Baryonification III: An accurate analytical model for the dispersion measure probability density function of fast radio bursts

TL;DR

The paper develops a fast, fully analytical framework to predict the one-point dispersion-measure PDF for fast radio bursts using the baryonification (BFC) model. By combining halo statistics, baryonic density profiles, and halo clustering, it derives the large-scale structure contribution to the DM PDF and validates it against both consistency simulations and the IllustrisTNG hydrodynamical simulation up to $z\approx5$, finding excellent agreement. The authors identify the gas-profile parameters $M_{\mathrm{c}}$, $\mu$, and $\delta$ as the primary drivers of the PDF shape and show that a log-normal DM distribution is a good description for a few hundred FRBs, with heterogeneity arising for larger samples. An emulator based on CosmoPower accelerates parameter inference, enabling future FRB-based constraints on baryonic feedback and CGM/IGM gas distributions. Overall, the work provides a self-consistent, efficient path to connect gas density profiles with DM statistics and to constrain baryonic processes using FRB observations.

Abstract

We develop a fully analytical framework for predicting the one-point probability distribution function (PDF) of dispersion measures (DM) for fast radio bursts (FRBs) using the baryonification (BFC) model. BFC provides a computationally efficient alternative to expensive hydrodynamical simulations for modelling baryonic effects on cosmological scales. By applying the halo mass function and halo bias, we convolve contributions from individual halos across a range of masses and redshifts to derive the large-scale structure contribution to the DM PDF. We validate our analytical predictions against consistency-check simulations and compare them with the IllustrisTNG hydrodynamical simulation across a range of redshifts up to $z = 5$, demonstrating excellent agreement. We demonstrate that our model produces consistent results when fitting gas profiles and predicting the PDF, and vice versa. We show that the BFC parameters controlling the gas profile, particularly the halo mass scale ($M_\mathrm{c}$), mass-dependent slope ($μ$), and outer truncation ($δ$), are the primary drivers of the PDF shape. Additionally, we investigate the validity of the log-normal approximation commonly used for DM distributions, finding that it provides a sufficient description for a few hundred FRBs. Our work provides a self-consistent model that links gas density profiles to integrated DM statistics, enabling future constraints on baryonic feedback processes from FRB observations.

Figures (11)

• Figure 1: Geometry of the projected DM as illustrated in \ref{['eq:DM_profile']}. Here $d_\mathrm{A}$ is the angular diameter distance at the redshift of the halo. The projection is carried out along the $x_2$-axis towards the observer $O$.
• Figure 2: Figure (a) illustrates an example of the simulation setup, where the volume is divided into equally spaced redshift bins. Figure (b) displays the halos projected onto a plane for an arbitrary bin. Halos that intersect with the LOS are shown in light blue, and only their contributions are included in the analysis. This serves as a consistency-check simulation, as it must reproduce, by definition, the analytical treatment of the unclustered case \ref{['eq:PDF_without_clustering']}.
• Figure 3: Comparison between the DM PDF obtained from simulations (blue) and the analytical result (black) at redshift $z = 1.5$. Both methods use the same BFC parameters and account only for the electron density fluctuations $\delta_\mathrm{e}$, excluding the mean contribution. The shaded region represent the $3\sigma$ confidence interval calculated using the covariance matrix.
• Figure 4: Comparison of the analytical PDF for the DM of FRBs with results from the TNG simulation across various redshifts. The solid lines represent the analytical predictions, while the shaded regions indicate the $68 \%$ confidence intervals. The dashed lines show the corresponding results from the TNG simulation.
• Figure 5: Model parameters obtained from fitting to the IllustrisTNG simulation as a function of redshift for $\sim 10^4$ FRBs. Red error bars indicate the 68% confidence intervals, and blue points mark the highest posterior probabilities.