Mass estimators in the Gaia era

TL;DR

This paper develops a new mass estimation method using Gaia's proper motion and velocity data, which naturally accounts for anisotropy and simplifies uncertainty propagation, aiding in measuring masses of stellar systems.

Contribution

It introduces a tracer mass estimator that incorporates proper motions without assuming anisotropy, applicable to Gaia data and extended to projected observations.

Findings

Mass estimators that include proper motions are developed.

The method naturally accounts for anisotropy.

Application potential for Galactic globular clusters.

Abstract

Forthcoming astrometric missions such as the Gaia satellite will bring to the fore the problem of estimating the enclosed mass from a set of positions, radial velocities and proper motions of tracer stars. Here, we show how to construct the tracer mass estimator when the proper motion data are available in addition to the usual line-of-sight velocity data. Notably, the mass estimators do not require any assumption on the anisotropy, as it is naturally incorporated through the different components of proper motions. In addition, the separate treatment of the proper motions and the line-of-sight velocities is desirable because they are observationally independent and thus the propagation of the combined uncertainties is rather straightforward. The extension to projected data is also sketched, together with a possible application of measuring the masses of Galactic globular clusters.