Soft gamma-ray repeaters in nearby galaxies: Rate, luminosity function, and fraction among short gamma-ray bursts

It was suggested that some of the short-duration gamma-ray bursts (GRBs) are giant flares of soft gamma-ray repeaters (GRs) in nearby galaxies. To test this hypothesis, I have constructed a sample of 47 short GRBs, detected by the Interplanetary Network (IPN), for which the position is constrained by at least one annulus on the celestial sphere. For each burst, I have checked whether its IPN 3 sigma error region coincides with the apparent disk of one of 316 bright, star-forming galaxies found within 20 Mpc. I find a single match of GRB 000420B with M74, which could, however, be due to a chance coincidence. I estimate the IPN efficiency as a function of fluence and derive the galaxy sample completeness. I find that assuming there is a cutoff in the observed energy distribution of SGR flares at <= 10(47) ergs, the fraction of SGRs among short GRBs with fluence above similar to 10(-5) ergs cm(-2) is < 16% (95% confidence). I estimate the number of active SGRs in each one of the galaxies in the sample, and combine it with the distances to these galaxies, the IPN efficiency, and the SGR flare energy distribution, to derive the rate of giant flares with energy above 4; 10(46) ergs. I find that the rate of such giant flares is about (0.4-5); 10(-4) yr(-1) per SGR. This rate is marginally consistent with the observed Galactic rate. Comparison of the Galactic rate with the inferred extragalactic rate implies a gradual cutoff (or steepening) of the flare energy distribution less than or similar to 3 x 10(46) ergs (95% confidence). Using the Galactic SGR flare rate, I set a lower limit of 1% on the fraction of SGR flares among short GRBs.