Letter to the Editor

A cautionary tale in fitting galaxy rotation curves with Bayesian techniques

Does Newton’s constant vary from galaxy to galaxy?

¹ Department of Astronomy, Case Western Reserve University, Cleveland, OH 44106, USA
e-mail: PengfeiLi0606@gmail.com; pxl283@case.edu
² School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, UK
³ Department of Physics, University of Oregon, Eugene, OR 97403, USA
⁴ Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro Gwangjin-gu, Seoul 05006, Republic of Korea

Received: 9 December 2020
Accepted: 27 January 2021

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 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_†).