The GRB luminosity function in the internal shock model confronted to observations

TL;DR

This paper models the gamma-ray burst luminosity function within the internal shock framework, showing it can have two branches and that current data cannot distinguish between different functional forms, but supports a low luminosity slope near -0.6.

Contribution

It introduces a detailed internal shock model predicting a dual-branch luminosity function and compares it with observational data, constraining the low luminosity slope.

Findings

Luminosity function has two branches at high and low luminosities.

Current observational data cannot distinguish between single and broken power-law forms.

Observed low luminosity slope (~ -0.6) aligns with internal shock model predictions.

Abstract

We compute the expected luminosity function of GRBs in the context of the internal shock model. We assume that GRB central engines generate relativistic outflows characterized by the respective distributions of injected kinetic power Edot and contrast in Lorentz factor Kappa = Gamma_max/Gamma_min. We find that if the distribution of contrast extends down to values close to unity (i.e. if both highly variable and smooth outflows can exist) the luminosity function has two branches. At high luminosity it follows the distribution of Edot while at low luminosity it is close to a power law of slope -0.5. We then examine if existing data can constrain the luminosity function. Using the log N - log P curve, the Ep distribution of bright BATSE bursts and the XRF/GRB ratio obtained by HETE2 we show that single and broken power-laws can provide equally good fits of these data. Present observations are therefore unable to favor one form of the other. However when a broken power-law is adopted they clearly indicate a low luminosity slope ~ -0.6 +- 0.2, compatible with the prediction of the internal shock model.