A fundamental test for MOND
  The Radial Acceleration Relation (RAR) shows a strong correlation between two
accelerations associated to galaxy rotation curves. The relation between these
accelerations is given by a nonlinear function which depends on an acceleration
scale $a_\dagger$. Some have interpreted this as an evidence for a gravity
model, such as Modified Newtonian Dynamics (MOND), which posits a fundamental
acceleration scale $a_0$ common to all the galaxies. However, it was later
shown, using Bayesian inference, that this seems not to be the case: the $a_0$
credible intervals for individual galaxies were not found to be compatible
among themselves. This type of test is a fundamental test for MOND as a theory
for gravity, since it directly evaluates its basic assumption and this using
the data that most favor MOND: galaxy rotation curves. Here we improve upon the
previous analyses by introducing a more robust method to assess the
compatibility between the credible intervals, in particular without Gaussian
approximations. We directly estimate, using a Monte Carlo simulation, that the
existence of a fundamental acceleration is incompatible with the data at more
than $5\sigma$. We also consider quality cuts in order to show that our results
are robust against outliers. In conclusion, the new analysis further supports
the claim that the acceleration scale found in the RAR is an emergent quantity.
