Probing diffuse gas with fast radio bursts

The dispersion measure—redshift relation of fast radio bursts (FRBs), $\mathrm{DM}(z)$, has been proposed as a potential new probe of the cosmos, complementary to existing techniques. In practice, however, the effectiveness of this approach depends on a number of factors, including (but not limited to) the intrinsic scatter in the data caused by intervening matter inhomogeneities. Here, we simulate a number of catalogues of mock FRB observations, and use Markov Chain Monte Carlo techniques to forecast constraints, and assess which parameters will likely be best constrained. In all cases, we find that any potential improvement in cosmological constraints are limited by the current uncertainty on the diffuse gas fraction, $f_{\mathrm{d}}(z)$. Instead, we find that the precision of current cosmological constraints allows one to constrain $f_{\mathrm{d}}(z)$ and possibly its redshift evolution. Combining Cosmic Microwave Background $+$ Baryon Acoustic Oscillations $+$ Supernovae $+$ $H_0$ constraints with just 100 FRBs (with redshifts), we find a typical constraint on the mean diffuse gas fraction of a few percent. A detection of this nature would alleviate the “missing baryon problem,” and therefore highlights the value of localization and spectroscopic follow-up of future FRB detections.

Figure 1

Modeling the DM. The left panel shows the probability distributions of ${\mathrm{DM}}_{\cos }$ and $X$ data ($X\equiv \ln ({\mathrm{DM}}_{\cos }+C)$), with colored blocks indicating the histogram density of the simulated data in bins of $\mathrm{\Delta }z=0.03$, derived from $10^4$ sightlines out to $z_{\lim }=3$. The solid colored lines in the bottom left indicate the best-fit Gaussian to the $X$ data in that redshift bin. The right panel shows the fiducial model for $f_{\mathrm{d}}(z)$ (top) and its impact on the data (below). A single realization of ${\mathrm{DM}}_{\cos }$ and corresponding $X$ data are shown (black points), with $N_{\mathrm{FRB}}={10}^2$, along with their mean values (red lines). For comparison, the mean values with constant $f_{\mathrm{d}}$ are also shown (dashed red lines).

Figure 2

Triangle plot of the marginalized posteriors parameter constraints, in the case where we it for $f_{\mathrm{d}}(z)={\overline{f}}_{\mathrm{d}}$. Orange contours correspond to catalogues with $N_{\mathrm{FRB}}={10}^2$ and blue contours to catalogues with $N_{\mathrm{FRB}}={10}^3$. The gray shaded area corresponds to forbidden regions where ${\overline{f}}_{\mathrm{d}}>0$. The CBSH priors on the cosmological parameters are coincident with the orange and blue contours, and so are not shown here. Inset: histograms of the 95% upper and lower bounds on ${\overline{f}}_{\mathrm{d}}$ derived from 50 different realizations of the data.

Figure 3

Posterior constraints on the two parameter model for $f_{\mathrm{d}}(z)$, for both values of $N_{\mathrm{FRB}}$ considered here. Left panel shows the two-dimensional constrain contours for ($f_0$, $f_a$). The right panel shows the fiducial model for $f_{\mathrm{d}}(z)$ used when simulating the data (black line), together with the reconstructed 1- and $2\text{−}\sigma$ confidence intervals. Blue contours correspond to $N_{\mathrm{FRB}}={10}^2$ and orange contours to $N_{\mathrm{FRB}}={10}^2$. Gray shaded areas indicate the forbidden region where $f_{\mathrm{d}}(z)>1$.