Intensity Distribution Function and Statistical Properties of Fast Radio Bursts

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.