Simulated Scatter: A Monte Carlo Approach to Understanding the Observed (sub)Stellar Mass-Accretion Rate Relation

The accretion process constitutes a crucial phase in star and brown dwarf formation. However, observational constraints on the relation between object mass and mass accretion rate demonstrate a scatter of ~5 orders of magnitude around the canonical relationship between these quantities. It is not clear whether this scatter is due mostly to physical processes (e.g. accretion variability, age, varying accretion paradigms), or to systematic uncertainties arising from observational biases and inconsistencies in scaling relationships. Even more uncertainty is present in the substellar regime, where formation mechanisms are ill-defined and derived relationships may not apply. Competing accretion diagnostics such as UV excess, accretion line strengths, and equivalent widths can return vastly different accretion rates even for the same object and epoch. We report on the results of a Monte Carlo simulation that attempts to disentangle these effects by unifying assumptions and propagating interrelated uncertainties throughout the extrapolation pathway from observational diagnostic to mass accretion rate estimate. The simulation tactic allows us to juxtapose purely systematic scatter around the theoretical relation with the observed scatter, to directly compare the stellar and substellar regimes, and to closely examine discrepancies between accretion tracers. This numerical approach permits combination (or isolation) of random uncertainties, systematic uncertainties, and physical sources of scatter in a flexible framework, enabling robust statistical comparisons of heterogeneous accretion observations and physical models of star and planet formation.