Comparative Analysis of the Observational Properties of Fast Radio Bursts at the Frequencies of 111 and 1400 MHz

A comparative analysis of the observational characteristics of fast radio bursts at the frequencies 111 and 1400 MHz is carried out. The distributions of radio bursts by the dispersion measure are constructed. At both frequencies, they are described by a lognormal distribution with the parameters $\mu =6.2$$\sigma = 0.7$. The dependence $\tau_{sc}(DM)$ of the scattering value on the dispersion measure at 111 MHz and 1400 MHz is also constructed. This dependence is fundamentally different from the dependence for pulsars. A comparative analysis of the relationship between the scattering of pulses and the dispersion measure at 1400 MHz and 111 MHz showed that for both frequencies it has the form $\tau_{sc}(DM)\sim DM^k$, where $k = 0.49 \pm 0.18$ and $k = 0.43 \pm 0.15$ for the frequencies 111 and 1400 MHz, respectively. The obtained dependence is explained within the framework of the assumption of the extragalactic occurrence of fast radio bursts and an almost uniform distribution of matter in intergalactic space. From the dependence $\tau_{sc}(DM)$ a total estimate of the contribution to the matter of the halo of our and the host galaxy to $DM$ is obtained $DM_{halo} + \frac{DM_{host}}{1+z}\approx 60\;{\rm pc/cm}^3$. Based on the LogN - LogS dependence, the average spectral index of radio bursts is derived $\alpha = - 0.63 \pm 0.20$ provided that the statistical properties of these samples at 111 and 1400 MHz are the same.