A $τ-$DM relation for FRB hosts?

TL;DR

This work examines whether a host τ–DM relation for FRBs can be reliably inferred from FRB observations to constrain host DM and redshift. By constructing 25,000 mock FRBs with realistic DM components ($DM_{cosmic}$, $DM_{MW}$, and $DM_{host}$) and injecting instrumental effects for ASKAP/CRAFT, the authors test both a pulsar-like $\tau$–$DM_{host}$ relation and the Cordes2022 cloudlet model. They find that, due to large cosmic DM variance around the Macquart relation, intrinsic scatter, and observational biases against large scattering times, the correlation is generally not recoverable in FRB data; only samples spanning a broad $DM_{host}$ range show potential for detecting it. Consequently, the absence of a τ–DM correlation in current surveys does not falsify intrinsic models and highlights the limited utility of such priors for redshift inference. The results emphasize caution in applying Milky Way–based scattering relations to FRBs and underline the need for wide-ranging DM_host measurements to reveal any latent τ–DM connection.

Abstract

It has been proposed that measurements of scattering times ($τ$) from fast radio bursts (FRB) may be used to infer the FRB host dispersion measure (DM) and its redshift. This approach relies on the existence of a correlation between $τ$ and DM within FRB hosts such as that observed for Galactic pulsars. We assess the measurability of a $τ- $DM$_{\rm host}$ relation through simulated observations of FRBs within the ASKAP/CRAFT survey, taking into account instrumental effects. We show that even when the FRB hosts intrinsically follow the $τ- $DM relation measured for pulsars, this correlation cannot be inferred from FRB observations; this limitation arises mostly from the large variance around the average cosmic DM value given by the Macquart relation, the variance within the $τ- $DM relation itself, and observational biases against large $τ$ values. We argue that theoretical relations have little utility as priors on redshift, e.g., for purposes of galaxy identification, and that the recent lack of an observed correlation between scattering and DM in the ASKAP/CRAFT survey is not unexpected, even if our understanding of a $τ- $DM$_{\rm host}$ relation is correct.

Figures (7)

• Figure 1: $p(z,{\rm DM_{cosmic}})$ distribution considering the characteristics of the CRAFT/ICS 1.3 GHz instrument, and used to create the redshift and cosmic DM values for the 25 000 mock FRBs. The black lines denote the 50, 90 and 99 percent contours.
• Figure 2: Host scattering time against dispersion measure inferred by subtracting the Milky Way and mean cosmic components from the total DM. The figures represent a random set of 100 FRB hosts selected from the sample of 25 000 mock FRBs, with an SNR threshold $\rm SNR=10$ in the left panel, and $\rm SNR=0$ in the right one. DM values below 500 ${\rm pc\,cm^{-3}}$ (dotted vertical line) in the horizontal axis are plotted in linear scale, and logarithmic above, for visualization. The colors indicate the redshift of the host, with different scale ranges between the two panels. The intrinsic correlation between the scattering and the dispersion measure represented by the black lines (mean and 1-sigma uncertainties, respectively, from MW pulsars) appears largely washed out, especially for the $\rm SNR>10$ case, where the observations are biased against high $\tau$ values. The stars represent the CRAFT data by Scott2025, for comparison.
• Figure 3: Distributions of correlation coefficients between $\tau$ and ${\rm DM}$ for $10^5$ realizations of one hundred FRB host observations drawn from our mock dataset. The left panel shows the cases with an SNR threshold of 10, while the right panel illustrates those with no threshold. Most realizations (84th percentile) present values below 0.5, indicating a weak correlation between scattering and DM. Measurements containing large average host DM values may show an apparent correlation (inset figures), but this occurs a small number of times.
• Figure 4: Same as Figure \ref{['fig:taudm']} but considering the $\tau - {\rm DM}^2$ relation arising from the cloudlet model by Cordes2022 and a uniform distribution for their geometric and turbulent parameters.
• Figure 5: Correlation coefficient with respect to FRB redshift (left) and DM (right) for the two SNR cuts (SNR$>10$ in orange and SNR$>0$ in blue). The SNR$>10$ cases do not extend below $z=0.1$ because of the small number of data points in those subsamples. The region $z>2$ effectively shows the same results as $z=2$. In no case the distributions reach correlation values above 0.6, indicating that no strong correlation can be inferred from the observations.