Modified Virial Formulae and the Theory of Mass Estimators

TL;DR

This paper develops and extends virial-based mass estimators for astrophysical systems, creating optimal methods that do not rely on density assumptions, with specific applications to dark matter halo mass estimation from stellar data.

Contribution

It introduces a systematic approach to construct optimal mass estimators for various potential models, improving upon traditional virial methods without requiring density profile information.

Findings

New estimators tailored for Hernquist and NFW dark matter haloes.

Establishes a framework for potential-dependent mass estimation.

Demonstrates estimators' robustness against density profile uncertainties.

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.