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

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 the situation, 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 $G_{\mathrm{N}}$ (and constant $g_{†}$).

Accepted for publication in A&A Letters

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• Dark matter profiles of SPARC galaxies: a challenge to fuzzy dark matter
• Normalized additional velocity distribution: testing the radial profile of dark matter halos and MOND
• WISDOM Project -- XIII. Feeding molecular gas to the supermassive black hole in the starburst AGN-host galaxy Fairall 49
• There is no universal acceleration scale in galaxies
• Superfluid dark matter in tension with weak gravitational lensing data
• Improved SED-Fitting Assumptions Result in Inside-Out Quenching at $z\sim 0.5$ and Quenching at All Radii Simultaneously at $z\sim 1$
• The isolated elliptical galaxy NGC 5812 -- MOND or Dark Matter?
• Gas thermodynamics meets galaxy kinematics: Joint mass measurements for eROSITA galaxy clusters