On the Relationship between Modified Newtonian Dynamics and Dark Matter

Abstract

Numerous astrophysical observations have shown that classical Newtonian dynamics fails on galactic scales and beyond, if only visible matter is taken into account. The two most popular theoretical concepts dealing with this problem are dark matter ({DM)} and modified Newtonian dynamics ({MOND).} In the first part of this Letter it is demonstrated that a generalized {MOND} equation can be derived in the framework of Newtonian {DM} theory. For systems satisfying a fixed relationship between the gravitational fields caused by {DM} and visible matter, this generalized {MOND} equation reduces to the traditional {MOND} law, first postulated by Milgrom. Therefore, we come to the conclusion that traditional {MOND} can be also interpreted as a special limit case of {DM} theory. In the second part of this Letter, a formal derivation of the Tully-Fisher relation is discussed.