Modified Virial Formulae and the Theory of Mass Estimators
arXiv:1012.5180 · doi:10.1111/j.1365-2966.2011.18251.x
Abstract
We show how to estimate the enclosed mass from the observed motions of an ensemble of test particles. Traditionally, this problem has been attacked through virial or projected mass estimators. Here, we examine and extend these systematically, and show how to construct an optimal estimator for any given assumption as to the potential. The estimators do not explicitly depend on any properties of the density of the test objects, which is desirable as in practice such information is dominated by selection effects. As particular examples, we also develop estimators tailored for the problem of estimating the mass of the Hernquist or NFW dark matter haloes from the projected positions and velocities of stars.
arXiv comment9 pages, MNRAS, in press
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- The mass of our Milky Way
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- Milky Way Mass with K Giants and BHB Stars Using LAMOST, SDSS/SEGUE, and Gaia: 3D Spherical Jeans Equation and Tracer Mass Estimator
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- Bayes versus the virial theorem: inferring the potential of a galaxy from a kinematical snapshot
- To the Galactic Virial Radius with Hyper Suprime-Cam
- A geometric approach to a generalized virial theorem
- Mass estimators in the Gaia era
- MUSE observations of dwarf galaxies and a stellar stream in the M83 group
- Line-of-Sight Velocity Projection Impact on the Local Group Mass
- Measuring the mass distribution in stellar systems