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

Abstract

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.

11 pages, 7 figures, 1 table

Cited by in corpus (9)

• Triaxial orbit based galaxy models with an application to the (apparent) decoupled core galaxy NGC 4365
• The Black Hole Mass and Extreme Orbital Structure in NGC1399
• A new implementation of the Schwarzschild method for constructing observationally-driven dynamical models of galaxies of all morphological types
• Constraining the Mass Profiles of Stellar Systems: Schwarzschild Modeling of Discrete Velocity Datasets
• A novel approach to optimize the regularization and evaluation of dynamical models using a model selection framework
• SMART: A new implementation of Schwarzschild's Orbit Superposition technique for triaxial galaxies and its application to an N-body merger simulation
• The Black Hole Mass of NGC 4151 from Stellar Dynamical Modeling
• The Subaru/XMM-Newton Deep Field - II. The 37 brightest radio sources
• Probabilistic distribution functions