Rahul Shetty, Brandon C. Kelly, Frank Bigiel
We develop a Bayesian linear regression method which rigorously treats measurement uncertainties, and accounts for hierarchical data structure for investigating the relationship between the star formation rate and gas surface density. The method simultaneously estimates the intercept, slope, and scatter about the regression line of each individual subject (e.g. a galaxy) and the population (e.g. an ensemble of galaxies). Using synthetic datasets, we demonstrate that the Bayesian method accurately recovers the parameters of both the individuals and the population, especially when compared to commonly employed least squares methods, such as the bisector. We apply the Bayesian method to estimate the Kennicutt-Schmidt (KS) parameters of a sample of spiral galaxies compiled by Bigiel et al. (2008). We find significant variation in the KS parameters, indicating that no single KS relationship holds for all galaxies. This suggests that the relationship between molecular gas and star formation differs between galaxies, possibly due to the influence of other physical properties within a given galaxy, such as metallicity, molecular gas fraction, and/or stellar mass. In four of the seven galaxies the slope estimates are well below unity, especially for M51, within the $2\sigma$ level. We estimate the mean index of the KS relationship for the population to be 0.84, with 95% range [0.63, 1.0]. The sub-linear KS relationship estimated from the ensemble and for individual galaxies suggests that CO emission is tracing some molecular gas which is not directly associated with star formation. The hierarchical Bayesian method can account for all sources of uncertainties, including variations in the conversion of observed luminosities to star formation rates and gas surface densities (e.g. the X_CO factor), and is therefore well suited for a thorough statistical analysis of the KS relationship.
View original:
http://arxiv.org/abs/1210.1218
No comments:
Post a Comment