Gamma‐Ray Bursts from Rich Concentrated Abell‐Corwin‐Olowin Clusters: The Luminosity‐Duration Relation

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Abstract
A likelihood statistic constructed from positions and positional uncertainties identifies 82 associations of BATSE sources with rich, concentrated Abell clusters. Random simulations indicate that 42 ± 9 of these pairs are chance associations. Among the approximately 40 physically associated cluster-gamma-ray burst (GRB) pairs (the nearest containing the Coma Cluster and GRB 2193), we find (1) a plateau between 15.8 and 16.2 mag in the integral (observed-minus-random) number distribution of mR(10), the magnitude of 10th brightest cluster member, which may indicate the presence of two burst populations with different characterstic intrinsic luminosities; (2) the dispersion in GRB fluences between 100 and 300 keV (represented as apparent magnitude, m[100-300 keV]) is smaller for bursts paired with mR(10) ≤ 16.2 clusters than for those with mR(10) > 16.2; (3) the average 100-300 keV isotropic intrinsic energy of GRBs associated with mR(10) ≤ 16.2 clusters with known redshift z < 0.07 (10 clusters including Coma) is 3.4 ± 2.3 × 1049 ergs; (4) the apparent luminosity of these 10 GRBs is anticorrelated with burst duration, t90 (Spearman rank correlation coefficient of 0.87, nonzero at between 99% and 99.9% confidence level); and (5) the absolute luminosity, L1024, of these 10 GRBs is more strongly anticorrelated with t90 (Spearman rank correlation coefficient of 0.93, nonzero at >99.9% confidence level). The slope of this relation indicates t90∝L−11024. These results suggest that the anticorrelation of apparent burst magnitude with duration is an intrinsic property of the bursts and is not caused by cosmological time dilation.

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