Finite-source and finite-lens effects in astrometric microlensing

TL;DR

This paper investigates how finite sizes of lenses and sources affect the astrometric signals in microlensing events, revealing effects that are generally below current detection limits but useful for distinguishing lens types.

Contribution

It provides a comprehensive analysis of finite-source and finite-lens effects on astrometric microlensing trajectories, including cases with luminous lenses, and discusses observational implications.

Findings

Finite-lens trajectories become continuous in the finite-source regime.

Finite-source effects are prominent during lens transit over the source surface.

Finite-lens signals are most detectable when the lens is very close to the source.

Abstract

The aim of this paper is to study the astrometric trajectory of microlensing events with an extended lens and/or source. We consider not only a dark lens but also a luminous lens as well. We find that the discontinuous finite-lens trajectories given by Takahashi (2003) will become continuous in the finite-source regime. The point lens (source) approximation alone gives an under (over)estimation of the astrometric signal when the size of the lens and source are not negligible. While the finiteness of the source is revealed when the lens transits the surface of the source, the finite-lens signal is most prominent when the lens is very close to the source. Astrometric microlensing towards the Galactic bulge, Small Magellanic Cloud and M31 are discussed, which indicate that the finite-lens effect is beyond the detection limit of current instruments. Nevertheless, it is possible to distinguish between self-lensing and halo lensing through a (non-)detection of the astrometric ellipse. We also consider the case where the lens is luminous itself, as has been observed where a lensing event was followed up with the Hubble Space Telescope. We show that the astrometric signal will be reduced in a luminous-lens scenario. The physical properties of the event, such as the lens-source flux ratio, the size of the lens and source nevertheless can be derived by fitting the astrometric trajectory.