Large-scale clustering as a probe of the origin and the host environment of fast radio bursts

We propose to use degree-scale angular clustering of fast radio bursts (FRBs) to identify their origin and the host galaxy population. We study the information content in autocorrelation of the angular positions and dispersion measures (DM) and in cross-correlation with galaxies. We show that the cross-correlation with Sloan Digital Sky Survey (SDSS) galaxies will place stringent constraints on the mean physical quantities associated with FRBs. If $\sim$10,000 FRBs are detected with $\lesssim \rm deg$ resolution in the SDSS field, the clustering analysis with the intrinsic DM scatter of $100\, {\rm pc}/{\rm cm}^3$ can constrain the global abundance of free electrons at $z\lt1$ and the large-scale bias of FRB host galaxies (the statistical relation between the distribution of host galaxies and cosmic matter density field) with fractional errors (with a $68\%$ confidence level) of $\sim10\%$ and $\sim20\%$, respectively. The mean near-source dispersion measure and the delay time distribution of FRB rates relative to the global star forming rate can be also determined by combining the clustering and the probability distribution function of DM. Our approach will be complementary to high-resolution ($\ll {\rm deg}$) event localization using e.g., VLA and VLBI for identifying the origin of FRBs and the source environment. We strongly encourage future observational programs such as CHIME, UTMOST, and HIRAX to survey FRBs in the SDSS field.