# On the Mesoscale Structure of CMEs at Mercury’s Orbit:
BepiColombo and Parker Solar Probe Observations

Erika Palmerio Predictive Science Inc., San Diego, CA 92121, USA  Fernando
Carcaboso Postdoctoral Program Fellow, NASA Goddard Space Flight Center,
Greenbelt, MD 20771, USA  Leng Ying Khoo Department of Astrophysical Sciences,
Princeton University, Princeton, NJ 08544, USA  Tarik M. Salman Heliophysics
Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Department of Physics and Astronomy, George Mason University, Fairfax, VA
22030, USA  Beatriz Sánchez-Cano School of Physics and Astronomy, University
of Leicester, LE1 7RH Leicester, UK  Benjamin J. Lynch Space Sciences
Laboratory, University of California, Berkeley, CA 94720, USA  Department of
Earth, Planetary, and Space Sciences, University of California, Los Angeles,
CA 90095, USA  Yeimy J. Rivera Center for Astrophysics, Harvard & Smithsonian,
Cambridge, MA 02138, USA  Sanchita Pal Postdoctoral Program Fellow, NASA
Goddard Space Flight Center, Greenbelt, MD 20771, USA  Teresa Nieves-
Chinchilla Heliophysics Science Division, NASA Goddard Space Flight Center,
Greenbelt, MD 20771, USA  Andreas J. Weiss Postdoctoral Program Fellow, NASA
Goddard Space Flight Center, Greenbelt, MD 20771, USA  David Lario
Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA  Johannes Z. D. Mieth Institut für Geophysik und extraterrestrische
Physik, TU Braunschweig, D-38106 Braunschweig, Germany  Daniel Heyner Institut
für Geophysik und extraterrestrische Physik, TU Braunschweig, D-38106
Braunschweig, Germany  Michael L. Stevens Center for Astrophysics, Harvard &
Smithsonian, Cambridge, MA 02138, USA  Orlando M. Romeo Space Sciences
Laboratory, University of California, Berkeley, CA 94720, USA  Department of
Earth and Planetary Science, University of California, Berkeley, CA 94720, USA
Andrei N. Zhukov Solar–Terrestrial Centre of Excellence—SIDC, Royal
Observatory of Belgium, B-1180 Brussels, Belgium  Skobeltsyn Institute of
Nuclear Physics, Moscow State University, 119991 Moscow, Russia  Luciano
Rodriguez Solar–Terrestrial Centre of Excellence—SIDC, Royal Observatory of
Belgium, B-1180 Brussels, Belgium  Christina O. Lee Space Sciences Laboratory,
University of California, Berkeley, CA 94720, USA  Christina M. S. Cohen
California Institute of Technology, Pasadena, CA 91125, USA  Laura Rodríguez-
García European Space Astronomy Centre, European Space Agency, E-28692
Villanueva de la Cañada, Madrid, Spain  Universidad de Alcalá, Space Research
Group (SRG-UAH), E-28801 Alcalá de Henares, Madrid, Spain  Phyllis L.
Whittlesey Space Sciences Laboratory, University of California, Berkeley, CA
94720, USA  Nina Dresing Department of Physics and Astronomy, University of
Turku, FI-20014 Turku, Finland  Philipp Oleynik Department of Physics and
Astronomy, University of Turku, FI-20014 Turku, Finland  Immanuel C. Jebaraj
Department of Physics and Astronomy, University of Turku, FI-20014 Turku,
Finland  David Fischer Space Research Institute, Austrian Academy of Sciences,
A-8042 Graz, Austria  Daniel Schmid Space Research Institute, Austrian Academy
of Sciences, A-8042 Graz, Austria  Ingo Richter Institut für Geophysik und
extraterrestrische Physik, TU Braunschweig, D-38106 Braunschweig, Germany
Hans-Ulrich Auster Institut für Geophysik und extraterrestrische Physik, TU
Braunschweig, D-38106 Braunschweig, Germany  Federico Fraschetti Center for
Astrophysics, Harvard & Smithsonian, Cambridge, MA 02138, USA  Department of
Planetary Sciences, Lunar and Planetary Lab, Tucson, AZ 85721, USA  Marilena
Mierla Solar–Terrestrial Centre of Excellence—SIDC, Royal Observatory of
Belgium, B-1180 Brussels, Belgium  Institute of Geodynamics of the Romanian
Academy, 020032 Bucharest-37, Romania

(Received October 25, 2023; Revised December 20, 2023; Accepted January 2,
2024)

###### Abstract

On 2022 February 15, an impressive filament eruption was observed off the
solar eastern limb from three remote-sensing viewpoints, namely Earth,
STEREO-A, and Solar Orbiter. In addition to representing the most-distant
observed filament at extreme ultraviolet wavelengths—captured by Solar
Orbiter’s field of view extending to above 6 $R_{\odot}$—this event was also
associated with the release of a fast ($\sim$2200 km$\cdot$s-1) coronal mass
ejection (CME) that was directed towards BepiColombo and Parker Solar Probe.
These two probes were separated by 2∘ in latitude, 4∘ in longitude, and 0.03
au in radial distance around the time of the CME-driven shock arrival in situ.
The relative proximity of the two probes to each other and to the Sun
($\sim$0.35 au) allows us to study the mesoscale structure of CMEs at
Mercury’s orbit for the first time. We analyse similarities and differences in
the main CME-related structures measured at the two locations, namely the
interplanetary shock, the sheath region, and the magnetic ejecta. We find
that, despite the separation between the two spacecraft being well within the
typical uncertainties associated with determination of CME geometric
parameters from remote-sensing observations, the two sets of in-situ
measurements display some profound differences that make understanding of the
overall 3D CME structure particularly challenging. Finally, we discuss our
findings within the context of space weather at Mercury’s distances and in
terms of the need to investigate solar transients via spacecraft
constellations with small separations, which has been gaining significant
attention during recent years.

Solar filament eruptions (1981); Solar coronal mass ejections (310);
Interplanetary magnetic fields (824); Interplanetary shocks (829)

††journal: ApJ††facilities: Bepi (MPO-MAG); GOES (SUVI); Parker (FIELDS,
SWEAP, WISPR); SOHO (LASCO); SolO (EUI); STEREO (SECCHI)††software: AstroPy
(Astropy Collaboration et al., 2022); SolarSoft (Freeland & Handy, 1998);
SunPy (SunPy Community et al., 2020)

##  1 Introduction

Coronal mass ejections (CMEs) can be enumerated amongst the most spectacular
and energetic events in the solar system, consisting of enormous clouds of
plasma and magnetic fields that are frequently launched from the Sun into the
heliosphere. As they travel (and expand) through the solar corona and
interplanetary space, CMEs can experience a myriad of processes, including
deflection (e.g., Wang et al., 2004; Liewer et al., 2015; Cécere et al.,
2020), rotation (e.g., Yurchyshyn et al., 2007; Vourlidas et al., 2011;
Thompson et al., 2012), erosion (e.g., Dasso et al., 2007; Ruffenach et al.,
2012; Pal et al., 2021), and deformation (e.g., Savani et al., 2010; Barnard
et al., 2017; Braga et al., 2022) due to e.g. interaction with the structured
solar wind (e.g., Isavnin et al., 2013; Heinemann et al., 2019; Davies et al.,
2021; Maunder et al., 2022) or other CMEs (e.g., Lugaz et al., 2012; Lugaz &
Farrugia, 2014; Temmer et al., 2014; Kilpua et al., 2019a). By the time they
reach 1 au, CMEs measure on average ${\sim}$0.3 au in radial size (e.g., Jian
et al., 2018) and may have lost their coherence as magnetohydrodynamic
structures (e.g., Owens et al., 2017). The plethora of phenomena that can act
on a CME as it journeys away from the Sun may result in structures encountered
in situ that are especially difficult to interpret, and even properties such
as geoeffectiveness can be altered significantly during propagation due to
these evolutionary processes (e.g., Lavraud et al., 2014; Möstl et al., 2015;
Liu et al., 2018; Scolini et al., 2020; Winslow et al., 2021; Palmerio et al.,
2022a).

Indeed, determination of the global 3D structure of CMEs from in-situ
measurements, each representing a single 1D trajectory through a humongous
plasma cloud, is not a trivial task even in the case of “simpler” situations
in which a CME is propagating more or less radially and self-similarly. In
this context, multi-point measurements can provide extra constraints on the
local structure of a CME at different points throughout its angular extent.
The power of multi-spacecraft observations of CMEs in situ has been known for
several decades (e.g., Burlaga et al., 1981), and because of data availability
over the recent years, multi-probe studies have been gaining increasing
attention. However, most multi-point measurements are attained over arbitrary
radial and angular separations of the spacecraft involved (e.g., Davies et
al., 2022; Möstl et al., 2022; Rodríguez-García et al., 2022), making it
particularly difficult to attribute structural and compositional differences
of the investigated CMEs to radial evolution, to longitudinal (local)
variations, or to both. Even more so, difficulties only increase as CMEs are
probed beyond 1 au and towards the outer heliosphere, mainly due to heightened
chances of interactions and mergers of initially-separated structures (e.g.,
Rodriguez et al., 2008; Witasse et al., 2017; Palmerio et al., 2021).
Nevertheless, there are some “special” cases of spacecraft configurations that
are of particular interest for CME studies, i.e. those that involve small
longitudinal separations, allowing focussed analyses on radial evolution
(e.g., Good et al., 2019; Vršnak et al., 2019; Salman et al., 2020), or small
radial separations, permitting investigations of the overall structure at one
snapshot in time (e.g., Kilpua et al., 2009; Farrugia et al., 2011; Lugaz et
al., 2022).

An additional “special” case in terms of relative spacecraft configurations
takes place when the probes involved are characterised by small longitudinal
and radial separations at the same time, thus providing the opportunity to
examine the mesoscale structure of CMEs. Such relative arrangements are rare
to attain fortuitously, but a few studies have taken advantage of a number of
favourable periods featuring pairs of probes that happened to orbit close to
each other in near-Earth space. For example, Lugaz et al. (2018) and Ala-Lahti
et al. (2020) analysed variations in the magnetic ejecta (for 21 events) and
sheath region (for 29 events) structures, respectively, observed by spacecraft
that were separated by ${\lesssim}$0.01 au in absolute distance. Lugaz et al.
(2018) found that, in the case of CME ejecta, the magnetic field magnitude has
typical scale lengths of longitudinal magnetic coherence of 0.25–0.35 au
(corresponding to 14–20∘ at 1 au), whilst the single magnetic components
maintain their coherence over scales of 0.06–0.12 au (corresponding to 3–7∘ at
1 au). On the other hand, Ala-Lahti et al. (2020) found that, in the case of
CME-driven sheaths, the largest scale of coherence is achieved by the
east–west component of the magnetic field, with values lying around
${\sim}$0.15 au (corresponding to ${\sim}$9∘ at 1 au), whilst the magnetic
field magnitude and the remaining components have typical scale lengths of
0.02–0.04 au (corresponding to 1–2∘ at 1 au). Other studies that investigated
the magnetic configuration of CMEs over relatively short spatial scales at the
heliocentric distance of ${\sim}$1 au include that of Davies et al. (2021),
who analysed a single event and did not report significant differences in the
structure observed at two spacecraft separated by ${\sim}$0.02 au radially and
${\sim}$1∘ longitudinally.

It is clear from the studies mentioned above that, in the context of CME
research, the mesoscale region of the parameter space—defined by Lugaz et al.
(2018) as the critical region characterised by radial separations of
0.005–0.050 au and angular separations of of 1–12∘—is left largely unexplored
to this day, especially considering that all investigations to date have been
possible only via measurements collected at Earth’s orbit. In this work, we
analyse in detail the in-situ structure of the 2022 February 15 CME. This
eruption has already gained attention in the heliophysics community because it
represents the most-distant filament observed at extreme ultra-violet (EUV)
wavelengths (Mierla et al., 2022), but the scientific significance of this
event goes beyond its exceptional remote-sensing measurements. In fact, the
CME associated with this eruption was seen in situ by BepiColombo (Bepi;
Benkhoff et al., 2021) and Parker Solar Probe (Parker; Fox et al., 2016),
which were relatively close to each other and only $\sim$0.35 au away from the
Sun (see Figure 1). Hence, the 2022 February 15 CME represents the first
occasion to investigate the mesoscale structure of CMEs at Mercury’s orbit.
The work presented here consists of a detailed analysis of the shock, sheath
region, and magnetic ejecta observed at the two spacecraft, and aims to
enhance our current understanding of the structure and evolution of CMEs at
relatively early stages of their journey through interplanetary space.

Figure 1: Position of planets and spacecraft within 1 AU from the Sun on 2022
February 15 at 21:45 UT, i.e. around the CME eruption time. The propagation
direction of the CME inferred from 3D reconstructions of the eruption in the
corona is indicated with an arrow. The orbits of Mercury, Venus, and Earth are
also shown.

##  2 Overview of the 2022 February 15 Eruption

In this section, we provide a brief overview of the remote-sensing
observations associated with the 2022 February 15 eruption, in both the EUV
and white-light (WL) regimes. For an in-depth discussion of the various sub-
structures that can be identified in the available multi-spacecraft imagery,
we direct the reader to Mierla et al. (2022).

###  2.1 Extreme-ultra-violet Observations

Figure 2: The 2022 February 15 filament eruption at ${\sim}$22:00 UT as
observed in EUV (304 Å channel) from the available viewpoints. (a)
STEREO/SECCHI/EUVI-A data. (b) SolO/EUI/FSI data. (c) GOES-16/SUVI data,
representing Earth’s view. In all images, the off-limb emission has been
enhanced with a radial filter.

As mentioned in the Introduction, a large filament was involved in the 2022
February 15 eruption. The event was observed at EUV wavelengths from three
viewpoints (see Figure 1 for their positions), namely the Solar Terrestrial
Relations Observatory Ahead (STEREO-A; Kaiser et al., 2008) and Solar Orbiter
(SolO; Müller et al., 2020) spacecraft, as well as near-Earth—in this work, we
use imagery from the Geostationary Operational Environmental Satellites 16
(GOES-16) probe. An overview of the remote-sensing EUV observations of the
erupting filament from these three locations is shown in Figure 2, displaying
data from the Extreme UltraViolet Imager (EUVI) telescope part of the Sun
Earth Connection Coronal and Heliospheric Investigation (SECCHI; Howard et
al., 2008) suite onboard STEREO-A, the Full Sun Imager (FSI) telescope part of
the Extreme Ultraviolet Imager (EUI; Rochus et al., 2020) suite onboard SolO,
and the Solar UltraViolet Imager (SUVI; Darnel et al., 2022) telescope onboard
GOES-16. From these observations, it is clear that the 2022 February 15
eruption appeared as a behind-the-eastern-limb event from all three
viewpoints, albeit to different extents. If we consider the average of the
spatial range spanned by various filament and CME features in 3D as
triangulated by Mierla et al. (2022), i.e. E138N35 in Stonyhurst coordinates,
then the event took place behind the eastern limb by ${\sim}$15∘ for STEREO-A,
${\sim}$30∘ for SolO, and ${\sim}$50∘ for Earth.

The erupting filament was first observed to emerge from behind the
northeastern limb from all three viewpoints around 21:50 UT on 2022 February
15. Its fine structure was best visible at 304 Å (i.e., the channel shown in
Figure 2), but its appearance was prominent also at 171 Å from all three
imagers, in addition to being observed at several other EUV wavelengths
(depending on the availability of each instrument). During the early phases of
the eruption, the filament appeared to be surrounded by a “bubble”-like
leading edge (see Figures 2 and 5 in Mierla et al., 2022), the resulting
structure being reminiscent of the classic three-part CME that is usually
observed in coronagraph data (e.g., Illing & Hundhausen, 1985; Vourlidas et
al., 2013). Throughout its evolution across the fields of view of the three
different telescopes (we note that the SolO/EUI/FSI field extended up to $>$6
$R_{\odot}$ at the time of this event, see Mierla et al., 2022), the filament
propagated in a northeasterly direction, away from the solar equatorial plane.
This suggests that any near-the-ecliptic probe detecting this CME in situ
would likely experience a flank encounter rather than a central one, assuming
that no dramatic equatorward deflections would take place in the outer corona
and/or interplanetary space (since stronger CMEs tend to be less affected by
the configuration of the coronal and interplanetary magnetic field; e.g., Gui
et al., 2011; Kay et al., 2015).

###  2.2 White-light Observations

The 2022 February 15 eruption was observed in WL imagery from two viewpoints,
i.e. the STEREO-A spacecraft and Earth—although SolO is equipped with a
coronagraph, the instrument was not operational at the time of this event.
From the STEREO-A viewpoint, the apex of the CME first appeared around 21:55
UT in the COR1 field of view and around 22:10 UT in the COR2 one, both cameras
being part of the SECCHI suite. From Earth’s viewpoint, the CME was observed
by the Large Angle Spectroscopic Coronagraph (LASCO; Brueckner et al., 1995)
onboard the Solar and Heliospheric Observatory (SOHO; Domingo et al., 1995),
emerging around 22:10 UT in the C2 field of view and around 22:30 UT in the C3
one. An overview of the remote-sensing WL observations of the CME in the solar
corona from these two locations is shown in Figure 3.

From coronagraph data, it is evident that the 2022 February 15 CME displayed
clear shock signatures, usually manifested as a fainter emission that
surrounds the brighter magnetic ejecta (e.g., Vourlidas et al., 2003;
Kouloumvakos et al., 2022). Additionally, the CME propagated towards the
northeast from both available viewpoints, in agreement with the EUV
observations presented in Section 2.1. To obtain a more quantitative estimate
of the CME geometric and kinematic parameters, we fit the Graduated
Cylindrical Shell (GCS; Thernisien, 2011) model to WL data. The GCS model
consists of a parameterised shell (described by six variables) that can be
projected onto nearly-simultaneous coronagraph images from different
perspectives and is then manually adjusted to best match the CME structures
seen in the data. Despite being associated with uncertainties due to the
user’s subjectivity when performing a fit (e.g., Verbeke et al., 2023), the
GCS model is widely used in CME and space weather research (see, e.g., Nieves-
Chinchilla et al., 2022; Palmerio et al., 2022b; Rodríguez-García et al.,
2022, for some recent applications). An example of GCS fitting applied to the
2022 February 15 CME is shown in the right panels of Figure 3. According to
our results, the CME apex propagates at a latitude of 33∘ and a longitude of
$-$130∘ (both values are given in Stonyhurst coordinates), the CME axis has a
tilt of $-$60∘ with respect to the solar equator (defined positive for
counterclockwise rotations from the solar west direction), the CME half-
angular width along its major axis is ${\sim}$45∘, and the CME radial speed in
the solar corona is ${\sim}$2200 km$\cdot$s-1. These values are in excellent
agreement with those reported in Mierla et al. (2022), who estimated a
propagation direction of 34∘ in latitude and $-$132∘ in longitude, as well as
a speed of ${\sim}$2200 km$\cdot$s-1. It is evident from the GCS fitting shown
in Figure 3 and our resulting parameters that the 2022 February 15 CME was
characterised by a high latitude and a high inclination. This indicates that a
near-the-ecliptic spacecraft encountering the ejecta in situ would likely
cross its southern flank, as already speculated when considering EUV
observations (see Section 2.1).

Figure 3: The 2022 February 15 CME at ${\sim}$23:00 UT as observed in WL
(coronagraph) difference imagery from the available viewpoints. (a)
STEREO/SECCHI/COR2-A data, shown also in (b) with the GCS wireframe overlaid.
(c) SOHO/LASCO/C3 data, shown also in (d) with the GCS wireframe overlaid.

After leaving the solar corona, the 2022 February 15 CME was observed in WL
heliospheric imagery by the Wide-Field Imager for Solar Probe Plus (WISPR;
Vourlidas et al., 2016) suite of cameras onboard Parker. Only the southern
portion of the full structure was captured in the fields of view of the WISPR
telescopes, further proving that the CME continued propagating in
interplanetary space with a prominent northward component, and that
equatorward deflections are not expected to have taken place. These
observations are presented and briefly discussed in Appendix A.

##  3 In-situ Observations at Bepi and Parker

In this section, we provide an overview of the available in-situ measurements
of the 2022 February 15 CME at Bepi and Parker. We first show a comparison of
the magnetic field data at both spacecraft, followed by a more detailed
summary of magnetic field and plasma observations at Parker—the plasma
instruments onboard Bepi are not regularly operational during cruise phase
(i.e., preceding the Mercury orbit insertion scheduled for December 2025).
Additionally, we remark that the magnetic field data from Bepi have been
subject to additional processing due to the spacecraft’s solar electric
propulsion system (SEPS) being activated during the period of interest (more
information is provided in Appendix B).

Table 1: Times and positions of Bepi and Parker when crossing CME-related
features.

| Time | Position
---|---|---
| [UT] | [r, ${\theta}$, ${\phi}$]
Bepi |  |
Shock | 2022-02-16T06:25 | [0.35, 1.71, $-142.73$]
Ejecta start | 2022-02-16T15:41 | [0.34, 1.78, $-140.99$]
Ejecta end | 2022-02-17T07:51 | [0.34, 1.91, $-137.89$]
Parker |  |
Shock | 2022-02-16T07:25 | [0.37, 3.71, $-145.92$]
Cloud start | 2022-02-16T15:18 | [0.36, 3.70, $-145.43$]
Cloud end | 2022-02-17T06:32 | [0.35, 3.67, $-144.39$]
Obstacle end | 2022-02-17T16:48 | [0.33, 3.64, $-143.58$]

  * •

_Notes._ The [r, ${\theta}$, ${\phi}$] triplets are reported in Stonyhurst
coordinates in units of [au, ∘, ∘]. See the text throughout Section 3 for a
discussion on the identification of all the boundaries.

###  3.1 Magnetic Field Measurements at the Two Spacecraft

Figure 4: Magnetic field measurements (1-min cadence) at (a) Bepi and (b)
Parker for the period 2022 February 15–18. Each plot shows, from top to
bottom: magnetic field magnitude, magnetic field Cartesian components in
radial–tangential–normal (RTN) coordinates, latitudinal angle of the magnetic
field, longitudinal angle of the magnetic field, and root-mean-square error of
the magnetic field (using a rolling-average over 15 min for each component,
the superposed orange curve displays the 30-min rolling average of the same
data). The ($r$, $\theta$, $\phi$) values displayed at the top of the panels
for both spacecraft refer to 2022 Feburary 16, 07:00 UT, and the angles are
reported in Stonyhurst coordinates. The vertical grey lines indicate the
arrival of the CME-driven shock at either spacecraft, whilst the shaded grey
areas highlight the CME ejecta. At Parker, the full ejecta (magnetic obstacle)
includes both grey regions, and the flux rope (magnetic cloud) structure
within it is represented by the lighter grey area. Additional details about
the identification of boundaries at Parker are provided in Section 3.2.

Given the high speed of the 2022 February 15 CME as inferred from remote-
sensing observations (see Section 2.2), we can expect a relatively rapid
propagation to ${\sim}$0.35 au, i.e., the heliocentric distance of Bepi and
Parker at the time of the event (see Figure 1). The two probes were located
${\sim}$15∘ to the east and ${\sim}$30∘ to the south of the CME nose
trajectory that was estimated from GCS fitting. By inspecting magnetic field
measurements from the Mercury Planetary Orbiter Magnetometer (MPO-MAG; Heyner
et al., 2021) onboard Bepi and the Fluxgate Magnetometer (MAG) part of the
FIELDS (Bale et al., 2016) investigation onboard Parker—both data sets are
shown in Figure 4—we find signatures of a solar wind transient starting on
February 16 around 07:00 UT (approximate average time between the two
spacecraft). This yields a travel time of ${\sim}$9.25 h, with an average
transit speed of km$\cdot$s-1. Specifically, we observe an abrupt increase in
the magnetic field magnitude at 06:25 UT in Bepi data and at 07:25 UT in
Parker data (marked with vertical grey lines in Figure 4), indicating the
passage of a CME-driven shock. The identification of this feature as a fast-
forward shock can be confirmed using plasma data from Parker (presented in
detail in Section 3.2), hence it is reasonable to assume that the same holds
true for Bepi.

After a period (${\sim}$8.5 h) characterised by highly fluctuating magnetic
field vectors, corresponding to the turbulent sheath region that usually
follows CME-driven shocks, both probes observed enhanced magnetic field
magnitudes, together with smoother profiles of the field components, which can
be attributed to the passage of the CME ejecta (highlighted as shaded grey
areas in Figure 4). Specifically, the leading edge of this structure is
identified on February 16 at 15:41 UT for Bepi and 15:18 UT for Parker At both
spacecraft, the magnetic field vectors rotated smoothly from east to west and
pointed mostly southwards throughout the structure, suggesting approximately
an east–south–west (ESW, right-handed) flux rope type from visual inspection
(e.g., Bothmer & Schwenn, 1998; Palmerio et al., 2018). Whilst at Bepi the
entire identified CME ejecta interval was characterised by flux-rope-like
signatures, at Parker the trailing portion of the structure featured more
turbulent magnetic fields (especially in the north–south component),
suggesting that the flux rope and, more generally, the ejecta boundaries may
not coincide (e.g., Richardson & Cane, 2010; Kilpua et al., 2013, more details
on this matter are provided in Section 3.2). For simplicity and to avoid
confusion, we shall refer henceforth to the flux rope interval as ‘magnetic
cloud’ (e.g., Burlaga et al., 1981) and to the whole CME ejecta as ‘magnetic
obstacle’ (e.g., Nieves-Chinchilla et al., 2019).

We also investigate the level of fluctuations in the interplanetary magnetic
field by computing the root-mean-square of the field vector, shown in Figure
4, using

$B_{\mathrm{rms}}=\sqrt{\sum_{i=R,T,N}\frac{(B_{i}-{\langle}B_{i}{\rangle})^{2}}{n}}\,,$
(1)

where for the averaged quantities we employ 15-min rolling averages of the
corresponding magnetic field component and $n$ is the number of data points
employed for each average (hence, $n=15$ here). It is evident that the portion
of solar wind identified as the sheath region in either data set features
generally the most fluctuations when compared to the ambient medium and to the
CME ejecta material, in agreement with statistical studies of interplanetary
CMEs detected at 1 au (e.g., Masías-Meza et al., 2016; Kilpua et al., 2019b).
At Bepi, the level of fluctuations displays a rather clear decrease inside the
magnetic ejecta with respect to the entire time series, as expected from
statistical studies of CMEs measured at 1 au (e.g., Rodriguez et al., 2016;
Regnault et al., 2020). At Parker, the same holds generally true, but we note
that the largest fluctuations of the entire time series are reached briefly in
the middle of the ejecta due to a sudden change in the magnetic field vector.
Additionally, we observe a relatively higher level of fluctuations in the
second part of the ejecta (i.e., outside of the magnetic cloud interval),
which is to be expected since flux rope ejecta tend to display more organised
magnetic fields (e.g., Li et al., 2018; Nieves-Chinchilla et al., 2019).

###  3.2 Magnetic Field and Plasma Measurements at Parker

As mentioned at the beginning this section, the available in-situ observations
at Parker for the 2022 February 15 event include plasma data, which, on the
other hand, do not find a direct comparison at Bepi due to the corresponding
instrument(s) being not operational. The whole set of in-situ observations at
Parker is presented in Figure 5, where the FIELDS magnetic field data are
complemented with plasma measurements from the Solar Wind Electrons Alphas and
Protons (SWEAP; Kasper et al., 2016) suite—specifically, using the Solar Probe
Cup (SPC; Case et al., 2020), Solar Probe ANalyzer-Ions (SPAN-i; Livi et al.,
2022), and Solar Probe ANalyzer-Electrons (SPAN-e; Whittlesey et al., 2020)
detectors. Here, we use the collective of these observations to better
constrain and define the various CME features and sub-structures that were
briefly introduced in Section 3.1. We note that there is a data gap in the SPC
proton moments immediately following the detection of the CME-driven shock due
to the solar wind being outside of the instrument’s energy range (bulk speed
${\gtrsim}$800 km$\cdot$s-1). SPAN-i data, on the other hand, despite
capturing the profile of the solar wind speed in its entirety, considerably
underestimates the proton density and temperature due to the full ion
distribution not being in the instrument’s field of view. Hence, we complement
the available proton density and temperature measurements from SPC with
electron data from SPAN-e derived from fitting to the electron core
distribution (using the procedure described in Romeo et al., 2023).

Figure 5: Overview of in-situ data at Parker for the period 2022 February
15–18. The plot shows, from top to bottom: (a) magnetic field magnitude, (b)
magnetic field Cartesian components in RTN coordinates, (c) latitudinal and
(d) longitudinal angles of the magnetic field, (e) solar wind bulk speed,
proton (f) density and (g) temperature, (h) plasma beta, (i) helium-to-proton
ratio, and (j) pitch-angle spectrogram of suprathermal 293 eV electrons. The
vertical grey line indicates the arrival of the CME-driven shock, whilst the
shaded grey areas highlight the magnetic obstacle (light+dark grey) and the
magnetic cloud (light grey) within it. The hatched area marks the HPS passage
immediately following the CME.

First of all, we note that the abrupt magnetic field jump that we had
identified as the CME-driven shock in Section 3.1 (vertical grey line in
Figure 5) is indeed accompanied by a prominent rise in the solar wind bulk
speed (from ${\sim}$550 to ${\sim}$850 km$\cdot$s-1), a moderate climb in the
electron density and temperature, as well as an intensification of
suprathermal electron fluxes . The following sheath region is characterised by
highly fluctuating magnetic fields, almost-constant speeds, a declining
temperature profile, and a plateauing density trend except for a high-density
feature close to its trailing portion. The density peak at the back of the
sheath is reminiscent of a piled-up compression (PUC) region that forms ahead
of the nose of a driver (in this case, the CME ejecta) often due to its large
expansion speed, which is known to usually be higher close to the Sun and then
to decrease gradually as the CME travels through interplanetary space (e.g.,
Farrugia et al., 2008; Das et al., 2011).

Regarding the CME ejecta (shaded grey area in Figure 5), we use the plasma
measurements to corroborate our initial assessment of non-coinciding magnetic
cloud and magnetic obstacle boundaries (see Section 3.1). Indeed, we note that
bidirectional suprathermal electrons—i.e., with the pitch angle distribution
(PAD) displaying peaks close to 0∘ and 180∘—are detected throughout the
identified CME ejecta interval. This feature is usually interpreted as the
result of two electron beams flowing along and against the magnetic field
lines, and are often associated with closed lines that are connected to the
Sun from both ends, especially in the case of CME ejecta (e.g., Gosling et
al., 1987; Carcaboso et al., 2020). Additionally, we find that the magnetic
cloud period (characterised by smoother and rotating magnetic fields) features
a declining speed profile, usually interpreted as a signature of expansion
(e.g., Zurbuchen & Richardson, 2006; Nieves-Chinchilla et al., 2018b). The
trailing portion of the magnetic obstacle (where magnetic fluctuations are
higher), on the other hand, displays first a plateauing and then a slightly
rising speed trend, suggesting that expansion of the structure had likely
ceased in that region and possibly related to the small rise in magnetic field
magnitude over the last ${\sim}$5 hr of the ejecta passage. The temperature
and plasma beta show rather irregular profiles, but they display periods with
values below the ambient ones throughout the ejecta interval. The density is
generally never below ambient values, and features an isolated peak inside the
magnetic cloud interval (coinciding with a local maximum in the electron
temperature as well). A possible cause for the observed mismatching magnetic
cloud and magnetic obstacle boundaries is flux erosion (more details on this
aspect are presented in Section 4.3).

From the He/H composition panel, we note that the He abundances rise
throughout the sheath towards the ejecta (grey region in Figure 5). Prior to
the shock, the solar wind He/H abundance appears below 1%, which is typical of
solar wind values (e.g., Borrini et al., 1981). The gradual rise in the He/H
values throughout the sheath indicates there is no sharp boundary between the
solar wind, the sheath/shocked plasma, and the main CME ejecta. The smooth
transition is consistent with a gradual accumulation and mixture of solar wind
and CME material in the front. Moreover, there are also some He/H enhancements
that appear throughout the trailing part of the ejecta, which is in
qualitative agreement with the Rodriguez et al. (2016) superposed epoch
profile obtained from 1 au events and may result from He gravitational
settling in the pre-eruption CME source region (e.g., Richardson & Cane,
2004). The fluctuations in the He abundance could indicate the passage of
coherent substructure in connection to the filament’s fragmented nature
observed in the remote-sensing images (see Section 2.1). However, due to the
field of view restrictions of SPAN-i, many of the measurements are omitted
across this time frame, making it difficult to examine with certainty.
Previous work has shown that He/H abundances are generally elevated in CMEs
compared to the solar wind (Borrini et al., 1982; Zurbuchen et al., 2016).
However, it remains unclear whether filaments themselves contain high He/H
abundances (Lepri & Rivera, 2021; Rivera et al., 2022). For a similarly
energetic CME, the Bastille Day CME that erupted on 2000 July 14 and reached
2000 km$\cdot$s-1 in the low corona, its compositional structure indicated
that the prominence material had elemental abundances that were less enhanced
in the low first-ionization-potential species than the surrounding flux rope
structure, suggesting more solar wind-like elemental properties (Rivera et
al., 2023).

Finally, we note a structure immediately following the ejecta characterised by
a low magnetic field magnitude as well as enhanced speed, density, and plasma
beta (hatched area in Figure 5). Additionally, both the longitudinal component
of the magnetic field and the suprathermal electron PAD display a ${\sim}$180∘
reversal after the passage of this feature, compared to the pre-CME ambient
wind. The structure shows all the typical characteristics of a heliospheric
plasma sheet (HPS) crossing (e.g., Crooker et al., 2004; Lavraud et al.,
2020), i.e., the passage of a high-density and high-beta region that surrounds
the heliospheric current sheet (HCS). We tentatively associate the HPS at
Parker (starting at ${\sim}$17:00 UT on February 17) with a similar structure
(featuring a low magnetic field magnitude as well as a reversal of the
longitudinal component of the field) detected at Bepi approximately one day
later (starting at ${\sim}$17:00 UT on February 18, see Figure 4), i.e. well
after the passage of the 2022 February 15 CME. Hence, the (spatial and
temporal) proximity of the HPS to the CME at Parker—and the resulting
interaction between the two—may explain the presence of more ambiguous
magnetic cloud and magnetic obstacle boundaries at Parker, which are on the
other hand not found at Bepi.

##  4 Analysis of the Mesoscale CME Structure

In this section, we analyse in detail the similarities and differences related
to observations of the 2022 February 15 CME at Bepi and Parker. We focus our
investigation on the three main regions and/or features of in-situ CMEs, i.e.,
the interplanetary shock, the sheath region, and the magnetic ejecta.

###  4.1 Interplanetary Shock

As mentioned in Section 3.1, an interplanetary shock was detected on 2022
February 16 at 06:25 UT by Bepi and 07:25 UT by Parker. Although it is not
possible to determine the passage of a shock with certainty at Bepi due to the
lack of corresponding plasma data, the prominent nature of the shock at Parker
(see Section 3.2), together with the spatial proximity of the two probes,
allows us to proceed with our analysis under the assumption that both
spacecraft measured the same feature.

Table 2: Shock parameters derived for both Bepi and Parker.

|  BepiColombo | Parker Solar Probe
---|---|---
Jumps |  |
$r_{B}$ | 2.04 | 2.04
$r_{n}$ | — | 1.80
${\Delta}V$ | — | 282 km$\cdot$s-1
MCT |  |
$\mathbf{\hat{n}}_{\mathrm{MCT}}$ | [0.76, 0.63, 0.16] | [0.45, $-$0.82, $-$0.37]
$\Theta_{\mathrm{MCT}}$ | 7.3∘ | 31.8∘
$\Lambda_{\mathrm{MCT}}$ | 40.5∘ | 63.3∘
$\Xi_{\mathrm{MCT}}$ | 9.0∘ |  $-$21.4∘
MVA |  |
$\mathbf{\hat{n}}_{\mathrm{MVA}}$ | [0.57, $-$0.25, $-$0.78] | [0.53, $-$0.42, $-$0.73]
$\Theta_{\mathrm{MVA}}$ | 80.4∘ | 42.6∘
$\Lambda_{\mathrm{MVA}}$ | 55.0∘ | 57.8∘
$\Xi_{\mathrm{MVA}}$ |  $-$51.3∘ |  $-$47.1∘
$\lambda_{2}$/$\lambda_{3}$ | 3.07 | 2.71
$B_{n}$/$B$ | 0.15 | 0.45
MD3 |  |
$\mathbf{\hat{n}}_{\mathrm{MD3}}$ | — | [0.49, $-$0.71, $-$0.51]
$\Theta_{\mathrm{MD3}}$ | — | 33.3∘
$\Lambda_{\mathrm{MD3}}$ | — | 60.9∘
$\Xi_{\mathrm{MD3}}$ | — |  $-$30.6∘

  * •

_Notes._ $r_{B}$ = magnetic compression ratio. $r_{n}$ = density compression
ratio. ${\Delta}V$ = velocity jump. $\mathbf{\hat{n}}$ = shock normal.
$\Theta$ = shock angle. $\Lambda$ = location angle. $\Xi$ = elevation angle.
$\lambda_{2}$/$\lambda_{3}$ = intermediate-to-minimum eigenvalue ratio.
$B_{n}$/$B$ = minimum-variance-to-total magnetic field ratio. MCT = magnetic
coplanarity theorem. MVA = minimum variance analysis. MD3 = mixed-mode method.

When investigating the properties of interplanetary shocks, the first step is
to define the plasma states upstream and downstream of the shock. In this
work, the criteria for determining the upstream and downstream conditions are
adopted from those used in the Heliospheric Shock Database (HSD111The
Heliospheric Shock Database is generated and maintained at the University of
Helsinki and can be accessed at http://ipshocks.fi; Kilpua et al., 2015), and
consist of averaging the quantities under consideration over 8 min intervals
that end 1 min before and start 2 min after the identified shock passage time,
i.e.:

$\begin{cases}t_{u}=[\,t_{\mathrm{shock}}-9\mathrm{min},t_{\mathrm{shock}}-1\mathrm{min}\,]\\\
t_{d}=[\,t_{\mathrm{shock}}+2\mathrm{min},t_{\mathrm{shock}}+10\mathrm{min}\,]\,,\end{cases}$
(2)

where the subscript ‘ _u_ ’ indicates the upstream state and the subscript ‘
_d_ ’ indicates the downstream state. These intervals ensure that the mean
upstream and downstream values are estimated sufficiently far from the shock
ramp (and the particularly turbulent region in the immediate shock
downstream). We remark, nevertheless, that the choice of the upstream and
downstream windows may significantly affect the resulting shock parameters
(e.g., Balogh et al., 1995; Trotta et al., 2022). Here, small variations in
the interval selections had minimal impact on our calculated normals, but we
did not perform an exhaustive parameter-dependency analysis. The various shock
properties calculated for both Bepi (where possible) and Parker are summarised
in Table 2, and they are described in detail below.

The first two shock characteristics reported in Table 2 are compression
ratios, defined as

$r_{X}=\frac{X_{d}}{X_{u}}\,,$ (3)

where $X$ indicates a general physical quantity—usually the magnetic field
magnitude, $B$, the proton density, $n_{p}$, and/or the proton temperature,
$T_{p}$. In the case of the event studied here, we report the magnetic
compression ratio, $r_{B}$, for both Bepi and Parker, whilst for the density
compression ratio, $r_{n}$, we use electron measurements at Parker as a
proxy—generally, a reasonable approximation under the assumption of quasi-
neutrality of the plasma—due to the lack of downstream proton data (see Figure
5). We note that $r_{B}$ features identical values of 2.04 at the two
spacecraft, whilst $r_{n}$ is found to equal 1.80 at Parker. These compression
ratios are usually considered as proxies for the strength of a shock (e.g.,
Burton et al., 1996; Oh et al., 2007), and their expected values have been
found to not vary significantly between 0.3 and 1 au (Volkmer & Neubauer,
1985; Lai et al., 2012). We find our compression ratios to be very similar to
the median values detected by the Helios mission between 0.3 and 0.8 au—i.e.,
1.84 for $r_{B}$ and 1.87 for $r_{n}$ (Pérez-Alanis et al., 2023), indicating
that the 2022 February 15 CME drove a shock of average strength. Nevertheless,
studies have found that interplanetary shocks tend to be stronger in the
proximity of their nose than along their flanks (e.g., Cane, 1988; Kallenrode
et al., 1993), suggesting that had the CME been encountered closer to its apex
(see Section 2.2 for an estimate of its propagation direction well north of
the ecliptic), Bepi and Parker may have measured higher values for the
corresponding compression ratios.

The next parameter reported in Table 2 is the shock speed jump, defined as

${\Delta}V=V_{d}-V_{u}\,.$ (4)

As in the case of $r_{n}$, ${\Delta}V$ can be calculated at Parker only,
resulting in a jump of 282 km$\cdot$s-1. Although shocks driven by fast CMEs
tend to slow down as they propagate through the inner solar system (e.g., Woo
et al., 1985; Neugebauer, 2013), this value is slightly higher than average,
since shock jumps measured inside 1 au are usually below 200 km$\cdot$s-1
(Luhmann, 1995). The high speed of the shock driven by the 2022 February 15
CME and detected at ${\sim}$0.35 au may be due to its propagation through a
rarefied (${\sim}$20 cm-3) and fast (${\sim}$600 km$\cdot$s-1) solar wind
stream (see Figure 5), which in turn hindered its deceleration due to drag
effects.

The following parameters reported in Table 2 all concern the shock normal,
$\mathbf{\hat{n}}$, and its related angles. Given the large uncertainties that
are known to be associated with shock normal determination methods (e.g.,
Russell et al., 1983; Schwartz, 1998), we compare in this work results using
three techniques: The magnetic coplanarity theorem (MCT; Colburn & Sonett,
1966), minimum variance analysis (MVA; Sonnerup & Cahill, 1967), and the
mixed-mode method (MD3; Abraham-Shrauner & Yun, 1976). We note that, whilst
MCT and MVA are based uniquely on magnetic field data and can hence be applied
to both probes, MD3 needs speed measurements and can thus be used at Parker
only. The shock normals resulting from the different methods are visualised in
3D in Figure 6.

Figure 6: Overview of the shock normals calculated with different methods at
both Bepi and Parker, shown from two different perspectives to provide a
better insight into their orientations in 3D. Normals calculated with the MCP
and MVA methods are displayed for both spacecraft, whilst the normal derived
using the MD3 technique is presented for Parker only since its derivation
requires plasma data. The location of the Sun is represented with a yellow
sphere, and the black arrow indicates the trajectory of the CME nose as
derived from the GCS fitting shown in Figure 3.

The MCT technique is based on the assumption that $\mathbf{B}_{u}$,
$\mathbf{B}_{d}$, and $\mathbf{\hat{n}}$ lie in a single plane, and the shock
normal is computed as

$\mathbf{\hat{n}}_{\mathrm{MCT}}=\pm\frac{(\mathbf{B}_{d}-\mathbf{B}_{u})\times(\mathbf{B}_{d}\times\mathbf{B}_{u})}{|(\mathbf{B}_{d}-\mathbf{B}_{u})\times(\mathbf{B}_{d}\times\mathbf{B}_{u})|}\,.$
(5)

The MVA technique assumes that, when a spacecraft crosses a “transition layer”
(e.g., a shock front), the divergence-free nature of the magnetic field
imposes the condition that the field component normal to such layer is
continuous. It solves the set of three equations for the eigenvectors and
eigenvalues of the magnetic variance matrix

$\sum_{\nu=1}^{3}M_{\mu\nu}n_{\nu}=\lambda n_{\mu}\,,$ (6)

where $M_{\mu\nu}=\langle B_{\mu}B_{\nu}\rangle-\langle B_{\mu}\rangle\langle
B_{\nu}\rangle$. The eigenvector associated with the smallest eigenvalue,
$\lambda_{3}$, is the direction of minimum variance of the magnetic field and
thus corresponds to the shock normal, $\mathbf{\hat{n}}_{\mathrm{MVA}}$. The
reliability of the solution can be investigated via the intermediate-to-
minimum eigenvalue ratio, $\lambda_{2}$/$\lambda_{3}$, and the minimum-
variance-to-total magnetic field ratio across the discontinuity, $B_{n}$/$B$.
Values of $\lambda_{2}$/$\lambda_{3}\geq$ 2 and $B_{n}$/$B\leq$ 0.3 are
usually considered to describe the shock normal as well-defined (Lepping &
Behannon, 1980).

Finally, the MD3 technique expands upon the MCT one by incorporating velocity
changes across the shock. This method is usually considered more robust than
those that only use magnetic field data, and the normal is calculated as

$\mathbf{\hat{n}}_{\mathrm{MD3}}=\pm\frac{(\mathbf{B}_{d}-\mathbf{B}_{u})\times((\mathbf{B}_{d}-\mathbf{B}_{u})\times(\mathbf{V}_{d}-\mathbf{V}_{u}))}{|(\mathbf{B}_{d}-\mathbf{B}_{u})\times((\mathbf{B}_{d}-\mathbf{B}_{u})\times(\mathbf{V}_{d}-\mathbf{V}_{u}))|}\,.$
(7)

Once the shock normals have been retrieved for each method and for each
spacecraft, we calculate three angles related to them. The first is the shock
angle, $\Theta$, between the shock normal and the upstream magnetic field,
defined as

$\Theta=\arccos\left(\frac{|\mathbf{B}_{u}\cdot\mathbf{\hat{n}}|}{\lVert\mathbf{B}_{u}\rVert\lVert\mathbf{\hat{n}}\rVert}\right)\,.$
(8)

The second angle is the so-called location angle, $\Lambda$, between the shock
normal and the radial direction (Janvier et al., 2014). It provides
information as to the spacecraft crossing location with respect to the shock
nose. Ideally, $\Lambda$ = 0∘ for a central encounter, and the larger the
value (up to $|\Lambda|$ = 90∘), the farthest the crossing location is from
the apex. The angle can be computed as

$\Lambda=\arctan\left(\frac{\sqrt{n_{T}^{2}+n_{N}^{2}}}{n_{R}}\right)\,.$ (9)

The third and final angle is the elevation angle, $\Xi$, between the shock
normal and the RT plane (in RTN coordinates), defined as

$\Xi=\arctan\left(\frac{n_{N}}{\sqrt{n_{R}^{2}+n_{T}^{2}}}\right)=\arcsin\left(\frac{n_{N}}{\lVert\mathbf{\hat{n}}\rVert}\right)\,.$
(10)

According to the shock normal results shown in Table 2 and Figure 6, all the
calculated normals point in a southeasterly way ($n_{y}<$ 0 and $n_{z}<$ 0)
apart from the MCT case for Bepi, which points towards the northwest ($n_{y}>$
0 and $n_{z}>$ 0). The shock is moderately quasi-parallel at Parker
(31${}^{\circ}<\Theta<$ 43∘), whilst for Bepi the MCT method retrieves a
strongly quasi-parallel shock ($\Theta$ = 7.3∘) and the MVA technique produces
a strongly quasi-perpendicular shock ($\Theta$ = 80.4∘). We note that quasi-
parallel shocks are expected to occur more often closer to the Sun ($<$1 au)
and quasi-perpendicular ones are more common at larger distances (${\sim}$1
au) due to the configuration of the Parker spiral (e.g., Richter et al., 1985;
Good et al., 2020). Regardless of the normal direction and nature of the
shock, all the obtained location angles suggest spacecraft crossings
considerably far from the shock nose (40${}^{\circ}<\Lambda<$ 65∘), as
expected from our remote-sensing analysis of the 2022 February 15 CME (see
Section 2).

Whilst the normals retrieved at Parker are all in general agreement, we
consider the ones retrieved with the MCT and MD3 methods to be more reliable,
given the large value of the $B_{n}$/$B$ ratio obtained with the MVA
technique. At Bepi, on the other hand, both MVA ratios suggest a robust
solution, which is in turn profoundly different from the one retrieved with
the MCT method. Given the idealised (semi-spherical) shock geometry expected
from the CME propagating to the northwest of the two probes (see Figure 6), it
follows that the normal should indeed point approximately towards the
southeast at the location of the spacecraft and, thus, one may intuitively
favour the MVA results. Additionally, the uncertainties associated with the
MCT method are known to become larger the closer a shock is to being fully
parallel or fully perpendicular (Viñas & Scudder, 1986). However, given the
prominent discrepancy between the two methods, we conclude that it is not
possible to estimate a shock normal at Bepi in a reliable way. Nevertheless,
it is clear that, despite the spatial proximity of Bepi and Parker, the two
sets of measurements of the shock passage are dissimilar enough to produce
fundamentally different results, possibly due to the shock being crossed
significantly far from its nose and/or to an irregular shock front (e.g.,
Koval & Szabo, 2010; Kajdič et al., 2019) as well as the pre-existing local
conditions of the turbulent solar wind (e.g., Guo et al., 2021; Lavraud et
al., 2021).

###  4.2 Sheath Region

The interplanetary shock detection was followed by a turbulent sheath region
at both probes (see Figure 4). We identify the sheath passage on 2022 February
16 during 06:25–15:41 UT at Bepi and 07:25–15:18 UT at Parker, resulting in a
duration of 9.3 hr at the former and 7.9 hr at the latter. We note that both
these values are significantly larger than what is expected at Mercury’s
orbit, where sheath passages have been found to last on average 2.4 hr by
Janvier et al. (2019), or 1.7 hr (2.2 hr) for fast (slow) CME drivers by
Salman et al. (2020). A possible explanation for the observed long duration is
that the CME was encountered by both probes close to its flank (as also
confirmed by the interplanetary shock analysis in Section 4.1), since the
thickness of a sheath is supposed to increase from the nose of the driving
ejecta towards its sides (e.g., Gopalswamy et al., 2009; Kilpua et al., 2017).
In such a case, Bepi would have encountered the CME farther from its nose than
Parker. The mean (maximum) magnetic field magnitude measured in the sheath is
43.7 nT (69.8 nT) at Bepi and 38.8 nT (54.4 nT) at Parker, with values at both
spacecraft being noticeably lower than the 57.8 nT (84.6 nT) determined by
Winslow et al. (2015) via a statistical analysis of 61 CMEs detected at
Mercury’s orbit. Again, a possible reason for the lower-than-average field
strength is the probes’ trajectory through the CME away from its nose.

Figure 7: The PMSs identified in the sheath regions at (a) Bepi and (b)
Parker. The top panels show magnetic field measurements around the time of the
sheath region passage (marked by the two vertical lines), with the PMS
interval highlighted in okra. The bottom panels show the corresponding
magnetic field vectors (within the PMS interval) on the $\theta$–$\phi$
surface, with the dashed curve representing the PMS plane and the $\odot$
($\otimes$) symbol indicating the normal direction out of (into) it.

As mentioned in Section 3.1, the sheath region is the part displaying overall
the highest magnetic field fluctuations in the time series shown in Figure 4
for either probe. In contrast to superposed epoch analyses performed on
sheaths detected at 1 au, which display a clear (absolute) maximum at the
shock passage and a local maximum at the ejecta leading edge time (e.g.,
Masías-Meza et al., 2016; Kilpua et al., 2019b; Salman et al., 2021), the
fluctuations observed at Bepi and Parker appear overall more uniformly
distributed throughout the region. This may be due to the tendency for sheaths
encountered closer to the Sun to generally display sharper field
discontinuities and rotations (see, e.g., Good et al., 2020, who investigated
the radial evolution of magnetic field fluctuation in sheath regions), or a
result of passing through the flank of the CME. We remark, however, that
statistical studies at 1 au often calculate $B_{\mathrm{rms}}$ over 1-min time
scales, whilst here we considered 15-min intervals due to the available
resolution of Bepi data for the period under analysis (see also Appendix B).
We find the average $B_{\mathrm{rms}}$ over the whole sheath region to amount
to 5.3 nT at Bepi and 4.5 nT at Parker. Whilst this suggests a more turbulent
sheath encountered at Bepi, it is important to bear in mind that this probe
was closer to the Sun by ${\sim}0.03$ au in radial distance. If we consider,
instead, the normalised $B_{\mathrm{rms}}$—obtained by dividing Equation 1 by
the time-dependent magnetic field magnitude ($B$)—the average sheath
fluctuations become ${\sim}0.13$ at either spacecraft, indicating similar
conditions in both sets of measurements.

To further analyse the fine structure of the sheath regions observed at the
two spacecraft, we investigate the presence (or lack thereof) of planar
magnetic structures (PMSs) using the algorithm of Palmerio et al. (2016). PMSs
are structures in the solar wind characterised by abruptly-changing magnetic
field vectors that remain nearly parallel to a single plane (e.g., Nakagawa et
al., 1989; Neugebauer et al., 1993) and are frequently found in CME-driven
sheath regions (e.g., Palmerio et al., 2016; Ruan et al., 2023). In brief, the
PMS search algorithm of Palmerio et al. (2016) first applies the MVA technique
to the full sheath, verifying whether the PMS conditions of
$\lambda_{2}$/$\lambda_{3}\geq 5$ (e.g., Savani et al., 2011) and
$B_{n}$/$B\leq 0.2$ (e.g., Jones & Balogh, 2000) are fulfilled, in which case
the entire region is considered planar. If one or both criteria are not
matched, then the algorithm scans through the sheath region using a “sliding
windows” procedure. At every iteration, the sheath duration is reduced by 5
min from its end part, and the shortened window is shifted back towards the
leading edge with 5-min increments, searching for the largest non-overlapping
intervals for which the PMS criteria hold (note that a single sheath may
contain more than one PMS). In the work of Palmerio et al. (2016), which
analysed 95 sheaths observed near Earth, the minimum possible PMS duration was
set to 1 hr. Here, to account for the fact that the structures under
investigation were encountered at ${\sim}0.35$ au, where sheaths are on
average more modest in size, we allow for a minimum PMS duration of 30 min.

Table 3: Results of the PMS analysis at Bepi and Parker.

|  BepiColombo | Parker Solar Probe
---|---|---
$D$ [hr] | 1.4 | 1.0
$\lambda_{2}$/$\lambda_{3}$ | 5.0 | 5.1
$B_{n}$/$B$ | 0.10 | 0.12
$O_{\mathrm{PMS}}$ | ($60^{\circ}$, $319^{\circ}$) | ($14^{\circ}$, $360^{\circ}$)
$\hat{n}_{\mathrm{PMS}}$ | [0.38, $-$0.33, 0.86] | [0.97, $-$0.00, 0.24]

  * •

_Notes._ $D$ = PMS duration. $\lambda_{2}$/$\lambda_{3}$ = eigenvalue ratio.
$B_{n}$/$B$ = magnetic field ratio. $O_{\mathrm{PMS}}$ = orientation of the
PMS plane in ($\theta$, $\phi$) format. $\hat{n}_{\mathrm{PMS}}$ = normal
vector to the PMS plane.

The results of the PMS analysis are shown in Figure 7 and Table 3. The PMS
search algorithm finds one planar structure lasting approximately one hour at
the centre of each sheath. Despite their similar duration and location within
their respective sheath regions, the two PMSs display different plane
orientations, with the one found at Bepi oriented towards the northeast and
the one found at Parker nearly aligned with the Sun–spacecraft line.
Additionally, we note that the presence of a PMS in the central region of a
sheath is a rather uncommon occurrence (e.g., Palmerio et al., 2016), since
planar structures are believed to form due to compression and alignment of
discontinuities downstream of a shock (e.g., Jones et al., 2002) and/or due to
magnetic field draping ahead of an ejecta (e.g., Kataoka et al., 2005).
Nevertheless, the excellent agreement between their respective positions
within the sheath as well as their temporal duration suggests that the
structures found at Bepi and Parker were the result of the same formation
mechanism. Given the turbulent nature of the solar wind, especially in the
downstream region of a shock, it is possible that the retrieved PMS
orientations are deeply reflective of the local sheath conditions, and hence
can vary more or less dramatically over relatively small spatial scales.

Figure 8: Magnetic field observations of the sheath region driven by the 2022
February 15 CME at Bepi and Parker. The Bepi measurements have been stretched
to match the sheath duration at Parker and time-shifted to align the two shock
arrival times. The dashed vertical green lines mark the beginning and the end
of the sheath region within which the magnetic field correlations are
computed. The solid profiles show 1-min measurements, whilst the scatter
points indicate the 10-min averaged data used to calculate the corresponding
Pearson correlation coefficients (reported on the bottom left of each panel
together with their p-values).

Indeed, this last point connects to the next step in our analysis, which is
aimed at investigating the level of coherence of the sheath magnetic fields
measured at the two spacecraft. To do so, we employ an approach similar to
that used by Ala-Lahti et al. (2020), who analysed the longitudinal spatial
coherence of CME-driven sheath regions observed at 1 au by spacecraft
characterised by non‐radial separations between 0.001 and 0.012 au
($0.06^{\circ}$–$0.69^{\circ}$). Specifically, they computed the Pearson
correlation coefficients ($r$) between each pair of magnetic field components
as well as the field magnitude. In the case explored here, the spacecraft non-
radial separation is ${\sim}0.03$ au, which corresponds to ${\sim}5^{\circ}$
at ${\sim}0.35$ au. We note that, whilst this relative distance is larger than
the range explored by Ala-Lahti et al. (2020), it is well within the estimated
scale lengths of typical magnetic field coherence in sheath regions resulting
from their study (see also the discussion in the Introduction).

The results of the sheath magnetic coherence analysis are shown in Figure 8.
To directly compare the two sheath regions, we have stretched (or, actually,
“shrunk”) the Bepi measurements onto the Parker ones by aligning both the
shock and the ejecta leading edge passage times. This approach is slightly
different from the one employed by Ala-Lahti et al. (2020), who examined the
two magnetic field data sets using two methods: The first consists of
maximising the cross-correlation of a combined Pearson coefficient that takes
into account the magnetic field magnitude as well as its components, and the
second consists of simply aligning the two shock arrival times (without
stretching one time series onto the other). We have computed our correlations
using the shock-aligning approach as well, and the results are qualitatively
comparable to the ones displayed in Figure 8. The Pearson correlation
coefficients emerging from our analysis are [$B$, $B_{R}$, $B_{T}$, $B_{N}$] =
[0.67, 0.28, 0.21, $-0.33$], hence, there is a good correlation in the
magnetic field magnitude, but weak-to-no correlation in the field components.
These results are in contrast to the ones from Ala-Lahti et al. (2020), who
reported the best correlation in the east–west component of the magnetic field
($B_{T}$) for sheath regions, with some degree of coherence maintained until
${\sim}0.15$ au (or ${\sim}9^{\circ}$) at 1 au. In fact, they suggested that
correlations in total magnetic field ($B$) as well as its radial ($B_{R}$) and
north–south ($B_{N}$) components are expected to cease for separations larger
than 0.04 au (or ${\sim}2^{\circ}$) at 1 au. The higher-than-expected degree
of coherence that we found in $B$ and $B_{R}$ for a ${\sim}5^{\circ}$
separation at ${\sim}0.35$ au might be related to the fact that changes in the
sheath properties are known to increase with heliocentric distance as a CME
propagates in interplanetary space (e.g., Salman et al., 2020; Winslow et al.,
2021). On the other hand, the lower-than-expected degree of coherence that we
found in $B_{T}$ may be due to the different Parker spiral orientation at
${\sim}0.35$ au when compared to 1 au—i.e., characterised by a significantly
smaller component in the east–west direction.

Finally, we inspect the available plasma data from Parker (see Figure 5) to
obtain a deeper insight into the sheath’s structure and evolution, including
the relationship with its driver. First of all, we focus on the speed profile
measured within the sheath region and apply a linear regression to it, finding
an overall decrease of ${\sim}3$% from the interplanetary shock to the ejecta
leading edge (speed decline by 26 km$\cdot$s-1 and average speed of 901
km$\cdot$s-1), with a slope relative to the average sheath speed of 0.37%
hr-1. The mean error associated with the regression, however, is 4.8% with
respect to the average sheath speed, making the structure encountered at
Parker akin to the “Category-D” sheaths of Salman et al. (2021), i.e. those
characterised by a complex (non-linear) speed profile. The statistical
analysis of Salman et al. (2021) was centred on sheaths preceded by shocks
encountered at 1 au and, amongst their findings, the authors reported that
Category-D sheaths tend to be driven by CMEs that are detected in situ far
from their apex, as is indeed the case for the 2022 February 15 event.

Another interesting aspect to investigate is the contribution of CME
propagation and CME expansion to the sheath formation—CME-driven sheaths, in
fact, are considered “hybrid” structures that feature aspects of propagation
sheaths, in which the solar wind flows around a propagating object, and
expansion sheaths, in which the solar wind piles up ahead of an expanding
object (e.g., Siscoe & Odstrcil, 2008). To do so, we calculate two Mach
numbers: $M_{\mathrm{prop}}$, based on the ejecta propagation speed, and
$M_{\mathrm{exp}}$, based on the ejecta expansion speed (see Equations 1 and 2
in Salman et al., 2021, for a definition of the two parameters). The
propagation speed is simply the ejecta average speed, $V_{\mathrm{prop}}=589$
km$\cdot$s-1, whilst the expansion speed is defined as the half-difference
between the speeds of the leading and trailing edges (Owens et al., 2005),
$V_{\mathrm{exp}}=142$ km$\cdot$s-1. We obtain $M_{\mathrm{prop}}=0.27$ and
$M_{\mathrm{exp}}=0.82$, indicating that the sheath driven by the 2022
February 15 CME was mainly an expansion one. This is consistent with the
presence of a PUC region immediately ahead of the ejecta leading edge (see the
prominent density enhancement in the trailing portion of the sheath in Figure
5), usually attributed to strong CME overexpansion. In fact, the CME analysed
in this work might still have been experiencing significant expansion by the
time it was detected at Parker since the sheath appears overall less dense
than the following ejecta, in agreement with Salman et al. (2021) who found
that expansion sheaths tend to display lower densities on average.
Furthermore, Temmer & Bothmer (2022) estimated that the sheath density tends
to overcome the ejecta density in the heliocentric distance range of 0.09–0.28
au, after which expansion of the driver generally weakens.

###  4.3 Magnetic Ejecta

The passage of the sheath region was followed by the arrival of the magnetic
ejecta at both probes (see Figure 4). We determine the ejecta boundaries on
2022 February 16–17 during 15:41–07:51 UT at Bepi and 15:18–16:48 UT at
Parker—noting that flux rope signatures at the latter spacecraft were
identified until 06:32 UT on February 17 (see Section 3). These intervals
result in ejecta durations of 16.2 hr at Bepi and 25.5 hr at Parker, i.e.
significantly larger than the average of 7.2 hr reported by Janvier et al.
(2019) for CMEs encountered at ${\sim}$0.4 au. The mean (maximum) magnetic
field magnitude measured in the ejecta is 41.3 nT (61.4 nT) at Bepi and 45.9
nT (66.3 nT) at Parker, noting that values at both spacecraft are lower than
the average values at Mercury’s orbit of 55.3 nT (86.2 nT) as reported by
Winslow et al. (2015). Overall, possible reasons for the longer durations and
lower field magnitudes measured in the two ejecta investigated here are the
fact that the event was encountered in situ only through its southern flank
(see Section 2) as well as the strong expansion experienced by the CME—as
mentioned in Section 4.2, we find an expansion speed (based on Parker
measurements), $V_{\mathrm{exp}}$, of ${\sim}142$ km$\cdot$s-1. When
considering the magnetic cloud interval only, the expansion speed is basically
unchanged (${\sim}144$ km$\cdot$s-1), since the trailing portion of the ejecta
features a plateau in the bulk velocity. These values are significantly higher
than the average CME expansion speeds of ${\sim}30$ km$\cdot$s-1 found at 1 au
(e.g., Nieves-Chinchilla et al., 2018b; Lugaz et al., 2020), but it remains
unclear what the corresponding “typical” expansion speeds at ${\sim}$0.35 au
may be due to the lack of systematic in-situ plasma measurements—although it
is generally assumed that CME expansion should somewhat decrease between the
Sun and Earth’s orbit (e.g., Wang et al., 2005; Zhuang et al., 2023).

Figure 9: Flux rope fitting results at (a) Bepi and (b) Parker, showing
magnetic field data at each spacecraft and the corresponding quantities
resulting from different flux rope models. Note that, at Parker, the fitting
is applied to the magnetic cloud interval only (see Appendix C for the
corresponding results when considering the full magnetic obstacle). Table 4:
Flux rope fitting results at Bepi and Parker.

| FF | CC | EC | FE
---|---|---|---|---
| Bepi | Parker | Bepi | Parker | Bepi | Parker | Parker
$H$ | +1 | +1 | +1 | +1 | +1 | +1 | +1
$\vartheta_{0}$ [∘] | $-78.8$ | $-29.0$ | $-72.5$ | $-66.8$ | $-63.4$ | $-51.1$ | $-53.2$
$\varphi_{0}$ [∘] | 167.5 | 190.8 | 64.0 | 251.7 | 15.0 | 233.1 | 290.7
$B_{0}$ [nT] | 63.8 | 66.5 | 60.1 | 51.0 | 50.3 | 43.8 | 76.2
$R_{0}$ [au] | 0.166 | 0.074 | 0.165 | 0.108 | 0.145 | 0.115 | 0.101
$p_{0}$ [$R_{0}^{-1}$] | 0.681 | 0.573 | 0.715 | 0.052 | 0.588 | 0.178 | 0.396
$\tau$ [au-1] | 5.21 | 11.69 | 0.53 | 0.95 | 0.71 | 2.05 | 8.54
$\Phi_{\mathrm{ax}}$ [1021 Mx] | 5.35 | 1.10 | 6.31 | 2.31 | 3.91 | 1.21 | 2.39
$\Phi_{\mathrm{po}}$ [1021 Mx/au] | 9.89 | 4.57 | 5.94 | 3.97 | 4.87 | 3.76 | 7.20
C1 | — | — | 1.71 | 1.42 | 1.50 | 0.96 | —
$\psi$ [∘] | — | — | — | — | 19.4 | 74.3 | —
$\delta$ | — | — | — | — | 0.96 | 0.54 | —

  * •

_Notes._ $H$: helicity sign (or chirality); $\vartheta_{0}$: axis latitude;
$\varphi_{0}$: axis longitude; $B_{0}$: axial magnetic field magnitude;
$R_{0}$: flux rope radius; $p_{0}$: normalised impact parameter; $\tau$:
twist; $\Phi_{\mathrm{ax}}$: axial flux; $\Phi_{\mathrm{po}}$: poloidal flux;
C1: ratio of the azimuthal-to-axial current at the flux rope outer boundary;
$\psi$: propagation angle (i.e., rotation around the flux rope axis);
$\delta$: cross-sectional distortion (equals 1 for a circular cross-section
and 0 for maximum distortion). The assumed average speed for the CME ejecta in
is 654 km$\cdot$s-1, .

To obtain an indication of the overall cross-sectional ejecta structure
encountered by either probe, we evaluate the distortion parameter (DiP)
introduced by Nieves-Chinchilla et al. (2018b). In brief, the DiP quantifies
the level of distortion in a CME, due to e.g. interactions with the background
solar wind, by examining the measured profile of the magnetic field magnitude,
and is defined as the fraction of the full ejecta interval where 50% of the
total $B$ is accumulated. We find a DiP at Bepi of 0.48, whilst at Parker we
obtain DiP = 0.39 for the magnetic obstacle and DiP = 0.43 for the magnetic
cloud interval. According to Nieves-Chinchilla et al. (2018b), events with DiP
= 0.50 $\pm$ 0.07 can be considered symmetric in their magnetic field profile,
which is the case for Bepi according to our results. For Parker, the magnetic
obstacle interval features a DiP that is consistent with compression at the
front and that, together with the high $V_{\mathrm{exp}}$ mentioned above,
indicates that the asymmetric nature of the $B$ profile is due to expansion of
the structure as it crosses the spacecraft—also known as the ‘ageing effect’
(e.g., Démoulin et al., 2008). However, if we consider only the magnetic cloud
portion of the ejecta at Parker, we find a DiP value that suggest an
approximately-symmetric profile alongside a high $V_{\mathrm{exp}}$. At the
same time, it is unlikely that the large speed gradient (between the ejecta
leading and trailing edges) found at Parker corresponds to a flat speed
profile at Bepi. Nieves-Chinchilla et al. (2018b), in their study of 337 CMEs
detected at 1 au, found only a few events characterised by 0.43 $\leq$ DiP
$\leq$ 0.57 and $V_{\mathrm{exp}}\geq 100$ km$\cdot$s-1, contradicting the
expected effect of CME expansion on the magnetic field strength. It is unclear
why this is the case here, but one possibility may be local distortions in the
structure—see, e.g., how both sets of measurements in Figure 4 feature
irregular profiles of the magnetic field magnitude, with several “bumps”
across the ejecta passage, and how the plasma data at Parker in Figure 5
display complex trends in the density and temperature.

Figure 10: Magnetic field observations of the 2022 February 15 CME ejecta at
Bepi and Parker. The Bepi measurements have been stretched to match the
durations of (a) the magnetic cloud and (b) the magnetic obstacle at Parker
and time-shifted to align the two ejecta leading edge times. The dashed
vertical green lines mark the leading and trailing edges within which the
magnetic field correlations are computed. The solid profiles show 1-min
measurements, whilst the scatter points indicate the 30-min averaged data used
to calculate the corresponding Pearson correlation coefficients (reported on
the bottom left of each panel together with their p-values).

To evaluate the large-scale internal magnetic structure of the ejecta
encountered at Bepi and Parker we apply three different flux rope fitting
models to the in-situ magnetic field measurements. Specifically, we employ the
force-free constant-$\alpha$ (FF; Lepping et al., 1990), the circular-
cylindrical (CC; Nieves-Chinchilla et al., 2016), and the elliptic-cylindrical
(EC; Nieves-Chinchilla et al., 2018a) analytical descriptions of flux ropes to
recover geometric and magnetic parameters that allow us to estimate
orientation, size, and flux content. All these methods require an average CME
ejecta speed, for which we employ a value of 654 km$\cdot$s-1 based on the
speed profile of the magnetic cloud portion at Parker (under the assumption
that Bepi encountered similar velocities). Results applied to the (full)
ejecta at Bepi and the magnetic cloud portion of the ejecta at Parker are
shown and summarised in Figure 9 and Table 4. The corresponding fits for the
magnetic obstacle interval at Parker are reported and discussed in Appendix C.

We note that, despite the different fits appearing overall consistent at
either spacecraft from visual inspection of Figure 9, the results reported in
Table 4 display some stark differences, in terms of both geometric and
magnetic parameters. Nevertheless, we can extrapolate some common trends: For
example, all techniques recover a right-handed flux rope at both probes (as
expressed by the positive helicity sign, $H$), determine a higher axis
inclination at Bepi when compared to Parker (as expressed by the latitude
angle, $\vartheta_{0}$), and estimate a more central encounter at Parker as
opposed to Bepi (as expressed by the impact parameter, $p_{0}$). It has been
shown that flux rope fitting results using different techniques can feature
some disagreement even in “simple” cases characterised by negligible expansion
speeds and symmetric magnetic field strength profiles (e.g., Al-Haddad et al.,
2018), hence it is not surprising to find discrepancies in this complex,
flank-encounter event. Overall, the most important conclusion to draw is that
each of the flux rope models, when considered individually, returns very
different “best fit” parameter sets for the large-scale structure observed at
Bepi and Parker, reflecting the significant differences in the (local)
magnetic field time series measured within the ejecta by each spacecraft. We
remark that the same holds true when considering the magnetic obstacle
interval at Parker, as seen in the results presented in Appendix C.

To further investigate the coherence of the magnetic fields measured by the
two probes, we analyse the corresponding correlations in the observed time
series by adopting a similar approach to Lugaz et al. (2018), who compared the
ejecta of CMEs measured near 1 au over non-radial separations of 0.005–0.012
au ($0.29^{\circ}$–$0.69^{\circ}$). As was the case for the coherence analysis
in the sheath, the non-radial separation between Bepi and Parker of
${\sim}0.03$ au (${\sim}5^{\circ}$) during 2022 February 16–17 is larger than
the range explored by Lugaz et al. (2018), but falls well within the typical
scales of magnetic field coherence emerging from their study (see also the
discussion in the Introduction). The results of our analysis are shown in
Figure 10. In their study, Lugaz et al. (2018) aligned the magnetic field
profiles by calculating the lag between the pairs of data that maximised the
Pearson correlations, with the lags being computed separately for the field
magnitude and each of the three components. Here, on the other hand, we adopt
the time series stretching approach that we employed for the sheath region in
Section 4.2, allowing us to compare directly the magnetic fields measured at
Bepi with those detected at Parker in the magnetic cloud (Figure 10(a)) as
well as in the magnetic obstacle (Figure 10(b)) intervals. By doing so, we
find an intriguing result: In fact, the Pearson correlation coefficients are
[$B$, $B_{R}$, $B_{T}$, $B_{N}$] = [0.48, $-0.02$, 0.68, 0.28] when
considering the Parker magnetic cloud only, but change dramatically into [$B$,
$B_{R}$, $B_{T}$, $B_{N}$] = [0.08, 0.40, 0.82, 0.60] when computed over the
Parker magnetic obstacle interval. Hence, for the magnetic cloud we find good
correlation in $B_{T}$, moderate correlation in $B$, and weak-to-no
correlation in $B_{R}$ and , whilst for the magnetic obstacle we obtain
moderate-to-strong correlation in all the components with no correlation in
the magnitude.

Figure 11: Overview of the flux erosion analysis for the 2022 February 15 CME
ejecta at Parker, showing time series of the accumulated poloidal flux (black)
as well as the magnetic field components $B_{T}$ (green) and $B_{N}$ (red).
The same analysis is performed for the (a) magnetic cloud and (b) magnetic
obstacle intervals. The dashed vertical line marks the time at which flux
asymmetry is estimated to begin.

These results are in contrast to the ones from Lugaz et al. (2018), who found
the greatest correlations in the magnetic field strength ($B$) and estimated
that some degree of coherence should be maintained up to separations of
0.25–0.35 au ($15^{\circ}$–$21^{\circ}$) at 1 au—for the single components,
typical coherence scales lie instead between 0.07–0.12 au
($4^{\circ}$–$7^{\circ}$). According to our results, the highest degree of
coherence is obtained in the east–west ($B_{T}$) component regardless of the
interval considered at Parker, and in the case of the magnetic obstacle
interval it is possible to encounter no correlation in the field magnitude
whilst, at the same time, the single components all display moderate-to-strong
agreement. A reasonable explanation for the generally lower-than-expected
degree of coherence found in the 2022 February 15 event is that the CME was
encountered far from its nose and with a high impact parameter by both
spacecraft, thus considerably away from the stronger, possibly more ordered
inner layers of the embedded flux rope. Furthermore, we note that Lugaz et al.
(2018) deemed the correlation coefficient for the radial component of the
magnetic field ($B_{R}$) ill-defined due to the lack of variation that is
often observed along the Sun–observer line in flux rope-like magnetic
obstacles. In the event studied here, $B_{R}$ is comparable in intensity to
the other components, hence its lower correlation coefficient when compared to
$B_{T}$ and $B_{N}$ (regardless of the interval under consideration at Parker)
appears to be due to intrinsic differences between the two ejecta—at Bepi,
$B_{R}$ is predominantly positive, whilst the opposite holds true at Parker.
Again, this may be due to the glancing nature of the spacecraft encounters
under investigation.

The magnetic field correlation analysis reported above suggests that, indeed,
the “longer” interval that we considered at Parker corresponds to the
“original”, full CME ejecta. Nevertheless, from all the instances in which
these data are shown (Figures 4, 5, 9, and 10) it is clear that there is a
transition between the two distinct magnetic field environments of what we
have defined as the magnetic cloud and the trailing portion of the magnetic
obstacle. In Section 3.2, we tentatively attributed these features to magnetic
flux erosion, which is a consequence of CME reconnection with the surrounding
solar wind. Here, we investigate whether this is indeed the case. Figure 11
provides an overview of the results emerging from our analysis aimed at
quantifying the amount of poloidal flux eroded due to reconnection in the
interplanetary medium (i.e., shortly before the CME was detected in situ).
These results employ as input outputs from the EC model, which allows for
elliptical, distorted cross-sections and thus has more degrees of freedom than
the remaining two techniques showcased in Figure 9—we remark that we have
repeated the same analysis using instead the FF model with expansion (FE)
introduced in Appendix C, and results are very well consistent with the EC
ones. Once geometric parameters (from any fitting model) such as flux rope
axis direction, radius, and impact parameter are provided, we calculate the
inbound–outbound flux asymmetry using the “direct method” of Dasso et al.
(2005) as described in Pal et al. (2022). We perform these computations for
both the magnetic cloud (Figure 11(a)) and the full magnetic obstacle (Figure
11(b)) intervals. According to the results shown in Figure 11, flux asymmetry
is found at the back of the ejecta in both cases, indicating reconnection and
erosion at the front of the rope (see the scenario depicted in Figure 6 of Pal
et al., 2022). The asymmetry starts on 2022 February 17 at 05:25 UT (08:35
UT), and the eroded poloidal flux is $1.4\times 10^{21}$ Mx$\cdot$au-1
($1.5\times 10^{21}$ Mx$\cdot$au-1) for the shorter (longer) interval (noting,
however, that the glancing nature of the encounter may introduce additional
errors in the results; e.g., Ruffenach et al., 2015). Our “by-eye” estimate of
such boundary fell on February 17 at 06:32 UT, i.e. comfortably in between the
two times obtained with the flux erosion computation method. Thus, what
emerges from this investigation is that the ejecta encountered at Parker was
eroded, which may explain (at least in part) some of the differences in the
structures encountered at the two spacecraft.

##  5 Discussion

The analysis and results presented in Section 4 reveal a series of
similarities but also differences in the local measurements of the 2022
February 15 CME from Bepi and Parker, despite their relative proximity
(${\sim}$0.03 au in radial distance and ${\sim}$5∘ in non-radial separation).
The eruption responsible for the event observed in situ was an impressive
filament eruption that resulted in a fast (${\sim}2200$ km$\cdot$s-1) CME (see
Mierla et al., 2022), observed in remote-sensing imagery to propagate with a
significant northward component and thus expected to impact any in-situ, near-
the-ecliptic location through its southern flank. Here, we shall summarise the
main findings with respect to the main structures that have been investigated,
namely the interplanetary shock, the sheath region, and the magnetic ejecta.

Analysis of the CME-driven interplanetary shock (Section 4.1) revealed that
the two data sets featured an equal magnetic compression ratio, but
determination of the shock normal and related parameters was inconsistent
between the two probes. Whilst at Parker the three employed methods (MCT, MVA,
and MD3) were generally in agreement in determining a moderately quasi-
parallel shock with its normal pointing approximately towards the southeast,
at Bepi the two adopted techniques (MCT and MVA, since plasma data necessary
for MD3 were not available) provided two extremely different results: one
suggesting a strongly parallel shock and the other indicating a strongly
perpendicular one, with contrasting normal directions. It is interesting to
note that the MVA method at the two spacecraft provided shock normal
directions that are almost identical, but resulted in an intermediate shock at
Parker and a perpendicular one at Bepi. Overall, we concluded that the shock
properties at Parker were at least qualitatively well-defined, whilst at Bepi
it was not possible to obtain reliable results. It is likely that availability
of plasma data at Bepi would have aided towards the solution of the
encountered discrepancies: apart from allowing determination of other
properties such as density compression ratio and velocity jump, including
speed changes across the discontinuity in shock normal estimations is known to
provide more robust results. The shock normal directions determined using all
methods at Parker and MVA at Bepi—i.e., roughly southeasterly—were at least
consistent with the idealised scenario of a bubble-like shock surface that
propagated to the northwest of the in-situ observers.

Analysis of the CME-driven sheath region (Section 4.2) showed that the two
spacecraft detected a comparable amount of magnetic field fluctuations on
average, indicating similar conditions of the corresponding magnetic
environment. Another encountered similarity was that both sheaths had a PMS
embedded in its middle, although the resulting PMS plane displayed different
orientations. We speculated that the PMSs at the two probes formed via the
same mechanism, and that the obtained orientations reflected the turbulent
nature of the local (pre-shock-passage) solar wind. A direct comparison of the
magnetic field measurements within the two sheath region data sets showed good
correlation in the field magnitude, but weak-to-no correlation in the field
components. It is well known that CME-driven sheaths are highly fluctuating
structures (e.g., Moissard et al., 2019; Kilpua et al., 2020), hence
variations over relatively close locations may be expected. For example,
Kilpua et al. (2021) found, in a sheath measured at 1 au over distances of
$0.01$ au in the radial direction, $0.5^{\circ}$ in latitude, and
$1.4^{\circ}$ in longitude, different sheath durations, different amounts and
positioning of magnetic field discontinuities within the sheath, and even
different locations within the structure of an embedded small-scale flux rope.
A more complete understanding of sheath region formation, evolution, and 3D
variation will require multi-spacecraft in-depth analyses of CME-driven
sheaths during periods featuring radially and/or longitudinally aligned probes
(e.g., Good et al., 2020; Salman et al., 2020).

Analysis of the CME magnetic ejecta (Section 4.3) showed a single, relatively
coherent structure at Bepi, but a “two-part ejecta” at Parker—we identified
the leading portion as the magnetic cloud (corresponding to the “core” flux
rope), and the higher-fluctuating trailing part as reconnected (open) field
signature of erosion at the front of the ejecta. We employed different flux
rope fitting techniques to recover geometric and magnetic properties of the
ejecta measured at Bepi and Parker—considering both the magnetic cloud and the
full magnetic obstacle intervals at the latter—and found more or less dramatic
difference not only between the different models, but also between the two
spacecraft within a single model. It is well known that different flux rope
fitting models applied to the same data set may display significant
discrepancies, especially in the case of flank encounters with high impact
parameters (e.g., Riley et al., 2004; Al-Haddad et al., 2013). In the case
investigated here, one may have expected better agreement due to the
measurements being taken significantly closer to the Sun than 1 au, i.e. where
less CME evolution has occurred. However, Lynch et al. (2022) showed that flux
rope fitting models perform generally worse for flank encounters even as close
as 10–30 $R_{\odot}$ using results from a magnetohydrodynamic model, which are
characterised by smoother fields and do not fully reproduce the highly
turbulent nature of the solar wind. Nevertheless, most fitting techniques
(with the notable exception of the FF model at Parker) recovered a high-
inclination flux rope, in agreement with GCS reconstruction results based on
remote-sensing coronagraph observations (see Figure 3) and suggesting that the
CME as a whole largely maintained its orientation as it travelled to
${\sim}0.35$ au. The magnetic field correlation analysis between the two
ejecta (comparing Bepi with both ejecta “options” at Parker) showed the
highest agreement for the $B_{T}$ component, whilst correlation in the field
strength and the remaining two components varied depending on the ejecta
interval under consideration at Parker. In particular, it was interesting to
observe moderate-to-high correlation in all the components, but no correlation
in the magnitude for the magnetic obstacle interval at Parker.

Overall, our investigation of the 2022 February 15 CME measured in situ at two
relatively close spacecraft revealed some significant (local) variations of
its large-scale structure. For example, the dramatically different duration of
the ejecta interval—16.2 hr at Bepi and 25.5 hr at Parker, for a total
difference of 9.3 hr—cannot be explained uniquely in light of CME expansion
for a radial separation between the two probes of 0.03 au. Likewise, the
different flux rope orientations recovered via fitting models (keeping in
mind, however, the large uncertainties involved, ) suggest, in agreement with
previous work (e.g., Farrugia et al., 2011; Möstl et al., 2012; Pal et al.,
2023), that the axial field direction is more of a “local” quantity rather
than part of a coherent, large-scale flux tube. In the case analysed here, it
is possible that interaction with a following HPS had some influence on the
orientation of the ejecta at Parker, as e.g. the events investigated by
Farrugia et al. (2011) and Pal et al. (2023) involved interactions with stream
interaction regions or those studied by Möstl et al. (2012) involved CME–CME
interactions. Finally, it is interesting to speculate on the uniqueness of the
2022 February 15 event that was the focus of this work. At both probes, we
found average shock strengths, as well as longer durations and lower magnetic
field magnitudes in both the sheath and ejecta when compared to typical values
measured at Mercury’s orbit. The strong expansion that we found based on
Parker observations is in agreement with Scolini et al. (2021), who found that
CMEs tend to expand rapidly until 0.4 au and shift to a more moderate growth
rate at larger distances. Altogether, these features are consistent with those
of a rather strong CME encountered towards its flank, where magnetic and
kinematic properties are generally weaker. A follow-up investigation that
could significantly complement the present work should compare these results
with observations of a central, near-nose encounter under similar positioning
conditions of the involved spacecraft. It is possible, in fact, that sampling
two close-by trajectories closer to a flux rope central axis would result in
much more consistent in-situ data sets, that would in turn inform us as to the
expected coherence of CMEs across their full 3D structure. However, such a
study would have to rely, as this one, on a fortuitous spacecraft conjunction
together with a CME launched in a near-optimal direction, the likeliness of
which can be estimated at the moment only in probabilistic terms.

##  6 Summary and Conclusions

In this work, we have analysed in detail for the first time the mesoscale
structure of a CME that was detected at Mercury’s orbit by two different
probes, i.e. Bepi and Parker, that were separated by ${\sim}$0.03 au in radial
distance, ${\sim}$2∘ in latitude, and ${\sim}$4∘ in longitude (corresponding
to a 3D separation of 0.0416 au or ${\sim}$8.95 $R_{\odot}$). We have focussed
on characterising and comparing properties of the interplanetary shock, sheath
region, and magnetic ejecta as measured by the two spacecraft. Overall, we
have found some similarities, but also some profound differences between the
two sets of in-situ data that, although resulting from flank encounters with
the structure as a whole, are characterised by a relative non-radial angular
separation (${\sim}5^{\circ}$) that is smaller than the typical errors
associated with 3D reconstructions of CMEs based on remote-sensing data—for
example, Verbeke et al. (2023) found minimum uncertainties of $6^{\circ}$ in
latitude and $11^{\circ}$ in longitude using the GCS model.

Ultimately, the findings of this work resonate with the conclusions and
recommendations outlined by Lugaz et al. (2018), i.e. that the mesoscale range
of the parameter space is still left largely unexplored in the context of
CMEs, resulting in a knowledge gap over radial separations of 0.005–0.050 au
and longitudinal separations of $1^{\circ}$–$12^{\circ}$ (i.e., the expected
size of the cross-section of a CME ejecta at 1 au). Even more so, the work
reported here shows that the results of Lugaz et al. (2018) and Ala-Lahti et
al. (2020) apply even at shorter heliocentric distances than 1 au, despite the
generally lower amount of evolutionary processes such as interactions and
deformations that are expected to have taken place. Fortunately, the
importance of investigating mesoscales in the solar wind has been gaining more
traction in recent years (e.g., Viall et al., 2021), and novel missions are
being proposed to investigate variations and variability of solar transient
events (e.g., Allen et al., 2022; Lugaz et al., 2023; Nykyri et al., 2023).
The potential benefits of a constellation of spacecraft designed to explore
the mesoscale region would be invaluable not only for improving upon our
knowledge of the fundamental physics of CMEs, but also of other transient
phenomena such as stream interaction regions and solar energetic particles.

The findings of this work have also implications in space weather research and
operations. First of all, we remark on the importance of improving upon the
available remote-sensing observations for trajectory and size determination of
CMEs, since in-situ measurements can show some prominent variability over
short spatial scales. This could be achieved by increasing the number of
operational telescopes in space, and/or by observing the Sun and its
environment from novel viewpoints such as from outside the ecliptic plane
(e.g., Gibson et al., 2018; DeForest et al., 2023; Howard et al., 2023;
Palmerio et al., 2023b). From a modelling and forecasting perspective, we
highlight the importance of considering “swarms” of virtual spacecraft (around
Earth or the target body of interest) when generating predictions, with
separations of the synthetic probes even as little as $5^{\circ}$ in non-
radial distance to properly account for uncertainties in the physical
processes that are being simulated as well as in the determination of CME
input parameters from observations (e.g., Scolini et al., 2019; Asvestari et
al., 2021; Maharana et al., 2023; Palmerio et al., 2023a). Additionally, this
work showcased the need for reaching a better understanding and improving
predictions of CME-driven sheath regions—an effort that is only in its infancy
at the time of writing (e.g., Kay et al., 2020).

The relevance of this work to space weather research is not limited to
improving predictions at Earth, but has also applications for planetary
science. The event studied here was encountered in situ by two spacecraft at
Mercury’s orbit, allowing us to analyse its characteristics at heliocentric
distances that are significantly closer to the Sun than 1 au. Understanding
the structure and evolution of CMEs within Mercury’s orbit, in fact, is of
high importance for the success of Bepi after its planned Mercury orbital
insertion, as solar eruptive transients are the sources of many of the
planetary dynamics on which the mission will focus (e.g., Milillo et al.,
2020). Our knowledge of space weather at Mercury, including solar wind
interaction with the Hermean magnetosphere, is at the moment rather limited,
although some progress has been achieved via data collected during a few
flybys (e.g., from Mariner 10) and orbital measurements from MESSENGER (e.g.,
Killen et al., 2004; Winslow et al., 2017). Future observations from Parker,
SolO, and Bepi (cruise phase) of CMEs at Mercury’s orbit in the solar wind, as
well as from Bepi at Mercury after orbital insertion, will greatly enhance our
understanding of space weather phenomena at the first planet from the Sun.

Finally, this analysis has been possible due to a fortuitous relative
configuration of two probes, Bepi and Parker, at a time during which a
remarkable CME was fortuitously launched in their direction. Even though such
events are understandably rare, taking advantage of these “special kinds” of
multi-spacecraft encounters, i.e. characterised by small radial _and_ angular
separations, is a concrete strategy that can be applied at present, at least
whilst we wait for one or more dedicated missions to help characterising the
solar wind and its transients over all the relevant spatial scales.

## Acknowledgments

E.P. acknowledges support from NASA’s Parker Solar Probe Guest Investigators
(PSP-GI; no. 80NSSC22K0349), Heliophysics Theory, Modeling, and Simulations
(HTMS; no. 80NSSC20K1274), and Living With a Star Strategic Capabilities (LWS-
SC; no. 80NSSC22K0893) programmes, as well as the Parker Solar Probe WISPR
contract no. NNG11EK11I to NRL (under subcontract no. N00173-19-C-2003 to
PSI). F.C., S.P., and A.J.W. acknowledge the financial support by an
appointment to the NASA Postdoctoral Program at the NASA Goddard Space Flight
Center, administered by USRA through a contract with NASA. B.S.-C.
acknowledges support from the UK-STFC Ernest Rutherford fellowship
ST/V004115/1 and the BepiColombo guest investigator grant ST/Y000439/1. B.J.L.
acknowledges support from NASA HSR no. 80NSSC20K1448 and HGI no.
80NSSC21K0731. B.J.L. and C.O.L. acknowledge NASA LWS grant no. 80NSSC21K1325.
D.L. acknowledges support from NASA Living With a Star (LWS) programme
NNH19ZDA001N-LWS. A.N.Z., L.R., and M.M. thank the Belgian Federal Science
Policy Office (BELSPO) for the provision of financial support in the framework
of the PRODEX Programme of the European Space Agency (ESA) under contract
numbers 4000112292, 4000134088, 4000134474, and 4000136424. L.R.-G.
acknowledges the financial support by the Spanish Ministerio de Ciencia,
Innovación y Universidades FEDER/MCIU/AEI Projects ESP2017-88436-R and
PID2019-104863RB-I00/AEI/10.13039/501100011033. L.R.-G. and N.D. acknowledges
support by the European Union’s Horizon 2020 research and innovation program
under grant agreement no. 101004159 (SERPENTINE). N.D. also acknowledges
funding of the Academy of Finland (SHOCKSEE, grant no. 346902).

BepiColombo is an ESA–JAXA mission, where MPO has been built and is operated
by ESA.

Parker Solar Probe was designed, built, and is now operated by the Johns
Hopkins Applied Physics Laboratory as part of NASA’s LWS programme (contract
no. NNN06AA01C). Support from the LWS management and technical team has played
a critical role in the success of the Parker Solar Probe mission.

Solar Orbiter is a space mission of international collaboration between ESA
and NASA, operated by ESA. The EUI instrument was built by CSL, IAS, MPS,
MSSL/UCL, PMOD/WRC, ROB, LCF/IO with funding from the Belgian Federal Science
Policy Office; the Centre National d’Etudes Spatiales (CNES); the UK Space
Agency (UKSA); the Bundesministerium für Wirtschaft und Energie (BMWi) through
the Deutsches Zentrum für Luft- und Raumfahrt (DLR); and the Swiss Space
Office (SSO).

##  Appendix A CME Observations by the WISPR Cameras Onboard Parker

Observations of the 2022 February 15 CME captured by the WISPR Inner (field of
view from $13.5^{\circ}$ to $53.0^{\circ}$) and Outer (field of view from
$50.0^{\circ}$ to $108.0^{\circ}$) cameras onboard Parker are part of the
observing sequence scheduled for the spacecraft’s Encounter 11 (E11) with the
Sun, with perihelion on 2022 February 25 at 13.3 $R_{\odot}$. An overview of
the Sun–WISPR observing geometry, available data, and science achievements
during E11 has been provided by Liewer et al. (2023).

A few images from the WISPR/Inner camera containing the 2022 February 15 CME
in its field of view are shown in Figure 12. These data were processed via the
L3 Algorithm developed by the WISPR instrument team and described in Liewer et
al. (2023). During our period of interest (2022 February 15–17, i.e.
approximately 10 days before the E11 perihelion), WISPR was pointing over the
western limb of the Sun (from Parker’s viewpoint), as can be seen by the
streamer emanating from the left of each frame in Figure 12. The CME was
observed to cross the telescope’s field of view from left to right
predominantly over its top half, indicating that Parker observed a CME that
propagated mostly towards the north and experienced little-to-no deflection
towards the equatorial plane after leaving the Sun, confirming the assessment
in Section 2 based on other available remote-sensing imagery.

Figure 12: Overview of the observations of the 2022 February 15 event taken by
the WISPR Inner camera onboard Parker. The CME is shown as it propagates in
three frames separated by 3 hr each. The planet (brightest point) in the
lower-left quadrant of each image is Earth.

As mentioned in Section 4.1, the CME-driven shock impacted Parker on February
16 at 07:25 UT, i.e. between the observation times of panels (b) and (c) of
Figure 12. This means that the spacecraft imaged the CME as it was being
impacted by it, an occurrence historically considered exceptional and that is
becoming more common during the Parker era (e.g., Romeo et al., 2023; Wood et
al., 2023) as the probe approaches the Sun by lowering its perihelion and the
Solar Cycle 25 activity levels increase. Shortly after the time of the ejecta
leading edge passage, i.e. February 16 at 15:18 UT, trailing flows from the
CME were observed in the WISPR/Outer camera—these images, however, are
characterised by high noise levels and moving features in them can be better
appreciated in video format222WISPR movies for the Inner and Outer cameras,
sorted chronologically by solar encounter number, are available at
https://wispr.nrl.navy.mil/wisprdata., hence they are not shown here.

##  Appendix B Processing and Calibration of the Bepi Magnetic Field Data

The primary objective of the magnetometer instrument MPO-MAG onboard the
Mercury Planetary Orbiter (MPO) of the BepiColombo mission is to map Mercury’s
magnetic field as well as the interaction of the hermean magnetosphere with
the solar wind. In order to characterise the solar wind at short distances
from the Sun (i.e., at Mercury’s orbit), MPO-MAG has been in operation during
most of the Bepi cruise phase to Mercury, contributing to studies of solar
wind turbulence and transient phenomena (Heyner et al., 2021).

Since launch, MPO-MAG has been in continuous operation outside the solar
electric propulsion periods (SEPS; Montagnon et al., 2021), until beginning of
2022 when it was decided that the instrument will remain in operation during
these periods in background mode. MPO-MAG observations during arcs remain of
high accuracy but special pre-processing cleaning by the instrument team is
needed as the two sensors of the instrument are influenced by the magnetic
disturbance field of the spacecraft. The 2022 February 15 event occurred
during one of these SEPS arcs, starting on 2022 February 15 at 02:17:20 UT.
The main consequences dependent on the individual thrusters being used and the
thrust levels, and a shift of the components by 10 nT was found, as well as an
increase in the noise floor. In this regard, the MPO-MAG team cleaned the data
phases and removed the noise for this study, by the field as well as

We consider that the version of the data used in this study is the most
accurate available for this event and the total field and components can be
trusted within an error of 10 nT in magnitude. We also note that the arrival
times of the shock and sheath match very well with the Bepi high-energy
particles observed by the BepiColombo Environment Radiation Monitor (BERM;
Pinto et al., 2022), the only other instrument in operation during this SEPS
arc . Therefore, we also trust that the timing of the crossing of the
different regions of the CME observed by MPO-MAG are accurate.

##  Appendix C Flux Rope Fits for the Magnetic Obstacle Interval at Parker

To compare the flux rope fitting results at Bepi with both ejecta interval
possibilities at Parker, we repeat the reconstructions shown in Figure 9(b)
for the magnetic cloud interval by considering the full magnetic obstacle
identified at Parker. These results are presented in Figure 13 and Table 5.

Figure 13: Flux rope fitting results at Parker obtained when considering the
full magnetic ejecta interval, showing magnetic field and bulk speed data as
well as the corresponding quantities resulting from different flux rope
models. Table 5: Flux rope fitting results for the full ejecta interval at
Parker.

| FF | CC | EC | FE
---|---|---|---|---
$H$ | +1 | +1 | +1 | +1
$\vartheta_{0}$ [∘] | $-7.1$ | $-49.8$ | $-51.4$ | $-59.7$
$\varphi_{0}$ [∘] | 181.2 | 1.0 | 326.5 | 312.6
$B_{0}$ [nT] | 71.0 | 41.6 | 28.2 | 83.7
$R_{0}$ [au] | 0.053 | 0.135 | 0.224 | 0.120
$p_{0}$ [$R_{0}^{-1}$] | 0.905 | 0.485 | 0.307 | 0.430
$\tau$ [au-1] | 16.32 | 0.84 | 1.79 | 7.21
$\Phi_{\mathrm{ax}}$ [1021 Mx] | 0.60 | 2.92 | 2.21 | 3.68
$\Phi_{\mathrm{po}}$ [1021 Mx/au] | 3.50 | 4.43 | 5.72 | 9.37
C1 | — | 1.30 | 0.65 | —
$\psi$ [∘] | — | — | 122.8 | —
$\delta$ | — | — | 0.41 | —

  * •

_Notes._ The parameters shown are in the same format as in Table 4. The
assumed average speed for the CME ejecta in the FF, CC, and EC fits is 589
km$\cdot$s-1, whilst the FE procedure uses the time-dependent speed shown in
the bottom panel of Figure 13.

In the case of the magnetic obstacle interval at Parker, the different flux
rope fitting techniques appear visually significantly less consistent with
each other than the ones shown in Figure 9 for both the ejecta at Bepi and the
magnetic cloud at Parker. This may be due to the strong asymmetry seen in the
magnetic field magnitude between the leading and trailing portions of the
magnetic obstacle. The inconsistencies are also reflected in the resulting
parameters presented in Table 5, which include e.g. flux rope axis directions
that differ by up to ${\sim}53^{\circ}$ in latitude and ${\sim}180^{\circ}$ in
longitude, as well as impact parameters that range between ${\sim}30$% and
${\sim}90$% away from the central axis along the cross-sectional radius.

Visually, the FE fit appears to better match the data, which is not surprising
since this model takes CME expansion into account and the 2022 February 15
event was strongly expanding when it was measured in situ by Parker (as shown
in the bottom panel of Figure 13). However, even the FE results do not
reproduce the $B_{R}$ profile particularly well, which on the other hand is
poorly fitted by all models even when considering the magnetic cloud interval
only (see Figure 9(b)). Overall, each technique applied to the full magnetic
obstacle at Parker retrieves a flux rope structure that is fundamentally
different from the corresponding results obtained from the magnetic cloud time
series, showcasing the complexity of the structure under analysis.

## References

  * Abraham-Shrauner & Yun (1976) Abraham-Shrauner, B., & Yun, S. H. 1976, J. Geophys. Res., 81, 2097, doi: 10.1029/JA081i013p02097
  * Al-Haddad et al. (2018) Al-Haddad, N., Nieves-Chinchilla, T., Savani, N. P., Lugaz, N., & Roussev, I. I. 2018, Sol. Phys., 293, 73, doi: 10.1007/s11207-018-1288-3
  * Al-Haddad et al. (2013) Al-Haddad, N., Nieves-Chinchilla, T., Savani, N. P., et al. 2013, Sol. Phys., 284, 129, doi: 10.1007/s11207-013-0244-5
  * Ala-Lahti et al. (2020) Ala-Lahti, M., Ruohotie, J., Good, S., Kilpua, E. K. J., & Lugaz, N. 2020, , 125, e2020JA028002, doi: 10.1029/2020JA028002
  * Allen et al. (2022) Allen, R. C., Smith, E. J., Anderson, B. J., et al. 2022, , 9, 1002273, doi: 10.3389/fspas.2022.1002273
  * Astropy Collaboration et al. (2022) Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935, 167, doi: 10.3847/1538-4357/ac7c74
  * Asvestari et al. (2021) Asvestari, E., Pomoell, J., Kilpua, E., et al. 2021, A&A, 652, A27, doi: 10.1051/0004-6361/202140315
  * Bale et al. (2016) Bale, S. D., Goetz, K., Harvey, P. R., et al. 2016, Space Sci. Rev., 204, 49, doi: 10.1007/s11214-016-0244-5
  * Balogh et al. (1995) Balogh, A., Gonzalez-Esparza, J. A., Forsyth, R. J., et al. 1995, Space Sci. Rev., 72, 171, doi: 10.1007/BF00768774
  * Barnard et al. (2017) Barnard, L. A., de Koning, C. A., Scott, C. J., et al. 2017, , 15, 782, doi: 10.1002/2017SW001609
  * Benkhoff et al. (2021) Benkhoff, J., Murakami, G., Baumjohann, W., et al. 2021, Space Sci. Rev., 217, 90, doi: 10.1007/s11214-021-00861-4
  * Borrini et al. (1982) Borrini, G., Gosling, J. T., Bame, S. J., & Feldman, W. C. 1982, J. Geophys. Res., 87, 7370, doi: 10.1029/JA087iA09p07370
  * Borrini et al. (1981) Borrini, G., Gosling, J. T., Bame, S. J., Feldman, W. C., & Wilcox, J. M. 1981, J. Geophys. Res., 86, 4565, doi: 10.1029/JA086iA06p04565
  * Bothmer & Schwenn (1998) Bothmer, V., & Schwenn, R. 1998, , 16, 1, doi: 10.1007/s00585-997-0001-x
  * Braga et al. (2022) Braga, C. R., Vourlidas, A., Liewer, P. C., et al. 2022, ApJ, 938, 13, doi: 10.3847/1538-4357/ac90bf
  * Brueckner et al. (1995) Brueckner, G. E., Howard, R. A., Koomen, M. J., et al. 1995, Sol. Phys., 162, 357, doi: 10.1007/BF00733434
  * Burlaga et al. (1981) Burlaga, L., Sittler, E., Mariani, F., & Schwenn, R. 1981, J. Geophys. Res., 86, 6673, doi: 10.1029/JA086iA08p06673
  * Burton et al. (1996) Burton, M. E., Smith, E. J., Balogh, A., et al. 1996, A&A, 316, 313
  * Cane (1988) Cane, H. V. 1988, J. Geophys. Res., 93, 1, doi: 10.1029/JA093iA01p00001
  * Carcaboso et al. (2020) Carcaboso, F., Gómez-Herrero, R., Espinosa Lara, F., et al. 2020, A&A, 635, A79, doi: 10.1051/0004-6361/201936601
  * Case et al. (2020) Case, A. W., Kasper, J. C., Stevens, M. L., et al. 2020, ApJS, 246, 43, doi: 10.3847/1538-4365/ab5a7b
  * Cécere et al. (2020) Cécere, M., Sieyra, M. V., Cremades, H., et al. 2020, , 65, 1654, doi: 10.1016/j.asr.2019.08.043
  * Colburn & Sonett (1966) Colburn, D. S., & Sonett, C. P. 1966, Space Sci. Rev., 5, 439, doi: 10.1007/BF00240575
  * Crooker et al. (2004) Crooker, N. U., Huang, C. L., Lamassa, S. M., et al. 2004, J. Geophys. Res., 109, A03107, doi: 10.1029/2003JA010170
  * Darnel et al. (2022) Darnel, J. M., Seaton, D. B., Bethge, C., et al. 2022, , 20, e2022SW003044, doi: 10.1029/2022SW003044
  * Das et al. (2011) Das, I., Opher, M., Evans, R., Loesch, C., & Gombosi, T. I. 2011, ApJ, 729, 112, doi: 10.1088/0004-637X/729/2/112
  * Dasso et al. (2005) Dasso, S., Mandrini, C. H., Luoni, M. L., et al. 2005, in ESASP, Vol. 592, Solar Wind 11/SOHO 16, Connecting Sun and Heliosphere, ed. B. Fleck, T. H. Zurbuchen, & H. Lacoste, Noordwijk: ESA Publications Division, 605
  * Dasso et al. (2007) Dasso, S., Nakwacki, M. S., Démoulin, P., & Mandrini, C. H. 2007, Sol. Phys., 244, 115, doi: 10.1007/s11207-007-9034-2
  * Davies et al. (2022) Davies, E. E., Winslow, R. M., Scolini, C., et al. 2022, ApJ, 933, 127, doi: 10.3847/1538-4357/ac731a
  * Davies et al. (2021) Davies, E. E., Möstl, C., Owens, M. J., et al. 2021, A&A, 656, A2, doi: 10.1051/0004-6361/202040113
  * DeForest et al. (2023) DeForest, C., Viall-Kepko, N., Fan, Y., Gibson, S., & Seaton, D. 2023, BAAS, 55, 089, doi: 10.3847/25c2cfeb.c02cba78
  * Démoulin et al. (2008) Démoulin, P., Nakwacki, M. S., Dasso, S., & Mandrini, C. H. 2008, Sol. Phys., 250, 347, doi: 10.1007/s11207-008-9221-9
  * Domingo et al. (1995) Domingo, V., Fleck, B., & Poland, A. I. 1995, Sol. Phys., 162, 1, doi: 10.1007/BF00733425
  * Farrugia et al. (2008) Farrugia, C. J., Erkaev, N. V., Taubenschuss, U., et al. 2008, J. Geophys. Res., 113, A00B01, doi: 10.1029/2007JA012953
  * Farrugia et al. (1999) Farrugia, C. J., Janoo, L. A., Torbert, R. B., et al. 1999, in AIP Conf. Ser., Vol. 471, Solar Wind Nine, ed. S. R. Habbal, R. Esser, J. V. Hollweg, & P. A. Isenberg, Melville, NY: AIP, 745–748, doi: 10.1063/1.58724
  * Farrugia et al. (2011) Farrugia, C. J., Berdichevsky, D. B., Möstl, C., et al. 2011, , 73, 1254, doi: 10.1016/j.jastp.2010.09.011
  * Fox et al. (2016) Fox, N. J., Velli, M. C., Bale, S. D., et al. 2016, Space Sci. Rev., 204, 7, doi: 10.1007/s11214-015-0211-6
  * Freeland & Handy (1998) Freeland, S. L., & Handy, B. N. 1998, Sol. Phys., 182, 497, doi: 10.1023/A:1005038224881
  * Giacalone et al. (2023) Giacalone, J., Cohen, C. M. S., McComas, D. J., et al. 2023, ApJ, 958, 144, doi: 10.3847/1538-4357/acfb86
  * Gibson et al. (2018) Gibson, S. E., Vourlidas, A., Hassler, D. M., et al. 2018, , 5, 32, doi: 10.3389/fspas.2018.00032
  * Good et al. (2020) Good, S. W., Ala-Lahti, M., Palmerio, E., Kilpua, E. K. J., & Osmane, A. 2020, ApJ, 893, 110, doi: 10.3847/1538-4357/ab7fa2
  * Good et al. (2019) Good, S. W., Kilpua, E. K. J., LaMoury, A. T., et al. 2019, , 124, 4960, doi: 10.1029/2019JA026475
  * Gopalswamy et al. (2009) Gopalswamy, N., Mäkelä, P., Xie, H., Akiyama, S., & Yashiro, S. 2009, J. Geophys. Res., 114, A00A22, doi: 10.1029/2008JA013686
  * Gosling et al. (1987) Gosling, J. T., Baker, D. N., Bame, S. J., et al. 1987, J. Geophys. Res., 92, 8519, doi: 10.1029/JA092iA08p08519
  * Gui et al. (2011) Gui, B., Shen, C., Wang, Y., et al. 2011, Sol. Phys., 271, 111, doi: 10.1007/s11207-011-9791-9
  * Guo et al. (2021) Guo, F., Giacalone, J., & Zhao, L. 2021, , 8, 27, doi: 10.3389/fspas.2021.644354
  * Heinemann et al. (2019) Heinemann, S. G., Temmer, M., Farrugia, C. J., et al. 2019, Sol. Phys., 294, 121, doi: 10.1007/s11207-019-1515-6
  * Heyner et al. (2021) Heyner, D., Auster, H. U., Fornaçon, K. H., et al. 2021, Space Sci. Rev., 217, 52, doi: 10.1007/s11214-021-00822-x
  * Howard et al. (2023) Howard, R., Liewer, P., & Vourlidas, A. 2023, BAAS, 55, 174, doi: 10.3847/25c2cfeb.9b5e6e6d
  * Howard et al. (2008) Howard, R. A., Moses, J. D., Vourlidas, A., et al. 2008, Space Sci. Rev., 136, 67, doi: 10.1007/s11214-008-9341-4
  * Illing & Hundhausen (1985) Illing, R. M. E., & Hundhausen, A. J. 1985, J. Geophys. Res., 90, 275, doi: 10.1029/JA090iA01p00275
  * Isavnin et al. (2013) Isavnin, A., Vourlidas, A., & Kilpua, E. K. J. 2013, Sol. Phys., 284, 203, doi: 10.1007/s11207-012-0214-3
  * Janvier et al. (2014) Janvier, M., Démoulin, P., & Dasso, S. 2014, A&A, 565, A99, doi: 10.1051/0004-6361/201423450
  * Janvier et al. (2019) Janvier, M., Winslow, R. M., Good, S., et al. 2019, , 124, 812, doi: 10.1029/2018JA025949
  * Jian et al. (2018) Jian, L. K., Russell, C. T., Luhmann, J. G., & Galvin, A. B. 2018, ApJ, 855, 114, doi: 10.3847/1538-4357/aab189
  * Jones & Balogh (2000) Jones, G. H., & Balogh, A. 2000, J. Geophys. Res., 105, 12713, doi: 10.1029/2000JA900003
  * Jones et al. (2002) Jones, G. H., Rees, A., Balogh, A., & Forsyth, R. J. 2002, Geophys. Res. Lett., 29, 1520, doi: 10.1029/2001GL014110
  * Kaiser et al. (2008) Kaiser, M. L., Kucera, T. A., Davila, J. M., et al. 2008, Space Sci. Rev., 136, 5, doi: 10.1007/s11214-007-9277-0
  * Kajdič et al. (2019) Kajdič, P., Preisser, L., Blanco-Cano, X., Burgess, D., & Trotta, D. 2019, ApJ, 874, L13, doi: 10.3847/2041-8213/ab0e84
  * Kallenrode et al. (1993) Kallenrode, M. B., Wibberenz, G., Kunow, H., et al. 1993, Sol. Phys., 147, 377, doi: 10.1007/BF00690726
  * Kasper et al. (2016) Kasper, J. C., Abiad, R., Austin, G., et al. 2016, Space Sci. Rev., 204, 131, doi: 10.1007/s11214-015-0206-3
  * Kataoka et al. (2005) Kataoka, R., Watari, S., Shimada, N., Shimazu, H., & Marubashi, K. 2005, Geophys. Res. Lett., 32, L12103, doi: 10.1029/2005GL022777
  * Kay et al. (2020) Kay, C., Nieves-Chinchilla, T., & Jian, L. K. 2020, , 125, e2019JA027423, doi: 10.1029/2019JA027423
  * Kay et al. (2015) Kay, C., Opher, M., & Evans, R. M. 2015, ApJ, 805, 168, doi: 10.1088/0004-637X/805/2/168
  * Kay & Palmerio (2023) Kay, C., & Palmerio, E. 2023, arXiv e-prints, arXiv:2311.10712, doi: 10.48550/arXiv.2311.10712
  * Khoo et al. (2024) Khoo, L. Y., Sánchez-Cano, B., Lee, C. O., et al. 2024, ApJ, in press
  * Killen et al. (2004) Killen, R. M., Sarantos, M., & Reiff, P. H. 2004, , 33, 1899, doi: 10.1016/j.asr.2003.02.020
  * Kilpua et al. (2017) Kilpua, E., Koskinen, H. E. J., & Pulkkinen, T. I. 2017, , 14, 5, doi: 10.1007/s41116-017-0009-6
  * Kilpua et al. (2013) Kilpua, E. K. J., Isavnin, A., Vourlidas, A., Koskinen, H. E. J., & Rodriguez, L. 2013, , 31, 1251, doi: 10.5194/angeo-31-1251-2013
  * Kilpua et al. (2015) Kilpua, E. K. J., Lumme, E., Andreeova, K., Isavnin, A., & Koskinen, H. E. J. 2015, , 120, 4112, doi: 10.1002/2015JA021138
  * Kilpua et al. (2009) Kilpua, E. K. J., Liewer, P. C., Farrugia, C., et al. 2009, Sol. Phys., 254, 325, doi: 10.1007/s11207-008-9300-y
  * Kilpua et al. (2019a) Kilpua, E. K. J., Good, S. W., Palmerio, E., et al. 2019a, , 6, 50, doi: 10.3389/fspas.2019.00050
  * Kilpua et al. (2019b) Kilpua, E. K. J., Fontaine, D., Moissard, C., et al. 2019b, , 17, 1257, doi: 10.1029/2019SW002217
  * Kilpua et al. (2020) Kilpua, E. K. J., Fontaine, D., Good, S. W., et al. 2020, , 38, 999, doi: 10.5194/angeo-38-999-2020
  * Kilpua et al. (2021) Kilpua, E. K. J., Good, S. W., Dresing, N., et al. 2021, A&A, 656, A8, doi: 10.1051/0004-6361/202140838
  * Kouloumvakos et al. (2022) Kouloumvakos, A., Kwon, R. Y., Rodríguez-García, L., et al. 2022, A&A, 660, A84, doi: 10.1051/0004-6361/202142515
  * Koval & Szabo (2010) Koval, A., & Szabo, A. 2010, J. Geophys. Res., 115, A12105, doi: 10.1029/2010JA015373
  * Lai et al. (2012) Lai, H. R., Russell, C. T., Jian, L. K., et al. 2012, Sol. Phys., 278, 421, doi: 10.1007/s11207-012-9955-2
  * Lavraud et al. (2014) Lavraud, B., Ruffenach, A., Rouillard, A. P., et al. 2014, , 119, 26, doi: 10.1002/2013JA019154
  * Lavraud et al. (2020) Lavraud, B., Fargette, N., Réville, V., et al. 2020, ApJ, 894, L19, doi: 10.3847/2041-8213/ab8d2d
  * Lavraud et al. (2021) Lavraud, B., Kieokaew, R., Fargette, N., et al. 2021, A&A, 656, A37, doi: 10.1051/0004-6361/202141149
  * Lepping & Behannon (1980) Lepping, R. P., & Behannon, K. W. 1980, J. Geophys. Res., 85, 4695, doi: 10.1029/JA085iA09p04695
  * Lepping et al. (1990) Lepping, R. P., Jones, J. A., & Burlaga, L. F. 1990, J. Geophys. Res., 95, 11957, doi: 10.1029/JA095iA08p11957
  * Lepri & Rivera (2021) Lepri, S. T., & Rivera, Y. J. 2021, ApJ, 912, 51, doi: 10.3847/1538-4357/abea9f
  * Li et al. (2018) Li, Y., Luhmann, J. G., & Lynch, B. J. 2018, Sol. Phys., 293, 135, doi: 10.1007/s11207-018-1356-8
  * Liewer et al. (2015) Liewer, P., Panasenco, O., Vourlidas, A., & Colaninno, R. 2015, Sol. Phys., 290, 3343, doi: 10.1007/s11207-015-0794-9
  * Liewer et al. (2023) Liewer, P. C., Vourlidas, A., Stenborg, G., et al. 2023, ApJ, 948, 24, doi: 10.3847/1538-4357/acc8c7
  * Liu et al. (2018) Liu, Y. A., Liu, Y. D., Hu, H., Wang, R., & Zhao, X. 2018, ApJ, 854, 126, doi: 10.3847/1538-4357/aaa959
  * Livi et al. (2022) Livi, R., Larson, D. E., Kasper, J. C., et al. 2022, ApJ, 938, 138, doi: 10.3847/1538-4357/ac93f5
  * Lugaz & Farrugia (2014) Lugaz, N., & Farrugia, C. J. 2014, Geophys. Res. Lett., 41, 769, doi: 10.1002/2013GL058789
  * Lugaz et al. (2012) Lugaz, N., Farrugia, C. J., Davies, J. A., et al. 2012, ApJ, 759, 68, doi: 10.1088/0004-637X/759/1/68
  * Lugaz et al. (2018) Lugaz, N., Farrugia, C. J., Winslow, R. M., et al. 2018, ApJ, 864, L7, doi: 10.3847/2041-8213/aad9f4
  * Lugaz et al. (2020) Lugaz, N., Salman, T. M., Winslow, R. M., et al. 2020, ApJ, 899, 119, doi: 10.3847/1538-4357/aba26b
  * Lugaz et al. (2022) Lugaz, N., Salman, T. M., Zhuang, B., et al. 2022, ApJ, 929, 149, doi: 10.3847/1538-4357/ac602f
  * Lugaz et al. (2023) Lugaz, N., Lee, C. O., Jian, L. K., et al. 2023, BAAS, 55, 249, doi: 10.3847/25c2cfeb.ac2c2454
  * Luhmann (1995) Luhmann, J. G. 1995, , 15, 355, doi: 10.1016/0273-1177(94)00117-J
  * Lynch et al. (2022) Lynch, B. J., Al-Haddad, N., Yu, W., Palmerio, E., & Lugaz, N. 2022, , 70, 1614, doi: 10.1016/j.asr.2022.05.004
  * Maharana et al. (2023) Maharana, A., Scolini, C., Schmieder, B., & Poedts, S. 2023, A&A, 675, A136, doi: 10.1051/0004-6361/202345902
  * Marubashi & Lepping (2007) Marubashi, K., & Lepping, R. P. 2007, , 25, 2453, doi: 10.5194/angeo-25-2453-2007
  * Masías-Meza et al. (2016) Masías-Meza, J. J., Dasso, S., Démoulin, P., Rodriguez, L., & Janvier, M. 2016, A&A, 592, A118, doi: 10.1051/0004-6361/201628571
  * Maunder et al. (2022) Maunder, M. L., Foullon, C., Forsyth, R., Barnes, D., & Davies, J. 2022, Sol. Phys., 297, 148, doi: 10.1007/s11207-022-02077-3
  * Mierla et al. (2022) Mierla, M., Zhukov, A. N., Berghmans, D., et al. 2022, A&A, 662, L5, doi: 10.1051/0004-6361/202244020
  * Milillo et al. (2020) Milillo, A., Fujimoto, M., Murakami, G., et al. 2020, Space Sci. Rev., 216, 93, doi: 10.1007/s11214-020-00712-8
  * Moissard et al. (2019) Moissard, C., Fontaine, D., & Savoini, P. 2019, , 124, 8208, doi: 10.1029/2019JA026952
  * Montagnon et al. (2021) Montagnon, E., Budnik, F., Casale, M., et al. 2021, Space Sci. Rev., 217, 32, doi: 10.1007/s11214-021-00805-y
  * Möstl et al. (2012) Möstl, C., Farrugia, C. J., Kilpua, E. K. J., et al. 2012, ApJ, 758, 10, doi: 10.1088/0004-637X/758/1/10
  * Möstl et al. (2015) Möstl, C., Rollett, T., Frahm, R. A., et al. 2015, , 6, 7135, doi: 10.1038/ncomms8135
  * Möstl et al. (2022) Möstl, C., Weiss, A. J., Reiss, M. A., et al. 2022, ApJ, 924, L6, doi: 10.3847/2041-8213/ac42d0
  * Müller et al. (2020) Müller, D., St. Cyr, O. C., Zouganelis, I., et al. 2020, A&A, 642, A1, doi: 10.1051/0004-6361/202038467
  * Nakagawa et al. (1989) Nakagawa, T., Nishida, A., & Saito, T. 1989, J. Geophys. Res., 94, 11761, doi: 10.1029/JA094iA09p11761
  * Neugebauer (2013) Neugebauer, M. 2013, Space Sci. Rev., 176, 125, doi: 10.1007/s11214-010-9707-2
  * Neugebauer et al. (1993) Neugebauer, M., Clay, D. R., & Gosling, J. T. 1993, J. Geophys. Res., 98, 9383, doi: 10.1029/93JA00216
  * Nieves-Chinchilla et al. (2019) Nieves-Chinchilla, T., Jian, L. K., Balmaceda, L., et al. 2019, Sol. Phys., 294, 89, doi: 10.1007/s11207-019-1477-8
  * Nieves-Chinchilla et al. (2018a) Nieves-Chinchilla, T., Linton, M. G., Hidalgo, M. A., & Vourlidas, A. 2018a, ApJ, 861, 139, doi: 10.3847/1538-4357/aac951
  * Nieves-Chinchilla et al. (2016) Nieves-Chinchilla, T., Linton, M. G., Hidalgo, M. A., et al. 2016, ApJ, 823, 27, doi: 10.3847/0004-637X/823/1/27
  * Nieves-Chinchilla et al. (2018b) Nieves-Chinchilla, T., Vourlidas, A., Raymond, J. C., et al. 2018b, Sol. Phys., 293, 25, doi: 10.1007/s11207-018-1247-z
  * Nieves-Chinchilla et al. (2022) Nieves-Chinchilla, T., Alzate, N., Cremades, H., et al. 2022, ApJ, 930, 88, doi: 10.3847/1538-4357/ac590b
  * Nykyri et al. (2023) Nykyri, K., Ma, X., Burkholder, B., et al. 2023, , 10, 1179344, doi: 10.3389/fspas.2023.1179344
  * Oh et al. (2007) Oh, S. Y., Yi, Y., & Kim, Y. H. 2007, Sol. Phys., 245, 391, doi: 10.1007/s11207-007-9042-2
  * Owens et al. (2005) Owens, M. J., Cargill, P. J., Pagel, C., Siscoe, G. L., & Crooker, N. U. 2005, J. Geophys. Res., 110, A01105, doi: 10.1029/2004JA010814
  * Owens et al. (2017) Owens, M. J., Lockwood, M., & Barnard, L. A. 2017, , 7, 4152, doi: 10.1038/s41598-017-04546-3
  * Pal et al. (2023) Pal, S., Balmaceda, L., Weiss, A. J., et al. 2023, , 10, 1195805, doi: 10.3389/fspas.2023.1195805
  * Pal et al. (2021) Pal, S., Kilpua, E., Good, S., Pomoell, J., & Price, D. J. 2021, A&A, 650, A176, doi: 10.1051/0004-6361/202040070
  * Pal et al. (2022) Pal, S., Lynch, B. J., Good, S. W., et al. 2022, , 9, 903676, doi: 10.3389/fspas.2022.903676
  * Palmerio et al. (2016) Palmerio, E., Kilpua, E. K. J., & Savani, N. P. 2016, , 34, 313, doi: 10.5194/angeo-34-313-2016
  * Palmerio et al. (2023a) Palmerio, E., Maharana, A., Lynch, B. J., et al. 2023a, ApJ, 958, 91, doi: 10.3847/1538-4357/ad0229
  * Palmerio et al. (2018) Palmerio, E., Kilpua, E. K. J., Möstl, C., et al. 2018, , 16, 442, doi: 10.1002/2017SW001767
  * Palmerio et al. (2021) Palmerio, E., Nieves-Chinchilla, T., Kilpua, E. K. J., et al. 2021, , 126, e2021JA029770, doi: 10.1029/2021JA029770
  * Palmerio et al. (2022a) Palmerio, E., Lee, C. O., Richardson, I. G., et al. 2022a, , 20, e2022SW003215, doi: 10.1029/2022SW003215
  * Palmerio et al. (2022b) Palmerio, E., Lee, C. O., Mays, M. L., et al. 2022b, , 20, e2021SW002993, doi: 10.1029/2021SW002993
  * Palmerio et al. (2023b) Palmerio, E., Lynch, B. J., Lee, C. O., et al. 2023b, BAAS, 55, 307, doi: 10.3847/25c2cfeb.ba5ccef8
  * Pérez-Alanis et al. (2023) Pérez-Alanis, C. A., Janvier, M., Nieves-Chinchilla, T., et al. 2023, Sol. Phys., 298, 60, doi: 10.1007/s11207-023-02152-3
  * Pinto et al. (2022) Pinto, M., Sanchez-Cano, B., Moissl, R., et al. 2022, Space Sci. Rev., 218, 54, doi: 10.1007/s11214-022-00922-2
  * Regnault et al. (2023) Regnault, F., Al-Haddad, N., Lugaz, N., et al. 2023, arXiv e-prints, arXiv:2311.14046, doi: 10.48550/arXiv.2311.14046
  * Regnault et al. (2020) Regnault, F., Janvier, M., Démoulin, P., et al. 2020, , 125, e2020JA028150, doi: 10.1029/2020JA028150
  * Richardson & Cane (2004) Richardson, I. G., & Cane, H. V. 2004, J. Geophys. Res., 109, A09104, doi: 10.1029/2004JA010598
  * Richardson & Cane (2010) Richardson, I. G., & Cane, H. V. 2010, Sol. Phys., 264, 189, doi: 10.1007/s11207-010-9568-6
  * Richter et al. (1985) Richter, A. K., Hsieh, K. C., Luttrell, A. H., Marsch, E., & Schwenn, R. 1985, , 35, 33, doi: 10.1029/GM035p0033
  * Riley et al. (2004) Riley, P., Linker, J. A., Lionello, R., et al. 2004, , 66, 1321, doi: 10.1016/j.jastp.2004.03.019
  * Rivera et al. (2022) Rivera, Y. J., Raymond, J. C., Landi, E., et al. 2022, ApJ, 936, 83, doi: 10.3847/1538-4357/ac8873
  * Rivera et al. (2023) Rivera, Y. J., Raymond, J. C., Reeves, K. K., et al. 2023, ApJ, 955, 65, doi: 10.3847/1538-4357/aceef8
  * Rochus et al. (2020) Rochus, P., Auchère, F., Berghmans, D., et al. 2020, A&A, 642, A8, doi: 10.1051/0004-6361/201936663
  * Rodriguez et al. (2008) Rodriguez, L., Zhukov, A. N., Dasso, S., et al. 2008, , 26, 213, doi: 10.5194/angeo-26-213-2008
  * Rodriguez et al. (2016) Rodriguez, L., Masías-Meza, J. J., Dasso, S., et al. 2016, Sol. Phys., 291, 2145, doi: 10.1007/s11207-016-0955-5
  * Rodríguez-García et al. (2022) Rodríguez-García, L., Nieves-Chinchilla, T., Gómez-Herrero, R., et al. 2022, A&A, 662, A45, doi: 10.1051/0004-6361/202142966
  * Romeo et al. (2023) Romeo, O. M., Braga, C. R., Badman, S. T., et al. 2023, ApJ, 954, 168, doi: 10.3847/1538-4357/ace62e
  * Ruan et al. (2023) Ruan, M., Zuo, P., Feng, X., et al. 2023, ApJ, 951, 47, doi: 10.3847/1538-4357/acd245
  * Ruffenach et al. (2012) Ruffenach, A., Lavraud, B., Owens, M. J., et al. 2012, J. Geophys. Res., 117, A09101, doi: 10.1029/2012JA017624
  * Ruffenach et al. (2015) Ruffenach, A., Lavraud, B., Farrugia, C. J., et al. 2015, , 120, 43, doi: 10.1002/2014JA020628
  * Russell et al. (1983) Russell, C. T., Mellott, M. M., Smith, E. J., & King, J. H. 1983, J. Geophys. Res., 88, 4739, doi: 10.1029/JA088iA06p04739
  * Salman et al. (2021) Salman, T. M., Lugaz, N., Winslow, R. M., et al. 2021, ApJ, 921, 57, doi: 10.3847/1538-4357/ac11f3
  * Salman et al. (2020) Salman, T. M., Winslow, R. M., & Lugaz, N. 2020, , 125, e2019JA027084, doi: 10.1029/2019JA027084
  * Savani et al. (2010) Savani, N. P., Owens, M. J., Rouillard, A. P., Forsyth, R. J., & Davies, J. A. 2010, ApJ, 714, L128, doi: 10.1088/2041-8205/714/1/L128
  * Savani et al. (2011) Savani, N. P., Owens, M. J., Rouillard, A. P., et al. 2011, ApJ, 732, 117, doi: 10.1088/0004-637X/732/2/117
  * Schwartz (1998) Schwartz, S. J. 1998, ISSI Scientific Reports Series, 1, 249
  * Scolini et al. (2021) Scolini, C., Dasso, S., Rodriguez, L., Zhukov, A. N., & Poedts, S. 2021, A&A, 649, A69, doi: 10.1051/0004-6361/202040226
  * Scolini et al. (2019) Scolini, C., Rodriguez, L., Mierla, M., Pomoell, J., & Poedts, S. 2019, A&A, 626, A122, doi: 10.1051/0004-6361/201935053
  * Scolini et al. (2020) Scolini, C., Chané, E., Temmer, M., et al. 2020, ApJS, 247, 21, doi: 10.3847/1538-4365/ab6216
  * Siscoe & Odstrcil (2008) Siscoe, G., & Odstrcil, D. 2008, J. Geophys. Res., 113, A00B07, doi: 10.1029/2008JA013142
  * Sonnerup & Cahill (1967) Sonnerup, B. U. O., & Cahill, L. J., J. 1967, J. Geophys. Res., 72, 171, doi: 10.1029/JZ072i001p00171
  * SunPy Community et al. (2020) SunPy Community, Barnes, W. T., Bobra, M. G., et al. 2020, ApJ, 890, 68, doi: 10.3847/1538-4357/ab4f7a
  * Temmer & Bothmer (2022) Temmer, M., & Bothmer, V. 2022, A&A, 665, A70, doi: 10.1051/0004-6361/202243291
  * Temmer et al. (2014) Temmer, M., Veronig, A. M., Peinhart, V., & Vršnak, B. 2014, ApJ, 785, 85, doi: 10.1088/0004-637X/785/2/85
  * Thernisien (2011) Thernisien, A. 2011, ApJS, 194, 33, doi: 10.1088/0067-0049/194/2/33
  * Thompson et al. (2012) Thompson, W. T., Kliem, B., & Török, T. 2012, Sol. Phys., 276, 241, doi: 10.1007/s11207-011-9868-5
  * Trotta et al. (2022) Trotta, D., Vuorinen, L., Hietala, H., et al. 2022, , 9, 1005672, doi: 10.3389/fspas.2022.1005672
  * Verbeke et al. (2023) Verbeke, C., Mays, M. L., Kay, C., et al. 2023, , 72, 5243, doi: 10.1016/j.asr.2022.08.056
  * Viñas & Scudder (1986) Viñas, A. F., & Scudder, J. D. 1986, J. Geophys. Res., 91, 39, doi: 10.1029/JA091iA01p00039
  * Viall et al. (2021) Viall, N. M., DeForest, C. E., & Kepko, L. 2021, , 8, 139, doi: 10.3389/fspas.2021.735034
  * Volkmer & Neubauer (1985) Volkmer, P. M., & Neubauer, F. M. 1985, , 3, 1
  * Vourlidas et al. (2011) Vourlidas, A., Colaninno, R., Nieves-Chinchilla, T., & Stenborg, G. 2011, ApJ, 733, L23, doi: 10.1088/2041-8205/733/2/L23