Testing a Galactic Lensing Hypothesis with the Prompt Emission of GRB 221009A

Abstract

Even at modest amplification, the optical depth to gravitational lensing through the Galaxy is $<10^{-5}$. However, the large apparent isotropic-equivalent energy of GRB 221009A coupled with a path through low Galactic latitude suggests that the conditional probability that this particular GRB was lensed is greater than the very low a priori expectation. With the extreme brightness of the prompt emission, this Galactic lensing hypothesis can be constrained by autocorrelation analysis of Fermi photons on 0.1-1000 ms timescales. In relating lensing mass, magnification, and autocorrelation timescale, I show that a lensed-induced autocorrelation signature by stellar lenses falls below the minimal variability timescale (MVT) expected from a black hole central engine. However, lensing by Galactic dark matter MACHOs ($M_l > 10-1000\,M_\odot$) could be confirmed with this approach. Regardless, at a peak $\gamma$-ray photon rate of $>30$ ms$^{-1}$, GRB 221009A represents a prime opportunity to measure the smallest MVTs of GRBs.