicted that a planet's composition should be linked to the location of its formation within the disk.…”

Highly inclined and eccentric massive planets

“…However, this process can only explain the eccentricity of very massive (≈5-10 M Jup ) planets. Xiang-Gruess & Papaloizou (2013) have recently studied the interactions between Jupiter-mass planets and circumstellar discs as well. However, they did not consider planets on eccentric orbits and they were using SPH simulations, while we use a grid-based code.…”