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 lambda = 20 cm allows direct comparison with the 20 cm Parkes rate, and we derive a power-law limit of gamma < -0.4 (95% confidence limit) on the index of FRB source counts, N(>S) proportional to S-gamma. 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 > lambda > 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 alpha(4cm)(20cm) < 5.8 and alpha(20cm)(90cm) > -7.6, where fluence F proportional to f(alpha) if we assume that the burst rate reported by Champion et al. of R(F similar to 0.6 Jy ms) = 7 x 10(3) sky(-1) day(-1) is accurate (for bursts of similar to 3 ms duration). This upper limit on alpha 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 similar to 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.