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 ( \tau _ { lag } ) , 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 \tau _ { lag } and V for 112 bursts .
( 1 ) A strong correlation between \tau _ { 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 \tau _ { 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 = 2 \times 10 ^ { 52 } erg .
The numbers in logarithmic bins scale as L ^ { -2.8 \pm 0.2 } above the break and as L ^ { -1.7 \pm 0.1 } below the break .
( 6 ) The number density of GRBs varies with red shift roughly as ( 1 + z ) ^ { 2.5 \pm 0.3 } between 0.2 < z < 5 .
This demonstrates that the burst rate follows the star formation rate at low red shifts , as expected since long bursts are generated by very massive stars .
Excitingly , this result also provides a measure of the star formation rate out to z \sim 5 with no effects from reddening , and the rate is rising uniformly for red shifts above 2 .