We present a comprehensive analysis aimed at proving the hypothesis that a train of small-scale features observed by the Wide-field Imager (WISPR) onboard the Parker Solar Probe (PSP) are the signature of a Kelvin–Helmholtz instability (KHI). These features were seen near the flank of a Coronal Mass Ejection (CME) wake between 7.5 Re and 9.5Re, lasting for about 30 minutes. The CME was a slow event, associated with a streamer blowout. We analyzed the size of the eddies and found growth during their evolution while maintaining separation distances and alignment typical of Kelvin–Helmholtz vortexes. We then assessed the magnetic field conditions that would make the observation of such an instability plausible. Two methods were used to cross-check our findings. The measured thickness of the boundary layer supports KHI candidacy, and the estimated linear growth rate suggests nonlinear saturation within the expected timescale. We conclude that a KHI is a plausible explanation for the observed features, and therefore that such instabilities might exist in the low and middle solar corona (within ∼15 Re) and can be detected in white light observations. Their observation, however, might be rare due to stringent conditions like the observer’s proximity, suitable viewing circumstances, magnetic field topology, and flow properties. This study highlights the unique capability of PSP/WISPR in observing such phenomena, especially as PSP perihelia reach closer distances to the Sun.

1. First Direct Imaging of a Kelvin–Helmholtz Instability by PSP/WISPR
Evangelos Paouris1,2
, Guillermo Stenborg2
, Mark G. Linton3
, Angelos Vourlidas2
, Russell A. Howard2
, and
Nour E. Raouafi2
1
George Mason University, 4400 University Drive, Fairfax, VA 22030, USA; epaouris@gmu.edu
2
The Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA
3
US Naval Research Laboratory, Washington, DC 20375, USA
Received 2023 December 10; revised 2024 January 18; accepted 2024 January 22; published 2024 March 27
Abstract
We present a comprehensive analysis aimed at proving the hypothesis that a train of small-scale features observed
by the Wide-field Imager (WISPR) onboard the Parker Solar Probe (PSP) are the signature of a Kelvin–Helmholtz
instability (KHI). These features were seen near the flank of a Coronal Mass Ejection (CME) wake between 7.5 Re
and 9.5 Re, lasting for about 30 minutes. The CME was a slow event, associated with a streamer blowout. We
analyzed the size of the eddies and found growth during their evolution while maintaining separation distances and
alignment typical of Kelvin–Helmholtz vortexes. We then assessed the magnetic field conditions that would make
the observation of such an instability plausible. Two methods were used to cross-check our findings. The measured
thickness of the boundary layer supports KHI candidacy, and the estimated linear growth rate suggests nonlinear
saturation within the expected timescale. We conclude that a KHI is a plausible explanation for the observed
features, and therefore that such instabilities might exist in the low and middle solar corona (within ∼15 Re) and
can be detected in white light observations. Their observation, however, might be rare due to stringent conditions
like the observer’s proximity, suitable viewing circumstances, magnetic field topology, and flow properties. This
study highlights the unique capability of PSP/WISPR in observing such phenomena, especially as PSP perihelia
reach closer distances to the Sun.
Unified Astronomy Thesaurus concepts: The Sun (1693); Solar corona (1483); Solar wind (1534); Solar coronal
mass ejections (310); Heliosphere (711)
1. Introduction
The Parker Solar Probe mission (PSP; Fox et al. 2016;
Raouafi et al. 2023) created a unique opportunity to observe the
environment around the Sun from an exceptionally close
distance with both in situ and remote-sensing instruments. The
remote-sensing instrument onboard PSP is the Wide-field
Imager (WISPR; Vourlidas et al. 2016). It consists of two
white-light telescopes covering a combined angular field of
view (FOV) from 13°
.5 to 108° elongation. The proximity to
the circumsolar structures and sensitivity of the WISPR
telescopes have enabled us to observe the evolution of both
small- and large-scale structures in unprecedented detail. This
is demonstrated by the complexity of the observed features
(e.g., Coronal Mass Ejections, or CMEs, and streamers) and the
increasing clarity of interactions among these features (Howard
et al. 2022). The short lines of sight (LOS), in particular, open
the possibility of studying the behavior of small-scale plasma
features, such as shearing instabilities, hitherto thought
inaccessible to direct imaging of the middle/outer corona.
Several types of instabilities can develop at the boundary
(“shear boundary”) between two plasma flows moving with
different speeds (Chandrasekhar 1961; Lau & Liu 1980). One
of them is known in fluid and gas dynamics as the Kelvin–
Helmholtz instability (KHI; Helmholtz 1868; Kelvin 1871). In
the case of space and astrophysical environments, the
interpretation of the KHI is challenging due to the complexity
of the real topology of the 3D magnetic plasma, the interaction
between the flows and the shocks, the preexisting turbulence,
etc. KHI can be manifested in numerous space plasma
configurations (see, e.g., Miura 1997, and references therein).
In the solar corona, KHI has been predicted, through
simulations, within solar jets (Ni et al. 2017), near jet-like
CMEs (Solanki et al. 2019), and at the boundaries of CMEs
(Gómez et al. 2016; Páez et al. 2017; Syntelis & Antolin 2019).
KHI has been observed in quiescent prominences at heights
below 20 Mm, using data from the Solar Optical Telescope
(SOT; Tsuneta et al. 2008) onboard Hinode (Kosugi et al.
2007) by Berger et al. (2010) and Ryutova et al. (2010). Direct
KHI observations in coronal structures were made possible
with Extreme Ultraviolet (EUV) imaging from the Atmospheric
Imaging Assembly (AIA; Lemen et al. 2012) on the Solar
Dynamics Observatory (SDO; Pesnell et al. 2012). Foullon
et al. (2011) reported vortex-like structures at a CME flank at
distances below 150 Mm from the solar surface. The instability
was detected only in the highest temperature AIA channel
(131 Å EUV bandpass) at 11 MK. Ofman & Thompson (2011)
observed another KHI associated with a CME eruption in six
out of seven AIA EUV channels. They examined vortexes
along a developing coronal dimming region’s perimeter and
found favorable qualitative agreement between observational
features and a 2.5D MHD simulation model of the KHI. Möstl
et al. (2013) reported quasiperiodic vortex-like structures at a
filament boundary of the associated CME observed primarily
on the 304 Å channel of AIA. Li et al. (2018) found a KHI in a
solar blowout jet and analyzed the detailed evolution with data
from the Interface Region Imaging Spectrograph (IRIS; De
Pontieu et al. 2014) mission. Solanki et al. (2019) studied the
blobs from a quiet-Sun blowout jet, in the 171 Å and
304 Å channels, that formed at the edge of a jet and moved
The Astrophysical Journal, 964:139 (15pp), 2024 April 1 https://doi.org/10.3847/1538-4357/ad2208
© 2024. The Author(s). Published by the American Astronomical Society.
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1

2. along the jetʼs spire. These plasma blobs were likely subjected
to the KHI, arising from the interaction between the sheared
motion of the northern part of the blowout jet and the stationary
local plasma in the surrounding area.
Higher in the corona, evidence for fluid instabilities has been
scant. The two reported detections are based on UV spectro-
scopic observations (Telloni et al. 2019, 2022). The first paper
proposes the Rayleigh–Taylor interpretation based on the
wavelet analysis of Lyα intensity fluctuations while the latter
offers some statistical evidence, based on the variance of O IV
line ratios, broadly consistent with the onset of KHI at coronal
hole boundaries. There has been no direct imaging detection of
KHI vortexes or related structures at coronagraphic heights
(say, >2Re) although there is robust in situ evidence from
Solar Orbiter (Müller et al. 2020) of the existence of KH waves
in the solar wind (Kieokaew et al. 2021).
We report here a set of intriguing observations from WISPR
that may be the first direct imaging of plasma instabilities in the
outer corona. Unlike the previous works in EUV/UV
wavelengths, the WISPR observations detected signatures of
KHI structures at much larger heliocentric distances, i.e.,
between 7.5 and 9.5 Re. As they are related to the interaction
between the erupting magnetic flux rope and the adjacent
coronal hole boundary, they may offer important clues on the
interplay between the emerging transient and its ambient
environment. The paper is organized as follows. In Section 2,
we present the WISPR observations, followed by their analysis
in Section 3. Section 4 discusses our findings and, finally, we
draw our conclusions and discuss future work in Section 5.
2. The Observations
Our analysis focuses on a set of small-scale features that
resemble a train of “eddies” observed in the wake of a CME
that was captured by the PSP/WISPR telescopes on 2021
November 19–20. We will refer to these features as “eddies” in
the rest of the paper to avoid confusion when discussing other
imaged features. The eddies were observed close to the
southern flank of the CME between 01:48 UT and 02:33 UT
on November 20. The CME event has been briefly described in
Howard et al. (2022). In Figure 1, we display two snapshots of
the event recorded by the PSP/WISPR inner telescope
(hereafter WISPR-I). All WISPR-I images were processed
with the image-enhancing technique described in Appendix A
of Howard et al. (2022). The technique is referred to as “LW”
processing. The colored asterisks in the left panel mark the two
edges we tracked to characterize the CME kinematics (see
Section 3.1). The region where the plausible signatures of a
KHI are observed is marked with the yellow rectangle in the
right panel. The location is a promising candidate for the
development of shearing instabilities because of its proximity
to the boundary between the CME and the surrounding solar-
wind flows. To characterize the spatial scales involved (e.g.,
radial size, width, and separation of the eddies) we use
exclusively observations from WISPR-I, the only instrument
where the eddies were discernible.
The CME event was also observed by the COR2
coronagraph of the Sun–Earth Connection Coronal and Helio-
spheric Investigation (SECCHI) suite (Howard et al. 2008)
onboard the Solar TErrestrial RElations Observatory (STEREO)
mission (Kaiser et al. 2008) and by the Large Angle and
Spectroscopic Coronagraph (LASCO, Brueckner et al. 1995)
onboard the Solar and Heliospheric Observatory (SOHO,
Domingo et al. 1995). The data from these instruments and
WISPR were used for the 3D reconstruction of the CME (see
Section 3.1). In Figure 2, we display in the Heliospheric Earth
ecliptic (HEE) system the position of PSP and the directions of
STEREO-A (ST-A) and Earth (SOHO) at the time of the CME
passage through the WISPR-I FOV. The blue, dashed lines
delimit the estimated half-angular width (i.e., about 18°) of the
CME as reconstructed with the Graduated Cylindrical Shell
Figure 1. The CME on 2021 November 20 at 00:03:20 UT and 02:18:20 UT as observed by WISPR-I. The asterisks mark the two features (Feature A in yellow and
Feature B in cyan) used to characterize the CME kinematics. The yellow, rectangular box points out the region where the plausible signatures of a KHI were observed.
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3. model (GCS, Thernisien et al. 2006; Thernisien 2011, see
Section 3.1) and the light gray shading area bordered with solid
red lines depicts the FOV of WISPR-I. The orbit of PSP is
depicted with the orange curve, while the position of the
perihelion for Encounter 10 on 2021 November 21 at 08:23 UT
is the orange diamond. The region where the electron scattering
efficiency along the LOS is around maximum, i.e., near the
Thomson sphere (Vourlidas & Howard 2006) is represented with
the gray circle.
To investigate whether the development of a KHI was
possible in the region of interest, the kinematical properties of
the features are needed for comparison with the ambient solar
wind. Likewise, geometrical parameters like size and distance
are also critical for the assessment. In the next section, we
report on the results of the CME forward modeling to
determine the CME deprojected trajectory, the kinematics
analysis of the CME and features of interest, and the
determination of the geometrical parameters of the eddies.
3. Analysis
3.1. The CME on 2021 November 19-20
The event was a slow CME (∼200 km s−1
; see its kinematic
characterization later in this section) that propagated along a
preexisting streamer and disrupted it. The CME entered the
WISPR-I FOV at 16:33:20 UT on 19 November 2021. The
evolution of the event can be seen in the movie available on the
summary page of encounter 10 on the WISPR web page:
https://wispr.nrl.navy.mil/wisprdata. The CME resembles a
circular structure composed of concentric loops. To reconstruct
the 3D CME flux-rope structure and estimate its direction
of propagation we used the GCS model with combined
observations obtained on November 19 at about 22:30 UT
from the three remote-sensing instruments (i.e., SOHO/
LASCO, STEREO-A/COR2, and WISPR-I).
From the GCS reconstruction, we estimated that the CME
propagated radially in a direction with a Carrington longitude
of 20° and latitude of 10°. The CME was slightly tilted by −7°
with a half-angular width4
of about 18°. The apex height was at
12.9 Re at 22:30 UT. The parameters we obtained with the
GCS reconstruction are in agreement with the ones presented
by McComas et al. (2023) using images one hour later
(∼23:30 UT). According to McComas et al. (2023) the PSP
spacecraft intercepted the southern flank of the CME trail
during the period between November 20 at 23:00 UT and
November 21 at 01:00 UT.
For the CME kinematics, we tracked two different features.
They are marked in the left panel of Figure 1 as Point A, below
the leading edge, and Point B, on the inner part of the CME at
the same position angle as Point A (yellow and cyan asterisks,
respectively). Point A is visible from November 19,
18:03:25 UT to November 20, 01:48:20 UT, and Point B from
November 19, 21:18:20 UT to November 20, 03:33:20 UT.
Using the GCS reconstruction and the known heliocentric
distance of the spacecraft (S/C) at the time of each observation,
we can obtain the deprojected kinematics with a simple
geometrical transformation. In the top panel of Figure 3, we
display the resulting height-time (HT) plot for the features
marked with the points A (diamonds) and B (circles). The blue,
dashed lines delimit the spatial region where the eddy train was
later observed (gray-shaded area). The red and black dots
depict the HT measurements of a few such eddies (see
Section 3.2 for a detailed explanation). The HT profiles for
features A and B are rather similar, with initial speeds
(acceleration) from a ballistic model of about 182 km s−1
(2.0 m s−2
) and 211 km s−1
(1.8 m s−2
), respectively. The
models are depicted with the dark and light green lines,
respectively. This result (combined with the visual examination
of the CME development) indicates that the CME would be
gradually contracting along the radial direction, without
exhibiting any discernible deformation and/or distortion during
the time period under analysis. In the lower panel of Figure 3,
we display the magnitude of the average velocity vector of the
two features as a function of distance (in orange color). The
shaded band delimits the range of speeds between the speed
profiles of each individual feature.
The CME transit across the combined FOV of the two
WISPR telescopes lasted for more than 24 hr. The slow speed
and clear magnetic flux-rope morphology point toward a
streamer-blowout event (Vourlidas et al. 2013; Vourlidas &
Webb 2018). The CME propagated right through the center of
the preexisting streamer disrupting it (see also Howard et al.
2022), as evidenced by the lack of emission behind the CME at
that latitude. To shed light on the CME initiation, we examined
wavelet-processed images5
(Stenborg et al. 2008) from the
Extreme UltraViolet Imager (EUVI; Wülser et al. 2007, one of
the telescopes in the SECCHI suite) onboard STEREO-A. A
filamentary structure emerging around November 18 at
∼04:00 UT from an area above the west limb of the solar
Figure 2. PSP position (red star) on 2021 November 20 at 02:30 UT in the
Heliocentric Earth Ecliptic (HEE) coordinate system. The CME angular width
(dashed blue lines) and direction of propagation (solid blue line), as defined by
the GCS reconstruction, are also indicated. The direction of ST-A (Earth) is
indicated with the solid magenta (green) line. The PSP orbit is depicted with
the orange line and its perihelion is represented with the orange diamond. The
FOV of WISPR-I is represented by the light gray-shaded region bordered with
solid red lines. The projection of the Thomson surface is delineated with a gray
circle.
4
From the GCS modeling, the CME exhibited an aspect ratio, κ, of ∼0.18;
and a half angle, α, of ∼8° (for a detailed description of the GCS parameters
see Thernisien 2011).
5
The wavelet-processed ST-A/EUVI images for the whole STEREO mission
are available at http://sd-www.jhuapl.edu/secchi/wavelets/.
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4. disk was observed in the images. After almost 35 hours on
November 19 at ∼15:00 UT this structure left the FOV of
EUVI. These times are in agreement with the white-light
observations from ST-A/COR2 where the broadening of the
streamer appeared around 11:30 UT and the CME was not
visible before November 19, 16:00 UT. This long-duration
process is definitely not a surprising one and is typical for very
slow streamer-blowout CMEs (Vourlidas & Webb 2018).
Magnetograms and SDO/AIA observations reinforce our
assessment that there is no visible active region on the surface
of the Sun on the northwest part that could be associated with
the CME.
3.2. White-light Signatures of the Plausible KHI
3.2.1. Spatial, Temporal, and Kinematic Characteristics
In Figure 4, we display six instances of the CME aftermath
in the region delimited by the yellow rectangle in Figure 1. The
yellow arrows in panels (C) through (E) point to the vortex-like
structures we hypothesize are the signatures of a KHI. We see
Figure 3. CME kinematics. Top panel: WISPR-I height-time plot (deprojected) for CME features A (diamonds), B (circles), and for features labeled v1 (red dots) and
v2 (black dots; see Figure 4). The dark and light green lines depict the second-degree polynomial used to estimate the speed profiles. The gray-shaded box indicates the
time-lapse and radial range covered when the train of eddies was visible. Lower panel: CME deprojected speed (VCME−j, j = A, B) as a function of heliocentric
distance for features A and B (dark and light green lines, respectively), and for their average (orange line). Extrapolated values are shown with the red dashed lines.
The orange line delineates the average speed, which we used as the speed of the CME bulk, and the gray-shaded area is the uncertainty. In both panels, the blue,
dashed lines indicate the radial distance range where the eddies were observed (between 7.5 Re and 9.5 Re).
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5. in the figure that these features, labeled as vi (i = 1,K,6),
appear in a wave-like pattern. To shed light on their physical
nature, we measure (i) the relative distance between their
centers, (ii) their sizes, and (iii) their speeds. The first plausible
appearance of v1 in the FOV of WISPR-I was at 01:33:20 UT
(panel (B)). We say “plausible” because it could barely be
spotted due to the high degree of signal contamination from
dust debris (i.e., dust particles impacting the S/C and
producing debris that is recorded by the detector; see, e.g.,
Zimmerman et al. 2021; Malaspina et al. 2022). In the frame at
01:48:20 UT (panel (C)), we distinguish the first two vortex-
like features (v1 and v2) possibly at the maximum of their
Figure 4. WISPR images focusing on the area where the eddies were observed. Their first and last appearance occurred on November 20 at 01:48:20 UT (panel (C))
and 02:33:20 UT (panel (E)), respectively. The eddies were clearly captured only in three WISPR-I frames. The images at 01:33:20 UT and 02:03:20 UT were
excluded from the analysis because they were largely affected by the effect of dust particles impacting PSP, i.e., production of debris that cross the WISPR-I FOV,
resulting in streaks that contaminate the background scene.
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6. growth. In the frame at 02:18:20 UT (panel (D)), four more
vortex-like features have appeared (v3 to v6). Features v1 and v2
appear to have deformed, which we hypothesize is an
indication of the lifetime of the instability, their shapes now
more resembling a typical Kelvin–Helmholtz vortex. The
direction of the eddies, which is counterclockwise, matches, as
expected, a situation with faster solar wind below and a slower
CME flow above. In the following frame at 02:33:20 UT (panel
(E)), the first four eddies are further deformed and, hence, it is
difficult to discern them without considering the previous
frame. Thus, it is not possible to make any measurements for
the first four eddies in this frame. Finally, in the last displayed
frame at 02:48:20 UT (panel (F)), all the eddies that were
previously observable have now deformed or dissipated to the
extent that they are no longer distinguishable at the resolution
of the images. Instead, what remains is a thin, continuous
region of plasma (indicated with two yellow arrows in each
direction) that is no longer visible in the next frame.
Numerous extended features are visible in the area
surrounding the eddies, making it challenging to distinguish
the boundaries between the CME and the ambient solar wind.
This is a common issue for the interpretation of white-light
images. However, in our case, several factors contributed to the
identification of the position of the eddies with these
boundaries. These factors include the 3D CME reconstruction
with the GCS model, the CME’s orientation as discussed
earlier, the spacecraft’s proximity to the CME, and the clear
view below the CME (as discussed in Section 4.2). Moreover,
within the CME itself, there are no velocity differences that are
comparable to the velocity differences between the CME and
the solar wind. In summary, the location of the thin line of
plasma in the image results from a projection effect of their
actual position in 3D space due to the optically thin nature of
the recorded signal. Collectively, all these elements support our
perspective that the eddies are located on the boundary of
the CME.
Since all the features exhibited a rather elliptical shape, to
characterize the typical scales involved, we measured the
length of the major and minor axes (the major axis is along the
propagation direction, while the minor axis is perpendicular to
this direction). Briefly, to objectively measure the longitudinal
and transversal size of the eddies (i.e., the length of the major
and minor axes, respectively), we plotted (not shown here) the
brightness profile along slits placed over the eddies in both
selected directions. After detrending the brightness and
deprojecting their location, we fitted them with an appropriate
polynomial function (a seventh-degree polynomial function
resulted in the smallest fitting errors while avoiding over-
fitting). We adopt the width of the modeled profiles at half
maximum as the sizes of the eddies. For each structure, we
repeated the measurement process N times (N > 10) varying
the slit position. The values obtained, which we report in
Table 1, correspond to the average of all measurements for any
given feature at any given time instance, with the standard
deviation (inside parentheses) indicating the dispersion of the
corresponding individual measurements. Note that in the frame
(C) the first appearance of v1 and v2 occurs, while the other
eddies are not visible yet, thus the corresponding cells in
Table 1 are intentionally left empty. In frame (D), all the eddies
are visible while, in frame (E), the deformation of the eddies v1
to v4 makes any attempt for a reliable measurement impossible.
From the time-lapse considered, we estimate that the lifetime of
the eddies (i.e., the temporal period) is less than 30 minutes.
To measure the separation between the features, we analyzed
the brightness profile in a slit placed (visually) along their
radial direction of propagation. The procedure was repeated N
times (N > 10), each time with a new visually selected slit
position. For each instance, we plotted the brightness profile as
a function of distance to the origin of the slit (the closest point
to the inner edge of the WISPR-I FOV) and applied a low-pass
filter to reduce the noise. In the left panel of Figure 5, we
display one such instance, the black circles depicting the excess
brightness and the blue line the low-pass filtered signal. The
magenta circles pinpoint the relative maxima, which are
representative of the centroids of the small-scale features.
The actual positions of the centroids on the respective WISPR-I
image in row and column coordinates are displayed on the right
panel. Then, we estimated the separation of the eddies as the
distance between adjacent centroids, d[vi,vi+1], at each
instance. In Table 2, we report the corresponding average
values and their dispersion (between parentheses) as estimated
by the standard deviation. The relative distance of the centroids
ranges between 169 and 306 Mm with an average value equal
to 237.5 Mm and a standard deviation of 58.6 Mm. The finding
of varying distances between the centroids of the eddies is not a
surprise. The specific spacing and arrangement of vortices in a
Kelvin–Helmholtz instability are complex and can vary
depending on various physical conditions and system para-
meters, including a combination of factors related to the fluid or
plasma properties, the velocity shear, and external forces or
magnetic fields (see, e.g., Thorpe 1971; Hwang et al. 2022).
Varying distances between the vortices have been noted in
observations (e.g., Möstl et al. 2013; Li et al. 2018) and in
simulations (e.g., Möstl et al. 2013; Kieokaew et al. 2021).
The eddies labeled v1 and v2 are the only ones that could be
tracked in three frames. The deformation of the eddies in the
last frame influences the measurements of their size, including
minor and major axis lengths. However, despite this deforma-
tion, the eddies remain visible for kinematic analysis. There-
fore, the kinematics analysis of the small-scale features that we
Table 1
Average Sizes (in Mm) of the Minor (top row) and Major (lower row) Axis of Observed Eddies
Time Frame v1 v2 v3 v4 v5 v6
01:48:20 UT (C) 80 (10) 89 (6) L L L L
158 (16) 146 (15) L L L L
02:18:20 UT (D) 114 (11) 117 (8) 52 (5) 40 (7) 39 (5) 36 (6)
174 (15) 167 (13) 81 (14) 92 (8) 95 (10) 104 (14)
02:33:20 UT (E) L L L L 54 (4) 47 (4)
L L L L 101 (10) 109 (12)
Note. The 1σ standard deviation is reported inside parenthesis.
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7. hypothesize are the signature of KHI was carried out only for
these two eddies. In spite of the limited measurements, we
applied a linear fit to their deprojected height-time measure-
ments and obtained a speed of ∼370 km s−1
. The eddies were
observed near the southern flank of the CME. This leads
consequently to the logical assumption that if they are a
signature of a KHI, the ambient solar wind beneath the CME
had to be flowing with a different speed. In the PSP/WISPR
movie for Encounter 10 (available on the WISPR home page),
we observe density inhomogeneities (which we associate with
tracers of the ambient solar wind) beneath the flank of the
CME, clearly moving faster than the eddies. To characterize the
kinematics of their development, we computed the average
speed of the flow in this region by tracking a feature that is
clearly and unambiguously visible a few hours later. This
feature entered the FOV of WISPR-I on November 20 at
∼06:33 UT. We tracked it up to ∼08:33 UT (i.e., in nine
frames) and found a linear, deprojected speed of ∼410 km s−1
.
In brief, as recorded on WISPR-I images, the deprojected,
average linear speed of the CME, train of eddies, and feature
outside the post-CME flow (i.e., a tracer of the solar wind) were
estimated at approximately 200 km s−1
, 370 km s−1
, and
410 km s−1
, respectively.
3.3. Theoretical Frame for the Development of a KHI
KHI has been observed primarily in EUV observations from
SDO/AIA at low-corona distances during the early stages of
CME formation (Foullon et al. 2011; Ofman & Thomp-
son 2011; Möstl et al. 2013). Páez et al. (2017) discussed the
possibility of KHI formation in the mid and outer corona, in
particular at heliocentric distances between 4 and 30 Re. In our
work, we assess the possibility that WISPR actually observed a
KHI in the wake of a CME, in particular, near its southern
flank, at heliocentric distances between 7.5 and 9.5 Re.
In our approach, we consider the case where the wavevector,
k̂, is parallel to the flows, namely to both the CME and the
ambient solar wind, which can be stabilized by the flow-aligned
magnetic field. For our case, we need to study the magnetic
field and density environment along the shear flow, for an
incompressible plasma without viscosity and in a thin layer
with an external magnetic field. Therefore, to evaluate where a
KHI can develop, we utilize the KHI magnetic condition as
proposed in Michael (1955) and Chandrasekhar (1961):
[ˆ · ( )] [(ˆ · ) (ˆ · ) ] ( )
p
- >
+
+
k V V k B k B
n n
m n n
4
, 1
1 2
2 1 2
p 1 2
1
2
2
2
where V1 and V2 are the velocities, n1 and n2 are the number
densities, B1 and B2 are the magnetic fields of the two
magnetized plasma flows, mp is the proton mass, and k̂ is the
wavevector of the shear flow. Equation (1) represents the
condition that is necessary for the development of the KHI in
the boundary layer between the two flows, considering that the
thickness of the boundary layer is negligible (i.e., Δ = 0), as
long as the left-hand side is greater than the right-hand side.
In the following, we investigate the constraints on the 2021
November 19 CME magnetic field as a function of distance
from the Sun that are required to create favorable conditions for
the formation of a KHI. To this aim, we follow a similar
methodology as in Páez et al. (2017).
The 2021 November 19 CME was a slow event, slower than
the ambient solar wind, and as a result, no shock or sheath
region around the CME was observed (Howard et al. 2022). In
Figure 6, we present a cartoon with a simplified view of the
CME and the fast ambient solar-wind environment (top panel),
and the magnetic configuration of the KHI on the CME flanks
(lower panel). In particular, in the lower panel, we display a
vertical cut of the helical magnetic field structure of the CME
where the dark blue arrows represent the outward and inward
magnetic field polarities on the plane of the image. For our case
study, in the region between the CME flanks and the ambient
solar wind, Equation (1) becomes:
( )
[ˆ · ( )] [(ˆ · ) (ˆ · ) ]
p
- >
+
+
2
k V V k B k B
n n
m n n
4
.
SW CME
2 SW CME
p SW CME
SW
2
CME
2
The term ˆ ·
k BCME on the right-hand side of Equation (2) can
be decomposed in two terms to account for the poloidal, BCME
Pol
,
and toroidal, BCME
Tor
, components of the CME magnetic field,
Figure 5. Determination of the eddy centroids. Left panel: excess brightness profile (black dots) along a slit covering the train of eddies on the WISPR-I image taken
on 2021 November 20 at 02:18 UT. The blue curve depicts the low-pass filtered profile used for the determination of the relative maxima. The magenta dots point out
the relative maxima, which are representative of the position of the centroids of the eddies. Right panel: estimated centroid locations (magenta dots) on the
corresponding cropped WISPR-I image.
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The Astrophysical Journal, 964:139 (15pp), 2024 April 1 Paouris et al.

8. i.e.,:
ˆ · ˆ · ˆ · ( )
= +
k B k B k B . 3
CME CME
Pol
CME
Tor
As shown in Figure 6 (lower panel), BCME
Pol
is perpendicular
to the shear flow k̂. Therefore, this term is zero, and hence it
does not affect the formation of the KHI (Chandrasekhar 1961).
On the other hand, since BCME
Tor
is parallel to k̂, the term
ˆ ·
k BCME
Tor
is the relevant one for the formation of the KHI.
Then, we can take this radial component equal to the CME
radial magnetic field, i.e.,
ˆ · ˆ · ( )
= =
k B k B B . 4
r
CME CME
Tor
CME,
Since both VSW and VCME are parallel to k̂, the left side of
Equation (2) can be defined as a shear function, S(r):
( ) ∣ ( ) ∣ ( )
= -
S r V V r , 5
SW CME
S(r) represents the shear flow between the CME and the
ambient solar wind. In our case, the solar-wind speed, as
estimated from a solar-wind tracer, was assumed to be constant
(∼410 km s−1
, see Section 3.2.1). On the other hand, the CME
speed, as estimated from two particular features of the bulk of
the CME (features A and B in Figure 1; see Section 3.1) was
found to exhibit a slight acceleration trend during its
development, varying from ∼175 km s−1
at a distance of
5 Re up to ∼290 km s−1
at 25 Re.
With the above constraints, we can transform Equation (2)
into a parametric form. To that aim, as we do not know the
actual values of the magnetic field and density of both the CME
and ambient solar wind, we define the ratios ξn =
n
n
CME
SW
and
x =
B
B
B
r
SW r
CME,
,
. Here, the solar-wind magnetic field is all in the
radial direction, so, BSW,r = BSW. Using these ratios in
Equation (2) and solving it for BCME,r, we obtain the parametric
form:
( ) ( ) ·
·
( ) · ( )
· ( )
( )
p
x x
x x
<
+ +
B r m n r S r
4
1 1
.
6
r
n B
n B
CME,
KH
p SW
2
2
Equation (6) shows that by just expressing the unknown
CME field and density values in units of the solar-wind
counterparts, we can estimate the magnetic field values of the
CME, B r
CME,
KH
, that might be favorable for the development of a
KHI. In particular, we note that B r
CME,
KH
depends on (1) the
density of the ambient solar wind, nSW(r); (2) the shear flow
function, S(r); and (3) the CME relative magnetic field strength
and density with respect to those of the solar wind, ξB and ξn.
To estimate the density of the ambient solar wind, nSW(r), we
use the Leblanc density model (Leblanc et al. 1998):
( ) ( · · · )
( )
= + +
- - -
n r d r r r
3.3 10 4.1 10 8.0 10 ,
7
SW
5 2 6 4 7 6
*
where d is the scaling factor. The scaling factor is used to
normalize the Leblanc density model to the instantaneous value
of the in situ density measurement obtained from the Advanced
Composition Explorer Solar Wind Electron, Proton, and Alpha
Monitor (ACE SWEPAM; McComas et al. 1998) instrument.
This allowed us to approximate the density value close to the
Sun following Thernisien & Howard (2006). Since the CME
event was associated with a streamer blowout, we scale the
model as in Thernisien & Howard (2006; i.e., d = 6.0). The
values resulting from this approach are within the density range
estimated from several electron density models close to a
coronal streamer (see, e.g., Figure 1 in Raouafi 2011 and
references therein).
The CME observed is denser than the ambient solar wind
(nCME > nSW). Hence, for the following parametric analysis,
we assume ξn = 2 (this choice is discussed in Section 4), and
ξB = j, with j = 1, 2, 3, q (q ? 1). Note that with ξB = 1
(ξB = q), we are assuming that the CME has a magnetic field
similar to (much larger than) that of the solar wind. This
represents a lower (upper) limit, for the ξn = 2 scenario, hence
constraining the range of possible B r
CME,
KH
. In the top panel of
Figure 7, we plot the output of the parametric analysis
(Equation (6)) for the cases mentioned above and the density
model considered. The continuous lines delineate B r
CME,
KH
at the
limit cases when the two sides of Equation (6) are equal. For
comparison, we also plot with the dashed, magenta line the
CME magnetic radial evolution assuming a power-law curve of
the form Br ∝ 1/r2
(see, e.g., Patsourakos & Georgoulis 2016,
and references therein) from a PSP/FIELDS in situ measure-
ment of the radial component of the magnetic field (∼550 nT,
magenta star) when PSP was at ∼14.1 Re and intersected with
the leg of the CME (November 20 23:00–November 21 01:00,
McComas et al. 2023). It must be noted that this in situ
magnetic field measurement was not taken at the time/location
when/where the eddies were observed but rather one day later.
This estimate of the CME magnetic field at lower coronal
heights is a valid approach. However, it should not be regarded
as the actual magnetic field of the CME at the boundary layer
where the eddies were observed. We also include two cases
representative of different scenarios: the very simple case
assuming ξn = ξB=1 (light green line) and the extreme case
where ξn = ξB=q, with q ?1 (light blue line). These two cases
serve as the boundaries of our analysis, representing the lower
and upper limits of the outputs from Equation (6). The area
delimited by the two vertical, blue dashed lines depicts the
distance range where the train of eddies was observed, i.e.,
between 7.5 Re and 9.5 Re. Therefore, the graded, shaded area
(ξB>1) indicates the range of B r
CME,
KH
values that support our
hypothesis (i.e., that the train of eddies observed is a signature
of a KHI instability). The graph shows, in brief, that the
assumptions taken lead to a case that can explain the
occurrence of the KHI. In fact, the top panel of Figure 7
clearly indicates an increase in instability with larger radii. At
Table 2
Relative Distance (in Mm) between the Centroids of the Eddies
Time Frame d[v1, v2] d[v2, v3] d[v3, v4] d[v4, v5] d[v5, v6]
01:48:20 UT (C) 278 (10) L L L
02:18:20 UT (D) 296 (17) 211 (11) 185 (6) 306 (10) 173 (8)
02:33:20 UT (E) 282 (21) L L L 169 (6)
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9. 5 Re, the magenta dashed curve is positioned above all
unstable curves, indicating stability under every tested condi-
tion. However, at 25 Re, it is situated below all curves except
for ξn = ξB = 1, signifying instability under all conditions
except that one.
To put our result in context, in the lower panel of Figure 7
(same color and labeling code), we display the output of the
parametric analysis considering the Leblanc density model
scaled by d = 0.54 to match the in situ density values measured
by PSP one day later at ∼14.1 Re. In this case, the graph shows
that, with this scaling of the density model, the conditions
would not be favorable for the development of a KHI.
Note that if we rearrange Equation (6) with the magnetic
field and density on the same side (and write =
B B
r r
CME,
KH
and
nSW = n), we get the relation between the Alfvén speed and
the shear flow function S(r):
( )
( )
( )
·
( ) · ( )
· ( ) ( )
p
x x
x x
º <
+ +
B r
m n r
V r S r
4 1 1
. 8
r
p
A
n B
n B
2
2
Equation (8) provides another way to examine the favorable
conditions for the development of the KHI by comparing the
Alfvén speed and the shear flow function S(r) as a function of
the ratios ξn and ξB. If we use the PSP in situ measurements at
∼14.1 Re (i.e., Br ∼ 500 nT and n ∼ 950 cm−3
) we get an
Alfvén speed of about 350 km s−1
, which is much higher than
the right part of Equation (8). This shows that the formation of
a KHI is rather sensitive to local conditions. This explains why
we cannot observe the eddies one day later (see Section 4.2).
According to McComas et al. (2023), PSP crossed the leg of
the CME between November 20, 23:00 UT and November 21,
01:00 UT, i.e., for a period of about 2 hr. PSP in situ
measurements of the electron density by the Solar Wind
Electrons Alphas and Protons (SWEAP) Investigation (Kasper
et al. 2016) before this interaction averaged a number density
of ∼950 cm−3
. Inside the CME, the density amounted to
∼ 1800 cm−3
(i.e., ξn ≈ 2). Note that the PSP measurements
were obtained at a distance of ∼14.1 Re, almost a day after the
observations of the eddies; therefore, they can be considered
only as a rough estimate of the density conditions at the
location of the eddies.
Among other cases, in Figure 7, we plotted Equation (6) for
various ξB considering ξn = 2. In particular, we explored the
CME magnetic field constraints for the development of KHI
assuming a scaling factor in the Leblanc density model as in
Thernisien & Howard (2006; i.e., d = 6.0; Figure 7 top panel).
Next, we considered a scaling factor d ≈ 0.5 to match the
in situ PSP/SWEAP density measurements when PSP crossed
the CME leg (Figure 7 lower panel). Now, we explore the case
when the density model is scaled such that the in situ PSP/
FIELDS measurements of the CME magnetic field match the
magnetic field constraints from Equation (6). The average
in situ PSP/FIELDS values of the magnetic field before the
interaction of PSP and the CME was ∼500 nT, and slightly
higher at ∼550 nT while inside the CME. By considering this
Figure 6. Top panel: 2D cartoon of the CME propagating in the solar wind. The candidate region favorable for the development of the KHI is at the flank of the CME.
The dark blue outward arrows with dotted gray inward lines represent the helical magnetic structure of the CME, enveloped by the ambient solar-wind magnetic field
(blue lines). The magenta arrow depicts the toroidal magnetic field. The direction of the shear flow close to the CME flanks is indicated with the vector k̂. Lower panel:
zoom-in of the region to detail the magnetic configuration. The helical magnetic field structure of the CME is represented with dark blue arrows for the outward
polarity starting from the lower of the orange rectangular box (indicating a part of the CME close to the flank) and ending in the top part of the box between the
symbols e and ⊗. The gray dashed arrows depict the inward polarity. The CME’s magnetic field BCME is decomposed into a poloidal (BCME
Pol
, in red) and a toroidal
(BCME
Tor
, in magenta) component. The ambient solar-wind magnetic field BSW is represented with the blue color lines.
9
The Astrophysical Journal, 964:139 (15pp), 2024 April 1 Paouris et al.

10. approach, we are assuming that the in situ PSP measurements
of the magnetic field (although they were taken one day later in
a region of space far away from the eddies location), serve as a
ground truth. Note, however, that, while this assumption is
speculative and not representative of the conditions where the
eddies were observed (see also Section 3.3), it might represent
a plausible approximation. These two values of the magnetic
field indicate ξB ≈ 1 while ξn = 2 (this set is represented by the
red line in Figure 7). We extrapolated them to shorter distances
assuming flux conservation, resulting in values 1915/1190 nT
of the magnetic field in the distance range where the eddies
were observed at 7.5/9.5 Re, respectively. To infer the
minimum density required for instability under these condi-
tions, the Leblanc density model must be scaled accordingly so
that this red line matches the extrapolated magnetic field of the
CME (i.e., the magenta dashed) at the distance where the
eddies were observed (i.e., between the vertical blue dashed
lines). To achieve this, the scaling factor becomes d ∼ 14.6.
This new case is illustrated in Figure 8. From our approach,
considering ξn = 2 and ξB = 1, we have that the KHI criterion is
Figure 7. CME magnetic field constraints for the development of KHI (Equation (6)). Top panel: assuming a scaling factor d in the Leblanc density model
(Equation (7)) as in Thernisien & Howard (2006; i.e., d = 6.0). Lower panel: assuming d ≈ 0.5 to match the in situ PSP/SWEAP (Kasper et al. 2016) density
measurements when PSP crossed the leg of the CME (S/C at ∼14.1 R☉, between November 20 23:00 UT and November 21 01:00 UT). The colored, continuous lines
delineate Equation (6) when both sides are equal for x = = 1, 2
n
n
n
CME
SW
and x = = q
1, 2, 3,
B
B
B
r
CME,
SW
(q ? 1). The magenta star depicts the magnetic field value
measured by the PSP/FIELDS (Bale et al. 2016) when PSP crossed the leg of the CME and the dashed, magenta line the 1/r2
extrapolation. The shaded, blue area
depicts the range of plausible B r
CME,
KH
in the heliocentric range where the train of eddies was observed.
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11. satisfied for CME magnetic fields less than 1915/1350 nT at
7.5/9.5 Re, respectively. The newly scaled density model
results in very high density values, so we shed light on this fact
by comparing it to instances of high density values recorded by
PSP. For example, the highest density measured by PSP up to
Orbit 15 (as obtained using the simplified quasi-thermal noise
spectroscopic technique or SQTN; Moncuquet et al. 2020) was
∼2.13 · 104
cm−3
. This measurement occurred on 2022 June 2
at approximately 14:10 UT when the S/C was at ∼15.8 Re.
This case is considered here as a special case and definitely not
assumed as typical of a background solar wind. The newly
scaled density model (d ∼ 14.6) predicts, at the corresponding
distance, a density value of ∼2.0 · 104
cm−3
, which is a
comparable estimate (∼7% lower) and certainly is not a
nonphysical estimate. As the CME under study was associated
with a streamer blowout, we expect that the compression of the
already dense plasma from the streamer becomes denser as the
CME develops. Consequently, this results in a higher local
density, favoring the formation of a KHI.
4. Discussion
4.1. Theoretical Support for the KHI Interpretation
In this work, we investigate the possibility that a train of
small vortex-like structures, detected in the aftermath of a
CME, are the signatures of Kelvin–Helmholtz instability. To
assess the likelihood of such a physical phenomenon, we
compare the measured dynamical and kinematic properties of
the eddies against theoretical expectations under certain
assumptions.
The relative distance between the centroids of the vortexes is
considered to be the characteristic length scale for the associated
projected wavelength, or spatial period λ. In many KHI
simulations or observations in solar coronal physics, the
wavelength estimates are on the order of a few megameters. In
particular, Foullon et al. (2011) reported a projected wavelength
of λ = 18 ± 0.4 Mm. Möstl et al. (2013) mentioned that the
vortex-like structures, which were observed at the northern side
of the embedded filament boundary of the 2011 February 24
CME, had a wavelength of approximately λ ∼14.4 Mm. Ofman
& Thompson (2011) reported a wavelength of λ = 7 Mm based
on the size of the initial ripples. Li et al. (2018) observed a KHI
in a solar blowout jet with a λ ∼5 Mm. All of the
aforementioned studies estimated the wavelength based on
EUV observations at low coronal heights (< 160 Mm).
Kieokaew et al. (2021) reported a KHI analysis based on
in situ measurements from Solar Orbiter. Their wavelength
estimates, λ = 66.4 ± 8.4 Mm, are larger than the coronal one.
We estimate a wavelength average of λ = 237.5 (58.6) Mm
based on the distances between the eddies (Table 2).
A key discriminant for a KHI is the wavelength of the fastest
growing mode. The fastest growing mode excited by a KHI at
the interface should have a spatial period, or wavelength λ,
between 2πΔ and 4πΔ (Miura & Pritchett 1982), where Δ is
the thickness of the boundary layer. Equation (6) was obtained
under the assumption of a boundary layer of zero thickness. We
can now relax this assumption. From the WISPR-I images, we
can estimate both Δ and λ independently. If the eddies are
signatures of KHI, they should satisfy the relation
2πΔ < λ < 4πΔ. If not, then the eddies are not a KHI
signature. In general, it is challenging to estimate Δ from
imaging observations due to the small scales involved. Thanks
to the proximity to the CME, WISPR-I resolves many small-
scale details. In particular, at 02:48:20 UT all the vortexes are
fully deformed, creating a thin line of plasma (Figure 4, panel
(F)). We take the width of this line, Δobs = 28 (7) Mm as the
upper limit of the boundary layer thickness. Therefore the
wavelength of the fastest growing mode should lie between
2πΔ = 176 Mm and 4πΔ = 352 Mm. From the observations,
we estimate λ as the relative distance between the vortexes
Figure 8. CME magnetic field constraints for the development of KHI (Equation (6)). Same as in Figure 7 for a Leblanc density model with scaling factor d ∼ 14.6
chosen to match the extrapolated magnetic field of the CME at 7.5 R☉ where the eddies were observed. Note that the extrapolated magnetic field values (magenta
dashed curve) are positioned below the most probable unstable case with ξn = 2 and ξB = 1 (red curve) indicating that is favorable for the development of the KHI. For
details, see the text.
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12. (169–306 Mm, see also Table 2), with an average value of
237.5 Mm. Thus, the observed λ satisfies the condition of the
fastest growing KH mode for most cases, which, in turn,
supports our hypothesis that the observed eddies are the results
of the development of a KHI.
Another physical parameter to check for the plausibility of a
KHI is the growth rate. The linear growth rate of a KHI in
incompressible, inviscid fluid layers with equal density, equal
field strength, separated discontinuously within a “vortex
sheet” (Chandrasekhar 1961; Frank et al. 1996), associated
with, and which leads to, the KHI criterion (Equation (1)), is
given by:
∣ · ∣[ ( ˆ · ˆ) (ˆ · ) ] ( )
g = D - D
k V k B k V
V
1
2
1 2 , 9
A
2 2 1 2
where the k is the wavevector whose magnitude is equal to 2π/
λ, Δ V is the velocity difference between the two layers
(i.e., the shear flow function S(r) defined in Equation (5)) and
VA is the Alfvén speed (see Equation (8)). In the case of an
interface region with finite thickness, the growth rate is even
smaller than the predicted value according to Equation (9) (see,
e.g., Miura & Pritchett 1982; Ofman & Thompson 2011).
Compressible plasma also tends to reduce the growth of the
instability. Based on the parameters we estimated before we
can compute the upper and lower limit values of the linear
growth rate of the KHI using Equation (9). If we use an Alfvén
speed range between 20 and 65 km s−1
(see Section 4.2 for
details), k = 2π/λ with λ the average value of 237.5 Mm, and
ΔV ∼200 km s−1
, we get, from Equation (9), upper and lower
γKH values of 0.0027 and 0.0022 s−1
, respectively. If we
assume that nonlinear saturation occurs on a timescale of a few
γ−1
(see, e.g., Kieokaew et al. 2021), which ranges in our case
from ∼6.1 to 7.6 minutes, the observed timescale evolution of
the eddies recorded in WISPR-I images (less than 30 minutes)
falls within the expected values. Table 3 compares various KHI
parameters from past works against the estimates described in
this section.
4.2. Modeling Support for the KHI Interpretation
According to Equation (8), the formation of a KHI is
possible if ΔV >2 · VA (Miura & Pritchett 1982), where ΔV is
the shear flow function S(r) (Equation (5)) and VA is the Alfvén
speed (Equation (8)), assuming equal densities (i.e., ξn = 1) and
magnetic fields (i.e., ξB = 1). With existing instrumentation, it
is impossible to measure the actual density and magnetic field,
and by extension VA, at the heliocentric distances where the
plausible KHI was observed (7.5 Re–9.5 Re). Since we know S
(r) for this region (lower panel of Figure 3), we can, provide an
upper limit on VA <
1
2
S(r)∼100 km s−1
for the onset of a
plausible KHI. This value appears to be low for such
heliocentric distances, especially for a CME-related feature.
However, we note that this speed corresponds to the
component parallel to the flow. It is conceivable that the
Alfvén speed perpendicular to the flow is much higher, leading
to a higher overall VA. An obvious scenario would be the
propagation of a curved magnetic structure in a parallel flow.
Figure 1 (and the movie available on the web at the WISPR
home page) indicate that the structures surrounding the area of
interest are indeed curved as they seem to form the lower
extensions of the helical structures comprising the CME
magnetic flux rope.
An alternative way to explore the constraints of the Alfvén
speed is to use the output of a model for this specific date. To
that aim, we utilize the thermodynamic MHD code “Magneto-
hydrodynamic Algorithm outside a Sphere” (MAS), which was
developed by and is maintained at Predictive Science Inc. (see,
e.g., Riley et al. 2012, and references therein). The VA as
estimated with the MAS model for Carrington rotation 2251 at
a distance of 8.43 Re (i.e., at a distance within the distance
range where the eddies were observed) is displayed in the top
panel of Figure 9. The propagation direction of the CME on
2021 November 20 at ∼02:00 UT (i.e., during the time of the
eddies) as estimated with the GCS model (Carrington longitude
and latitude of 20° and 10°, respectively; Section 3.1) is
indicated with the magenta star symbol. We notice in the figure
that VA for the ambient solar wind near the CME is
<30 km s−1
. The propagation direction of the CME is almost
above the location of the heliospheric current sheet (HCS) and
as a result, the very low Alfvén speeds at these positions are
reasonable. This result provides another supporting evidence
for our hypothesis.
Recently, Verbeke et al. (2023) showed that the error in
determining the longitude and latitude of a CME direction
using the GCS model when two or three viewpoints is
approximately 2°. Thus, to assess the effect of our estimate of
the CME direction, we consider this error in the lower panel of
Figure 9. For all the combinations of these two coordinates
available, we created the VA radial profiles for the ambient solar
wind, which we display in the lower panel of Figure 9 with the
Table 3
Comparison of Critical Parameters Estimates on Selected Observations of KHI among Different Works Including Ours
Publication Observations Wavelength λ Thickness Δ Growth Rate γ Heliocentric Distance
(Mm) (Mm) (s−1
) (Re)
Foullon et al. (2013) EUVa
18.5 4.1 0.033 < 1.22
Möstl et al. (2013) EUVa
14.4 1–2 L L
Ofman & Thompson (2011) EUVa
7 0.4 0.003–0.009 L
Li et al. (2018) EUVb
5 0.5 0.063 L
Kieokaew et al. (2021) in situc
66.4 5.3–10.5 0.0015 148.3
This work White Lightd
237.5 28 0.0022–0.0027 7.5–9.5
Notes.
a
[SDO/AIA].
b
[IRIS].
c
[Solar Orbiter/MAG,SWA].
d
[PSP/WISPR-I].
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13. light blue lines. In this case, VA is Š75 km s−1
at 7.5 Re and
Š55 km s−1
at 9.5 Re. For a more ample case, we also assumed
ad hoc a larger error (5°, represented by the gray lines). The red
line represents the radial profile considering the direction of
propagation of the CME, and the dashed green line represents
the limit condition VA =
1
3
S(r) for ξn = 2 and ξB = 1
(Equation (8)). The magenta curve represents the VA assuming
ξn = ξB=1 (as in Miura & Pritchett 1982). The black star
symbol represents the Alfvén speed calculated using the
extrapolated magnetic field Br and density values similar to
the values used in Figure 8. We note that, in the range where
the eddies are observed (delimited by the dashed blue lines), all
the VA radial profiles satisfy Equation (8), regardless of the
error, and hence support our hypothesis.
This condition perhaps offers an indication of why KHI
observations are rare at these heights. From our analysis, it
becomes clear that the development of a KHI (and its
observation in white light) requires a combination of conditions
to be in place:
1. two flows with varying speeds;
2. an unusually low Alfvén speed or an interaction geometry
leading to a weak parallel and strong perpendicular VA
components relative to the flow to satisfy the
Equation (8);
Figure 9. Top panel: Alfvén speed, VA, on a Carrington projection (rotation 2251) from the MAS model at 8.43 Re. The propagation direction of the CME on 2021
November 20 at 02:00 UT is pointed out with the magenta star symbol (i.e., about the time the eddies were observed). This direction is very close to the heliospheric
current sheet (delineated with the white line). The local Alfvén speeds in this area are very low (of the order of 30 km s−1
). Lower panel: VA radial profiles from the
MAS model for the Carrington longitude and latitude of the CME considering a 2° (in light blue) and a 5° (in gray) error. The red line represents the radial profile
considering the CME direction of propagation, and the dashed green line represents the limit condition VA =
1
3
S(r) for ξn = 2 and ξB = 1 (Equation (8)). The
magenta line depicts VA assuming ξn = ξB=1 (as in Miura & Pritchett 1982). The black star symbol represents the Alfvén speed calculated using the extrapolated
magnetic field values Br (magenta dashed line in Figure 8). The blue dashed vertical lines indicate the distance range where the eddies were observed (7.5 Re–9.5 Re).
13
The Astrophysical Journal, 964:139 (15pp), 2024 April 1 Paouris et al.

14. 3. short LOS imaging observations to resolve small scales
(PSP is the only platform capable of providing this
vantage point so far; therefore, it is unsurprising that
white-light signatures of KHI have not been detected
before).
4. favorable viewing conditions, in addition to short LOS.
The location of PSP below the CME plane offered a
favorable viewing angle for observing the complex CME
structure across a wide longitude and further avoiding
LOS overlap. Furthermore, PSP was transiting over a
coronal hole region at the time, and hence the WISPR-I
LOS was crossing through a partially depleted region,
resulting in a “cleaner” LOS. Stenborg et al. (2023)
recently showed that the presence of even small
equatorial Coronal Holes (CHs) can directly affect the
overall brightness observed by WISPR-I. This is another
argument in support of the assumption that the ambient
solar wind below the CME has a larger speed than
the CME.
As a final thought, the 2021 November 19 CME was associated
with a streamer blowout (Howard et al. 2022), and originated in a
quiet-Sun region. Therefore, it must have had lower magnetic field
strengths than CMEs associated with active regions (Vourlidas &
Webb 2018). Thus, the weak magnetic obstacle in combination
with the orientation of the magnetic field could have been
favorable for the formation of a KHI.
5. Summary and Conclusions
In this paper, we examined the possibility that a train of
small-scale features observed by WISPR-I was the signature of
a KHI. To test this hypothesis, we performed a comprehensive
theoretical and observational analysis. Candidate KHI features
were observed along the southern flank of a CME between
7.5 Re and 9.5 Re and lasted about 30 minutes. The kinematic
analysis of the CME indicated a slow event, most likely
associated with a streamer blowout, developing with a
(deprojected) speed of ∼200 km s−1
. By measuring the speed
of solar-wind tracers, we estimated the speed of the ambient
solar wind to be ∼410 km s−1
. On the basis of KHI theoretical
considerations, we investigated the magnetic field conditions
and estimated the values favorable for the development of a
KHI under certain assumptions. We found that a KHI
interpretation is reasonable under certain conditions. For
instance, assuming that the extrapolated values of the magnetic
field values recorded by PSP/FIELDS at 14.1 Re are a
reasonable choice at lower heights, then the KHI occurs
1. if the magnetic field strength of the CME6
and ambient
wind are similar while the density of the CME is higher
(i.e., ξB = 1 and ξn = 2; red line in Figure 8);
2. if the magnetic field strength of the CME is larger than
that of the ambient solar wind (i.e., ξB > 1; all cases in
Figure 8).
In both cases, high local densities are required (Leblanc
model scaled by a factor of d ∼ 14.6). On the other hand, if we
ignore the constraint imposed by the magnetic field measure-
ments at 14.1 Re, and simply assume a Leblanc model scaled
by a factor that can be considered typical of a streamer (d = 6),
then the KHI occurs for various combinations of ξB and ξn
(Figure 7, top panel).7
Furthermore, we used the MAS model to estimate the Alfvén
speed, VA, in the distance range where the eddies were
observed. In all the cases considered (Figure 9) the modeled VA
satisfies the criterion for the development of the KHI
(Equation (8)).
We also measured the longitudinal and transverse size of the
vortex-like features via a technique that offers an objective
estimation. From these measurements, we showed that the
eddies increased in size while maintaining a relatively constant
separation distance. These characteristics are consistent with
the evolution of Kelvin–Helmholtz vortexes and hence are in
support of our hypothesis.
To further evaluate our interpretation, we used the following
approach. First, we measured the thickness of the boundary
layer along which the KHI candidate signatures were observed
(∼28 Mm). This is probably an upper limit to the true
thickness. Then, we consider that the wavelength, λ, of the
fastest growing mode at the interface should lie between 2πΔ
and 4πΔ (Miura & Pritchett 1982). In fact, we found that λ lies
between 176 and 352 Mm and these values are in agreement
with the relative distances between the eddies we measured in
WISPR-I images. These two independent quantities, measured
using WISPR-I images, satisfy the relation 2πΔ < λ < 4πΔ
(Miura & Pritchett 1982), thereby supporting our hypothesis
that the observed eddies are signatures of KHI.
Assuming equal densities and magnetic fields (i.e., ξn = 1
and ξB = 1), we estimated a linear growth rate of the KHI, γ,
between ∼0.0022 and ∼0.0027 s−1
. Since nonlinear saturation
occurs within a few γ−1
, this also determines the lifetime of
KHI. The WISPR features lasted ∼30 minutes, which
corresponds to about 6γ − 8γ and hence is consistent with
the KHI interpretation.
The comparisons between theoretical expectations and
observational estimates of the properties of these vortex-like
features lead us to conclude that they are consistent with KHIs.
This marks the first direct imaging of such plasma phenomena
in the middle corona (r < 15 Re). If it is verified with additional
detections and theoretical/modeling analysis, it will open a
new observing window into coronal plasma dynamics. The
study of plasma instabilities may help understand the role of
viscosity in CME development and propagation. Finally, the
dimensions of the KHI, as presented in our study, coupled with
the intricate structures discerned within CMEs in WISPR
images, underscore the significance of further investigation into
mesoscale structures (a few tens to 2000–3000 Mm). However,
such observations are likely exceedingly rare given the
requirement of appropriate physical conditions, i.e., the
observer’s proximity to the region, favorable viewing condi-
tions, the topology and orientation of the local magnetic fields,
and the necessary combination of the densities and speeds of
the different flows. On the other hand, PSP/WISPR offers a
unique, possibly the only, means to image such events
especially as the PSP continues to approach closer to the Sun.
Acknowledgments
The authors thank A. Kouloumvakos and V. Jagarlamudi for
useful discussions. E.P. was supported by NASA grant
6
Magnetic field Š1915/1350 nT at 7.5/9.5 Re, respectively.
7
For example, in the simplest approach of ξB = ξn=1, the KHI occurs for
CME magnetic fields Š1060/750 nT at 7.5/9.5 Re.
14
The Astrophysical Journal, 964:139 (15pp), 2024 April 1 Paouris et al.

15. 80NSSC19K0069. G.S., A.V., and R.H. were supported by
WISPR Phase E funds and NASA grant 80NSSC22K0970. M.
G.L. was supported by WISPR Phase E funds under NASA
grant NNG11EK11I and by the NASA Living with a Star
Focused Science Topic program NNH21ZDA001NLWS “The
Origin of the Photospheric Magnetic Field: Mapping Currents
in the Chromosphere and Corona” (PI P. Schuck). Parker Solar
Probe was designed, built, and is now operated by the Johns
Hopkins Applied Physics Laboratory as part of NASAʼs Living
with a Star (LWS) program (contract NNN06AA01C). Support
from the LWS management and technical team has played a
critical role in the success of the Parker Solar Probe mission.
The Wide-Field Imager for Parker Solar Probe (WISPR)
instrument was designed, built, and is now operated by the U.S.
Naval Research Laboratory in collaboration with JHU Applied
Physics Laboratory, California Institute of Technology/Jet
Propulsion Laboratory, University of Goettingen, Germany,
Centre Spatiale de Liege, Belgium, and University of
Toulouse/Research Institute in Astrophysics and Planetology.
The STEREO SECCHI data are produced by a consortium of
RAL (UK), NRL (USA), LMSAL (USA), GSFC (USA), MPS
(Germany), CSL (Belgium), IOTA (France), and IAS (France).
The FIELDS instrument suite was designed and built and is
operated by a consortium of institutions including the
University of California, Berkeley, University of Minnesota,
University of Colorado, Boulder, NASA/GSFC, CNRS/
LPC2E, University of New Hampshire, University of Mary-
land, UCLA, IFRU, Observatoire de Meudon, Imperial College
and Queen Mary University, London. The SWEAP Invest-
igation is a multi-institution project led by the Smithsonian
Astrophysical Observatory in Cambridge, Massachusetts.
Other members of the SWEAP team come from the University
of Michigan, University of California, Berkeley Space Sciences
Laboratory, the NASA Marshall Space Flight Center, the
University of Alabama Huntsville, the Massachusetts Institute
of Technology, Los Alamos National Laboratory, Draper
Laboratory, JHU Applied Physics Laboratory, and NASA
Goddard Space Flight Center.
ORCID iDs
Evangelos Paouris https:/
/orcid.org/0000-0002-8387-5202
Guillermo Stenborg https:/
/orcid.org/0000-0001-
8480-947X
Mark G. Linton https:/
/orcid.org/0000-0002-4459-7510
Angelos Vourlidas https:/
/orcid.org/0000-0002-8164-5948
Russell A. Howard https:/
/orcid.org/0000-0001-9027-8249
Nour E. Raouafi https:/
/orcid.org/0000-0003-2409-3742
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