Microlensing Parallax for Observers in Heliocentric Motion

TL;DR

This paper revisits the geometrical foundations of microlensing parallax measurement in a heliocentric frame, emphasizing observer motion effects and their importance for interpreting joint satellite and ground observations.

Contribution

It extends the Gould (1994) relationship to moving observers and highlights the significance of observer motion in accurately recovering microlensing parameters.

Findings

Extended the microlensing parallax equation for moving observers.

Demonstrated the importance of observer motion in breaking degeneracies.

Analyzed joint ground and satellite observations for upcoming campaigns.

Abstract

Motivated by the ongoing Spitzer observational campaign, and the forecoming K2 one, we revisit, working in an heliocentric reference frame, the geometrical foundation for the analysis of the microlensing parallax, as measured with the simultaneous observation of the same microlensing event from two observers with relative distance of order AU. For the case of observers at rest we discuss the well known fourfold microlensing parallax degeneracy and determine an equation for the degenerate directions of the lens trajectory. For the case of observers in motion, we write down an extension of the Gould (1994) relationship between the microlensing parallax and the observable quantities and, at the same time, we highlight the functional dependence of these same quantities from the timescale of the underlying microlensing event. Furthermore, through a series of examples, we show the importance of taking into account the motion of the observers to correctly recover the parameters of the underlying microlensing event. In particular we discuss the cases of the amplitude of the microlensing parallax and that of the difference of the timescales between the observed microlensing events, key to understand the breaking of the microlensing parallax degeneracy. Finally, we consider the case of the simultaneous observation of the same microlensing event from ground and two satellites, a case relevant for the expected joint K2 and Spitzer observational programs in 2016.