Luminosity Functions of Gamma-Ray Burst Afterglows

TL;DR

This study uses the standard fireball model to generate virtual gamma-ray burst afterglow populations, analyzing their luminosity functions and comparing them with observational data to evaluate the model's consistency.

Contribution

It introduces a method to simulate gamma-ray burst afterglows with varied parameters and assesses the model's ability to reproduce observed luminosity functions.

Findings

Luminosity functions resemble a log-normal distribution with an exponential cutoff.

Frequency affects the luminosity function parameters more than model parameter variations.

Standard fireball model aligns with data generally but struggles to explain X-ray and optical emissions simultaneously.

Abstract

Aims: Use the standard fireball model to create virtual populations of gamma-ray burst afterglows and study their luminosity functions. Methods: We randomly vary the parameters of the standard fireball model to create virtual populations of afterglows. We use the luminosity of each burst at an observer's time of 1 day to create a luminosity function and compare our results with available observational data to assess the internal consistency of the standard fireball model. Results: We show that the luminosity functions can be described by a function similar to a log normal distribution with an exponential cutoff. The function parameters are frequency dependent but not very dependent on the model parameter distributions used to create the virtual populations. Comparison with observations shows that while there is good general agreement with the data, it is difficult to explain simultaneously the X-ray and optical data. Possible reasons for this are discussed and the most likely one is that the standard fireball model is incomplete and that decoupling of the X-ray and optical emission mechanism may be needed.