Mass estimates from stellar proper motions: The mass of $\omega$ Centauri

Abstract

We lay out and apply methods to use proper motions of individual kinematic tracers for estimating the dynamical mass of star clusters. We first describe a simple projected mass estimator and then develop an approach that evaluates directly the likelihood of the discrete kinematic data given the model predictions. Those predictions may come from any dynamical modelling approach, and we implement an analytic King model, a spherical isotropic Jeans equation model and an axisymmetric, anisotropic Jeans equation model.We apply these approaches to the enigmatic globular cluster omega Centauri, combining the proper motion from van Leeuwen et al (2000) with improved photometric cluster membership probabilities. We show that all mass estimates based on spherical isotropic models yield $(4.55\pm 0.1)\times 10^6{M}_{\odot }[D/5.5\pm 0.2kpc{]}^3$, where our modelling allows us to show how the statistical precision of this estimate improves as more proper motion data of lower signal-to-noise are included. MLM predictions, based on an anisotropic axisymmetric Jeans model, indicate for $\omega$ Cen that the inclusion of anisotropies is not important for the mass estimates, but that accounting for the flattening is: flattened models imply $(4.05\pm 0.1)\times 10^6{M}_{\odot }[D/5.5\pm 0.2kpc{]}^3$, 10% lower than when restricting the analysis to a spherical model. The best current distance estimates imply an additional uncertainty in the mass estimate of 12%.

Accepted for publication in MNRAS

References in corpus (4)

• Measuring the inclination and mass-to-light ratio of axisymmetric galaxies via anisotropic Jeans models of stellar kinematics
• Interloper treatment in dynamical modelling of galaxy clusters
• Relative distances of Omega Centauri and 47 Tucanae
• A mass estimate of an intermediate-mass black hole in omega Centauri

Cited by in corpus (37)

• Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies
• The HST large programme on $\omega$ Centauri - II. internal kinematics
• Rotating Globular Clusters
• A Sequoia in the Garden: FSR 1758 - Dwarf Galaxy or Giant Globular Cluster?
• The Nuclear Cluster of the Milky Way: Total Mass and Luminosity (long version)
• Efficient solution of the anisotropic spherically-aligned axisymmetric Jeans equations of stellar hydrodynamics for galactic dynamics
• Discrete dynamical modelling of omega Centauri
• On the RR Lyrae stars in globulars: IV. $\omega$ Centauri Optical UBVRI Photometry
• The Populations of Carina. II. Chemical Enrichment
• A Deep X-ray Survey of the Globular Cluster Omega Centauri
• The VVV Survey RR Lyrae Population in the Galactic Centre Region
• The State-of-the-Art HST Astro-Photometric Analysis of the core of $\omega$ Centauri. II. Differential-Reddening Map
• R-process-rich stellar streams in the Milky Way
• The Most Metal-poor Stars in Omega Centauri (NGC 5139)
• Chemical Compositions of Field and Globular Cluster RR~Lyrae Stars: II. omega Centauri
• Hubble Space Telescope analysis of stellar populations within the globular cluster G1 (Mayall II) in M31
• Dark and luminous mass components of Omega Centauri with stellar kinematics
• The HST large programme on $\omega$ Centauri -- V. Exploring the Ultracool Dwarf Population with Stellar Atmosphere and Evolutionary Modelling
• Orbital decay of Globular Clusters in the galaxy with little dark matter
• UV Insights into the Complex Populations of M 87 Globular Clusters
• Ultra-compact dwarfs beyond the centre of the Fornax galaxy cluster: Hints of UCD formation in low-density environments
• Detecting Axion Dark Matter through the Radio Signal from Omega Centauri
• Near-IR period-luminosity relations for pulsating stars in $\omega$ Centauri (NGC 5139)
• The Mg-K anti-correlation in Omega Centauri
• New constraints on the central mass contents of Omega Centauri from combined stellar kinematics and pulsar timing
• Tidal debris from Omega Centauri discovered with unsupervised machine learning
• Spatial and kinematic segregation in star cluster merger remnants
• Formation of massive globular clusters with dark matter and its implication on dark matter annihilation
• A possible solution to the Milky Way's binary-deficient retrograde stellar population. Evidence that $\omega$ Centauri has formed in an extreme starburst
• Probing the dark matter-electron interactions via hydrogen-atmosphere pulsating white dwarfs
• What to expect when using globular clusters as tracers of the total mass distribution in Milky Way-mass galaxies
• Early formation of supermassive black holes from the collapse of strongly self-interacting dark matter
• Anisotropic Jeans models of stellar kinematics: second moments including proper motions and radial velocities
• Globular clusters vs dark matter haloes in strong lensing observations
• Constraining Black Hole Populations in Globular Clusters using Microlensing: Application to Omega Centauri
• A Search for Annihilating Dark Matter in 47 Tucanae and Omega Centauri
• Profiling stellar environments of gravitational wave sources