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Context.Fast radio bursts (FRBs) are very energetic pulses in the radio wavelengths that have an unknown physical origin. They can be used to study the intergalactic medium thanks to their dispersion measure (DM). The DM has several contributions that can be measured (or estimated), including the contribution from the host galaxy itself, DM_host. The DM_hostis generally difficult to measure, thus limiting the use of FRBs as cosmological probes and our understanding of their physical origin(s). Aims.In this work we empirically estimated DM_hostfor a sample of 12 galaxy hosts of well-localized FRBs at 0.11 < z < 0.53 using a direct method based solely on the properties of the host galaxies themselves, referred to as DM_host^direct. We also explored possible correlations between DM_hostand some key global properties of galaxies. Methods.We used VLT/MUSE observations of the FRB hosts to estimate our empirical DM_host^direct. The method relies on estimating the DM contribution of both the FRB host galaxy’s interstellar medium (DM_host^ISM) and its halo (DM_host^halo) separately. For comparison purposes, we also provide an alternative indirect method for estimating DM_hostbased on the Macquart relation (DM_host^Macquart). Results.We find an average ⟨DM_host⟩ = 80 ± 11 pc cm⁻³with a standard deviation of 38 pc cm⁻³(in the rest frame) using our direct method, with a systematic uncertainty of ∼30%. This is larger than the typically used value of 50 pc cm⁻³but consistent within the uncertainties. We report positive correlations between DM_hostand both the stellar masses and the star formation rates of their hosts galaxies. In contrast, we do not find any strong correlation between DM_hostand the redshift nor the projected distances to the center of the FRB hosts. Finally, we do not find any strong correlation between DM_host^directand DM_host^Macquart, although the average values of the two are consistent within the uncertainties. Conclusions.Our reported correlations between DM_host^directand stellar masses and/or the star formation rates of the galaxies could be used in future studies to improve the priors used in establishing DM_hostfor individual FRBs. Similarly, such correlations and the lack of a strong redshift evolution can be used to constrain models for the progenitor of FRBs, for example by comparing them with theoretical models. However, the lack of correlation between DM_host^directand DM_host^directindicates that there may be contributions to the DM of FRBs not included in our DM_host^directmodeling, for example large DMs from the immediate environment of the FRB progenitor and/or intervening large-scale structures not accounted for in DM_host^Macquart. 

Abstract The dispersion measure of fast radio bursts (FRBs), arising from the interactions with free electrons along the propagation path, constitutes a unique probe of the cosmic baryon distribution. Their constraining power is further enhanced in combination with observations of the foreground large-scale structure and intervening galaxies. In this work, we present the first constraints on the partition of the cosmic baryons between the intergalactic medium (IGM) and circumgalactic medium (CGM), inferred from the FLIMFLAM spectroscopic survey. In its first data release, the FLIMFLAM survey targeted galaxies in the foreground of eight localized FRBs. Using Bayesian techniques, we reconstruct the underlying ∼Mpc-scale matter density field that is traced by the IGM gas. Simultaneously, deeper spectroscopy of intervening foreground galaxies (at impact parametersb_⊥≲r₂₀₀) and the FRB host galaxies constrains the contribution from the CGM. Applying Bayesian parameter inference to our data and assuming a fiducial set of priors, we infer the IGM cosmic baryon fraction to be $f_{\mathrm{igm}}={0.59}_{-0.10}^{+0.11}$and a CGM gas fraction of $f_{\mathrm{gas}}={0.55}_{-0.29}^{+0.26}$for 10¹⁰M_⊙≲M_halo≲ 10¹³M_⊙halos. The mean FRB host dispersion measure (rest-frame) in our sample is $〈{\mathrm{DM}}_{\mathrm{host}}〉={90}_{-19}^{+29}\mathrm{pc}{\mathrm{cm}}^{-3}$, of which $〈{\mathrm{DM}}_{\mathrm{host}}^{\mathrm{unk}}〉={69}_{-19}^{+28}\mathrm{pc}{\mathrm{cm}}^{-3}$arises from the host galaxy interstellar medium (ISM) and/or the FRB progenitor environment. While our currentf_igmandf_gasuncertainties are too broad to constrain most galactic feedback models, this result marks the first measurement of the IGM and CGM baryon fractions, as well as the first systematic separation of the FRB host dispersion measure into two components: arising from the halo and from the inner ISM/FRB engine.