Convergence Studies of Mass Transport in Disks with Gravitational Instabilities. I. The Constant Cooling Time Case

Details Convergence Studies of Mass Transport in Disks with Gravitational Instabilities. I. The Constant Cooling Time Case Convergence Studies of Mass Transport in Disks with Gravitational Instabilities. I. The Constant Cooling Time Case

Feb 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012apj...746...98m&link_type=abstract

The Astrophysical Journal, Volume 746, Issue 1, article id. 98 (2012).

Astronomy and Astrophysics

Astronomy

Accretion, Accretion Disks, Protoplanetary Disks, Stars: Formation

Scientific paper

We conduct a convergence study of a protostellar disk, subject to a constant global cooling time and susceptible to gravitational instabilities (GIs), at a time when heating and cooling are roughly balanced. Our goal is to determine the gravitational torques produced by GIs, the level to which transport can be represented by a simple α-disk formulation, and to examine fragmentation criteria. Four simulations are conducted, identical except for the number of azimuthal computational grid points used. A Fourier decomposition of non-axisymmetric density structures in cos (mphi), sin (mphi) is performed to evaluate the amplitudes Am of these structures. The Am , gravitational torques, and the effective Shakura & Sunyaev α arising from gravitational stresses are determined for each resolution. We find nonzero Am for all m-values and that Am summed over all m is essentially independent of resolution. Because the number of measurable m-values is limited to half the number of azimuthal grid points, higher-resolution simulations have a larger fraction of their total amplitude in higher-order structures. These structures act more locally than lower-order structures. Therefore, as the resolution increases the total gravitational stress decreases as well, leading higher-resolution simulations to experience weaker average gravitational torques than lower-resolution simulations. The effective α also depends upon the magnitude of the stresses, thus αeff also decreases with increasing resolution. Our converged αeff is consistent with predictions from an analytic local theory for thin disks by Gammie, but only over many dynamic times when averaged over a substantial volume of the disk.

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