A bar stability criterion distinguishing between modified gravity and dark matter in galaxies

ABSTRACT This paper presents a study on the distinguishability of dark matter and Modified Newtonian Dynamics (MOND) at galactic scales based on the stability criterion proposed by Efstathiou, Lake, and Negroponte (ELN criterion). First, we test the statistical validity of this stability criterion against the presence of bars within the Spitzer Photometry and Accurate Rotation Curves and Calar Alto Legacy Integral Field spectroscopy Area data bases, successfully identifying ${\sim} 70~{{\ \rm per\ cent}}$ of barred galaxies. Then, we employ a series of N-body galaxy simulations to exhibit a direct observable difference between the dark matter and MOND theoretical frameworks, at least in gas-poor galaxies. We present N-body models that satisfy the stability requirement of the ELN criterion, and so are stable against bar formation in the presence of a dark matter halo, and that do actually exhibit bar instabilities in MOND. On the other hand, the question of how to inhibit bar formation in gas-poor galaxies in MOND is posed, and requires a detailed investigation of the external field effect.