11institutetext: ASTRON - the Netherlands Institute for Radio Astronomy, Oude
Hoogeveensedijk 4, 7991PD Dwingeloo, the Netherlands
11email<EMAIL_ADDRESS>22institutetext: Department of Electronic and
Electrical Engineering, University of Bath, Claverton Down, Bath, BA2 7AY, UK
33institutetext: RAL Space, United Kingdom Research and Innovation – Science &
Technology Facilities Council – Rutherford Appleton Laboratory, Harwell
Campus, Oxfordshire, OX11 0QX, UK 44institutetext: Dipartimento di Fisica “G.
Occhialini”, Università di Milano-Bicocca, Piazza della Scienza 3, 20126
Milano, Italy 55institutetext: INFN, Sezione di Milano-Bicocca, Piazza della
Scienza 3, I-20126 Milano, Italy 66institutetext: INAF, Osservatorio
Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius, Italy

# The scintillating tail of comet C/2020 F3 (Neowise)

R.A. Fallows 1133 B. Forte 22 M. Mevius 11 M. A. Brentjens 11 C. G. Bassa 11
M. M. Bisi 33 A. Offringa 11 G. Shaifullah 445566 C. Tiburzi 66 H. Vedantham
11 P. Zucca 11

(Received May 31, 2022; accepted July 31, 2022)

###### Abstract

Context. The occultation of a radio source by the plasma tail of a comet can
be used to probe structure and dynamics in the tail. Such occultations are
rare, and the occurrence of scintillation, caused by small-scale density
variations in the tail, remains somewhat controversial.

Aims. We present a detailed observation taken with the Low-Frequency Array
(LOFAR) of a serendipitous occultation of the compact radio source 3C196 by
the plasma tail of comet C/2020 F3 (Neowise). 3C196 tracked almost
perpendicularly behind the tail, providing a unique profile cut only a short
distance downstream from the cometary nucleus itself.

Methods. Interplanetary scintillation (IPS) is observed as the rapid variation
of the intensity received of a compact radio source due to density variations
in the solar wind. We observed IPS in the signal received from 3C196 for five
hours, covering the full transit behind the plasma tail of comet C/2020 F3
(Neowise) on 16 July 2020, and allowing an assessment of the solar wind in
which the comet and its tail are embedded.

Results. The results reveal a sudden and strong enhancement in scintillation
which is unequivocally attributable to the plasma tail. The strongest
scintillation is associated with the tail boundaries, weaker scintillation is
seen within the tail, and previously unreported periodic variations in
scintillation are noted, possibly associated with individual filaments of
plasma. Furthermore, contributions from the solar wind and comet tail are
separated to measure a sharp decrease in the velocity of material within the
tail, suggesting a steep velocity shear resulting in strong turbulence along
the tail boundary.

###### Key Words.:

Comets: Individual: C/2020 F3 (Neowise) – (Sun:) solar wind – Scattering

##  1 Introduction

Interplanetary scintillation (IPS - Clarke (1964); Hewish et al. (1964)),
observed as the rapid variation of intensity received from a compact radio
source due to density variations in the solar wind, has been used for several
decades to observe the solar wind throughout the inner heliosphere. Such
observations are typically used to measure solar wind velocity (e.g. Coles,
1996; Manoharan & Ananthakrishnan, 1990; Kojima & Kakinuma, 1990), or to use
the strength of the scintillation as a proxy for solar wind density (e.g.
Jackson et al., 1998; Tappin, 1986). The occultation of a radio source by the
plasma tail of a comet provides an opportunity to use this phenomenon to probe
turbulent-scale density structure and dynamics in the tail. However, such
occultations are rare, and the occurrence of scintillation attributable
directly to the tail itself remains somewhat controversial.

Positive results, where scintillation attributable to a comet plasma tail
could be seen, were reported for comets Kohoutek (Ananthakrishnan et al.,
1975), Halley (Alurkar et al., 1986; Slee et al., 1987), Wilson (Slee et al.,
1990), Austin (Janardhan et al., 1991; Prasad, 1994), Schwassmann-Wachmann 3-B
(Roy et al., 2007), and ISON (C/2012 S1) (Iju et al., 2015). However, negative
detections have also been reported for comet Halley by Ananthakrishnan et al.
(1987) and there was some debate over the positive results for this comet
expressed in the correspondence section of Nature (Ananthakrishnan et al.,
1989). Furthermore, Hajivassiliou & Duffett-Smith (1987) questioned all of the
results published prior to their paper, claiming various inconsistencies that
led them to conclude that there was no convincing evidence for enhanced
scintillation due to comet ion tails. Slee et al. (1990) revisited their
earlier results and those of Hajivassiliou & Duffett-Smith (1987) and were
able to account for the majority of the negative detections reported. All of
these results, and the debate surrounding them, illustrate the importance of
being able to unambiguously identify scintillation from the comet tail, and
separate it from contributions from the solar wind in which it sits and, at
lower observing frequencies, the ionosphere.

An opportunity arose on 16 July 2020 to observe an occultation of the strong
radio source 3C196 by the tail of comet C/2020 F3 (Neowise) using the Low-
Frequency Array (LOFAR - van Haarlem et al. (2013). As an instrument with a
large number of stations across western Europe and capable of recording
wideband high-resolution dynamic spectra from each station individually, LOFAR
is ideally suited to observing interplanetary scintillation (Fallows et al.,
2022a) and ionospheric scintillation (Fallows et al., 2020), with ways of
separating the two (Fallows et al., 2016) where necessary; there also exists
the possibility to use the wealth of such data already taken to identify rarer
phenomena. At this time, the nucleus of the comet passed at a closest angular
separation to the radio source of only $0\aas@@fstack{\circ}42$. Furthermore,
the track of 3C196 relative to the comet tail was close to being perpendicular
to the tail, meaning that the result is an almost direct cut across the tail.
This is in marked contrast to almost all prior results, where the radio source
tracks have tended to traverse more along the tail.

The LOFAR observation had a duration of five hours, allowing time both before
and after the occultation for an assessment of background solar wind
conditions, and enabling the additional contribution to the scintillation
pattern from the comet tail to be obvious in the observation. The result is
therefore a unique observation which represents a natural laboratory for
scattering theory, with the results having implications for the wider
interpretation of radio scattering across both interplanetary and ionospheric
scintillation regimes.

##  2 Observation and initial processing

3C196 was observed from 15:30 UT to 19:14 UT on 16 July 2020, covering the
full transit behind the plasma tail of comet C/2020 F3 (Neowise). At this
time, 3C196 was at an elongation of $27\aas@@fstack{\circ}2$ from the Sun and
the comet passed at a closest angular separation to the radio source of only
$0\aas@@fstack{\circ}42$. Figure 1 illustrates the geometry in the
Sun–Earth–line-of-sight plane, and plots the track of 3C196 relative to the
comet in the sky on a photograph taken of the comet on the following evening
(Image credit: Michael Jäger, reproduced with permission).

Figure 1: Top: Geometry of the line of sight to 3C196 relative to the Sun and
comet (not to scale). P represents the point of closest approach of the line
of sight to the Sun. Bottom: Track of 3C196 relative to the comet (blue dashed
line), in the sky plane, overplotted on an image of the comet taken at 20:46
UT on 17 July 2020 by Michael Jäger (reproduced with permission). The green
segment of the track marks the period of enhanced scintillation detailed in
Section 3.

The proposed observation setup was designed to achieve two objectives: one was
to investigate whether or not any refraction of the radio source due to the
plasma tail could be directly detected from an interferometric analysis, and
the other was to assess the intensity scintillation pattern received for any
contribution that could be attributable to it. The first objective required
interferometric data be collected and it was hoped that beamformed data could
be taken simultaneously for the second. Unfortunately, this proved beyond the
limits of the system at that time. The LOFAR data were therefore taken using
only the interferometry mode, recording visibilities (correlated complex
voltages from X- and Y- polarisations) for all stations (core stations, remote
stations with the exception of RS306 and RS509, and international stations
with the exception of PL611) available for observation at the time, with a
time integration of 0.167 s over a bandwidth of 78.125 MHz between 110 and 189
MHz, divided into frequency bins of 12.2 kHz. In LOFAR observation-
specification parlance, this is 400 sub-bands (each 195.3125 kHz wide)
subdivided into 16 channels per sub-band. For the purposes of analysing the
data for intensity scintillation, the visibilities from the auto-correlations
were converted into Stokes intensity via a standard formula, $I=re(XX+YY),$
and averaged to one channel per sub-band by taking the tenth percentile of the
intensities. This has the effect of reducing contributions from radio
frequency interference (RFI) and the resulting intensity dynamic spectra had a
final time resolution of 0.167 s and frequency resolution of 195.3125 kHz, and
were saved to a separate HDF5 file. An intensity dynamic spectrum was also
generated via the same method for visibilities formed from the coherent sum of
all core stations (forming a ‘tied-array beam’ in LOFAR parlance). The raw and
processed visibilities and HDF5 dynamic spectra are stored in the LOFAR long-
term archive111https://lta.lofar.eu/Lofar under project code DDT14_001, where
they are available for download. Whilst it is recognised that this time
resolution is not ideal for interplanetary scintillation, it proved sufficient
in this instance for the analyses described here.

Processing of the intensity dynamic spectra to produce a set of time series
for power spectra calculation and cross-correlation follows the same basic
methods described in Fallows et al. (2022a) and Fallows et al. (2020), with
some minor differences. RFI remaining in the dynamic spectra was identified
using the following steps:-

  * •

Applying a median filter with a [time,frequency] dimension of [3.34 s,1.95
MHz], corresponding to [20,10] data points;

  * •

Subtract the median filtered data from the original to form a flattened array,
normalised to 1.0;

  * •

Calculate the standard deviation of the flattened data about the median;

  * •

Apply a threshold of 20 standard deviations;

  * •

Frequency channels where the mean of normalised RFI-excluded points is less
than 0.8 are flagged in their entirety.

Whilst the threshold might seem quite high, it should be noted that the
standard deviation about the median is a small value and the threshold must be
low enough to exclude the majority of RFI but high enough not to falsely
identify strong peaks in the scintillation intensity pattern. The threshold
multiple of 20 was identified as being reasonable based on trial and error.
The original data, with identified RFI now flagged were detrended in time by
dividing each frequency channel by a third-order polynomial fitted to the
channel data.

The scintillation pattern received at Earth has a drift velocity resulting
from the solar wind flowing in a direction perpendicular to the lines of sight
between radio source and receivers. This drift velocity therefore represents a
line-of-sight integration of solar wind velocity components perpendicular to
the lines of sight. However, as the amount of scattering falls with distance
from the Sun as $R^{-4}$, it is commonly assumed that the drift velocity
corresponds closely to the solar wind velocity around the point of closest
approach of the line of sight to the Sun (the P-point labelled in 1), and this
assumption is broadly reasonable if a single solar wind stream is dominant in
the line of sight. A cross-correlation analysis represents the most accurate
method to calculate the velocity, as detailed in Fallows et al. (2022a) and
references therein.

For the cross-correlation analysis, intensity time series were calculated by
taking the median of the dynamic spectra across the 150-169 MHz section of the
band, chosen such that the intensity structure remains well correlated over
the band and strong interference from digital broadcast signals at the higher
frequencies is excluded. A subset of predominantly international stations
(Core, RS508, DE602, DE603, DE604, DE605, FR606, SE607, UK608, IE613, and
LV614) were used in this analysis; remaining stations were found to have a
higher level of interference which adversely affected the analysis. The
intensity time series were divided into five-minute segments, advanced every
10 s. A high-pass filter at 0.05 Hz (this choice is lower than normally
applied to IPS data, but is justified by the power spectra presented in
subsection 3.3) and low-pass filter at 2.3 Hz were applied to the power
spectra calculated from the time series before cross-correlation.

##  3 Results

###  3.1 Dynamic spectra

Figure 2 shows a dynamic spectrum of the variation in intensity received by
the LOFAR core, along with details of particular features. A period of strong
scintillation lasting nearly 25 minutes is obvious in the figure. The same
pattern is seen in data from all international stations of LOFAR, covering an
area from Ireland to Latvia, which immediately discounts the possibility of
the ionosphere being the source of the enhanced scintillation. Furthermore, no
such short-duration burst of scintillation has been observed in many years of
IPS data taken using LOFAR and other instruments by the primary author,
including during extended observations covering the passage of coronal mass
ejections. Therefore, the plasma tail of the comet is the most likely source
of the scintillation, and this is further indicated by its occurrence
corresponding to the period when 3C196 was immediately downstream from the
comet, as illustrated in Figure 1.

Figure 2: Dynamic spectra of the variation in normalised intensity received by
the LOFAR core. Top: One hour of data showing the obvious enhancement in
scintillation between approximately 16:15 UT and 16:40 UT. Lower left: Two
minutes of data from near the start of the period of enhancement. Lower right:
Two minutes of data from near the end of the period of enhancement.

The majority of the scintillation is visible as a rapid variation that remains
well-correlated across the observing band, but a change is obvious near the
start and end of the period of enhancement (lower plots of Figure 2). Here,
the intensity shows a structure of longer duration, curved towards lower
frequencies, with opposite curvatures of the earlier and later times,
demonstrating that intensity enhancements at the lower frequencies were first
to arrive and last to leave. Similar effects are seen weakly within the period
of enhancement.

###  3.2 Scintillation indices

The scintillation index, a normalised measure of the strength of the
scintillation, can be defined as (Briggs & Parkin, 1963):

$S_{4}^{2}=\frac{\langle I^{2}\rangle-\langle I\rangle^{2}}{\langle
I\rangle^{2}},$ (1)

where $I$ represents the zero-mean normalised intensity fluctuations;
$\langle\rangle$ denotes ensemble averaging, which is substituted by temporal
averaging in the case of experimental observations. Here, $S_{4}$ was
estimated on the basis of the standard deviation of the zero-mean normalised
intensity fluctuations over time intervals of both 5 min and 2 min for all the
radio wave frequencies observed, using the data from the tied-array beam
formed from the core stations. Figure 3 shows a median of indices for
frequencies above 150 MHz.

Figure 3: Scintillation indices calculated for segments of intensity data for
the tied-array beam formed from the core stations averaged over the frequency
band 150-190 MHz, of both 2 min and 5 min duration.

An enhancement in scintillation is obvious between 16:12 and 16:37 UT, showing
a sharp twin-peak structure with a dip in the centre. A periodic structure is
seen in the two-minute indices, which is somewhat averaged out in the five-
minute calculations. This period of enhancement corresponds to the green
segment of track of 3C196 relative to the comet given in Figure 1,
illustrating a strong correspondence with the passage of the plasma tail over
the line of sight.

Figure 4:  $S_{4}$ scintillation index estimated for scintillation occurring
on radio wave frequencies when intersecting comet C/2020 F3 (NEOWISE) and
observed by the tied-array beam formed from the core stations between 15:30
and 17:30 UT on 16 July 2020. Top: S4 calculated over intervals of 5 min.
Bottom: S4 calculated over intervals of 2 min.

This is further illustrated in Figure 4, which shows the S4 indices for all
frequencies observed. The enhancement in the scintillation index $S_{4}$ is
characterised across the observing band by the two main peaks, which
correspond to the intersection of the line of sight with the outer edges of
the plasma tail. However, towards the lower frequencies, the scintillation
indices become stronger (as would be expected within the weak scattering
regime) and the dip in between the two main peaks becomes less distinct.
Indeed the multiple peaks of the two-minute indices almost reach the same
maximum as the main peaks at the lowest frequencies.

###  3.3 Power spectra

Figure 5 shows example power spectra for IE613 (Birr, Ireland) and LV614
(Ventspils, Latvia) for four time intervals, corresponding to times well
before and after the period of enhanced scintillation and of the peaks in
enhanced scintillation.

Figure 5: Power spectra from IE613 (left) and LV614 (right) for time intervals
starting at 16:00 UT, 16:20 UT, 16:35 UT, and 17:00 UT, for five-minute
segments of data averaged over the frequency band 150-169 MHz. The white noise
floor is indicated by the black dotted lines for reference.

The scintillation power below 0.2 Hz increases strongly in the spectra at
16:20 UT and 16:35 UT compared to times before and after for both stations.
Such an increase would normally be assumed to be ionospheric in nature (e.g.
Fallows et al., 2016) but in this case it is present in the power spectra from
all stations simultaneously and only during the period of enhanced
scintillation. Such a phenomenon could not be ionospheric, and so is assumed
to be associated with the comet plasma tail for the purposes of the cross-
correlation analysis. The location of the high-pass filter was therefore moved
from a more usual 0.2 Hz to 0.05 Hz for the cross-correlation analysis.

Given the low level of scintillation observed outside of the period of
enhancement, the radio-wave propagation problem can be approximated during the
period of enhancement by assuming a single phase-changing screen in the comet
tail. In this approach, fluctuations in the refractive index are due to
fluctuations in the spatial distribution of the electron density. A turbulent
distribution of irregularities described through a power-law spatial spectrum
within the phase screen then gives rise to asymptotic behaviour in the power
spectrum of the intensity fluctuations. Thus, the power spectrum of intensity
fluctuations under the assumption of weak scatter typically exhibits a power-
law similar to that of the irregularity spectrum for temporal frequencies
greater than the Fresnel frequency (Equation 2), but approaches,
approximately, a constant for temporal frequencies smaller than the Fresnel
frequency. This results in a characteristic knee in the spectrum at the
Fresnel frequency, given by:

$\nu_{F}=\frac{V^{REL}}{\sqrt{2\lambda z}},$ (2)

where $V^{REL}$ is the relative drift between the ray path and the phase
screen, $\lambda$ is the wavelength of the radio wave, and $z$ is the distance
between the phase screen and the receiver.

By taking the wavelength as 2 m (150 MHz), the distances from Earth to the
phase-changing screens as being 133352260 km (191.6 RSun) to the P-point of
the line of sight and 112499000 km as the distance to the comet at 16:25 UT on
16 July 2020, and $\nu_{F}$ as 0.8 Hz and 0.08 Hz for the solar wind and comet
plasma tail, respectively, a calculation of VREL yields 584 km s-1 for the
solar wind and 54 km s-1 for the plasma tail of the comet. It should be noted
that these calculations become 1012 m s-1 and 101 m s-1 respectively if an
ionospheric distance of 400 km is assumed. Whilst the former is unlikely to be
taken as being reasonable for the mid-latitude ionosphere, the latter could
be, illustrating a case of possible confusion (detailed theoretically in Forte
et al., in press 2022) between scintillation from different possible origins.

###  3.4 Velocity

Components of the baseline length between each pair of stations are calculated
in terms of the radial direction from the Sun, and the direction perpendicular
to it, for the baselines projected onto the sky plane. As the solar wind is
commonly assumed to be radial in direction from the Sun, least-squares fits to
plots of the radial baseline versus the time lag of the peaks of the cross-
correlation functions were performed to estimate velocity for each time
segment through the observation, following the methods detailed in Fallows et
al. (2022a). For the bulk of the observation, these plots show little scatter
after obvious outliers —typically due to segments of poor data from one or
more stations— were excluded, demonstrating a single solar wind velocity.
However, during the period of enhanced scintillation, significant extra
scatter is seen, indicating the presence of a different velocity. Separate
fits were therefore performed, excluding points consistent with the background
solar wind velocity and any obvious further outliers. The results from fits to
both velocities are shown in Figure 6.

Figure 6: Velocity calculated from least-squares fits to plots of radial
baseline versus cross-correlation peak time lag. The velocity calculated for
the background solar wind is plotted in blue, and that for the comet tail in
orange. The range in velocity in each case is the standard deviation
calculated from the fits, although this is too small to be easily visible
here. The grey shaded area represents the period of enhanced scintillation.

A main velocity of around 700 km s-1, consistent with a fast solar wind
stream, is seen throughout the observation, with some variation during the
period of enhanced scintillation. A second velocity at a little over 100 km
s-1 is found only during the period of enhanced scintillation, and was found
to be prominent throughout this period only when the excess power below 0.2 Hz
in the spectra was included in the cross-correlation analysis. If the high-
pass filter was set at a more usual 0.2 Hz this velocity was less obvious,
particularly in the middle of the period of enhanced scintillation.

###  3.5 Intensity interferometry

The primary purpose of interferometry in radio astronomy is to obtain a
detailed image of the radio source or field being observed, which entails
careful calibration for signal delays resulting from variations in the
observing system itself and the effects of propagation through intervening
media. Fallows et al. (2022a) demonstrated that applying the techniques of
intensity interferometry (involving the cross-correlation of signal
intensities instead of complex voltages) can result in the visualisation of
properties related to the turbulent structure giving rise to scintillation
itself. Full details of how this technique is used and applied are given in
that paper and will not be repeated here, but we provide a brief summary
below.

For any time lag in the intensity, cross-correlation functions calculated as
above the corresponding cross-correlation values can be plotted on a spatial
grid with components in the radial direction from the Sun and tangential to
it. Each value is plotted on this grid according to the (radial,tangential)
components of the baseline between the associated pair of stations. Cross-
correlation values at the positive time lag are plotted assuming the baseline
vector is taken in the positive radial direction (i.e. away from the Sun), and
the cross-correlation values at the equivalent negative time lag are
simultaneously plotted assuming the baseline vector is in the negative radial
direction (i.e. towards the Sun). The resulting scatter plot is then contoured
and the contours displayed as the final image, which is henceforth referred to
as a ‘spatial correlation’ image.

Figure 7: Spatial correlation image of zero time-lag values of the intensity
cross-correlation functions, along with the individual data points used to
form it. The minimum and maximum cross-correlation values used in the colour
scale are chosen to saturate the image such that the basic shape is
emphasised.

Example cross-correlation values at zero time lag for 16:00 UT, prior to the
occultation of 3C196 by the comet tail, are given in Figure 7. The minimum and
maximum cross-correlation values used in the colour scale are chosen to
saturate the image such that the basic shape is emphasised, which is what is
important here. This shape is a result of the convolution of the structure of
the radio source itself and that of the spatial spectrum of density
irregularities giving rise to the IPS observed. The individual values used to
form the image are overplotted to illustrate how the contours were formed.
There is a dearth of data points with short baselines, resulting from the fact
that data from several remote stations in the Netherlands were considered too
poor for use, meaning that the central area of the image contains no data.
However, additional structure is not expected in this region for a normal
solar wind and the shape presented here mostly matches that of the solar wind
given in Fallows et al. (2022a).

The remainder of the CCF contains a great deal of additional information when
viewed in spatial plots such as these, and by cycling through all the time
lags, a movie of the spatial cross-correlation can be made that visualises not
only structure but also motion. Figure 8 illustrates this for spatial
correlation images at different time lags for 16:00 UT, and shows how the
structure moves with the solar wind across the field of view. It should be
noted that, although the non-zero time-lag images are less affected by radio
source structure and are therefore more indicative of solar wind density
structure, they are still strongly biased by the available data points used to
form them.

Figure 8: Spatial correlation images at time lags [top to bottom] 0 s, 0.84 s,
and 1.85 s for 16:00 UT.

Figure 9 presents several images at different time lags for 16:15 UT and 16:35
UT, times towards the start and end of the occultation, respectively. These
show a very different structure from that shown in Figure 8 and motion within
the structure cannot be clearly discerned in the images presented. Gaps within
the broad structure remain static and are therefore a result of the available
data points. However, motion is apparent in movies created from images at all
time lags for these times and these are available in the online material. The
movies illustrate both the motion associated with the solar wind, similar to
that shown in Figure 8, and a —less clear but certainly appreciable— slow-
speed motion of material within the broader structure itself.

Figure 9: Spatial correlation images at time lags [top to bottom] 0 s, 3.36 s,
and 6.71 s for [left] 16:15 UT and [right] 16:35 UT. Movies of images at all
available time lags are given in online material.

##  4 Discussion

The results presented show unequivocally that the enhanced scintillation seen
here is a result of scattering through the plasma tail of the comet. It
appears only when the line of sight passes through the tail, is seen by all
LOFAR stations —thus discounting an ionospheric origin—, and is associated
with a second velocity at a little over 100 km s-1, itself far slower than
typically observed in the solar wind at these distances and too fast to be
ionospheric.

The background solar wind stream is fast, at around 700 km s-1, which is
expected given the high heliographic latitude of 66∘ of the point of closest
approach to the Sun of the line of sight at the time. There is some obvious
variation during the period of enhanced scintillation which is not present at
other times; the exact reason can only be postulated at this time, but perhaps
it is a result of some buffeting between the solar wind and the comet tail.
The second velocity has a mean value of 123 km s-1, which is consistent with
the value expected from within the comet tail close to the comet itself. The
location of the comet within the line of sight is known, which means that the
foreshortening of the velocity can be corrected by division by cos(16.8) (the
angle given in Figure 1). This correction is small, increasing the mean value
to 128 km s-1. The physical distance of the line of sight from the comet is
estimated to be $\sim$860 000 km at closest approach. This velocity therefore
fits with what would be expected from spacecraft measurements covering a few
different distances from their respective comets (see e.g. a summary table
presented in Neugebauer et al., 2007), as well as the assumption of Iju et al.
(2015).

In the presence of weak scattering and under the assumption that radio-wave
scintillation is produced from scattering through a single phase-changing
screen, it can be shown that the amount of scintillation is in direct
proportion to the strength of the small-scale variations in density, $\Delta
N_{e}$. This quantity is commonly assumed to be related to the density $N_{e}$
in observations of IPS (e.g. Jackson et al., 1998), but the nature of this
relationship is not exact for all circumstances. Iju et al. (2015) assumed
proportionality between $\Delta N_{e}$ and $N_{e}$ in their estimation of
$N_{e}$ within the tail of comet ISON (C/2012 S1). However, direct spacecraft
measurements of density within the plasma tail (e.g. Bame et al., 1986; Meyer-
Vernet et al., 1986) suggest a very sharp peak in density, and do not indicate
any dip in the centre that could be consistent with the ‘hollow-tube’ plasma
distribution postulated by Bird et al. (1984) and inferred from the $N_{e}$
results of Iju et al. (2015). The curved intensity structure in the dynamic
spectra presented in Figure 2 suggest refraction through the edges of a denser
region of plasma and the application of a simple numerical scattering model
(Boyde et al., 2022) to a single scattering screen with an assumed Gaussian
density structure results in such a curved structure in a dynamic spectrum
(Boyde, private communication). The sharply peaked nature of the scintillation
profile shown here therefore suggests a relation with strong turbulence along
the tail boundary, but the dip in scintillation index between the peaks is
unlikely to be associated with a dip in density, illustrating a case where the
assumed proportionality between $\Delta N_{e}$ and $N_{e}$ breaks down. Given
that the velocity of the tail material remains almost constant and only
detectable within the period of enhanced scintillation, and that the analysis
of white-light measurements of a different comet plasma tail indicate a flow
at solar wind speeds (e.g. Clover et al., 2010), we postulate that a steep
velocity shear exists between the tail boundary and the surrounding solar wind
and that this is the likely cause of the strong turbulence.

The power spectra shown in Figure 5 also show the dual contributions from the
solar wind and the plasma tail, with a low-frequency excess evident from all
stations throughout the period of enhanced scintillation. Under normal
circumstances this excess could easily be confused with an ionospheric
contribution (as illustrated by the Fresnel frequency calculations in Section
3.3 and the theoretical treatment in Forte et al. (in press 2022)),
illustrating the necessity for simultaneous data from multiple, widely spaced
stations and/or observations of additional radio sources not occulted by the
plasma tail to discount this possibility.

The spatial correlation images shown in Figure 9 provide further confirmation
of the comet tail being the source of the enhanced scintillation. The
structure shown, which primarily reflects the small-scale density variations
giving rise to scintillation, shows a highly elongated structure which broadly
matches in direction the elongated tendrils of plasma seen in photographs such
as that given in Figure 1. Furthermore, the spatial correlation structure can
be seen to move across the field of view as the comet itself moves with
respect to the LOFAR lines of sight. In the movies, structure associated with
the background solar wind can be seen propagating quickly out of the field of
view in the same way as can be seen in Figure 8, while further substructure
within the main elongated ribbon can be observed to propagate within it at the
speed calculated for the cometary material. These images illustrate that
material within the plasma tail of the comet is not flowing exactly in a
radial direction away from the Sun, but is slightly off-radial with the flow
orientation being opposite on different sides of the tail. The images at 16:35
UT show a slightly greater orientation with respect to the radial direction
than those at 16:15 UT, which appears to reflect the orientations of plasma
tendrils in the photograph.

##  5 Conclusions

This observation represents a unique combination of highly detailed data from
a world-leading radio telescope and a fortuitous geometry whereby the radio
source cuts an almost direct profile across the plasma tail of the comet. The
effects of scintillation due to the tail itself are unequivocally visible,
enabling us to gain insight into the turbulence within the tail and the
interaction between it and the surrounding solar wind.

The velocity of material within the plasma tail of the comet is found to be
just over 100 km -1 at a distance of approximately 860 000 km downstream from
the comet itself. This velocity is detected simultaneously with the $\sim$700
km -1 of the background fast solar wind and remains constant throughout almost
the entire period of enhanced scintillation.

Scintillation indices show a twin-peak structure indicating strong turbulence
along the tail boundaries. When combined with the velocity information, this
suggests that the turbulence is the result of a strong velocity shear between
the comet tail and the surrounding solar wind. The curved intensity structure
in the dynamic spectra indicate refraction through the edges of a denser
density structure, whereas the dip in scintillation indices between the twin
peaks would typically suggest a density decrease, representing an occasion
where the usual assumption of proportionality between $\Delta N_{e}$ and
$N_{e}$ breaks down.

The spatial correlation images offer a unique view of the turbulent structure,
and further confirm the association of the IPS observed with the comet tail.
The turbulent structure appears highly elongated in off-radial directions,
which appear to match the tendrils of plasma seen in detailed photographs.

The duration of the enhanced scintillation in combination with the known
distance to the comet leads to an estimate of the comet tail diameter of
$\sim$100 000 km. This is a tiny distance compared to the length of the line
of sight through the inner heliosphere ($\sim$2 AU), and yet the comet tail is
both dense enough and turbulent enough to lead to an obvious change in the
observed IPS, at least at this close pass of the comet to the line of sight. A
common assumption in the analysis of scintillation is that the scattering is
due to a ‘thin screen’ in the line of sight, with the line of sight
integration accomplished through the addition of several such screens (e.g.
Coles, 1996). The scintillation from the narrow comet tail presented here can
be pictured as being due to only a single screen in the line of sight, making
this observation a natural laboratory with which to test scattering theory and
associated assumptions applied to observations of radio scintillation covering
any of the interstellar, interplanetary, and ionospheric regimes.

###### Acknowledgements.

This paper is based on data obtained with the International LOFAR Telescope
(ILT) under project code DDT14_001. LOFAR (van Haarlem et al., 2013) is the
Low Frequency Array designed and constructed by ASTRON. It has observing, data
processing, and data storage facilities in several countries, that are owned
by various parties (each with their own funding sources), and that are
collectively operated by the ILT foundation under a joint scientific policy.
The ILT resources have benefitted from the following recent major funding
sources: CNRS-INSU, Observatoire de Paris and Université d’Orléans, France;
BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI), Department of
Business, Enterprise and Innovation (DBEI), Ireland; NWO, The Netherlands; The
Science and Technology Facilities Council, UK; Ministry of Science and Higher
Education, Poland. Two of us (RAF and MMB) were partially supported by the
LOFAR4SW project, funded by the European Community’s Horizon 2020 Programme
H2020 INFRADEV-2017-1 under grant agreement 777442. MMB was also supported in
part by the STFC In-House Research grant to the Space Physics and Operations
Division at UKRI STFC RAL Space. BF was supported by the UK Natural
Environment Research Council (Grant number NE/V002597/1).

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