Hierarchical Bayesian Inference of Globular Cluster Properties

Abstract

We present a hierarchical Bayesian inference approach to estimating the structural properties and the phase space center of a globular cluster (GC) given the spatial and kinematic information of its stars based on lowered isothermal cluster models. As a first step towards more realistic modelling of GCs, we built a differentiable, accurate emulator of the lowered isothermal distribution function using interpolation. The reliable gradient information provided by the emulator allows the use of Hamiltonian Monte Carlo methods to sample large Bayesian models with hundreds of parameters, thereby enabling inference on hierarchical models. We explore the use of hierarchical Bayesian modelling to address several issues encountered in observations of GC including an unknown GC center, incomplete data, and measurement errors. Our approach not only avoids the common technique of radial binning but also incorporates the aforementioned uncertainties in a robust and statistically consistent way. Through demonstrating the reliability of our hierarchical Bayesian model on simulations, our work lays out the foundation for more realistic and complex modelling of real GC data.

arXiv comment16 pages, 12 figures, and 2 tables

References in corpus (38)

• Gaia Data Release 2. Summary of the contents and survey properties
• MCMC using Hamiltonian dynamics
• Resolved Massive Star Clusters in the Milky Way and its Satellites: Brightness Profiles and a Catalogue of Fundamental Parameters
• Gaia Data Release 2: Kinematics of globular clusters and dwarf galaxies around the Milky Way
• A catalogue of masses, structural parameters and velocity dispersion profiles of 112 Milky Way globular clusters
• Gaia EDR3 view on Galactic globular clusters
• Proper motions and dynamics of the Milky Way globular cluster system from Gaia DR2
• Hubble Space Telescope proper motion (HSTPROMO) catalogs of Galactic globular clusters. II. Kinematic profiles and maps
• Star count density profiles and structural parameters of 26 Galactic globular clusters
• The ACS Survey of Galactic Globular Clusters. X. New Determinations of Centers for 65 Clusters
• No Energy Equipartition in Globular Clusters
• Reconstructing Galaxy Histories from Globular Clusters
• A family of lowered isothermal models
• The eye of Gaia on globular clusters kinematics: internal rotation
• Overview of the LAMOST survey in the first decade
• The effect of stellar-mass black holes on the central kinematics of omega Cen: a cautionary tale for IMBH interpretations
• Globular cluster number density profiles using Gaia DR2
• The cumulative mass profile of the Milky Way as determined by globular cluster kinematics from Gaia DR2
• Velocity anisotropy in tidally limited star clusters
• Self-consistent models of quasi-relaxed rotating stellar systems
• Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys
• The SLUGGS Survey: Wide Field Imaging of the Globular Cluster System of NGC 4278
• Mass models of NGC 6624 without an intermediate-mass black hole
• Testing lowered isothermal models with direct N-body simulations of globular clusters
• On the black hole content and initial mass function of 47 Tuc
• Estimating the Galactic Mass Profile in the Presence of Incomplete Data
• The orbital anisotropy profiles of nearby globular clusters from Gaia Data Release 2
• Mass modelling globular clusters in the Gaia era: a method comparison using mock data from an $N$-body simulation of M4
• Spherical models of star clusters with potential escapers
• Hierarchical Bayesian inference of photometric redshifts with stellar population synthesis models
• The Globular Cluster System of NGC 5128: Ages, Metallicities, Kinematics, and Structural Parameters
• Multimass modelling of Milky Way globular clusters -- I. Implications on their stellar initial mass function above 1 M${}_{\odot }$
• Estimating the Milky Way's Mass via Hierarchical Bayes: A Blind Test on MUGS2 Simulated Galaxies
• Structure and Internal Kinematics of Nine Inner Milky Way Globular Clusters
• Globular Cluster Scale Sizes in Giant Galaxies: The Case of M87 and the Role of Orbital Anisotropy and Tidal Filling
• Truncated $\gamma$-exponential models for tidal stellar systems
• Investigating Dynamical Properties of Globular Clusters through a Family of Lowered Isothermal Models
• Bayesian Inference of Globular Cluster Properties Using Distribution Functions

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