On the normalised FRB luminosity function

TL;DR

This study measures the normalized luminosity function of FRBs using Bayesian methods, revealing a power-law distribution over three orders of magnitude, which constrains their intrinsic energy output and informs their origins.

Contribution

The paper introduces a Bayesian approach to accurately determine the FRB luminosity function, accounting for various observational and astrophysical systematics, and demonstrates its robustness across different models.

Findings

FRB luminosities follow a power-law distribution with index -1.8 to -1.2.

The luminosity function spans approximately three orders of magnitude.

Results are robust against uncertainties in galaxy and environment models.

Abstract

Thirty-three fast radio bursts (FRBs) had been detected by March 2018. Although the sample size is still limited, meaningful statistical studies can already be carried out. The normalised luminosity function places important constraints on the intrinsic power output, sheds light on the origin(s) of FRBs, and can guide future observations. In this paper, we measure the normalised luminosity function of FRBs. Using Bayesian statistics, we can naturally account for a variety of factors such as receiver noise temperature, bandwidth, and source selection criteria. We can also include astronomical systematics, such as host galaxy dispersion measure, FRB local dispersion measure, galaxy evolution, geometric projection effects, and Galactic halo contribution. Assuming a Schechter luminosity function, we show that the isotropic luminosities of FRBs have a power-law distribution that covers approximately three orders of magnitude, with a power-law index ranging from $-1.8$ to $-1.2$ and a cut off $\sim 2\times 10^{44}\,\rm erg\,s^{-1}$. By using different galaxy models and well-established Bayesian marginalisation techniques, we show that our conclusions are robust against unknowns, such as the electron densities in the Milky Way halo and the FRB environment, host galaxy morphology, and telescope beam response.