Constraints on the Intergalactic and Local Dispersion Measure of Fast Radio Bursts with the CHIME/FRB far side-lobe events

We study the 10 fast radio bursts (FRBs) detected in the far side-lobe region of the CHIME telescope from 2018 August 28 to 2021 August 31. We find that the far side-lobe events have on average $\sim$500 times greater fluxes than events detected in CHIME's main lobe. We show that the side-lobe sample is therefore statistically $\sim$20 times closer than the main-lobe sample. The median dispersion measure (DM) excess, after removing the Galactic disk component using the NE2001 for the free electron density distribution of the Milky Way, of the 10 far side-lobe and 471 non-repeating main-lobe FRBs in the first CHIME/FRB catalog is 183.0 and 433.9 pc\;cm$^{-3}$, respectively. By comparing the DM excesses of the two populations under reasonable assumptions, we statistically constrain that the local degenerate contributions (from the Milky Way halo and the host galaxy) and the intergalactic contribution to the excess DM of the 471 non-repeating main-lobe FRBs for the NE2001 model are 131.2$-$158.3 and 302.7$-$275.6 pc cm$^{-3}$, respectively, which corresponds to a median redshift for the main-lobe FRB sample of $\sim$0.3. These constraints are useful for population studies of FRBs, and in particular for constraining the location of the missing baryons.