Effective Alphas and Mixing for Disks with Gravitational Instabilities: Convergence Testing in Global 3D Simulations

Details Effective Alphas and Mixing for Disks with Gravitational Instabilities: Convergence Testing in Global 3D Simulations Effective Alphas and Mixing for Disks with Gravitational Instabilities: Convergence Testing in Global 3D Simulations

May 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008aas...212.0905m&link_type=abstract

American Astronomical Society, AAS Meeting #212, #9.05; Bulletin of the American Astronomical Society, Vol. 40, p.201

Astronomy and Astrophysics

Astronomy

Scientific paper

Using 3D simulations of a cooling disk undergoing gravitational instabilities (GIs), we compute the effective Shakura and Sunyaev (1973) alphas due to gravitational torques and compare them to predictions from an analytic local theory for thin disks by Gammie (2001). Our goal is to determine how accurately a locally defined alpha can characterize mass and angular momentum transport by GIs in disks. Cases are considered both with cooling by an imposed constant global cooling time (Mejia et al. 2005) and with realistic radiative transfer (Boley et al. 2007). Grid spacing in the azimuthal direction is varied to investigate how the computed alpha is affected by numerical resolution. The azimuthal direction is particularly important, because higher resolution in azimuth allows GI power to spread to higher-order (multi-armed) modes that behave more locally. We find that, in many important respects, the transport of mass and angular momentum by GIs is an intrinsically global phenomenon. Effective alphas are variable on a dynamic time scale over global spatial scales. Nevertheless, preliminary results at the highest resolutions for an imposed cooling time show that our computed alphas, though systematically higher, tend on average to follow Gammie's prediction to within perhaps a factor of two. Our computed alphas include only gravitational stresses, while in Gammie's treatment the effective alpha is due equally to hydrodynamic (Reynolds) and gravitational stresses. So Gammie's prediction may significantly underestimate the true average stresses in a GI-active disk. Our effective alphas appear to be reasonably well converged for 256 and 512 azimuthal zones. We also have a high-resolution simulation under way to test the extent of radial mixing by GIs of gas and its entrained dust for comparison with Stardust observations. Results will be presented if available at the time of the meeting.

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