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Dispersion measure components within host galaxies of Fast Radio Bursts: observational constraints from statistical properties of FRBs

Dispersion measure (DM) of Fast Radio Bursts (FRBs) are commonly used as a indicator of distance assuming that DM in excess of the expected amount within the Milky Way in the direction of each FRB arise mostly from the inter-galactic medium. However, the assumption might not be true if, for example, most FRB progenitors are embedded in ionized circumstellar material (CSM, e.g. supernova remnant). In this study, we jointly analyze distributions of DM, flux density, and fluence of the FRB samples observed by the Parkes telescope and the Australian Square Kilometre Array Pathfinder (ASKAP) using analytical models of FRBs, to constrain fractions of various DM components that shape the overall DM distribution and emission properties of FRBs. Comparing the model predictions with the observations we find that the typical amount of DM in each FRB host galaxy is $\sim 120$ cm$^{-3}$pc which is naturally explained as a combination of interstellar medium (ISM) and halo of an ordinary galaxy, without additional contribution from ionized CSM that is directly associated with an FRB progenitor. Furthermore, we also find that observed flux densities of FRBs do not statistically suffer strong $K$-correction, i.e. the typical luminosity density of FRBs does not significantly change within the range of emitting frequency $ν_{\rm rest} \sim$ 1--4 GHz.