Redshifts and Luminosities for 112 Gamma-Ray Bursts

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 (τ 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 τ lag and V for 112 bursts. (1) A strong correlation between τ 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 τ 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 × 10 52 erg. The numbers in logarithmic bins scale as L −2.8±0.2 above the break and as L −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. 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 ∼ 5 with no effects from reddening, and the rate is rising uniformly for red shifts above 2.

Gamma-Ray Burst Prompt Correlations

“…A remarkably consistent relation was found by Schaefer et al [121], who used a sample of 112 BATSE GRBs and reported that log peak = 52.46 − (1.14 ± 0.20) log lag ,…”

Gamma‐Ray Burst Intensity Distributions

“…Comparison to other studies is more difficult, particularly since we study the probability distribution of E iso , while others ( Fenimore & Ramirez-Ruiz 2000;Schaefer et al 2001;Schmidt 2001;Lloyd-Ronning et al 2002;Norris 2002) studied the luminosity function of L B . In addition, these studies use different definitions of the luminosity, e.g., for BATSE's 50-300 keV trigger band (Fenimore & Ramirez-Ruiz 2000;Lloyd-Ronning et al 2002) .…”

“…For example, Schaefer et al (2001) and Lloyd-Ronning et al (2002) find that the luminosity function for L B is a broken power law.…”

Imprint of Gravitational Lensing by Population III Stars in Gamma‐Ray Burst Light Curves

“…They include the variability-luminosity relation (Fenimore & Ramirez-Ruiz 2000), the lag-luminosity relation (Norris et al 2000), the E p -luminosity relation (Amati et al 2002), and the spectral peak energy-toluminosity relation ( Yonetoku et al 2004). Applying these relations to GRBs, the redshift distributions of GRBs are derived (Fenimore & Ramirez-Ruiz 2000;Norris et al 2000;Schaefer et al 2001;Lloyd-Ronning et al 2002;Yonetoku et al 2004). Some analyses conclude that a portion of GRBs are located at z k10.…”