2016ApJ...826..223B

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)∝§^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∝{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.