Disks as Inhomogeneous, Anisotropic Gaussian Random Fields

13 Nov 2020  ·  Lee Daeyoung, Gammie Charles F. ·

We model astrophysical disk surface brightness fluctuations as an inhomogeneous, anisotropic, time-dependent Gaussian random field. The field locally obeys the stochastic partial differential equation of a Mat\'ern field, which has a power spectrum that is flat at large scales and falls off as a power law at small scales. We provide a series of pedagogical examples and along the way provide a convenient parameterization for the local covariance. We then consider two applications to disks. In the first we generate a movie of a disk. In the second, by integrating over a movie of a disk, we generate synthetic light curves and show that the high frequency slope of the resulting power spectrum depends on the local covariance model. We finish with a summary and a brief discussion of other possible astrophysical applications.

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Instrumentation and Methods for Astrophysics Astrophysics of Galaxies High Energy Astrophysical Phenomena