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Casey Law edited revision.tex
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\section{Revised FRB Rate}
Existing FRB rate measurements were done to order of magnitude precision. These approximations were complicating our ability to estimate the chance success for the VLA, particularly since
it the VLA is more sensitive than
Parkes. 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. detectability, as described in \citet{bsb}. 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
with for assumed pulse widths of 5 and 1 ms, respectively. \citet{bsb} and \citet{petroff} 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
they even before correction for Galactic effects, these rates likely represent the extragalactic rate that the VLA FRB project is sensitive to.
The figures show the range of constraints of the current and full VLA FRB observing. The largest uncertainty in estimating the FRB rate One possible exception is the
apparent temporal width. The published FRBs have widths ranging from roughly 1 to 10 ms with a mean rate of
about 4 ms. The physical process defining these widths is \citet{2007Sci...318..777L}, which did not
clear, define an overall SNR limit for their search. We assume a $7\sigma$ limit as in other Parkes surveys, but
the VLA this is likely optimistic, so this point should
see similar or larger widths, due to its higher sensitivity and implied distance horizon for cosmological events. likely be placed further right in the plot.
The figures show the range of constraints of the current and full VLA FRB observing. The largest uncertainty in estimating the FRB rate is the apparent temporal width. 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.