Dynamical Constraints on Alternatives to Supermassive Black Holes in Galactic Nuclei

The compelling dynamical evidence for massive dark objects in galactic nuclei does not uniquely imply massive black holes (BHs). To argue convincingly that these objects are BHs we must rule out alternatives to a BH, and the alternative to a point mass is a cluster of some sort of nonluminous objects, such as a cluster of brown dwarfs or stellar remnants. We use simple physical considerations to derive the maximum possible lifetime of a dark cluster which may consist of any plausible form of non-luminous gravitating objects -- from brown dwarfs and very low-mass objects of cosmic composition, to white dwarfs, neutron stars, and black holes. The lower this limit relative to the galaxy age, the more implausible is the cluster hypothesis, thus arguing for a point mass. A cluster with a lifetime much shorter than ~10 Gyr is unacceptable, since observing it at the present epoch would be highly improbable. Since the goal is to rule out a dark cluster by showing that its lifetime must be very short, we make the most generous assumptions possible under the observational constraints to allow for its survival. We find that the lifetime of such an hypothetical cluster must be much shorter than the galaxy age only in the cases of NGC 4258 and our Galaxy, thus strongly arguing for a point mass. In all other galaxies, the case of a massive BH, although compelling, is not yet watertight. We also note that there are two exotic alternatives to a massive BH that cannot be ruled out even in the cases of NGC 4258 and the Galaxy: clusters of elementary particles (e.g. bosons), and clusters of very low-mass BHs. We point out, however, serious difficulties with these alternatives, and argue that they are highly implausible.