Observational Constraints on WIMP Mini-Spikes Around Stellar-Mass Primordial Black Holes with 17 Years of Fermi-LAT Data

Abstract

The quest to identify the true nature of dark matter remains one of the most pressing challenges in modern physics. We present a novel approach to probe the Weakly Interacting Massive Particle (WIMP) paradigm by analyzing density enhancements, or ``mini-spikes,'' around stellar-mass black holes (sBHs) using 17 years of data from the \textit{Fermi} Large Area Telescope. Motivated by the anomalous orbital decay observed in the black hole low-mass X-ray binaries A0620--00 and XTE J1118+480, we model these systems under the hypothesis of adiabatic spike formation around primordial black holes, incorporating the effects of tidal disruption in the Galactic disk. Finding no statistically significant gamma-ray excess at either location ($TS < 1$), we derive 95\% C.L. upper limits on the WIMP annihilation cross section. Our results exclude the canonical thermal relic cross section ($3 \times 10^{-26} \, \text{cm}^3\text{s}^{-1}$) across the 10~GeV to 10~TeV mass range for $b\bar{b}$ and $W^+W^-$ channels, and up to $\sim$6~TeV for the $\tau^+\tau^-$ channel. Recasting these results into a Galactic discovery reach, we demonstrate that \textit{Fermi}-LAT is sensitive to $10\,M_\odot$ mini-spikes even at distances surpassing the Galactic Center, provided the WIMP mass is below 1~TeV. These findings establish a significant tension between the dynamical friction interpretation of orbital decay in these systems and the WIMP hypothesis, providing robust observational constraints on the coexistence of primordial black holes and annihilating dark matter.