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[29.07] Constraining the Luminosity Function of GRBs from Time Dilation, Brightness Distribution and Redshift Data

M. Deng, B. Schaefer (Yale University)

We constrain the luminosity function of gamma ray bursts (GRBs) by testing several cosmological models versus a combination of (1) observed time dilation in the peak-to-peak time scales of GRB light curves, (2) the Log N - Log P number counts relation, and (3) GRB luminosities directly determined from recent redshift measurements and apparent GRB brightness. A power law luminosity function \phi(L) = C \cdot L^-\beta (L_min < L < L_max) is examined within three cosmological models, with cosmological parameters (\Omega₀, \Omega_\Lambda) = (1.0, 0.0), (0.3, 0.0), or (0.3, 0.7). It is found that GRB models with constant comoving density rate do not fit the data while models with GRB density evolution tracing the observed star formation rate can accomodate all the observed data. The width K = L_max / L_min of the luminosity function is found to be K > 100 at the 1 \sigma level, while the average luminosity is found to be 4 ±2 \times 10⁵¹ ergs \cdot s^-1 at the 3 \sigma level, this implies that bursts at the BATSE 100 % efficiency threshold have typical red shifts of 0.42> = 2.7 ±0.5.