Redshifts and Luminosities for 112 Gamma-Ray Bursts

Two different luminosity indicators have recently been proposed for Gamma RayBursts that use gamma-ray observations alone. They relate the burst luminosity(L) with the time lag between peaks in hard and soft energies, and thespikiness or variability of the burst's light curve (V). These relations arecurrently justified and calibrated with only 6 or 7 bursts with known redshifts. We have examined BATSE data for the lag and V for 112 bursts. (1) Astrong correlation between the lag and V exists, and it is exactly as predictedfrom the two proposed relations. This is proof that both luminosity indicatorsare reliable. (2) GRB830801 is the all-time brightest burst, yet with a small Vand a large lag, and hence is likely the closest known event being perhaps asclose as 3.2 Mpc. (3) We have combined the luminosities as derived from bothindicators as a means to improve the statistical and systematic accuracy whencompared with the accuracy from either method alone. The result is a list of112 bursts with good luminosities and hence red shifts. (4) The burst averagedhardness ratio rises strongly with the luminosity of the burst. (5) The burstluminosity 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 thebreak and -1.7+-0.1 below the break. (6) The number density of GRBs varies withred shift roughly as (1+z)^(2.5+-0.3) between 0.2

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