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 10σ fluence upper limits of ≈0.036 Jy ms at 1.4 GHz and ≈0.063 Jy ms at 4.5 GHz for the AO data and fluence upper limits of ≈0.085 Jy ms at 1.4 GHz and ≈0.098 Jy ms at 1.9 GHz for the GBT data, for a maximum pulse width of ≈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 (α -1.1) and a large cut-off luminosity (L0 ≳ 1041 erg s-1).