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 three years. 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 $\approx 0.036$ Jy ms at 1.4 GHz and $\approx 0.063$ Jy ms at 4.5 GHz for AO data and fluence upper limits of $\approx 0.085$ Jy ms at 1.4 GHz and $\approx 0.098$ Jy ms at 1.9 GHz for GBT data, for a maximum pulse width of $\approx 42$ 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 favor a steep power--law index ($\alpha\lesssim-1.0$) and a large cut--off luminosity ($L_0 \gtrsim 10^{42}$ erg/s).