Confidence intervals for the correlation between the gamma-ray burst peak energy and the associated supernova peak brightness

dc.contributor.authorKoen, Chris
dc.date.accessioned2013-11-13T08:26:01Z
dc.date.available2013-11-13T08:26:01Z
dc.date.issued2009
dc.description.abstractA 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.en_US
dc.description.accreditationWeb of Scienceen_US
dc.identifier.citationKoen, C. (2009). Confidence intervals for the correlation between the gamma-ray burst. Monthly Notices of the Royal Astronomical Society, 393: 1370–1376en_US
dc.identifier.issn0035-8711
dc.identifier.urihttp://hdl.handle.net/10566/801
dc.language.isoenen_US
dc.privacy.showsubmitterfalse
dc.publisherOxford University Pressen_US
dc.rights© 2009 copyright Oxford University Press. This file may be freely used for educational purposes, as long as it is not altered in any way. Acknowledgement of the authors and the source is required.
dc.source.urihttp://dx.doi.org/10.1111/j.1365-2966.2008.14116.x
dc.status.ispeerreviewedtrue
dc.subjectMethods: statisticalen_US
dc.subjectSupernovae: generalen_US
dc.subjectGamma-rays: burstsen_US
dc.titleConfidence intervals for the correlation between the gamma-ray burst peak energy and the associated supernova peak brightnessen_US
dc.typeArticleen_US

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