Limits on Fast Radio Bursts from Four Years of the V-FASTR Experiment

The V-FASTR experiment on the Very Long Baseline Array was designed to detect dispersed pulses of milliseconds in duration, such as fast radio bursts (FRBs). We use all V-FASTR data through 2015 February to report V-FASTR’s upper limits on the rates of FRBs, and compare these with rederived rates from Parkes FRB detection experiments. V-FASTR’s operation at λ =20 {{cm}} allows direct comparison with the 20 cm Parkes rate, and we derive a power-law limit of γ \lt -0.4 (95% confidence limit) on the index of FRB source counts, N(\gt S)\propto {S}^γ . Using the previously measured FRB rate and the unprecedented amount of survey time spent searching for FRBs at a large range of wavelengths (0.3 {{cm}}\gt λ \gt 90 cm), we also place frequency-dependent limits on the spectral distribution of FRBs. The most constraining frequencies place two-point spectral index limits of {α }_{20 {cm}}^{4 {cm}}\lt 5.8 and {α }_{90 {cm}}^{20 {cm}}\gt -7.6, where fluence F\propto {f}^α if we assume that the burst rate reported by Champion et al. of R(F∼ 0.6 {Jy} {ms})=7× {10}³ {{sky}}^-1 {{day}}^-1 is accurate (for bursts of ∼3 ms duration). This upper limit on α suggests that if FRBs are extragalactic but noncosmological, on average they are not experiencing excessive free-free absorption due to a medium with high optical depth (assuming temperature ∼8000 K), which excessively inverts their low-frequency spectrum. This in turn implies that the dispersion of FRBs arises in either or both of the intergalactic medium or the host galaxy, rather than from the source itself.