An archival search for gamma-ray bursts gravitationally lensed by galaxy clusters
Discoveries of gamma-ray bursts (GRBs) have become commonplace in recent decades, totalling $\mathcal{O}(10^4)$ unique detections across various missions. However, there have been no confirmed discoveries of a gravitationally-lensed GRB, despite expected lensing rates of $\sim1$ in $10^{3}$. In light of this, we complete an archival search for lensed GRBs by cross-matching well-localised \emph{Swift}/XRT-detected bursts with a large all-sky sample of galaxy clusters as potential lenses. We find a total of 17 candidate lensed GRBs defined by a 2 arcminute search radius from a cluster in our sample. 14 of our candidates are either confirmed to be at higher redshifts than their cross-matched cluster, or are consistent with a higher redshift origin based on the Amati relation between $E_{p,i}$ and $E_{\rm iso}$ of GRBs, indicating they are, at some level, lensed by their nearby cluster. Using the Amati relation and the lens-GRB separation, we quantify the magnification experienced by each GRB. We find $\mu < 10$ for all except for one candidate, GRB~071031, which is consistent with $\mu > 10$, but is uncertain. Another candidate, GRB~050509B, does not have a directly measured redshift, but was previously assumed to be at the redshift of its nearby cluster, $z=0.225$. We produce a lens model of this cluster and show that GRB~050509B is consistent with $z>1$ and magnified by $\mu\simeq2-6$. We present these findings in anticipation of future lensed GRB discoveries enabled by facilities such as the Vera C. Rubin Observatory in the coming years.