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B. E. Schaefer (Univ. Texas Austin), D. L. Band (Los Alamos), M. Deng (Yale)
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, Tlag, 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 Tlag and V for many bursts. (1) A strong correlation between Tlag and V exists, and it is exactly as predicted from the two proposed relations. This is proof that both luminosity indicators are reliable. (2) We have combined the luminosities as derived from both indicators as a means to improve the statistical and systematic accuracy when compared to the accuracy from either method alone. The result is that we have 112 bursts with good luminosities and hence red shifts. (3) The burst luminosity function is a broken power law, with the break at L=1052erg. The numbers in logarithmic bins scale as L-2.0+-0.2 above the break and as L0.4+-0.4 below the break. (4) The number density of GRBs varies with red shift roughly as (1+z)2.3+-1.0 from z=0.4 to z~6. The burst number density is proportional to the star formation rate since bursts are seen to be associated with star forming regions and since they are produced with little delay by massive stars. So we conclude that the star formation rate in our Universe is rising steeply for red shifts between 2 and ~6, in contrast to optical results which show a flat rate at most. This new method (using gamma radiation) does not suffer any problems from extinction, and this is a substantial advantage over the older methods (using optical light) which can suffer greatly from extinction.