Disk stability under MONDian gravity
  Toomre's $Q$ stability parameter has long been shown through various
theoretical arguments and numerical simulations, to be the principal
determinant of stability against self-gravity in a galactic disk, under
classical gravity. Comparison with observations however, has not always
confirmed the condition of $Q=Q_{crit}$ to be well correlated with various
critical galactic radii. In this paper we derive the analogous critical
parameter, $Q_{M}$, under MONDian gravity. The result is a modification by a
factor of $(\sigma \Omega)/a_{0}$, $Q_{M}=(\sigma \Omega)^{2}/(a_{0}G \Sigma)$,
where $a_{0}$ is the critical acceleration scale of MOND. We then show through
a direct comparison to a homogeneous sample of observed disk galaxies with
measured brightness profiles, rotation velocity curves and internal velocity
dispersion profiles, that the critical radii at which brightness profiles dip
below the exponential fit, are much more accurately predicted by $Q_{M}$ than
by the $Q$ of classical gravity. This provides a new and completely independent
argument supporting the reality of a change in the form of gravity on reaching
the low acceleration regime.
