Microlens Masses from 1-D Parallaxes and Heliocentric Proper Motions

TL;DR

This paper analyzes how 1-D microlens parallaxes combined with proper motions can determine lens masses and distances, revealing a quadratic relation and conditions to resolve degeneracies, with potential for widespread future use.

Contribution

It provides the first mathematical analysis of the method, deriving explicit formulas and conditions for breaking degeneracies in microlensing mass and distance measurements.

Findings

The relation can be expressed as a quadratic equation.

Degeneracies can often be broken with available 2-D parallax data.

The technique is likely to become common in the next decade.

Abstract

One-dimensional (1-D) microlens parallaxes can be combined with heliocentric lens-source relative proper motion measurements to derive the lens mass and distance, as suggested by Ghosh et al. (2004). Here I present the first mathematical anlysis of this procedure, which I show can be represented as a quadratic equation. Hence, it is formally subject to a two-fold degeneracy. I show that this degeneracy can be broken in many cases using the relatively crude 2-D parallax information that is often available for microlensing events. I also develop an explicit formula for the region of parameter space where it is more difficult to break this degeneracy. Although no mass/distance measurements have yet been made using this technique, it is likely to become quite common over the next decade.