Evidence for an intermediate-mass black hole from a gravitationally lensed gamma-ray burst

If gamma-ray bursts are at cosmological distances, they must be gravitationally lensed occasionally. The detection of lensed images with millisecond-to-second time delays provides evidence for intermediate-mass black holes, a population that has been difficult to observe. Several studies have searched for these delays in gamma-ray burst light curves, which would indicate an intervening gravitational lens. Among the $\sim 10^4$ gamma-ray bursts observed, there have been a handful of claimed lensing detections, but none have been statistically robust. Here we present a Bayesian analysis identifying gravitational lensing in the light curve of GRB950830. The inferred lens mass depends on the unknown lens redshift $z_l$, and is given by $(1+z_l)M_l = 5.5^{+1.7}_{-0.9}\times 10^4$ M$_\odot$ (90% credibility), which we interpret as evidence for an intermediate-mass black hole. The most probable configuration, with a lens redshift $z_l\sim 1$ and a gamma-ray burst redshift $z_s\sim 2$, yields a present day number density of $n_\text{imbh}\approx 2.3^{+4.9}_{-1.6}\times10^{3} \text{ Mpc}^{-3}$ (90% credibility) with a dimensionless energy density $\Omega_\text{imbh} \approx 4.6^{+9.8}_{-3.3}\times10^{-4}$. The false alarm probability for this detection is $\sim0.6\%$ with trial factors. While it is possible that GRB950830 was lensed by a globular cluster, it is unlikely since we infer a cosmic density inconsistent with predictions for globular clusters $\Omega_\text{gc} \approx 8 \times 10^{-6}$ at 99.8% credibility. If a significant intermediate-mass black hole population exists, it could provide the seeds for the growth of supermassive black holes in the early Universe.