Disks as Inhomogeneous, Anisotropic Gaussian Random Fields

TL;DR

This paper models astrophysical disk surface brightness fluctuations as an inhomogeneous, anisotropic Gaussian random field using a Matérn field approach, enabling the generation of synthetic disk movies and light curves.

Contribution

It introduces a novel Gaussian random field model for disk brightness fluctuations, providing a parameterization for local covariance and applications to synthetic disk imaging and light curve analysis.

Findings

Generated synthetic disk movies demonstrating brightness fluctuations.

Showed high-frequency power spectrum slope depends on local covariance.

Provided a flexible framework for modeling astrophysical disk variability.

Abstract

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.