# Flux rope modeling of the 2022 Sep 5 CME observed by Parker Solar Probe and
Solar Orbiter from 0.07 to 0.69 au

Emma E. Davies Austrian Space Weather Office, GeoSphere Austria, Graz, Austria
Emma E. Davies<EMAIL_ADDRESS>Hannah T. Rüdisser Austrian Space
Weather Office, GeoSphere Austria, Graz, Austria  Institute of Physics,
University of Graz, Graz, Austria  Ute V. Amerstorfer Austrian Space Weather
Office, GeoSphere Austria, Graz, Austria  Christian Möstl Austrian Space
Weather Office, GeoSphere Austria, Graz, Austria  Maike Bauer Austrian Space
Weather Office, GeoSphere Austria, Graz, Austria  Institute of Physics,
University of Graz, Graz, Austria  Eva Weiler Austrian Space Weather Office,
GeoSphere Austria, Graz, Austria  Institute of Physics, University of Graz,
Graz, Austria  Tanja Amerstorfer Austrian Space Weather Office, GeoSphere
Austria, Graz, Austria  Satabdwa Majumdar Austrian Space Weather Office,
GeoSphere Austria, Graz, Austria  Phillip Hess U.S. Naval Research Laboratory,
Washington, DC, USA  Andreas J. Weiss NASA Postdoctoral Program Fellow, NASA
Goddard Space Flight Center, Greenbelt, MD, USA  Martin A. Reiss Community
Coordinated Modeling Center, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA  Lucie M. Green University College London, Mullard Space Science
Laboratory, Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK  David M. Long
School of Physical Sciences, Dublin City University, Glasnevin Campus, Dublin,
D09 V209, Ireland  Teresa Nieves-Chinchilla Heliophysics Science Division,
NASA Goddard Space Flight Center, Greenbelt, MD, USA  Department of Physics
and Astronomy, George Mason University, Fairfax, VA, USA  Domenico Trotta
Imperial College London, South Kensington Campus, London SW7 2AZ, UK  Timothy
S. Horbury Imperial College London, South Kensington Campus, London SW7 2AZ,
UK  Helen O’Brien Imperial College London, South Kensington Campus, London SW7
2AZ, UK  Edward Fauchon-Jones Imperial College London, South Kensington
Campus, London SW7 2AZ, UK  Jean Morris Imperial College London, South
Kensington Campus, London SW7 2AZ, UK  Christopher J. Owen University College
London, Mullard Space Science Laboratory, Holmbury St. Mary, Dorking, Surrey,
RH5 6NT, UK  Stuart D. Bale Physics Department and Space Sciences Laboratory,
University of California, Berkeley, USA  Justin C. Kasper School of Climate
and Space Sciences and Engineering, University of Michigan, Ann Arbor,
Michigan, USA

(Received May 17, 2024; Revised July 15, 2024; Accepted July 16, 2024)

###### Abstract

As both Parker Solar Probe (PSP) and Solar Orbiter (SolO) reach heliocentric
distances closer to the Sun, they present an exciting opportunity to study the
structure of CMEs in the inner heliosphere. We present an analysis of the
global flux rope structure of the 2022 September 5 CME event that impacted PSP
at a heliocentric distance of only 0.07 au and SolO at 0.69 au. We compare in
situ measurements at PSP and SolO to determine global and local expansion
measures, finding a good agreement between magnetic field relationships with
heliocentric distance, but significant differences with respect to flux rope
size. We use PSP/WISPR images as input to the ELEvoHI model, providing a
direct link between remote and in situ observations; we find a large
discrepancy between the resulting modeled arrival times, suggesting that the
underlying model assumptions may not be suitable when using data obtained
close to the Sun, where the drag regime is markedly different in comparison to
larger heliocentric distances. Finally, we fit the SolO/MAG and PSP/FIELDS
data independently with the 3DCORE model and find that many parameters are
consistent between spacecraft, however, challenges are apparent when
reconstructing a global 3D structure that aligns with arrival times at PSP and
Solar Orbiter, likely due to the large radial and longitudinal separations
between spacecraft. From our model results, it is clear the solar wind
background speed and drag regime strongly affect the modeled expansion and
propagation of CMEs and need to be taken into consideration.

Solar coronal mass ejections(310) — Heliosphere(711) — Dynamical
evolution(421) — Solar wind(1534)

##  1 Introduction

Coronal mass ejections (CMEs) are large-scale expulsions of plasma and
magnetic fields that are driven from the solar atmosphere. As they propagate
and expand outwards through the heliosphere, the heliospheric counterparts to
CMEs measured in situ by spacecraft, are known as interplanetary coronal mass
ejections (ICMEs). ICMEs can be distinguished from the ambient solar wind by
features such as an enhanced magnetic field strength, low plasma $\beta$,
declining velocity profile and decreased proton temperature amongst many
others (e.g. Zurbuchen & Richardson, 2006).

Until recently, in situ properties of ICMEs have been studied over varying
heliocentric distances, mostly between 0.3 and 5.4 au, utilising both
dedicated solar wind missions e.g. Helios (0.3–1 au, e.g. Cane et al., 1997;
Bothmer & Schwenn, 1998), ACE/Wind, STEREO (at 1 au, e.g. Cane & Richardson,
2003; Richardson & Cane, 2010; Jian et al., 2018) and Ulysses (1–5.4 au, e.g.
Liu et al., 2005; Wang et al., 2005; Ebert et al., 2009; Du et al., 2010;
Richardson, 2014), as well as planetary missions when outside of their
respective planetary environments such as BepiColombo (Davies et al., 2021b;
Möstl et al., 2022; Palmerio et al., 2024), MESSENGER (Winslow et al., 2015;
Good & Forsyth, 2016), Venus Express (Good & Forsyth, 2016), and Juno (1–5.4
au, e.g. Davies et al., 2021a). Unfortunately, many of the planetary mission
measurements of ICMEs only consist of magnetic field observations, often
lacking complementary measurements of the solar wind plasma. However, with the
addition of the Solar Orbiter (SolO; Müller et al., 2020) and Parker Solar
Probe (PSP; Fox et al., 2016) missions, we are now able to study ICMEs much
closer to the Sun, with a full-suite of instruments capable of analyzing their
properties and structure in detail.

The generally accepted picture of the global structure of an ICME comprises a
magnetic flux rope, where helical field lines are wound around a central axis,
which is driven outwards from the Sun where both legs remain connected to the
solar corona. If traveling faster than the local magnetosonic speed, such a
structure drives a forward shock, behind which there is a turbulent and
compressed region of magnetic field known as the sheath (see, e.g., Figure 2
in Zurbuchen & Richardson, 2006). Such ICMEs, with a clear magnetic flux rope
structure, are often described as magnetic clouds, where an enhanced magnetic
field, smooth rotation of the magnetic field vector, low plasma $\beta$ and a
drop in proton temperature (Burlaga et al., 1981) are observed in situ.
However, not all ICMEs are observed to have such a magnetic cloud structure;
Gosling (1990) classified $\sim$ 30% of ICMEs at 1 au as magnetic clouds, the
proportion varying with the solar cycle (Cane & Richardson, 2003). For events
where all the features necessary to be classified as a magnetic cloud are not
met, studies often use the more general term of magnetic ejecta (ME) to
describe this interval.

As in situ measurements of ICMEs are often taken by just a single spacecraft,
observations of the rotation of the magnetic field taken along the single 1D
trajectory can be interpreted as the spacecraft measuring the magnetic flux
rope (Burlaga et al., 1981; Marubashi, 1986; Burlaga, 1988), and the 3D global
structure recreated by fitting the magnetic field vector with force-free flux
rope models such as the Lundquist (Lundquist, 1950) or Gold-Hoyle solutions
(Gold & Hoyle, 1960).

However, in reality, reconstructing the global structure of ICMEs is more
complex; as ICMEs propagate through the heliosphere, they may undergo many
processes including rotations, deflections, interactions with other solar wind
transients and erosion via magnetic reconnection (see review by Manchester et
al., 2017). A study by Scolini et al. (2022) found that fundamental
alterations or re-orientations of the ICME occurred for $\sim$65% of ICMEs as
they propagated between 0.3 and 1 au, attributing the complication in their
evolution primarily to interactions with other large-scale solar wind
structures. Even simply propagating through the ambient and structured solar
wind, deformations of the ICME cross-section can occur (Riley & Crooker, 2004;
Owens et al., 2006; Savani et al., 2010; Davies et al., 2021b). There are also
many questions that remain about the global picture of ICMEs affecting their
reconstruction with flux rope models e.g.: to what extent can ICMEs be
considered coherent structures (e.g. Owens et al., 2017; Scolini et al.,
2022), and do the ICME legs also contain a twisted flux rope structure (e.g.
Owens 2016, Rüdisser et al. 2024 (ApJ, in revision))?

To truly understand the global structure of ICMEs and their evolution as they
propagate through the heliosphere, multi-spacecraft measurements of the same
ICME over varying radial and longitudinal separations are necessary (Lugaz et
al., 2018). Multi-spacecraft ICME studies such as Good et al. 2018, Salman et
al. 2020, Davies et al. 2022, and Möstl et al. 2022 took advantage of
conjunctions between spacecraft including MESSENGER, Venus Express, Wind, ACE,
STEREO-A, Juno, SolO, BepiColombo, and Parker Solar Probe, where an ICME was
observed by more than one spacecraft. Measurements of the same ICME taken
during these different spacecraft configurations mean that ICME properties are
often tracked over a varying range of radial and longitudinal separations,
making it hard to disentangle radial and longitudinal (and in some cases,
latitudinal) effects on ICME evolution. These studies found that although the
evolution of ICME properties with increasing heliocentric distance was
consistent with previous statistical trends, individual ICMEs display
significant variability when compared to average trends.

The CME launched on 2022 September 5 is the subject of great interest (e.g.
Long et al., 2023; Romeo et al., 2023; Patel et al., 2023; Trotta et al.,
2024; Liu et al., 2024), as it is the closest CME observed to Sun to date,
observed by PSP at a heliocentric distance of just 0.07 au, and later by SolO
at 0.69 au. Such a spacecraft configuration presents a unique opportunity for
a direct comparison of ICME observations at an early stage of its evolution,
with those much further in its evolution. Long et al. (2023) focused on the
solar source of the CME, identifying plasma flows along a filament channel to
infer the magnetic field configuration of the flux rope and relate these to
the in situ observations at PSP. The location of PSP so close to the Sun
provides a direct intersection between remote and in situ observations; Romeo
et al. (2023) compared the in situ observations at PSP to remote-sensing
observations, and found that due to the complexity of the ICME, it was hard to
reconcile the observations into one simple description of the event. Focusing
on the in situ PSP observations, Romeo et al. (2023) and Liu et al. (2024)
also found that the CME played a significant role in the evolution of the
heliospheric current sheet (HCS).

In this study, we compare the observations at PSP with those at SolO. Trotta
et al. (2024) previously compared observations of the ICME shock, comparing
typical shock parameters and small-scale features at both spacecraft,
revealing important differences in the local environment in which the shocks
were propagating. Here, we aim to reconcile observations at PSP with those at
SolO to reconstruct the global structure of the ICME. In Section 2, we present
the in situ magnetic field and solar wind plasma data at each spacecraft. In
Section 3, we use remote images taken by PSP to model the arrival time at the
two spacecraft using the ELEvoHI model, and Section 4 presents the results of
fitting the magnetic field data at both spacecraft with the 3DCORE model to
reconstruct the global structure of the ICME flux rope.

##  2 Spacecraft Data and Observations

###  2.1 Spacecraft data

To identify the ICME in situ, we present magnetic field (FIELDS; Bale et al.,
2016) observations and solar wind plasma (SWEAP; Kasper et al., 2016) data
measured by the Solar Probe ANalyzer for Ions (SPAN-I; Livi et al., 2022)
instrument at Parker Solar Probe (PSP; Fox et al., 2016), as well as
measurements of the magnetic field (MAG; Horbury et al., 2020) and solar wind
plasma (SWA; Owen et al., 2020) at Solar Orbiter (SolO; Müller et al., 2020).
We are particularly thankful to the Solar Orbiter MAG team, who have provided
updated files replacing those with previously missing data during the event.
These files are available on request from the MAG team and will be publicly
available on the ESA Solar Orbiter Archive soon
(https://soar.esac.esa.int/soar/).

In addition to the in-situ data, this work also incorporates the use of data
from various remote sensing instruments, presenting the solar source of the in
situ observations. Disk imaging observations from the 17.4 nm passband of the
Full Sun Imager (FSI), one of the telescopes of the Extreme Ultraviolet Imager
(EUI; Rochus et al., 2020) suite onboard SolO, are shown. Coronagraph images
from the Large Angle Spectroscopic COronagraph C2 (LASCO; Brueckner et al.,
1995) onboard the Solar and Heliospheric Observatory (SOHO; Domingo et al.,
1995), and the outer coronagraph COR-2 onboard the Solar Terrestrial Relations
Observatory (STEREO; Kaiser et al., 2008) are presented. Images taken by the
Wide-Field Imager for Solar Probe (WISPR; Vourlidas et al., 2016) onboard PSP
are also used to model CME arrival times in Section 3.

###  2.2 Spacecraft configuration

Figure 1: Spacecraft positions presented in Heliocentric Earth Equatorial
(HEEQ) coordinates, on 2022 September 5 18:00 UT, around the time of arrival
of the CME at PSP. SolO is represented by the green square marker, and PSP by
the black square marker. The spacecraft trajectories shown cover a time range
of 80 days before (dashed) and after (solid) the event. Exact spacecraft
positions for defined ICME boundaries during the event are given in Table 1.

Figure 1 presents an overview of the spacecraft configuration within 1 au on
2022 September 5 18:00 UT, around the time the ICME was observed at PSP. At
this time, PSP (represented by the black square marker) was located at a
heliocentric distance of 0.07 au and longitude of 122.1∘ in Heliocentric Earth
Equatorial (HEEQ) coordinates, and SolO (represented by the green square
marker) was located at a heliocentric distance of 0.70 au and longitude of
149.2∘. PSP and SolO were thus well aligned to observe the same ICME, with a
longitudinal separation within 30∘ throughout the event.

Such a configuration occurred due to SolO performing a gravity assist maneuver
(GAM) at Venus on September 4, whilst PSP was undergoing Encounter 13,
reaching a perihelion of 0.062 au on September 6. Figure 1 shows that both
spacecraft were located on the far side of the Sun with respect to Earth, with
STEREO-A located at -19.5∘ and BepiColombo at -99.6∘ HEEQ longitude. Compared
to the positions of PSP and SolO, these separations are wider than typical
longitudinal extents of ICMEs (e.g. Good & Forsyth, 2016; Lugaz et al., 2024).
We checked the magnetic field data at both spacecraft, and while STEREO-A did
not observe any ICME signature, BepiColombo saw a shock and sheath on early
September 7. However, these signatures may also be caused by a different CME,
but this observation could warrant further investigation in connection with
the event discussed here.

###  2.3 Solar source of the in situ observations

On 2022 September 5, the CME was observed as a full halo event in the field of
view of the coronagraph STEREO-A/COR-2. Figure 2a shows the coronagraph image
for the CME at 17:24 UT in the COR-2 field of view and Figure 2b shows the CME
as observed in the LASCO-C2 field of view at 16:48 UT. The embedded flux rope
and the associated shock front can be identified (shown in yellow and white
arrows respectively) in the two images. The white solid line in Figure 2a
indicates the trajectory of PSP. The white and grey dots represent the arrival
time of the CME associated shock and the end time of the magnetic ejecta (ME)
at PSP respectively, while the yellow dot denotes the PSP position at the
shock arrival time at SolO.

Coronagraph images are however, not always sufficient to clearly understand
the propagation direction of a CME. This is particularly important for halo
CMEs, as the determination of the propagation direction is crucial to identify
if the CME is traveling towards or away from the Earth, and the halo
appearance of the CME front makes it more tricky to ascertain the direction.
In such cases, identifying the source region of the halo CME on the solar disk
provides conclusive evidence on whether the CME was traveling towards or away
from the Earth. The source region of the CME in this study was observed by the
FSI telescope (in the 17.4 nm passband) of the EUI payload onboard SolO. The
source region was identified by creating running difference images using the
JHelioviewer software (Müller et al., 2017). The erupting active region was
located at a latitude of -25∘ and a longitude of 180∘ (denoted by a white box
in Figure 2c) in Stonyhurst heliographic coordinates (for details of the
source region, please refer to Majumdar et al., 2023). The Stonyhurst
coordinate system is directly relatable to the HEEQ system, and therefore, we
expect the CME to propagate in a southwards direction with respect to the
solar equatorial plane, and that PSP and SolO will likely observe the flank of
the CME.

The identified source region is in agreement with that identified by Long et
al. (2023). They studied the source region in detail, and identified a
filament channel rooted in the strong magnetic field of the active region
which stretched out across the disk into the quiet Sun. From their
observations, they were able to infer the right-handed rotation of the
magnetic field early in its evolution using the plasma flow observed along the
channel. The active region itself also shows a right-handed nature, for
example, through the flare loops that formed as a result of the reconnection
associated with the CME (see Palmerio et al., 2017, and references therein for
determining handedness of active regions).

Although the CME was observed by both the LASCO-C2 and STEREO-A/COR-2
coronagraphs, only a couple of frames were available from LASCO due to a data
outage, and therefore, STEREO-A/COR-2 was the only imager with continuous
observation of the CME. Using the STEREO-A/COR-2 and source region information
observed by SolO EUI/FSI, Patel et al. (2023) was able to constrain and
implement the Graduated Cylindrical Shell model (GCS; Thernisien et al., 2009)
to the COR-2 images. The results of the GCS fitting indicated a southwards
propagation direction, with a latitude of $\sim$ -18∘ and a longitude of
$\sim$ 166∘, with an axis tilt of $\sim$ 58∘ (R. Patel, private
correspondence).

Figure 2: Coronagraph and solar observations. (a) The halo CME as observed by
STEREO-A/COR-2 at 2022 Sep 5 17:24 UT, with the trajectory of PSP as the white
solid line. The white dot indicates the PSP position at the arrival time of
the CME shock at PSP (2022 Sep 5 17:27 UT), the grey dot the position at the
PSP ME end time (2022 Sep 6 00:57), and the yellow dot the PSP position at the
shock arrival time at SolO (2022 Sep 6 10:01). The yellow and white arrows
point at the flux-rope and the white light shock signature associated with the
CME. (b) The same CME as observed in the SOHO/LASCO-C2 field of view at 16:48
UT. The white and yellow arrows indicate the shock front and the flux-rope
associated with the CME. (c) The source region of the CME (denoted inside the
white rectangle) as observed by the first SolO/EUI telescope FSI in the 17.4
nm passband at 2022 Sep 5 16:20 UT.

###  2.4 In situ spacecraft observations at PSP and Solar Orbiter

| PSP | SolO
---|---|---
ICME start, t1 [UT] | 2022-09-05 17:27 | 2022-09-06 10:01
ME start, t2 [UT] | 2022-09-05 18:50 | 2022-09-07 01:25
ME end, t3 [UT] | 2022-09-06 00:57 | 2022-09-08 04:10
R1,2,3 [AU] | 0.070, 0.068, 0.063 | 0.695, 0.689, 0.677
lat1,2,3 [∘] | -1.83, -2.06, -3.05 | -3.55, -3.66, -3.86
lon1,2,3 [∘] | 120.72, 124.67, 144.20 | 149.66, 149.91, 150.38
ME $\langle$B$\rangle$ [nT] | 896.9 | 15.8
ME Bmax [nT] | 1167.9 | 33.8
ME $\langle$V$\rangle$ [ km s-1] | 697.0 | 684.0
ME $\langle$N${}_{p}\rangle$ [cm-3] | 1082.2 | 11.2
ME $\langle$T${}_{p}\rangle$ [MK] | 2.98 | 0.00
Table 1: ICME properties at PSP and Solar Orbiter. ICME shock, ME start and
end times are given, along with the mean (maximum) magnetic field strength
measured within the ME. Plasma properties i.e. bulk velocity, temperature and
density, within the ME are given in the same format. The spacecraft positions
in HEEQ (radial distance, latitude, and longitude) corresponding to the three
ICME boundary times defined are also listed.

Table 1 summarizes the arrival times of the ICME (in this case, the shock
arrival time, $t_{1}$), the start of the magnetic ejecta ($t_{2}$), and the
end of the magnetic ejecta ($t_{3}$) at both PSP and SolO. The spacecraft
heliocentric distance, latitude, and longitude (in HEEQ coordinates) at those
times are also listed, as well as mean and maximum ICME parameters calculated
over the duration of the magnetic ejecta at each spacecraft.

Figure 3: PSP in situ magnetic and plasma data. The top panel presents the
magnetic field data, where the magnetic field magnitude is shown in black, and
the magnetic field components in Radial-Tangential-Normal (RTN) coordinates in
magenta, orange, and blue, respectively. The following panels present the bulk
proton velocity, proton density, and proton temperature of the solar wind,
respectively. The vertical dashed line mark the time of the shock front, and
the solid vertical lines mark the start and end of the ME, which is also
represented by the grey shaded area.

Figure 3 presents the magnetic field and plasma measurements taken by PSP
during the event. We observe a fast-forward shock driven by the CME at 17:27
UT, characterized by a sudden jump in magnetic field magnitude from $\sim$600
nT to 1600 nT, proton bulk velocity from 340 to 1340 km s-1, and proton
temperature from 0.8 to 22 MK. The shock was observed by PSP while located at
a heliocentric distance of 0.07 au ($\sim$15 $R_{\odot}$), making this the
closest ICME to the Sun observed to date. Analysis conducted by Trotta et al.
(2024) used the Mixed Mode 3 method (MX3; Paschmann & Schwartz, 2000) and a
systematic variation of upstream/downstream averaging windows (see Trotta et
al., 2022) to determine an average shock normal of $n=(0.5,-0.8,0.2)$ (in RTN
coordinates), where $\theta=53^{\circ}$ and therefore, the shock is oblique
and consistent with a scenario in which PSP crosses the flank of the ICME (see
discussion and Figure 9a in Romeo et al., 2023).

We define the start of the ME at 2022-09-05 18:50 UT, coincident with a sharp
change in the bulk proton velocity from 850 to 670 km s-1, and the end of the
ME at 2022-09-06 00:57 UT. This ME interval was defined as such to capture
most of the rotation of the magnetic field observed by PSP, in this case, the
radial magnetic field component (BR), and is consistent with the boundaries
defined using the $H_{m}$-PVI technique in Long et al. (2023). Across the ME
interval, the magnetic field magnitude remains fairly constant, with a mean
magnetic field strength of 896.9 nT. The plasma properties i.e. the bulk
proton velocity, proton density and proton temperature also all remain at
consistent values during this interval (mean values of 697 km s-1, 1082 cm-3,
2.98 MK, respectively), before returning to pre-ICME levels in the case of the
bulk velocity and the temperature, and rising further in the case of the
density. We attribute the sharp drop in density following this rise to the
core of the ion distribution being largely outside of the SPAN-i field of view
(Livi et al., 2022). These plasma properties are not the typical features
observed near 1 au described in Zurbuchen & Richardson (2006) e.g. a declining
speed profile, low proton temperature, and low density. In this case, the
proton temperature within the ME is much higher than that preceding the shock,
and thus also possesses a high plasma $\beta$ (not shown). Such features are
indicative of a young ME at an early stage of its evolution, and a non-force-
free magnetic field structure, which may have implications when fitting the
magnetic field components with the typical force-free model solutions. Lynch
et al. (2022) previously explored the application of both force-free and non-
force-free in situ flux rope models to flux ropes between 10 and 30 Rs, and
found that both forms of model decently approximated the magnetic field
structure. However, the usual caveats associated with the models still apply
to flux ropes at such close distances to the Sun, perhaps even more so than
when applied to observations at further heliocentric distances.

As discussed in Romeo et al. (2023) and Liu et al. (2024), the ICME
observations at PSP display more complex features. Liu et al. (2024) describes
how the magnetic field angle with respect to the radial direction ($\theta$)
changes throughout the ME, likely indicating multiple structures within the
ME. In addition, both Romeo et al. (2023) and Liu et al. (2024) identify the
discontinuity in the radial magnetic field vector around 2022-09-06 17:30 UT
to be a crossing of the HCS.

Figure 4: SolO in situ magnetic and plasma data, presented in the same format
as Figure 3.

Figure 4 presents the ICME magnetic field and plasma measurements observed by
SolO, where we define the ICME start as the shock front identified at
2022-09-06 10:01 UT, coincident with a jump in magnetic field magnitude from
$\sim$ 12 to 32 nT and bulk proton velocity from 460 to 890 km s-1. The sheath
region has a duration of approximately 15.4 hours, based on the enhanced
proton temperature observations, and a largely varying magnetic field
magnitude, possibly comprising many different structures. During the first 1.5
hours within the sheath, the proton temperature is very enhanced, around
$\sim$4 MK. This structure is not coincident with a particularly large spike
in proton density: this occurs later between approximately 2022-09-06 14:30
and 16:00 UT. Using the same technique as above, Trotta et al. (2024)
calculated a shock normal of $n=(0.6,-0.2,0.7)$, thus $\theta=51^{\circ}$ and
the shock can be described as oblique, consistent with the result obtained at
PSP.

At SolO, we define the start of the ME at 2022-09-07 01:25 UT, coincident with
a large enhancement of the magnetic field strength, lower variation of the
magnetic field components, and a drop in proton temperature. However, defining
the ME boundary in this case is rather subjective, as it could also be defined
as 2022-09-07 04:35 UT, coincident with the start of the declining bulk
velocity profile also typically displayed by ICMEs.

From the magnetic field measurements, we are able to determine that the flux
rope within the ME mostly rotates from North to South (from the start of the
declining velocity profile), as shown by the positive to negative transition
of the normal component (blue) after 2022-09-07 04:35 UT, whilst the
transverse component (orange) remains pointing East (negative). We can
therefore classify the ME flux rope as NES (Bothmer & Schwenn, 1998): a right-
handed flux rope, with a low inclination with respect to the ecliptic plane.
The observations of the flux rope in situ are consistent with the analysis of
the remote observations of its solar source, where Long et al. (2023) were
able to deduce the right-handed rotation of the magnetic field from
observations of the plasma flow along the filament channel.

Table 1 also lists the ICME parameters calculated within the ME at SolO. We
calculated a mean magnetic field strength within the ME of 15.8 nT, with a
maximum field strength of 33.8 nT. Assuming the ICME expands following
$B\propto r^{-\alpha}$, we use the mean magnetic field strength with the ME to
calculate the global expansion of the CME, resulting in a power of -1.74.
Salman et al. (2024) recently cataloged ICMEs observed by PSP prior to this
event between 2018 October and 2022 August over a heliocentric distance range
of 0.23 to 0.83 au, and found the relationship between mean magnetic field
strength of the ME and heliocentric distance to have a power of -1.21 $\pm$
0.44. As discussed in Salman et al. (2024), the expansion rate is much lower
than those found previously within 1 au e.g. -1.85 $\pm$ 0.07 for ICMEs
observed by Helios 1 and 2 (Gulisano et al., 2010), -1.95 $\pm$ 0.19 for ICMEs
observed by MESSENGER and ACE (Winslow et al., 2015), and -1.76 $\pm$ 0.04 for
ICMEs observed by MESSENGER, Venus Express, STEREO A/B, and Wind (Good et al.,
2019). The calculated power of -1.74 for the event in this study is in
agreement with those studies, although outside of the range of Salman et al.
(2024).

Considering the proton velocity data, we are also able to compare the global
expansion of the ICME to its local expansion at SolO. The dimensionless
expansion parameter, $\zeta$, is a measure independent of radial distance,
requiring only the cruise velocity, $V_{c}$ (i.e. speed at the mid-point of
the flux rope), the rate of expansion, $\Delta V/\Delta t$, and heliocentric
distance, $d$, of the spacecraft (for more detail, see Démoulin & Dasso, 2009;
Gulisano et al., 2010). Gulisano et al. (2010) found that $\zeta$ can be
related to the global expansion of the ICME, where the magnetic field strength
would be expected to decrease as $r^{-2\zeta}$ and radial size expected to
increase as $r^{\zeta}$, therefore $\zeta$ = 0.5$\alpha$ as calculated above.
For the velocity observations at SolO, if we take the start of the ME based on
the start of the declining velocity profile i.e. at 2022-09-07 04:35 UT:
$V_{c}$ = 640.6 km s-1, $\Delta V/\Delta t$ = 0.00396 km s-2, and $d$ = 0.682
au. Using these values, we find $\zeta$ = 0.925, and therefore expect the
magnetic field strength to decrease with heliocentric distance as $r^{-1.85}$
and the size of the flux rope to scale as $r^{0.925}$. The resulting magnetic
field relationship calculating using $\zeta$ is in fairly good agreement with
that calculated using the observed mean values above (-1.74), which is often
not the case as previous studies have found a weak correlation between
measures of global and local expansion (Lugaz et al., 2020; Davies et al.,
2022). To calculate the radial width of the ME at PSP and SolO, we simply
multiply the duration by the cruise velocity, producing a value of 0.103 au at
PSP and 0.375 au at SolO. Assuming a power law relationship as above, we find
the size of the flux rope to scale as $r^{0.576}$. This power is much lower
than the calculated $\zeta$, therefore, the dimensionless expansion parameter
calculated using the velocity values at SolO, overestimates the rate of
expansion of the ICME. This discrepancy may be due to a number of reasons: the
different measurement tracks through the ICME taken by the spacecraft due to
their longitudinal separation, the encounter with the flank rather than
towards the nose of the ICME, or the different drag regimes due to very
different heliocentric distances of the two spacecraft (discussed further in
Section 3).

##  3 Arrival time modeling: ELEvoHI

Figure 5: Consecutive images as PSP crossed the CME, observed by WISPR. The
diamond-shaped marker indicates where the CME front was tracked along SolO’s
orbital plane.

To demonstrate the connection between remote images and the observations in
situ, we use the ELlipse Evolution model based on Heliospheric Imager data
(ELEvoHI) introduced by Rollett et al. (2016) to predict the arrival time of
the CME at SolO and PSP. ELEvoHI combines the ELlipse Evolution model (ELEvo;
Möstl et al., 2015) with drag-based model fitting (DBM fitting; Vršnak et al.,
2013) and can be run using an ensemble approach, as presented in Amerstorfer
et al. (2018) and Amerstorfer et al. (2021). It assumes a fixed propagation
direction for an elliptical CME front whose evolution is governed by the solar
wind drag. ELEvoHI requires the observed time-elongation profile of the event
as input, which is obtained by tracking the leading edge of the CME in WISPR
images, as shown in Figure 5. We focus on the propagation along the plane in
which SolO is located, which was quite close to that of PSP at the time of the
event.

Furthermore, ELEvoHI requires ranges of values for the inverse ellipse aspect
ratio $f$, the direction of motion $\Phi$ of the CME apex relative to the
observing spacecraft, the angular half-width $\lambda$, and the background
solar wind speed $v_{sw}$. The parameters $f$, $\Phi$, and $\lambda$ are
necessary inputs for the ELlipse Conversion (ELCon) method, which is used to
transform the time-elongation into a time-distance profile, relying on the
same assumptions about CME geometry that underpin ELEvoHI as a whole. The
CME’s elongation $\epsilon$ is the angle between the spacecraft’s line-of-
sight (LOS) and the Sun-spacecraft vector. ELCon treats the LOS as tangent to
the CME’s leading edge. A more detailed overview of the ELCon geometry can be
found in Figure 6, parameters from which will also be referenced in the
following abbreviated derivation.

Figure 6: Overview of ELCon geometry, taken from Rollett et al. (2016).

To derive the distance of the CME apex from the Sun, $R_{ell}$, it is
necessary to calculate parameters $c$ and $b$:

$R_{ell}=c+b$ (1)

$c=\frac{r_{\lambda}\sin(90+\theta-\lambda)}{\sin(\lambda)}$ (2)

$b=\frac{d_{\rm
o}\sin(\epsilon)\sin(\lambda)\Omega_{\theta}\,\Omega_{\varphi}}{\sin(90+\theta-\lambda)\sin(\omega)\Omega_{\varphi}+\sin(90+\varphi-\omega)\sin(\lambda)\Omega_{\theta}}$
(3)

with

$\Omega_{x}=\sqrt{f^{2}\cos^{2}x+\sin^{2}x},\quad x\in\\{\theta,\varphi\\}.$
(4)

To obtain the distance from the Sun at any point along the CME front, it is
necessary to calculate the off-axis correction, which considers the angular
offset $\Delta$ between the direction of the CME apex and the location of
interest:

$R_{is}=\frac{c\cos\Delta+\sqrt{(b^{2}-c^{2})f^{2}\sin^{2}\Delta+b^{2}\cos^{2}\Delta}}{f^{2}\sin^{2}\Delta+\cos^{2}\Delta}.$
(5)

ELCon has so far been exclusively applied to analyze events observed by the HI
instruments onboard the STEREO twin-spacecraft, which orbit the Sun at a
distance of around 1 au. As demonstrated by Patel et al. (2023), the
assumptions used to convert elongations into distances are non-trivial when
working with WISPR data and can significantly influence the reconstructed CME
kinematics. Nindos et al. (2021) proposed a new approach, so-called R-Maps,
based on the assumption that the signal of each pixel originates at the
intersection between the LOS and the Thomson surface (Vourlidas & Howard
2006).

While the basic geometric principles governing ELCon remain valid independent
of the observer’s distance to the Sun, complications may arise due to the fast
motion of the spacecraft and the observer-directed nature of the event. Rapid
changes in the observer’s location could result in different parts of the CME
being tracked, distorting results. If the observer enters the CME, inferring
kinematics using ELCon is no longer possible due to the initial assumption of
the LOS being tangent to the front becoming unreasonable. The track used for
our prediction covers a time span of around one hour, from 16:30 UT to 17:35
UT. The in-situ arrival time of the CME at PSP was determined to be 17:27 UT,
meaning our assumptions are valid for most of the time-elongation profile. The
limited duration of the track also minimizes the impact of spacecraft motion
on CME reconstruction. Comparison between distances obtained using ELCon and
R-Maps seems to indicate that ELCon yields plausible results for this time
period, but further study is needed to fully gauge to what extent ELCon is
applicable to different observing geometries.

After using ELCon, we fit a drag-based equation of motion (Vršnak et al.,
2013) to the derived CME kinematics. In that way we gain the drag-parameter,
$\gamma$, and the ambient solar wind speed, $v_{sw}$, which are further used
for modeling the CME evolution using the last part of the ELEvoHI model suite,
ELEvo (Möstl et al., 2015).

Running ELEvoHI in ensemble mode allows us to explore different combinations
of input parameters, giving us an estimate of the modeling uncertainty. For
this study, the values for $\Phi$ ranged from 0 to 60∘ and were chosen to
cover the range of possible values modeled by 3DCORE (see Section 4), as well
as the location of the source region. $\lambda$ was specified based on
estimates from the DONKI catalog, resulting in a variation between 40 and 80∘.
We varied the solar wind speed between 250 and 700 km s-1 and the inverse
ellipse aspect ratio from 0.7 to 1.0.

Figure 7 shows the propagation of the CME as modeled by ELEvoHI for all
ensemble members at a particular timestamp (2022 Sep 6 16:00 UT). The 468
ensemble runs yield a mean average arrival error of 0.3 hours for PSP and 18.4
hours for SolO. This discrepancy between the modeled arrival times suggests
that the underlying model assumptions may not be suitable for making
predictions based on time-elongation tracks obtained from close proximity to
the Sun. Usually, DBM fitting is done at distances greater than 20 $R_{\odot}$
from the Sun, as it has been shown that the drag force becomes dominant while
the influence of the Lorentz force becomes increasingly negligible for most
cases at this distance (Vršnak et al., 2010, 2013). However, in our study, the
CME is tracked much closer to the Sun, resulting in the time-distance profile
only extending to 14 $R_{\odot}$. The drag regime at larger distances is
markedly different from that closer to the Sun, where additional factors can
significantly alter the expected trajectory and arrival time of the CME.
Furthermore, the solar wind speed derived via fitting is assumed to stay
constant during CME propagation, which is not usually the case. For most
ensemble members an ambient solar wind speed of 700 km s-1 was found based on
the CME kinematics in the early propagation phase, where the propagation is
not governed by the drag-force alone, as mentioned above. Additionally, it is
possible that effects related to observing geometry introduce distortions in
the reconstruction of CME kinematics using ELCon (e.g. Hinterreiter et al.,
2021a, b).

A second CME was observed by SOHO LASCO/C2 on 2022 Sep 5 18:39 UT. Remnants of
the preceding CME largely obscured it, resulting in only faint visibility in
LASCO/C2 and STEREO-A/COR2 images. Estimates using coronagraph images by
NASA’s Moon to Mars Space Weather Analysis Office placed the CME at a
longitude of -144∘, making it a far-sided event. Simulations carried out using
the WSA-ENLIL+Cone model (Arge & Pizzo 2000, Odstrcil 2003, Arge et al. 2004,
Odstrcil et al. 2004) showed that it is unlikely to have impacted SolO or PSP
(see https://kauai.ccmc.gsfc.nasa.gov/DONKI/view/CMEAnalysis/21563/1), leaving
the first CME as the one most likely to have been observed in situ at both
spacecraft.

However, it cannot be ruled out that the second event interacted with the
preceding CME, impacting its propagation. Considering this, as well as the
variability in solar wind conditions at the time the events took place, it is
likely that the initial CME experienced some degree of deformation, further
complicating the modeling when using ELEvoHI’s assumption of a rigid
elliptical front.

Figure 7: Results of the ELEvoHI model ensemble runs based on WISPR data for
the time 2022 Sep 6 16:00 UT in HEEQ coordinates, 6 hours after the observed
shock arrival at SolO. Different CME fronts represent the different ensemble
members produced by varying the input parameters. SolO is represented by the
orange marker, and PSP by the black marker.

##  4 Flux rope modeling: 3DCORE

In order to reconstruct the parameters of the flux rope of the ICME observed
by PSP and SolO, we use the semi-empirical 3D Coronal Rope Ejection (3DCORE)
model, which was introduced by Möstl et al. (2018), and further developed by
Weiss et al. (2021a) and Weiss et al. (2021b). The version used in this paper
is thoroughly described in Rüdisser et al. (2024) (ApJ, in revision).

3DCORE assumes a Gold-Hoyle-like magnetic field embedded within a toroidal
flux rope with an elliptical cross-section that expands self-similarly while
the both ends of the flux rope remain attached to the Sun. The propagation of
the 3DCORE flux rope outwards through the heliosphere is considered by using a
drag-based model (Vršnak et al., 2013). 3DCORE can be used to infer flux rope
parameters by fitting in situ magnetic field observations, using an
Approximate Bayesian Computation - Sequential Monte Carlo algorithm (first
introduced for 3DCORE by Weiss et al., 2021b). This algorithm utilizes the
model’s advantage of being able to produce mega ensembles on the order of
$10^{6}$ runs per second, to search the input parameter space for possible
fits to the in situ data. By accordingly restricting the input parameter
range, priors from either auxiliary measurements or physical considerations
can be incorporated.

During the fitting process, the model is evaluated at a given set of fitting
points and compared to the measured in situ data. Model runs that produce a
non-zero magnetic field at the boundaries of the event are rejected, as well
as runs that do not produce signatures at the fitting points. This leads to a
restriction of the input parameters to combinations that generate a “hit” at
the observing spacecraft. Each iteration of the fitting process then serves to
further confine the input parameters to minimize the root mean square error
(RMSE) between model values at the fitting points and the corresponding in
situ measurements. This procedure finally yields an ensemble of accepted
combinations of input parameters.

3DCORE is able to simultaneously fit multiple magnetic field measurements from
different spacecraft (Weiss et al., 2021a), however, this only works well when
the spacecraft are relatively close together. In the case of larger
separations, the general assumptions of 3DCORE, such as a constant background
solar wind speed, cannot be modeled through a single value that complies with
both measurements. Due to the large radial separation of PSP and SolO for the
event under study ($\sim$ 0.625 au), we apply 3DCORE to both observations
separately.

3DCORE also has the ability to take into account the motion of the spacecraft,
which is especially useful considering the faster movement of PSP in
comparison to other spacecraft at further heliocentric distances. The
spacecraft motion is considered by fitting the magnetic field observations in
the HEEQ coordinate frame. We use the same version 3DCORE to fit both the PSP
and SolO magnetic field observations, although we expect the spacecraft motion
of SolO to have little effect on the fitting results in comparison to those at
PSP.

Table 2: Parameter ranges and the corresponding results of the 3DCORE fitting
for SolO and PSP.

|  | SolO |  | PSP
---|---|---|---|---
Parameters | Units | Minimum | Maximum | Solution |  | Minimum | Maximum | Solution
longitude | deg | $100.$ | $200.$ | $128.5\pm 5.95$ |  | $110.$ | $170.$ | $135.11\pm 11.69$
latitude | deg | $-40.$ | $40.$ | $-5.86\pm 7.01$ |  | $-40.$ | $40.$ | $5.85\pm 10.11$
inclination | deg | $-45.$ | $45.$ | $5.61\pm 6.16$ |  | $0.$ | $60.$ | $20.99\pm 12.39$
d1AU | au | $0.2$ | $0.35$ | $0.34\pm 0.01$ |  | $0.25$ | $0.45$ | $0.42\pm 0.02$
$\delta$ |  | $1.$ | $4.$ | $2.78\pm 0.77$ |  | $1.$ | $5.$ | $3.43\pm 1.04$
Tfac |  | $0.$ | $200.$ | $9.7\pm 2.87$ |  | $0.$ | $200.$ | $17.68\pm 10.32$
$v_{0}$ | km s-1 | $500.$ | $1900.$ | $1619.28\pm 173.09$ |  | $200.$ | $1500.$ | $318.79\pm 87.93$
B1AU | nT | $5.$ | $20.$ | $10.64\pm 1.23$ |  | $5.$ | $20.$ | $12.6\pm 4.06$
$\Gamma$ |  | $0.2$ | $3.$ | $0.39\pm 0.12$ |  | $0.2$ | $3.$ | $1.69\pm 0.76$
$v_{\mathrm{sw}}$ | km s-1 | $100.$ | $900.$ | $440.32\pm 70.86$ |  | $100.$ | $700.$ | $267.79\pm 119.57$
$n_{a}$ |  | $1.$ | $1.3$ | $1.17\pm 0.08$ |  | $1.$ | $1.3$ | $1.04\pm 0.03$
$n_{b}$ |  | $1.$ | $2.$ | $1.76\pm 0.18$ |  | $1.2$ | $2.$ | $1.47\pm 0.15$

Note. — The launch radius $r_{0}$ is fixed to be $10.7$ $R_{\odot}$. The
propagation longitude and latitude of the flux rope are given in HEEQ
coordinates, and the inclination (orientation of the axis of the flux rope),
width of cross-section at 1 au (d1AU), aspect ratio of cross-section at 1 au
($\delta$), a twist factor (Tfac) which is related to the number of twists
over the whole torus, launch speed ($v_{0}$), launch radius ($r_{0}$),
magnetic field strength at 1 au (B1AU), drag parameter ($\Gamma$), global
solar wind speed ($v_{\mathrm{sw}}$), expansion rate ($n_{a}$) of the cross-
section diameter, and the rate at which the magnetic field decreases ($n_{b}$)
are listed.

Table 2 presents the parameter ranges chosen for both the SolO and PSP
fitting. 3DCORE takes the following input parameters: propagation direction
(longitude and latitude) in HEEQ coordinates, orientation of the axis of the
flux rope (inclination), width of cross-section at 1 au (d1AU), aspect ratio
of cross-section at 1 au ($\delta$), a twist factor (Tfac) which is related to
the number of twists over the whole torus, launch speed ($v_{0}$), launch
radius ($r_{0}$), magnetic field strength at 1 au (B1AU), drag parameter
($\Gamma$), global solar wind speed ($v_{\mathrm{sw}}$), expansion rate
($n_{a}$) of the cross-section diameter, and the rate at which the magnetic
field decreases ($n_{b}$). The launch time was chosen as 2022 Sep 5 16:00 UT
at a launch radius $r_{0}$ of $10.7$ $R_{\odot}$, to coincide with WISPR
observations. Choosing the input parameter ranges, we attempt to include
physical knowledge gained from additional sources and physical considerations,
such as flux rope type (low inclination and positive twist factor) or
spacecraft position restricting the propagation direction (longitude and
latitude). This approach ensures timely convergence of the model, while still
keeping the remaining model parameters rather free for the algorithm to
optimize.

The results obtained for the SolO fit were then used to restrict the input
parameter ranges for the PSP fit. Additionally, allowing higher values for
d1AU and $\delta$, as well as an unusually low $v_{0}$ due to the extremely
close distance of PSP to the Sun, increased the possibility of generating hits
in the first place. This approach was chosen as 3DCORE appeared to have
difficulties converging to a minimum. Due to PSP being very close to the Sun
as well as its rapidly changing position, a highly varying range of input
parameters can be used to generate more or less equally “good” signatures.
This behavior was somewhat expected, as even characteristics such as flux rope
type were difficult to establish visually. While these circumstances hinder
the inference of flux rope parameters through solely utilizing the PSP
measurements, we can still test which of the assumptions from SolO hold for
the PSP fit.

Figure 8 presents the reconstructed 3DCORE flux rope (dashed lines) together
with the in situ magnetic field observations of SolO (solid lines), where the
shaded area corresponds to the 2$\sigma$ spread of the ensemble. The vertical
grey dashed lines throughout the defined ME indicate the fitting points used
for comparing the model output to the in situ data. As discussed in Section
2.4, the observations display a magnetic field rotation that indicates a low-
inclination right-handed NES flux rope type. As shown in Table 2, we restrict
the inclination between -45 and 45∘ to reflect a low inclination flux rope,
and restrict the twist factor to positive values to align with the in situ
observations. For the case of the SolO observations, 3DCORE was able to
reconstruct the flux rope without too many adjustments of parameter fitting
limits and in a short computational time.

Figure 8: SolO magnetic field measurements (solid lines) together with the
3DCORE flux rope ensemble. The shaded area corresponds to the 2$\sigma$ spread
of the ensemble. The dashed colored lines show one specific flux rope from the
ensemble. The vertical black dashed lines denote the beginning and the end of
the reconstruction interval used by 3DCORE. The vertical grey dashed lines
denote the fitting points used for comparing the model output to the in situ
data. The magnetic field measurements are in local spacecraft RTN coordinates.

Similarly, Figure 9 shows the PSP in situ magnetic field measurements with the
flux rope ensemble generated by 3DCORE. Despite the flux rope type being
difficult to establish visually from the in situ observations, 3DCORE fits the
PSP data relatively well when restricted to positive twist values, consistent
with the SolO in situ observations of a right-handed flux rope type, as well
as with the inferred magnetic field rotation due to the plasma flows observed
along the solar source of the flux rope (Long et al., 2023). The fitting
captures the overall trend of the in situ observations quite well, however, we
see some substantial deviation especially in the BR component, which exhibits
strong variations hinting at additional processes affecting the flux rope, as
discussed in Romeo et al. (2023) and Liu et al. (2024).

Similar 3DCORE fitting was performed using the PSP in situ observations in
Long et al. (2023). We note that in Long et al. (2023), the model assumed a
stationary spacecraft when fitting the data. Although the assumption of a
stationary spacecraft holds at larger distances from the Sun, in this study,
we improve on the fitting to capture the fast movement of PSP relative to the
motion of the flux rope over the spacecraft.

Figure 9:  PSP magnetic field measurements (solid lines) together with the
3DCORE flux rope ensemble, presented in the same format as Figure 8.

Table 2 also presents the flux rope parameters inferred by 3DCORE for the
observations at PSP and SolO. Comparing the values in Table 2, we can see that
even some of the less restricted parameters are similar for both
reconstructions, for example, the propagation longitude and the scaled mean
magnetic field strength at 1 au, B1AU. The modeled launch speed of 1619.28
$\pm$ 173.09 km s-1 for SolO is comparable with the mean shock speed of 1520
km s-1 calculated in Trotta et al. (2024). The non-physically low launch speed
of 318.79 $\pm$ 87.93 km s-1 for the PSP reconstruction hints towards the
models inability to accurately reproduce the CME evolution close to the Sun.

Larger differences are seen in the propagation latitude, the inclination,
$\delta$, Tfac, $\Gamma$, and $v_{\mathrm{sw}}$. The propagation latitude of
-5.86 $\pm$ 7.01∘ produced at SolO, indicates a southwards propagation
(albeit, very slightly) with respect to the Earth-equatorial plane, in
agreement with the southwards propagation observed in the coronagraphs and
indicated by the location of the solar source, and the GCS fitting results of
R. Patel (Patel et al., 2023) mentioned in Section 2.3. The PSP value of 5.85
$\pm$ 10.11∘ suggests a propagation direction slightly above the solar
equatorial plane, however, the two results lie within the calculated 2$\sigma$
spread of the ensemble members. These larger uncertainties are likely produced
due to the way in which PSP crosses the flank of the ICME.

The inclination value produced by 3DCORE at SolO is 5.61 $\pm$ 6.16∘, in
agreement with the low inclination flux rope type determined from
observations. At PSP, 3DCORE produces a value of 20.99 $\pm$ 12.39∘, a more
intermediate flux rope inclination than that of SolO. As the inclination value
can be used to set the flux rope type for a 3DCORE model (Rüdisser et al.,
2024), the high uncertainty regarding the inclination at PSP reflects the
ambiguity in visually determining the flux rope type from the PSP in situ
observations. The higher inclination at PSP is also not surprising given the
estimated inclination of 58∘ from the GCS fitting results using the
STEREO-A/COR-2 images. The declining inclination between coronagraph
observations, PSP, and SolO, is in agreement with previous suggestions that
ICME magnetic flux ropes may align with the HCS as they propagate (Yurchyshyn,
2008; Isavnin et al., 2014), and multi-spacecraft studies which found small
decreases in flux rope axis inclination as ICMEs propagated to larger
heliocentric distances (Good et al., 2019; Davies et al., 2022).

The magnetic field expansion rates, $n_{b}$, produced by 3DCORE are -1.47
$\pm$ 0.15 at PSP and -1.76 $\pm$ 0.18 at SolO. These values are directly
comparable to the magnetic expansion rate of -1.74 calculated using the in
situ observations in Section 2.4. The magnetic field expansion rate for SolO
is in very good agreement with that calculated using the in situ magnetic
field observations at both spacecraft. The rate at PSP is much lower, however,
it is within the uncertainty range of -1.21 $\pm$ 0.44, calculated using
events prior to this event observed by PSP in Salman et al. (2024).

Similarly to the magnetic field expansion rate, we are also able to compare
the expansion rate of the cross-section diameter produced by 3DCORE to
previous calculations based on the in situ observations in Section 2.4. There,
we found the size of the flux rope expected to scale as $r^{0.576}$. In
comparison, the expansion rates produced by the 3DCORE fitting are 1.04 $\pm$
0.03 and 1.17 $\pm$ 0.08 at PSP and SolO, respectively: much greater than that
observed. Interestingly, we find that the expansion rate value at PSP is
actually more similar to the value of the dimensionless expansion parameter,
$\zeta$ = 0.925, calculated in Section 2.4 using the plasma velocities
observed at SolO.

At both SolO and PSP, the estimated cross-section at 1 au produced by the
model, d1AU, is toward the larger side of ICMEs at 1 au (typically around 0.2
au; Lepping et al., 1990) and should be taken with caution. The scaling law
used in 3DCORE is also most probably not applicable for every ICME throughout
the whole Sun to spacecraft propagation. As discussed in Section 3, the drag
regime at larger distances is very different from that closer to the Sun, and
we expect this to affect the expansion rate; at PSP, it is clear that the
expansion is overestimated by 3DCORE.

3DCORE provides only one global background solar wind speed, and due to the
large radial separation of the two spacecraft, the background solar wind
speed, $v_{\mathrm{sw}}$, is very different for the two fits: 267.79 $\pm$
119.57 km s-1 at PSP, and 440.32 $\pm$ 70.86 km s-1 at SolO. Comparing these
to the mean measured in situ background solar wind speeds at the two
spacecraft (calculated over the preceding 12 hours before the ICME arrival
time), we find a mean background solar wind speed of 429.61 km s-1 at PSP and
504.93 km s-1 at SolO. The modeled $v_{\mathrm{sw}}$ is much more similar to
the observed mean value at SolO, whereas at PSP, the modelled
$v_{\mathrm{sw}}$ is 60% of the observed mean value. Such a low modeled
$v_{\mathrm{sw}}$ is a product of the 3DCORE fitting procedure at PSP, where
the model was more likely to find hits at lower speeds so close to the Sun, as
is also seen in the very low launch velocity obtained by 3DCORE. 3DCORE was
mainly developed to reconstruct flux rope signatures further out from the Sun,
thus it has more difficulty when fitting the in situ signature at PSP so close
to the Sun. The small modeled background solar wind speed for the PSP flux
rope therefore results in a stronger deceleration compared to the SolO flux
rope. Together with the already low launch speed, this leads to a very slow
propagation speed for the PSP flux rope. This is clearly demonstrated in
Figure 10 which presents the 3D reconstructions of the global structure using
the 3DCORE parameters at SolO (represented by the orange grid) and PSP (black
grid), where views from top down and along the solar equatorial plane are
shown. Figure 10a presents the reconstructed flux ropes around the time of
observation at PSP (2022 Sep 5 21:00 UT) and Figure 10b presents the
reconstructed flux ropes around the time of observation at SolO (2022 Sep 7
06:00 UT), one day and 9 hours later, giving a sense of the time evolution of
the flux rope as it propagated. The differences between the arrival times are
not as distinct at the earlier PSP observation time, however, the difference
in timing is very clear at the later SolO observation time, highlighting the
large difference in deceleration produced due to the background solar wind
speeds.

Figure 10: Representative flux ropes reconstructed by 3DCORE from the PSP
(black) and SolO (orange) observations, (a) at a time of observation of the
magnetic ejecta by PSP (2022 Sep 5 21:00 UT) and (b) at a time of observation
the magnetic ejecta at SolO (2022 Sep 7 06:00 UT). The solid lines inside of
the flux rope grids depict a magnetic field line and its twist. Top: top view
down from solar equatorial north, bottom: side view along the solar equatorial
plane. The black solid and dashed line shows the trajectory of PSP before and
after the observation time; the orange dashed line is the trajectory of SolO
after the observation.

##  5 Summary and Conclusions

The CME launched on 2022 September 5 is the closest to the Sun detected in
situ to date, observed by PSP at a distance of only 0.07 au. Due to a
longitudinal separation within 30∘, the same CME was also observed in situ by
SolO at a heliocentric distance of 0.69 au. Such a spacecraft configuration
has provided an excellent opportunity to investigate how the flux rope of the
CME evolved between a very early stage of its evolution, out to heliocentric
distances much further away.

In this study, we used both in situ observations at PSP and SolO to determine
its radial evolution, as well as two models: ELEvoHI, which provided a direct
link between remote images of the CME at PSP to in situ arrival times of the
ICME, and 3DCORE, a semi-empirical 3D flux rope model, capable of inferring
flux rope parameters by fitting in situ magnetic field observations and
reconstructing the global 3D structure of the CME.

The in situ observations at PSP appear very different to those at SolO. The
strong rotation in the radial component of the magnetic field observed by PSP,
implies that the spacecraft crossed through the flux rope at an angle to the
solar equatorial plane (e.g. see Figure 2 of DiBraccio et al., 2015, for
examples of different trajectories through the flux rope cross section). This
situation is reflected in the changing latitude of PSP as the ICME passed over
the spacecraft (see Table 1), and the southwards propagation of the CME
itself. Such observations make determining the flux rope type, and thus
handedness and inclination, much trickier. At SolO, the magnetic field
components are observed to rotate from North-East-South, and thus we are able
to determine that the flux rope was of low-inclination with a right-handed
rotation. This right-handed rotation is in agreement with the right-handed
motion of plasma flows along its solar source filament channel (Long et al.,
2023) and the right-handed nature of the active region.

Observations of the solar source of the CME and results from GCS fitting show
that the CME propagated in a southwards direction with respect to the solar
equatorial plane, and thus PSP and SolO likely observe the flank of the CME.
This interpretation is consistent with the in situ observations, where Trotta
et al. (2024) determined the shock front to be oblique. Despite the flank
encounter, the global expansion relationship calculated using observations of
the mean magnetic field within the ME, $B\propto r^{-1.74}$, is surprisingly
consistent with that determined by calculating the dimensionless expansion
parameter (a measure of local expansion) at SolO, $B\propto r^{-1.85}$.
However, similar scaling relationships between the size of the magnetic flux
rope determined from in situ observations, $D\propto r^{0.576}$, and that of
the dimensionless expansion parameter, $D\propto r^{0.925}$, are not
consistent, where the dimensionless expansion parameter significantly
overestimates the expansion rate.

To demonstrate the connection between remote images and the observations in
situ, we use the ELEvoHI model to predict the arrival time of the CME at SolO
and PSP. In this case, we use a time-elongation profile obtained by tracking
the leading edge of the CME in WISPR images as an input. We find a large
discrepancy between modeled arrival times at PSP and SolO: a mean arrival
error of 0.3 hours and 18.4 hours, respectively. These results suggest that
the underlying model assumptions may not be suitable for making predictions
based on time-elongation tracks obtained from close proximity to the Sun (up
to only 14 $R_{\odot}$), where the drag regime is markedly different in
comparison to larger heliocentric distances.

The 3DCORE model is capable of fitting the magnetic field observations at each
spacecraft to estimate parameters such as the propagation direction,
inclination, and expansion rate of the CME flux rope. Due to the large radial
separation of PSP and SolO, we applied 3DCORE to both observations separately,
including physical knowledge gained from additional sources and physical
considerations, and taking the results of the SolO fit to restrict the input
parameters for the PSP fit. We find that although many parameter results are
similar between the two fits, it is difficult to reconstruct a completely
consistent global 3D structure between the in situ observations at PSP and
SolO. This is likely due to the single spacecraft trajectories through the
CME, with large radial and longitudinal separations, as features often differ
throughout the flux rope and are perhaps more localized to the in situ
measurement site. When reconstructing and propagating the ICME, the difference
between the background solar wind speeds produced by 3DCORE for PSP and SolO
were strongly apparent, with the low speed at PSP decelerating the CME
significantly. From our model fitting results, it is clear the solar wind
background and drag regime strongly affects the modeled expansion and
propagation of CMEs and needs to be considered.

These results underscore the importance of refining our models and questioning
the validity of our assumptions for CME propagation as we seek to improve the
accuracy of space weather forecasting tools. As PSP and SolO continue their
missions, validation of such models with in situ multi-spacecraft observations
is crucial towards creating a more realistic picture of CME evolution across
large heliocentric distance ranges and differing solar wind regimes, and
incorporated into models continuing to improve our understanding of CME
propagation throughout the heliosphere.

E. D., U.V. A., H.T. R., C. M., and E. W. are funded by the European Union
(ERC, HELIO4CAST, 101042188). Views and opinions expressed are however those
of the author(s) only and do not necessarily reflect those of the European
Union or the European Research Council Executive Agency. Neither the European
Union nor the granting authority can be held responsible for them. M. B. and
T. A. acknowledge that this research was funded in whole, or in part, by the
Austrian Science Fund (FWF) [P 36093]. S. M. and M. A. R. acknowledge that
this research was funded in whole, or in part, by the Austrian Science Fund
(FWF) [P 34437]. For the purpose of open access, the author has applied a CC
BY public copyright licence to any Author Accepted Manuscript version arising
from this submission. D.T. received funding from the European Unions Horizon
2020 research and innovation programme under grant agreement no. 101004159
(SERPENTINE, www.serpentine-h2020.eu). Views and opinions expressed are,
however, those of the authors only and do not necessarily reflect those of the
European Union or the European Research Council Executive Agency. Neither the
European Union nor the granting authority can be held responsible for them.
Solar Orbiter is a space mission run as an international collaboration between
ESA and NASA and operated by ESA. Solar Orbiter magnetometer operations are
funded by the UK Space Agency (grant ST/X002098/1). T. H. is supported by STFC
grant ST/W001071/1. T.N-C. thanks for the support of the Solar Orbiter and
Parker Solar Probe missions, Heliophysics Guest Investigator Grant
80NSSC23K0447 and the GSFC-Heliophysics Innovation Funds. Solar Orbiter SWA
data were derived from scientific sensors that were designed and created and
are operated under funding provided by numerous contracts from UKSA, STFC, the
Italian Space Agency, CNES, the French National Centre for Scientific
Research, the Czech contribution to the ESA PRODEX programme and NASA. SO SWA
work at the UCL/Mullard Space Science Laboratory is currently funded by STFC
(Grant Nos. ST/W001004/1 and ST/X/002152/1). P.H. acknowledges the support of
the PSP program office and the Office of Naval Research. Parker Solar Probe
was designed, built, and is now operated by the Johns Hopkins Applied Physics
Laboratory as part of NASA’s Living with a Star (LWS) program (contract
NNN06AA01C). Support from the LWS management and technical team has played a
critical role in the success of the Parker Solar Probe mission. The Wide-Field
Imager for Parker Solar Probe (WISPR) instrument was designed, built, and is
now operated by the US Naval Research Laboratory in collaboration with Johns
Hopkins University/Applied Physics Laboratory, California Institute of
Technology/Jet Propulsion Laboratory, University of Gottingen, Germany, Centre
Spatiale de Liege, Belgium and University of Toulouse/Research Institute in
Astrophysics and Planetology.

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