The Performance and Calibration of the CRAFT Fly's Eye Fast Radio Burst Survey

Since January 2017, the Commensal Real-time ASKAP Fast Transients survey (CRAFT) has been utilising commissioning antennas of the Australian SKA Pathfinder (ASKAP) to survey for fast radio bursts (FRBs) in fly's eye mode. This is the first extensive astronomical survey using phased array feeds (PAFs), and a total of 20 FRBs have been reported. Here we present a calculation of the sensitivity and total exposure of this survey, using the pulsars B1641-45 (J1644-4559) and B0833-45 (J0835-4510, i.e.\ Vela) as calibrators. The design of the survey allows us to benchmark effects due to PAF beamshape, antenna-dependent system noise, radio-frequency interference, and fluctuations during commissioning on timescales from one hour to a year. Observation time, solid-angle, and search efficiency are calculated as a function of FRB fluence threshold. Using this metric, effective survey exposures and sensitivities are calculated as a function of the source counts distribution. The implied FRB rate is significantly lower than the $37$\,sky$^{-1}$\,day$^{-1}$ calculated using nominal exposures and sensitivities for this same sample by \citet{craft_nature}. At the Euclidean power-law index of $-1.5$, the rate is $10.7_{-1.8}^{+2.7}\,{\rm (sys)} \, \pm \, 3\,{\rm (stat)}$\,sky$^{-1}$\,day$^{-1}$ above a threshold of $57\pm6\,{\rm (sys)}$\,Jy\,ms, while for the best-fit index for this sample of $-2.1$, it is $16.6_{-1.5}^{+1.9} \,{\rm (sys)}\, \pm 4.7\,{\rm (stat)}$\,sky$^{-1}$\,day$^{-1}$ above a threshold of $41.6\pm1.5\,{\rm (sys)}$\,Jy\,ms. This strongly suggests that these calculations be performed for other FRB-hunting experiments, allowing meaningful comparisons to be made between them.