Constraining black hole masses from stellar kinematics by summing over all possible distribution functions

Details Constraining black hole masses from stellar kinematics by summing over all possible distribution functions Constraining black hole masses from stellar kinematics by summing over all possible distribution functions

2006-09-08

arxiv.org/abs/astro-ph/0609238v1

Mon.Not.Roy.Astron.Soc.373:425-434,2006

Astronomy and Astrophysics

Astrophysics

11 pages, 7 figures, 1 table

Scientific paper

10.1111/j.1365-2966.2006.11054.x

When faced with the task of constraining a galaxy's potential given limited stellar kinematical information, what is the best way of treating the galaxy's unknown distribution function (DF)? Using the example of estimating black hole (BH) masses, I argue that the correct approach is to consider all possible DFs for each trial potential, marginalizing the DF using an infinitely divisible prior. Alternative approaches, such as the widely used maximum penalized likelihood method, neglect the huge degeneracies inherent in the problem and simply identify a single, special DF for each trial potential. Using simulated observations of toy galaxies with realistic amounts of noise, I find that this marginalization procedure yields significantly tighter constraints on BH masses than the conventional maximum-likelihood method, although it does pose a computational challenge which might be solved with the development of a suitable algorithm for massively parallel machines. I show that in practice the conventional maximum-likelihood method yields reliable BH masses with well-defined minima in their chi^2 distributions, contrary to claims made by Valluri, Merritt & Emsellem.

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