A Targeted Search For Repeating Fast Radio Bursts Associated With Gamma-Ray Bursts

The origin of fast radio bursts (FRBs) still remains a mystery, even with the increased number of discoveries in the last 3 yr. Growing evidence suggests that some FRBs may originate from magnetars. Large, single-dish telescopes such as Arecibo Observatory (AO) and Green Bank Telescope (GBT) have the sensitivity to detect FRB 121102-like bursts at gigaparsec distances. Here, we present searches using AO and GBT that aimed to find potential radio bursts at 11 sites of past gamma-ray bursts that show evidence for the birth of a magnetar. We also performed a search towards GW170817, which has a merger remnant whose nature remains uncertain. We place 10 sigma fluence upper limits of approximate to 0.036 Jy ms at 1.4 GHz and approximate to 0.063 Jy ms at 4.5 GHz for the AO data and fluence upper limits of approximate to 0.085 Jy ms at 1.4 GHz and approximate to 0.098 Jy ms at 1.9 GHz for the GBT data, for a maximum pulse width of approximate to 42 ms. The AO observations had sufficient sensitivity to detect any FRB of similar luminosity to the one recently detected from the Galactic magnetar SGR 1935+2154. Assuming a Schechter function for the luminosity function of FRBs, we find that our non-detections favour a steep power-law index (alpha less than or similar to -1.1) and a large cut-off luminosity (L-0 greater than or similar to 10(41) erg s(-1)).