# Modelling Annual Scintillation Velocity Variations of FRB 20201124A

R. A. Main1, S. Bethapudi1, V. R. Marthi2, M. L. Bause1, D. Z. Li4, H.-H.
Lin5,6, L. G. Spitler1, R. S. Wharton3,
1Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn,
Germany
2National Centre for Radio Astrophysics, Tata Institute of Fundamental
Research, Post Bag 3, Ganeshkhind, Pune - 411 007, India
3NASA Postdoctoral Program Fellow, Jet Propulsion Laboratory, California
Institute of Technology, Pasadena, CA 91109, USA
4Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA
5Institute of Astronomy and Astrophysics, Academia Sinica, Astronomy-
Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan,
R.O.C
6Canadian Institute for Theoretical Astrophysics, 60 St. George Street,
Toronto, ON M5S 3H8, Canada
Email<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Compact radio sources exhibit scintillation, an interference pattern arising
from propagation through inhomogeneous plasma, where scintillation patterns
encode the relative distances and velocities of the source, scattering
material, and Earth. In previous work, we showed that the scintillation
velocity of the repeating fast radio burst FRB20201124A could be measured by
correlating burst spectra pairs, with low values of the scintillation velocity
and scattering timescale suggesting scattering nearby the Earth at $\sim
0.4\,$kpc. In this work, we have measured the scintillation velocity at 10
epochs spanning a year, observing an annual variation which strongly implies
the screen is within the Milky Way. Modelling the annual variation with a 1D
anisotropic or 2D isotropic screen results in a screen distance $d_{l}=0.40\pm
0.04\,$kpc or $d_{l}=0.46\pm 0.06\,$kpc from Earth respectively, possibly
associated with material outside of the Local Bubble or the edge of the Orion-
Eridanus Superbubble. Additional measurements particularly at times of low
effective velocity will help probe changes in screen properties, and
distinguish between screen models. Where scintillation of an FRB originates in
its host galaxy or local environment, these techniques could be used to detect
orbital motion, and probe the FRB’s local ionised environment.

###### keywords:

transients: Fast Radio Bursts

††pubyear: 2022††pagerange: Modelling Annual Scintillation Velocity Variations
of FRB 20201124A–References

##  1 Introduction

Fast radio bursts (FRBs) are a powerful probe of intervening plasma. The total
electron content along their line of sight is contained in their dispersion
measure, while inhomogeneities in electron density result in scattering and
scintillation, often concentrated in regions of high electron density.
Scintillation encodes the time delay of scattered paths, and the relative
distances and velocities of the emitting source, Earth, and scattering surface
(Cordes & Rickett, 1998).

Many repeating FRBs undergo periods of extreme activity (e.g. Gajjar et al.
2018; Li et al. 2021; Nimmo et al. 2022a; McKinven & Chime/Frb Collaboration
2022). In Main et al. (2022) (hereafter M22A), we showed that in sufficiently
active FRBs (i.e. such that there are many burst pairs separated by $\sim$
minutes), the scintillation timescale $t_{s}$ can be measured through the
pairwise correlation of bursts. From this, and the easily measured
scintillation bandwidth $\nu_{s}$, one can derive a scintillation velocity. As
an extragalactic source, only the Earth’s velocity will matter for
scintillation within the Milky Way, while the source’s velocity will matter if
the screen is in the host galaxy.

In this paper, we measure the scintillation velocity of FRB 20201124A over a
full year, and we model the annual variation to determine the properties of
the dominant scattering screen. We describe our data in Sec. 2 and our
scintillation measurements in Sec. 3. In Sec. 4 we describe the annual
scintillation model, and in Sec. 5 we discuss our conclusions and
ramifications for future work.

##  2 Data

M22A focused on a single Effelsberg and uGMRT observation. We continued
observing the source with Effelsberg and the uGMRT, with slightly different
observing parameters described here.

FRB20201124A has been precisely localised with VLBI to $\alpha=05^{\rm
h}08^{\rm m}03.^{\rm s}5074\pm 2.7\textrm{mas}$,
$\delta=+26^{\circ}03^{{}^{\prime}}38.^{"}5052\pm 2.6\textrm{mas}$ (Nimmo et
al., 2022b). This corresponds to a sightline below the plane towards the
galactic anticentre, at $l=178.13^{\circ},b=-7.92^{\circ}$, while the ecliptic
longitude and latitude are $\lambda=79.03^{\circ},\beta=3.15^{\circ}$,
important for the annual scintillation variations modelled in Section 4.

The first Effelsberg observation on MJD 59313 used the PSRIX system (Lazarus
et al., 2016), recording baseband in a contiguous 1210–1520 MHz band
(Hilmarsson et al., 2021). One day later, many Effelsberg bursts were detected
as part of the EVN campaign to localise the source (Nimmo et al., 2022b). All
subsequent Effelsberg observation were made using the Effelsberg Direct
Digitization system, recording baseband of the contiguous 1200–1600 MHz band.
We restrict ourselves to the 200 MHz band 1270–1470 MHz throughout, to avoid
sensitivity loss in the bandpass edges.

The first uGMRT observation on MJD 59309 used the beam of the incoherent array
(IA) due to the uncertain source position, with 2048 channels across 550-750
MHz, and $655.36\,\mu$s time resolution (Marthi et al., 2022). From these
observations we obtained an arcsecond localisation (Wharton et al., 2021), so
subsequent observations used the phased array (PA) at this position, and our
final data product was PA-IA beam, to greatly remove RFI. Additionally, these
observations used 4096 channels, to better resolve the scintillation.

Bursts were searched for using PRESTO, as described in Hilmarsson et al.
(2021); Marthi et al. (2022). Burst detections were made in 3 periods of
heightened activity spanning a year, March$-$May 2021 (MJD 59313$-$59359),
September 2021 (MJD 59478), and February$-$March 2022 (MJD 59611$-$59655); we
summarise our observing campaign, and burst detections in Table 1.

Table 1: Summary of all observations from which we had sufficient bursts to derive $t_{s}$. Observations marked with ∗ were included in Main et al. (2022), with slightly different observing parameters as described in Section 2, and the observation labelled with $\dagger$ comes from the Effelsberg data from the observation used in the EVN localisation (Nimmo et al., 2022b). The properties of the detected bursts will be analysed in further work.  MJD | Tobs | Nburst | $\nu_{\rm s}$ | $t_{\rm s}$ | $W$
---|---|---|---|---|---
| (hr) |  | (MHz) | (min) | (km/s/$\sqrt{\rm kpc}$)
Effelsberg (1270–1470 MHz)
59313$*$ | 4 | 20 | $1.24\pm 0.08$ | $21.3\pm 1.7$ | $24.5\pm 2.1$
59314$\dagger$ | 3 | 13 | $1.24\pm 0.08$ | $19.0\pm 1.2$ | $27.5\pm 2.0$
59478 | 4 | 9 | $1.27\pm 0.23$ | $78.3\pm 9.6$ | $6.7\pm 1.0$
59611 | 3 | 53 | $1.29\pm 0.15$ | $20.8\pm 1.0$ | $25.5\pm 1.9$
59612 | 5 | 49 | $1.29\pm 0.15$ | $22.0\pm 1.2$ | $24.2\pm 1.9$
59624 | 4 | 12 | $1.5\pm 0.4$ | $27.0\pm 4.6$ | $21.2\pm 4.5$
59655 | 2 | 7 | $1.6\pm 0.4$ | $39.0\pm 10.8$ | $15.4\pm 5.0$
uGMRT (550–750 MHz)
59310$*$ | 3 | 48 | $0.09\pm 0.01$ | $8.4\pm 2.4$ | $36.2\pm 11.4$
59348 | 2 | 13 | $0.07\pm 0.01$ | $6.8\pm 1.3$ | $39.8\pm 8.4$
59359 | 3 | 38 | $0.07\pm 0.01$ | $6.2\pm 2.2$ | $43.6\pm 17.4$

##  3 Scintillation Measurements

Extraction of burst spectra and scintillation measurements are almost
identical to M22A, we briefly summarise the steps, and note differences here.

At Effelsberg, we channelise the baseband data with 1024 channels,
corresponding to $195.3125\,$kHz, while at uGMRT the channel size is
$97.65625$ kHz for the first and $48.828125$ kHz for subsequent observations.
First, channels corrupted by RFI were manually identified and masked. For each
burst, the ‘on’ region is identified as a contiguous window where the burst is
detected with $>5\sigma$, and an ‘off’ region $100-50\,$ms preceding each
burst. The data were divided by the background from the off-region,
subtracting 1, and burst spectra were obtained by averaging in time over the
on-window. The smooth intrinsic spectrum of each burst is estimated as a
Gaussian filter of each spectrum, with kernel size of $BW/8$. The frequency
extent of each burst is determined by the region the smoothed spectrum is
above $0.5\sigma_{I}$, the noise estimated in the off-region. Finally, each
measured spectrum is divided by the smoothed spectrum, leaving only the
variations caused by scintillation.

For each observation, we then had $N$ burst scintillation spectra
$I(t_{i},\nu)$ at discrete times $t_{i}$ sampling the scintillation pattern
unevenly in time (e.g. Fig. 1). We correlate each burst pair, giving a measure
of $r(\Delta t_{ij},\Delta\nu)$, with the error on each $r_{ij}$ generated
through MCMC method with the off-region noise $\sigma_{I}$ as described in
M22A.

A Gaussian is fit to all values of $r(\Delta t_{ij},\Delta\nu=0)$, and the
scintillation timescale $t_{s}$ is the half width at $1/e$. We note that
contrary to M22A, $t_{s}$ is fit to the correlation of each burst pair, rather
than the ACF binned in time. To measure the scintillation bandwidth for each
observation, we restrict ourselves only to bursts detected over more than half
of the band. To account for frequency evolution, at Effelsberg we split the
band into two, and at uGMRT in four, and fit each sub-band separately with a
Lorentzian. The scintillation bandwidth $\nu_{s,i}$ in each subband is the
half-width at half maximum (HWHM), and the final measurement $\nu_{s}$ is the
weighted sum of $\nu_{s,i}(\nu_{\rm band}/\nu_{\rm ref})^{4}$, and the error
is the weighted error on the mean, referenced to 650 MHz at uGMRT and 1400 MHz
at Effelsberg. The refractive timescale
$t_{r}\approx\frac{2\nu}{\nu_{s}}t_{s}$ (Rickett, 1990), which is $\gtrapprox
30\,$days for all of the Effelsberg observations. As the scintillation
bandwidth is not expected to vary significantly below this timescale, we
average $\nu_{s}$ for observations on subsequent days (MJDs 59313$-$59314,
59611$-$59612), to reduce noise.

With enough burst pairs, a uniformily sampled 2D autocorrelation function
(ACF) $R(\Delta t,\Delta\nu)$ can be constructed through the weighted sum of
all burst pairs in bins of $\Delta t$. We show the ACF from MJD 59611 with 2
minute bins in Figure 2, along with cuts through $R(\Delta t,\Delta\nu=0)$,
$R(\Delta t=0,\Delta\nu)$ and the Gaussian and Lorentzian corresponding the
best fit scintillation timescale and bandwidth overplotted. The ACF cuts are
fit well, although there is a clear tilt in the 2D ACF which is unaccounted
for. Such tilts reflect a spatial asymmetry in the scattered power, likely
reflecting local phase gradients across the screen (Cordes et al., 2006;
Rickett et al., 2014), and suggesting the screen is not isotropic.

As seen in pulsar giant pulses, nano- or micro-shots result in additional
intrinsic spectral structure (e.g. Bilous et al. (2015)), and would reduce the
expected correlation of adjacent pulses to $1/3$ (Cordes et al., 2004; Main et
al., 2021). The spectra of nearby bursts correlate at $\sim 100\,\%$,
suggesting there is no intrinsic spectral structure beyond the smooth burst
envelope used for normalising the burst spectrum.

Figure 1: Dynamic spectrum from MJD 59611, the Effelsberg observation with the
largest number of burst detections. The scintillation pattern of nearby bursts
are evidently highly correlated.  Figure 2: Image: Binned 2D Autocorrelation
function of the burst spectra from MJD 59611, slices through $\Delta\nu=0$
(top panel) and $\Delta t=0$ (right panel). The orange lines show the model
fit for scintillation timescale and bandwidth. We note that the ACF is non-
uniformally sampled in time leading to the vertical artefacts; $R(\Delta
t,\Delta\nu=0)$ is fit to the correlation of each burst pair (shown as blue
points), rather than the binned ACF. There is a clear tilt in the ACF
suggesting an asymmetric power distribution across the scattering screen (see
Sec. 3)

##  4 Annual Scintillation Model

In M22A, we used the expression for scintillation velocity from Cordes &
Rickett (1998), which in the limit of an extragalactic source with $D\gg
d_{l}$ (where $D$ is the source distance, and $d_{l}$ is the screen distance),
the scintillation velocity $V_{\mathrm{ISS}}$ of a thin screen is related to
$\nu_{s},t_{s}$ as

$W\equiv\frac{V_{\mathrm{ISS}}}{\sqrt{d_{l}}}\approx
27800\frac{\sqrt{2\nu_{s}}}{ft_{s}}~{}\textrm{km~{}s}^{-1}\textrm{kpc}^{-0.5}\approx\frac{|\textbf{v}_{\earth}-\textbf{v}_{l}|_{||}}{\sqrt{d_{l}}},$
(1)

with reference frequency $f$ in GHz, $\nu_{s}$ in MHz, $t_{s}$ in seconds, and
where the scaled effective velocity $W$ was defined for convenience,
separating the unknowns from the measured values.

We consider two limiting cases of a fully anisotropic 1D screen, an isotropic
2D screen. We have full knowledge of $\boldsymbol{\textbf{v}}_{\earth}$, so
the only unknowns are the screen distance, and two parameters describing the
geometry and velocity of the screen. For a 1D screen, we are only sensitive to
the velocity parallel to the screen’s axis on the sky; the two unknowns are
the screen axis $\psi$, and the screen velocity parallel to $\psi$,
$v_{l,\psi}$,

$W_{\rm 1D}=\frac{1}{\sqrt{d_{l}}}|v_{\earth,\rm ra}\sin(\psi)+v_{\earth,\rm
dec}\cos(\psi)-v_{l,\psi}|$ (2)

For a 2D, isotropic screen, the scintillation pattern is sensitive to the
total transverse velocity, and the only additional unknown is the 2D velocity
of the screen $v_{l,\rm ra},v_{l,\rm dec}$,

$W_{\rm 2D}=\frac{1}{\sqrt{d_{l}}}\sqrt{(v_{\earth,\rm ra}-v_{l,\rm
ra})^{2}+(v_{\earth,\rm dec}-v_{l,\rm dec})^{2}}.$ (3)

We predict Earth’s velocity vector in right ascension and declination towards
FRB 20201124A using scintools (Reardon, 2020). We fit our data using a Markov
chain Monte Carlo (MCMC), using emcee, with uniform priors on the screen
parameters. The results of our model fitting are shown in Figure 3, the
posteriors shown in Figure 4, and best fit parameters are in Table 2.

Table 2: Results of the annual scintillation models, with parameters defined in Sec. 4.  Parameters | 1D/anisotropic | 2D/isotropic
---|---|---
$d_{l}$ (kpc) | $0.40\pm 0.04$ | $0.46\pm 0.05$
$\psi$ (∘) | $76\pm 13$ | $-$
$v_{\psi}$ (km/s) | $1.4\pm 0.4$ | $-$
$v_{l,\rm ra}$ (km/s) | $-$ | $1.9\pm 0.6$
$v_{l,\rm dec}$ (km/s) | $-$ | $-3.1\pm 2.1$
Reduced $\chi^{2}$ | 0.75 | 0.6

Figure 3: Measurements of the scintillation velocity, and the best fit 1D and
2D annual models (top), and residuals from the 2D (top) and 1D fit (bottom).

Figure 4: Posterior plots for the 1D (top) and 2D (bottom) annual models
described in Sec. 4, plotted using corner.py (Foreman-Mackey, 2016). The
contours show the $68\%$ and $95\%$ confidence intervals.  Figure 5: Screen
constraints overlaid over an XZ slice through the local differential
extinction map of Lallement et al. (2019), where the blue and red points show
the screen distance constraints from our annual 1D and 2D models,
respectively. The colorbar show the logarithmic differential extinction in
magnitude/pc, and positive values of $X$ point towards the galactic centre,
and $Z$ angles above and below the galactic plane. FRB 20201124A is only
$1.88^{\circ}$ of longitude away from the Galactic anticentre, motivating the
choice of overplotting with the Y=0 slice.

###  4.1 Screen Association

Both the 1D and 2D model fit the data well, with reduced $\chi^{2}$ of $0.75$
and $0.6$ respectively. While the 2D isotropic model is slightly preferred,
The ACFs are tilted, suggesting local DM slopes and screen anisotropies which
are not accounted for; a general anisotropic screen model with screen axis and
axial ratio could also be used, but the reduced $\chi^{2}$ values less than 1
already suggest that the model is overconstrained. The annual variation
conclusively places the screen in the local region of the Milky Way, with
screen distances of $d_{l,1D}=0.40\pm 0.04$ kpc and $d_{l,2D}=0.46\pm 0.06$
kpc. There is significant correlation between $d_{l}$ and $\psi$. This
degeneracy arises form the low ecliptic latitude of $\beta=3.15^{\circ}$,
where the main contribution from changing $\psi$ will be to change the
amplitude of $W$ variations, while the phase of an annual scintillation curve
will be almost unchanged.

The Sun lies within a $\sim 200\,$pc cavity of hot ($\sim 10^{6}\,$K) and
tenuous ($n_{e}\approx 0.005\,\textrm{cm}^{-3}$) plasma, known as the Local
Bubble (for reviews, see Cox & Reynolds 1987; Frisch & Dwarkadas 2017). It has
long been suggested that the Local Bubble boundary is a dominant source of
scattering for pulsars (Phillips & Clegg, 1992; Bhat et al., 1998),
reinvigorated in recent times as precise screen distances are measured through
annual variations of scintillation arcs (Mall et al., 2022; Sprenger et al.,
2022; McKee et al., 2022; Stinebring et al., 2022).

To investigate this connection for FRB20201124A, we compare our screen
constraints to a map of the Local Bubble in Lallement et al. (2019) derived
from GAIA and 2MASS dust extinction (Fig. 5). Pelgrims et al. (2020) use this
same map to model the inner edge of the Local Bubble boundary, and in Zucker
et al. (2022) it is found that the majority of star forming complexes lie on,
or just beyond this boundary, providing a natural location for dense ionised
gas.

Towards FRB 20201124A, the inner edge of the Local Bubble boundary from this
model is at a distance of 156 pc. This is inconsistent with our derived screen
distances, although the Local Bubble is not a sharp edge, as can be seen from
the clear overdensity extending from $\sim 150-400\,$pc along this sightline.

This sightline also passes near the edge of the Orion-Eridanus superbubble, a
large $\sim 20^{\circ}\times 45^{\circ}$ expanding shell at a distance $\sim
400\,$pc, ionised by UV radiation, and driven by supernovae and stellar winds
from the Orion OB association (Ochsendorf et al., 2015; Tahani et al., 2022).
This would also provide a natural location for plasma overdensities, and the
distance roughly matches our screen estimates.

##  5 Conclusions and Future Avenues

We have modelled annual variation of the scintillation velocity in FRB
20201124A, finding the screen originates in the local region of the Milky Way,
potentially associated with ionized material beyond the Local Bubble. With a
higher density of scintillation velocity measurements, particularly at the
times of lowest effective velocity where the models are most different, the
axial ratio and variable screen velocity could be constrained and the screen’s
distance measured more precisely. Unmodeled ACF tilts from phase gradients
across the screen will introduce systematic errors in the scintillation
measurements, especially if they are changing over time. In observations with
even higher number densities of bursts, the phase gradient could be fitted in
the 2D ACF as in Rickett et al. (2014), or measurements could be made using
scintillation arcs (Stinebring et al., 2001), which are a more reliable
measure of the relative velocities (e.g. Reardon et al. 2020).

It is often unknown a priori whether the scintillation screen originates in
the Milky Way or the host galaxy of the FRB. A regular annual curve of
scintillation velocity breaks this degeneracy. The scintillation screen can
also be unambiguously constrained to the Milky Way if there is a
correspondence between scattering time and angular broadening measured through
VLBI (Ocker et al., 2021). With new large-scale VLBI projects coming online,
the scattering structures along thousands of sightlines could be constrained;
combining all such results will lead to greatly improved models and
understanding of the Galactic electron content (Cordes & Lazio, 2002; Yao et
al., 2017).

Many repeating FRBs have undergone periods of high activity, sufficient to
perform similar scintillation analysis. These include FRB20121102A and
FRB20180989B, both sources with periodic active windows (Rajwade et al., 2020;
Cruces et al., 2021; Chime/Frb Collaboration et al., 2020), and variable
magnetised local environments (Michilli et al., 2018; Mckinven et al., 2022).
FRB20190520B shows large magnetic field reversal (Anna-Thomas et al., 2022;
Dai et al., 2022), and variable scattering on the timescale of minutes (Ocker
et al., 2023). Such periodicities, and variable scattering and RM could be
explained by an orbit with a windy companion star (Lin et al., 2021; Li et
al., 2022), where an orbital dependence of scintillation velocity would be a
smoking gun.

In cases with scintillation and scattering were present on different scales,
it has been argued that scintillation would be quenched unless the two
scattering screens obey an inequality such that each screen appears pointlike
to the other (Masui et al., 2015; Cordes & Chatterjee, 2019). However, in PSR
B1508+55, Sprenger et al. (2022) found evidence of intertwined scintillation
from 2 screens; the scintillation pattern of the screen nearby the source is
imprinted onto the screen nearby the Earth, providing additional constraints
on the geometry and extent of the scattering material. Incorporating these
different propagation constraints will help in elucidating FRB host
environments, and determining their progenitors.

## ACKNOWLEDGEMENTS

RAM thanks Vincent Pelgrims for sharing their model of the Local Bubble
surface. We thank the PRECISE team for sharing the dynamic spectra from the
EVN localisation campaign. We thank the staff of the GMRT and Effelsberg who
have made these observations possible. The Effelsberg 100-m telescope is
operated by the Max-Planck-Institut für Radioastronomie. The GMRT is run by
the National Centre for Radio Astrophysics of the Tata Institute of
Fundamental Research. VRM acknowledges the support of the Department of Atomic
Energy, Government of India, under project no. 12-R&D-TFR-5.02-0700. RSW is
supported by an appointment to the NASA Postdoctoral Program at the Jet
Propulsion Laboratory, administered by Oak Ridge Associated Universities under
contract with NASA. Part of this research was carried out at the Jet
Propulsion Laboratory, California Institute of Technology, under a contract
with the National Aeronautics and Space Administration.

## DATA AVAILABILITY

The data underlying this article will be shared on reasonable request to the
corresponding author.

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