Redshifts and Luminosities for 112 Gamma Ray Bursts

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Abstract
Two different luminosity indicators have recently been proposed for Gamma Ray Bursts that use gamma-ray observations alone. They relate the burst luminosity (L) with the time lag between peaks in hard and soft energies, and the spikiness or variability of the burst's light curve (V). These relations are currently justified and calibrated with only 6 or 7 bursts with known red shifts. We have examined BATSE data for the lag and V for 112 bursts. (1) A strong correlation between the lag and V exists, and it is exactly as predicted from the two proposed relations. This is proof that both luminosity indicators are reliable. (2) GRB830801 is the all-time brightest burst, yet with a small V and a large lag, and hence is likely the closest known event being perhaps as close as 3.2 Mpc. (3) We have combined the luminosities as derived from both indicators as a means to improve the statistical and systematic accuracy when compared with the accuracy from either method alone. The result is a list of 112 bursts with good luminosities and hence red shifts. (4) The burst averaged hardness ratio rises strongly with the luminosity of the burst. (5) The burst luminosity function is a broken power law, with the break at L = 2x10^{52} erg/s. The luminosity function has power law indices of -2.8+-0.2 above the break and -1.7+-0.1 below the break. (6) The number density of GRBs varies with red shift roughly as (1+z)^(2.5+-0.3) between 0.2<z<5. Excitingly, this result also provides a measure of the star formation rate out to z~5 with no effects from reddening, and the rate is rising uniformly for red shifts above 2.

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