Intensity Distribution Function and Statistical Properties of Fast Radio Bursts

TL;DR

This paper analyzes the statistical properties of Fast Radio Bursts, including their dispersion measures, energy distribution, and intensity distribution function, providing insights into their cosmological origins and detection prospects with FAST.

Contribution

It derives the first intensity distribution function for FRBs based on current data, revealing a flatter power-law index than expected for standard candles.

Findings

FRBs have a mean dispersion measure of ~660 pc/cm^3, indicating cosmological origin.

Radio energy of FRBs spans two orders of magnitude, averaging ~10^39 ergs.

FAST can detect approximately 5 FRBs every 1000 hours based on the derived intensity distribution.

Abstract

Fast Radio Bursts (FRBs) are intense radio flashes from the sky that are characterized by millisecond durations and Jansky-level flux densities. We carried out a statistical analysis on FRBs discovered. Their mean dispersion measure, after subtracting the contribution from the interstellar medium of our Galaxy, is found to be $\sim 660\,\rm pc\,cm^{-3}$, supporting their being from cosmological origin. Their energy released in radio band spans about two orders of magnitude, with a mean value of $\sim 10^{39}$ ergs. More interestingly, although the FRB study is still in a very early phase, the published collection of FRBs enables us to derive a useful intensity distribution function. For the 16 non-repeating FRBs detected by Parkes telescope and the Green Bank Telescope, the intensity distribution can be described as $dN/dF_{\rm obs} = (4.1 \pm 1.3) \times 10^3 \, F_{\rm obs}^{-1.1\pm0.2} \; \rm sky^{-1}\,day^{-1}$, where $F_{\rm obs}$ is the observed radio fluence in units of Jy~ms. Here the power-law index is significantly flatter than the expected value of 2.5 for standard candles distributed homogeneously in a flat Euclidean space. Based on this intensity distribution function, the Five-hundred-meter Aperture Spherical radio Telescope (FAST) will be able to detect about 5 FRBs for every 1000 hours of observation time.