Quantifying the Imprecision of Accretion Theory and Implications for Multi-Epoch Observations of Protoplanetary Discs

TL;DR

This paper quantifies the intrinsic imprecision in accretion disc spectral predictions caused by turbulence and averaging, providing guidelines for optimal spectral resolution and implications for multi-epoch observations of protoplanetary discs.

Contribution

It introduces a method to quantify stochastic imprecision in accretion theory and identifies optimal averaging strategies for interpreting multi-epoch spectral data.

Findings

Imprecision minimized at specific radial averaging choices.

Optimal spectral resolution depends on turbulence scales.

Little variability expected at large radii with longer eddy turnover times.

Abstract

If accretion disc emission results from turbulent dissipation, then axisymmetric accretion theory must be used as a mean field theory: turbulent flows are at most axisymmetric only when suitably averaged. Spectral predictions therefore have an intrinsic imprecision that must be quantified to interpret the variability exhibited by a source observed at different epochs. We quantify contributions to the stochastic imprecision that come from azimuthal and radial averaging and show that the imprecision is minimized for a particular choice of radial averaging, which in turn, corresponds to an optimal spectral resolution of a telescope for a spatially unresolved source. If the optimal spectral resolution is less than that of the telescope then the data can be binned to compare to the theoretical prediction of minimum imprecision. Little stochastic variability is predicted at radii much larger than that at which the dominant eddy turnover time ($\sim$ orbit time) exceeds the time interval between observations; the epochs would then be sampling the same member of the stochastic ensemble. We discuss the application of these principles to protoplanetary discs for which there is presently a paucity of multi-epoch data but for which such data acquisition projects are underway.