Imprint of Gravitational Lensing by Population III Stars in Gamma-Ray Burst Light Curves

We propose a novel method of extracting the imprint of gravitational lensing by Population III stars in the light curves of gamma-ray bursts (GRBs). Significant portions of GRBs can originate in hypernovae of Population III stars and be gravitationally lensed by foreground Population III stars or their remnants. If the lens mass is on the order of 10²-10³ M_☉ and the lens redshift is greater than 10, the time delay between two lensed images of a GRB is ≈1 s and the image separation is ≈10 μas. Although it is difficult to resolve the two lensed images spatially with current facilities, the light curves of the two images are superimposed with a delay of ≈1 s. GRB light curves usually exhibit noticeable variability, where each spike is less than 1 s. If a GRB is lensed, all spikes are superimposed with the same time delay. Hence, if the autocorrelation of the light curve with changing time interval is calculated, it should show resonance at the time delay of the lensed images. Applying this autocorrelation method to GRB light curves that are archived as the BATSE catalog, we demonstrate that more than half of the light curves show recognizable resonance they are lensed. Furthermore, in 1821 GRBs we actually find one candidate for a GRB lensed by a Population III star, which may be located at redshift 20-200. The present method is quite straightforward and therefore provides an effective tool for searching for Population III stars at redshift greater than 10. Using this method, we may find more candidates for GRBs lensed by Population III stars in the data of the Swift satellite.