CONVERGENCE STUDIES OF MASS TRANSPORT IN DISKS WITH GRAVITATIONAL INSTABILITIES. I. THE CONSTANT COOLING TIME CASE
- Astronomy Department, Indiana University, Bloomington, IN 47405 (United States)
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 {alpha}-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 (m{phi}), sin (m{phi}) is performed to evaluate the amplitudes A{sub m} of these structures. The A{sub m} , gravitational torques, and the effective Shakura and Sunyaev {alpha} arising from gravitational stresses are determined for each resolution. We find nonzero A{sub m} for all m-values and that A{sub m} 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 {alpha} also depends upon the magnitude of the stresses, thus {alpha}{sub eff} also decreases with increasing resolution. Our converged {alpha}{sub eff} 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.
- OSTI ID:
- 22011780
- Journal Information:
- Astrophysical Journal, Vol. 746, Issue 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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