A cautionary tale in fitting galaxy rotation curves with Bayesian techniques

Abstract

The application of Bayesian techniques to astronomical data is generally non-trivial because the fitting parameters can be strongly degenerated and the formal uncertainties are themselves uncertain. An example is provided by the contradictory claims over the presence or absence of a universal acceleration scale (g†) in galaxies based on Bayesian fits to rotation curves. To illustrate this we present an analysis in which the Newtonian gravitational constant GN is allowed to vary from galaxy to galaxy when fitting rotation curves from the SPARC database, in analogy to g† in the recently debated Bayesian analyses. When imposing flat priors on GN, we obtain a wide distribution of GN which, taken at face value, would rule out GN as a universal constant with high statistical confidence. However, imposing an empirically motivated log-normal prior returns a virtually constant GN with no sacrifice in fit quality. This implies that the inference of a variable GN (or g†) is the result of the combined effect of parameter degeneracies and unavoidable uncertainties in the error model. When these effects are taken into account, the SPARC data are consistent with a constant GN (and constant g†).