Asking Fast Radio Bursts for More than Reionization History

TL;DR

This work proposes leveraging dispersion measures from fast radio bursts to probe the intergalactic medium during the Epoch of Reionization by developing estimators such as sky-averaged DM, DM derivatives with redshift, DM variance, and a DM structure function. It demonstrates that line-of-sight DM fluctuations bias the mean DM and that derivatives of DM and of the structure function carry distinct information about the reionization history and ionized-bubble sizes, validated with both toy ionization models and realistic grizzly simulations. The study also shows that realistic FRB redshift distributions and post-EoR contamination can significantly affect the data required to distinguish between reionization histories, providing quantitative FRB-count benchmarks under optimistic, moderate, and pessimistic removal scenarios. Overall, the results indicate that with sufficiently large FRB samples (potentially enabled by upcoming facilities like SKA-Mid), DM-based statistics offer a complementary avenue to constrain the timing, duration, and morphology of reionization beyond traditional probes.

Abstract

We propose different estimators to probe the intergalactic medium (IGM) during epoch of reionization (EoR) using the dispersion measure (${\rm DM}$) of the fast radio bursts. We consider three different reionization histories, which we can distinguish with a total of $\lesssim 1000\,{\rm DM}$ measurements during EoR if their redshifts are known. We note that the redshift derivatives of ${\rm DM}$ are also directly sensitive to the reionization history. The major point of this work is to explore the variance in the ${\rm DM}$ measurements and the information encoded in them. We find that the all-sky average $\overline{\rm DM}(z)$ gets biased from the line-of-sight (LoS) fluctuations in the ${\rm DM}$ measurements introduced by the ionization of IGM during EoR. We find that the ratio $σ_{\rm DM}/\overline{\rm DM}$ depends directly on the ionization bubble sizes as well as the reionization history. On the other hand, we also find that angular variance (coined as $\textit{structure function}$) of ${\rm DM}$ encodes the information about the duration of reionization and the typical bubble sizes as well. We establish the usefulness of variances in ${\rm DM}$ using toy models of reionization and later verify it with the realistic reionization simulations.

Figures (16)

• Figure 1:
• Figure 2: Left: asymmetrical $\tanh(z)$ ionization histories. Different colors represent three ionization histories corresponding to the simulated toy models. Right: mean DM estimates and $1\sigma$ fluctuations. Colors represent different reionization histories as shown in the left panel. Solid lines and the shaded regions are the average DM and corresponding $1\sigma$ errors estimated over all grid points available in the simulation volume. Dashed lines correspond to the DM estimated using the mean ionization fraction directly in eq. \ref{['eq:DM_reion']}. Three vertical lines mark the redshift of mid-reionization.
• Figure 3: Top: the ratio $\sigma_{\rm DM}/{\rm \overline{{DM}}_{EoR}}$ as a function of redshift $z$. The three different line styles correspond to the three reionization histories. Bottom: the redshift derivative of ${\rm \overline{{DM}}_{EoR}}(z)$. The green lines show the fluctuating estimates, whereas the orange lines are after a Gaussian smoothing.
• Figure 4: Density distribution of the double derivative of the structure function $\partial^2\Xi /\partial z~\partial \delta \theta$. The three different panels correspond to the different reionization histories considered. The different colored filled contours here represent various percentages of the area encompassed by the $\partial^2\Xi /\partial z~\partial \delta \theta$ surface, as shown in the labels. The horizontal dashed lines mark $z_{\rm mid}$. The dashed lines represent the angular size of bubbles varying with $z$.
• Figure 5: The distribution shown in Figure \ref{['fig:struct_toy_diffz']} marginalized along $\delta \theta$. The three solid lines represent $\int (\partial^2\Xi /\partial z~\partial \delta \theta)~ d \delta \theta$ for the three reionization histories. The dashed vertical lines correspond to the respective $z_{\rm mid}$ values.