Stellar irradiated discs and implications on migration of embedded planets

Abstract

Context. The strength and direction of migration of embedded low mass planets depends on the disc's thermodynamic state. It has been shown that, in discs where the viscous heating is balanced by radiative transport, the migration can be directed outwards, a process which extends the lifetime of growing planetary embryos. Aims. We investigate the influence of opacity and stellar irradiation on the disc thermodynamics. We focus on equilibrium discs, which have no net mass flux. Utilizing the resulting disc structure, we determine the regions of outward migration in the disc. Methods. We performed two-dimensional numerical simulations of equilibrium discs with viscous heating, radiative cooling, and stellar irradiation. We used the explicit/implicit hydrodynamical code NIRVANA that includes a full tensor viscosity and stellar irradiation, as well as a two temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration of embedded planets was studied by using torque formulae. Results. In the constant opacity case, our code reproduces the analytical results corresponding to a black-body disc: the stellar irradiation dominates in the outer regions -leading to flaring (H/r ∝ r 2/7 ) -while the viscous heating dominates close to the star. In particular, we find that the inner edge of the disc should not be significantly puffed-up by the stellar irradiation. If the opacity depends on the local density and temperature, the structure of the disc is different, and several bumps in the aspect ratio H/r appear, due to transitions between different opacity regimes. The bumps in the disc structure are very important, as they can shield the outer disc from stellar irradiation. Conclusions. Stellar irradiation is an important factor for determining the disc structure and has dramatic consequences for the migration of embedded planets. Compared to discs with only viscous heating and radiative cooling, a stellar irradiated disc features a much smaller region of outward migration for a range of planetary masses. This suggests that the region where the formation of giant planet cores takes place is smaller, which in turn might lead to a shorter growth phase.

Accretion of Uranus and Neptune from inward-migrating planetary embryos blocked by Jupiter and Saturn

“…We are aware that the direction of type I migration is extremely sensitive to the disk thermodynamics and to the planet mass (e.g., Kley & Nelson 2012;Baruteau et al 2014). Combination of different torques acting on the planet from the gas disk may result in inward or outward migration (Paardekooper & Mellema 2006;Baruteau & Masset 2008;Paardekooper & Papaloizou 2008b;Bitsch & Kley 2011;Kretke & Lin 2012;Bitsch et al 2013Bitsch et al , 2014). Outward migration is only possible in specific regions of a non-isothermal disk Kley et al 2009;Bitsch et al 2014).…”

“…This is because the disk irradiates efficiently and behaves like an isothermal disk when it becomes optically thin (Paardekooper & Mellema 2008a). When this occurs, type I migrating planets simply migrate inward at the type I isothermal rate (Bitsch et al 2013(Bitsch et al , 2014Cossou et al 2014). Because we assumed that Jupiter and Saturn are already fully formed, we considered for simplicity that the disk has evolved sufficiently to behave as an isothermal disk.…”

Radiation magnetohydrodynamics in global simulations of protoplanetary discs

“…These approximations are well suited to our applications (v c), but not necessarily to other regimes like the dynamic diffusion (Krumholz et al 2007). A similar method was presented in Bitsch et al (2013b) and Kolb et al (2013).…”

Accretion of Jupiter-Mass Planets in the Limit of Vanishing Viscosity

“…The first is that we wish to focus our paper on the role of numerical viscosity and on viscosity-independent transport mechanisms within the CPD, which have never been thoroughly discussed before; these considerations should be independent of the EOS assumed. Second, radiative simulations imply additional, badly constrained parameters such as those in the prescription for the opacity laws (e.g., Ayliffe & Bate 2009;Bitsch et al 2013). We want to focus the discussion on the objectives stated above without distraction.…”