Convergence studies of mass transport in disks with gravitational instabilities. I. the constant cooling time case

dc.altmetrics.displayfalseen
dc.contributor.authorMichael, S.en
dc.contributor.authorSteiman-Cameron, T.Y.en
dc.contributor.authorDurisen, R.H.en
dc.contributor.authorBoley, A.C.en
dc.date.accessioned2014-10-27T17:12:07Zen
dc.date.available2014-10-27T17:12:07Zen
dc.date.issued2012en
dc.description.abstractWe 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 ($m\phi$), sin ($m\phi$) is performed to evaluate the amplitudes $A_{m}$ of these structures. The $A_{m}$, gravitational torques, and the effective Shakura & Sunyaev α arising from gravitational stresses are determined for each resolution. We find nonzero $A_{m}$ for all $m$-values and that $A_{m}$ 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 $\alpha_{\text{eff}}$ also decreases with increasing resolution. Our converged $\alpha_{\text{eff}}$ 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.en
dc.identifier.citationMichael, S., Steiman-Cameron, T. Y., Durisen, R. H., & Boley, A. C. (2012). Convergence studies of mass transport in disks with gravitational instabilities. I. the constant cooling time case. Astrophysical Journal, 746(1). http://dx.doi.org/10.1088/0004-637X/746/1/98en
dc.identifier.urihttps://hdl.handle.net/2022/19066
dc.language.isoen_USen
dc.publisherThe American Astronomical Societyen
dc.relation.isversionofhttps://doi.org/10.1088/0004-637X/746/1/98en
dc.rights© 2012 The American Astronomical Society. All rights reserved.en
dc.subjectaccretionen
dc.subjectaccretion disksen
dc.subjectprotoplanetary disksen
dc.subjectstars: formationen
dc.titleConvergence studies of mass transport in disks with gravitational instabilities. I. the constant cooling time caseen
dc.typeArticleen

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