Impact of propagation effects on the spectro-temporal properties of Fast Radio Bursts

TL;DR

The paper investigates how propagation effects, notably multipath scattering and residual dispersion, distort the spectro-temporal properties of Fast Radio Bursts within the Triggered Relativistic Dynamical Model. It develops a centroid-based analytical framework to quantify these distortions, deriving explicit expressions for the centroid and duration under scattering, dispersion, and their combination, and applies them to standard and ultra-short (ultra-FRB) sub-bursts. Key findings include that scattering preserves the inverse sub-burst slope–duration relation with a frequency-dependent offset, while residual DM can steepen, invert, or flatten the slope depending on over- or under-dispersion; their combination yields non-linear, regime-dependent tracks. Ultra-FRBs show heightened sensitivity to propagation effects, implying high-frequency observations and precise dedispersion (e.g., $|\Delta\mathrm{DM}|<0.05\ \mathrm{pc\,cm^{-3}}$) are essential to recover intrinsic correlations and constrain FRB emission models.

Abstract

We present a mathematical analysis of propagation-induced distortions in the spectro-temporal properties of Fast Radio Bursts (FRBs). Within the Triggered Relativistic Dynamical Model, we derive a centroid-based formulation of the sub-burst slope law, which is an inverse relation between frequency-drift rate and temporal width of sub-bursts. We extend our analysis to include two frequency-dependent propagation effects: (i) multipath scattering, characterized by a pulse-broadening timescale $τ_\mathrm{sc} \propto ν^{-4}$, and (ii) residual dispersion, parameterized by $Δ\mathrm{DM}\propto ν^{-2}$. Our analysis shows that scattering preserves the inverse relation between sub-burst slope and duration, but increases the scaling coefficient when $τ_\mathrm{sc}$ exceeds the intrinsic width ($t_\mathrm{w}$) of sub-bursts. Residual DM errors act asymmetrically: under-dedispersion flattens the sub-burst slope, whereas over-dedispersion causes a non-linear increase and eventually a change of sign. When both effects are present, scattering counterbalances the steepening induced by over-dedispersion and augments the flattening produced by under-dedispersion, yielding characteristically distorted curves. We repeat measurements for ultra-short duration bursts (ultra-FRBs) with $t_\mathrm{w} = 50\ μ\mathrm{s}$ at 1 GHz and found them to be far more sensitive to propagation errors. Deviations become measurable for $\left | Δ\mathrm{DM} \right |\sim0.05$ pc cm$^{-3}$ and for $τ_\mathrm{sc} \sim0.1$ ms at 1 GHz, levels that have negligible impact on the standard-width sub-bursts. Our analysis provides practical diagnostics to disentangle propagation effects from the observed spectro-temporal properties of FRBs, thereby recovering true correlations among their intrinsic parameters.

Figures (10)

• Figure 1: Comparison of two formulations of the sub-burst slope laws: the dashed red line represents the sub-burst slope law when measured relative to the time of arrival $t_\mathrm{D}$ (Equation \ref{['eq:slplaw']}), whereas the solid black line corresponds to the sub-burst slope law measured relative to the centroid time $t_\mathrm{c}$ (Equation \ref{['eq:slp_law_tc']}).
• Figure 2: The relationship between the (negative of the) frequency-normalized sub-burst slope (Equation \ref{['eq:slp_law_scat']}) and the duration (Equation \ref{['eq:lam_scat']}) at the center frequency for different values of scattering timescales ($\Lambda_\mathrm{sc}$). The black line shows the ideal law without scattering, given by Equation (\ref{['eq:slp_law_tc']}).
• Figure 3: The (negative of the) frequency-normalized sub-burst slope against the sub-burst central frequency in range of 0.4 GHz to 8 GHz for different scattering timescales ($\Lambda_\mathrm{sc}$). The solid black line corresponds to the unscattered law (Equation \ref{['eq:sub_slope_tc_freq']}).
• Figure 4: Sub-burst slope vs. sub-burst duration for residual dispersion measures in the interval $-5.0$pc cm$^{-3}$$\leq\Delta \mathrm{DM} \leq$ to $5.0$pc cm$^{-3}$. The solid black curve represents the undispersed reference given by Equation (\ref{['eq:slp_law_tc']}). For all curves, $\tau_\mathrm{sc}=0$, and therefore, $\lambda_\mathrm{c}=t_\mathrm{w}(\nu_0)$.
• Figure 5: The frequency-normalized sub-burst slope vs. frequency for $\Delta\mathrm{DM}$ in the range of $-5.0$pc cm$^{-3}$ to $5.0$pc cm$^{-3}$. The solid black curve represents the baseline law for sub-bursts with no residual dispersion.