Testing modified Newtonian dynamic with Local Group spiral galaxies

The rotation curves and the relative mass distributions of the two nearby Local Group spiral galaxies, M31 and M33, show discrepancies with modified Newtonian dynamic (MOND) predictions. In M33, the discrepancy lies in the kinematics of the outermost regions. It can be alleviated by adopting tilted ring models compatible with the 21-cm datacube but different from the one that best fits the data. In M31, MOND fails to fit the falling part of the rotation curve at intermediate radii, before the curve flattens out in the outermost regions. Newtonian dynamics in a framework of a stellar disc embedded in a dark halo can explain the complex rotation curve profiles of these two galaxies, while MOND has some difficulties. However, given the present uncertainties in the kinematics of these nearby galaxies, we cannot address the success or failure of MOND theory in a definite way. More sensitive and extended observations around the critical regions, suggested by MOND fits discussed in this paper, may lead to a definite conclusion.