Confidence intervals for the correlation between the gamma-ray burst peak energy and the associated supernova peak brightness
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Date
2009
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Publisher
Oxford University Press
Abstract
A strong correlation between the gamma-ray burster peak energy and the peak luminosity
of the associated supernova was discovered by Li for four GRBs. Despite the fact that the
formal significance level of the correlation is 0.3 per cent, the smallness of the data set requires
careful further evaluation of the result. Subject to the assumption that the data are bivariate
Gaussian, a 95 per cent confidence interval of (−0.9972, 0.02) for the correlation is derived.
Using data from the literature, it is shown that the distribution of known peak GRB energies is
not Gaussian if X-ray flashes are included in the sample. This leads to a proposed alternative
to the bivariate Gaussian model, which entails describing the dependence between the two
variables by a Gaussian copula. The copula is still characterized by a correlation coefficient.
The Bayesian posterior distribution of the correlation coefficient is evaluated using a Markov
chain Monte Carlo method. The mean values of the posterior distributions range from −0.33
to about zero, depending on the specifics of the supernova (SN) peak brightness distribution.
The implication is that the existing data favour a modest correlation between the GRB peak
energy and the SN peak brightness; confidence intervals are very wide and include zero.
Description
Keywords
Methods: statistical, Supernovae: general, Gamma-rays: bursts
Citation
Koen, C. (2009). Confidence intervals for the correlation between the gamma-ray burst. Monthly Notices of the Royal Astronomical Society, 393: 1370–1376