Disk stability under MONDian gravity

Understand

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.