# A Survey of Coronal Mass Ejections Measured In Situ by Parker Solar Probe
During 2018–2022

Tarik Mohammad Salman Department of Physics and Astronomy, George Mason
University, 4400 University Dr., MSN 3F3, Fairfax, VA 22030, USA  Heliophysics
Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Teresa Nieves-Chinchilla Heliophysics Science Division, NASA Goddard Space
Flight Center, Greenbelt, MD 20771, USA  Lan K. Jian Heliophysics Science
Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Noé
Lugaz Institute for the Study of Earth, Oceans, and Space, University of New
Hampshire, Durham, NH 03824, USA  Fernando Carcaboso Postdoctoral Program
Fellow, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Emma E.
Davies Austrian Space Weather Office, GeoSphere Austria, Graz 8020, Austria
Yaireska M. Collado-Vega Heliophysics Science Division, NASA Goddard Space
Flight Center, Greenbelt, MD 20771, USA

###### Abstract

We present a statistical investigation of the radial evolution of 28
interplanetary coronal mass ejections (ICMEs), measured in situ by the Parker
Solar Probe (PSP) spacecraft from 2018 October to 2022 August. First, by
analyzing the radial distribution of ICME classification based on magnetic
hodograms, we find that coherent configurations are more likely to be observed
close to the Sun. In contrast, more complex configurations are observed
farther out. We also notice that the post-ICME magnetic field is more impacted
following an ICME passage at larger heliocentric distances. Second, with a
multi-linear robust regression, we derive a slower magnetic ejecta (ME)
expansion rate within 1 au compared to previous statistical estimates. Then,
investigating the magnetic field fluctuations within ICME sheaths, we see that
these fluctuations are strongly coupled to the relative magnetic field
strength gradient from the upstream solar wind to the ME. Third, we identify
ME expansion as an important factor in forming sheaths. Finally, we determine
the distortion parameter (DiP) which is a measure of magnetic field asymmetry
in an ME. We discover lower overall asymmetries within MEs. We reveal that
even for expanding MEs, the time duration over which an ME is sampled does not
correlate with DiP values, indicating that the aging effect is not the sole
contributor to the observed ME asymmetries.

sun, coronal mass ejection

††journal: ApJ

##  1 Introduction

Investigating the evolution of interplanetary counterparts of coronal mass
ejections (CMEs), hereafter ICMEs, is crucial to develop an improved
generalization of the embedded complexities in ICME propagation. The dynamic
propagation of ICMEs in the heliosphere is governed by its nature of expansion
and interactions with the background solar wind and other transients therein
(see Manchester et al., 2017, for a review). However, the degree of their
influence on ICME evolution is also reliant upon the heliospheric conditions
that the ICME encounters during propagation (e.g., Temmer et al., 2011; Kilpua
et al., 2012; Liu et al., 2013). The complex manifestations of ICME
propagation in the structured solar wind, such as deflections from an expected
radial path (e.g., Wang et al., 2004; Rodriguez et al., 2011; Lugaz et al.,
2012; Isavnin et al., 2014; Wang et al., 2014), deformations and distortions
(e.g., Riley & Crooker, 2004; Temmer et al., 2014; Owens et al., 2017; Vršnak
et al., 2019; Owens, 2020; Davies et al., 2021b), erosion (e.g., Dasso et al.,
2006; Lavraud et al., 2014; Ruffenach et al., 2015; Pal et al., 2020, 2021;
Stamkos et al., 2023), resulting from the co-action of internal and external
factors complicate the conceptualization and quantification of ICME evolution
in the inner heliosphere.

Our knowledge of the governing physics of CME/ICME propagation has been
primarily achieved through remote-sensing observations closer to the Sun and
in situ measurements at 1 au. Much fruitful science has been gleaned from in
situ measurements of ICMEs. Statistical investigations of ICMEs, based on
single-point measurements at different heliocentric distances have provided us
with significant information about average ICME characteristics in the inner
heliosphere with robust data sets (e.g., Jian et al., 2006; Richardson & Cane,
2010; Jian et al., 2011; Vech et al., 2015; Winslow et al., 2015; Good &
Forsyth, 2016; Jian et al., 2018; Nieves-Chinchilla et al., 2018, 2019). In
addition, reconstruction techniques and theoretical models (e.g., Burlaga,
1988; Lepping et al., 1990; Hu & Sonnerup, 2002; Démoulin et al., 2008;
Nieves-Chinchilla et al., 2016) and superposed epoch analysis (e.g., Masías-
Meza et al., 2016; Rodriguez et al., 2016; Jian et al., 2018; Janvier et al.,
2019; Carcaboso et al., 2020; Lanabere et al., 2020; Regnault et al., 2020;
Salman et al., 2020a) have been performed to deduce the global ICME properties
by using a single spacecraft. However, such measurements provide a limited and
localized view of the large and complex ICME structure, covering several
tenths of an au in the radial direction near/at 1 au (e.g., Jian et al., 2006;
Richardson & Cane, 2010; Jian et al., 2018). Thus, a single 1D trajectory
through an ICME is not enough to determine its global 3D structure (see Al-
Haddad et al., 2013). Also, the aforementioned approaches are based on
assumptions of ICME geometries and spacecraft trajectories. They are not
always able to provide information regarding the plethora of physical
processes that the ICME might have undergone during its propagation (e.g.,
Reinard et al., 2012; Lugaz et al., 2020a).

To better understand the global configuration and evolution of ICMEs, multi-
spacecraft measurements with various radial and longitudinal separations are
crucial (Winslow et al., 2022; Scolini et al., 2023). Statistical studies of
in situ measurements of distinct ICMEs (e.g., Bothmer & Schwenn, 1998; Liu et
al., 2005; Leitner et al., 2007; Jian et al., 2008a, b; Winslow et al., 2015;
Janvier et al., 2019) or the same ICME (e.g., Kilpua et al., 2011; Good et
al., 2019; Vršnak et al., 2019; Lugaz et al., 2020a; Salman et al., 2020b;
Davies et al., 2022; Scolini et al., 2022; Regnault et al., 2023) from
multiple spacecraft at different heliocentric distances have provided
important information and a global perspective of the evolution of ICME
structures in the inner heliosphere.

It is important to note that multi-spacecraft measurements of the same ICME
are still difficult to attain due to the limited number of space assets and
lack of continuous solar wind measurements at different locations. With the
appropriate alignment of existing spacecraft in space, it is possible to track
the propagation of a CME from the Sun to Mercury, 1 au orbit, Mars, Saturn,
New Horizons (at 32 au), and Voyager 2 (at 110 au), as shown in Witasse et al.
(2017). It has also been seen that it is even possible to encounter the same
ICME at points in space that have a 110∘ longitudinal separation (see
Carcaboso et al., 2024). However, such multi-spacecraft encounters also depend
on fortuitous radial and longitudinal lineups of space probes. Also, factors
such as inclination (e.g., Kilpua et al., 2009; Davies et al., 2021b),
longitudinal separation (e.g., Farrugia et al., 2011; Kilpua et al., 2011;
Winslow et al., 2015; Lugaz et al., 2018; Mishra et al., 2021; Pal et al.,
2023; Palmerio et al., 2024), interactions with other structures (e.g., Möstl
et al., 2012; Prise et al., 2015; Winslow et al., 2016, 2021; Lugaz et al.,
2022), physical effects such as erosion, deformation, distortion (e.g.,
Ruffenach et al., 2012; Wang et al., 2018; Palmerio et al., 2021; Weiss et
al., 2021) can induce fundamental changes in ICME measurements from one
spacecraft to another and limit the generality of the findings. Another
intrinsic drawback of most of the previous statistical approaches has been
examining ICME evolution with clusters of in situ measurements at certain
locations rather than a more continuous coverage. The addition of the Parker
Solar Probe (PSP; Fox et al., 2016; Raouafi et al., 2023) and Solar Orbiter
(SolO; Müller et al., 2013, 2020) missions to the Heliophysics System
Observatory (HSO) improves upon the existing clusters of measurements at
specific points in the inner heliosphere and provide more opportunities for
multi-spacecraft encounters as well.

In this study, we take advantage of the extensive radial spread of PSP
observations to investigate ICME evolution from different perspectives. Before
the PSP mission, such investigations of the evolution of the magnetic field
and plasma quantities inside an ICME have been limited to a radial extent
beyond 0.29 au only. With PSP now in the fold and providing data coverage of
the innermost heliosphere below 0.29 au, this enables us to advance our
current understanding of ICME evolution in the inner heliosphere.

This paper is organized as follows. In Section 2, we introduce the data and
method used for the identification of ICMEs. In Section 3, we present the
compiled PSP ICME list, statistical results, and brief discussions. In Section
4, we summarize the findings and make our conclusions.

##  2 Data and Methodology

The PSP mission was launched on 2018 August 12. The mission consists of 24
highly elliptical orbits and 7 Venus gravity assist flybys (used to gradually
decrease the perihelion every few orbits). The perihelion of orbit 22 will
reach 9.86 solar radii on 2024 December 24 (Raouafi et al., 2023). During the
mission, PSP will provide unprecedented measurements of the solar wind closer
to the Sun. Such measurements will offer crucial insights into creating a more
complete scenario of the CME/ICME-related phenomena, from the genesis at the
Sun to the inner heliosphere.

To compile the PSP ICME list, we use Level 2 magnetic field data with a 1-min
cadence from the Fluxgate Magnetometer (MAG) part of the FIELDS (Bale et al.,
2016) instrument and 28-sec moment averages of bulk solar wind measurements
from the Solar Probe Cup (SPC; Case et al., 2020), which is part of the Solar
Wind Electrons Alphas and Protons (SWEAP; Kasper et al., 2016) instrument
suite onboard PSP, in Radial Tangential Normal (RTN) coordinates (Fränz &
Harper, 2002). Because the PSP ICMEs investigated in this study are all beyond
0.2 au (see Table 1 in Section 3), SPC data can describe the solar wind well
compared to the Solar Probe ANalyzer-Ions (SPAN-i; Livi et al., 2022) and
Solar Probe ANalyzer-Electrons (SPAN-e; Whittlesey et al., 2020) detectors.
This is because SPC has a better field of view (FOV) beyond encounter mode,
whereas SPAN has a better FOV during encounter mode, meaning that SPC
generally has better measurements outside 0.25 au. In addition, we use only
the good-quality SPC data (quality flag=0) filtered using the data quality
indicator.

In this manuscript, the term “ICME” refers to the whole structure, including
the shock (if present), sheath (if present), and magnetic ejecta (ME). The
identification of ICMEs in PSP observations is not always straightforward.
Unlike near/at 1 au, it is not possible to adopt a quantitative approach since
the position of PSP is not stationary. Due to this, we also have to be careful
about features that are artifacts of PSP moving closer to the Sun or farther
out, rather than a part of an ICME. Therefore, we adopt a more qualitative
approach, reliant upon visual identification. We classify an ICME if the
corresponding measurements match the majority of the following identification
criteria (for the ME) given the available data: (i) significant enhancement of
the magnetic field, (ii) rotation in the magnetic field vector, (iii)
coherence of the magnetic field (smooth rotations and fewer fluctuations),
(iv) low proton density, (v) low proton thermal speed, and (vi) proportionate
duration to distinguish between small-scale structures that are not ICMEs (see
e.g., Moldwin et al., 2000; Janvier et al., 2014). However, due to the
unavailability of good-quality SPC data for several events, the identification
is primarily based on criteria (i)–(iii) and (vi).

Figure 1: PSP observations of an ICME on 2022 Jan 29 at 0.67 au. From top to
bottom, the panels represent the total magnetic field strength, magnetic field
vector in RTN coordinates, proton density, proton radial (most probable)
thermal speed, proton beta, and proton bulk speed. The vertical solid black
line indicates the shock arrival, the region between the solid black line and
the first dashed green line is the sheath, and the region between the two
dashed green lines is the ME. Magnetic hodograms, overlaid with smoothed,
connected traces (magenta lines) in RTN coordinates for the ME duration (the
magenta circle denotes the ME start) are shown in the three subplots at the
bottom.

Figure 1 shows the magnetic field and plasma observations of an example ICME
encountered by PSP. All the ICME identification criteria are satisfied by this
event. The ME magnetic field strength is ${\sim}$100% stronger compared to the
upstream solar wind (defined as an 8-hr interval before the ICME arrival). The
field rotations are smooth for the entire ME duration. The ME also exhibits
low proton density and temperature. The duration of the ME is ${\sim}$15
hours. Although this ICME is not fast, at ${\sim}$400 km$\cdot$s-1, it drives
a shock and has an ${\sim}$10.7-hr sheath region.

##  3 PSP ICME List

Table 1 lists the ICMEs that we identified from PSP observations based on the
criteria mentioned in Section 2. The ICME list has PSP observations ranging
from 0.23 au to 0.83 au.

Figure 2: Annual occurrences of ICMEs (in blue) and CIR/SIRs (in red) measured by PSP as a function of time. Green dots indicate the annual mean SSN with the error bars as the standard deviations. For the years 2018 and 2022, the ICME and CIR/SIR counts and mean SSN correspond to 3-month (from October to December) and 8-month (from January to August) periods respectively and are not normalized to whole years. The CIR/SIRs are listed from Allen et al. (2021) and extend until the end of 2021. Table 1: The PSP ICME list. Column 1 shows the chronological order of events. Column 2 represents PSP’s heliocentric distance (r) at the onset of the ICME arrival. Column 3 lists the shock (for events with both shock and sheath)/sheath (for events with no shock but a sheath)/ME (for events with no shock and sheath) arrival times. Column 4 and Column 5 highlight the ME start and end times respectively. Column 6 and Column 7 report the ME classes (see Subsection 3.1 for explanation) and average ME magnetic field strengths (B${}_{\textrm{ME}}$) in order, whereas Column 8 has the distortion parameter (DiP, see Subsection 3.4 for details) values.  Event No | r | ICME Start Time | ME Start Time | ME End Time | ME Class | B${}_{\textrm{ME}}$ | DiP
---|---|---|---|---|---|---|---
| au | YYYY MM/DD hh:mm | YYYY MM/DD hh:mm | YYYY MM/DD hh:mm |  | nT |
1 | 0.28 | 2018 10/30 20:55 | 2018 10/30 20:55 | 2018 10/31 08:10 | F- | 52.11 | 0.56
2 | 0.23 | 2018 11/11 23:51 | 2018 11/11 23:51 | 2018 11/12 06:07 | F- | 82.08 | 0.53
3 | 0.55 | 2019 03/15 09:00 | 2019 03/15 12:14 | 2019 03/15 17:45 | F- | 31.30 | 0.52
4 | 0.41 | 2019 03/23 19:15 | 2019 03/23 19:15 | 2019 03/24 17:45 | F- | 25.98 | 0.15
5 | 0.80 | 2019 10/13 19:03 | 2019 10/13 22:48 | 2019 10/14 21:07 | F${}_{\textrm{r}}$ | 13.27 | 0.40
6 | 0.83 | 2019 12/16 18:04 | 2019 12/16 18:04 | 2019 12/17 08:03 | E${}_{\textrm{j}}$ | 13.37 | 0.49
7 | 0.34 | 2020 01/20 19:00 | 2020 01/20 19:00 | 2020 01/21 06:30 | F- | 41.55 | 0.53
8 | 0.41 | 2020 02/11 05:08 | 2020 02/11 05:08 | 2020 02/11 11:45 | F${}_{\textrm{r}}$ | 40.05 | 0.52
9 | 0.36 | 2020 05/28 09:20 | 2020 05/28 09:20 | 2020 05/28 14:50 | F${}_{\textrm{r}}$ | 35.46 | 0.51
10 | 0.45 | 2020 06/22 20:40 | 2020 06/23 03:20 | 2020 06/23 16:50 | E${}_{\textrm{j}}$ | 15.74 | 0.55
11 | 0.51 | 2020 06/25 11:53 | 2020 06/25 15:59 | 2020 06/26 08:15 | F- | 19.63 | 0.41
12 | 0.48 | 2020 09/12 10:23 | 2020 09/12 13:33 | 2020 09/12 19:35 | E${}_{\textrm{j}}$ | 15.47 | 0.44
13 | 0.69 | 2020 10/27 04:50 | 2020 10/27 07:15 | 2020 10/27 15:40 | - | - | -
14 | 0.81 | 2020 11/29 23:07 | 2020 11/30 03:21 | 2020 11/30 16:26 | C${}_{\textrm{x}}$ | 10.75 | 0.50
15 | 0.81 | 2020 11/30 18:35 | 2020 12/01 02:24 | 2020 12/01 11:17 | F${}_{\textrm{r}}$ | 28.39 | 0.40
16 | 0.62 | 2021 02/11 16:18 | 2021 02/11 16:18 | 2021 02/12 03:56 | C${}_{\textrm{x}}$ | 12.16 | 0.42
17 | 0.64 | 2021 02/12 11:18 | 2021 02/12 11:18 | - | - | - | -
18 | 0.68 | 2021 05/28 03:00 | 2021 05/28 08:10 | 2021 05/29 12:04 | F${}_{\textrm{r}}$ | 18.36 | 0.18
19 | 0.69 | 2021 05/30 08:08 | 2021 05/30 14:18 | 2021 06/01 02:50 | - | - | -
20 | 0.76 | 2021 06/10 04:38 | 2021 06/10 16:52 | 2021 06/11 08:54 | C${}_{\textrm{x}}$ | 11.34 | 0.45
21 | 0.77 | 2021 06/12 03:40 | 2021 06/12 07:20 | 2021 06/13 01:12 | F+ | 19.98 | 0.53
22 | 0.76 | 2021 06/30 14:58 | 2021 06/30 22:10 | 2021 07/01 17:12 | F+ | 25.75 | 0.31
23 | 0.69 | 2021 07/11 10:25 | 2021 07/11 10:25 | 2021 07/11 23:25 | - | - | -
24 | 0.78 | 2021 09/26 08:56 | 2021 09/26 23:04 | 2021 09/27 12:50 | F- | 14.39 | 0.48
25 | 0.44 | 2021 11/09 16:22 | 2021 11/09 18:40 | 2021 11/10 04:20 | F${}_{\textrm{r}}$ | 53.89 | 0.50
26 | 0.67 | 2022 01/29 00:00 | 2022 01/29 10:40 | 2022 01/30 02:00 | F${}_{\textrm{r}}$ | 22.42 | 0.51
27 | 0.58 | 2022 02/05 08:40 | 2022 02/05 08:40 | 2022 02/05 14:00 | F- | 14.51 | 0.56
28 | 0.38 | 2022 02/16 07:25 | 2022 02/16 15:18 | 2022 02/17 06:32 | F- | 45.88 | 0.43
29 | 0.52 | 2022 03/14 16:30 | 2022 03/14 16:30 | 2022 03/16 16:00 | E${}_{\textrm{j}}$ | 15.46 | 0.46
30 | 0.69 | 2022 07/02 04:40 | 2022 07/02 18:30 | 2022 07/04 16:30 | E${}_{\textrm{j}}$ | 15.50 | 0.47
31 | 0.76 | 2022 07/18 22:30 | 2022 07/18 22:30 | 2022 07/19 18:00 | C${}_{\textrm{x}}$ | 18.29 | 0.47
32 | 0.56 | 2022 08/18 13:30 | 2022 08/18 16:00 | 2022 08/19 00:00 | F${}_{\textrm{r}}$ | 56.46 | 0.44

The ICME list covers the period from 2018 October to 2022 August. This period
includes the minimum and rising phases of the current solar cycle (SC), SC25.
Figure 2 shows ICMEs and co-rotating/stream interaction regions (CIR/SIRs)
measured by PSP. The CIR/SIR counts are from the compiled list of Allen et al.
(2021). The plot shows a clear rise in the annual ICME occurrences from the
solar minimum to the rising phase. The number of ICMEs has risen from 4 events
in 2019 to 10 in 2021. The CIR/SIR occurrences also follow a similar
progression. In Figure 2, we also plot the annual mean sunspot number (SSN)
from the Solar Influences Data Analysis Center
(SIDC111http://sidc.be/silso/home) for the years 2018–2022. The annual mean is
computed from the 13-month smoothed monthly total SSN. Previous studies have
found good correlations between the ICME rate and SSN (e.g., Jian et al.,
2006; Gopalswamy et al., 2010; Jian et al., 2018; Li et al., 2018; Möstl et
al., 2020). Similarly, for this period as well, the SSN exhibits positive
relationships with the annual ICME and CIR/SIR occurrences.

Due to the unique orbits of PSP, we cannot do the usual averages as we also
have to incorporate the radial spread in observations. Thus, we separate the
ICMEs into two radial blocks. The first block consists of 14 ICMEs from 0.23
au to 0.56 au, whereas the second block also consists of 14 ICMEs but from
0.58 au to 0.83 au. The average ME magnetic field strengths
(B${}_{\textrm{ME}}$) in the first and second blocks are 37.9$\pm$19.3 nT and
17.0$\pm$5.4 nT respectively. The lower average field strength (by
${\sim}$55%) in the second block is consistent with the decrease in average
values reported in previous statistical studies (e.g., Winslow et al., 2015;
Janvier et al., 2019; Salman et al., 2020b). We also perform Welch’s t-test to
measure the statistical difference between the average values. We find the
difference between the average field strengths of the two populations to be
statistically significant with 95% confidence (p-value=0.001).

In total, we list 32 ICMEs measured by PSP. However, our statistical analyses
presented in the following subsections are based on 28 ICMEs (excluding events
13, 17, 19, and 23 which are marked by gray fonts in Table 1) rather than 32
since these four ICMEs have considerable MAG data gaps within respective ME
durations.

###  3.1 ME Complexity

The common consensus in the heliophysics community is that CMEs erupt with a
flux-rope (FR) configuration (e.g., Chen, 1996; Bothmer & Schwenn, 1998; Green
et al., 2018), where nested, helical magnetic field lines are wrapped around a
central axis (Lundquist, 1951; Goldstein, 1983). As the transition from CME to
ICME occurs and during ICME propagation, different physical phenomena can
alter this FR configuration. In addition, such changes in coherent
configurations can also be attributed to spacecraft crossings farther from FR
centers (e.g., Jian et al., 2006; Kilpua et al., 2011) and interactions with
other large-scale structures (i.e., high-speed streams, CIR/SIRs, the
heliospheric current/plasma sheet).

To investigate the radial evolution of ME configurations, we use the
morphological classification scheme of Nieves-Chinchilla et al. (2018, 2019).
In this scheme, magnetic hodograms are divided into five categories based on
rotation in the magnetic field vector within the ME duration. The categories
are: (i) F- is a single rotation less than 90∘, (ii) F${}_{\textrm{r}}$ is a
single rotation between 90∘–180∘, (iii) F+ is a single rotation greater than
180∘, (iv) C${}_{\textrm{x}}$ includes multiple rotations, and (v)
E${}_{\textrm{j}}$ represents an unclear rotation. The categories represent
different ME topologies and/or spacecraft trajectories. F- and
F${}_{\textrm{r}}$ populations can arise from large and small impact parameter
crossings respectively (Nieves-Chinchilla et al., 2019). F+ configurations may
correspond to MEs with significant curvatures or complex topologies like
spheromaks (Vandas et al., 1997; Nieves-Chinchilla et al., 2019; Scolini et
al., 2021) or double FRs (Lugaz et al., 2013; Osherovich et al., 2013; Nieves-
Chinchilla et al., 2019). C${}_{\textrm{x}}$ class can be associated with
eruptions from complex active regions at the Sun (Nieves-Chinchilla et al.,
2019) or interactions between multiple ICMEs (Lugaz et al., 2017).
E${}_{\textrm{j}}$ group may be indicative of spacecraft crossings through ME
legs with untwisted magnetic field lines (Owens, 2016; Scolini et al., 2022).

Figure 3: Distribution of average ME magnetic field strength (in nT) as a
function of heliocentric distance (in au). The ICMEs are color-coded based on
the classification scheme of Nieves-Chinchilla et al. (2018, 2019). The two
shaded regions correspond to the two radial blocks (see text for details).

We now examine how the ME configurations evolve with heliocentric distance (r,
see Figure 3). From our observations of 28 ME configurations, we find that 17
(61%) are F- or F${}_{\textrm{r}}$, 2 (7%) are F+, 4 (14%) are
C${}_{\textrm{x}}$, and 5 (18%) are E${}_{\textrm{j}}$. Also, we see that
closer to the Sun, most of the ME configurations are either F- or
F${}_{\textrm{r}}$, whereas more complex configurations like
C${}_{\textrm{x}}$ and E${}_{\textrm{j}}$ are observed at larger r. Another
important finding is that in a similar radial range, weaker ICMEs tend to be
more complex.

However, it is also important to mention how PSP’s longitudinal trajectory and
relative speed can lead to observations of different magnetic signatures
within a single encounter. Closer to the Sun, the significantly faster speed
of PSP could mean that a CME is crossed twice. At 0.23 au, for specific
instances, PSP’s speed of ${\sim}$72 km$\cdot$s-1 can be more than 10% of a
CME speed and may affect the observations of field rotations. As an example,
Möstl et al. (2020) modeled such an encounter at <0.1 au to demonstrate how
the crossings of two different portions of the CME (apex and leg) could result
in differences in field rotations. Möstl et al. (2020) also highlighted the
importance of CME parameters (i.e., speed, shape) and FR inclination on the
double-crossing as a flatter cross-section would increase the probability of
such an encounter.

This finding is another illustration that ME complexity can increase with r
(e.g., Riley & Richardson, 2013). The same was identified by Scolini et al.
(2022) as well from a statistical analysis of 31 ICMEs listed in Salman et al.
(2020b) that are observed in radial alignment between 0.3 and 1 au. Scolini et
al. (2022) found that interactions with other large-scale structures are the
primary drivers of increased ME complexities. Richardson & Cane (2010) in a
previous study indicated that the occurrence of complex configurations is also
strongly dependent on the SC phase since the probability of an ICME
interacting with other large-scale structures and losing its coherent
configuration is greater during solar maxima than minima.

We also examine how the solar wind is impacted following an ICME transit. Even
after the ICME passage, the post-ICME solar wind goes through a relaxation
period to return to the same level of magnetic field strength as the pre-ICME
solar wind (see Janvier et al., 2019). At 1 au, this period can extend up to 2
to 5 days, as pointed out by Temmer et al. (2017). Carcaboso et al. (2020)
observed a notable amount of bidirectional suprathermal electrons (BDE) in the
post-ICME solar wind at 1 au where the post-ICME region was defined as 1.2
times the ICME duration. Herein, we define an interval equivalent to the ME
duration as the post-ICME region. Then, we determine the percentage
increase/decrease in the post-ICME magnetic field strength compared to its
pre-ICME value. We define an 8-hr interval before the ICME arrival as the pre-
ICME region. Due to the nature of PSP’s transitory orbit, we assign a scaling
factor $r^{2}$ to the pre-ICME and post-ICME values. This normalizes the
effect of r on the average values. We find that in the first radial block
(0.23–0.56 au), the post-ICME magnetic field strength is 13% stronger on
average compared to its pre-ICME value. However, in the second radial block
(0.58–0.83 au), we see that the post-ICME magnetic field strength is on
average ${\sim}$44% stronger compared to the pre-ICME value.

Again, similar to how PSP’s trajectory and speed can affect how we see field
rotations, this finding of the post-ICME magnetic field being significantly
more impacted for the second radial block can be a manifestation of the nature
of PSP’s orbit. This is because, in the first or closest radial block, we have
PSP observations when the spacecraft is moving inwards more often, whereas,
for the second or farthest radial block, we have a nearly equal number of
inbound and outbound observations.

###  3.2 ICME Magnetic Field

Expansion is an integral component of ICME evolution as it governs parameters
such as the ME magnetic field strength, density, and size. Previous studies
have found that the expansion rate is greater within 1 au than beyond 1 au
(e.g., Leitner et al., 2007; Davies et al., 2021a, 2022). Even within the 1 au
range, the expansion is known to be occurring at a higher rate closer to the
Sun due to the strong initial ME magnetic pressure, sometimes causing
overexpansion (e.g., Gosling et al., 1994, 1998) and then this rate decreases
gradually as the ICME travels through interplanetary space (e.g., Farrugia et
al., 2008; Vršnak et al., 2019; Lugaz et al., 2020a). However, the ICME
expansion rate in interplanetary space can also significantly vary within a
wide range, depending on the pressure balance with the background solar wind
and possible interactions (e.g., Luhmann et al., 2020; Gopalswamy et al.,
2020).

ME properties such as magnetic field strength can be used as a deterministic
feature to determine its radial evolution. The variation of the ME magnetic
field strength with r is also considered an indirect measure of its global
expansion. Based on theoretical assumptions and statistical fits, the magnetic
field strength is expected to fall off as a power-law with r (e.g., Farrugia
et al., 2005; Wang et al., 2005; Leitner et al., 2007; Démoulin & Dasso, 2009;
Gulisano et al., 2010; Winslow et al., 2015; Good et al., 2019; Vršnak et al.,
2019; Salman et al., 2020b; Davies et al., 2021a, 2022). To examine this, we
adopt a similar technique as Winslow et al. (2015); Salman et al. (2020b). We
perform a multi-linear robust regression in logarithmic space to fit a power
law curve to our data set (see Figure 4). The basis of this fitting technique
is an iterative re-weighted least squares approach with a bi-square weighting
function to ensure that less weight is attributed to outliers than in ordinary
least squares fitting. From this, we find the relationship,
B${}_{\textrm{ME}}$= $11.13^{+4.05}_{-2.96}$ $r^{(-1.21\pm 0.44)}$. The
uncertainties assigned to the power-law index represent a 95% confidence
interval.

This relationship between B${}_{\textrm{ME}}$ and r indicates a lower ME
expansion rate than previous studies. Using Helios 1 and 2 measurements,
Gulisano et al. (2010) found this power-law index to be -1.85$\pm$0.07,
whereas from MErcury Surface, Space ENvironment, GEochemistry, and Ranging
(MESSENGER; Solomon et al., 2001) and Advanced Composition Explorer (ACE;
Stone et al., 1998) measurements, Winslow et al. (2015) reported this power-
law index to be -1.95$\pm$0.19. In a recent study, Davies et al. (2022)
determined this power-law index to be -1.49$\pm$1.12 within the 1 au range.

However, it is also important to note that statistical fits can mask the
behavior of individual events (see discussion in Farrugia et al., 2005; Good
et al., 2019; Vršnak et al., 2019; Salman et al., 2020b; Davies et al., 2022).
The large spread in radial dependencies, seen from the limits of the power-law
index (-1.65 to -0.77) is a possible reflection of such ICME-to-ICME
variability. A similarly large spread, $r^{(-1.34\pm 0.71)}$ was also reported
in Good et al. (2019) when the power-law index was calculated for individual
events. In a similar approach, taking advantage of multi-spacecraft
measurements, Salman et al. (2020b) calculated the exponential decrease of the
peak ME magnetic field strength with r for individual ICMEs and made a
comparison with the derived statistical relationship. Salman et al. (2020b)
found that 37 out of the 45 ICMEs showed a rate of decrease outside of the 95%
confidence interval of the statistical fit. In a recent multi-spacecraft
study, Davies et al. (2022) also calculated the average power-law index for
individual events observed within 1 au and found the limits of the index to
have noticeable differences compared to the limits of the index derived from a
statistical fit.

Figure 4: Average ME magnetic field strength (in nT) from PSP observations
plotted as a function of heliocentric distance (in au). The power-law curve
(in green) represents the best-fit curve to our data set. The error bars (in
red) represent the standard deviations.

We also investigate the magnetic field fluctuations within ICME sheaths (e.g.,
Masías-Meza et al., 2016; Kilpua et al., 2019, 2020; Regnault et al., 2020;
Salman et al., 2020a; Kilpua et al., 2021; Salman et al., 2021). Such
fluctuations are a consequential feature of different physical mechanisms
(i.e., shock compression, field line draping) in action (e.g., McComas et al.,
1988; Neugebauer et al., 1993; Kataoka et al., 2005). Previous studies have
also investigated fluctuations in different portions of the sheath (see Kilpua
et al., 2019, 2020). Here, we consider the fluctuations as a whole. To
quantify magnetic field fluctuations within sheaths, we adopt a similar
approach as Salman et al. (2020a, 2021). We introduce a total root-mean-square
[B${}_{\textrm{rms(tot)}}$] that is the sum of root-mean-square-deviations for
each 5-min time interval (B${}_{\textrm{rms}}$), as defined in Equation 1 and
normalized by the average sheath magnetic field strength.

$\text{B${}_{\textrm{rms}}$}=\sqrt{\sum_{i=1}^{n}\frac{(B_{i}-\langle
B\rangle)^{2}}{n}\\\ }$ (1)

Here, Bi (i=1…5) and $\langle$B$\rangle$ represent the magnetic field strength
for each 1-min time step and the temporal average for 5-min intervals
respectively, and n is the number of measurements.

We now explore correlations between B${}_{\textrm{rms(tot)}}$ with $r$, sheath
duration (T${}_{\textrm{sheath}}$), and the ratio of the average ME magnetic
field strength to the upstream magnetic field
(B${}_{\textrm{ME}}$/B${}_{\textrm{SW}}$, here B${}_{\textrm{SW}}$ is the
average magnetic field strength of an 8-hr interval before the ICME arrival).
We find no correlation between B${}_{\textrm{rms(tot)}}$ and $r$ (Pearson’s
correlation coefficient or PCC=0.12 with p-value=0.657) and
B${}_{\textrm{rms(tot)}}$ and T${}_{\textrm{sheath}}$ (PCC=-0.14 with
p-value=0.616). However, we report a strong positive correlation between
B${}_{\textrm{rms(tot)}}$ and B${}_{\textrm{ME}}$/B${}_{\textrm{SW}}$
(PCC=0.76 with p-value=0.001).

The nonexistent correlation between B${}_{\textrm{rms(tot)}}$ and $r$ is
surprising. The evolution of the sheath involves continuous accumulation of
upstream solar wind plasma and magnetic field. This accumulation occurs at
different r locations during ICME propagation. Therefore, the layers of the
sheath correspond to a heterogeneous plasma and magnetic field distribution
(e.g., Kaymaz & Siscoe, 2006; Siscoe et al., 2007), with various possible
confined waves, discontinuities, and reconnection exhausts (e.g., Kataoka et
al., 2005; Ala-Lahti et al., 2018). For this reason, a positive correlation
between B${}_{\textrm{rms(tot)}}$ and $r$ can be expected since with
increasing $r$, the time-scale of the accumulation process will increase,
which can result in increased inhomogeneity within the sheath, leading to
possible increased fluctuations. A possible reason for this observed no
correlation could be that there are processes in the solar wind itself (such
as wave-particle interactions) to decrease the inhomogeneity.

On the other hand, we see a strong positive correlation between
B${}_{\textrm{rms(tot)}}$ and B${}_{\textrm{ME}}$/B${}_{\textrm{SW}}$. Using
logistic regression, Salman et al. (2021) found that B${}_{\textrm{ME}}$ and
M${}_{\textrm{pseudo}}$ (defined as the ratio between the ME leading-edge
speed in the solar wind frame to the characteristic speed of the solar wind)
are influential factors behind the observed distinct speed profiles (i.e.,
constant, increasing, decreasing) within sheaths near 1 au. Previous studies
have also shown strong ME speed-magnetic field correlations for magnetic
clouds (MCs; Burlaga et al., 1981, 1982; Klein & Burlaga, 1982) at 1 au (e.g.,
Owens et al., 2005) and for ICMEs that do not change ME configurations from
one measuring spacecraft in the inner heliosphere to another (Scolini et al.,
2022). Thus, it is possible that the quantity
B${}_{\textrm{ME}}$/B${}_{\textrm{SW}}$ is coupled to the ME kinematics
(propagation and expansion). The ME kinematics significantly contributes to
the arrangement of the plasma layers within the sheath. The layers are not
only stacks of simple compressed plasma in the radial direction as the layers
can slide laterally as well by different amounts (see Siscoe & Odstrcil,
2008). Therefore, the ordering of the compressed plasma layers within the
sheath can be a measure of sheath fluctuations and related to the quantity
B${}_{\textrm{ME}}$/B${}_{\textrm{SW}}$.

###  3.3 Formation and Expansion of Sheath

The formation and development of the sheath is a topic that is still not well
understood. Remote-sensing observations and in situ composition measurements
have provided great insights into possible distances for sheath formation
(e.g., DeForest et al., 2013; Kilpua et al., 2017; Lugaz et al., 2020b; Temmer
et al., 2021). The basis of such considerations is that as CMEs primarily
consist of coronal material (cooler, denser material likely of chromospheric
or photospheric origin can also be present occasionally), composition
signatures, consisting of both coronal and compressed (also shocked if there
is a preceding shock) solar wind materials in the sheath or traces of only
solar wind material can be an indicator of the approximate sheath formation
distance.

Figure 5: Sheath duration (in h) plotted as a function of heliocentric
distance (in au) with the ratio of sheath duration to ME duration as a second
scale in the color bar. The magenta dashed line represents the best linear
least squares fit reported in Salman et al. (2020b).

In our PSP ICME list, there are 16 ICMEs with a well-defined sheath. From a
linear approximation, Salman et al. (2020b) found the sheath formation to
start around 0.24 au. In a recent study, from a statistically derived density
evolution over r using Helios and PSP observations, Temmer & Bothmer (2022)
theorized the sheath to start forming even before that, at ${\sim}$0.06 au.
However, we observe that only 2 out of the 8 ICMEs in our list within 0.44 au
have sheaths and none before 0.38 au. This finding can be a manifestation of
our sampling technique as well. Both magnetic field and plasma measurements
are required for the identification of sheaths with precision. Since for the
majority of the mentioned 16 ICMEs, the sheaths are identified based on
magnetic field measurements only (due to the lack of good-quality plasma
data), this could have led to the non-identification of some sheaths. However,
this finding can also hint at how the ME magnetic field strength and expansion
closer to the Sun play an important role in sheath formation.

The sheath formation has contributions from both the ME propagation, where the
solar wind is deflected at the nose, and expansion, which prevents the
deflected solar wind from going around the ICME body (see Siscoe & Odstrcil,
2008). Closer to the Sun, the expansion occurs because of the strong internal
ME magnetic pressure. Since the period of this study primarily covers the
minimum and early rising phase of SC25, the ICMEs are expected to be weaker in
terms of magnetic field strengths. This means that expansion closer to the Sun
may be occurring at a lower rate than usual. This will make it easier for the
deflected solar wind at the nose of the ICME to go around, ceasing the
possible pile-up of solar wind plasma in front of the ME.

In SC24, the ME expansion was generally stronger than expected for weaker
ICMEs due to an evident drop in the magnetic field and heliospheric pressure
(e.g., Gopalswamy et al., 2015; Jian et al., 2018). So, this hypothesis of
weaker ICME expansion needs to be further evaluated by including ICMEs from
the maximum phase of SC25. In addition, local ICME expansion from plasma
measurements will provide knowledge regarding whether this expansion behavior
persists throughout the inner heliosphere, as it did in SC24.

After this, we investigate the expansion of the sheath. Due to expansion, the
quantity T${}_{\textrm{sheath}}$ is expected to increase with r during ICME
propagation (e.g., Janvier et al., 2019; Salman et al., 2020b). Salman et al.
(2020b) performed a linear least squares fitting of sheaths observed in radial
alignment between 0.3 and 1 au for the periods 2006–2013 and 2011–2015 and
reported a correlation coefficient of 0.78 between T${}_{\textrm{sheath}}$ and
r for a larger set of events. However, the correlation seen between
T${}_{\textrm{sheath}}$ and r from our observation (see Figure 5) is poor
(PCC=0.35 with p-value=0.185). We also examine how the ratio of the duration
of the sheath over that of the ME evolves with r. This ratio was found to
increase from MESSENGER to ACE by Janvier et al. (2019). But we also find a
poor correlation between this pair of parameters (PCC=0.28 with
p-value=0.293). A possible reason for the identified poor correlations in our
case compared to previous studies is the small number of events and the
observed event-to-event variability. In our data set, we have a few sheaths
that are already 6–8 hours long within 0.45 au, comparable to the average
sheath duration of 8–9 hours near 1 au (see Salman et al., 2020a). On the
other hand, we have a few sheaths that are only 3–4 hours long around 0.80 au.
Such discrepancies are also possible manifestations of spacecraft crossings as
the sheath duration has been shown to increase from the nose of the ICME
toward the flanks in previous studies (e.g., Kilpua et al., 2017; Salman et
al., 2020b).

###  3.4 Distortion of ME Magnetic Field

The ME expansion, combined with the global motion can lead to distortion of
the observed ME magnetic field (e.g., Farrugia et al., 1995; Démoulin et al.,
2008; Masías-Meza et al., 2016; Janvier et al., 2019; Démoulin et al., 2020;
Regnault et al., 2023). From superposed epoch analysis at 1 au, Masías-Meza et
al. (2016) found the magnetic field strength profiles inside MCs to be
strongly asymmetric, with the peak shifted to the front of the MC. This can be
attributed to the time-delay factor (termed the “aging” effect) as the
spacecraft encounters the front of the ICME structure earlier than the rear.
As a result, since expansion affects the time evolution of the measured
magnetic field, the weakening of the magnetic field during the spacecraft
encounter will result in a decrease in magnetic field strength from the front
to the rear. This will correspond to an apparent asymmetry and observed
compression of the magnetic field near the front of the structure.

Previous studies have attempted to quantify this asymmetry of the magnetic
field within an ME (e.g., Nieves-Chinchilla et al., 2018; Janvier et al.,
2019; Démoulin et al., 2020; Lanabere et al., 2020). In this study, we follow
the mathematical formulation of Nieves-Chinchilla et al. (2018) and determine
the quantity DiP from the temporal average of the ME magnetic field strength.
The DiP value is the fraction of the total ME duration where 50% of the total
magnetic field is accumulated. From this definition, DiP values range between
0 to 1 and provide a quantitative measure of the nature and extent of the
asymmetry. DiP values <0.5 and >0.5 correspond to compression at the front and
rear respectively. A DiP value of 0.50$\pm$0.07 corresponds to a symmetric
magnetic field profile (Nieves-Chinchilla et al., 2018), meaning no
significant amount of front or rear compression. The DiP value will approach 0
for higher compression at the front and 1 for higher compression at the rear.

Figure 6: DiP values plotted as a function of heliocentric distance (in au)
with the ratio of the average ME magnetic field strength to the upstream
magnetic field as a second scale in the color bar. The dashed magenta line
represents a DiP value of 0.5 that corresponds to a symmetric ME magnetic
field profile.

Figure 6 shows the radial distribution of DiP values. Examining the DiP
values, we find the range between 0.15–0.56. 18 of the MEs have DiP values
<0.5, whereas 10 have DiP values >0.5. However, a closer look at the values
reveals that 50% of the DiP values lie within the range between 0.45–0.55,
indicating approximately symmetric magnetic field profiles. This is in
agreement with Janvier et al. (2019) who found that slower ME profiles (like
most of the ICMEs in our list) are more symmetric as the MEs relax with
increasing $r$.

We also find no correlation between DiP values and $r$ (PCC=-0.18 with
p-value=0.344). Janvier et al. (2019) found that at MESSENGER, magnetic field
profiles within MEs are more peaked toward the front. However, we do not
observe a similar trend within Mercury’s orbit (0.31–0.47 au). Lugaz et al.
(2020a) theorized that the front of the ME can expand relatively freely in the
presence of a sheath. In such a scenario, the front portion of the ME exhibits
more expansion compared to the rear, resulting in the peak being shifted more
toward the front. Since in our list, only 3 out of the 9 ICMEs within 0.47 au
have sheaths, the constrained nature of ME front expansion can be a possible
reason for the observed distribution of DiP values within Mercury’s orbit
where most of the DiP values are around or above the 0.50 line (see Figure 6).

We also investigate two other correlations: whether the level of enhancement
in the ME magnetic field (B${}_{\textrm{ME}}$/B${}_{\textrm{SW}}$) and ME
duration (T${}_{\textrm{ME}}$) have influence on the nature of asymmetries. We
find no correlation between DiP values and
B${}_{\textrm{ME}}$/B${}_{\textrm{SW}}$ (PCC=-0.25 with p-value=0.208). For
the second inspection, we only consider DiP values <0.5. However, we also find
no correlation between DiP values and T${}_{\textrm{ME}}$ (PCC=-0.14 with
p-value=0.587). ME expansion has consequences on the measured magnetic fields
and a correlation is thus expected between DiP values and T${}_{\textrm{ME}}$.
Because of aging, in theory, the influence of ME expansion shall increase for
a more extended ME. However, since we do not find such a correlation, this is
consistent with previous studies that mention aging is not the only origin
(possible presence of an intrinsic asymmetry as well) and therefore can not
solely explain the observed asymmetries within MEs (e.g., Démoulin et al.,
2008, 2020; Nieves-Chinchilla et al., 2022; Regnault et al., 2023).

##  4 Summary and Conclusion

In this study, we perform a statistical investigation of 28 ICMEs measured in
situ between 0.23–0.83 au by the PSP spacecraft from 2018 October to 2022
August. The overarching goal is to address the radial evolution of ICME
structures in the inner heliosphere, using the widespread spatial distribution
of PSP observations. We examine the radial evolution of four ICME aspects: (i)
ME complexity, (ii) ICME magnetic field, (iii) expansion of sheath, and (iv)
distortion of ME magnetic field. The main results can be summarized as
follows:

  1. 1.

We find that ME configurations show evolution with heliocentric distance. The
likelihood of observing coherent configurations (F- or F${}_{\textrm{r}}$) is
higher close to the Sun, whereas the likelihood of observing complex
configurations (C${}_{\textrm{x}}$ and E${}_{\textrm{j}}$) increases farther
out. In addition, weaker ICMEs seem to be more complex in terms of ME
configurations. We also observe that the post-ICME magnetic field undergoes a
continued relaxation period even after the ICME passage to go back to the pre-
ICME levels. The level of impact in the post-ICME magnetic field depends on
the heliocentric distance of the ICME encounter. Farther out from the Sun
(>0.58 au), the post-ICME magnetic field is considerably stronger on average
(${\sim}$44%) compared to the pre-ICME value than encounters close (<0.56 au)
to the Sun (13%). Overall, the observations confirm previous findings that the
ME complexity is strongly coupled to the heliocentric distance (e.g., Riley &
Richardson, 2013; Scolini et al., 2022).

  2. 2.

From multi-linear robust regression, we find the average ME magnetic field
strength to scale as $r^{(-1.21\pm 0.44)}$. This power-law index hints at a
less steep fall-off of the magnetic field with heliocentric distance, compared
to previous results (e.g., Gulisano et al., 2010; Winslow et al., 2015; Davies
et al., 2022). However, considering the large uncertainties assigned to the
power-law index, similar to Good et al. (2019); Davies et al. (2022), the
derived statistical relationship is comparable with previous studies. Still,
it suggests that the expansion close to the Sun is not as strong as expected
in the period studied.

  3. 3.

For normalized magnetic fluctuations within ICME sheaths, we find no
correlations between fluctuations and heliocentric distance (PCC=0.12) and
sheath duration (PCC=-0.14). However, we report a significant positive
correlation between fluctuations and the level of enhancement in the ME
magnetic field compared to the upstream value (PCC=0.76). This is in agreement
with Salman et al. (2021) who highlighted that the ME properties are prominent
factors behind the observed sheath variability near 1 au.

  4. 4.

We find no sheaths for ICMEs encountered by PSP within 0.38 au. This finding
is different compared to the approximate sheath formation distances reported
in Salman et al. (2020b); Temmer & Bothmer (2022), but hints at the important
contribution of the ME magnetic pressure and the corresponding expansion rate
closer to the Sun to the sheath formation. We also observe a weak positive
correlation between the sheath duration and heliocentric distance (PCC=0.35).
However, the observed weak correlation can also be a byproduct of a small
sample size with considerable event-to-event variability.

  5. 5.

We find the DiP values to vary between 0.15–0.56. Even though we have more DiP
values <0.5 (18) than DiP values >0.5 (10), half of the DiP values (50%) are
around 0.50$\pm 0.05$. We notice that the distribution of DiP values has no
radial dependence (PCC=-0.18). We also observe no correlation between DiP
values and the level of enhancement in the ME magnetic field compared to the
background (PCC=-0.25) and duration of the ME (PCC=-0.14). To examine the
second correlation, we only consider DiP values (<0.5) that correspond to
compression at the front of the ME (an apparent feature of expansion). Since
we do not see the expected correlation with ME duration, this is an indication
that aging or time evolution alone is not enough to characterize the
distortion of the ME magnetic field. This was mentioned in previous studies as
well (e.g., Démoulin et al., 2008, 2020; Nieves-Chinchilla et al., 2022;
Regnault et al., 2023).

The PSP ICMEs analyzed in this study provide a unique opportunity to
investigate the radial evolution of ICME structures with a more continuous
spread of observations. Statistical analyses based on such observations allow
us to derive overall statistical trends for ICME radial evolution in the inner
heliosphere. However, assumptions of simple geometry (not taking into account
ICME shapes and curvatures) and quantitative limitations (small data set)
leave room for future in-depth exploration. In addition, the lack of
continuous good-quality plasma data limits our ability to perform a
comprehensive analysis of the nature of the ICMEs. With an extended timeline
and inclusion of SolO encountered events, this will be possible in upcoming
projects.

## acknowledgments

The authors wish to thank the PSP mission team for providing the data. The
authors acknowledge using NASA/Goddard Space Flight Center’s Space Physics
Data Facility’s CDAWeb service (available at
https://cdaweb.gsfc.nasa.gov/index.html/). T. S. and T. N. -C. acknowledge
support from the Parker Solar Probe and Solar Orbiter missions. T. S. and L.
J. thank the support of NASA’s STEREO mission and Heliophysics Guest
Investigator (HGI; no. 80NSSC23K0447) program. N. L. acknowledges support from
NASA grants 80NSSC20K0700 and 80NSSC20K0431. F. C. acknowledges the financial
support by an appointment to the NASA Postdoctoral Program at NASA Goddard
Space Flight Center, administered by Oak Ridge Associated Universities through
a contract with NASA. E. D. acknowledges funding 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. We also thank the
anonymous reviewer for critically reading the paper and suggesting
improvements.

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