Microlensing of dark matter models in the Milky Way

TL;DR

By analyzing five years of OGLE microlensing data, this work probes PBH dark matter under two alternative Milky Way halo profiles, Einasto and Burkert, extending prior NFW-based results. The authors compute differential microlensing event rates for PBHs with a monochromatic mass function and compare them to the OGLE MS-dominated signal, finding that fully PBH-dominated DM is inconsistent for both profiles but ultrashort events can be explained by PBHs with $M_{\rm PBH}\sim 10^{-5}M_\odot$ and small to moderate $f_{\rm PBH}$. A Poisson likelihood analysis yields 95% C.L. upper bounds on $f_{\rm PBH}$ that are significantly weaker for Burkert than for Einasto, illustrating the sensitivity of PBH constraints to the assumed inner Galactic density profile. Overall, the results highlight the necessity of accurate Galactic center density modeling to robustly assess PBH dark matter scenarios and motivate future refinements, including finite-source effects and PBH clustering.

Abstract

We investigate constraints on the abundance of primordial black holes (PBHs) as dark matter (DM) candidates using five years of microlensing data from the OGLE survey. While the majority of OGLE's $\sim\!2000$ microlensing events are well-explained by stellar populations such as brown dwarfs, main-sequence stars, and compact remnants, a subset of six ultrashort-timescale events ($t_E \sim 0.1\text{--}0.3~\mathrm{days}$) may signal the presence of PBHs. Building upon prior work that adopted the Navarro-Frenk-White (NFW) DM profile, we examine how alternative DM halo models -- specifically the Einasto and Burkert profiles, affect microlensing predictions and the constraints on PBH abundance. In light of kinematic data of Milky Way, we could obtain the range of ($r_s, ρ_s$) for both profiles. We computed differential microlensing event rates for both profiles, using the main-sequence star rate as an observational benchmark. Our results show that neither the Einasto nor Burkert profiles reproduce the distribution of main-sequence star events, yet both allow for viable explanations of the ultrashort-timescale events with PBH masses $M_{\mathrm{PBH}} \sim 10^{-5} M_\odot$. Using a Poisson likelihood analysis under the null hypothesis that no PBH is observed in OGLE dataset, we derive $95\%~\text{C.L.}$ upper and lower bounds on $f_{\mathrm{PBH}}$ for both profiles, finding that the constraints are significantly relaxed under Burkert profiles compared to the NFW case. These results show the sensitivity of PBH constraints to the assumed DM halo structure and highlight the importance of accurately modeling the inner Galactic density profile to robustly assess PBH dark matter scenarios.

Figures (10)

• Figure 1: The enclosed mass of Einasto profile for Milky Way. The black dots are constraints from kinematic measurements 2025NewAR.10001721H. Orange curves represent Einasto profile, the blue curve represents NFW profile. The parameters are labeled in the figure. Two Einasto profiles intersect at $r=r_\mathrm{vir}$ as we have assumed the virial mass $10^{12} M_\odot$.
• Figure 2: The enclosed mass for Burkert profile of Milky Way. The black dots are constraints from kinematic measurements 2025NewAR.10001721H. Orange curves represent Burkert profile, the blue curve represents NFW profile. The parameters are labeled in the figure. Two Burkert profiles intersect at $r=r_\mathrm{vir}$ as we have assumed the virial mass $10^{12} M_\odot$.
• Figure 3: Schematic diagram of gravitational microlensing geometry. $S$ denotes the source, $L$ the lens, and $O$ the observer. $b$ is the impact parameter and $\alpha$ is the deflection angle. Distances between the source, lens, and observer are labeled as $D_S$, $D_L$, and $D_{LS}$, respectively.
• Figure 4: The expected differential number of microlensing events per logarithmic interval of the light curve timescale $t_E$ for the Einasto profile, where there is only one single star in the bulge region. And we have assumed that the five years data of the OGLE data for the MS stars. The quantity of $\frac{dN_{\rm event}}{d\ln t_{\rm E}}=5\times \rm years\times \frac{d\Gamma_a}{dt_{\rm E}}$, including Eq. \ref{['differential event rate for pbh']}, Eq. \ref{['differential event rate for disk region']} and Eq. \ref{['differential event rate for bulge region']}. The other parameters are set in the figure. For each PBH mass, the lower bound corresponds to the profile with a lower scale density, $\rho_s = 1.53 \times 10^{-3} \, M_\odot \, \mathrm{pc}^{-3}$, and a larger characteristic radius, $r_s = 20 \times 10^{3} \, \mathrm{pc}$. On the other side, the upper bound represents the profile with a higher scale density, $\rho_s = 59 \times 10^{-3} \, M_\odot \, \mathrm{pc}^{-3}$, and a smaller characteristic radius, $r_s = 5 \times 10^{3} \, \mathrm{pc}$.
• Figure 5: Expected number of microlensing events per logarithmic interval of the Einstein timescale $t_E$ for the Burkert dark matter profile, assuming a single source star located in the Galactic bulge. Specifically, the plotted quantity is defined as$\frac{dN_{\mathrm{event}}}{d\ln t_E} = 5 \times \mathrm{years} \times \frac{d\Gamma_a}{dt_E}$, corresponding to a 5-year observation period, consistent with the OGLE dataset. Shaded regions represent the model predictions for PBHs with a monochromatic mass distribution, while dashed curves show results for MS stars with masses in the range $0.08 < M/M_\odot < 1$. The differential event rates $\frac{d\Gamma_a}{dt_E}$ for lens populations in the disk, bulge, and PBH scenarios are given by Eqs. (\ref{['differential event rate for disk region']}), (\ref{['differential event rate for bulge region']}), and (\ref{['differential event rate for pbh']}), respectively. For each PBH mass, the lower bound corresponds to the profile with a lower scale density, $\rho_s = 6.05 \times 10^{-3} \, M_\odot \, \mathrm{pc}^{-3}$, and a larger characteristic radius, $r_s = 20 \times 10^{3} \, \mathrm{pc}$. On the other side, the upper bound represents the profile with a higher scale density, $\rho_s = 215 \times 10^{-3} \, M_\odot \, \mathrm{pc}^{-3}$, and a smaller characteristic radius, $r_s = 5 \times 10^{3} \, \mathrm{pc}$.