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.

arXiv comment11 pages, 7 figures, 1 table

References in corpus (14)

• Rates of tidal disruption of stars by massive central black holes
• Axisymmetric Dynamical Models of the Central Regions of Galaxies
• A Family of Models for Spherical Stellar Systems
• Improved evidence for a black hole in M32 from HST/FOS spectra - II. Axisymmetric dynamical models
• The counterrotating core and the black hole mass of IC1459
• Difficulties with Recovering The Masses of Supermassive Black Holes from Stellar Kinematical Data
• The velocity and mass distribution of clusters of galaxies from the CNOC1 cluster redshift survey
• Mapping stationary axisymmetric phase-space distribution functions by orbit libraries
• The orbital structure and potential of NGC 1399
• The central kinematics of NGC 1399 measured with 14pc resolution
• Gemini Near Infrared Spectrograph observations of the central supermassive black hole in Centaurus A
• Kinematical signatures of hidden stellar discs
• On the reliability of the black hole mass and mass to light ratio determinations with Schwarzschild models
• Deprojection of Axially Symmetric Objects

Cited by in corpus (23)

• The M-sigma and M-L Relations in Galactic Bulges and Determinations of their Intrinsic Scatter
• A direct dynamical measurement of the Milky Way's disk surface density profile, disk scale length, and dark matter profile at 4 kpc < R < 9 kpc
• Triaxial orbit based galaxy models with an application to the (apparent) decoupled core galaxy NGC 4365
• Estimating Black Hole Masses in Triaxial Galaxies
• Orbit-based dynamical models of the Sculptor dSph galaxy
• The Black Hole Mass and Extreme Orbital Structure in NGC1399
• The flattening and the orbital structure of early-type galaxies and collisionless N-body binary disk mergers
• A new implementation of the Schwarzschild method for constructing observationally-driven dynamical models of galaxies of all morphological types
• Analysing surveys of our Galaxy -- II. Determining the potential
• A novel approach to optimize the regularization and evaluation of dynamical models using a model selection framework
• Constraining the Mass Profiles of Stellar Systems: Schwarzschild Modeling of Discrete Velocity Datasets
• Bayes versus the virial theorem: inferring the potential of a galaxy from a kinematical snapshot
• Hobby-Eberly Telescope Observations of the Dark Halo in NGC 821
• Constraining the Galactic potential via action-based distribution functions for mono-abundance stellar populations
• 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
• Made-to-measure modeling of observed galaxy dynamics
• Dynamical Modeling of Galaxies and Supermassive Black Holes: Axisymmetry in Triaxial Schwarzschild Orbit Superposition Models
• The Subaru/XMM-Newton Deep Field - II. The 37 brightest radio sources
• Orbit-superposition models of discrete, incomplete stellar kinematics: application to the Galactic centre
• Axisymmetric Schwarzschild models of an isothermal axisymmetric mock dwarf spheroidal galaxy
• Probabilistic distribution functions
• Measuring the mass distribution in stellar systems