# Causes and Consequences of Magnetic Complexity Changes within Interplanetary
Coronal Mass Ejections: a Statistical Study

Camilla Scolini Institute for the Study of Earth, Oceans, and Space,
University of New Hampshire, Durham, NH, USA  CPAESS, University Corporation
for Atmospheric Research, Boulder, CO, USA  Réka M. Winslow Institute for the
Study of Earth, Oceans, and Space, University of New Hampshire, Durham, NH,
USA  Noé Lugaz Institute for the Study of Earth, Oceans, and Space, University
of New Hampshire, Durham, NH, USA  Tarik M. Salman Institute for the Study of
Earth, Oceans, and Space, University of New Hampshire, Durham, NH, USA  Emma
E. Davies Institute for the Study of Earth, Oceans, and Space, University of
New Hampshire, Durham, NH, USA  Antoinette B. Galvin Institute for the Study
of Earth, Oceans, and Space, University of New Hampshire, Durham, NH, USA

(Received October 13, 2021; Revised November 19, 2021; Accepted November 24,
2021)

###### Abstract

We present the first statistical analysis of complexity changes affecting the
magnetic structure of interplanetary coronal mass ejections (ICMEs), with the
aim of answering the questions: How frequently do ICMEs undergo magnetic
complexity changes during propagation? What are the causes of such changes? Do
the in situ properties of ICMEs differ depending on whether they exhibit
complexity changes? We consider multi-spacecraft observations of 31 ICMEs by
MESSENGER, Venus Express, ACE, and STEREO between 2008 and 2014 while radially
aligned. By analyzing their magnetic properties at the inner and outer
spacecraft, we identify complexity changes which manifest as fundamental
alterations or significant re-orientations of the ICME. Plasma and
suprathermal electron data at 1 au, and simulations of the solar wind enable
us to reconstruct the propagation scenario for each event, and to identify
critical factors controlling their evolution. Results show that $\sim$65% of
ICMEs change their complexity between Mercury and 1 au and that interaction
with multiple large-scale solar wind structures is the driver of these
changes. Furthermore, 71% of ICMEs observed at large radial ($>$0.4 au) but
small longitudinal ($<15^{\circ}$) separations exhibit complexity changes,
indicating that propagation over large distances strongly affects ICMEs.
Results also suggest ICMEs may be magnetically coherent over angular scales of
at least 15∘, supporting earlier theoretical and observational estimates. This
work presents statistical evidence that magnetic complexity changes are
consequences of ICME interactions with large-scale solar wind structures,
rather than intrinsic to ICME evolution, and that such changes are only partly
identifiable from in situ measurements at 1 au.

Solar coronal mass ejections (310); Solar wind (1534); Corotating streams
(314); Interplanetary magnetic fields (824)

††journal: ApJ

##  1 Introduction

Coronal mass ejections (CMEs) consist of large-scale plasma and magnetic field
structures erupted from the Sun into interplanetary space (Webb & Howard,
2012). When probed in situ by spacecraft monitoring the conditions of the
interplanetary medium, they are referred to as interplanetary CMEs (hereafter
ICMEs) and appear as magnetically-dominated (i.e. low plasma $\beta$, that is
the ratio of the plasma pressure to the magnetic pressure) structures often
exhibiting smoothly-rotating magnetic fields, which are typically interpreted
as flux-rope (FR) structures with a helical magnetic field wrapping around a
central axis (Klein & Burlaga, 1982; Kilpua et al., 2017). Additionally, ICMEs
that are faster than the local magnetosonic speed in the solar wind reference
frame drive forward shocks and sheaths (Richardson & Cane, 2010; Kilpua et
al., 2017; Jian et al., 2018). ICMEs are observed passing over Earth at an
average rate of 1–2 per month (Richardson & Cane, 2010), where, together with
their shocks and sheaths, they are the main drivers of strong geomagnetic
storms (Gosling et al., 1991; Zhang et al., 2007; Lugaz et al., 2016; Kilpua
et al., 2017, 2019).

Expanding on earlier datasets, recent cruise phase and orbital data from
heliospheric and planetary missions has shed new light on ICME characteristics
at different heliocentric distances (e.g. Liu et al., 2005; Ebert et al.,
2009; Winslow et al., 2015; Good & Forsyth, 2016; Lee et al., 2017; Davies et
al., 2021), revealing different parameter properties from those observed near
Earth’s orbit, which can also be extremely variable in space and time. In
fact, the evolution of ICMEs during propagation through interplanetary space
is shaped by the interplay of internal and external factors controlling the
interaction of ICMEs with the surrounding solar wind and other transients
therein (Manchester et al., 2017). These manifest into four main forms: (1)
ICME expansion, which controls its size, internal density, pressure, and
magnetic field magnitude (Démoulin & Dasso, 2009); (2) the interaction with
the surrounding solar wind via drag forces, which controls the ICME kinematic
properties (Cargill, 2004; Vršnak et al., 2010); (3) other forms of
energy/momentum exchanges due to the interaction with, e.g., interplanetary
shocks driven by various interplanetary structures, which affects the thermal,
magnetic, kinematic, and size properties of ICMEs (e.g. Lugaz et al., 2015;
Zhuang et al., 2019; Scolini et al., 2020); and (4) magnetic reconnection
phenomena occurring at ICME boundaries (i.e. magnetic erosion and flux
injection; Dasso et al., 2006; Ruffenach et al., 2012) or in their interiors
(Crooker et al., 1998), which can alter the connectivity, topology, and size
of ICME magnetic structures.

Each of these phenomena contributes to the ultimate evolutionary path of
individual ICMEs, but the degree of their influence on the evolution of large-
scale ICME properties greatly depends on the ambient solar wind conditions
through which an ICME propagates. Observational and modeling studies
established that during propagation, ICMEs undergo a number of large-scale
structural changes which include kinks, front flattening (e.g. Savani et al.,
2011; Davies et al., 2021), rotations and deflections of ICME magnetic
structures (e.g. Isavnin et al., 2014; Wang et al., 2014; Kay & Opher, 2015),
deformations of their front convexity (e.g. Odstrčil & Pizzo, 1999a;
Manchester et al., 2004), as well as local magnetic field distortions (e.g.
Török et al., 2018). Most importantly, all of the aforementioned effects
appear amplified by interactions with high-speed streams (HSSs),
corotating/stream interaction regions (CIRs/SIRs), the heliospheric
current/plasma sheet (HCS/HPS) (e.g. Odstrčil & Pizzo, 1999b, c; Rodriguez et
al., 2016; Winslow et al., 2016, 2021b; Zhou & Feng, 2017; Liu et al., 2019;
Davies et al., 2020; Scolini et al., 2021), as well as other ICMEs (e.g. Lugaz
et al., 2017; Scolini et al., 2020).

Direct quantification of the radial evolution of ICMEs can only be achieved
through high-quality in situ measurements of approximately the same portion of
a given ICME at different heliocentric distances via multi-spacecraft
crossings, i.e. by radially-aligned spacecraft configurations. However, such
observations are difficult to achieve due to the limited number of assets
available (in terms of missions and instruments), and the paucity of
continuous observations of the solar wind properties, particularly for studies
relying on missions orbiting in and out of planetary
magnetospheres/atmospheres. Overcoming the scarcity of data, statistical
studies combining multiple ICME datasets obtained at different heliocentric
distances allowed the characterization of general trends affecting ICME
evolution, particularly in the case of events observed by multiple spacecraft
in radial alignment (Good et al., 2019; Lugaz et al., 2020b; Salman et al.,
2020). Nonetheless, such studies have so far only provided an average picture
of the evolution of ICMEs during propagation, rather than diving deep into the
analysis of individual events necessary to determine the causes behind the
non-ideal evolutionary behavior observed in a number of ICMEs (as recently
reported by, e.g., Lugaz et al. (2020b) and Winslow et al. (2021b)). Moreover,
past statistical studies investigating the evolution of ICME magnetic
topologies during propagation have almost entirely focused on the
investigation of ICMEs exhibiting classical FR signatures (e.g. Good et al.,
2019), whose properties can be investigated through numerous in situ fitting
techniques (e.g. Al-Haddad et al., 2013), and neglected non-flux rope
configurations, which although more difficult to characterize, are
nevertheless frequently observed at 1 au (Nieves-Chinchilla et al., 2019) (for
a notable exception, see Lugaz et al., 2020a). As discussed in the following
sections, complex magnetic configurations within ICMEs are in fact often the
result of magnetic complexity changes attributable to the interaction of ICMEs
with other solar wind structures, while classical FR structures are often a
proxy for unperturbed propagation. Given their bias towards ideal ICME
magnetic structures, it is therefore hardly surprising that previous studies
often highlighted little changes in the FR properties between different
observing spacecraft, suggesting a propagation scenario compatible with self-
similar evolution.

In-depth studies of individual ICMEs observed by multiple spacecraft during
periods of radial alignment have been extremely insightful for our
understanding of the various phenomena controlling the evolution of their
magnetic structures. Such studies have showcased a wide variety of
evolutionary behavior, ranging from essentially self-similar (Nakwacki et al.,
2011; Möstl et al., 2012; Good et al., 2015, 2018) to strongly atypical
(Leitner et al., 2007; Nieves-Chinchilla et al., 2012; Winslow et al., 2016,
2021b; Vršnak et al., 2019; Weiss et al., 2021), posing questions on the
frequency and causes of such a large variation of evolutionary trends.
Advances towards a more comprehensive and fundamental understanding of the
radial variations affecting ICMEs have come from tailored investigations of
magnetic complexity changes for a limited set of case studies (Winslow et al.,
2016, 2021b, 2021a), all of which stressed the role of solar wind
interplanetary structures as drivers of magnetic complexity changes observed
within ICMEs. Yet, the limited number of events considered provided only a
partial picture of such phenomenon, necessitating a more extensive
investigation. We also point out that a careful consideration of the effect of
different spacecraft trajectories through a given ICME structure, particularly
in the case of non-perfect radial alignments, is critical to the
interpretation of multi-spacecraft ICME observations at different heliocentric
distances (e.g. Lugaz et al., 2018). In this respect, previous studies also
suggested that highly inclined magnetic flux ropes might appear very different
even when observed at $\sim 5^{\circ}$ in longitudinal separation (e.g. Kilpua
et al., 2009), while in comparison, low-inclination flux ropes might appear
highly coherent over similar angular scales (e.g. Davies et al., 2021). To
what extent the inclination of ICME magnetic flux ropes influences magnetic
complexity changes and estimates of the scale of magnetic coherence (Owens et
al., 2017; Owens, 2020; Lugaz et al., 2018) within ICMEs observed by radially-
aligned spacecraft is currently an open question.

This work is motivated by the need to further explore the relationship between
large-scale changes affecting ICMEs, and interactions with solar wind
structures, particularly HSSs, CIRs/SIRs, and the HCS/HPS, beyond individual
case studies. In particular, we perform a statistical analysis of magnetic
complexity changes occurring within ICMEs observed by multiple inner
heliospheric spacecraft in radial alignment, with the aim of answering the
following science questions: (1) How frequently do ICMEs undergo magnetic
complexity changes during propagation through interplanetary space? (2) What
are the causes of such changes? (3) Do the in situ properties of ICMEs differ
depending on whether they exhibit complexity changes during propagation?

We tackle the questions above by analyzing a statistical set of 31 ICMEs that
were observed in situ by multiple spacecraft at different heliocentric
distances between Mercury’s orbit and 1 au in the period 2008–2014. Compared
to previous studies, we do not restrict our investigation to ICMEs exhibiting
FR magnetic signatures, which allows us to consider a higher number of events
and achieve statistical results. We also use in situ observations to identify
any intervening structure in the ambient solar wind that might have affected
the propagation of the ICMEs of interest. In addition, to place any observed
changes in ICME magnetic properties into context, we use simulations of the
ambient solar wind obtained via the WSA-ENLIL model hosted at the NASA
Community Coordinated Modeling Center (CCMC; https://ccmc.gsfc.nasa.gov) to
identify additional interactions with solar wind structures that might have
gone undetected in the available in situ data.

The paper is structured as follows. In Section 2, we describe the event
selection procedure and the in situ plasma and magnetic field data used to
identify the boundaries of ICME structures observed in situ at different
spacecraft. In Section 3, we introduce the methodology used to classify ICME
magnetic signatures, we define the measures of complexity changes between
observing spacecraft, and we elaborate on the identification of interplanetary
structures that interacted with the ICMEs during their propagation from the
inner to the outer spacecraft. In Section 4, we present the results of our
statistical analysis and interpret them in light of available observations,
theoretical arguments, and numerical evidences. Finally, in Section 5, we
summarize the main findings and present our conclusions.

##  2 Event Selection and Boundary Identification

We select events based on the ICME catalog recently compiled by Salman et al.
(2020), which includes 47 ICMEs measured in situ by two or three radially-
aligned spacecraft (i.e. MESSENGER, Venus Express, STEREO, Wind/ACE) between
2008 and 2014, and in addition to the ICME in situ properties, it also
contains information on their CME counterparts and kinematic properties close
to the Sun as measured by coronagraphs. ICMEs were selected according to the
following criteria: each event had to be observed by at least two spacecraft
in radial alignment. The longitudinal separation between observing spacecraft
had to be less than $35^{\circ}$, so to increase the likelihood of two or more
radially aligned spacecraft observing both the sheath and the ejecta, rather
than only the sheath itself (Good & Forsyth, 2016). Yet, for more than two-
thirds of the ICMEs, longitudinal separations between the measuring spacecraft
were within $20^{\circ}$. Coronagraphic observations were used to identify CME
counterparts, as inferred from the agreement between the CME launch direction
and the positioning of the corresponding spacecraft during the event time
interval. Additionally, in situ timings were verified against arrival times
predicted from coronagraphic observations with the help of the drag-based
propagation model (DBM; Vršnak et al., 2013), to identify actual multi-
spacecraft events. As also mentioned by Salman et al. (2020), some of the
CME–ICME associations were difficult to verify for all instances, with
specific cases having multiple possible CME counterparts or no clear CME
counterparts. To further support CME–ICME associations based on coronagraphic
and in situ data, in this paper, we have searched for their heliospheric
counterparts as observed by the STEREO Heliospheric Imager (HI; Harrison et
al., 2005) and listed in available databases, in particular the Heliospheric
Cataloguing, Analysis and Techniques Service (HELCATS et al., 2018,
https://doi.org/10.6084/m9.figshare.5803152.v1) catalog (Harrison et al.,
2018). Heliospheric CME counterparts from the HELCATS catalog are provided in
Table S1 (included as supporting information) and in Table 1 (providing a
sample) for each ICME considered in this study. For some of the events, the
association between the coronal and HI CME counterparts, and the ICMEs
detected in situ could be confirmed against the HELCATS WP4 LINKCAT catalog
(Moestl et al., 2017, https://doi.org/10.6084/m9.figshare.4588330.v2).
However, due to the difficulty in analyzing HI data and the fact that HI
detectors are designed to function better for Earth-directed CMEs, we found
that not all CME–ICME pairs were tracked by heliospheric imagers, and that the
information provided by such data products should not be considered as
definitive in improving the accuracy of the CME–ICME associations in all
cases.

We analyze each event from this catalog using in situ data available at the
locations of observation. To investigate ICMEs at 1 au, we use 1-sec magnetic
field data from the magnetometer (MAG; Smith et al., 1998) and 64-sec plasma
data from the Solar Wind Electron, Proton and Alpha Monitor (SWEPAM; McComas
et al., 1998), on board the Advanced Composition Explorer (ACE) mission (Stone
et al., 1998) orbiting the Sun–Earth Lagrange 1 (L1) point; we also use 1-sec
magnetic field data from the magnetometer (MAG; Acuña et al., 2008), and 1-min
plasma data from the In situ Measurements of Particles And CME Transients
(IMPACT; Luhmann et al., 2008) and the Plasma And Suprathermal Ion Composition
(PLASTIC; Galvin et al., 2008) on board the Solar TErrestrial RElations
Observatory-Ahead (STEREO-A) and -Behind (STEREO-B) twin spacecraft (Kaiser et
al., 2008). Additionally, we use electron pitch angle distribution (PAD) data
from ACE/SWEPAM at 272 eV
(http://www.srl.caltech.edu/ACE/ASC/DATA/level3/swepam/data/) and from the
STEREO/IMPACT Solar Wind Electron Analyzer (SWEA; Sauvaud et al., 2008,
http://stereo.irap.omp.eu/CEF/PAD/) at energies above $\sim 100$ eV, i.e. in
the suprathermal energy range (Shodhan et al., 2000; Zurbuchen & Richardson,
2006). At Mercury, orbiting at heliocentric distances between 0.31 au and 0.46
au, we make use of 0.5-sec high-resolution magnetic field data provided by the
magnetometer (MAG; Anderson et al., 2007) on board the MErcury Surface, Space
ENvironment, GEochemistry, and Ranging (MESSENGER; Solomon et al., 2007)
mission. Finally, at Venus, located at 0.7 au from the Sun, we make use of
4-sec magnetic field data provided by the magnetometer (MAG; Zhang et al.,
2006) on board the Venus Express (VEx; Titov et al., 2006) mission. Magnetic
field data obtained by different spacecraft are converted to radial-
tangential-normal (RTN) coordinates in order to compare signatures at
different spacecraft.

In this work, we use the term “magnetic ejecta” (ME) in a similar manner to
the way it was used by Winslow et al. (2015) and Salman et al. (2020) to refer
to the magnetically-dominated portion of the ICME. This is because for
observations at MESSENGER and VEx, no plasma observations are available, and
therefore it cannot be verified whether ICMEs also exhibited the expected
density, plasma $\beta$, and temperature decreases associated with magnetic
clouds (MCs; Burlaga et al., 1981). In this study, we therefore identify as ME
that part of an ICME exhibiting enhanced magnetic field and low levels of
magnetic fluctuations compared to the preceding and following interplanetary
magnetic field. We also note that to determine the ME boundaries, we started
from the boundaries listed in existing catalogs compiled by Winslow et al.
(2015), Good & Forsyth (2016), Nieves-Chinchilla et al. (2018b)
(https://wind.nasa.gov/ICME_catalog/ICME_catalog_viewer.php), and Jian et al.
(2018) (https://stereo-
ssc.nascom.nasa.gov/data/ins_data/impact/level3/ICMEs.pdf). We further
modified some of these boundaries to better reflect our ME identification
criteria, i.e. of enhanced magnetic field and low levels of fluctuations, as
documented in Table S1 provided as supporting information. A sample is
provided in Table 1.

Table 1: Sample of the ICMEs considered in this work. Each event is labeled by
a unique number. The inner and outer observing spacecraft (referred to as
“SC1” and “SC2” in brief) and their longitudinal separation ($\Delta\phi$) are
listed. “M” stands for MESSENGER, “STA” for STEREO-A, and “STB” for STEREO-B.
The timings at both spacecraft include: the shock/discontinuity time (if
present), the ME start and end times, and the FR start and end times (if
present). The heliocentric distance of the inner and outer spacecraft ($r_{1}$
and $r_{2}$) are also provided. The FR/ME class observed at each observing
spacecraft, together with the index $\Delta\mathbb{C}$ indicating the presence
or absence of complexity changes detected between the inner and outer
spacecraft, are indicated. The final six columns list the interactions with
various solar wind structures, the presence or absence of BDEs during the FR
(when present) or ME passage, and the ID(s) of the heliospheric CME
counterparts from the HELCATS catalog.

# | SC1–SC2 | $\Delta\phi$ | SC1 Timing [yyyy-mm-dd HH:MM] | $r_{1}$ | SC2 Timing [yyyy-mm-dd HH:MM] | $r_{2}$ | FR/ME class | FR/ME class | $\Delta\mathbb{C}$ | Interaction | Interaction | Interaction | Interaction | BDEs | HELCATS
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| Name | $[^{\circ}]$ | Shock/Discontinuity | ME start | ME end | FR start | FR end | [au] | Shock/Discontinuity | ME start | ME end | FR start | FR end | [au] | at SC1 | at SC2 |  | with HSS | with SIR | with HCS | with shock | within FR/ME | event ID(s)
1 | M–VEx | $1.6$ | 2011-10-15 08:27 | 2011-10-15 11:14 | 2011-10-16 06:43 | 2011-10-15 11:14 | 2011-10-16 06:43 | 0.46 |  | 2011-10-16 06:06 | 2011-10-17 09:39 | 2011-10-16 06:06 | 2011-10-17 09:39 | 0.73 | $Fr$ | $F^{-}$ | 0 |  | No | No | No | Not available | Not observed
2 | M–VEx | $1.1$ | 2012-03-07 04:38 | 2012-03-07 06:11 | 2012-03-07 18:01 | – | – | 0.32 |  | 2012-03-07 20:14 | 2012-03-08 11:43 | – | – | 0.72 | $E$ | $E$ | 0 |  | Probable | No | No | Not available |  HCME_A__20120307_01, HCME_B__20120307_01
4 | M–STB | $4.8$ | 2011-11-04 15:09 | 2011-11-05 00:45 | 2011-11-05 15:41 | 2011-11-05 00:45 | 2011-11-05 15:41 | 0.44 |  | 2011-11-06 22:50 | 2011-11-09 04:00 | 2011-11-06 22:50 | 2011-11-08 13:00 | 1.09 | $Fr$ | $Fr$ | 1 |  | No | No | No | Partial | Not observed
5 | M–STA | $4.6$ | 2011-12-30 16:27 | 2011-12-30 21:00 | 2011-12-31 09:20 | 2011-12-30 21:00 | 2011-12-31 09:20 | 0.42 |  | 2012-01-01 17:00 | 2012-01-02 04:00 | 2012-01-01 17:00 | 2012-01-02 04:00 | 0.96 | $Fr$ | $F^{+}$ | 1 |  | Yes | Yes | No | No | HCME_A__20111229_02
16 | VEx–STB | $8.5$ | 2008-12-29 20:46 | 2008-12-29 20:46 | 2008-12-30 04:58 | 2008-12-29 20:46 | 2008-12-30 04:58 | 0.72 |  | 2008-12-31 02:00 | 2009-01-01 07:20 | 2008-12-31 04:00 | 2009-01-01 01:00 | 1.03 | $Fr$ | $Fr$ | 0 |  | No | No | No | No | HCME_A__20081227_01
17 | VEx–STA | $9.2$ | 2009-06-02 18:39 | 2009-06-02 18:39 | 2009-06-03 12:20 | 2009-06-02 18:39 | 2009-06-03 12:20 | 0.73 |  | 2009-06-03 00:00 | 2009-06-04 22:40 | – | – | 0.96 | $Fr$ | $C_{x}$ | 1 |  | No | No | Yes | Partial | HCME_B__20090530_01

Note. — Table 1 is provided in its entirety as supplementary material. A
sample is presented here for guidance regarding its form and content.

In addition to the ME boundaries, for each event we determine whether the ME
or a significant portion of it (lasting more than $\sim 25-30$% of the ME
duration) exhibited smooth rotations of the magnetic field component, i.e.
signatures compatible with an FR configuration. Hereafter, we refer to these
as FRs. We find that some of the events have no FR within the ME, some have an
FR that extends throughout the whole ME, and some have an FR that only covers
a portion of the ME. If present, the FR portion of the ME is used as a
reference to identify complexity changes affecting MEs during propagation
because it allows us to identify finer structural changes including rotations,
e.g., by means of in situ fitting techniques (see Section 3.1.2). If no FR is
present within the ME, we consider the whole ME in order to evaluate
complexity changes. An example of this boundary identification procedure is
provided in Figure 1 for event 17 observed at VEx and STEREO-A. A discussion
on the relationship between ME and FR boundaries is provided in Section 4.3.4.

Figure 1: Identification of ICMEs from magnetic field time series for Event 17
in Table S1, arriving at VEx and STEREO-A on June 2 and 3, 2009, respectively.
In this case, the two observing spacecraft were separated by $9^{\circ}$ in
longitude and 0.23 au in the radial direction. (a)–(e): signatures at VEx.
(f)–(m): signatures at STEREO-A. Panels (a), (f) show the magnetic field time
series, and panels (b), (g) show the magnetic field standard deviation. Panels
(h), (i), and (j) shows the speed, and the proton number density, and the
normalized suprathermal electron pitch angle distribution data detected at
STEREO A. The vertical solid lines mark the FR boundaries. Panels (c)–(e) and
(k)–(m) show the magnetic hodograms for the FR/ME periods. An $Fr$ class is
identified at VEx, while a $C_{x}$ class is visible at STEREO-A.

For the purposes of this paper, we further remove from the initial list all
the events that have significant data gaps, i.e. gaps extending more than half
of the ME duration, and for which the available data show no obvious rotation
in the magnetic field components. We also discard all the events associated
with interacting ICMEs, i.e. those events for which an interaction among
multiple ICMEs is recognizable in situ, as the investigation of ICME–ICME
interactions goes beyond the scope of this study. This results in a total of
31 suitable ICMEs identified, while 16 events were discarded from our
analysis. Each event was observed at two spacecraft (i.e. the inner spacecraft
is either MESSENGER or VEx, and the outer spacecraft is either VEx, ACE,
STEREO-A or STEREO-B) during periods of radial alignment, with longitudinal
separations among the observing spacecraft ranging between 1∘ and 32∘. The 31
ICMEs used in this study, including the details of spacecraft alignments and
arrival times at each spacecraft, are listed in Table S1. Further details
about this database are given later on in the text (see Section 4).

##  3 Methods

###  3.1 Definition of Magnetic Complexity Changes

In the following subsections, we formalize the definition of ICME magnetic
complexity changes which will be used throughout this work to identify major
alterations in the magnetic configuration of ICMEs detected between two
spacecraft, in a manner that is as unbiased as possible. As detailed in
Sections 3.1.1 and 3.1.2 below, we consider two major indicators of magnetic
complexity changes within ICMEs: (1) fundamental alterations of the ICME
magnetic structure as indicated by the change in FR (when present) or ME
category detected between the two observing spacecraft; and (2) significant
re-orientations of ICME structures as inferred from magnetic hodograms and in
situ fitting techniques. We summarize the evolution of magnetic complexity of
each ICME using the index $\Delta\mathbb{C}$, which assumes a value of
$\Delta\mathbb{C}=0$ in the case of events that do not change their magnetic
complexity between the inner and outer spacecraft, and of $\Delta\mathbb{C}=1$
in the case of events that do change their magnetic complexity between the
inner and outer spacecraft.

####  3.1.1 Condition A: Fundamental Alteration of FR/ME Structures

We construct the magnetic hodograms for each ICME FR (when present) or ME in
our list, and visually classify their internal magnetic structure at a given
spacecraft using a morphological classification scheme based on the one
proposed by Nieves-Chinchilla et al. (2018b, 2019). This classification sorts
FRs/MEs into five classes, which encompass the wide variety of signatures
observed: $Fr$, exhibiting a maximum rotation in any magnetic component close
to $180^{\circ}$; $F^{-}$, with maximum rotation in any magnetic component
smaller than $120^{\circ}$; $F^{+}$, with maximum rotation in any magnetic
component larger than $240^{\circ}$; $C_{x}$, complex structures with more
than one rotation, e.g. with different radii of curvature and/or different
rotation directions; and $E$, characterized by a lack of clear rotations. An
example of $Fr$ and $C_{x}$ signatures are shown in Figure 1. Such a
classification allows the categorization of FR/ME signatures without imposing
a priori restrictions on them other than having a high magnetic field with low
levels of fluctuations. Nevertheless, this classification developed from the
assumption that the internal magnetic structure of ICMEs in their lowest
energy state can be locally described as a single FR with a helical magnetic
field wrapped around a central axis. We remark that this idea has been debated
and contrasted in previous works (Owens, 2016; Al-Haddad et al., 2019). It
also remains unclear whether any individual FR model, among the many that have
been developed (e.g. Burlaga, 1988; Lepping et al., 1990; Hidalgo et al.,
2002a, b; Isavnin, 2016; Nieves-Chinchilla et al., 2016, 2018a; Möstl et al.,
2018), is sufficient to describe the observed variety of FR and ME signatures,
including $F^{+}$, $E$, and $C_{x}$ classes.

In the aforementioned classification scheme, all $F$ types are compatible with
crossings through single FR structures. In the following analysis, we consider
$Fr$ and $F^{-}$ classes as a single category, since rotations close to and
smaller than $180^{\circ}$ in the magnetic field components are both
compatible with different spacecraft trajectories through a helical magnetic
field wrapped around an axis, e.g. arising from small and large impact
parameter crossings, respectively (Nieves-Chinchilla et al., 2019). Magnetic
field rotations significantly larger than $180^{\circ}$ ($F^{+}$ class) can be
interpreted as signatures of FRs with significant curvature, e.g. spheromaks
(Scolini et al., 2021), or potentially double FRs (Lugaz et al., 2013), and
are therefore kept as a separate category for the sake of clarity. Neither of
the remaining two classes ($C_{x}$ and $E$) can be reproduced by an FR model,
and due to their distinct characteristics, they are maintained as separate
categories and considered as indicative of crossings through fundamentally
different magnetic structures. We note that Owens (2016) argued that some ICME
legs might actually have non-flux rope configurations such as untwisted
magnetic field lines. In this scenario, $E$ types may also be consistent with
crossings through untwisted legs carrying little-to-no magnetic field
rotation.

For each ICME, we then compare the classifications obtained at the inner and
outer spacecraft, and use them as prime indicators to assess whether a given
ICME has undergone a magnetic complexity change during propagation, i.e. we
define a complexity change as any change in the FR/ME category detected
between the two observing spacecraft.

####  3.1.2 Condition B: Re-orientation of FR/ME Structures

We further scrutinize events that retained their magnetic configuration as
defined in Section 3.1.1 above, searching for complexity changes that manifest
as significant re-orientations (i.e. longitudinal and latitudinal rotations)
of FR/ME structures.

For those events that are observed as $Fr$/$F^{-}$ types at both spacecraft,
we fit observational data using a linear force-free (LFF) fitting model based
on the force-free constant-$\alpha$ FR model developed by Burlaga (1988) and
subsequently optimized by Lepping et al. (1990). Lepping et al. (2003) showed
that different noise levels can affect the results of the LFF fitting
technique leading to uncertainties up to $\pm 13^{\circ}$ and $\pm 30^{\circ}$
in the reconstructed latitudinal and longitudinal FR axial directions, while
Al-Haddad et al. (2013, 2018) assessed that different fitting models can
differ up to $\pm 45^{\circ}$ in latitude and/or $\pm 60^{\circ}$ in longitude
in the reconstructed orientation of the FR axis. Since we use a single fitting
technique, we take a conservative approach and consider changes in the
reconstructed FR axis direction that are greater than $\pm 45^{\circ}$ in
latitude and/or $\pm 60^{\circ}$ in longitude as indicators of complexity
changes having occurred during propagation between the two spacecraft. These
thresholds have been chosen based on the results obtained by Al-Haddad et al.
(2013, 2018), who showed that larger differences in latitude/longitude are
most often indicative of actual structure re-orientations rather than due to
the particular model used.

In a similar way, events that are observed as $F^{+}$, $E$, or $C_{x}$ types
at both spacecraft are further scrutinized, and complexity changes are
identified when the magnetic hodograms exhibit significant changes in the
magnetic field polarities between the two spacecraft, i.e. corresponding to
drastic rotations of the ME.

###  3.2 Identifying the Drivers of Magnetic Complexity Changes

To identify the causes of magnetic complexity changes, we search for possible
interactions of each ICME with other solar wind structures, namely HSSs, SIRs,
the HCS/HPS, as well as isolated interplanetary shocks, that might have
occurred during propagation between the two observing spacecraft. To do so, we
first investigate the presence of solar wind structures interacting with each
ICME based on in situ plasma and magnetic field data available at each
spacecraft. We then cross-check our identifications with publicly available
catalogs, particularly the Heliospheric Shock Database, generated and
maintained at the University of Helsinki (Kilpua et al., 2015,
http://ipshocks.fi), the Level 3 STEREO IMPACT/PLASTIC ICME, SIR and
interplanetary shock lists (Jian et al., 2013, 2018, 2019, https://stereo-
dev.epss.ucla.edu/l3_events), and the Near-Earth ICME catalog by Cane &
Richardson (2003) and Richardson & Cane (2010)
(http://www.srl.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm). We note that
in in situ data, we identify HSSs as regions of $v_{r}\geq 500$ km/s, or more
generally as solar wind structures propagating faster than the a given ICME at
1 au (Cranmer et al., 2017). In the rest of this paper, we refer to in situ
evidence of interactions between ICMEs and solar wind structures as
“confirmed” interactions.

To account for additional interactions that might have started and ended
between the ICME passages at the inner spacecraft and outer spacecraft, we
check WSA-ENLIL simulations of the ambient solar wind available on the NASA
CCMC server (https://ccmc.gsfc.nasa.gov; keywords: Dan_Aksim, YYYY amb (from
restart), where YYYY is the year of interest) to verify the presence of other
solar wind structures that might have interacted with the ICME between the two
spacecraft encounters. In particular, we look at the presence of solar wind
interplanetary structures between the two observing spacecraft in the period
between the ICME arrival at the inner observing spacecraft, and the ICME end
at the outer observing spacecraft. We remark that typical ICME propagation
times between the inner and outer spacecraft are around 1 day for
MESSENGER–VEx and VEx–1 au conjunctions, and around 2 days for MESSENGER–1 au
conjunctions. In WSA-ENLIL simulations, we identify HSSs as regions of
$v_{r}\geq 500$ km/s, and SIRs as dense regions generated by the interaction
of fast and slow solar wind, characterized by a scaled number density
$n(r\,\,[\mathrm{au}]/1\,\,\mathrm{au})^{2}$ larger than $\sim 10$ cm-3 (Jian
et al., 2019). We note that in WSA-ENLIL simulations, the modeled arrival
times of HSSs at given spacecraft locations are not always consistent with the
arrival times observed by spacecraft in situ (e.g. Gressl et al., 2014). In
this study, we use WSA-ENLIL results as a guide on the global structure of the
ambient wind, working under the assumption that HSS arrival times modeled by
WSA-ENLIL are approximately correct. Therefore, in what follows, we label
interactions between ICMEs and solar wind structures inferred from WSA-ENLIL
results as “probable” interactions.

##  4 Results and Discussion

###  4.1 Frequency of FR/ME Types and Complexity Changes

Figure 2: Distribution of FR/ME types observed by spacecraft at MESSENGER (a),
VEx (b), and 1 au (c).

As listed in Table S1, our database consists of a total of 31 ICMEs, each
observed at two spacecraft, for a total of 62 observations. Table S1 also
reports, for each event, the morphological classification assigned to the FR
(when present) or ME magnetic structure at each observing spacecraft. The
index $\Delta\mathbb{C}$ is used to indicate an unchanged
($\Delta\mathbb{C}=0$) or changed ($\Delta\mathbb{C}=1$) complexity as
detected between the two observing spacecraft. We note that in the latter
column, the index $\Delta\mathbb{C}$ has been determined by applying both
Conditions A (Section 3.1.1) and B (Section 3.1.2) to each event. The results
of the LFF fits for those events that maintained an $Fr/F^{-}$ category at
both spacecraft are provided in Table 2 for completeness.

Overall, the categorization of MEs/FRs yields the following: 35 $Fr$/$F^{-}$
types ($\sim 56\%$), 7 $F^{+}$ types ($\sim 11\%$), 7 $E$ types ($\sim 11\%$),
and 13 $C_{x}$ types ($\sim 21\%$) (shown in Figure 2 at MESSENGER, VEx, and 1
au). However, as visible from Figure 2, the FR/ME class distribution is
significantly more similar between VEx and 1 au than it is at MESSENGER. In
particular, at 1 au we observe less $Fr$/$F^{-}$ (53%), and more $C_{x}$ (25%)
types than at MESSENGER (67% and 13%, respectively). This simple result is
already indicative of a general trend in ICME complexity increase from the
inner heliosphere to 1 au. Furthermore, the distribution at 1 au is similar to
the one reported by Nieves-Chinchilla et al. (2019) throughout the past two
solar cycles, with minor differences (e.g. a higher fraction of $C_{x}$ events
reported in this study) possibly ascribable to solar cycle variations. For
completeness, we report the results from previous studies investigating the
fraction of ICMEs having MC signatures at different heliocentric distances.
Bothmer & Schwenn (1996) found that $\sim 41\%$ of the fast ICMEs observed by
the Helios spacecraft between 1979 and 1981 exhibited MC characteristics.
Richardson & Cane (2010) reported an approximate fraction of one third of
ICMEs showing MC signatures at 1 au. Beyond Earth’s orbit, Rodriguez et al.
(2004) found $\sim 27\%$ ICMEs to be MCs between 1 and 5 au based on Ulysses
observations. MCs are a subcategory of $Fr/F^{-}$ types, which explains the
lower fractions reported in previous studies compared to those retrieved in
this work. Yet, the decreasing trends in the fractions of both $Fr/F^{-}$
types and MCs detected at increasing heliocentric distances provide
independent indications that ICMEs become more complex as they propagate
through the inner heliosphere.

Of the 31 events under study, 18 ($\sim 58$%) did not exhibit fundamental
alterations of their internal magnetic configuration as defined using
Condition A, while 13 ($\sim 42$%, a substantial fraction) did. Moreover, 7
among the 18 events that did not exhibit fundamental alterations in their
magnetic structure, underwent significant re-orientations as determined from
LFF fits and the magnetic hodograms observed at the two observing spacecraft
(i.e. as defined by Condition B, see Table 2). By combining Conditions A and B
together, we conclude that 11 events ($\sim 35$%) did not change their
complexity, while 20 ($\sim 65$%) did. These results show that complexity
changes in interplanetary space are much more frequent than estimated by
previous studies considering FR ICMEs only (e.g. Good et al., 2018; Palmerio
et al., 2018), and that they in fact affect the majority of ICMEs observed
between Mercury and 1 au.

| SC1 | SC2 |
---|---|---|---
Event # | $H$ |  $\theta_{0}$ (∘) |  $\phi_{0}$ (∘) | $y_{0}$ |  $B_{0}$ (nT) | $\chi^{2}_{\mathrm{red}}$ | $H$ |  $\theta_{0}$ (∘) |  $\phi_{0}$ (∘) | $y_{0}$ |  $B_{0}$ (nT) | $\chi^{2}_{\mathrm{red}}$ |  $|\Delta\theta_{0}|$ (∘) |  $|\Delta\phi_{0}|$ (∘)
1 | $-1$ | $-2$ | 0 | $-0.70$ | 93 | 0.04 | $-1$ | $-9$ | 1 | $-0.78$ | 50 | 0.02 | 7 | 1
4 | $-1$ | 16 | 54 | $-0.26$ | 44 | 0.06 | $-1$ | 3 | 166 | $0.65$ | 12 | 0.03 | 13 | 112
6 | $1$ | 15 | 92 | $0.26$ | 38 | 0.12 | $1$ | 12 | 14 | $0.53$ | 25 | 0.05 | 2 | 77
9 | $-1$ | 6 | 69 | $-0.60$ | 134 | 0.08 | $-1$ | 17 | 152 | $0.12$ | 16 | 0.06 | 11 | 83
10 | $1$ | 14 | 326 | $0.64$ | 56 | 0.05 | $1$ | 27 | 279 | $-0.44$ | 7 | 0.03 | 12 | 47
12 | $1$ | $-3$ | 328 | ${0.79}$ | 64 | 0.03 | $1$ | 17 | 259 | ${-0.71}$ | 21 | 0.05 | 20 | 69
14 | $-1$ | $-6$ | 85 | ${-0.09}$ | 47 | 0.04 | $-1$ | $-22$ | 105 | ${-0.04}$ | 14 | 0.04 | 16 | 20
16 | $-1$ | $-2$ | 167 | $0.87$ | 17 | 0.04 | $-1$ | $-11$ | 138 | $0.59$ | 10 | 0.06 | 9 | 29
18 | $-1$ | 10 | 36 | $-0.66$ | 19 | 0.06 | $-1$ | $-25$ | 68 | $-0.02$ | 9 | 0.05 | 35 | 32
20 | $-1$ | 7 | 9 | $-0.92$ | 40 | 0.01 | $-1$ | 4 | 3 | $-0.92$ | 20 | 0.02 | 3 | 6
22 | $-1$ | 0 | 5 | $-0.78$ | 21 | 0.05 | $-1$ | 1 | 4 | $-0.79$ | 13 | 0.06 | 1 | 1
23 | $1$ | $-6$ | 312 | $0.23$ | 17 | 0.06 | $1$ | $-25$ | 290 | $0.75$ | 12 | 0.02 | 19 | 22
25 | $1$ | 57 | 134 | $-0.62$ | 27 | 0.09 | $1$ | $-1$ | 229 | $-0.74$ | 9 | 0.04 | 58 | 95
Table 2: LFF fit parameters for the events categorized as $Fr$/$F^{-}$ types
at both spacecraft. $H$ – magnetic chirality, $\theta_{0}$ – latitude of FR
axis, $\phi_{0}$ – longitude of FR axis, $y_{0}$ – impact parameter
(normalized by FR radius), $B_{0}$ – magnetic field at FR axis,
$\chi^{2}_{\mathrm{red}}$ – reduced $\chi^{2}$. $|\Delta\theta_{0}|$ and
$|\Delta\phi_{0}|$ estimate the FR axis rotation between the two spacecraft.
The values in bold mark significant re-orientations as defined by Condition B.

####  4.1.1 Effect of Spacecraft Radial and Longitudinal Separations

Figure 3: Complexity change $\Delta\mathbb{C}$ as a function of the spacecraft
radial ($\Delta r$) and longitudinal ($\Delta\phi$) separations. Different
markers are used to indicate different pairs of spacecraft in radial
alignment. The vertical and horizontal lines show the average radial and
longitudinal spacecraft separation for events exhibiting (dashed) and not
exhibiting (dotted) complexity changes, respectively.

Figure 3 shows the complexity evolution of individual ICMEs as a function of
the radial and longitudinal separations between the observing spacecraft.
ICMEs that preserve their magnetic complexity are observed over shorter
spatial and temporal scales than ICMEs that do change their complexity. We
find that unchanged and changed events are observed by spacecraft with mean
radial separation of 0.32 au and 0.44 au, respectively. The mean longitudinal
separations for spacecraft observing unchanged and changed events are 7∘ and
18∘, respectively. We further apply the Welch’s t-test (i.e. a two-sample
location test which is used to test the hypothesis that two populations have
equal means) to determine if differences between events that change and that
do not change complexity during propagation are statistically significant. We
impose a 95% confidence level, meaning that we can reject the null hypothesis
of the test (i.e. that the two populations have equal means) for p-values
smaller than 0.05 (5%). We find p-values of 0.03 and 0.0001 for radial and
longitudinal separations, and conclude that there is a statistically-
significant difference in mean values between the two groups.

In more detail, roughly 82% (9 out of 11) of the ICMEs that preserve their
magnetic complexity are observed by spacecraft in close radial alignment
($\Delta\phi<15^{\circ}$) and at radial separations $\Delta r\leq 0.4$ au. At
such small longitudinal and radial separations, they make up 90% of the ICMEs
(10 out of 11 events). The remaining $\sim 18\%$ of unchanged events (2 out of
11) are observed in close radial alignment but at larger radial separations
than 0.4 au. In this region, however, 71% (5 out of 7) of the ICMEs do change
their magnetic complexity, while only 29% (2 out of 7) do not. As these ICMEs
are observed by spacecraft in close radial alignment, and therefore both
spacecraft cross through approximately the same region of the ICME, such
complexity changes can be most likely attributed to propagation (i.e.
“nurture” effects), rather than to large-scale pre-existing differences in the
internal properties within different ME regions. Oppositely, all of the events
observed at smaller radial separations ($\Delta r\leq 0.4$ au) but at larger
angular separations ($\Delta\phi>15^{\circ}$) exhibit complexity changes,
possibly resulting from a combination of initial or pre-existing
irregularities in their internal magnetic structure (i.e. “nature” effects),
and propagation effects (due to “nurture”), which can also include
inhomogeneous and variable ambient solar wind conditions through which
different parts of an ICME propagate. Complexity changes are also detected in
all ICMEs observed at large radial separations ($>0.4$ au) and large angular
separations ($\Delta\phi>15^{\circ}$).

We note that for the majority of the events considered, the radial separation
between the observing spacecraft also underlies a trend in the spacecraft
heliocentric distances, with observations at smaller $\Delta r$ being
typically taken at larger distances from the Sun (i.e. at Venus and 1 au)
compared to observations at larger $\Delta r$ (i.e. at Mercury and 1 au).
However, as reported by Scolini et al. (2021), for a given $\Delta r$, a
higher probability of developing complexity changes is expected for ICMEs
observed by an inner spacecraft located within $\sim 0.5$ au. Further
observational insights on the radial scale at which ICMEs preserve their
magnetic complexity as a function of the heliocentric distance would therefore
require additional observations spanning the whole space of possible $r$ and
$\Delta r$ parameters.

We also point out that only two out of the 13 events listed in Table 2 (i.e.
events 12 and 25) were observed at angular separations larger than
$15^{\circ}$, and both were associated with complexity changes likely
resulting from the interaction with multiple interplanetary structures (as
further discussed in Section 4.2). This suggests that the significant re-
orientations and magnetic complexity changes identified through the
application of Condition B cannot be explained in terms of large-scale
geometric effects due to spacecraft crossings through different parts of
stretched FRs, as was the case, for example, in the events investigated by
Möstl et al. (2012). Additionally, the common assumption that an unperturbed
ICME magnetic structure should exhibit relatively similar characteristics
along different directions implies that drastic magnetic complexity changes as
defined by Condition A cannot be explained only in terms of the angular
separations among the spacecraft, particularly for $\Delta\phi$ significantly
smaller than the ICME angular width (estimated to be around $\sim
40^{\circ}-60^{\circ}$ on average; Yashiro et al., 2004; Kilpua et al., 2011).
In such a scenario, the FR/ME category should not change when crossing through
the same ICME structure from different directions. As this is most probably an
over-simplification of the real situation and subject of debate (see e.g.
Lugaz et al., 2018; Davies et al., 2020; Owens, 2020), we took a closer look
at the events observed above $15^{\circ}$ of angular separation that exhibited
complexity changes as defined by Condition A. We found that out of 12 events,
4 (33%; i.e. events 3, 11, 26 and 29) exhibited a complexity change that could
not be attributed to any interaction with other solar wind structures (as
further discussed in Section 4.2). For the remaining 8 cases (66% of the
events), the interaction with interplanetary structures was likely the major
contributor to the detected complexity change. Overall, these arguments
suggest that in the large majority of cases, the results reflect actual
magnetic complexity changes affecting ICMEs, rather than geometrical effects
due to the particular spacecraft trajectories along a given structure.

With respect to the question of whether complexity changes might be
significantly affected by the spacecraft trajectory through the ICME magnetic
structure depending on its inclination, we also note that in this work, all
events that could be fitted using the LFF fitting technique except one (Event
25 at the inner spacecraft) were reconstructed as having a low inclination
with respect to the equatorial plane (indicated by the small $\theta_{0}$
values in Table 2). The determination of the inclination of the remaining
magnetic structures was complicated by the lack of clear flux rope signatures,
and could not be performed. Overall, at least with respect to the subset
listed in Table 2, the aforementioned results were therefore derived for a
population of low-inclination flux ropes, whose signatures appear to be less
affected by trajectory effects than highly-inclined flux ropes (e.g. Kilpua et
al., 2009; Davies et al., 2021). The assessment of possible inclination
effects on ICME magnetic complexity changes and magnetic coherence will
require the consideration of highly-inclined ICMEs in future studies.

Remarkably, the $\Delta\phi\sim 15^{\circ}$ breaking point retrieved in this
study (i.e., above this longitudinal separation all events exhibit complexity
change) is only slightly smaller than previous estimates of the maximum
angular width at which ICME magnetic structures behave coherently (i.e.
$17^{\circ}-26^{\circ}$ reported by Owens (2020), and $14^{\circ}-20^{\circ}$
by Lugaz et al. (2018) based on theoretical and observational arguments,
respectively). Although making an accurate estimate of the actual scale of
ICME coherence is not possible due to the non-negligible radial separations
affecting the observations considered in this study, the results in Figure 3
suggest ICMEs might retain some level of coherence over angular scales of the
order of $15^{\circ}$. We also argue that if multi-point observations with
negligible radial separation were available for the events considered, i.e.
once any effects related to propagation were removed, coherence would be most
probably observed over scales even larger than 15∘.

Finally, for the 9 events observed in perfect alignment, i.e. with angular
separation $<5^{\circ}$, we report that 6 of them ($\sim 67$%) did not change
their FR/ME class, while only 3 ($\sim 33$%) did. These values validate
previous conclusions by Scolini et al. (2021) based on the results from
numerical simulations (reporting a 69% to 54% probability for ICMEs to
maintain their FR class, and a 31% to 46% probability to change their FR
class, depending on the ambient solar wind conditions). In this case, the
average radial separation for ICMEs observed in perfect conjunction is 0.34 au
for events that did not change complexity, and 0.58 au for events that did
change complexity.

###  4.2 Drivers of Magnetic Complexity Changes

Figure 4: Interaction with solar wind structures as a function of the FR/ME
category detected at the outer spacecraft, and of the complexity evolution
history. Black bars indicate confirmed interactions, while grey bars indicate
probable interactions based on WSA-ENLIL simulations of the ambient solar
wind.

As stated in Section 4.1, we found that out of the 31 ICMEs considered, 11 did
not change their magnetic complexity, while 20 did. Figure 4 reports their
probability of interaction with other solar wind structures as a function of
the FR/ME category detected at the outer spacecraft, and of the complexity
evolution history determined from the analysis described in Section 3.2. In
total, we were able to identify 26 confirmed interactions from in situ data,
involving 15 ICMEs, and 6 probable interactions from WSA-ENLIL simulations,
involving 5 ICMEs. In the following, these two types of interactions are
discussed together, while in Figure 4 their contributions are presented in
different colors for completeness. A detailed list of the confirmed and
probable interactions identified for each ICME is also included in Table S1.

We find that 50% of $Fr$/$F^{-}$ types (8 of 16 events) and 75% of $F^{+}$
types (3 of 4 events) do not interact with any structure. This fraction is
down to 25% and 0% for $E$ types (1 of 4 events) and $C_{x}$ types (0 of 7
events), respectively (Figure 4 (a), (b), (c), (d)), indicating that
interactions with solar wind structures associate in particular with $E$ and
$C_{x}$ types. As a note of caution, we remark that the $F^{+}$ and $E$
fractions above are likely to have been influenced by the small number of
events observed at outer observing spacecraft (4 for both categories), and
might therefore change significantly if more events were available.

Out of the 11 events that do not change their complexity, 6 (55%) do not
interact with any structure, while 5 (45%) do interact with one (4 events, 36%
of the total) or two (1 event, 9% of the total) structures (Figure 4 (e), (f),
(g), (h)), suggesting that interaction with solar wind structures does not
always induce a change in magnetic complexity. We also find that out of the 20
events that do change their complexity, 6 (30%) do not interact with any
structure, while 14 (70%) do interact with one (25%, 5 events in total), two
(30%, 6 events in total), or three (15%, 3 events in total) structures. We
conclude that while an interaction with another structure does not always
result in a change in complexity, it does increase the probability for ICMEs
to undergo a complexity change. In fact, most of the unchanged events ($\sim
90$%) either do not interact with any structure, or only interact with a
single structure. On the contrary, events that changed their complexity
interact with two or more structures much more frequently (in $\sim 45$% of
the cases considered).

When considering the interaction with specific structures (i.e. HSSs, SIRs,
HCS, and isolated shocks), we find that $C_{x}$ types, which have the highest
association with interactions, are most often the result of interactions with
the HCS (57%, Figure 4 (l)). They also have high associations with all other
structures (43% to 29%, Figure 4 (j), (k), (m)). The remaining FR/ME
categories are more often linked to interactions with HSSs and SIRs (50% to
25%), and less often with the HCS (less than 25%) and isolated shocks (less
than 12% of the cases).

Figure 4 (n), (o), (p), (q) show that events that change their complexity are
more likely to have interacted with any of the structures considered than
events that do not change their magnetic configuration. In particular, the
primary cause of complexity changes is the interaction with HSSs (found in 50%
of the events exhibiting complexity changes, Figure 4 (n)), followed by the
interaction with SIRs (found in 40% of the events exhibiting complexity
changes, Figure 4 (o)), HCS (found in 25% of the events exhibiting complexity
changes, Figure 4 (p)), and isolated shocks (found in 15% of the events
exhibiting complexity changes, panel n). For comparison, only 18% of the
events do not change their complexity were found to have interacted with HSSs,
SIRs (Figure 4 (n), (o)), and 9% with the HCS or with isolated shocks (Figure
4 (p), (q)). We note that the correlation between magnetic complexity changes
and interactions with solar wind structures presented here has been determined
with the aid of in situ magnetic field and (when available) bulk solar wind
data, as well as with global simulations of the inner heliospheric solar wind
conditions. We investigate in Section 4.3.1 below whether additional data
products, in particular suprathermal electron PAD data, can provide valuable
additional information for the identification of ICME complexity changes.

###  4.3 Characteristics of ICMEs Exhibiting Complexity Changes

####  4.3.1 Bi-directional Electrons

Since the presence of bi-directional suprathermal electron flows (BDEs) is
tied to the magnetic topology of ICMEs (e.g. Gosling et al., 1987; Kahler &
Reames, 1991; Crooker et al., 1998; Shodhan et al., 2000), it is reasonable to
expect some degree of correlation between BDEs and magnetic complexity changes
as well. To investigate this characteristic, we compare FR/ME categories and
their complexity evolution history with information on the PAD of suprathermal
electrons at 1 au (when available).

In particular, we consider electron PAD data available at energies above $\sim
100$ eV, i.e. in the suprathermal range. For the events observed by
ACE/SWEPAM, we use data in the 272 eV energy channel, while for events
observed by the SWEA detector of STEREO/IMPACT, we integrate among the six
energy channels operating above $\sim 100$ eV, i.e. at 1716.84 eV, 1056.95 eV,
650.70 eV, 400.60 eV, 246.62 eV, and 151.83 eV. At STEREO, we compared the
results obtained by integrating over all channels above $\sim 100$ eV, with
those obtained from the 246.62 eV channel alone (i.e. covering energies
closest to those available at ACE), detecting no significant difference. We
nevertheless considered it preferable to use multiple energy channels when
possible, in order to ensure sufficient count rates for all periods under
investigation. For each event, PADs are normalized to the peak flux observed
at each time step, in order to have distributions running between 0 and 1
throughout the ICME passage period. The process of selecting BDE intervals
within MEs is somewhat subjective, and becomes questionable for pitch angle
distributions approaching isotropy and for cases where the flux of one of the
counter-streaming beams is weaker than the other (Shodhan et al., 2000). In
this work, we apply the following identification procedure. For each ICME
observed at 1 au, we determine the presence of BDEs within the ME or FR
structure by identifying periods of counter-streaming particle beams located
around $0^{\circ}$ and $180^{\circ}$ with respect to the nominal magnetic
field direction. To account for cases where the two beams have different
fluxes, we identify as BDEs periods of counter-streaming beams that are both
reaching normalized fluxes of at least 0.5. As unbalanced suprathermal
electron fluxes may indicate encounters with closed structures characterized
by largely asymmetric legs, i.e. one of which extends out into the heliosphere
well beyond the spacecraft location (Pilipp et al., 1987), placing a limit on
the minimum flux of each beam may impose a limit to the maximum length of a
closed magnetic field line before it is considered open (Shodhan et al.,
2000). However, such an approach provides an unbiased, objective criterion to
identify BDEs, hence for the purpose of this study, we consider the advantages
to outweigh the limitations.

PAD data are scanned by eye, and periods approaching isotropy are discarded as
non-BDE periods. We then classify BDE events according to the percentage of
time during the FR (when present) or ME passage when counter-streaming
electrons were observed. We bin the events into four categories: $75\%-100\%$
(BDEs throughout), $50\%-75\%$ (extended BDEs), $25\%-50\%$ (partial BDEs),
and $0\%-25\%$ (no BDEs). The presence or absence of BDEs for each ICME is
provided in Table S1.

Figure 5: Occurrence of BDEs at 1 au as a function of the FR/ME category
(left) and complexity evolution (right).

In total, 28 ICMEs were observed at 1 au, all of which had associated
suprathermal electron PAD data available. We find that 64% of the events at 1
au show some evidence of BDEs (partial to throughout), which is in good
agreement with the 67% estimate by Richardson & Cane (2010). As shown in
Figure 5 (left), we find that 33% of $Fr/F^{-}$ types (out of a total of 15
events) exhibit no BDEs, 40% exhibit partial BDEs for less than half of the FR
(when present) or ME duration, 20% exhibit extended BDEs, and 7% exhibit BDEs
thoughout the whole structure. These percentages are only partially consistent
with earlier (upper) estimates by Shodhan et al. (2000), who found $17\%-27\%$
out of the 48 MCs considered (roughly corresponding to $Fr/F^{-}$ types in
this study) did not contain BDEs for longer than 25% of their duration,
$10\%-21\%$ had partial BDEs, $15\%-27\%$ had extended BDEs, and $29\%-42\%$
had BDEs throughout. We argue that the discrepancies between our results and
those reported by Shodhan et al. (2000) may be due to the different criteria
used to identify BDEs, particularly in the case of unbalanced beam fluxes. At
the opposite end of the spectrum, we find that none among the 7 $C_{x}$ types
at 1 au exhibited BDEs for more than half of the FR/ME structure, with 57% of
the cases exhibiting partial BDEs, and 43% completely lacking BDEs. Finally,
$F^{+}$and $E$ types were observed in a small number of cases (3 each), and
thus no statistical conclusion can be drawn due to the low number of events
available. The higher occurrence of prolonged BDEs within $Fr/F^{-}$ than
within $C_{x}$ types is consistent with the interpretation of $Fr/F^{-}$ types
typically reflecting closed, well-ordered FR structures (e.g. Zurbuchen &
Richardson, 2006), while $C_{x}$ types reflect more complex magnetic
topologies which likely generated through extensive magnetic interaction
(implying, e.g., reconnection and reconfiguration of magnetic fields lines;
Crooker et al. (1998); Winslow et al. (2016)) with their surroundings.

When considering the presence of BDEs with respect to the complexity evolution
history of our events (Figure 5, right), we restrict ourselves to those events
that were observed to have an $Fr/F^{-}$ configuration at the inner
spacecraft, and neglect $F^{+}$, $E$, and $C_{x}$ types. We consider only
events whose initial magnetic structure is consistent with that of a closed,
twisted FR rooted at the Sun as they are more likely to have had extended BDEs
at the inner spacecraft according to the standard interpretation of BDEs
within ICMEs (e.g. Zurbuchen & Richardson, 2006). This is done to ensure that
the BDE properties observed at 1 au are actually the result of the evolution
history between the inner and outer observing spacecraft, and not the result
of evolution closer to the Sun. We report 11 events that change complexity and
7 that do not change complexity. Of those that change complexity, only 1 (9%)
exhibit BDEs for more than a half of the FR/ME duration: $\sim 45$% show
partial BDEs, and $\sim 45$% no BDEs whatsoever. Among the events that do not
change their complexity, 3 (43%) exhibit throughout or extended BDEs, 1 (14%)
has partial BDEs, and 3 (43%) have no BDEs. We note that of these 3 events
(i.e. events 16, 18, 22), 2 exhibit prolonged unidirectional electron beams
compatible with magnetic field lines open at one end and possibly originated
by reconnection occurring close to the Sun (Gosling et al., 1995; Crooker et
al., 2002), i.e. not by interplanetary sources. Only one event (event 18)
among those that do not change complexity exhibit a highly-variable PAD
including unidirectional and isotropic electron flows, potentially reflecting
local and extended sources of reconnection.

Overall, prolonged BDEs are found to be more common among events that do not
change complexity, i.e. that likely did not interact with other interplanetary
structures. However, a similar fraction of events that change and that do not
change complexity lack BDE signatures (43% to 45%). Interactions with the HCS
seem to be the most disruptive condition for BDEs, consistent with a scenario
of extensive magnetic reconnection taking place between the ICME and the
interplanetary magnetic field near the HCS, as discussed for example by
Winslow et al. (2016). In conclusion, our results indicate that the duration
of BDEs within FR/ME structures at the outer observing spacecraft does reflect
the evolution history of ICMEs to some extent, but identifying complexity
changes from these data products alone, even when in combination with magnetic
field data, would be complicated by the large fraction of events lacking BDEs
among both changed and unchanged populations.

####  4.3.2 ICME Speed and Magnetic Field at 1 au

We further investigate whether the complexity evolution history affects the
internal properties at 1 au for a given ICME population. We focus on the
relationship between the ICME speeds and magnetic fields at 1 au, which has
been previously investigated because of its potential for the forecasting of
geomagnetic storms (Gonzalez et al., 1998; Owens & Cargill, 2002, 2004; Owens
et al., 2005). Compared to previous studies, the novelty of our analysis lies
in the investigation of ICME internal properties not only with respect to
their magnetic field configuration, e.g. presence or absence of smooth
magnetic field rotations within MEs, but also with respect to their complexity
evolution and interaction histories.

Figure 6: (a) FR/ME category and (b) complexity changes $\Delta\mathbb{C}$ as
a function of the average speed and magnetic fields detected within ME and FR
structures at 1 au. Different markers are used to indicate different pairs of
spacecraft in radial alignment.

Figure 6 (a) shows the relationship between the mean speeds and magnetic
fields observed at 1 au, by FR/ME category. $Fr/F^{-}$ and $C_{x}$ events
(i.e. for which we have 15 and 7 events, respectively) have average speed
values of 404 km s-1 and 431 km s-1, respectively. Yet, the application of the
Welch’s t-test reveals no statistical significance in the mean speed of
complex ($C_{x}$) and well-ordered ($Fr/F^{-}$) events, as indicated by the
p-value of 0.36. The mean magnetic field observed at 1 au for both subsets is
10.5 nT. We also report modest correlations between the ICME speed and
magnetic field at 1 au for both $Fr/F^{-}$ and $C_{x}$ categories (Pearson’s
correlation coefficients, $PCC=0.48$ and $0.28$, respectively). These values
are comparable to the correlation coefficients reported by Owens et al. (2005)
for MC and non-MC ICMEs.

Figure 6 (b) shows the relationship between the mean speeds and magnetic
fields observed at 1 au, this time categorized by the complexity evolution
history of ICMEs. In this case, we have 9 events that do not change
complexity, and 19 that do change complexity, and the average speed observed
at 1 au is 393 km s-1 and 436 km s-1 for unchanged and changed events,
respectively. The mean magnetic field observed at 1 au is 9.6 nT and 11.3 nT
for unchanged and changed events, respectively. For these events, we note that
similar trends in the mean magnetic field strengths are also observed at the
inner observing spacecraft, where average values for unchanged and changed
events are 36.4 nT and 60.1 nT at MESSENGER, and 15.3 nT and 19.4 nT at VEx,
respectively. However, the Welch’s t-test reveals there is no statistically
significant difference in the mean values between the two groups at 1 au, as
indicated by the p-values of 0.17 and 0.22 for the speed and magnetic field,
respectively. On the other hand, grouping events by their complexity evolution
history reveals a high correlation between the ICME speed and magnetic field
at 1 au for events that do not change their complexity ($PCC=0.70$). The
p-value is 0.04, indicating a 4% probability for an uncorrelated system to
produce datasets that have a $PCC$ at least as high as the one computed from
the observed dataset of unchanged events. Further testing on the specific
dataset considered reveals that by randomly picking 9 events among the 28
observed at 1 au (over 1 million realizations), there is an $\sim 8$%
probability to produce datasets that have a $PCC$ at least as high as the one
computed from the observed dataset of unchanged events. Overall, this
indicates a $\sim 92$% confidence level that the speed and magnetic field
within ICMEs that do not change their complexity are actually correlated. A
correlation is not found for events that change their complexity ($PCC=0.07$,
with p-value of 0.79).

The high correlation between the ICME speed and magnetic field at 1 au
observed for unchanged events, and the lack of correlation found for changed
events, suggest that interaction with other solar wind structures (and, in
turn, complexity changes) randomize the ICME internal properties, which, for
unchanged events, appear relatively ordered. This may have important
implications for space weather forecasting efforts, and for the usefulness of
in situ magnetic field monitors located along the Sun–Earth line at inner
heliocentric distances, as further discussed in Section 5.

####  4.3.3 ICME Magnetic Field Scaling with Heliocentric Distance

Another quantity that has been extensively investigated in previous studies is
the scaling of the ICME magnetic field with heliocentric distance, which
provides information on ICME global expansion (e.g. Démoulin & Dasso, 2009;
Lugaz et al., 2020a). Estimates of the decay of the average magnetic field
inside MEs range between $-1.30\pm 0.09$ and $-1.95\pm 0.19$ (e.g. Liu et al.,
2005; Wang et al., 2005; Leitner et al., 2007; Gulisano et al., 2010; Winslow
et al., 2015; Davies et al., 2021), while estimates of the decay of the
maximum magnetic field inside MEs range between $-1.73$ and $-1.89\pm 0.14$
(e.g. Farrugia et al., 2005; Winslow et al., 2015), with variations across
different studied being the result of different ICME identification criteria
and different ranges of heliocentric distances considered (Gulisano et al.,
2010). All of the aforementioned studies considered statistical sets of ICMEs
observed at different heliocentric distances, but not necessarily in radial
alignment at multiple spacecraft. Salman et al. (2020) did perform a fitting
of the ME maximum magnetic field at different heliocentric distances for ICMEs
observed at multiple spacecraft, finding a decay index of $-1.91$, but this
value was calculated treating observations of the same ICME as independent
from one another, and does not take into account specific trends underwent by
individual events. More recently, Lugaz et al. (2020a) estimated the average
magnetic field decay within MEs by combining estimates obtained from
individual ICMEs observed at multiple spacecraft in radial alignment. Using a
set of 42 events taken from the catalog by Salman et al. (2020), they reported
decay indices of $-1.81\pm 0.84$ and $-1.91\pm 0.85$ for the maximum and
average ME magnetic field, respectively. Considering a set of 18 FR ICMEs
observed by radially-aligned spacecraft, Good et al. (2019) reported a scaling
of the magnetic field along FR axes (as estimated by performing LFF fits to
the observed FR magnetic structures) equal to $-1.34\pm 0.71$.

Figure 7: Complexity change $\Delta\mathbb{C}$ as a function of the radial
evolution of the maximum (left) and mean (right) magnetic field within ME and
FR structures. The points connected by a dotted line link observations of the
same event at two spacecraft. Different markers are used to indicate different
pairs of spacecraft in radial alignment.

Similarly to Good et al. (2019) and Lugaz et al. (2020b), we estimate the
decay index of the average and maximum magnetic field within MEs with
heliocentric distance by taking the average of the decay indices computed for
individual events (Figure 7). We provide the standard deviation as a measure
of the uncertainty. We find that the mean magnetic field scales as $-1.81\pm
0.78$ and $-1.66\pm 0.63$ for events that change and do not change their
complexity, respectively. The maximum magnetic field scales as $-1.84\pm 0.85$
and $-1.82\pm 0.62$ for events that change and do not change their complexity,
respectively. Overall, these numbers are consistent with previous studies and
do not highlight any significant difference in the typical radial scaling of
the magnetic field for events with different evolution histories. We further
apply the Welch’s t-test to determine if differences between events that
change and that do not change complexity during propagation are statistically
significant. We find p-values of 0.62 and 0.92 for the mean and maximum
magnetic field slopes, indicating no statistically significant difference in
the mean values between the two groups. Yet, we note that the decay indices of
events that change their complexity during propagation are characterized by
larger standard deviations, indicating distributions more broadly-scattered
around the mean compared to those of unchanged events. This result is
consistent with the interpretation of a randomization of the ICME properties
induced by interactions with other solar wind structures, as discussed in
Section 4.3.2.

####  4.3.4 FR-to-ME Duration Scaling with Heliocentric Distance

Finally, we investigate the relationship between ME and FR boundaries in terms
of duration and its evolution with heliocentric distance. To the best of our
knowledge, this aspect of ICME evolution has never been investigated before,
and it may provide valuable information on magnetic erosion, occurring when
magnetic reconnection between FR-contained plasma and the surrounding
interplanetary magnetic field “peels away” the FR outer layers (Dasso et al.,
2006; Ruffenach et al., 2012). Magnetic erosion affects $\sim$30% of the ICMEs
at 1 au, and it can be most reliably identified from the presence of
reconnection exhausts and bifurcated current sheets near FR boundaries
(Ruffenach et al., 2015). Erosion also implies large-scale magnetic field
topological changes occurring within ICMEs (Ruffenach et al., 2012; Pal et
al., 2021), and yet, the full breadth of effects on magnetic field
configurations within MEs and FRs therein remains unclear. In the following,
we investigate the relationship between ME and FR duration as a potential
proxy for magnetic erosion.

Figure 8 shows the radial evolution of the ratio between the FR duration
($\Delta t_{\mathrm{FR}}$) and ME duration ($\Delta t_{\mathrm{ME}}$) for the
events exhibiting an FR magnetic structure (i.e. $Fr$, $F^{-}$, $F^{+}$
configurations) at least at one observing spacecraft. Overall, 27 ICMEs
exhibit an FR structure at least at one observing spacecraft. We find that 18
of them ($\sim 58\%$ of the 31 ICMEs considered in total) exhibit an FR
structure that is shorter than the whole ME structure at least at one
observing spacecraft. Among the 62 detected ICME signatures (i.e. two per
ICME), 22 ($\sim 25\%$) have this characteristic. At 1 au, the percentage of
signatures exhibiting an FR-to-ME duration ratio below 1 is $\sim 46\%$. On
average, the ratio between the FR and ME duration decreases with heliocentric
distance from 0.96 at MESSENGER (number of observations: 11), to 0.88 at VEx
(number of observations: 13), and 0.79 at 1 au (number of observations: 18),
indicating FRs tend to shorten with respect to MEs during propagation. This
decreasing trend is also reflected in the minimum values recorded at each
heliocentric distance, which decreases from 0.65 at MESSENGER, to 0.52 at VEx
and to 0.32 at 1 au. We note that while identifying ME and FR boundaries as
described in Section 3, we tried to treat the magnetic field data at 1 au in
an as consistent manner as possible to the magnetic field data at inner
distances, in order to minimize the bias due to the additional availability of
plasma information at 1 au compared to MESSENGER and VEx data. The behavior of
individual events varies, but except for one event (number 25), all ICMEs are
found to either decrease or maintain this ratio approximately constant (within
$\pm 10\%$), regardless of their complexity evolution history. Moreover, we
note that events that change their complexity are consistently able to reach
shorter minimum FR-to-ME duration ratios than events that do not change their
complexity, at all heliocentric distances considered. Overall, our findings
indicate that FR shortening is ubiquitous and it affects both ICMEs that do
change as well as those that do not change their magnetic complexity during
propagation.

Figure 8: Complexity change $\Delta\mathbb{C}$ as a function of the radial
evolution of the ratio between the FR duration ($\Delta t_{\mathrm{FR}}$) and
ME duration ($\Delta t_{\mathrm{ME}}$) for the events exhibiting $F$-type
magnetic structures at a given observing spacecraft. The dotted lines connect
observations of the same event at two spacecraft, while points not connected
by lines indicate ICMEs observed as $F$ types only at one observing
spacecraft.

The investigation of the relationship between the observed FR-to-ME
shortening, magnetic erosion, and suprathermal electron PADs discussed in
Section 4.3.1 goes beyond the scope of this work, and is left for future
studies. Nevertheless, the fact that FRs shorten compared to MEs during
propagation even for events that do not change their complexity may indicate
that magnetic reconnection at the FR edges is not necessarily inducing
complexity changes, and may naturally happen during propagation irrespective
of the complexity evolution and interaction history of a particular ICME.

We also acknowledge two major limitations for statistical investigations of
FR-to-ME shrinking and magnetic erosion phenomena from multi-spacecraft ICME
observations based on existing data at different heliocentric distances.
First, the lack of information on the plasma conditions (e.g. bulk properties
as well as particle PADs), together with the numerous data gaps and bow shock
and magnetospheric crossings affecting MAG data at MESSENGER and VEx,
complicate the identification of ME front and rear boundaries at inner
heliocentric distances (see e.g. Lugaz et al., 2020b, for a detailed analysis
of an ICME sheath/ME boundary at MESSENGER). Second, high-cadence plasma data
is also critical to identify signatures of magnetic reconnection (e.g. the
presence of current sheets and Alfvénic fluctuations), which is likely the
prime physical phenomenon responsible for the observed FR shortening. Such
data is also currently missing for most ICME events within 1 au. At the time
of writing, the arrival of new data from e.g., Parker Solar Probe (Fox et al.,
2016), Solar Orbiter (Müller et al., 2020) and BepiColombo (Benkhoff et al.,
2010) is already providing essential additions to pre-existing datasets (Möstl
et al., 2021). Yet, current solar minimum conditions may require a number of
years before a sufficient number of ICME magnetic structures are observed in
radial alignment with a statistically-significant coverage of a broad spectrum
of heliocentric distance combinations (Möstl et al., 2020).

##  5 Summary and Conclusions

In this paper, we performed the first statistical analysis of magnetic
complexity changes occurring within ICMEs observed by multiple inner
heliospheric spacecraft in radial alignment. Our aim was to answer the
following main open questions: (1) How frequently do ICMEs undergo magnetic
complexity changes during propagation through interplanetary space? (2) What
are the causes of such changes? (3) Do the in situ properties of ICMEs differ
depending on whether they exhibit complexity changes during propagation? To
address these questions, we considered multi-spacecraft observations of 31
ICMEs from MESSENGER, VEx, ACE, and the STEREO spacecraft between December
2008 and February 2014 during periods of radial alignment. By analyzing the
changes in the ICME magnetic field properties between the inner and outer
observing spacecraft, we were able to identify magnetic complexity changes
which manifested as fundamental alterations of the magnetic configuration, or
as significant re-orientations of the structure. From the inspection of plasma
and suprathermal electron PAD data at 1 au, and simulations of the ambient
solar wind performed with the WSA-ENLIL model, we reconstructed the
propagation scenario for each of the 31 events, and identified the decisive
factors determining their evolution between the inner and outer observing
spacecraft. The main results can be summarized as follows:

  1. 1.

We found that, on average, ICMEs tend to increase their magnetic complexity
with radial distance. MEs with $Fr/F^{-}$ configurations are less frequently
observed at 1 au ($\sim 53\%$) than they are at Mercury ($\sim 67\%$), while
complex $C_{x}$ types appear more frequently at 1 au ($\sim 25\%$) than at
Mercury ($\sim 13\%$). We stress that the detection of an FR configuration at
1 au is not sufficient to conclude that a given ICME did not undergo any
complexity change earlier during propagation. In fact, many FRs at 1 au are
found to have gone through significant changes at closer heliocentric
distances. Overall, results indicated that roughly $42\%$ of the events
undergo drastic alterations of their magnetic configuration during
propagation, and $63$% exhibit significant changes in their magnetic
complexity, including major rotations of FR structures. Magnetic complexity
changes within ICMEs therefore occur more frequently than previously
estimated, and they in fact affect the majority of ICMEs between Mercury and 1
au.

  2. 2.

Based on our results, ICMEs tend to preserve their magnetic topology and
orientation only over short spatial and temporal scales, i.e. when observed in
close radial alignment ($\Delta\phi<15^{\circ}$) and at radial separations
$\Delta r\leq 0.4$ au. At such separations, the fraction of ICMEs preserving
their complexity is $\sim 90\%$. This fraction drops to $\sim 29\%$ for
observations at $\Delta r>0.4$ au. Similar fractions are also observed by
spacecraft in perfect radial alignment ($\Delta\phi<5^{\circ}$). These results
suggests that propagation (“nurture”) effects are likely the main cause of
complexity changes observed by spacecraft separated by
$\Delta\phi<15^{\circ}$. Observations at $\Delta\phi>15^{\circ}$ detected
complexity changes for all events, regardless of the spacecraft radial
separation. In principle, this result could be interpreted as a combination of
different factors: pre-existing inhomogeneities in the internal structure of
ICMEs (“nature” effects), variable ambient solar wind conditions through which
different parts of ICMEs propagate, and ultimately, changes during propagation
due to interaction with other structures (both “nurture” effects).

However, the majority of complexity changes involving significant re-
orientations of ICME FRs were detected by spacecraft separated by less than
$15^{\circ}$ in longitude, indicating that magnetic complexity changes
identified through the application of Condition B (previously defined in
Section 3.1.2) cannot be explained in terms of large-scale geometric effects
due to spacecraft crossings through different parts of stretched FRs. In most
of the cases considered, we also found that fundamental alterations to FR/ME
structures as defined by Condition A (previously defined in Section 3.1.1)
were associated with different kinds of interactions, suggesting the
relatively large angular separations among the observing spacecraft was not
the primary cause of such changes. Overall, these arguments suggest that for
the majority of the events considered, the results reflect actual magnetic
complexity changes affecting ICMEs, rather than geometrical effects due to the
particular spacecraft trajectories along a given structure. Additionally,
despite the caveat of non-negligible radial separations affecting our
observations, we found a $\Delta\phi\sim 15^{\circ}$ breaking point which
likely provides a lower limit to the characteristic scale of ICME magnetic
coherence, and it supports previous estimates set to $17^{\circ}-26^{\circ}$
and $14^{\circ}-20^{\circ}$ by Owens (2020) and Lugaz et al. (2018) based on
theoretical and observational arguments, respectively. Reconstructions of the
inclination of magnetic flux rope structures using a LFF fitting technique
over a subset of events considered in this study also indicate that the
aforementioned results apply to low-inclination flux ropes. Establishing
possible effects of inclination on ICME magnetic complexity changes and
estimates of ICME magnetic coherence will require the consideration of highly-
inclined ICME magnetic flux ropes by future studies.

  3. 3.

We found that ICME magnetic complexity changes are tightly related to their
interaction with solar wind structures in interplanetary space. Although such
kind of interactions are not always inducing a detectable change in ICME
complexity, they do increase the probability for ICMEs to undergo a complexity
change. On the one hand, most ICMEs that preserved their magnetic
configuration during propagation ($\sim 90\%$) either did not interact with
any interplanetary structure, or only interacted with a single structure. On
the other hand, events that changed their magnetic complexity were more likely
to have interacted with two or more structures (in $\sim 45\%$ of the cases
considered). We also report that $C_{x}$-class, complex MEs are always
associated with ICME–solar wind interactions, particularly with the HCS (in
$\sim 57\%$ of the cases).

  4. 4.

At 1 au, we were able to identify prolonged BDEs within $\sim 25\%$ of the MEs
characterized by a twisted flux-rope configuration, while prolonged BDEs are
completely absent within $C_{x}$ types. This supports the interpretation of
$Fr/F^{-}$ types often being characterised by closed magnetic loops rooted at
the Sun, while $C_{x}$ types may be fundamentally different structures likely
generated through extensive magnetic reconfiguration with the surroundings.
Prolonged BDEs are also more commonly found within events that do not change
complexity during propagation (in 43% of the cases compared to 9% of changed
events). Our results suggest that the duration of BDE flows detected from
suprathermal electron PAD data at the outer observing spacecraft do reflect
the evolution history of ICMEs, but considered alone, they would not be
sufficient to identify magnetic complexity changes. Additionally, the low
percentage of prolonged BDEs even within the events showing no complexity
change indicates there might be in fact even more complexity changes underwent
at closer heliocentric distances, which we were unable to quantify due to the
lack of PAD data closer to the Sun.

  5. 5.

We reported a significant correlation ($PCC=0.70$) between the mean speed and
magnetic field detected at 1 au for ICMEs that preserved their magnetic
complexity during propagation. This correlation is lost in the case of events
that undergo complexity changes ($PCC=0.07$), indicating the interaction with
solar wind structures likely randomizes the average ICME internal properties,
making them hardly predictable.

The correlation observed for unchanged events revives previous attempts to
apply speed-magnetic field correlations to space weather forecasting (Owens et
al., 2005), and it may have important implications for the usefulness of in
situ magnetic field monitors located along the Sun–Earth line at inner
heliocentric distances. The achievement of more accurate and timely
predictions of the arrival time and location of SIRs and the HCS by solar wind
models, particularly in the Earth-facing hemisphere, is being boosted by the
launch of new heliospheric missions, the availability of increased numerical
capabilities, and the application of novel techniques such as data
assimilation, machine learning, and ensemble modeling (e.g. Gressl et al.,
2014; Reiss et al., 2019, 2020; Szabo et al., 2020; Bailey et al., 2021; Lang
et al., 2021; Samara et al., 2021). Such methods can allow prompt
identification of ICMEs that are going to propagate through a quiet solar wind
environment, with computationally-fast ICME propagation models such as drag-
based models that can further provide reliable predictions of the ejecta speed
at 1 au (Čalogović et al., 2021). Our results suggest that such a combination
of tools may therefore be sufficient to provide a reliable estimate of the
ejecta magnetic field at 1 au for ICMEs propagating through a quiet
environment. Moreover, by our definition (Section 3.1), unchanged events do
not undergo significant restructuring nor rotation of their internal magnetic
structure during propagation through interplanetary space. In the near future,
remote-sensing observations of CME magnetic fields during early propagation
phases (such as coronal magnetic field measurements provided by DKIST; Rast et
al., 2021) may allow accurate extrapolations of the ICME magnetic field
orientation to 1 au, at least for those events expected not to interact with
any structure during propagation to a given impact location. If used in
combination, these two approaches may bring significant improvement to
prediction capabilities not only of the ICME magnetic field magnitude at the
impact location, but also of its orientation (including the most geo-effective
$B_{z}$ magnetic field component). Similarly, early measurements of the ICME
magnetic field orientation performed in situ by spacecraft orbiting upstream
of Earth as close as 0.3 au from the Sun may provide accurate predictions of
their magnetic field direction at Earth. In turn, our results set a caveat on
the use of inner heliospheric observations upstream of the Earth to predict
the geoeffectiveness of ICMEs in the presence of large interplanetary
structures in the ICME propagation space. The scenario is more complicated at
times when solar wind structures are present in the ICME transit path from the
Sun to 1 au. In such cases, neither estimates of the speed at 1 au, nor situ
magnetic field data upstream of the Earth would be sufficient to accurately
estimate the magnetic field strength and orientation at the impact location.
Our results provide a statistical confirmation to earlier suggestions by
Winslow et al. (2016) based on a single ICME case study.

  6. 6.

On average, ICMEs with different evolution histories are found to behave
similarly when considering the scaling of the FR/ME magnetic field with
heliocentric distance. However, we reported a wider variety of magnetic field
radial behaviors among events that changed their magnetic complexity,
supporting the interpretation that interactions with other interplanetary
structures drive major changes to the internal ICME properties, randomizing
their characteristics and complicating their prediction at given target
locations. Additionally, FR structures most often shorten with respect to MEs
during propagation from Mercury to 1 au, regardless of whether a particular
ICME changes or does not change its magnetic configuration. We interpret this
result as an indication that magnetic reconnection, and particularly magnetic
erosion at the front and rear of MEs, does not necessarily induces complexity
changes. In fact, FR erosion likely naturally happen during propagation
irrespective of the complexity evolution and interaction history of a
particular ICME.

The consideration of a statistical set of ICMEs allowed us to generalize
previous results by Winslow et al. (2016, 2021b) and to draw, for the first
time, conclusions on the frequency, causes, and effects of magnetic complexity
changes on ICMEs. Most importantly, such an investigation provided evidence of
the ubiquitousness of complexity changes affecting ICMEs propagating
throughout the inner heliosphere, and allowed us to identify interactions with
other large-scale solar wind structures as their primary drivers. This result
places magnetic complexity changes as a consequence of ICME interactions with
large-scale interplanetary structures in their surroundings, rather than as
intrinsic to ICME evolution during propagation.

The details of how magnetic complexity changes propagate throughout ICME
magnetic structures, as well as of the physical mechanisms mediating such
changes, remain open questions to be addressed in future studies. In this
respect, despite the observational limitations affecting past missions (e.g.
the uneven and inhomogenous datasets available at different heliocentric
distances, and the low number of radially-aligned observations of rare ME
configurations, such as $F^{+}$ and $E$ categories), new observational sources
will help unlock additional areas of investigation in the future. Over the
short and medium term, the availability of both high-cadence magnetic field
and plasma data from recently-launched heliospheric and planetary missions,
such as Parker Solar Probe, Solar Orbiter, and BepiColombo, will open up new
windows of opportunity for dedicated studies on the effect of interactions on
ICME magnetic structures and their large-scale topology and connectivity,
especially for selected case studies that will be observed within the current
solar cycle. In the longer-term perspective of achieving more comprehensive
and statistically-valid results regarding the evolution of ICMEs throughout
the inner heliosphere, e.g. throughout the exploration of the full parameter
space of spacecraft radial distances and separations, we also stress the
importance of initiatives aimed at increasing the number of missions equipped
with magnetometers and plasma instruments orbiting at different distances from
the Sun.

Support for this work was provided by NASA grant 80NSSC19K0914. C.S.
acknowledges the NASA Living With a Star Jack Eddy Postdoctoral Fellowship
Program, administered by UCAR’s Cooperative Programs for the Advancement of
Earth System Science (CPAESS) under award no. NNX16AK22G. R.M.W. and E.E.D
acknowledge support from NASA grant 80NSSC19K0914, and R.M.W. also
acknowledges partial support from the NASA STEREO TRANSITION grant. N.L.
acknowledges support from NASA grants 80NSSC20K0431 and 80NSSC20K0700. All the
data analyzed in this study are publicly available. ACE data have been
obtained from the Space Physics Data Facility’s Coordinated Data Analysis Web
(https://cdaweb.gsfc.nasa.gov/) and the ACE Science Center
(http://www.srl.caltech.edu/ACE/ASC/). STEREO data have been downloaded from
the STEREO Data Server at UCLA (https://stereo-dev.epss.ucla.edu/l1_data/),
the Space Physics Data Facility’s Coordinated Data Analysis Web
(https://cdaweb.gsfc.nasa.gov/), and the IRAP SWEA server
(http://stereo.irap.omp.eu/CEF/PAD/). MESSENGER data have been obtained from
the Space Physics Data Facility’s Coordinated Data Analysis Web
(https://cdaweb.gsfc.nasa.gov/), while Venus Express data are available on the
Planetary Science Archive (PSA) at ESA (https://archives.esac.esa.int/psa/).

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