Searching for Gravitationally Lensed Gamma-Ray Bursts with Their Afterglows

Gamma-ray bursts (GRBs) at high redshifts are expected to be gravitationally lensed by objects of different mass scales. Other than a single recent claim, no lensed GRB has been detected so far by using gamma-ray data only. In this paper, we suggest that multiband afterglow data might be an efficient way to search for lensed GRB events. Using the standard afterglow model, we calculate the characteristics of the lensed afterglow lightcurves under the assumption of two popular analytic lens models: the point-mass and singular isothermal sphere models. In particular, when different lensed images cannot be resolved, their signals would be superimposed together with a given time delay. In this case, the X-ray afterglows are likely to contain several X-ray flares of similar width in linear scale and similar spectrum, and the optical afterglow lightcurve will show re-brightening signatures. Since the lightcurves from the image arriving later would be compressed and deformed in the logarithmic timescale, the larger time delay (i.e., the larger mass of the lens), the easier it is to identify the lensing effect. We analyzed the archival data of optical afterglows and found one potential candidate of the lensed GRB (130831A) with time delay similar to 500 s; however, observations of this event in gamma-ray and X-ray bands seem not to support the lensing hypothesis. In the future, with the cooperation of the all-sky monitoring gamma-ray detectors and multiband sky survey projects, the method proposed in this paper would be more efficient in searching for strongly lensed GRBs.