The Mass Discrepancy–Acceleration Relation: Disk Mass and the Dark Matter Distribution

The mass discrepancy in disk galaxies is shown to be well correlated with acceleration, increasing systematically with decreasing acceleration below a critical scale a0 = 3700 km²/s²/kpc = 1. 2E-10 m/s/s. For each galaxy, there is an optimal choice of stellar mass-to-light ratio which minimizes the scatter in this mass discrepancy-acceleration relation. The same mass-to-light ratios also minimize the scatter in the baryonic Tully-Fisher relation and are in excellent agreement with the expectations of stellar population synthesis. Once the disk mass is determined in this fashion, the dark matter distribution is specified. The circular velocity attributable to the dark matter can be expressed as a simple equation which depends only on the observed distribution of baryonic mass. It is a challenge to understand how this very fine-tuned coupling between mass and light comes about.