# On the wave optics effect on primordial black hole constraints from optical microlensing search

## TL;DR

This paper investigates how wave optics effects influence the detection and constraints of primordial black holes via optical microlensing, especially in the low-mass range where wave effects become significant.

## Contribution

It analyzes the impact of wave optics on microlensing constraints of primordial black holes and discusses observational strategies to detect wave effects or improve constraints.

## Key findings

- Wave effects are negligible compared to finite source size effects for PBHs in the mass range 10^{-11} to 10^{-10} solar masses.
- Wave optics effects could be detectable with high-cadence, g-band observations of white dwarfs.
- Current constraints from M31 star monitoring are not significantly affected by wave effects in the studied mass range.

## Abstract

Microlensing of stars, e.g. in the Galactic bulge and Andromeda galaxy (M31), is among the most robust, powerful method to constrain primordial black holes (PBHs) that are a viable candidate of dark matter. If PBHs are in the mass range $M_{\rm PBH} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$} 10^{-10}M_\odot$, its Schwarzschild radius ($r_{\rm Sch}$) becomes comparable with or shorter than optical wavelength ($\lambda)$ used in a microlensing search, and in this regime the wave optics effect on microlensing needs to be taken into account. For a lensing PBH with mass satisfying $r_{\rm Sch}\sim \lambda$, it causes a characteristic oscillatory feature in the microlensing light curve, and it will give a smoking gun evidence of PBH if detected, because any astrophysical object cannot have such a tiny Schwarzschild radius. Even in a statistical study, e.g. constraining the abundance of PBHs from a systematic search of microlensing events for a sample of many source stars, the wave effect needs to be taken into account. We examine the impact of wave effect on the PBH constraints obtained from the $r$-band (6210\AA) monitoring observation of M31 stars in Niikura et al. (2019), and find that a finite source size effect is dominant over the wave effect for PBHs in the mass range $M_{\rm PBH}\simeq[10^{-11},10^{-10}]M_\odot$. We also discuss that, if a denser-cadence (10~sec), $g$-band monitoring observation for a sample of white dwarfs over a year timescale is available, it would allow one to explore the wave optics effect on microlensing light curve, if it occurs, or improve the PBH constraints in $M_{\rm PBH}\lower.5ex\hbox{$\; \buildrel < \over \sim \;$} 10^{-11}M_\odot$ even from a null detection.