1. Introduction
Fast radio bursts (FRBs) are transient radio signals characterised by their short duration and high brightness temperatures (Lorimer et al. Reference Lorimer, Bailes, McLaughlin, Narkevic and Crawford2007). The FRB population is diverse, exhibiting various properties such as apparent ‘one-off ’ events or strong repeaters (see Petroff et al. Reference Petroff, Hessels and Lorimer2019, Reference Petroff, Hessels and Lorimer2022, for recent reviews), highly variable polarisation angles (PAs), linear and circular polarisation fractions, rotation measures (RMs), as well as complex temporal and spectral profiles with multiple peaks and varying widths (e.g. Sherman et al. Reference Sherman2024; Sand et al. Reference Sand2025; Scott et al. Reference Scott2025). The study of these structures is essential for deciphering FRB generation mechanisms and the media through which they propagate.
FRBs show diverse PA behaviour. Only one FRB is well fit by a rotating vector model (RVM; Mckinven et al. Reference Mckinven2025), a characteristic of a rotating neutron star, with circumstantial evidence for two more (Bera et al. Reference Bera2024). Attempts to fit RVMs to a large population of repeater bursts show that some are well fit; however, their results are inconsistent with each other (Liu et al. Reference Liu2025). Other FRBs show a variety of PA swings (Luo et al. Reference Luo2020), or apparently flat PA profiles (e.g. Pandhi et al. Reference Pandhi2024). The Canadian Hydrogen Mapping Experiment (CHIME) and the Deep Synoptic Array 110 (DSA-110) previously catagorised FRBs by their spectro-temporal morphology (Pleunis et al. Reference Pleunis2021; Sand et al. Reference Sand2025), the smooth PA evolution measured across the burst envelope (Pandhi et al. Reference Pandhi2024) and their polarisation fractions (Sherman et al. Reference Sherman2024). These are highly dependent on S/N, time resolution, and propagation effects and leads to arbitrary classifications as suggested by Scott et al. (Reference Scott2025). Studying burst-envelope-scale PA behaviour may be useful for identifying rotational signatures or probing large-scale, spatially averaged magnetic field structure, and can inform us of potential progenitors; however, it may provide limited insight into the rapid local plasma processes that generate the emission, which may arise either in the magnetosphere (e.g. Lu & Kumar Reference Lu and Kumar2018) or in more distant outflow/shock regions (e.g. Lyubarsky Reference Lyubarsky2014).
Scott et al. (Reference Scott2025) present high-time-resolution (HTR) polarisation properties of 35 FRBs from the Commensal Real-time ASKAP Fast Transients (CRAFT) Incoherent-Sum Survey (Shannon et al. Reference Shannon2025). They move away from previous classifications, showing that all FRBs likely have multiple components and have intrinsically variable PAs. However, measuring these temporal structures can be influenced by several factors, including the intrinsic properties of the source and its environment, and particularly scattering along the line of sight. When sampled with HTR, FRBs with little-to-no scattering and high signal-to-noise (S/N) can exhibit complex, narrow intrinsic widths (nanoseconds–microseconds; Nimmo et al. Reference Nimmo2022) and highly variable PAs within the burst envelope (e.g. Gupta et al. Reference Gupta2022; Snelders et al. Reference Snelders2023; Scott et al. Reference Scott2025). Observations of these structures can place stringent constraints on the size of the emitting region and emission mechanisms of FRBs, as well as the various propagation media (e.g. Beniamini & Kumar Reference Beniamini and Kumar2020).
The idea of radio pulses being comprised of multiple smaller ‘shots’ was first suggested by Rickett (Reference Rickett1975) in the amplitude-modulated noise model for pulsars. This idea was extended by Cordes (Reference Cordes1976) who implemented polarisation variations to explain short-time scale polarisation structures, the so-called ‘polarised shot noise’ (PSN) model. Many further developments have since been made to the model to account for stochastic processes (e.g. Melrose & Macquart Reference Melrose and Macquart1998; McKinnon Reference McKinnon2006; Osłowski et al. Reference Osłowski, van Straten, Hobbs, Bailes and Demorest2011). The most famous application of the shot-models is to the Crab pulsar, which displays nanosecond duration shots (nanoshots) with PA microstructure (Hankins & Eilek Reference Hankins and Eilek2007; Hankins et al. Reference Hankins, Eilek and Jones2016). Nimmo et al. (Reference Nimmo2022) and Scott et al. (Reference Scott2025) similarly note that their FRB samples have structures resembling Crab nanoshots.
Of the Crab pulsar’s many components, single pulses in the main pulse and interpulse exhibit similar polarimetric nanostructure to FRBs. They often appear substantially depolarised at time resolutions of order tens of
$\mu$
s to ms, but at nanosecond time resolution and with minimal scattering they resolve into 100% polarised nanoshots with random PAs (Hankins et al. Reference Hankins, Jones and Eilek2015, Reference Hankins, Eilek and Jones2016). Though, the PA variability of these very bright pulses observed at HTR can be affected by self-noise and small-number statistics when the averaging is insufficient (van Straten Reference van Straten2009). Hankins et al. (Reference Hankins, Eilek and Jones2016) show that unresolved microbursts generally have highly disordered PA profiles, consistent with shots having random PAs. Occasionally, their PAs show ordered swings (see their Figure 4), which may trace underlying plasma or magnetic field structures from the emission environment. They also show that microbursts are in fact unresolved collections of narrowband nanoshots, with some demonstrating substructures of timescales less than 4 ns (see their Figure 8). This behaviour is consistent with expectations from the PSN model. Giant pulses (GPs) are a subclass of single pulses with luminosities several orders of magnitude greater than the average pulses, a distinct energy distribution (power law), and a narrow emission phase window (compared to the average pulse profile). In terms of duration and energetics, Crab GPs and their underlying nanoshot mechanism are the most analogous phenomena to FRBs (e.g. Nimmo et al. Reference Nimmo2022). These Crab phenomena each show intense PA variability on nanosecond to microsecond timescales (e.g. Jessner et al. Reference Jessner2010; Hankins et al. Reference Hankins, Eilek and Jones2016) and a variety of spectro-temporal morphologies, on durations similar to FRBs observed at very-high time resolution.
A natural question is whether depolarisation in FRBs may arise from the superposition of many microshots, analogous to the behaviour of Crab microbursts. Other contributors include depolarisation from scattering, Faraday rotation through turbulent media, or the intrinsic emission mechanism itself. Disentangling these possibilities requires controlled forward modelling of FRB microstructure and polarisation at HTR. However, the current sample of high-S/N, low-scatter FRBs with nanosecond-microsecond resolution remains limited, motivating the need for realistic simulations.
Several existing packages offer pulsar-signal simulation capabilities (e.g. Hotan et al. Reference Hotan, van Straten and Manchester2004; Hazboun et al. Reference Hazboun2021), but these are generally unsuited to FRBs because they model emission profiles with simple Gaussian components and lack polarisation-analysis tools. In this paper, we introduce the Fast, Intense Radio Emission Simulator (FIRES),Footnote a a Python package for simulating and analysing FRB dynamic spectra under the PSN model. We describe FIRES, and demonstrate how FIRES can reproduce key observed FRB properties,including PA variance, depolarisation, and linear polarisation fractions, show how microshot superposition can naturally generate the diversity of polarimetric structures seen in FRBs, and show to what extent FRB parameters can be constrained.
2. Modelling dynamic spectra
Following the idea that all FRBs intrinsically have multiple components (Scott et al. Reference Scott2025), we model the dynamic spectra of FRBs as a superposition of Gaussian microshots with different PAs (Cordes Reference Cordes1976) using FIRES. Each microshot is defined by its amplitude, time of arrival (TOA), width, PA, and polarisation fractions, with the latter specifying that each microshot is partially elliptically polarised. For our initial model, we assume that each microshot has a Gaussian intensity profile with a peak amplitude sampled from a power law distribution, consistent with Crab GP energetics (e.g. Bera & Chengalur Reference Bera and Chengalur2019). In principle, a degeneracy exists between the number of shots and their amplitudes: an alternative model could instead assume a constant number of shots whose amplitudes vary to reproduce the envelope. The amplitude distribution of Crab nanoshots does seem consistent with a power law (e.g. Figure 8 from Hankins et al. Reference Hankins, Eilek and Jones2016); however, this has not yet been quantitatively constrained (see Appendix C.1 for a comparison of amplitude distribution power laws).
We further assume that their TOAs are distributed normally, and we ignore frequency dependence in intrinsic power. Given the high linear polarisation of FRBs and commonly assumed neutron star magnetospheric emission models (e.g. Lu & Kumar Reference Lu and Kumar2018), we adopt a picture in which the emitting magnetic field is predominantly ordered with only small perturbations. We therefore sample microshot PAs from a normal distribution. Each microshot has its full-width half-maximum (FWHM) sampled from a uniform distribution, and all other parameters are fixed. The microshots are then scattered by convolution with a thin-screen scattering response, diffractive interstellar scintillation (DISS) is applied as a multiplicative gain field, and noise is added to create realistic FRB dynamic spectra. FIRES can apply Faraday rotation and PA trends, however, we do not use them here. The list of parameters used in the model are presented in Table 1.
Model parameters used in FIRES as assumed inputs for representative simulations.
Table 1. Long description
The table compares model parameters used in FIRES for representative simulations of fast radio bursts. It includes parameters such as the number of microshots, peak amplitude, time of arrival, and various scattering and polarization characteristics. The table has 20 rows and 4 columns, with headers labeled Parameter, Description, FRB 20191001A, and FRB 20240318A. Key parameters include the number of microshots, peak amplitude, time of arrival, and scattering timescale. The table provides specific values for each parameter, highlighting differences and similarities between the two fast radio bursts.
$^{\rm a}$
Data from Scott et al. (Reference Scott2025).
$^{\rm b}$
Defined in units of the characteristic scattering angle (see Section 2.2).
The Stokes I dynamic spectrum, comprised of N microshots in time t (ms) and frequency
$\nu$
(MHz), is
\begin{align*} D_I[t,\nu] = \left[ \sum_{i=1}^{N} A_i \exp\!\left(-\frac{(t - t_i)^2}{2\sigma_{w,i}^2}\right) \right] * h_\nu(t), \\ \sigma_{w,i} = \frac{w_i}{2\sqrt{2\log{2}}}, \end{align*}
where
$*$
denotes convolution in time with the frequency-dependent, thin-screen scattering response
$h_\nu(t)$
. Each microshot has a peak amplitude
$A_i$
Jy, drawn from a power law distribution with index
$\alpha = -3$
, and a Gaussian FWHM
$w_i$
, where
$W_0$
(ms) is the envelope FWHM and the fractional microshot width
$w_i/W_0$
is drawn from
\begin{equation} \frac{w_i}{W_0} \sim \mathcal{U}\!\left(w_{\min},\, w_{\max}\right),\end{equation}
with
$w_{\min}$
and
$w_{\max}$
the minimum and maximum fractional microshot widths, respectively.
$t_i$
is the arrival time of the i-th microshot, which is distributed as
$t_i \sim \mathcal{N}\!\left(t_0,\, \sigma_t\right)$
, where
$t_0$
is the arrival time of the envelope, and
\begin{equation} \sigma_t = \frac{W_0}{2\sqrt{ 2\log{2}}}.\end{equation}
With per–microshot PAs
$\psi_i \sim \mathcal{N}(\psi_0,\sigma_\psi)$
, where
$\psi_0$
is the mean intrinsic PA and
$\sigma_\psi$
is the standard deviation of the intrinsic microshot-to-microshot PA scatter, and fixed intrinsic fractional linear and circular polarisations
$\Pi_{L,0}$
and
$\Pi_{V,0}$
, we write
\begin{align*} D_Q[t, \nu] &= D_I[t, \nu] \cdot \Pi_{L,0} \cdot \cos\!(2\psi_i), \\ D_U[t, \nu] &= D_I[t, \nu] \cdot \Pi_{L,0} \cdot \sin\!(2\psi_i), \\ D_V[t, \nu] &= D_I[t, \nu] \cdot \Pi_{V,0}.\end{align*}
2.1 Thin-screen scattering
We apply scattering via a discrete, causal impulse response per frequency channel. The continuous thin–screen scattering response is
\begin{equation*} h_\nu(t) \;=\; \frac{1}{\tau_\nu}\,e^{-t/\tau_\nu}\,H(t),\end{equation*}
with Heaviside step H(t) and timescale
$\tau_\nu$
. Let
$\delta t$
be the time resolution and let
\begin{equation*} n \equiv \left\lceil 5\,\frac{\tau_\nu}{\delta t} \right\rceil + 1\end{equation*}
be the number of kernel samples. Then, the implemented kernel is the truncated, sum-normalised exponential
\begin{align*} \mathrm{IRF}_{\nu}[k] =& \frac{e^{-k\delta t / \tau_\nu}}{\displaystyle \sum_{k=0}^{n-1} e^{-k\delta t / \tau_\nu}} \\ =& \frac{\bigl(1 - e^{-\delta t / \tau_\nu}\bigr)\, e^{-k\delta t / \tau_\nu}}{1 - e^{-n\delta t / \tau_\nu}}, \qquad k=0,\dots,n-1,\end{align*}
so that
$\sum_{k=0}^{n-1} \mathrm{IRF}_{\nu}[k]=1$
(preserving flux), where k indexes the k-th discrete time sample. We zero-pad each time series on the right by
$(n-1)$
samples, perform a linear (FFT) convolution, and truncate to the original timespan; any power beyond the simulated window is discarded.
The frequency-scaled scattering timescale is
\begin{equation} \tau_\nu = \tau_{0}\left(\frac{\nu}{\nu_\tau}\right)^{\alpha},\end{equation}
with reference
$\nu_\tau = 1\,\mathrm{GHz}$
, frequency dependence
$\alpha$
, and
$\tau_{0}$
the timescale at the reference frequency in milliseconds.
2.2 Scintillation
We include DISS as a multiplicative gain field
$G(t,\nu)$
applied to all Stokes vectors. We generate a complex electric field
$E(t,\nu)$
using ScintillationMaker
Footnote
b
with four control parameters: the decorrelation bandwidth
$\nu_s$
, characteristic timescale
$t_s$
, number of images drawn from the scattering disk
$N_\mathrm{im}$
, and the (dimensionless) angular extent of the scattering disk
$\theta_\mathrm{lim}$
, defined in units of the characteristic scattering angle (so that
$\theta_\mathrm{lim} = 3$
corresponds to sampling the disk out to
$\sim3\sigma$
). In our simulations we set
$t_s = 300~\mathrm{s}$
,
$N_\mathrm{im} = 5\,000$
, and
$\theta_\mathrm{lim} = 3.0$
to adequately sample the scattering disk and produce a realistic scintillation pattern while keeping computations manageable.
$\nu_s$
is taken from Scott et al. (Reference Scott2025) when available, otherwise it is measured by fitting a single Lorentzian in the frequency power spectrum. The observed intensity gain is
\begin{equation*} G(t,\nu) \equiv \frac{\bigl|E(t,\nu)\bigr|^2}{\left\langle \bigl|E(t,\nu)\bigr|^2 \right\rangle_{t,\nu}},\end{equation*}
so that
$\langle G\rangle=1$
over the simulated
$(t,\nu)$
grid (preserving mean flux). The scintillated Stokes parameters are then
\begin{equation*} D_X^{(\mathrm{DISS})}(t,\nu) = G(t,\nu)\, D_X(t,\nu), \qquad X \in \{I,Q,U,V\}.\end{equation*}
For the large-batch simulations presented in the main text and appendices, scintillation is omitted to reduce computational cost. As discussed in Appendix E, tests including representative scintillation modulation patterns do not affect the results obtained in this work.
2.3 Noise
To mimic telescope noise, we add Gaussian noise to the dynamic spectra with
\begin{equation*} \varepsilon_X(t,\nu) \sim \mathcal{N}\!\left(0,\, \sigma_X\right),\end{equation*}
where
$\sigma_X$
is the noise level calculated from the radiometer equation,
\begin{equation} \sigma_X = \frac{\mathrm{SEFD}}{\sqrt{n_\mathrm{pol}\delta\nu \delta t}}.\end{equation}
SEFD is the system equivalent flux density in Jy,
$n_\mathrm{pol}=2$
is the number of polarisations ‘recorded,’
$\delta\nu$
is the frequency resolution in Hz, and
$\delta t$
is the time resolution in seconds. For the ASKAP data considered here, this Gaussian approximation is appropriate. At substantially higher time and frequency resolution, however, the noise can become non-Gaussian (e.g. closer to a
$\chi^2$
distribution in minimally averaged baseband data), so alternative noise models may be required in future applications of FIRES. The observed Stokes are
\begin{equation*} D_X \leftarrow D_X^{(\mathrm{DISS})} + \varepsilon_X, \qquad X \in \{I,Q,U,V\}.\end{equation*}
2.4 Polarisation angles
We calculate the final PAs and their errors as performed by Day et al. (Reference Day2020) and similarly debias the linear polarisation following (the typographically corrected) Equation (11) in (Everett & Weisberg Reference Everett and Weisberg2001),
\begin{equation*} L_\mathrm{debias} = \begin{cases}\sigma_{L}\sqrt{\frac{L_{\text{meas}}}{\sigma_{L}}^{2}-1}, & \dfrac{L_{\text{meas}}}{\sigma_{L}} \ge 1.57 \\[6pt]0, & \text{otherwise}, \end{cases}\end{equation*}
except using
$\sigma_L$
instead of
$\sigma_I$
to accommodate cases where
$\sigma_I \neq \sigma_Q \neq \sigma_U$
. Further, we discard
$\psi$
where
$L_\mathrm{debias} \lt 2\sigma_{L}$
, along with those outside the on-pulse region, the minimum boxcar width that contains 95% of the flux in the pulse profile. If PA values are in a sequence of length
$ \lt 5$
, then we also discard them.
3. Reproducing real FRB structures
Figure 1 shows the dynamic spectra of three stages of a FIRES simulation. Starting with a noiseless, unscattered FRB comprised of
$N=100$
microshots with a uniform distribution of widths ranging from 25–100
$\unicode{x03BC}$
s (see Equation 1); the FWHM of the full envelope is 0.5 ms. Then we add scattering,
$\tau_\mathrm{1\,GHz} = 1.78$
ms and scintillation decorrelation bandwidth
$\nu_s = 2.05$
MHz with characteristic timescale
$t_s=300$
s, and draw the phase screen with
$N_\mathrm{im}=5\,000$
images and truncation parameter
$\theta_\mathrm{lim}=3.0$
. Then we add noise (
$\mathrm{SEFD}=1.2\mathrm{\,Jy}$
, see Equation (4); on-pulse S/N
$=213$
), and finally compare to real CRAFT FRB 20191001A data reproduced from Scott et al. (Reference Scott2025) with ILEX
Footnote
c
(on-pulse S/N
$=194$
, corrected for RM
$=53.47$
rad m
$^{-2}$
). The simulated dynamic spectra are generated over a frequency range 751.5–900.5 MHz with 1 MHz resolution, and a time resolution of 0.023 ms chosen such that (the real) FRB 20191001A has a peak S/N
$\sim20$
. The frequency dependence for scattering is
$\alpha = -4.85$
. Post-processing measurements of the on-pulse polarisation fractions show
$\Pi_L = 0.55$
and
$\Pi_V = -0.05$
. We assume that, intrinsically, each microshot is
$\sim$
100% polarised, and so we set
$\Pi_{L,0} = 0.99$
and
$\Pi_{V,0} = -0.05$
(similar to crab nanoshots, Hankins et al. Reference Hankins, Eilek and Jones2016). Their PAs are drawn from
$\mathcal{N}\left(20.0\,\mathrm{deg}, 30.0\,\mathrm{deg} \right)$
.
$\tau_{1\,\mathrm{GHz}}$
and
$\alpha$
are taken from Table 2 of Scott et al. (Reference Scott2025), while the rest of the parameters are estimates made by-eye to mimic the properties of FRB 20191001A. The top PA panels include zoomed insets of the leading part of the burst to make the unresolved short-timescale PA structure easier to inspect. This initial comparison (Figure 1) is qualitative and intended to visually demonstrate that FIRES can generate realistic-looking bursts. The remainder of this work focuses on quantitative metrics that enable direct comparison between simulated and real FRBs. The full list of model parameters are presented in Table 1.
A FIRES recreation of FRB 20191001A. (a): a noiseless, unscattered FRB comprised of 100 microshots. The bottom panel is the time-frequency dynamic spectrum, the middle panel is the frequency-summed pulse profile (black = total intensity, red = linear polarisation, blue = circular polarisation), and the top panel is the polarisation angle profile. Each top panel includes a zoomed inset spanning the leading phase (from burst onset to the Stokes I peak) to highlight fine PA structure. (b): scattering timescale
$\tau_{1\,\mathrm{GHz}} = 1.78$
ms and scintillation added to the top left plot. (c): noise added to the top right plot (on-pulse S/N
$=180$
). (d): real FRB 20191001A data reproduced from Scott et al. (Reference Scott2025) (on-pulse S/N
$=194$
, RM corrected from RM = 53.47 rad m
$^{-2}$
). The full list of parameters used are presented in Table 1 and are described in Section 2. The top panels show the polarisation angle, the centre panels show the pulse profile, and the bottom panels show the dynamic spectra. The blue shaded regions in the centre panels are the minimum boxcar width that contains 95% of the total flux in the pulse profile.
Figure 1. Long description
The image contains four sets of graphs labeled (a) through (d), each showing different aspects of the recreation of FRB 20191001A. Each set includes three panels: the top panel displays the polarisation angle profile, the middle panel shows the pulse profile with total intensity in black, linear polarisation in red, and circular polarisation in blue, and the bottom panel presents the time-frequency dynamic spectrum. In (a), the graphs show a noiseless, unscattered FRB comprised of 100 microshots. The top panel includes a zoomed inset highlighting fine polarisation angle structure. In (b), scattering timescale and scintillation are added to the top left plot. In (c), noise is added to the top right plot with an on-pulse signal-to-noise ratio. In (d), real FRB 20191001A data is reproduced with on-pulse signal-to-noise ratio and rotation measure corrected. The blue shaded regions in the middle panels indicate the minimum boxcar width containing 95% of the total flux in the pulse profile.
3.1 Polarisation angle variance
FRBs show variable PA properties (e.g. Luo et al. Reference Luo2020; Mckinven et al. Reference Mckinven2025), and when probed at high time resolutions, reveal systematic fluctuations (Nimmo et al. Reference Nimmo2021; Hewitt et al. Reference Hewitt2023; Scott et al. Reference Scott2025). It has been suggested that the strength and duration of these PA microstructures may correspond to the magnetic field conditions in the emission environment (e.g. Scott et al. Reference Scott2025), and so, disentangling intrinsic and extrinsic PA fluctuations is crucial for constraining emission models. Propagation effects such as scattering introduce frequency- and time-dependent effects that obfuscate intrinsic FRB structures, and so, determining under what conditions and which portions of the FRB dynamic spectra still contain original properties is also important.
Figure 1 shows that the PA of the simulated bursts is not constant, but varies with time, scattering timescale, and noise. We define two regions in the on-pulse phase (light-blue-shaded region); the leading region is from the onset of the on-pulse to and including the peak of the burst, and the trailing region is from the peak to the end of the on-pulse. As expected, scattering flattens the PA throughout the trailing region of the burst, reducing intrinsic variability (Li & Han Reference Li and Han2003), while the leading region comparatively remains largely unchanged. The introduction of noise dominates the macrostructure, introducing higher PA variance in the trailing edge.
To quantify the effects of scattering on PA in different burst regions, we introduce the metric,
\begin{equation} \mathcal{R}_\psi = \frac{\mathbb{V}(\psi)}{\mathbb{V}(\psi_{i})},\end{equation}
where
$\mathbb{V}(\psi)$
is the PA variance across the on-pulse phase and
$\mathbb{V}(\psi_{i})$
is the PA variance across the individual microshots that form the FRB. This parameter quantifies how much of the intrinsic microshot PA variance remains after taking their superposition. We can approximate the expected (noiseless) PA variance in deg.
$^2$
with,
\begin{equation} \mathbb{V}_{\exp}(\psi) \;=\; \frac{\sigma_\psi^2}{N}\! \left(\frac{W_{\mathrm{tot}}}{w_{\mathrm{tot}}} - 1\right)\left(\frac{180}{\pi}\right)^2\end{equation}
where
$W_\mathrm{tot}$
and
$w_\mathrm{tot}$
are the envelope and microshot FWHMs after scattering. We derive this expression in Appendix A. This approximation is only accurate for cases with high S/N and low
$\sigma_\psi$
. Substituting this into Equation (5), we can find the expected value of
$\mathcal{R}_\psi$
.
In Figure 2, we show how
$\mathcal{R}_\psi$
modulates as a function of the input scattering timescale,
$\tau_0$
, weighted by the input FWHM of the envelope,
$W_0$
, for different frequency bands and phase regions of a high S/N case of the simulated FRB shown in Figure 1(c).
$\mathcal{R}_\psi$
exhibits three regimes, which are highlighted in the figure by light orange, light green, and light purple shaded regions, respectively. In the negligible-scattering regime,
$\mathcal{R}_\psi$
remains constant with
$\tau_0$
, since the scattering timescale is small compared to the intrinsic PA variation timescales (i.e. the width of each microshot). As
$\tau_0$
increases,
$\mathcal{R}_\psi$
then decreases, as scattering blends random microshots together, reducing the variance. At very large
$\tau_0$
, noise begins to dominate and variance increases. As expected,
$\mathcal{R}_\psi$
in the lower frequency band is initially lower due to the frequency dependence of scattering, but becomes higher at large
$\tau_0$
once the PA is flattened by scattering and noise dominates. The trailing region follows the same trend but is more strongly affected by scattering, leading to a more rapid decline in
$\mathcal{R}_\psi$
. Similarly, the highest-quarter and full-band with total phase, also decrease as they become scatter dominated, but transition to the noise-dominated regime at larger
$\tau_0$
owing to their higher S/N.
$\mathcal{R}_\psi$
(see Equation 5) versus
$\tau_0$
weighted by initial Gaussian envelope width,
$W_0$
, for a high S/N case of the mock FRB 20191001A (Figure 1(c)). The solid lines are the median value of 500 random FRB realisations at each scattering timescale, and the shaded regions represent the 16th and 84th percentiles of the realisations. The black-dotted line is the (noiseless) expected value from Equation (6).
$\mathcal{R}_\psi$
exhibits three regimes, highlighted by the light orange, light green, and light purple shaded regions, respectively: a negligible-scattering regime where
$\mathcal{R}_\psi$
remains approximately constant, an intermediate regime where scattering blends random microshots together and reduces the variance, and a large-scattering regime where noise dominates and the variance increases. (a): frequency band comparison; The red line is the contribution from the lowest quarter of the band, the blue line is the contribution from the highest quarter of the band, and the purple line is the contribution from the full band. (b): phase comparison; The orange line is the contribution from the first half of the burst, the green line is the contribution from the second half of the burst, and the purple line is the contribution from the entire burst. At
$\tau_0/W_0=0, 60$
, S/N
$\sim 2300, 150$
, respectively.
Figure 2. Long description
Two line graphs compare the behavior of fast radio bursts (FRBs) under different conditions, showing median values and percentiles across scattering timescales. The graphs illustrate the variance in FRB behavior as a function of scattering timescale. The top graph (a) compares frequency bands, with the red line representing the lowest quarter of the band, the blue line the highest quarter, and the purple line the full band. The bottom graph (b) compares phases, with the orange line representing the first half of the burst, the green line the second half, and the purple line the entire burst. The shaded regions indicate the 16th and 84th percentiles of the realizations, while the black-dotted line shows the noiseless expected value. The graphs highlight three regimes: a negligible-scattering regime where the variance remains constant, an intermediate regime where scattering reduces the variance, and a large-scattering regime where noise increases the variance. All values are approximated.
By contrast, the leading edge consistently retains a larger fraction of the intrinsic PA variance at increasing scattering timescales. In high S/N cases, this makes the leading edge the most robust phase region for preserving information about the intrinsic PA structure, and therefore the most informative probe of the initial emission and generation conditions.
The black dotted line shows the expected value of
$\mathcal{R}_\psi$
(Equation 6) in the noiseless regime and is in general agreement with all regions in the low-scattering, high-S/N limit.
3.2 Linear polarisation fraction
FRBs generally exhibit high linear polarisation fractions (Sherman et al. Reference Sherman2024; Pandhi et al. Reference Pandhi2024; Scott et al. Reference Scott2025), and so it has been thought that all FRBs are intrinsically 100% linearly polarised, with any depolarisation or polarisation conversion occurring due to rotation measure (RM) scattering (Feng et al. Reference Feng2022; Uttarkar et al. Reference Uttarkar2025). However, Sand et al. (Reference Sand2025) and Scott et al. (Reference Scott2025) show no correlation between scattering and polarisation fraction. Further, Scott et al. (Reference Scott2025) rule out depolarisation due to unresolved, random PA structures as there is no correlation between decreases in linear polarisation fraction and PA fluctuations. Sherman et al. (Reference Sherman2024) also suggest that this case may be less significant than propagation effects.
Measured linear polarisation fraction,
$\Pi_{L}$
, versus measured PA variance,
$\mathbb{V}(\psi)$
, as a function of the standard deviation of the intrinsic microshot PA,
$\sigma_\psi$
, for the leading phases of the mock FRB 20191001A (panels (a)–(b) with intrinsic linear polarisation fractions
$\Pi_{L,0}=0.99$
and
$0.55$
, respectively) and FRB 20240318A (panels (c)–(d),
$\Pi_{L,0}=0.98$
and
$red{0.78}$
). For
$N=5,10,20,100,1000$
microshots, at each
$\sigma_\psi$
we generate 500 random realisations of each FRB with fixed S/N (FRB 20191001A: median
$\sim 194$
; FRB 20240318A: median
$\sim110$
) and plot the medians of the
$\Pi_{L}$
and
$\mathbb{V}(\psi)$
distributions as solid lines. The shaded regions mark only the 16th–84th percentiles of the
$\Pi_{L}$
distributions; they do not show percentile ranges in
$\mathbb{V}(\psi)$
. The magenta and cyan stars show the measured values for FRB 20191001A and FRB 20240318A, respectively (see Figures 1d and Figure B1b), with shaded bands indicating errors from off-pulse RMS noise. Blue dashed lines connect points of constant
$\sigma_\psi$
and are linearly extended using the slopes of their first and last segments (FRB 20191001A:
$\sigma_\psi = 4^\circ, 10^\circ, 31^\circ, 40^\circ$
; FRB 20240318A:
$\sigma_\psi = 15^{\circ}, 22^{\circ}, 40^{\circ}$
).
Figure 3. Long description
The image contains four line graphs labeled (a), (b), (c), and (d). Each graph plots the measured linear polarisation fraction (ΠL) against the measured PA variance (V(ψ)) for different standard deviations of the intrinsic microshot PA (σψ). Graphs (a) and (b) represent data for FRB 20191001A with intrinsic linear polarisation fractions of 0.99 and 0.55, respectively. Graphs (c) and (d) represent data for FRB 20240318A with intrinsic linear polarisation fractions of 0.98 and 0.78, respectively. Each graph includes solid lines representing the medians of the ΠL and V(ψ) distributions, with shaded regions indicating the 16th-84th percentiles. Magenta and cyan stars mark the measured values for FRB 20191001A and FRB 20240318A, respectively, with shaded bands showing errors from off-pulse RMS noise. Blue dashed lines connect points of constant ΠL and are linearly extended using the slopes of their first and last segments.
Within the PSN framework, Figure 1 provides an illustrative example in which depolarisation arises from the superposition of microshots with differing PAs. The intrinsic microshot polarisation fractions are
$\Pi_{L,0} = 0.99$
and
$\Pi_{V,0} = -0.05$
; however, when superimposing
$N=100$
microshots with PAs sampled from a normal distribution with a standard deviation of
$\sigma_\psi=30^\circ$
, then
$\Pi_{L} = 0.55$
as measured from the real FRB.
We illustrate this for the leading edge (see Section 3.1) of FRB 20191001A in Figure 3(a), (b) where we sweep
$\sigma_\psi=0$
–
$45^\circ$
for different values of N. In Figure 3, the shaded percentile regions quantify the spread in
$\Pi_L$
only; they do not represent the spread in
$\mathbb{V}(\psi)$
. Starting with
$N=5$
in Figure 3(a), the left-most point corresponds to
$\sigma_\psi=0^\circ$
, and the right-most point corresponds to
$\sigma_\psi=45^\circ$
. At
$\sigma_\psi=0^\circ$
the intrinsic PA profile is completely flat, no depolarisation due to microshot superposition occurs and so
$\Pi_{L} = \Pi_{L,0} = 0.99$
. Here the only contribution to
$\mathbb{V}(\psi)$
is from noise, as described by Equation (4) which determines the minimum
$\mathbb{V}(\psi)$
for all values of N at
$\sigma_\psi=0^\circ$
. As we increase
$\sigma_\psi$
,
$\mathbb{V}(\psi)$
increases and microshots with different PAs start overlapping, causing a reduction in
$\Pi_L$
. As we move to larger values of N, we increase the effective shot-rate (
$N_\mathrm{eff}\,\mathrm{shots\,}s^{-1}$
; see Appendix A) since the envelope width,
$W_0$
, remains constant. So, as N increases, microshots overlap more often and stronger depolarisation occurs for a given
$\sigma_\psi \gt 0$
. This also means that, since more averaging of PAs occurs,
$\mathbb{V}(\psi)$
decreases for a given
$\sigma_\psi \gt 0$
. If we decrease
$\Pi_{L,0}$
, we decrease our signal in L and noise becomes more significant. So a decrease in
$\Pi_{L,0}$
also corresponds to an increase in
$\mathbb{V}(\psi)$
which we see when comparing to Figure 3(b) where we have reduced
$\Pi_{L,0}$
to 0.55. Under the PSN model, we reproduce observable parameters and use these tracks to identify allowed combinations of N and
$\sigma_\psi$
for assumed
$\Pi_{L,0}$
, rather than to uniquely constrain a solution. The allowed regions are therefore conditional on the adopted microshot width and amplitude distributions (Appendix C.1, Appendix C.2).
We show the same analysis for FRB 20240318A in Figures 3(c), (d) and B1 using the parameters listed in Table 1. Post-processing measurements of the on-pulse polarisation fractions in Figure B1(b) show
$\Pi_L = 0.78$
and
$\Pi_V = -0.17$
.
4. Discussion
Here, we first show that FIRES qualitatively reproduces FRB behaviour, then proceed to quantitatively constrain the allowed parameter space. In order to visually reproduce the properties of FRB 20191001A (Figure 1(c)), we adopt a ‘single-component’ envelope (Table 2 of Scott et al. Reference Scott2025), implying an intrinsic FWHM
$W_0 \sim 0.5$
ms given the measured scattering timescale
$\tau_\mathrm{1\,GHz}=1.78$
ms. As an illustrative example within the PSN model, we choose
$N=100$
microshots with intrinsic linear polarisation fraction
$\Pi_{L,0}=0.99$
arriving within
$W_0$
, for which matching the observed linear polarisation fraction requires
$\sigma_\psi \sim 30^\circ$
(Figure 3(a)). In this example, superposition of microshots with differing intrinsic PAs produces a time-variable PA profile, while scattering preferentially suppresses this variability on the trailing edge, broadly consistent with observations (Scott et al. Reference Scott2025). While more rigorous statistical comparisons against the full HTR CRAFT sample remain for future work, the quantitative constraints below demonstrate the viability of the PSN framework.
4.1 Depolarisation mechanisms and parameter degeneracy
Scattering is not the sole mechanism that suppresses observable PA structure. Finite instrumental sampling further averages intrinsic PA fluctuations (Beniamini et al. Reference Beniamini, Kumar and Narayan2022): when the sampling time
$\delta t$
exceeds the characteristic microshot separation, rapid PA variations are smoothed and depolarisation occurs, yielding an apparently flat PA profile even for relatively large
$\sigma_\psi$
. A similar degeneracy exists in the construction of the burst envelope itself: in our simulations the envelope is produced by varying the number of microshots with amplitudes,
$A_i$
, sampled from a power law and uniformly sampled widths,
$w_i$
, but comparable averaged behaviour could also arise from a constant number of shots with time-varying amplitudes, and different amplitude distributions and ranges, an effect that would likewise be smoothed by superposition and finite sampling (see Appendix C.1 and Appendix C.2).
In the PSN framework, depolarisation is set mainly by effective averaging: microshot overlap (
$N\,w_i/W_0$
), propagation smearing, and instrumental sampling. For
$N\,w_i \gg W_0$
, vector averaging in (Q, U) suppresses
$\Pi_L$
and flattens or disorders PA; for
$N\,w_i \lesssim W_0$
, shots are more resolved, so strong PA variation can coexist with comparatively high
$\Pi_L$
.
The Appendix and simulations show the same behaviour in
$\Delta\psi \equiv \psi-\bar{\psi}$
versus
$\Delta\Pi_{L} \equiv \Pi_{L}-\bar{\Pi}_{L}$
(Figure D1; Appendix D): the noiseless no-scattering case is a near-random walk about (0, 0), while a clear anti-correlation appears only when scattering is strong enough to enforce substantial averaging. With realistic noise, this anti-correlation is largely erased.
This interpretation is consistent with observations: more highly scattered bursts tend to show flatter PA (Scott et al. Reference Scott2025), yet PA fluctuations do not robustly track
$L/I$
(Scott et al. Reference Scott2025), and
$L/I$
shows no clear dependence on scattering timescale (Sand et al. Reference Sand2025). Within PSN, these results imply that large-
$\sigma_\psi$
averaging is not the sole or primary depolarisation driver; instead, the observed behaviour reflects a coupled degeneracy among
$\sigma_\psi$
, N,
$\tau$
,
$\delta t$
,
$A_i$
,
$w_i$
, and S/N, with a likely non-negligible contribution from external depolarising media along the propagation path (e.g. Uttarkar et al. Reference Uttarkar2026).
4.2 FRB case studies
These degeneracies are illustrated in Figure 3(b), where all simulations converge to identical
$\Pi_L$
and
$\mathbb{V}(\psi)$
at
$\sigma_\psi=0$
. Shifts in
$\mathbb{V}(\psi)$
require changes in the effective S/N: increasing S/N reduces the measured PA variance, while decreasing the S/N of the linearly polarised intensity L (lowering
$\Pi_{L,0}$
) increases the contribution of noise to
$\mathbb{V}(\psi)$
. The measured values for FRB 20191001A (Figure 1(d)) therefore do not uniquely select a single intrinsic configuration, nor do they tightly determine the intrinsic linear fraction itself; rather, they define a model-dependent allowed region of
$(N,\sigma_\psi,\mathbb{V}(\psi),\Pi_{L,0})$
space.
Under the PSN model with a set of assumptions about microshot width and amplitude distributions, Figure 3(a) shows that reproducing the observed properties of FRB 20191001A with intrinsically 100% polarised microshots (
$\Pi_{L,0}=0.99$
,
$\Pi_{V,0}=-0.05$
) is compatible with intrinsic PA dispersions of order
$\sigma_\psi \sim 31^\circ$
when the number of microshots is
$N \gtrsim 100$
. This reflects efficient averaging of intrinsically misaligned PAs through microshot superposition, scattering, and finite instrumental sampling. However, once these averaging effects and the contribution of noise are accounted for, comparable levels of measured PA variance can also be obtained without invoking such large intrinsic dispersions. In particular, Figure 3(b) demonstrates that reducing the intrinsic linear fraction to the measured value of
$\Pi_{L,0}=0.55$
allows models with more modest PA dispersion (
$\sigma_\psi \sim 4^\circ$
) and
$N \lesssim 5$
to reproduce the observations. Larger values of N combined with slightly reduced
$\Pi_{L,0}$
and smaller
$\sigma_\psi$
remain equally consistent. Taken together, the data for FRB 20191001A are best described by a broad, model-dependent region of parameter space in which modest intrinsic PA dispersion is compatible with the observed near-constant PA once instrumental resolution, propagation effects, noise statistics, and the assumed microshot-property distributions are properly incorporated.
By contrast, FRB 20240318A exhibits a significant, observable variable PA trend (Scott et al. Reference Scott2025). Assuming a 100% polarised microshots (
$\Pi_{L,0}=0.98$
,
$\Pi_{V,0}=-0.17$
), Figure 3(c) allows configurations with
$N=5$
–20 and intrinsic PA dispersion
$\sigma_\psi \sim 22^\circ$
. Relaxing this assumption to the measured
$\Pi_{L,0}=0.78$
shifts the allowed region toward fewer microshots, with Figure 3(d) favouring
$N \lt 5$
and more modest PA dispersion (
$\sigma_\psi \sim 15^\circ$
). A stricter interpretation of the resolved PA structure is that the data contain multiple independent PA excursions across the burst window; under that interpretation, very low-N solutions (e.g.
$N \lt 5$
) are less physically plausible in the PSN framework unless each observable excursion is produced by unresolved blends of multiple microshots. These solutions therefore occupy a different part of the same
$(N,\sigma_\psi,\Pi_{L,0})$
space explored for FRB 20191001A, rather than requiring a fundamentally larger intrinsic PA dispersion. The observed PA variability therefore reflects a combination of reduced microshot averaging and intrinsic PA structure, rather than uniquely implying broader intrinsic PA distributions.
4.3 Model alternatives and interpretation
At the phenomenological level considered here, the main alternative to a multi-shot description is a single-shot or effectively single-component model in which the observed burst structure is generated within one emission episode rather than by superposition of many narrower shots. We do not rule out such alternatives in the present work. However, a single-shot picture appears to struggle more naturally to explain the rapid,
$\unicode{x03BC}$
s PA variations seen in HTR bursts (e.g. Nimmo et al. Reference Nimmo2022; Scott et al. Reference Scott2025), whereas the PSN framework can reproduce qualitatively and quantitatively similar behaviour through the superposition, propagation, and sampling of many polarised microshots. We therefore view the current results as providing a first-order demonstration that the PSN model is viable over a broad parameter space, rather than as definitive evidence that it is uniquely required. Stronger support for, or against, the shot-noise interpretation will require a future statistical comparison of FIRES against the growing sample of HTR CRAFT FRBs and, ideally, against explicitly formulated alternative models.
4.4 Limitations and caveats
A key limitation of the present analysis is the use of PA variance as the primary diagnostic of intrinsic structure. Variance is not sensitive to how the PA varies in time, encoding neither coherence, intermittency, nor ordered swings. Consequently, distinct PA behaviours can yield similar
$\mathbb{V}(\psi)$
, particularly in noise-dominated or temporally averaged regimes (see Figure 2). Likewise, the present implementation treats the intrinsic PA structure primarily as stochastic microshot-to-microshot scatter, and so does not yet capture more complicated time-dependent PA evolution, such as coherent swings or other structured behaviour across the burst envelope. Structure-based metrics that explicitly quantify PA organisation (e.g. Scott et al. Reference Scott2025) are therefore likely to provide a more informative and robust characterisation of intrinsic PA behaviour than variance alone. Future extensions of FIRES will incorporate such measures.
Finally, comparisons between FRB microstructure and Galactic pulsars such as the Crab must be interpreted cautiously. The extreme PA swings observed in Crab nanoshots occur on nanosecond timescales and would be strongly averaged out at the millisecond-to-microsecond resolutions of current FRB observations. As a result, present data probe only a temporally averaged manifestation of any underlying nanoshot structure, and unresolved Crab-like PA variability in FRBs cannot be ruled out. In addition, for very bright pulses observed at high time resolution, the inferred polarimetric variability can itself be affected by self-noise and small-number statistics when the averaging is insufficient (van Straten Reference van Straten2009). Apparent differences in polarimetric behaviour may therefore reflect observational limitations rather than fundamentally distinct emission physics.
4.5 Future model considerations
The present iteration of FIRES lacks several physical ingredients that will be incorporated into future versions:
-
• Multiple scattering and scintillation screens: Currently only a single thin-screen model is implemented, preventing realistic modelling of multi-path propagation and frequency-dependent scintillation structure.
-
• Thick-screen scattering: The code assumes an infinitely thin screen, whereas a volumetric or extended medium would alter temporal broadening and pulse-shape evolution.
-
• Generalised Faraday rotation: FIRES uses standard Faraday rotation, but cannot yet capture mode-coupling or birefringent effects expected in magnetised, relativistic plasmas.
-
• Structured intrinsic PA evolution and PA diagnostics: Future versions should incorporate more complicated time-dependent PA evolution, including coherent swings across the burst envelope, together with structure-based diagnostics that quantify PA organisation rather than variance alone.
-
• Alternative noise models: For the ASKAP data considered here, Gaussian noise is adequate, but at substantially higher time and frequency resolution the noise can become non-Gaussian. Future applications of FIRES should therefore generate the FRB and noise as electric fields at Nyquist resolution, allowing for noise to occupy a
$\chi^2$
distribution. -
• Intrinsic spectral structure: Extending FIRES to include intrinsic spectral structure would improve the interpretation of its effects on FRB polarisation and flux variability.
5. Conclusions
We have introduced FIRES, an emission-mechanism-independent framework for modelling FRB dynamic spectra as the superposition of Gaussian microshots with varying PAs, followed by propagation effects and noise. Applied to CRAFT FRBs 20191001A and 20240318A, FIRES reproduces key polarimetric behaviours: scattering suppresses PA variability on burst trailing edges, while the leading edge preferentially preserves intrinsic structure. Depolarisation arises naturally from incoherent microshot superposition, with the relative contributions of N,
$\sigma_\psi$
,
$\mathbb{V}(\psi)$
, and
$\Pi_{L,0}$
defining a degenerate but physically bounded parameter space.
For both FRBs, modest intrinsic PA dispersion remains viable once scattering, sampling, and noise are properly accounted for, and current data do not require fundamentally distinct intrinsic PA statistics between the sources. The leading-edge window and higher-frequency sub-bands provide the most robust access to intrinsic information. However, PA variance alone is an incomplete statistic and does not capture how PA varies in time; more structure-sensitive diagnostics are needed to fully characterise intrinsic PA evolution.
Future work will extend FIRES to incorporate multiple scattering screens, generalised Faraday rotation, and intrinsic spectral structure. Observationally, application to high-time-resolution, low-scattering FRBs will test whether FIRES can reliably recover intrinsic microshot properties and break current parameter degeneracies. Such observations will also directly test whether FRBs exhibit Crab-like nanoshot PA variability on unresolved timescales.
Acknowledgements
This research was supported by an Australian Government Research Training Program (RTP) Scholarship (https://doi.org/10.82133/C42F-K220). AB acknowledges support through project CORTEX (NWA.1160.18.316) of the research programme NWA-ORC, which is financed by the Dutch Research Council (NWO).
Data availability statement
ASKAP data used in this work are available online at https://doi.org/10.25917/1RG2-C612. The FIRES codebase and simulated data are available at https://github.com/JoelBalzan/FIRES.
Appendix A. Back-of-the-envelope derivation of the expected variance of the polarisation angle
We give a sanity check for the expected variance of the polarisation angle (PA) under the microshot model introduced in the main text. Let the envelope have FWHM
$W_0$
(ms) and each microshot have FWHM
$w_i$
, with fractional width
$w_i/W_0 \in [w_{\min}, w_{\max}]$
. For an order-of-magnitude estimate we replace the fractional width by its mean
\begin{equation*} \bar{w} \;=\; \tfrac{1}{2}\!\left(w_{\min}+w_{\max}\right),\qquad w \equiv \bar{w}\,W_0.\end{equation*}
Write
$\kappa \equiv 2\sqrt{2\log{2}}$
so that FWHM
$\to\sigma$
via
$\sigma = \text{FWHM}/\kappa$
. A thin-screen exponential scattering response with timescale
$\tau_0$
(ms) broadens Gaussian widths in quadrature,
\begin{equation*}\sigma_{W,\mathrm{tot}} \;=\; \sqrt{\sigma_W^2 + \tau_0^2},\qquad \sigma_{w,\mathrm{tot}} \;=\; \sqrt{\sigma_w^2 + \tau_0^2},\end{equation*}
with
$\sigma_W = W_0/\kappa$
and
$\sigma_w = w/\kappa$
. The corresponding broadened FWHM measures are
\begin{equation*}W_{\mathrm{tot}} \;=\; \kappa\,\sigma_{W,\mathrm{tot}},\qquad w_{\mathrm{tot}} \;=\; \kappa\,\sigma_{w,\mathrm{tot}}.\end{equation*}
If N microshots occur within the envelope, the number that effectively contribute at any time scales with the broadened-width ratio. Defining
\begin{equation*}r \;\equiv\; \frac{w_{\mathrm{tot}}}{W_{\mathrm{tot}}}\;=\; \frac{\sigma_{w,\mathrm{tot}}}{\sigma_{W,\mathrm{tot}}},\qquad N_{\mathrm{eff}} \;=\; N\,r,\end{equation*}
and letting
$\sigma_\psi$
be the intrinsic single-shot PA scatter (radians), the rms PA scatter is
\begin{equation}\psi_{\mathrm{rms}} \;\approx\; \frac{\sigma_\psi}{\sqrt{N_{\mathrm{eff}}}},\end{equation}
so the basic variance estimate is
\begin{equation}\mathbb{V}_{\exp}(\psi)\;=\; \psi_{\mathrm{rms}}^2\;=\; \frac{\sigma_\psi^2}{N\,r}\;=\; \frac{\sigma_\psi^2\,W_{\mathrm{tot}}}{N\,w_{\mathrm{tot}}}.\end{equation}
When estimating fluctuations about the mean PA across the envelope, subtracting the mean introduces a degrees-of-freedom correction. Approximating the number of independent samples by
$M \approx W_{\mathrm{tot}}/w_{\mathrm{tot}} = 1/r$
gives
$(M-1)/M \approx 1-r$
, yielding
\begin{equation}\mathbb{V}_{\exp}(\psi)\;=\; \frac{\sigma_\psi^2}{N\,r}\,\bigl(1-r\bigr)\;=\; \frac{\sigma_\psi^2\,W_{\mathrm{tot}}}{N\,w_{\mathrm{tot}}}\!\left(1 - \frac{w_{\mathrm{tot}}}{W_{\mathrm{tot}}}\right).\end{equation}
Simplifying and converting to deg.,
$^2$
\begin{equation} \mathbb{V}_{\exp}(\psi) \;=\; \frac{\sigma_\psi^2}{N}\! \left(\frac{W_{\mathrm{tot}}}{w_{\mathrm{tot}}} - 1\right)\left(\frac{180}{\pi}\right)^2.\end{equation}
This corrected estimate tends to zero as scattering grows large (
$r\to 1$
). It ignores amplitude weighting, detailed temporal structure, and the full width distribution, but provides a rapid order-of-magnitude check. If needed for discretely sampled data with time resolution
$\delta t$
, one may downweight
$N_{\mathrm{eff}}$
by
$\min(1,\,\sigma_{w,\mathrm{tot}}/(\delta t/\kappa))$
to account for unresolved microshots.
Appendix B. FRB 20240318A FIRES recreation and data
A FIRES comparison with FRB 20240318A. Top: A FIRES recreation of FRB 20240318A comprised of 100 microshots,
$\tau_{1\,\mathrm{GHz}} = 0.128$
ms and scintillation (on-pulse S/N
$=109$
). Bottom: real FRB 20240318A data reproduced from Scott et al. (Reference Scott2025) (on-pulse S/N
$\sim110$
, RM corrected from RM=
$-48.03$
rad m
$^{-2}$
). The full list of parameters used are presented in Table 1 and are described in Section 2. The top panels show the polarisation angle, the centre panels show the pulse profile, and the bottom panels show the dynamic spectra. The blue shaded regions in the centre panels is the minimum boxcar width that contains 95% of the total flux in the pulse profile.
Figure B1. Long description
The image contains two sets of graphs comparing simulated and real data of FRB 20240318A. Each set includes three graphs: polarisation angle, pulse profile, and dynamic spectra. The top set represents a simulation with 100 microshots and scintillation, while the bottom set shows real data from Scott et al. 2025, corrected for RM. The polarisation angle graphs display fluctuations over time. The pulse profile graphs show the intensity of the signal, with blue shaded regions indicating the minimum boxcar width containing 95% of the total flux. The dynamic spectra graphs illustrate frequency variations over time. The x-axis for all graphs represents time in milliseconds, while the y-axes represent degrees for polarisation angle, arbitrary units for pulse profile, and frequency in megahertz for dynamic spectra. The graphs highlight the similarities and differences between simulated and observed data, providing insights into the behavior of fast radio bursts.
Appendix C. FRB 20240318A parameter distribution comparisons
Appendix C.1. Amplitude distributions
Here we compare power law amplitude distributions with
$\alpha=-1 \textrm{ and } -2$
. Figure C1 shows that the distributions aren’t strongly distinguishable in the
$\Pi_L$
–
$\mathbb{V}(\psi)$
plane, with the
$\alpha=-1$
distribution producing slightly lower
$\Pi_L$
and
$\mathbb{V}(\psi)$
at fixed
$\sigma_\psi$
and
$N \gt 20$
. This is because the
$\alpha=-1$
distribution has more high-amplitude microshots that can dominate the polarisation properties. The differences between these distributions and the
$\alpha=-3$
distribution used in Section 3.2 are relatively subtle compared to the effects of varying N and
$\sigma_\psi$
, and all three distributions can reproduce the observed properties of FRB 20240318A within the uncertainties. We thus adopt the
$\alpha=-3$
distribution for our main analysis as it is more consistent with observed Crab GP energy distributions (Bera & Chengalur Reference Bera and Chengalur2019).
Measured linear polarisation fraction
$\Pi_{L}$
versus PA variance
$\mathbb{V}(\psi)$
for mock FRB 20240318A power law amplitude distribution comparison. Left:
$\alpha=-1$
. Right:
$\alpha=-2$
. Top/bottom rows: intrinsic linear polarisation fraction
$\Pi_{L,0}=0.98$
and
$0.78$
. Lines show medians for
$N=10,20,100$
(500 realisations per
$\sigma_\psi$
); shaded regions are the 16th–84th percentiles. Cyan star: measured FRB 20240318A (S/N
$\sim110$
) with off-pulse RMS uncertainty. Blue dashed lines: loci of constant
$\sigma_\psi$
.
Figure C1. Long description
The image contains four graphs comparing the measured linear polarisation fraction versus PA variance for mock FRB 20240318A with a power law amplitude distribution. The graphs are arranged in a 2x2 grid. The left column represents one set of conditions, while the right column represents another. The top row shows data for an intrinsic linear polarisation fraction of 0.98, and the bottom row shows data for an intrinsic linear polarisation fraction of 0.78. Each graph includes lines representing medians for different values of N (10, 20, and 100), with shaded regions indicating the 16th to 84th percentiles. A cyan star marks the measured FRB 20240318A with off-pulse RMS uncertainty. Blue dashed lines represent loci of constant values. The graphs illustrate how the polarisation fraction varies with PA variance under different conditions.
Appendix C.2. Width distributions
We note that varying microshot widths introduces a degeneracy to varying shot amplitudes. Here we compare simulations with width distributions of 1–5% and 20–40% of the burst width. Figure C2 shows that the narrower width distribution produces a more extended track in the
$\Pi_L$
–
$\mathbb{V}(\psi)$
plane, with the
$N=5$
track extending to higher
$\sigma_\psi$
values. The wider width distribution produces more compact tracks. This is because wider microshots are more likely to overlap and therefore produce more depolarisation and PA variance damping at fixed N and
$\sigma_\psi$
. This degeneracy makes it difficult to distinguish between a scenario with fewer, wider microshots and one with more, narrower microshots.
Comparison of width distributions for mock FRB 20240318A. Measured linear polarisation fraction
$\Pi_{L}$
versus PA variance
$\mathbb{V}(\psi)$
. Left/right columns: microshot fractional FWHM in
$[1\%,5\%]$
and
$[20\%,40\%]$
. Top/bottom rows: intrinsic microshot
$\Pi_{L,0}=0.98$
and
$0.78$
. Lines show medians for
$N=5,10,20,100$
(500 realisations per
$\sigma_\psi$
); shaded regions are the 16th–84th percentiles. Cyan star: measured FRB 20240318A (S/N
$\sim110$
) with off-pulse RMS uncertainty. Blue dashed lines: loci of constant
$\sigma_\psi$
. Some lines have been omitted for visual clarity.
Figure C2. Long description
The image contains four graphs comparing width distributions for mock FRB 20240318A. Each graph plots the measured linear polarisation fraction (ΠL) against PA variance (V(ψ)) on a logarithmic scale. The graphs are divided into two columns and two rows, representing different microshot fractional FWHM and intrinsic microshot values. The left column shows microshot fractional FWHM of 1 percent, while the right column shows 20 percent. The top row represents an intrinsic microshot value of 0.98, and the bottom row represents 0.78. Each graph includes lines showing medians for different values of N (5, 10, 20, 100) with shaded regions indicating the 16th-84th percentiles. A cyan star marks the measured FRB 20240318A with off-pulse RMS uncertainty. Blue dashed lines represent loci of constant σψ (15, 22, 40). Some lines are omitted for visual clarity. The graphs illustrate how different parameters affect the polarisation fraction and PA variance.
Appendix D. Correlations between
$\Delta\psi$
–
$\Delta\Pi_L$
Our simulations for
$\Delta\psi \equiv \psi-\bar{\psi}$
versus
$\Delta\Pi_{L} \equiv \Pi_{L}-\bar{\Pi}_{L}$
(Figure D1) show that depolarisation is governed by effective averaging (microshot overlap plus propagation/instrumental smoothing), rather than by intrinsic PA scatter alone.
In the noiseless scattered case (
$\tau_0=0.128$
ms), there is a clear anti-correlation, consistent with incoherence in (Q, U) under strong overlap. The phase-space evolution in
$(\Delta\psi,\Delta\Pi_L)$
is also consistent with this picture: as effective averaging increases across the burst, the point cloud contracts toward the mean state (0, 0), reflecting suppression of both large PA excursions and large linear-polarisation offsets. Early-time bins can deviate because intrinsic structure is less averaged (Section 3.1). By contrast, in the noiseless no-scattering baseline (
$\tau_0=0$
), the correlation is weaker, indicating that intrinsic PA spread alone is insufficient to guarantee strong
$\Pi_L$
suppression. With realistic noise (S/N
$\sim110$
; L masked where
$I \lt 2\sigma_I$
), the relation disappears, implying that moderate intrinsic trends can be erased by measurement uncertainty and finite sensitivity. With noise added, the relation only begins to become visible at extremely high S/N.
Correlations between polarisation-angle and linear-polarisation fluctuations for mock FRB 20240318A, demonstrating noise-dominated behaviour. Left column:
$\Delta\psi \equiv \psi-\bar{\psi}$
versus
$\Delta\Pi_{L} \equiv \Pi_{L}-\bar{\Pi}_{L}$
, with points coloured by time. Right column: corresponding 3D visualisation with time as the explicit axis. Rows (top to bottom): no noise, no scattering (
$\tau_0=0$
ms); no noise, with scattering (
$\tau_0=0.128$
ms); and with scattering plus realistic noise (S/N
$\sim110$
). We have increased the sampling rate
$10\times$
compared to the main text to better inspect the tracks. Top: scattering plus noise (S/N
$\sim4\,900$
), showing the correlation only becomes visible at unrealistically high sensitivity. Bottom: Real FRB 20240318A data from Figure B1b.
Figure D1. Long description
The image contains six graphs arranged in a 3x2 grid. The left column features 2D plots showing the relationship between polarisation-angle (x-axis) and linear-polarisation fluctuations (y-axis), with data points colored by time. The right column presents corresponding 3D visualizations, where time is the explicit axis. The top row illustrates data without noise and without scattering. The middle row shows data without noise but with scattering. The bottom row includes data with scattering and realistic noise. The graphs demonstrate how correlations between polarisation-angle and linear-polarisation fluctuations vary under different conditions. The bottom row also includes real data from FRB 20240318A for comparison. All values are approximated.
Overall, the observed
$\Delta\psi$
–
$\Delta\Pi_L$
behaviour is therefore controlled by a coupled parameter space – intrinsic PA scatter, number of emitting elements, overlap fraction (
$Nw_i/W_0$
), scattering timescale, sampling interval, amplitude/width distributions, and S/N – rather than any single parameter. This explains why flattened PA, PA variability, and low
$\Pi_L$
need not map one-to-one across bursts, and why robust inference requires joint constraints on source microphysics and propagation/sensitivity effects (Section 4.1; cf. Sand et al. Reference Sand2025; Scott et al. Reference Scott2025).
Appendix E. Impact of spectral modulation on PA variance
To assess whether fine spectral structure affects the inferred PA variance constraints, we repeated the mock-burst simulations shown in Figure 3 after applying representative scintillation modulation patterns to the spectra using the procedure described in Section 2.2. We found that the resulting
$(\Pi_L,\mathbb{V}(\psi))$
relations were visually indistinguishable from those obtained without scintillation, with no systematic shifts apparent beyond the intrinsic simulation scatter.
This behaviour is expected because any diffractive scintillation pattern is effectively static over the duration of an FRB burst – for Galactic scintillation at GHz frequencies, the characteristic scintillation timescale is many orders of magnitude longer than the millisecond burst durations considered here. While scintillation modulates the burst spectrum and local S/N, it cannot directly generate coherent time-dependent PA variations. We note that in principle, scintillation could indirectly affect PA results by introducing S/N-weighted frequency gaps that bias RM estimation; however, the RMs and scintillation strengths of the bursts in our sample are insufficient for this to be a concern.
While self-noise contributes to the uncertainty of spectral estimates, it does not produce correlated spectral modulation; instead, it manifests as uncorrelated variance in intensity estimates that averages down with the number of independent voltage samples within each integration. Stochastic wide-band impulse modulated self-noise (SWIMS; Osłowski et al. Reference Osłowski, van Straten, Hobbs, Bailes and Demorest2011) can produce temporally correlated noise variance when subpulse structure is resolved; however, since CRAFT data are Nyquist-sampled at 3 ns (Shannon et al. Reference Shannon2025), yielding
$\gt$
$10^3$
independent voltage samples per time bin at the time resolutions used here, any such cross-bin correlations in the Stokes parameters are significantly suppressed. Consequently, neither interstellar scintillation nor self-noise can generate the coherent time-dependent PA structure analysed in this work; self-noise may only contribute stochastic scatter to PA estimates.
τ1GHz=1.78
=180
=194
−2
Rψ
τ0
W0
Rψ
Rψ
τ0/W0=0,60
∼2300,150
ΠL
V(ψ)
σψ
ΠL,0=0.99
0.55
ΠL,0=0.98
red0.78
N=5,10,20,100,1000
σψ
∼194
∼110
ΠL
V(ψ)
ΠL
V(ψ)
σψ
σψ=4∘,10∘,31∘,40∘
σψ=15∘,22∘,40∘
τ1GHz=0.128
=109
∼110
−48.03
−2
ΠL
V(ψ)
α=−1
α=−2
ΠL,0=0.98
0.78
N=10,20,100
σψ
∼110
σψ
ΠL
V(ψ)
[1%,5%]
[20%,40%]
ΠL,0=0.98
0.78
N=5,10,20,100
σψ
∼110
σψ
Δψ≡ψ−ψ¯
ΔΠL≡ΠL−Π¯L
τ0=0
τ0=0.128
∼110
10×
∼4900
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