New techniques in the fitting of gamma-ray burst cyclotron lines

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Abstract
We provide an approximate prescription for determining the Bayesian odds favoring spectral models with lines over models without lines, using a new line parametrization which has several advantages over previous parametrizations. we use an exponentiated Gaussian line model, parameterized in terms of the equivalent width, W E , and the full width at half maximum, W 1/2, of the line itself (not the full width of the Gaussian). Unlike other, equivalent, parameterizations, this parametrization yields Bayesian posterior probability distributions (and frequentist χ2 surfaces) which are approximately Gaussian near the maximum likelihood parameter values, and allows the formulation of prior probability distributions for the continuum and line parameters which are independent of each other. It has the additional advantage that it easily treats ‘‘saturated’’ lines, in which W E =W 1/2. We use Bayesian inference and this parameterization to determine whether the Burst and Transient Source Experiment (BATSE) Spectroscopy Detector (SD) can detect the single and harmonically‐spaced spectral lines observed by Ginga in the time periods S1 and S2 of GB870303. We find that a single SD can marginally detect the single, strong line in S1 at ≊20 keV at burst incidence angles ≲45°, and the harmonically‐spaced, weaker, lines in S2 at ≊20 and 40 keV at incidence angles ≲60°.

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