What required consistency check must both Dark Matter and modified gravity models pass regarding galaxy properties?

Accounting for the observed relationship between intrinsic luminosity and final rotation speed, such as the Tully-Fisher relation.

For any physical theory attempting to resolve the rotation curve problem, whether invoking invisible matter (Dark Matter) or altering fundamental laws (like MOND), success hinges on its ability to maintain consistency across the entire population of galaxies. A truly fundamental theory must explain the observed correlations between a galaxy's inherent properties and its dynamics. One key empirical relationship is the Tully-Fisher relation, which links a galaxy's intrinsic luminosity (how bright it is) to its final measured rotation speed. A successful model must predict or explain this observed empirical link consistently, rather than requiring arbitrary, finely tuned parameters for each individual galaxy.