Inner Boundary Condition in Quasi-Lagrangian Simulations of Accretion Disks. (arXiv:2002.05164v1 [astro-ph.EP])

<a href="http://arxiv.org/find/astro-ph/1/au:+Dempsey_A/0/1/0/all/0/1">Adam M. Dempsey</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Munoz_D/0/1/0/all/0/1">Diego Muñoz</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lithwick_Y/0/1/0/all/0/1">Yoram Lithwick</a>

In simulations of viscously evolving accretion disks, the inner boundary

condition is particularly important. If treated incorrectly, it induces

incorrect behavior very quickly, because the viscous time is shortest near the

inner boundary. Recent work has determined the correct inner boundary in

Eulerian simulations. But in quasi-Lagrangian simulations (e.g., SPH, moving

mesh, and mesh-less), where the inner boundary is modeled by removing mass

within a finite zone, the inner density profile typically becomes anomalously

depleted. Here we show how the boundary condition should be applied in such

codes, via a simple modification of the usual approach: when one removes mass,

one must speed up the remaining material so that the disk’s angular momentum is

unchanged. We show with both 1D and 2D moving-mesh (AREPO) simulations that

this scheme works as desired in viscously evolving disks. It produces no

spurious density depletions and is independent of the mass removal rate. This

“torque-free” mass removal technique permits the use of quasi-Lagrangian codes

to simulate viscously evolving disks, while including a variety of additional

effects. As an example, we apply our scheme to a 2D simulation of an accretion

disk perturbed by a very massive planet, in which the disk is evolved to

viscous steady state.

In simulations of viscously evolving accretion disks, the inner boundary

condition is particularly important. If treated incorrectly, it induces

incorrect behavior very quickly, because the viscous time is shortest near the

inner boundary. Recent work has determined the correct inner boundary in

Eulerian simulations. But in quasi-Lagrangian simulations (e.g., SPH, moving

mesh, and mesh-less), where the inner boundary is modeled by removing mass

within a finite zone, the inner density profile typically becomes anomalously

depleted. Here we show how the boundary condition should be applied in such

codes, via a simple modification of the usual approach: when one removes mass,

one must speed up the remaining material so that the disk’s angular momentum is

unchanged. We show with both 1D and 2D moving-mesh (AREPO) simulations that

this scheme works as desired in viscously evolving disks. It produces no

spurious density depletions and is independent of the mass removal rate. This

“torque-free” mass removal technique permits the use of quasi-Lagrangian codes

to simulate viscously evolving disks, while including a variety of additional

effects. As an example, we apply our scheme to a 2D simulation of an accretion

disk perturbed by a very massive planet, in which the disk is evolved to

viscous steady state.

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