A cautionary tale in fitting galaxy rotation curves with Bayesian techniques. Does Newton's constant vary from galaxy to galaxy?

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 G_N 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 G_N, we obtain a wide distribution of G_N which, taken at face value, would rule out G_N as a universal constant with high statistical confidence. However, imposing an empirically motivated log-normal prior returns a virtually constant G_N with no sacrifice in fit quality. This implies that the inference of a variable G_N (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 G_N (and constant g_†).