The fragmentation criteria in local vertically stratified self-gravitating disk simulations

TL;DR

This study compares 2D and 3D simulations of self-gravitating disks to understand fragmentation, finding that 3D simulations converge at high resolution and support a critical cooling timescale of beta=3.

Contribution

The paper demonstrates that 3D simulations of disk fragmentation converge at high resolution, addressing issues present in 2D models and confirming the critical cooling timescale.

Findings

3D simulations converge at ~40 grid cells per scale height.

Convergence supports a critical beta value of 3 for fragmentation.

3D models mitigate the overestimation of self-gravity effects seen in 2D.

Abstract

Massive circumstellar disks are prone to gravitational instabilities, which trigger the formation of spiral arms that can fragment into bound clumps under the right conditions. Two dimensional simulations of self-gravitating disks are useful starting points for studying fragmentation, allowing for high-resolution simulations of thin disks. However, convergence issues can arise in 2D from various sources. One of these sources is the 2D approximation of self-gravity, which exaggerates the effect of self-gravity on small scales when the potential is not smoothed to account for the assumed vertical extent of the disk. This effect is enhanced by increased resolution, resulting in fragmentation at longer cooling timescales $\beta$. If true, it suggests that the 3D simulations of disk fragmentation may not have the same convergence problem and could be used to examine the nature of fragmentation without smoothing self-gravity on scales similar to the disk scale height. To that end, we have carried out local 3D self-gravitating disk simulations with simple $\beta$ cooling with fixed background irradiation to determine if 3D is necessary to properly describe disk fragmentation. Above a resolution of $\sim 40$ grid cells per scale height, we find that our simulations converge with respect to the cooling timescale. This result converges in agreement with analytic expectations which place a fragmentation boundary at $\beta_\mathrm{crit} = 3$.