Collapsar Gamma-Ray Bursts: how the luminosity function dictates the duration distribution

TL;DR

This paper demonstrates that the observed luminosity and duration distributions of long gamma-ray bursts can be explained by the jet breakout process, linking the luminosity function to the duration distribution and implications for supernovae.

Contribution

It introduces a model connecting jet breakout timescales with luminosity, explaining the GRB luminosity function and duration distribution, and explores the role of failed jets in supernovae.

Findings

The broken power-law luminosity function naturally arises from jet breakout physics.

The duration distribution shape is determined by the luminosity function and breakout time scaling.

Failed jets may contribute to all Type Ib/c supernovae, not just successful GRBs.

Abstract

Jets in long-duration $\gamma$-ray bursts (GRBs) have to drill through the collapsing star in order to break out of it and produce the $\gamma$-ray signal while the central engine is still active. If the breakout time is shorter for more powerful engines, then the jet-collapsar interaction acts as a filter of less luminous jets. We show that the observed broken power-law GRB luminosity function is a natural outcome of this process. For a theoretically motivated breakout time that scales with jet luminosity as $L^{-\chi}$ with $\chi\sim 1/3-1/2$, we show that the shape of the $\gamma$-ray duration distribution can be uniquely determined by the GRB luminosity function and matches the observed one. This analysis has also interesting implications about the supernova-central engine connection. We show that not only successful jets can deposit sufficient energy in the stellar envelope to power the GRB-associated supernovae, but also failed jets may operate in all Type Ib/c supernovae.