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

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°; F⁻, with maximum rotation in any magnetic component smaller than 120°; F⁺, with maximum rotation in any magnetic component larger than 240°; 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 is shown in Figure 1. Such a classification allows for 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, 2002b; 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° 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° (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-FR 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.

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 reorientations (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-α 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 ±13° and ±30° 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 ±45° in latitude and/or ±60° 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 ±45° in latitude and/or ±60° 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 reorientations 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.

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 separations 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 that 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.

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In more detail, roughly 82% (nine out of 11) of the ICMEs that preserve their magnetic complexity are observed by spacecraft in close radial alignment (Δϕ < 15°) and at radial separations Δr ≤ 0.4 au. At such small longitudinal and radial separations, they make up 90% of the ICMEs (10 out of 11 events). The remaining ∼18% of unchanged events (two out of 11) are observed in close radial alignment but at larger radial separations than 0.4 au. In this region, however, 71% (five out of seven) of the ICMEs do change their magnetic complexity, while only 29% (two out of seven) 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 preexisting differences in the internal properties within different ME regions. Oppositely, all of the events observed at smaller radial separations (Δr ≤ 0.4 au) but at larger angular separations (Δϕ > 15°) exhibit complexity changes, possibly resulting from a combination of initial or preexisting 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 (Δϕ > 15°).

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 Δr being typically taken at larger distances from the Sun (i.e., at Venus and 1 au) compared to observations at larger Δr (i.e., at Mercury and 1 au). However, as reported by Scolini et al. (2021), for a given Δr, a higher probability of developing complexity changes is expected for ICMEs observed by an inner spacecraft located within ∼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 Δr 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°, 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 reorientations 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 Δϕ significantly smaller than the ICME angular width (estimated to be around ∼40°–60° 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° of angular separation that exhibited complexity changes as defined by Condition A. We found that out of 12 events, four (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 eight 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 θ₀ values in Table 2). The determination of the inclination of the remaining magnetic structures was complicated by the lack of clear FR 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 FRs, whose signatures appear to be less affected by trajectory effects than highly inclined FRs (e.g., Kilpua et al. 2009; Davies et al. 2021b). 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 Δϕ ∼ 15° 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°–26° reported by Owens 2020, and 14°–20° 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°. We also argue that if multipoint 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 nine events observed in perfect alignment, i.e., with angular separation <5°, we report that six of them (∼67%) did not change their FR/ME class, while only three (∼33%) did. These values validate previous conclusions by Scolini et al. (2021) based on the results from numerical simulations (reporting a 69%–54% probability for ICMEs to maintain their FR class, and a 31%–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.

Since the presence of bidirectional 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 ∼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 ∼100 eV, i.e., at 1716.84, 1056.95, 650.70, 400.60, 246.62, and 151.83 eV. At STEREO, we compared the results obtained by integrating over all channels above ∼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° and 180° 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.

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 throughout 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 seven 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 (three 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 that were 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.

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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 seven that do not change complexity. Of those that change complexity, only one (9%) exhibited BDEs for more than a half of the FR/ME duration: ∼45% showed partial BDEs, and ∼45% showed no BDEs whatsoever. Among the events that do not change their complexity, three (43%) exhibit throughout or extended BDEs, one (14%) has partial BDEs, and three (43%) have no BDEs. We note that of these three events (i.e., events 16, 18, and 22), two 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 exhibits 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%–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.

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., the presence or absence of smooth magnetic field rotations within MEs, but also with respect to their complexity evolution and interaction histories.

Figure 6(a) shows the relationship between the mean speeds and magnetic fields observed at 1 au, by the FR/ME category. Fr/F⁻ and C_x events (i.e., for which we have 15 and seven 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.

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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 nine events that do not change complexity, and 19 that do change complexity, and the average speeds observed at 1 au are 393 km s⁻¹ and 436 km s⁻¹ for unchanged and changed events, respectively. The mean magnetic fields observed at 1 au are 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 data sets that have a PCC at least as high as the one computed from the observed data set of unchanged events. Further testing on the specific data set considered reveals that by randomly picking nine events among the 28 observed at 1 au (over 1 million realizations), there is an ∼8% probability of producing data sets that have a PCC at least as high as the one computed from the observed data set of unchanged events. Overall, this indicates a ∼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) randomizes 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.

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 ± 0.09 and −1.95 ± 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. 2021a), while estimates of the decay of the maximum magnetic field inside MEs range between −1.73 and −1.89 ± 0.14 (e.g., Farrugia et al. 2005; Winslow et al. 2015), with variations across different studies 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 ± 0.84 and −1.91 ± 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 ± 0.71.

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 ± 0.78 and −1.66 ± 0.63 for events that change and do not change their complexity, respectively. The maximum magnetic field scales as −1.84 ± 0.85 and −1.82 ± 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.

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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 ∼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 (Δt_FR) and ME duration (Δt_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 (∼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 (∼25%) have this characteristic. At 1 au, the percentage of signatures exhibiting an FR-to-ME duration ratio below 1 is ∼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 that 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 a 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 as approximately constant (within ±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.

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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 multispacecraft 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 identifying 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 preexisting data sets (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).