Modeling the Light Curves of Cosmic Gamma-Ray Bursts

Lobachevskii Journal of Mathematics. 2025. Vol. 46. No. 4. P. 1459–1470.

Khabibullin A., A. S. Pozanenko

It is known that the light curve of a prompt emission of cosmic gamma-ray bursts consists of separate pulses. Moreover, in a real light curve these pulses often overlap so that it becomes impossible to study separately the pulses in each light curve. However, spectral analysis, in particular, the power spectral density (PSD) of light curves, bears the imprints of both the pulse shape and the distribution of pulses in a particular light curve. This paper is devoted to solving the problem of finding the distribution of the parameters of these pulses by comparing the PSD of model light curves and the PSD of an ensemble of real light curves. The problem is solved by modeling light curves composed of a set of pulses whose parameters have some distributions. Several analytic forms of pulses are considered: bilateral exponent, log-normal form, and a function known in the literature as Fast Rise Exponential Decay (FRED). The light curves are generated using a single type of pulses, assuming that there is some distribution for each pulse parameter. The influence of the analytic pulse shape and the distribution of pulse parameters on the PSD of the ensemble of modeled light curves is investigated. It is shown that only the duration and symmetry parameters affect the appearance of the PSD of the ensemble of light curves composed of these pulses. The distributions of the pulse parameters that produce the power spectral density of the ensemble of modeled light curves coinciding with the power spectral density of the ensemble of real light curves consisting of these pulses have been found. It is shown that for this purpose it is necessary to introduce a dependency between the parameters of duration and symmetry of the pulse.

Keywords: modeling, power spectral density, light curve, Gamma-ray burst, solution of the inverse problem, pulse profile