Stellar microlensing as a probe of Primordial Black Holes: status and prospects

TL;DR

Stellar microlensing provides a direct probe of compact dark matter objects, including primordial black holes, by measuring the frequency and timescale distribution of microlensing events toward the Magellanic Clouds and M31. The paper synthesizes the theory of photometric and astrometric microlensing, detailing how optical depth, event rates, and differential rates constrain the PBH mass function and halo fraction under standard assumptions. It then surveys decades of observations (MACHO, EROS, OGLE, M31, Kepler) and summarizes robust constraints which exclude PBHs as the dominant DM across roughly $10^{-11}$ to $10^{4}$ solar masses, with stronger bounds in many subranges. Looking forward, space-based missions like the Roman Space Telescope and Rubin Observatory, together with improved theoretical modeling of PBH clustering and velocity distributions, hold the potential to push sensitivity to $f\sim10^{-3}-10^{-4}$ for certain masses, providing a crucial test of PBH dark matter scenarios.

Abstract

Stellar microlensing is a powerful tool for probing dark matter in the form of planetary and stellar mass compact objects (COs), in particular primordial black holes (PBHs). Under standard assumptions, current observations exclude COs in the mass range $10^{-11} \lesssim M/M_{\odot} \lesssim 10^{4}$ making up all of the dark matter. We provide an overview, aimed at theorists working on PBHs, of the history, theory, observational status, and future prospects of the field.

Figures (4)

• Figure S1: The geometry of a stellar microlensing event. The left and right panels show the view perpendicular to and along the line of sight respectively. The solid black and dashed grey lines shows the trajectory of the compact object and the Einstein radius, $R_{\rm E}$, respectively. The orange star, black circle and blue square denote the source, the lens and the observer respectively. In the left panel the dotted green lines show the distance from the observer to the lens and source, $D_{\rm L}= x D_{\rm S}$ and $D_{\rm S}$ respectively. In the right panel the green dotted lines show the impact parameter, $b$, and its minimum value $b_{\rm min}$.
• Figure S2: The magnification factor, $A$, Eq. (\ref{['eq:ut']}), as a function of $2 t/\hat{t}$ for $u_{\rm min}=b_{\rm min}/R_{\rm E} = 0.25, 0.5$ and $1.0$ (from top to bottom). The horizontal dotted black line shows the threshold for a microlensing event, $A_{\rm T} = 1.34$.
• Figure S3: The differential event rate, ${\rm d} \Gamma / {\rm d} \hat{t}$, as a function of Einstein diameter crossing time, $\hat{t}$, for a standard halo (see text for details) composed entirely, $f=1$, of COs with mass $M=1 M_{\odot}$ as given by Eq. (\ref{['dfsh']}).
• Figure S4: Constraints on the CO mass, $M$, and MW halo fraction, $f$, at 95% confidence, assuming all CO have the same mass. The solid lines show the exclusion limits from EROS ('E') 2007AA...469..387T (yellow), MACHO long timescale ('M-long') Macho:2000nvd (red), EROS plus MACHO long timescale ('E+M') Blaineau:2022nhy (orange), OGLE Mroz:2024wag and OGLE high cadence ('OGLE-hc') Mroz:2024wia (blue), and Kepler ('K') Griest:2013aaa (green). The purple lines are from high cadence observations of M31 using the Subaru-HSC. 'HSC19' shows the original exclusion limit Niikura:2017zjd as calculated in Ref. Croon:2020ouk, while 'HSC26' shows the exclusion limit from the latest analysis, under the assumption that none of the events observed are due to CO in the MW halo. The dashed line shows the allowed parameter values assuming that the 4 'secure' high-significance events are due to CO in the MW halo. The dashed red line shows the allowed parameter values from the 13 set A events in the final 5.7 year MACHO data set, as published in Ref. MACHO:2000qbb. Subsequent observations indicate that some of these events are not microlensing (see Sec. \ref{['subsec:macho']} and Refs. 2007AA...469..387TMroz:2025aor for discussion). The dotted blue line, labeled 'OGLE?', shows the parameter values found assuming that the ultra-short duration events observed towards the Galactic bulge by OGLE are due to COs in the MW halo Niikura:2019kqi. The dot-dashed black line shows the envelope of the tightest constraint for each value of $M$. This plot was made using a modified version of Kavanagh's PBHBounds PBHbounds.