On the Mesoscale Structure of Coronal Mass Ejections at Mercury's Orbit: BepiColombo and Parker Solar Probe Observations

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

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

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

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

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

Given the high speed of the 2022 February 15 CME as inferred from remote-sensing observations (see Section 2.2), we can expect a relatively rapid propagation to ∼0.35 au, i.e., the heliocentric distance of Bepi and Parker at the time of the event (see Figure 1). The two probes were located ∼15° to the east and ∼30° to the south of the CME nose trajectory that was estimated from GCS fitting. By inspecting magnetic field measurements from the Mercury Planetary Orbiter Magnetometer (MPO-MAG; Heyner et al. 2021) on board Bepi and the Fluxgate Magnetometer part of the FIELDS (Bale et al. 2016) investigation on board Parker—both data sets are shown in Figure 4—we find signatures of a solar wind transient starting on February 16 around 07:00 UT (approximate average time between the two spacecraft). This yields a travel time of ∼9.25 hr, with an average transit speed of 1620 km s⁻¹. Specifically, we observe an abrupt increase in the magnetic field magnitude at 06:25 UT in Bepi data and 07:25 UT in Parker data (marked with vertical gray lines in Figure 4), indicating the passage of a CME-driven shock; by considering the exact shock arrival times and positions for each spacecraft, we obtain average transit speeds of 1672 km s⁻¹ at Bepi and 1606 km s⁻¹ at Parker. The identification of this feature as a fast-forward shock can be confirmed using plasma data from Parker (presented in detail in Section 3.2); hence, it is reasonable to assume that the same holds true for Bepi.

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After a period (∼8.5 hr) characterized by highly fluctuating magnetic field vectors corresponding to the turbulent sheath region that usually follows CME-driven shocks, around 15:30 UT (approximate average time between the two spacecraft), both probes observed enhanced magnetic field magnitudes, together with smoother profiles of the field components, which can be attributed to the passage of the CME ejecta (highlighted as gray shaded areas in Figure 4). This corresponds to a travel time of ∼17.67 hr, with an average transit speed of 823 km s⁻¹. Specifically, the leading edge of this structure is identified on February 16 at 15:41 UT for Bepi and 15:18 UT for Parker, resulting in average ejecta transit speeds of 798 and 861 km s⁻¹, respectively. We note that Parker observed the ejecta leading edge slightly earlier despite being ∼0.02 au farther from the Sun than Bepi at the time (see Table 1). This suggests that Parker may have been somewhat closer to the CME nose given its higher heliocentric latitude and the CME propagation direction being mainly above the ecliptic, or that the probes encountered a highly distorted CME front. At both spacecraft, the magnetic field vectors rotated smoothly from east to west and pointed mostly southward throughout the structure, suggesting approximately an east–southwest (right-handed) flux rope type from visual inspection (e.g., Bothmer & Schwenn 1998; Palmerio et al. 2018). While at Bepi, the entire identified CME ejecta interval was characterized by flux-rope-like signatures, at Parker, the trailing portion of the structure featured more turbulent magnetic fields (especially in the north–south component), suggesting that the flux rope and, more generally, the ejecta boundaries may not coincide (e.g. Richardson & Cane 2010; Kilpua et al. 2013; more details on this matter are provided in Section 3.2). For simplicity and to avoid confusion, we shall refer henceforth to the flux rope interval as the "magnetic cloud" (e.g., Burlaga et al. 1981) and to the whole CME ejecta as the "magnetic obstacle" (e.g., Nieves-Chinchilla et al. 2019).

We also investigate the level of fluctuation in the interplanetary magnetic field by computing the rms of the field vector, shown in Figure 4, using

$\begin{eqnarray}&&{B}_{\mathrm{rms}}=\sqrt{\displaystyle \sum _{i=R,T,N}\displaystyle \frac{{({B}_{i}-\langle {B}_{i}\rangle )}^{2}}{n}},\end{eqnarray} \tag{ 1 }$

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

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

First of all, we note that the abrupt magnetic field jump that we had identified as the CME-driven shock in Section 3.1 (vertical gray line in Figure 5) is indeed accompanied by a prominent rise in the solar wind bulk speed (from ∼550 to ∼850 km s⁻¹), a moderate climb in the electron density and temperature, as well as an intensification of suprathermal electron fluxes (the electron flux enhancements observed prior to the shock arrival are due to the strong particle event associated with this eruption analyzed by, e.g., Giacalone et al. 2023; Khoo et al. 2024). The following sheath region is characterized by highly fluctuating magnetic fields, almost-constant speeds, a declining temperature profile, and a plateauing density trend except for a high-density feature close to its trailing portion. The density peak at the back of the sheath is reminiscent of a piled-up compression (PUC) region that forms ahead of the nose of a driver (in this case, the CME ejecta), often due to its large expansion speed, which is known to usually be higher close to the Sun and then to decrease gradually as the CME travels through interplanetary space (e.g., Farrugia et al. 2008; Das et al. 2011).

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

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

Finally, we note a structure immediately following the ejecta characterized by a low magnetic field magnitude as well as enhanced speed, density, and plasma beta (hatched area in Figure 5). Additionally, both the longitudinal component of the magnetic field and the suprathermal electron PAD display a ∼180° reversal after the passage of this feature, compared to the pre-CME ambient wind. The structure shows all the typical characteristics of a heliospheric plasma sheet (HPS) crossing (e.g., Crooker et al. 2004; Lavraud et al. 2020), i.e., the passage of a high-density and high-beta region that surrounds the heliospheric current sheet. We tentatively associate the HPS at Parker (starting at ∼17:00 UT on February 17) with a similar structure (featuring a low magnetic field magnitude as well as a reversal of the longitudinal component of the field) detected at Bepi approximately 1 day later (starting at ∼17:00 UT on February 18; see Figure 4), i.e., well after the passage of the 2022 February 15 CME. Hence, the (spatial and temporal) proximity of the HPS to the CME at Parker—and the resulting interaction between the two—may explain the presence of more ambiguous magnetic cloud and magnetic obstacle boundaries at Parker, which are, on the other hand, not found at Bepi.

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

When investigating the properties of interplanetary shocks, the first step is to define the plasma states upstream and downstream of the shock. In this work, the criteria for determining the upstream and downstream conditions are adopted from those used in the Heliospheric Shock Database ²¹ (Kilpua et al. 2015) and consist of averaging the quantities under consideration over 8 minute intervals that end 1 minute before and start 2 minutes after the identified shock passage time, i.e.,

$\begin{eqnarray}&&\left\{\begin{array}{l}{t}_{u}=[{t}_{\mathrm{shock}}-9\,\mathrm{minutes},\,{t}_{\mathrm{shock}}-1\,\mathrm{minute}\,]\\ {t}_{d}=[{t}_{\mathrm{shock}}+2\,\mathrm{minutes},\,{t}_{\mathrm{shock}}+10\,\mathrm{minutes}],\end{array}\right.\end{eqnarray} \tag{ 2 }$

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

Table 2. Shock Parameters Derived for both Bepi and Parker

Shock Parameter	Bepi	Parker
Jumps
rB	2.04	2.04
rn	⋯	1.80
ΔV	⋯	282 km s−1
MCT
${\hat{{\boldsymbol{n}}}}_{\mathrm{MCT}}$	[0.76, 0.63, 0.16]	[0.45, −0.82, −0.37]
ΘMCT	73	318
ΛMCT	405	633
ΞMCT	90	−214
MVA
${\hat{{\boldsymbol{n}}}}_{\mathrm{MVA}}$	[0.57, −0.25, −0.78]	[0.53, −0.42, −0.73]
ΘMVA	804	426
ΛMVA	550	578
ΞMVA	−513	−471
λ2/λ3	3.07	2.71
Bn /B	0.15	0.45
MD3
${\hat{{\boldsymbol{n}}}}_{\mathrm{MD}3}$	⋯	[0.49, −0.71, −0.51]
ΘMD3	⋯	333
ΛMD3	⋯	609
ΞMD3	⋯	−306

Note. r_B = magnetic compression ratio. r_n = density compression ratio. ΔV = velocity jump. $\hat{{\boldsymbol{n}}}$ = shock normal. Θ = shock angle. Λ = location angle. Ξ = elevation angle. λ₂/λ₃ = intermediate-to-minimum eigenvalue ratio. B_n /B = minimum-variance-to-total magnetic field ratio.

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

$\begin{eqnarray}&&{r}_{X}=\displaystyle \frac{{X}_{d}}{{X}_{u}},\end{eqnarray} \tag{ 3 }$

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

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

$\begin{eqnarray}&&{\rm{\Delta }}V={V}_{d}-{V}_{u}.\end{eqnarray} \tag{ 4 }$

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

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

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The MCT technique is based on the assumption that B _u , B _d , and $\hat{{\boldsymbol{n}}}$ lie in a single plane, and the shock normal is computed as

$\begin{eqnarray}&&{\hat{{\boldsymbol{n}}}}_{\mathrm{MCT}}=\pm \displaystyle \frac{({{\boldsymbol{B}}}_{d}-{{\boldsymbol{B}}}_{u})\times ({{\boldsymbol{B}}}_{d}\times {{\boldsymbol{B}}}_{u})}{| ({{\boldsymbol{B}}}_{d}-{{\boldsymbol{B}}}_{u})\times ({{\boldsymbol{B}}}_{d}\times {{\boldsymbol{B}}}_{u})| }.\end{eqnarray} \tag{ 5 }$

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

$\begin{eqnarray}&&\displaystyle \sum _{\nu =1}^{3}{M}_{\mu \nu }{n}_{\nu }=\lambda {n}_{\mu },\end{eqnarray} \tag{ 6 }$

where M_{μ ν} = 〈B_μ B_ν 〉 − 〈B_μ 〉〈B_ν 〉. The eigenvector associated with the smallest eigenvalue, λ₃, is the direction of minimum variance of the magnetic field and thus corresponds to the shock normal, ${\hat{{\boldsymbol{n}}}}_{\mathrm{MVA}}$. The reliability of the solution can be investigated via the intermediate-to-minimum eigenvalue ratio, λ₂/λ₃, and the minimum-variance-to-total magnetic field ratio across the discontinuity, B_n /B. Values of λ₂/λ₃ ≥ 2 and B_n /B ≤ 0.3 are usually considered to describe the shock normal as well defined (Lepping & Behannon 1980).

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

$\begin{eqnarray}&&{\hat{{\boldsymbol{n}}}}_{\mathrm{MD}3}=\,\pm \displaystyle \frac{({{\boldsymbol{B}}}_{d}-{{\boldsymbol{B}}}_{u})\times (({{\boldsymbol{B}}}_{d}-{{\boldsymbol{B}}}_{u})\times ({{\boldsymbol{V}}}_{d}-{{\boldsymbol{V}}}_{u}))}{| ({{\boldsymbol{B}}}_{d}-{{\boldsymbol{B}}}_{u})\times (({{\boldsymbol{B}}}_{d}-{{\boldsymbol{B}}}_{u})\times ({{\boldsymbol{V}}}_{d}-{{\boldsymbol{V}}}_{u}))| }.\end{eqnarray} \tag{ 7 }$

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

$\begin{eqnarray}&&{\rm{\Theta }}=\arccos \left(\displaystyle \frac{| {{\boldsymbol{B}}}_{u}\cdot \hat{{\boldsymbol{n}}}| }{\Vert {{\boldsymbol{B}}}_{u}\Vert \Vert \hat{{\boldsymbol{n}}}\Vert }\right).\end{eqnarray} \tag{ 8 }$

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

$\begin{eqnarray}&&{\rm{\Lambda }}=\arctan \left(\displaystyle \frac{\sqrt{{n}_{T}^{2}+{n}_{N}^{2}}}{{n}_{R}}\right).\end{eqnarray} \tag{ 9 }$

The third and final angle is the elevation angle, Ξ, between the shock normal and the RT plane (in radial–tangential–normal, RTN, coordinates), defined as

$\begin{eqnarray}&&{\rm{\Xi }}=\arctan \left(\displaystyle \frac{{n}_{N}}{\sqrt{{n}_{R}^{2}+{n}_{T}^{2}}}\right)=\arcsin \left(\displaystyle \frac{{n}_{N}}{\Vert \hat{{\boldsymbol{n}}}\Vert }\right).\end{eqnarray} \tag{ 10 }$

According to the shock normal results shown in Table 2 and Figure 6, all the calculated normals point in a southeasterly way (n_y < 0 and n_z < 0) apart from the MCT case for Bepi, which points toward the northwest (n_y > 0 and n_z > 0). The shock is moderately quasi-parallel at Parker (31° < Θ < 43°), while for Bepi, the MCT method retrieves a strongly quasi-parallel shock (Θ = 73), and the MVA technique produces a strongly quasi-perpendicular shock (Θ = 804). We note that quasi-parallel shocks are expected to occur more often closer to the Sun (<1 au), and quasi-perpendicular ones are more common at larger distances (∼1 au) due to the configuration of the Parker spiral (e.g., Richter et al. 1985; Good et al. 2020). Regardless of the normal direction and nature of the shock, all the obtained location angles suggest spacecraft crossings considerably far from the shock nose (40° < Λ < 65°), as expected from our remote-sensing analysis of the 2022 February 15 CME (see Section 2).

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

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

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

To further analyze the fine structure of the sheath regions observed at the two spacecraft, we investigate the presence (or lack thereof) of planar magnetic structures (PMSs) using the algorithm of Palmerio et al. (2016). PMSs are structures in the solar wind characterized by abruptly changing magnetic field vectors that remain nearly parallel to a single plane (e.g., Nakagawa et al. 1989; Neugebauer et al. 1993) and are frequently found in CME-driven sheath regions (e.g., Palmerio et al. 2016; Ruan et al. 2023). In brief, the PMS search algorithm of Palmerio et al. (2016) first applies the MVA technique to the full sheath, verifying whether the PMS conditions of λ₂/λ₃ ≥ 5 (e.g., Savani et al. 2011) and B_n /B ≤ 0.2 (e.g., Jones & Balogh 2000) are fulfilled, in which case the entire region is considered planar. If one or both criteria are not matched, then the algorithm scans through the sheath region using a "sliding windows" procedure. At every iteration, the sheath duration is reduced by 5 minutes from its end part, and the shortened window is shifted back toward the ejecta leading edge with 5 minute increments, searching for the largest nonoverlapping intervals for which the PMS criteria hold (note that a single sheath may contain more than one PMS). In the work of Palmerio et al. (2016), which analyzed 95 sheaths observed near Earth, the minimum possible PMS duration was set to 1 hr. Here, to account for the fact that the structures under investigation were encountered at ∼0.35 au, where sheaths are, on average, more modest in size, we allow for a minimum PMS duration of 30 minutes.

The results of the PMS analysis are shown in Figure 7 and Table 3. The PMS search algorithm finds one planar structure lasting approximately 1 hr at the center of each sheath. Despite their similar duration and location within their respective sheath regions, the two PMSs display different plane orientations, with the one found at Bepi oriented toward the northeast and the one found at Parker nearly aligned with the Sun–spacecraft line. Additionally, we note that the presence of a PMS in the central region of a sheath is a rather uncommon occurrence (e.g., Palmerio et al. 2016), since planar structures are believed to form due to compression and alignment of discontinuities downstream of a shock (e.g., Jones et al. 2002) and/or due to magnetic field draping ahead of an ejecta (e.g., Kataoka et al. 2005). Nevertheless, the excellent agreement between their respective positions within the sheath as well as their temporal duration, suggests that the structures found at Bepi and Parker were the result of the same formation mechanism. Given the turbulent nature of the solar wind, especially in the downstream region of a shock, it is possible that the retrieved PMS orientations are deeply reflective of the local sheath conditions and hence can vary more or less dramatically over relatively small spatial scales.

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Table 3. Results of the PMS Analysis at Bepi and Parker

PMS Property	Bepi	Parker
D [hr]	1.4	1.0
λ2/λ3	5.0	5.1
Bn /B	0.10	0.12
OPMS	(60°, 319°)	(14°, 360°)
${\hat{n}}_{\mathrm{PMS}}$	[0.38, −0.33, 0.86]	[0.97, −0.00, 0.24]

Note. D = PMS duration. λ₂/λ₃ = eigenvalue ratio. B_n /B = magnetic field ratio. O_PMS = orientation of the PMS plane in (θ, ϕ) format. ${\hat{n}}_{\mathrm{PMS}}$ = normal vector to the PMS plane.

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Indeed, this last point connects to the next step in our analysis, which is aimed at investigating the level of coherence of the sheath magnetic fields measured at the two spacecraft. To do so, we employ an approach similar to that used by Ala-Lahti et al. (2020), who analyzed the longitudinal spatial coherence of CME-driven sheath regions observed at 1 au by spacecraft characterized by nonradial separations between 0.001 and 0.012 au (006–069). Specifically, they computed the Pearson correlation coefficients (r) between each pair of magnetic field components as well as the field magnitude. In the case explored here, the spacecraft nonradial separation is ∼0.03 au, which corresponds to ∼5° at ∼0.35 au. We note that, while this relative distance is larger than the range explored by Ala-Lahti et al. (2020), it is well within the estimated scale lengths of typical magnetic field coherence in sheath regions resulting from their study (see also the discussion in the Introduction).

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

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

Another interesting aspect to investigate is the contribution of CME propagation and expansion to the sheath formation—CME-driven sheaths, in fact, are considered "hybrid" structures that feature aspects of propagation sheaths, in which the solar wind flows around a propagating object, and expansion sheaths, in which the solar wind piles up ahead of an expanding object (e.g., Siscoe & Odstrcil 2008). To do so, we calculate two Mach numbers: M_prop, based on the ejecta propagation speed, and M_exp, based on the ejecta expansion speed (see Equations (1) and (2) in Salman et al. 2021 for a definition of the two parameters). The propagation speed is simply the ejecta average speed, V_prop = 589 km s⁻¹, while the expansion speed is defined as the half-difference between the speeds of the leading and trailing edges (Owens et al. 2005), ${V}_{\exp }=142$ km s⁻¹. We obtain M_prop = 0.27 and ${M}_{\exp }=0.82$, indicating that the sheath driven by the 2022 February 15 CME was mainly an expansion one. This is consistent with the presence of a PUC region immediately ahead of the ejecta leading edge (see the prominent density enhancement in the trailing portion of the sheath in Figure 5), usually attributed to strong CME overexpansion. In fact, the CME analyzed in this work might still have been experiencing significant expansion by the time it was detected at Parker, since the sheath appears overall less dense than the following ejecta, in agreement with Salman et al. (2021), who found that expansion sheaths tend to display lower densities, on average. Furthermore, Temmer & Bothmer (2022) estimated that the sheath density tends to overcome the ejecta density in the heliocentric distance range of 0.09–0.28 au, after which expansion of the driver generally weakens. We also note that Giacalone et al. (2023) came to the same conclusion (i.e., that the 2022 February 15 CME was overexpanding by the time it impacted Parker) by observing the intensity of energetic particle increase behind the shock, possibly resulting from ions filling an expanding volume associated with the propagation of a blast wave.

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

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

To evaluate the large-scale internal magnetic structure of the ejecta encountered at Bepi and Parker, we apply three different flux rope fitting models to the in situ magnetic field measurements. Specifically, we employ the force-free constant-α (FF; Lepping et al. 1990), the circular-cylindrical (CC; Nieves-Chinchilla et al. 2016), and the elliptic-cylindrical (EC; Nieves-Chinchilla et al. 2018a) analytical descriptions of flux ropes to recover geometric and magnetic parameters that allow us to estimate orientation, size, and flux content. All these methods require an average CME ejecta speed, for which we employ a value of 654 km s⁻¹ based on the speed profile of the magnetic cloud portion at Parker (under the assumption that Bepi encountered similar velocities). Additionally, we employ the linear force-free self-similarly expanding (FE; Marubashi & Lepping 2007) cylindrical flux rope model, which is, in other words, an FF model that includes expansion. The FE technique requires fitting a full speed profile alongside the magnetic field components and thus is applicable in this case only to Parker data—here, we obtain our speed profile via a second-order polynomial fit to the in situ measurements. Results applied to the (full) ejecta at Bepi and the magnetic cloud portion of the ejecta at Parker are shown and summarized in Figure 9 and Table 4. The corresponding fits for the magnetic obstacle interval at Parker are reported and discussed in Appendix C.

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Table 4. Flux Rope Fitting Results at Bepi and Parker

Flux Rope Parameter	FF		CC		EC		FE
	Bepi	Parker	Bepi	Parker	Bepi	Parker	Parker
H	+1	+1	+1	+1	+1	+1	+1
ϑ0 [deg]	−78.8	−29.0	−72.5	−66.8	−63.4	−51.1	−53.2
φ0 [deg]	167.5	190.8	64.0	251.7	15.0	233.1	290.7
B0 [nT]	63.8	66.5	60.1	51.0	50.3	43.8	76.2
R0 [au]	0.166	0.074	0.165	0.108	0.145	0.115	0.101
p0 $[{R}_{0}^{-1}]$	0.681	0.573	0.715	0.052	0.588	0.178	0.396
τ [au−1]	5.21	11.69	0.53	0.95	0.71	2.05	8.54
Φax [1021 Mx]	5.35	1.10	6.31	2.31	3.91	1.21	2.39
Φpo [1021 Mx au−1]	9.89	4.57	5.94	3.97	4.87	3.76	7.20
C1	⋯	⋯	1.71	1.42	1.50	0.96	⋯
ψ [deg]	⋯	⋯	⋯	⋯	19.4	74.3	⋯
δ	⋯	⋯	⋯	⋯	0.96	0.54	⋯

Note. H: helicity sign (or chirality); ϑ₀: axis latitude; φ₀: axis longitude; B₀: axial magnetic field magnitude; R₀: flux rope radius; p₀: normalized impact parameter; τ: twist; Φ_ax: axial flux; Φ_po: poloidal flux; C1: ratio of the azimuthal-to-axial current at the flux rope outer boundary; ψ: propagation angle (i.e., rotation around the flux rope axis); δ: cross-sectional distortion (equals 1 for a circular cross section and 0 for maximum distortion). The assumed average speed for the CME ejecta in the FF, CC, and EC fits is 654 km s⁻¹, while the FE procedure uses a polynomial fit to the observed speed profile.

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We note that, despite the different fits appearing consistent overall at either spacecraft from visual inspection of Figure 9, the results reported in Table 4 display some stark differences in terms of both geometric and magnetic parameters. Nevertheless, we can extrapolate some common trends. For example, all techniques recover a right-handed flux rope at both probes (as expressed by the positive helicity sign, H), determine a higher axis inclination at Bepi when compared to Parker (as expressed by the latitude angle, ϑ₀), and estimate a more central encounter at Parker as opposed to Bepi (as expressed by the impact parameter, p₀). It has been shown that flux rope fitting results using different techniques can feature some disagreement even in "simple" cases characterized by negligible expansion speeds and symmetric magnetic field strength profiles (e.g., Al-Haddad et al. 2018); hence, it is not surprising to find discrepancies in this complex flank encounter event. One example can be seen in the B_R profiles shown in Figure 9, which display, on average, opposite polarities at the two spacecraft. If a different flux rope model were used that fit the B_R component with a more linear profile (such as the uniform-twist geometry; e.g., Farrugia et al. 1999), there could perhaps be less disagreement between the orientations obtained for each spacecraft. Nevertheless, flank encounter trajectories tend to be especially challenging for all in situ flux rope models (see the "problematic cases" discussed by Lynch et al. 2022). Overall, the most important conclusion to draw is that each of the flux rope models, when considered individually, returns very different "best-fit" parameter sets for the large-scale structure observed at Bepi and Parker, reflecting the significant differences in the (local) magnetic field time series measured within the ejecta by each spacecraft. We remark that the same holds true when considering the magnetic obstacle interval at Parker, as seen in the results presented in Appendix C.

To further investigate the coherence of the magnetic fields measured by the two probes, we analyze the corresponding correlations in the observed time series by adopting a similar approach to Lugaz et al. (2018), who compared the ejecta of CMEs measured near 1 au over nonradial separations of 0.005–0.012 au (029–069). As was the case for the coherence analysis in the sheath, the nonradial separation between Bepi and Parker of ∼0.03 au (∼5°) during 2022 February 16–17 is larger than the range explored by Lugaz et al. (2018) but falls well within the typical scales of magnetic field coherence emerging from their study (see also the discussion in the Introduction). The results of our analysis are shown in Figure 10. In their study, Lugaz et al. (2018) aligned the magnetic field profiles by calculating the lag between the pairs of data that maximized the Pearson correlations, with the lags being computed separately for the field magnitude and each of the three components. Here, on the other hand, we adopt the time series stretching approach that we employed for the sheath region in Section 4.2, allowing us to directly compare the magnetic fields measured at Bepi with those detected at Parker in the magnetic cloud (Figure 10(a)) as well as in the magnetic obstacle (Figure 10(b)) intervals. By doing so, we find an intriguing result. In fact, the Pearson correlation coefficients are [B, B_R , B_T , B_N ] = [0.48, −0.02, 0.68, 0.28] when considering the Parker magnetic cloud only but change dramatically into [B, B_R , B_T , B_N ] = [0.08, 0.40, 0.82, 0.60] when computed over the Parker magnetic obstacle interval. Hence, for the magnetic cloud, we find good correlation in B_T , moderate correlation in B, and weak-to-no correlation in B_R and B_N , while for the magnetic obstacle, we obtain moderate-to-strong correlation in all the components with no correlation in the magnitude.

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

The magnetic field correlation analysis reported above suggests that, indeed, the "longer" interval that we considered at Parker corresponds to the "original," full CME ejecta. Nevertheless, from all the instances in which these data are shown (Figures 4, 5, 9, and 10), it is clear that there is a transition between the two distinct magnetic field environments of what we have defined as the magnetic cloud and the trailing portion of the magnetic obstacle. In Section 3.2, we tentatively attributed these features to magnetic flux erosion, which is a consequence of CME reconnection with the surrounding solar wind. Here, we investigate whether this is indeed the case. Figure 11 provides an overview of the results emerging from our analysis aimed at quantifying the amount of poloidal flux eroded due to reconnection in the interplanetary medium (i.e., shortly before the CME was detected in situ). These results employ as input outputs from the EC model, which allows for elliptical, distorted cross sections and thus has more degrees of freedom than the remaining two techniques showcased in Figure 9; we remark that we have repeated the same analysis, instead using the FF model that includes self-similar expansion, i.e. the FE model, and the results are very well consistent with the EC ones. Once geometric parameters (from any fitting model) such as flux rope axis direction, radius, and impact parameter are provided, we calculate the inbound–outbound flux asymmetry using the "direct method" of Dasso et al. (2005) as described in Pal et al. (2022). We perform these computations for both the magnetic cloud (Figure 11(a)) and the full magnetic obstacle (Figure 11(b)) intervals. According to the results shown in Figure 11, flux asymmetry is found at the back of the ejecta in both cases, indicating reconnection and erosion at the front of the rope (see the scenario depicted in Figure 6 of Pal et al. 2022). The asymmetry starts on 2022 February 17 at 05:25 UT (08:35 UT), and the eroded poloidal flux is 1.4 × 10²¹ Mx au⁻¹ (1.5 × 10²¹ Mx au⁻¹) for the shorter (longer) interval (noting, however, that the glancing nature of the encounter may introduce additional errors in the results; e.g., Ruffenach et al. 2015). Our "by-eye" estimate of such a boundary fell on February 17 at 06:32 UT, i.e., comfortably in between the two times obtained with the flux erosion computation method. Thus, what emerges from this investigation is that the ejecta encountered at Parker was eroded, which may explain (at least in part) some of the differences in the structures encountered at the two spacecraft.

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