Statistical Analysis of Spectral Line Candidates in Gamma‐Ray Burst GRB 870303

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Abstract
The Ginga data for the gamma-ray burst GRB 870303 exhibit low-energy dips in two temporally distinct spectra, denoted S1 and S2. S1, spanning 4 s, exhibits a single line candidate at ≈20 keV, while S2, spanning 9 s, exhibits apparently harmonically spaced line candidates at ≈20 and 40 keV. The centers of the time intervals corresponding to S1 and S2 are separated by 22.5 s. We rigorously evaluate the statistical evidence for these lines, using phenomenological continuum and line models which in their details are independent of the distance scale to gamma-ray bursts. We employ the methodologies based on both frequentist and Bayesian statistical inference that we develop in a forthcoming paper. These methodologies utilize the information present in the data to select the simplest model that adequately describes the data from among a wide range of continuum and continuum-plus-line(s) models. This ensures that the chosen model does not include free parameters that the data deem unnecessary and that would act to reduce the frequentist significance and Bayesian odds of the continuum-plus-line(s) model. We calculate the significance of the continuum-plus-line(s) models using the χ2 maximum likelihood ratio test. We describe a parameterization of the exponentiated Gaussian absorption line shape that makes the probability surface in parameter space better behaved, allowing us to estimate analytically the Bayesian odds. We find that the significance of the continuum-plus-line model requested by the S1 data is 3.6 × 10-5, with the odds favoring it being 114:1. The significance of the continuum-plus-lines model requested by the S2 data is 1.7 × 10-4, with the odds favoring it being 7:1. We also apply our methodology to the combined (S1 + S2) data. The significance of the continuum-plus-lines model requested by the combined data is 4.2 × 10-8, with the odds favoring it being 40,300:1.
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