Existing FRB rates were estimated with order of magnitude precision. These approximations were complicating our ability to estimate the chance of success for the VLA, particularly since the VLA is more sensitive than Parkes and we use a scaling law to infer our chance of success. Therefore, we developed a new, homogeneous system for measuring the flux limit based on the radiometer equation. This approach uses the known Galactic brightness distribution, dispersion, and scattering to include effects known to hinder detectability, as described in BSB14. The result is a calculation of the mean flux limit for each survey assuming that the pulses are cosmological and are dispersed and scattered by the Galaxy before being detected.
Figures \ref{recalcrate5} and \ref{recalcrate1} show the measured FRB rate for all four publications with detections for assumed pulse widths of 5 and 1 ms, respectively. The revised flux limits bring all four published rates into agreement over this range of assumed pulse widths. These estimates converge to an overall rate about 3 times smaller than typically inferred from \citet{2013Sci...341...53T}, since that rate limit was defined for a mean detected fluence, not a fluence limit. This fact has been widely overlooked and we are including a discussion of this fact in our coming paper on the VLA FRB project.
BSB14 and \citet{2014arXiv1405.5945P} have found a significant deficit of FRB detections at low Galactic latitudes, suggesting that FRBs originate from beyond the Galaxy. All detections in Figures \ref{recalcrate5} and \ref{recalcrate1} have been made in regions with relatively low Galactic dispersion (either high latitude or outer Galaxy), so even before correction for Galactic effects, these rates are close approximations to the VLA FRB target fields.
The figures show the range of constraints of the current and full VLA FRB observing. The temporal width of FRBs introduces the largest uncertainty in our rate estimate. The published FRBs have widths ranging from roughly 1 to 10 ms with a mean of about 4 ms. The physical process defining these widths is not clear, but the VLA should see similar or larger widths, due to its higher sensitivity and implied distance horizon for cosmological events.