# Analysis of the Internal Structure of the Streamer Blowout Observed by the Parker Solar Probe During the First Solar Encounter

Teresa Nieves-Chinchilla, Adam Szabo, Kelly E. Korreck, Nathalia Alzate, Laura A. Balmaceda, Benoit Lavraud, Kristoff Paulson, Ayris A. Narock, Samantha Wallace, Lan K. Jian, et al.

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Teresa Nieves-Chinchilla, Adam Szabo, Kelly E. Korreck, Nathalia Alzate, Laura A. Balmaceda, et al. Analysis of the Internal Structure of the Streamer Blowout Observed by the Parker Solar Probe During the First Solar Encounter. The Astrophysical Journal Supplement Series, 2020, 246, 17 pp. 10.3847/1538-4365/ab61f5. insu-03560769

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# Analysis of the Internal Structure of the Streamer Blowout Observed by the Parker Solar Probe During the First Solar Encounter

Teresa Nieves-Chinchilla<sup>1,2</sup> ◊, Adam Szabo<sup>1</sup> ◊, Kelly E. Korreck<sup>3</sup> ◊, Nathalia Alzate<sup>1</sup> ◊, Laura A. Balmaceda<sup>1,4</sup> ◊,
Benoit Lavraud<sup>5</sup> ◊, Kristoff Paulson<sup>3</sup> ◊, Ayris A. Narock<sup>1,6</sup>, Samantha Wallace<sup>1,7</sup> ◊, Lan K. Jian<sup>1</sup> ◊, Janet G. Luhmann<sup>8</sup> ◊,
Huw Morgan<sup>9</sup> ◊, Aleida Higginson<sup>10,11</sup> ◊, Charles N. Arge<sup>1</sup> ◊, Stuart D. Bale<sup>8,11,12,13</sup> ◊, Anthony W. Case<sup>3</sup> ◊,
Thierry Dudok de Wit<sup>14</sup> ◊, Joe Giacalone<sup>15</sup>, Keith Goetz<sup>16</sup> ◊, Peter R. Harvey<sup>8</sup> ◊, Shaela I. Jones-Melosky<sup>1</sup> ◊, J. C. Kasper<sup>3,17</sup> ◊,
Davin E. Larson<sup>8</sup> ◊, Roberto Livi<sup>8</sup> ◊, David J. McComas<sup>18</sup> ◊, Robert J. MacDowall<sup>1</sup> ◊, David M. Malaspina<sup>19</sup> ◊, Marc Pulupa<sup>8</sup> ◊,
Nour E. Raouafi<sup>10</sup> ◊, Nathan Schwadron<sup>20</sup> ◊, Michael Louis Stevens<sup>3</sup> ◊, and Phyllis L. Whittlesey<sup>8</sup> ◊

Received 2019 October 12; revised 2019 December 12; accepted 2019 December 13; published 2020 February 3

## Abstract

In this paper, we present an analysis of the internal structure of a coronal mass ejection (CME) detected by in situ instruments on board the *Parker Solar Probe (PSP)* spacecraft during its first solar encounter. On 2018 November 11 at 23:53 UT, the FIELDS magnetometer measured an increase in strength of the magnetic field as well as a coherent change in the field direction. The SWEAP instrument simultaneously detected a low proton temperature and signatures of bidirectionality in the electron pitch angle distribution (PAD). These signatures are indicative of a CME embedded in the slow solar wind. Operating in conjunction with *PSP* was the *STEREO A* spacecraft, which enabled the remote observation of a streamer blowout by the SECCHI suite of instruments. The source at the Sun of the slow and well-structured flux rope was identified in an overlying streamer, the details of which are described in Korreck et al. Our detailed inspection of the internal transient structure magnetic properties suggests high complexity in deviations from an ideal flux rope 3D topology. Reconstructions of the magnetic field configuration reveal a highly distorted structure consistent with the highly elongated “bubble” observed remotely. A double-ring substructure observed in the SECCHI-COR2 field of view (FOV) is suggestive of a double internal flux rope. Furthermore, we describe a scenario in which mixed topology of a closed flux rope is combined with the magnetically open structure, which helps explain the flux dropout observed in the measurements of the electron PAD. Our justification for this is the plethora of structures observed by the EUV imager (SECCHI-EUVI) in the hours preceding the streamer blowout evacuation. Finally, taking advantage of the unique observations from *PSP*, we explore the first stages of the effects of coupling with the solar wind and the evolutionary processes in the magnetic structure. We found evidence of bifurcated current sheets in the structure boundaries, suggestive of magnetic reconnection. Our analysis of the internal force imbalance indicates that internal Lorentz forces continue to dominate the evolution of the structure in the COR2 FOV and serve as the main driver of the internal flux rope distortion detected in situ at *PSP* solar distance.

*Unified Astronomy Thesaurus concepts: Solar coronal mass ejections (310); Solar wind (1534); Interplanetary magnetic fields (824); Space plasmas (1544); Solar magnetic reconnection (1504)*

*Supporting material: animation*

## 1. Introduction

The first solar encounter of the *Parker Solar Probe (PSP)* during its mission (Fox et al. 2016) in 2018 offered a remarkable opportunity to observe in situ imprints of two

magnetic structures passing over the spacecraft, and was complemented by ancillary space-based observations from instruments located at 1 au. The first obstacle, observed on October 31 during the inbound leg of the first solar encounter

<footnote n="1"><sup>1</sup> NASA, Goddard Space Flight Center, Greenbelt, MD 20771, USA; Teresa.Nieves@nasa.gov</footnote>

<footnote n="2"><sup>2</sup> The Catholic University of America, Washington, DC, USA</footnote>

<footnote n="3"><sup>3</sup> Smithsonian Astrophysical Observatory, Cambridge, MA 02138, USA</footnote>

<footnote n="4"><sup>4</sup> George Mason University, Fairfax, VA, USA</footnote>

<footnote n="5"><sup>5</sup> IRAP, Université Toulouse III—Paul Sabatier, CNRS, CNES, Toulouse, France</footnote>

<footnote n="6"><sup>6</sup> ADNET Systems Inc., Greenbelt, MD, USA</footnote>

<footnote n="7"><sup>7</sup> University of New Mexico, Albuquerque, NM, USA</footnote>

<footnote n="8"><sup>8</sup> Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA</footnote>

<footnote n="9"><sup>9</sup> Aberystwyth University, Aberystwyth, UK</footnote>

<footnote n="10"><sup>10</sup> Applied Physics Laboratory, Johns Hopkins University, Laurel, MD, USA</footnote>

<footnote n="11"><sup>11</sup> School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK</footnote>

<footnote n="12"><sup>12</sup> Physics Department, University of California, Berkeley, CA 94720-7300, USA</footnote>

<footnote n="13"><sup>13</sup> The Blackett Laboratory, Imperial College London, London, SW7 2AZ, UK</footnote>

<footnote n="14"><sup>14</sup> LPC2E, CNRS and University of Orléans, Orléans, France</footnote>

<footnote n="15"><sup>15</sup> University of Arizona, AZ, USA</footnote>

<footnote n="16"><sup>16</sup> School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA</footnote>

<footnote n="17"><sup>17</sup> Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109, USA</footnote>

<footnote n="18"><sup>18</sup> Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA</footnote>

<footnote n="19"><sup>19</sup> Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA</footnote>

<footnote n="20"><sup>20</sup> University of New Hampshire, Durham, NH, USA</footnote>
(at 0.24 au), was identified as an asymmetric increase in magnitude of the magnetic field, accompanied by a smooth change in the magnetic field direction, albeit not a full 180° rotation. The second structure on (2018) November 11, which was observed during the outbound leg at a distance of 0.25 au from the Sun, exhibited in situ signatures indicative of an interplanetary coronal mass ejection that was confirmed by remote sensing observations from the COR2 coronagraph instrument on board the STEREO RELations Observatory (STEREO A or STA; Kaiser et al. 2008). The work described in this paper focuses on understanding the internal magnetic structure of this second event.

Coronal mass ejections (CMEs) are large structures in the solar wind that transport large amounts of plasma and magnetic field away from the Sun. It is known that they remove built-up energy, magnetic helicity, and mass from the solar corona (e.g., Low 1996; Webb et al. 2012). In coronagraph images, CMEs manifest themselves in different ways, e.g., as increases in brightness or density. However, the question remains: how do the features of CMEs observed remotely reflect their in situ signatures? Typical CMEs exhibit a three-part structure (a bright leading front, a cavity, and a bright central core) in coronagraph images (e.g., Vourlidas et al. 2013). Thus, a dark area or cavity, surrounded by brightness or a bright leading front, is accepted to be the signature of an expanding magnetic structure that is associated with in situ helical magnetic fields (Dere et al. 1999; Wood et al. 1999). The bright leading edge in front of the cavity corresponds to a sheath region, and frequently to an interplanetary (IP) shock measured in situ (e.g., Kilpua et al. 2011) that contains plasma piled up as the CME propagates outward. However, comprehensive analyses to reconcile in situ with remote views have demonstrated the lack of consensus (e.g., Nieves-Chinchilla et al. 2012; Wood et al. 2017).

The observational structure and evolution of CMEs in coronagraph images may offer clues into the variety of phenomena with which they are associated in the Sun, and thus provide an insight into the initiation process(es) (Moore & Labonte 1980; Amari et al. 2003a; Gopalswamy et al. 2006; Green et al. 2018; Georgoulis et al. 2019). Currently, different theories on the magnetic configurations in the solar surface are competing to explain CME trigger mechanisms and different flux-rope formation processes, e.g., mechanisms based on the shear motion in the photosphere (e.g., Barnes & Sturrock 1972; Linton et al. 2001; Kusano et al. 2004), flux cancellation (Moore & Labonte 1980; van Ballegooijen & Martens 1989; Moore et al. 2001; Amari et al. 2003b), the magnetic breakout model (Antiochos et al. 1999; Lynch et al. 2004; Sterling & Moore 2004; Archontis & Török 2008), or flux emergence (e.g., Chen & Shibata 2000). A common factor in all magnetic configuration theories is the end result of a single flux rope topology describing the internal structure of CMEs.

These large structures can also be classified based on their kinematic aspects. CMEs with speeds less than 500–800 km s⁻¹ are generally referred to as “slow,” while CMEs with speeds larger than 800–900 km s⁻¹ are considered “fast” (Howard et al. 1985; St. Cyr et al. 2000; Evans et al. 2013). Interrelated with the internal dynamics, Sachdeva et al. (2015, 2017) found that “very fast” CMEs (ν > 1000 km s⁻¹ near the Sun) are accelerated due to the Lorentz forces acting on them near the Sun, with peak forces acting between 1.65 and 2.45 R<sub>s</sub>, and are later decelerated due to the aerodynamic drag caused as a result of the ambient

solar wind. In the case of “slow” CMEs (with speeds comparable to the solar wind speed near the Sun and on the order of a few hundred km s⁻¹), these are accelerated in the proximity of the Sun by the solar wind aerodynamic drag, albeit the Lorentz forces could play some role in the dynamics of “slow” CME evolution. Although the dynamical aspects of these events are not fully understood, it is known that they are relevant in the kinematic evolution of the CME. In the interconnection between the initiation aspects and the kinematic/dynamical aspects, we barely understand the role that different characteristics in the solar sources could play in the subsequent coupling with the solar wind and how it can affect the internal structure evolution.

Even in its infancy, the PSP spacecraft has already proven to provide the unique opportunity to improve our understanding of the internal structure of CMEs and identify possible diversity in the internal magnetic topology. The first observations made by the Wide-field Imager for Solar PRObe (WISPR; Vourlidas et al. 2016) instrument revealed a quasi-circular shape with a pinch at the back of the structure (Howard et al. 2019). This implies there to be a departure of the internal force distribution from the force-free equilibrium due to the magnetic tension that forces the structure to recover into the expected circular cross section of a twisted flux rope (Klimchuk 2000; Klimchuk et al. 2000), at least locally in the distorted area. In general, the local distortion or global deformation of the CME remain unsolved issues, and are still topics of discussion in the community. The remotely observed elongated dark cavity shape, known as “pancaking,” is observationally described as a highly distorted global structure, providing evidence of the interaction of the magnetic structure with the solar wind (Odstrcil & Pizzo 1999; Riley & Crooker 2004; Owens 2006; Savani et al. 2010; DeForest et al. 2013; Owens et al. 2017). Another interpretation is that the observed deformation is a projection effect from a 3D structure in the plane of the sky (Vourlidas et al. 2013; Nieves-Chinchilla et al. 2013). Studies such as the one carried out by Subramanian et al. (2014) have demonstrated that both the current (J) and magnetic field (B) within the flux rope of a CME with a self-similar expansion can be substantially misaligned, thus indicating the non-force-free nature of flux-rope CMEs, and hence the basis for Lorentz self-force driving. Recent work by Nieves-Chinchilla et al. (2016, 2018b) generalized the circular-cylindrical model originally published by Hidalgo et al. (2000) and introduced the elliptic-cylindrical analytical flux rope model, which describes a magnetic flux rope topology with a distorted cross section as a result of the flux rope-solar wind interaction. This model parallels the Grad–Shafranov reconstruction technique by Hu & Sonnerup (2001), in that it does not apply any internal dynamic constraints. As a result, as part of the reconstruction technique derived from in situ measurements of the magnetic field and plasma composition, the models provide information about the force-free nature of the structure. Furthermore, the internal force distribution can be gauged from the misalignment of *B* and *J*. The model was developed in order to reconcile in situ measurements with any distortions identified in remote sensing observations, and thus define the impact of evolutionary dynamical processes on the internal flux rope structure.

In this paper, we describe our analysis of the internal structure of a streamer blowout (SBO)–CME observed by PSP on (2018) November 11 during the first solar encounter, which occurred at a distance of 53 R<sub>s</sub>. The event has been identified as
an SBO; for further details, see Korreck et al. (2020). The ancillary space-based observations made by STA (STEREO A)-COR2 provide context on the Sun in terms of solar source initiation activity, the evolutionary processes, and their impact on the internal structure of the event. The combined analysis of the derived coronal field from Wang-Sheeley-Arge (WSA) model (Arge & Pizzo 2000; Arge et al. 2003, 2004) with the processed images from STA-COR1 (N. Alzate et al. 2019, in preparation) allowed us to identify the solar source region as underlying closed magnetic field lines located next to a coronal hole that expand upward through the field of view (FOV) of STA-COR1. These events are characterized by a gradual swelling of the overlying streamer (see Sheeley et al. 1982; Howard et al. 1985; Sheeley et al. 1997, and references therein). SBOs are the primary type of CME sources around solar minimum, and in general, they exhibit flux rope morphology at a much higher rate (61%) than regular CMEs (40%) (Vourlidas & Webb 2018). As in our case, they are easily recognized in coronagraph images as a slow evacuation (from hours to days) and a well-structured flux-rope "bubble" shape. These signatures make it difficult to identify the structures at 1 au and therefore to fully characterize the internal structure of the SBOs.

This paper is organized as follows. Section 2 describes in situ measurements made by PSP in the heliospheric context (i.e., from solar source reconstruction), and Section 3 describes our 3D reconstruction of the internal magnetic structure based on well-established models and reconstruction techniques. Using remote-sensing observations, we investigated the solar source and/or initiation processes as the potential cause(s) of the internal complexity of the SBO in Section 4. Finally, in Section 5, we discuss our results and conclusions.

## 2. PSP In Situ Observations on (2018) November 11–12

Figure 1 represents a subset of the in situ measurements collected by the FIELDS Experiment (Bale et al. 2016) and the Solar Wind Electrons Alphas and Protons (SWEAP; Kasper et al. 2016) instrument suite on board PSP on 2018 November 11 and 12, during the first solar encounter. On November 11, 2018 at 23:51 UT (indicated by the first dashed vertical line in the figure), the PSP magnetometer recorded an increase in magnitude of the magnetic field that lasted for 6.43 hr (until 06:07 UT on 2018 November 12th; third dashed vertical line), a smooth change in the magnetic field direction, and signatures in the plasma parameters that indicate a confined plasma, i.e., low proton plasma beta ($\beta_p$) and a drop in the proton temperature. The structure was moving with an average speed of $\approx 391 \text{ km s}^{-1}$ and with a maximum magnetic field strength of $B_{mx} = 97 \text{ nT}$. The average magnetic field strength was 80 nT, almost twice that in the solar wind leading the structure ($B = 37 \text{ nT}$). These signatures describe a magnetic obstacle in the solar wind, sometimes called a magnetic cloud or a flux rope (Burlaga et al. 1981; Klein & Burlaga 1982).

Front and rear boundaries are selected based on the signatures associated with the magnetic structures. There is not a distinguished front shock wave or sheath associated with the propagation of the structure from the Sun to PSP. The CME was embedded in slow wind with a front speed of $395 \text{ km s}^{-1}$ (within the 2 hr before the leading boundary) and an average speed of $396 \text{ km s}^{-1}$ after the rear boundary (within an interval of 2 hr). Thus, the lack of difference in speed within and outside the structure could be an indication that the propagation

is driven by the drag forces—and therefore the CME would not drive the formation of the shock wave at the front (see Section 5). There are no remote sensing signatures of the CME shock-sheath formation in the first stages of the evolution. More details about the CME propagation are included in Korreck et al. (2020).

The boundaries of structure indicates a duration of 6.43 hr at $0.25 \text{ au}$. Assuming $400 \text{ km s}^{-1}$ as the average CME speed, the CME width from the start to the end of the encounter is about $0.062 \text{ au}$. From the empirical relation of CME width ($W$) and heliocentric distance ($D$) $W = 0.37 \times D^{0.85}$ (Figure 13 of Jian et al. 2008), the CME width would be about $0.216 \text{ au}$ when it reaches 1 au, falling in the lower spectrum of the CME widths (Figure 10 of Jian et al. 2011).

During this same time period, PSP measured an increase in the electron flux at 315 eV aligned with the magnetic field. The electron pitch angle distribution (PAD) at 315 eV is strongly enhanced during most of the time interval at 0° (in the direction of the local magnetic field). The 315 eV energy channel is selected because, at this energy, the electrons are in the suprathermal energy range—and thus, we can still clearly identify the strahl electrons streaming away from the Sun and bidirectional periods with both legs of the field lines still connected to the Sun. Bidirectional heat flux electrons are observed even before the magnetic obstacle, and end abruptly inside the structure at around 04:16 UT on November 12 (dotted line). During the period of bidirectionality, the suprathermal electron flux is higher at 0° pitch angle, possibly corresponding to the flow away from the field line footpoint that is closer to PSP (Zurbuchen & Richardson 2006). The absence of bidirectionality at the end of the structure indicates that the CME magnetic field lines may have reconnected with open magnetic field lines (e.g., Gosling et al. 1995).

The Integrated Science investigation of the Sun (ISOIS; McComas et al. 2016) Epi-Lo low-energy particle observations in the range 3–200 eV (not shown here) indicate that energetic particle intensities started to gradually increase a few hours before PSP encountered the magnetic obstacle. Though the peak occurs before PSP enters the magnetic structure, and thus the energetic particle intensities were already declining, a significant drop was observed at the boundary of the structure itself (see Giacalone et al. 2020). This would indicate a closed magnetic structure, but one that was penetrated by some energetic particles.

Based on visual inspection, the magnetic configuration of the structure can be described as a single flux rope with a south-north (SN) $B_N$ polarity and a south-west-north configuration (Bothmer & Schwenn 1998; Nieves-Chinchilla et al. 2019). The magnetic field strength profile shows slight asymmetry with a distortion parameter $= 0.52$, which indicates a slight compression at the back of the structure; see Nieves-Chinchilla et al. (2018a) for further details. The structure exhibits low signatures of expansion in the solar wind speed profile, $V_{exp} \approx 11 \text{ km s}^{-1}$, as compared to the average velocity at 1 au of $25 \text{ km s}^{-1}$ (Nieves-Chinchilla et al. 2019, and references therein). A detailed inspection of the magnetic field components indicates a deformation or change in the vector direction, with a pronounced effect in the $B_N$ component that reaches the maximum of $B_N^{max} = 87 \text{ nT}$ and changes the polarity from the northward direction to southward at $\sim 04:50 \text{ UT}$, 34 minutes after the sharp change in the electron PAD described previously. This interval is bounded by the last
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Overview of in situ measurements of the event observed by PSP during the first solar encounter on 2018 November 11–12. From top to bottom, the plots show magnetic field magnitude ([B]), magnetic field components in the radial-tangential-normal ($B_R$, $B_T$, $B_N$) coordinates, solar wind R-velocity component ($V_R$), T-(red) and N-(black) solar wind velocity components ($V_{T, N}$), proton density ($N_p$), proton temperature ($T_p$), proton beta plasma, 315 eV electron pitch angle distribution (PAD), normalized 315 eV electron PAD. Dashed vertical lines bounded the magnetic structure. Dotted vertical line marks the boundary of the internal substructure.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Three combined magnetic hodograms in the RTN coordinate system. Magnetic field components are represented in units of nT. Pink and blue lines (from 1 to 3) indicate the entire interval of the analysis. Pink line (from 1 to 2) marks the first interval from 315.994 to 316.178 DOY. Blue line marks the second interval (from 2 to 3) from 316.178 to 316.262 DOY.</figcaption></figure>

two vertical dashed lines in Figure 1 and aids in addressing the following question. Is this structure one flux rope with internal complexity, or the interaction of several structures (e.g., flux ropes)?

To tackle this question, we first explore magnetic field rotations by visual inspection. Nieves-Chinchilla et al. (2018b, 2019) utilized the known magnetic hodograms to evaluate the plane where the magnetic vector rotates. Figure 2
exhibits the three possible combined hodograms from the magnetic field components ($B_R, B_T, B_N$) in the time range between November 11 14:24 UT (DOY = 315.6) and November 12 12:00 UT (DOY = 316.5). Overplotted with colored lines (pink and blue), the highlighted time periods of the magnetic structure are indicated with vertical lines in Figure 1. The substructures are marked with pink (1–2) and blue (2–3) color, while the entire magnetic structure is within the interval 1–3 including the two colored lines. In our case, the maximum magnetic field direction rotation is in the T–N plane. Two observations can be made: (1) there is not a full (180°) rotation, from the minimum value ($B_N^{min} = -27$ nT) around the beginning of the structure to the maximum (mentioned previously, $B_N^{max} = 87$ nT) before the structure ends; and (2) there is not a unique smooth rotation, but rather two that confirm the internal substructure/complexity. The electron PADs reveal a similar picture: a real change between the first part that has clear electron counterstreaming and field rotation, and the second part that has diminished electron flux at 315 eV.

Another possible interpretation of the observations in Figure 1 is that only the first part of the structure is described by a flux rope-type model, while the second part, where the electron counterstreaming is replaced by a combination of unidirectional streaming and a flux dropout (at this energy), is instead an adjacent bundle of interchanged and disconnected flux. Figure 3 illustrates the possible scenario (blue color sketch) as a combination of the two sketches described previously by Crooker et al. (2002). Thus, the internal structure could be paralleled by a magnetic helical structure confining a magnetized plasma plus a magnetically open structure. Such an alternate interpretation would be consistent with past 1 au results from Shodhan et al. (2000), as well as the even earlier discussion by Gosling et al. (1995), in which it is highlighted that electron observations that suggest multiple topologies with different coronal connectivities can be present in ejecta—even in a structure that appears as a coherent magnetic cloud. It may also be consistent with coronagraph observations in which structures exhibit “V”-shaped structures at times (Hess & Wang 2017). Note that the ability to detect these distinctive parts of a transient structure and relate them to coronal behavior is a unique capability of PSP, due to its proximity to the Sun.

Finally, in terms of the survival of this structure in the solar wind, few statistical studies have attempted to quantify the evolution of the internal magnetic field strength in the heliosphere; see, for instance, Liu et al. (2005), Leitner et al. (2007), and Gulisano et al. (2010). These studies were based on encounters of the Helios mission with flux ropes at solar distances of 0.3 au to 1 au, as well as on outer heliospheric missions such as *Ulysses*. For instance, Liu et al. (2005) and Forsyth et al. (2006) found that, in general, B (nT) = 7.35D (au)$^{-1.4}$, where B (nT) is the central magnetic field and D (au) is the heliospheric distance from the Sun. Recently, Al-Haddad et al. (2019) found that the magnetic field strength decreases as B (nT) = 34.8D (au)$^{-1.8}$ from the Sun surface to ~0.4 au for a simulated twisted flux rope. Thus, for our purposes, we have considered these two empirical relationships in order to evaluate the survival of the magnetic field structure.

Figure 4 shows the results from simulations of the structure evolution from 0.1 to 1 au of the central magnetic field, based on the Liu et al. (2005), Forsyth et al. (2006), Winslow et al. (2015), and Al-Haddad et al. (2019) relationships:

$$B^{\text{Al-haddad}}(nT) = A * D(au)^{-1.8}, \quad (1)$$

$$B^{\text{LF}}(nT) = L * D(au)^{-1.4}, \quad (2)$$

$$B^{\text{Winslow}}(nT) = W * D(au)^{-1.95}. \quad (3)$$

Here, B (nT) and D (au) are the magnetic field strength and the heliospheric distance of the CME center. The coefficients A, W, and L have been adjusted to obtain a value of B = ~100 and B = ~200 nT at a distance of 53 R<sub>s</sub>. Thus, assuming that the maximum value observed in the magnetic structure is the central magnetic field, a spacecraft would measure a central value between 8, 13, and 14 nT at 1 au. In the case where PSP has crossed the structure far from its center, and thus assuming the central magnetic field is ~200 nT at 53 R<sub>s</sub>, the central magnetic field would be within 13–24 nT at 1 au. These are substantially smaller magnetic field strengths than are typically observed in 1 au CMEs.

### 3. In Situ 3D Reconstruction

This section is devoted to the analysis and 3D reconstruction of the CME–SBO internal structure based on our interpretation of the in situ observations. To carry out the analysis, we have followed three well-established flux rope models and techniques in order to better understand the morphology, axis orientation, and physical parameters.

The first two models, the circular-cylindrical (henceforth, the CC model) and elliptical-cylindrical (henceforth, the EC model) analytical flux rope models, were described in Nieves-Chinchilla et al. (2016, 2018b). These models assume a flux rope magnetic topology, i.e., an axially symmetric magnetic field cylinder with twisted magnetic field lines of circular cross section for the CC model or elliptical cross section for the EC model.

The magnetic field components in the CC coordinate system are described by:

$$ \begin{aligned} B_r &= 0 \\ B_y &= B_y^0 \left[ 1 - \left( \frac{r}{R} \right)^2 \right] \\ B_\varphi &= -H \frac{B_y^0}{|C_{10}|} \left( \frac{r}{R} \right), \end{aligned} \quad (4) $$

where the model estimates $B_y^0$, the magnetic field at the center of the flux rope, and $C_{10}$, a measure of the force-freeness along with $H$ (+1 or -1) that indicates if the flux rope is right- or left-handed. The radius of the flux rope cross section, R, is a derived parameter (see Equation (5) in Hidalgo et al. 2002) and r is the radial distance from the axis that describes the spacecraft trajectory.

The magnetic field components in the EC coordinate system are:

$$ \begin{aligned} B_r &= 0, \\ B_y &= \delta B_y^0 \left[ 1 - \left( \frac{r}{R} \right)^2 \right], \\ B_\varphi &= -H \frac{2h\delta}{(\delta^2 + 1)} \frac{B_y^0}{|C_{10}|} \left( \frac{r}{R} \right), \end{aligned} \quad (5) $$

where $h = [\delta \sin^2 \varphi + \cos^2 \varphi]^{1/2}$. This model has one additional fitted parameter, $\delta$, that provides information on the distortion of the cross section (i.e., $\delta = 1$ is circular, $\delta < 1$ is elliptical).
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Possible magnetic field topologies. Illustrations (a) and (b) correspond to the topologies described by Crooker et al. (2002), while (c) displays a combination of the (a) and (b) topologies.</figcaption></figure>

Apart from $B_y^0$ and $C_{10}$, the CC model also fits for the longitude ($\phi$), the tilt ($\theta$) of the flux rope axis, and for the impact parameter ($y_0$), which is the closest approach normalized by the radius of the flux rope. The EC model has two additional fitting parameters: $\delta$, the distortion measure discussed above, and the $\xi$ angle, which is the third Euler rotation from the local coordinate system to the RTN coordinate system. For the propagation angle, see more details in Nieves-Chinchilla et al. (2018b). The CC and EC models then use a $\chi^2$ minimization technique to obtain a set of

parameters that best fit the measured data (Nieves-Chinchilla et al. 2016, 2018b).

Figure 5 exhibits the fitting results treating the structure as a single entity. The resulting fit parameters are listed in Table 1. Despite the models following the trend of the magnetic field components, none of them capture the change in the $B_N$ direction at the rear. The EC model better captures the rear asymmetry in the field magnitude. When the two substructures are fitted separately (Figure 6), the trend is very similar; the EC model fits the magnetic field magnitude and components better
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Radial variation of the magnetic field at the center of the CME for a twisted flux rope. Black lines correspond to the empirical relationship obtained by Al-Haddad et al. (2019), and pink lines correspond to Liu et al. (2005). Thick lines are adjusted to obtain ~100 nT at D = 53 R<sub>s</sub>, and thin lines are adjusted to ~200 nT at the same heliocentric distance.</figcaption></figure>

than the CC model. Thus, by assuming the CME–SBO internal structure to be a single flux rope, we could conclude that the flux rope has a significant distortion from a single circular cross section.

In terms of the orientation and geometry of the flux rope, we also found differences between the CC and EC model results. When the whole structure is fitted as a single entity, the CC model predicts an axis orientation longitude (φ) 13° different from that of the EC model. However, both models agree that the flux rope axis has a very small elevation angle (θ). The angle, ξ, is unique to the EC model, and has a value of 110°. In the context of the other two angles, this means that the distorted structure is aligned with the spacecraft trajectory, consistent with the STA/COR2 observations. Figures 5(b) and 6(b) display the 3D reconstruction of the fitted EC model from the perspective of STEREO A. The dashed red line represents the trajectory of the PSP spacecraft with an impact parameter of Y₀ = 0.007 au (~29% from the center), which is similar for both models.

The fitted axis magnetic field strength (B<sub>y</sub><sup>0</sup>) also differs significantly between the two reconstructions because of the high distortion (δ = 0.41) obtained with the EC model. Such a difference is important because a higher central field strength ensures the survival of the structure to 1 au, as discussed at the end of Section 2 (see Figure 4). The final fitted parameter, C<sub>10</sub>, determines the Lorentz force distribution along the radius of the structure. This parameter will be discussed in the next section as part of the analysis of the evolutionary processes controlling the internal structure.

For the detailed analysis of the substructures, we have considered one more technique in order to explore the internal complexity. The flux rope properties can also be numerically reconstructed under particular assumptions satisfying the

<figure><img src="image_7.png" /><figcaption>**Figure 5.** (a) Comparison of the fitting results from the CC model (pink) and EC model (blue) with PSP magnetic field observations spanning the whole event. From the top, the panels display the magnetic field strength and the three magnetic field RTN components, respectively. (b) Three-dimensional reconstruction of the magnetic structure from the EC model. The spacecraft trajectory is indicated by a red dashed line, and the red dot indicates the start time. The structure is oriented and projected as observed by Stereo A, with the Sun at the right. (c) Front view of the reconstruction.</figcaption></figure>

Grad–Shafranov (GS) equation:

$$ \nabla^2 A = -\mu_0 \frac{d}{dA} \left( p + \frac{B_z^2}{2\mu_0} \right). \quad (6) $$
<table><caption>**Table 1**
Output Fitting Parameters for the Three Intervals Indicated in Column (1)</caption><thead><tr><th>Interval<br>(1)</th><th>Model<br>(2)</th><th>C<sub>10</sub><br>(3)</th><th>B<sub>y</sub><sup>0</sup><br>(4)</th><th>δ<br>(5)</th><th>φ<br>(6)</th><th>θ<br>(7)</th><th>ξ<br>(8)</th><th>Y<sub>0</sub><br>(9)</th><th>R<br>(10)</th><th>Φ<sub>v</sub><br>(11)</th><th>Φ<sub>φ</sub><br>(12)</th><th>H<br>(13)</th><th>χ<sup>2</sup><br>(14)</th><th>Res<br>(15)</th></tr></thead><tbody><tr><td rowspan="2">11/11 23:51-(+1)06:07</td><td>CC</td><td>1.4</td><td>95</td><td>...</td><td>46</td><td>8</td><td>...</td><td>-0.007</td><td>0.023</td><td>1.67</td><td>116</td><td>+</td><td>0.31</td><td>...</td></tr><tr><td>EC</td><td>1.02</td><td>202</td><td>0.41</td><td>39</td><td>11</td><td>110</td><td>-0.007</td><td>0.025</td><td>0.76</td><td>107</td><td>+</td><td>0.29</td><td>...</td></tr><tr><td rowspan="3">11/11 23:51-(+1)04:16</td><td>CC</td><td>2.9</td><td>192</td><td>...</td><td>23</td><td>-4</td><td>...</td><td>-0.011</td><td>0.014</td><td>1.24</td><td>66.</td><td>+</td><td>0.30</td><td>...</td></tr><tr><td>EC</td><td>2.7</td><td>203</td><td>0.68</td><td>37</td><td>-1</td><td>106</td><td>-0.021</td><td>0.031</td><td>3.29</td><td>114</td><td>+</td><td>0.14</td><td>...</td></tr><tr><td>GS</td><td>...</td><td>98.8</td><td>...</td><td>72</td><td>-3</td><td>...</td><td>0.001</td><td>0.016</td><td>...</td><td>...</td><td>+</td><td>...</td><td>0.072</td></tr><tr><td rowspan="3">11/12 04:16-06:07</td><td>CC</td><td>2.68</td><td>183</td><td>...</td><td>169</td><td>21</td><td>...</td><td>0.016</td><td>0.017</td><td>1.76</td><td>84</td><td>+</td><td>0.36</td><td>...</td></tr><tr><td>EC</td><td>1.95</td><td>189</td><td>0.63</td><td>136</td><td>40</td><td>79</td><td>0.024</td><td>0.036</td><td>3.36</td><td>147</td><td>+</td><td>0.26</td><td>...</td></tr><tr><td>GS</td><td>...</td><td>113</td><td>...</td><td>127</td><td>69</td><td>...</td><td>0.002</td><td>0.012</td><td>...</td><td>...</td><td>+</td><td>...</td><td>0.071</td></tr></tbody></table>

**Note.** Column (2) indicates the model/technique: CC is based on Nieves-Chinchilla et al. (2016), EC is based on Nieves-Chinchilla (2018), and GS is based on the Grad–Shafranov reconstruction technique of Hu & Sonnerup (2001). Columns (3)–(9) are the fitting output parameters: (3) force-freeness; (4) the center magnetic field (nT); (5) distortion; (6)–(8) longitude, tilt, and propagation angle for distorted cross section (o); (9) closest approach to the flux rope center (au). Columns (10)–(12) are derived quantities: (10) maximum cross section radius (au); (11) axial magnetic flux (10²¹ Mx); (12) poloidal magnetic flux (10⁸ Mx m⁻¹); (13) handedness (“+” is right-handed and “−” is left-handed). Columns (14)–(15) indicate the goodness of the fitting: (14) χ²; (15) fitting residue (Res) for P<sub>t</sub>(A) (GS)

Here, the vector potential $A = A(x,y)\hat{z}$ is defined such that the transverse pressure $P_t(A) = p + B_z^2/2\mu_0$ is solely dependent on A and is single-valued across the trajectory of the spacecraft through the flux rope. Routines employing this method were first applied to the magnetopause by Hau & Sonnerup (1999), and have since been adapted to the reconstruction of magnetic flux ropes by Hu & Sonnerup (2001). The assumptions inherent in this solution are that the structure is invariant in the axial ($\hat{z}$) direction and stationary in the appropriate frame of reference, and that the structure is magnetohydrostatic (i.e., $\nabla P = j \times B$).

The invariance along $\hat{z}$ for an appropriate scale length is an inherent property of magnetic flux ropes in the solar wind. We find the numerical solution to the GS equation (shown in Table 1) in the Hoffman-Teller frame of reference for each structure to ensure they are stationary, the velocities (in km s⁻¹) of which were found to be $v_{HT1} = (380.9, 1.4, -16.5)$ and $v_{HT2} = (376.1, 3.5, -6.6)$ in order of observation in the RTN coordinate system. The static nature of the flux rope over the period of time it takes for the spacecraft to traverse the structures is a matter of some debate (see Section 5.1), but we have fit the data for several concentric inner subsets of the observations in order to verify the consistency of the results.

Comparison of the reconstruction of the first substructure with the three techniques discussed above indicates that the flux rope axis orientations obtained with the CC and EC models are within 14° longitude of each other, but 49° and 35° away from the GS reconstruction. In the case of the latitude, the differences are barely 4° between all techniques. For the second (rear) substructure, the differences in the flux rope axis orientation obtained by the CC and EC models from that of the GS model are 42° and 9° for the longitude. The GS reconstruction obtains a highly tilted axis with a 69° elevation angle, 29° more tilted than the EC model and 48° more titled than the CC model reconstructions.

A comparison of the fitting results based on χ² and visual inspection (Figure 6) indicates that the EC model gives a significantly better fit for both substructures. However, at this point, it is difficult to make a direct comparison with the GS reconstruction technique, since we do not have goodness parameters or reconstructed PSP observations. Figure 6(b) displays the 3D reconstruction of both substructures based on

EC model. In the case of the central magnetic field, $B_y^0$, the difference is primarily between the CC/EC and GS models, with the CC/EC models predicting double the $B_{max}$ estimated by the GS technique.

One more scenario, as described in Section 2, would be to consider just the first part of the structure as a confined plasma within a magnetic flux rope still connected at the Sun and the second structure showing “fake” in situ signatures of a flux rope, coherent with the first substructure but with open magnetic field lines. One possible scenario is illustrated in Figure 7, considering the first substructure as a flux rope followed by a set of open magnetic field lines plus a disconnected magnetic structure. The three parts combination appears as a coherent magnetic flux rope.

In order to evaluate the effect of the spacecraft velocity, we have computed the solar wind speed in the spacecraft frame of reference. The effective structure speed as observed by the spacecraft would be $\approx 441$ km s⁻¹ for the whole structure and substructures. Thus, the size of the structure is determined using the solar wind speed in the spacecraft frame of reference, and is 0.014–0.031 au for the first substructure and 0.017–0.036 au for the second. The spacecraft deviation from the Sun–spacecraft line is $\approx 4°$.

# 4. Investigation of the Internal Complexity Based on the Solar-heliospheric Context

## 4.1. STEREO A Euvi/Cor1/Cor2 Observations

Fortunately, the conjunction of the STA telescopes with PSP trajectory provided us an unique opportunity to reconcile the in situ and remote sensing almost instantaneously. We have reviewed the imaging observations for STEREO A in order to understand the internal structure of a flux rope and the link between its signature from the local (in situ) measurements with the global (remote sensing) observations. Thus, in situ observations provide one measurement in time, and while PSP is proving to be a significant source of information for our understanding of the corona, it is through the exploitation of all available data sets that we can create a map with which we can navigate through the different aspects of a solar flux rope event—in our case, its internal structure.
<figure><img src="image_8.png" /><figcaption>**Figure 6.** (a) Comparison of the fitting results from the CC model (pink) and EC model (blue) to PSP magnetic field observations, with the two substructures fitted separately. From the top, the panels display the magnetic field strength and the three magnetic field RTN components, respectively. (b) Three-dimensional reconstruction of the magnetic structure from the EC model. The spacecraft trajectory is indicated by a red dashed line, and the red dot indicates the start time. The structured is oriented and projected as observed by Stereo A, with the Sun at the right. (c) Front view of the reconstruction.</figcaption></figure>

Figure 1 in Korreck et al. (2020) depicts a map with the locations of multiple solar-heliospheric spacecraft during the 2018 November 11–12 time period. We refer the reader to this figure for visualization of the connection between PSP measurements and STA observations of the estimated solar source region and heliospheric transit of this event. The lack of

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Illustration of a scenario of a complex substructures of the CME–SBO as an adjacent bundle of interchanged and disconnected magnetic structure. Shown is a 3D reconstruction that considers a first magnetic substructure reconstructed by the EC model and the possible configuration of open magnetic field lines plus a disconnected structure. The spacecraft trajectory is indicated by a red dashed line, and the red dot indicates the start time. The structured is oriented and projected as observed by Stereo A, with the Sun at the right.</figcaption></figure>

stereoscopic views prevents us from estimating the structure angular width projected in the ecliptic plane. Assuming radial propagation and an angular width of ≈60°, we would expect the structure to cross the spacecraft at its front, and therefore to obtain an axis longitude angle closer to 90° (φ ≈ 90°). However, the comparison with the in situ reconstruction indicates a deviation of φ = ≈45° from the expected 90° value. This could be because the SBO–CME has a smaller angular width than the regular CME angular width previously indicated. To the best of our knowledge, there is no statistical analysis of SBO angular width.

Figure 8 is composed of various images of the low corona from observations by the coronagraph and EUV instruments on board the STA spacecraft. The images shown have been processed with advanced image processing techniques that reveal structure at many spatial scales. Coronagraph images from COR1 and COR2 were processed with a temporal filter with a transmission bandpass to suppress both high-frequency noise and low-frequency variations (N. Alzate et al. 2019, in preparation). Multiwavelength images from EUVI were processed using the Multiscale Gaussian Normalization technique (MGN; Morgan & Druckmüller 2014). The FOV of COR2 of the images shown extends from 3 to 15 *R*<sub>s</sub> and overlaps with the FOV of COR1, which extends from 1.4 to 4 *R*<sub>s</sub> in the images shown. The overlap is of 1 *R*<sub>s</sub> and allows us to identify—and hence connect—structures in both data sets. There is a structure that crosses the FOV of COR1, which is shown in panels (f)–(g) and indicated by the top arrows. The bright tip reached the outer edge of the FOV at 12:05 UT (panel (g)) on November 10. It then entered the COR2 FOV at 12:08 UT, as indicated by the top arrow in panel (a). In this time frame, we see the beginning of what will be the “observational flux rope” in subsequent frames, i.e, an isolated structure in the telescope FOV with a typical three-part that consists of a bright, circular front, followed by a darker area or cavity (Illing & Hundhausen 1986). At 17:08 UT (shown in panel (b) and enclosed in a dotted square), there is a widening
<figure><img src="image_10.png" /><figcaption>**Figure 8.** STA coronagraph and EUV observations of the low corona for 2018 November 10-11. Panels (a)–(e) and (h)–(k) are COR2 images with an FOV of 3-15 $R_*$, (f)–(g) are COR1 images with an FOV of 1.4–4 $R_*$, and (l)–(p) are EUVI images, which have an FOV that extends out to 1.6 $R_*$. The COR1 and COR2 data were processed using a temporal filter with a transmission bandpass (N. Alzate et al. 2019, in preparation), while EUVI data were processed using the MGN (Morgan & Druckmüller 2014). Shown are (l)–(n) 171, (o) 195, and (p) 284 Å images. The COR2 images illustrate the evolution of the flux rope through the FOV. Prior to the signature in COR2, a bright enhancement in the streamer is evident in COR1 observations (indicated by the arrows). A plethora of activities dominate the EUVI FOV. An animation of the event in COR2 (panels (a)–(e) and (h)–(k)) is available. The video begins on 2018 November 2018 00:08:15 and ends at 2018 November 12 21:08:15. The realtime duration of the video is 7 s.</figcaption></figure>

(An animation of this figure is available.)

of the plasma surrounding the east equatorial region where the tip of the COR1 structure has entered. This morphology is in agreement with the in situ measurements of electron PADs (see Figure 1). At 22:08 UT (panel (c)), the top of the flux rope is widened and develops as it propagates outward (panel (d)). It continues to develop and exhibit observational flux rope morphology for approximately 12 hr. At 04:08 UT on November 11, the structure is still tethered to the Sun, but has widened into a “rose-bud” shape with double-ring substructures, as shown in panel (i) (traced with white dotted lines), and enveloped in a “V”-shaped boundary (traced with red dotted lines). The “tether”

appears as a horizontal line protruding from below the inner FOV at near the equator, in the same region as the horizontal structure in COR1, and reaches the back end of the flux rope (right half of panel (h)). This structure moves at the same apparent speed as the front end of the observational flux rope, and so indicates that the structure has yet to disconnect. At 07:08 UT, the front end of the structure has exited the FOV and the back end begins to disconnect (i.e., the “tether” is no longer visible in the images), until the entire *structure* is no longer visible beginning around 09:08 UT (panel (e)). Following this, a few density enhancements cross the FOV, along the same
<figure><img src="image_11.png" /><figcaption>**Figure 9.** (a) Height-time of the CME leading edge (black) derived from the model. Ninety percent confidence interval (black) and prediction interval (dark gray) are shown. Diamonds represent height measurements in COR2 FOV. The radius vs. time derived from the model is shown in red, with the corresponding 90% prediction interval. Red diamonds represent the radius measured on COR2 images. (b) Speed profile in the inner heliosphere based on Sachdeva et al. (2015, 2017). Vertical dashed lines in both panels indicate the time and heliocentric distance of PSP.</figcaption></figure>

<figure><img src="image_12.png" /></figure>

apparent path as the structure (panels (j)–(k)). These substructures may have been the remnants of the “tether” or post-CME blobs. These substructures, as well as the evolution of the flux rope, are best appreciated when viewed in a movie (available online). Further analysis is required to definitively characterize these substructures.

The observational flux rope entered the COR2 FOV as it evolved, thus suggesting formation took place below this region. Indeed, the COR1 images in panels (f)–(g) show an increase in brightness that began a few hours earlier. As the brightness increased, and then decreased, an elongated structure took shape and remained visible in COR1 for several hours after. The online movie for this figure convincingly shows this as an eruption coming up from below, along the edge of the streamer. Though the structure appeared to move outward slowly, it restructured over time, so we were able to track it through the COR1 FOV and into COR2. At 10:20 UT, there was a distinct bright front (panel (f)) that propagated toward the outer edge of the FOV (see movie for full evolution), and in panel (g), it had reached a distance of about three-fourths the FOV. This height (~3R_s) is also the inner FOV of COR2. Though the bright front was no longer visible, the elongated shape remained, with an almost horizontal bright “line” protruding from the equator and extending through the entire FOV, thus allowing us to identify it in COR2 around the same time (panel (a)).

Our analysis of EUVI observations revealed a plethora of structures in the hours preceding the observations of the flux rope. Panels (l)–(p) show a few examples of these structures in the EUVI FOV, and could explain the origins of the flux rope. The WSA-derived 3D global coronal field shown in Figure 5(b) of Korreck et al. reveals a large helmet streamer formed between the northern polar coronal hole, as well as a midlatitude coronal hole at the time when this event became visible on the east limb of STA/COR1. Our EUV and coronagraph observations are consistent with this modeling. The substructures we identified in EUVI are comparable to the substructures identified in the in situ data. Though structures at this scale are likely to be hidden underneath the large and bright streamer, our advanced image processing techniques (see figures and text for references) reveal information in EUV data

on different spatial scales that would otherwise be hidden. They also filter out large-scale structure to reveal high-frequency changes and substructures within the streamers. As a result, our techniques reveal closed field structures that rise and expand over time, as shown in the figures. In the animations provided online, the frequency of these small-scale structures in the hours leading up to the time of the CME can be fully appreciated.

Though the method used for processing COR1 has been developed to account for the nonradial nature of structures observed in this region of the corona (N. Alzate et al. 2019, in preparation), we applied the same method to COR2 data. The bandpass filter used in this method can be applied to data observations by both instruments. The method is essential for observations of the low corona, because it suppresses high levels of noise in coronagraph data. Important to note is the fact that the COR1 instrument scatters more light than does COR2, and so has a lower signal-to-noise ratio. This can account for the difference in how structures look in images from one instrument compared to those from the other, in terms of brightness and the fine details of the structures. The overall shape and evolution of the main structure, however, is obvious in both data sets, hence we are able to track these features between the different FOVs.

## 4.2. Analysis of the CME Speed Based on the Drag Model

Figure 9 displays the height-time profiles for the CME in the STA/COR2 FOV (diamonds). The observations indicate that the SBO-CME disconnection is happening high in the corona in the COR2 FOV, and so we expect that the drag interaction between the CMEs and the solar wind causes momentum exchange between them. Such interaction has an effect on the propagation speed (i.e., V_cme) of the CMEs. Furthermore, the pressure in the ambient solar wind has the effect of preventing the free expansion of CMEs.

Based on the work of Sachdeva et al. (2015, 2017), we calculated the speed profile in the inner heliosphere. We estimated the F_drag as

$$F_{\text{drag}} = -\frac{1}{2} C_D A_{\text{cme}} n_{\text{sw}} m_p (V_{\text{cme}} - V_{\text{sw}}) |V_{\text{cme}} - V_{\text{sw}}| \quad (7)$$
using observationally derived parameters, such as the solar wind density, $n_{sw}$, and the CME and solar wind speeds, $V_{cme}$ and $V_{sw}$. The remaining quantities are: the drag coefficient $C_D$ (Subramanian et al. 2012), which gives the strength of the momentum coupling between the CME and the solar wind as described; the cross sectional area of the CME, $A_{cme}$; and the proton mass, $m_p$.

To determine the ambient conditions at the time of the CME launch, we took the average solar wind electron number density $n_{sw} \sim 200 \text{ cm}^{-3}$ and speed $V_{sw} \sim 390 \text{ km s}^{-1}$ from PSP in situ measurements made prior to the arrival of the CME. We then used Leblanc et al. (1998) and Sheeley et al. (1997, 1999) models to extrapolate these quantities back to the Sun. The initial CME speed of $V_{cme} \sim 200 \text{ km s}^{-1}$ and initial height of $h_0 = 3.0$ solar radii came from the values calculated using COR2 observations. We compared the model solutions with the observed height-time data at distances below 15 solar radii, and found that they agree reasonably well. We determined the 90% confidence and prediction bands of the model solution by using a Monte Carlo approach with multiple random realizations of the input parameters within a noise range of $\pm 10\%$.

It should be noted that solar wind drag can affect a CME by decelerating it, as well as accelerating it. The velocity profile indicates that the structure is accelerating in the solar wind, reaching a speed of $389 \text{ km s}^{-1}$ 90% CI [383,394] at 53 solar radii. This is consistent with the average velocity measured by PSP ($\sim 391 \text{ km s}^{-1}$). By the time the structure arrives at PSP, the in situ solar wind speed measurement indicates there is very little expansion at this height. As shown by the red diamonds in Figure 9, the maximum radius measured in the COR2 FOV is $\lesssim 2$ solar radii. The radius derived from the model that assumes the radial expansion from Liu et al. (2005) yields a value of $\sim 5$ solar radii (0.023 au) at PSP distance (red curve), which is in agreement with the analysis presented in Section 3 for the single flux rope scenario.

# 5. Analysis of the Evolutionary Effects on the Internal Structure

## 5.1. Magnetic Erosion and Magnetic Reconnection

In this section, we analyze the properties of the magnetic field of the structure in terms of asymmetry in azimuthal magnetic flux and the possible occurrence of magnetic erosion by magnetic reconnection at its boundaries. For that purpose, we first employ the method developed by Dasso et al. (2006, 2007), which consists of analyzing the variation of the accumulated azimuthal magnetic flux per unit length ($L_{in}$), defined as Ruffenach et al. (2015):

$$ \frac{F_y(x)}{L_{in}} = \int_{t_{in}}^{t(x)} B_y^{\text{struc}}(t') V_x^{\text{struc}} dt', \quad (8) $$

where $t_{in}$ is the time of the structure front boundary, $B_y^{\text{struc}}$ and $V_x^{\text{struc}}$ are the respective components of the magnetic field and velocity in the structure frame, and $L_{in}$ is total length along the flux tube. The structure frame is defined (e.g., Dasso et al. 2006; Ruffenach et al. 2012, 2015) such that $Z_{\text{struc}}$ points along the main axis of the structure.

The direction $d$ is defined by the rectilinear trajectory of the spacecraft (antiradial direction in RTN), $Y_{\text{struc}}$ is given by $Z_{\text{cloud}} \times d$, and $X_{\text{struc}}$ completes the right-handed coordinate system. Parameters $\theta$ and $\phi$ are defined in the RTN coordinates.

In Figure 10(a), we display the magnetic field data in RTN coordinates, as well as the azimuthal magnetic field component (purple) and accumulated azimuthal flux (green curve). This accumulated magnetic flux is calculated by starting the integration of the component $B_y^{\text{structure}}$ at the front boundary, and using the axis orientation given by the CC fitting method applied on the whole structure (with $\phi = 46^\circ$ and $\theta = 8^\circ$). As discussed in Ruffenach et al. (2012, 2015), the appearance of asymmetry in azimuthal flux may be interpreted as a signature of erosion by magnetic reconnection. In Figure 10(a), the green curve, representing the accumulated azimuthal flux, crosses the abscissa before the end of the magnetic structure. This is consistent with a short “back” region, possibly corresponding to some erosion at the front of the magnetic structure since eruption.

However, the orientation of the magnetic structure axis is a key parameter for estimating the eroded azimuthal flux. As listed in Table 1, there is a significant variability in the results as a function of the fitting method used, i.e., the CC and EC models and the GS reconstruction technique. In Figure 10(b), we thus employ the same method as in Ruffenach et al. (2012) to estimate the impact of any change in magnetic structure axis orientation on the results of the accumulated flux and implied asymmetry. Figure 10(b) shows the amount of eroded magnetic flux as a function of axis orientation in a parametric fashion. It shows that the amount of erosion changes very rapidly for rather low angular changes of the axis, primarily in $\theta$. The white region is inconsistent with erosion at the front boundary, but would instead be consistent with some erosion at the rear. The red region is consistent with very strong erosion (more than 50% erosion), such that there is no more bipolar change in the azimuthal magnetic field (which is not realistic). Overall, just a change of $10^\circ$, as shown by the circles, changes the analysis substantially. We also show, with a second red diamond, the result for the EC method axis orientation ($\phi = 39^\circ$ and $\theta = 11^\circ$), which is inconsistent with erosion at the front, but would instead be consistent with a slight erosion at the rear. This analysis is thus not very conclusive; we cannot determine with certainty whether this magnetic structure is eroded or not.

These results suggest that magnetic reconnection has not been at work at the magnetic structure boundaries—or that it has been at work since eruption, but in similar amounts at the front and the rear (Ruffenach et al. 2015). We looked for magnetic reconnection signatures in situ at the two boundaries, and found some evidence for bifurcated current sheets (two sharp consecutive steps in the magnetic field components (Phan et al. 2020) at both the front and rear boundary when analyzing the highest resolution magnetic field data (not shown). However, the time resolution of the plasma data at both boundaries is insufficient to confirm the possible presence of an associated small reconnection exhaust.

## 5.2. Force Imbalance

In this section, we describe the observed magnetic structure distortion as a consequence of the imbalance among the forces acting on the SBO-CME structure, i.e., the internal (within the flux rope) and external forces (within the CME) acting on the magnetic structure. For this analysis, we selected the previously discussed scenario where the SBO is a single flux rope, relegating the analysis of scenarios with more complex internal structure for future research.
<figure><img src="image_13.png" /><figcaption>**Figure 10.** (a) Parker Solar Probe magnetic field data (in RTN coordinates; respectively in black, blue, and red colors), as well as the azimuthal magnetic field component (purple) and accumulated azimuthal flux (green curve). The vertical black dashed lines correspond to the start and end times of the accumulation interval. See text for further details. (b) Parametric study of the impact of an arbitrary MC axis orientation on the amount of azimuthal magnetic flux eroded from the front of the MC, as defined in the text—and similar to the analysis performed in Ruffenach et al. (2012). The figure center, with a red diamond, corresponds to the orientation obtained from the CC method fitting (values $\phi = 46^\circ$ and $\theta = 8^\circ$). The center red diamond ($\phi = 39^\circ$ and $\theta = 11^\circ$) corresponds to the results using the EC method fitting. The line separating the dark blue and the white region corresponds to axes orientations for which the azimuthal flux is exactly balanced (in the front and back parts of the magnetic structure). Regions with other colors (blue to red) are consistent with erosion occurring at the front of the cloud, of various amounts as shown (see color scale for magnetic structure flux erosion percentage). The white region is inconsistent with erosion at the front, but it may potentially occur at the rear instead (Ruffenach et al. 2015).</figcaption></figure>

In the case of the internal forces, the Lorentz force distribution within the confined magnetized plasma flux rope structure is shown in Figure 11. The CC and EC models, by definition, lack any force-free constraints. Thus, as previously discussed, the $C_{10}$ parameter is one of the direct output parameters that provides the opportunity to evaluate the internal Lorentz force distribution in the structure. This evaluation is based on the analysis of the misalignment between the current density and the magnetic field. The behavior of this parameter has been largely discussed in Nieves-Chinchilla et al. (2016, 2018b). Figure 11 displays the profile of the misalignment along the radius in the case of the whole interval. The blue line represents the CC model, and the pink lines indicate the EC model, with the thick pink line representing the minor radius ($\delta R$) and the dashed pink line the major radius. The two parallel dashed gray horizontal lines mark an arbitrary threshold for the force-freeness. When the resulting misalignment is within the dashed lines, the system is assumed to be force-free, while any non-force-free system would have values outside of this interval with an absolute value greater than 0.3; that is, the angle between the current density and the magnetic fields is greater than 18°.

For this specific event, in both models, the force distribution exhibits a force-free core. In the case of the CC model, the magnetic rope remains force-free in ~65% of the flux rope core, with an increase of the Lorentz forces along the radial distance to the axis. This is a consequence of the increase of the magnetic tension due to the magnetic field lines' curvature. In the case of the EC model, the misalignment indicates that the system remains force-free within a smaller ellipse with minor radius of ~0.2 *R* and major radius of 0.4 *R*. The core follows the distortion in the cross section as the whole structure. Out of this smaller ellipse, the misalignment is more significant than in

the CC model, being stronger at the end of the major radius. Thus, the Lorentz forces are significant in both radial (minor, major) directions, and are more propounded in the major radius. Ergo, in addition to the internal magnetic tension due to the twisting, there is an additional internal dynamics that leads the structure to reach a more circular—and therefore more stable—cross section.

In the analysis of the forces acting on the structure based on the remote sensing observations, the observed speed, well below $500 \text{ km s}^{-1}$, indicates that the magnetic and pressure forces are the drivers of the CME propagation, dominating over the ballistic force (Low 1984, 1996). Following the approach described by Mishra & Wang (2018), we use the kinematic profile of the CME derived from COR2 observations to infer the evolution of the internal forces at distances close to the Sun. These include the changes of the average Lorentz force (*fem*) and thermal pressure force (*fth*). The approach also considers the centrifugal force (*fp*) as the CME propagated away from the Sun, although it is not discussed in this paper.

Figure 11(c) depicts the variation of the ratio of the absolute values of the Lorentz and thermal forces acting inside the CME with the heliocentric distance in the STA/COR2 FOV. We find that, at distances from 6 to 12 solar radii, the Lorentz force dominates over the thermal force, with their difference decreasing from ~20% to ~5%. We also find that the thermal force acting over the magnetic structure inside the SBO-CME is the driver of CME expansion (outward) while the Lorentz force prevents the CME from expanding (inward).

We measure a mean expansion velocity in the in situ observations and in the COR2 FOV. The value obtained from the linear fitting of the solar wind bulk velocity is ~11 km s⁻¹ and the expansion velocity (lateral direction) is ~47 km s⁻¹ in COR2 FOV. This result implies that the net force (considering
<figure><img src="image_14.png" /><figcaption>**Figure 11.** (a) Misalignment between the current density and the magnetic field along the radial distance. Pink lines represent the major (dashed line) and minor radii in the EC model reconstruction. Blue line represents the CC model. (b) Sketches of the Lorentz force distribution along the flux rope cross section from the CC and EC mode. (c) Variation of the ratio of the absolute values of the Lorentz and thermal forces acting on the CME with the heliocentric distance in the STA/COR2 FOV.</figcaption></figure>

the centrifugal force also) should be positive, albeit all three forces could decrease as the CME propagates away from the Sun. According with Figure 11(c), the effect of the Lorentz forces upon thermal forces decreases with time, and therefore the effect of the inward force upon the internal structure decreases, with a tendency to reverse the *fem/fth* ratio. Thus, without knowing what will happen after 12 *R*<sub>s</sub>, we can only speculate that the *fem* forces will balance the *fth* (*fem/fth* ≈ 1, or even less). In that case, any electromagnetic force, including the magnetic tension due to the curvature, will be balanced by the internal pressure, and the structure will become a force-free system and no longer distorted.

Comparing these results with those previously obtained in the in situ analysis, the interpretation could be different based on the results from the CC or the EC model. In the case of the CC model, a highly twisted structure would maintain the internal forces dominated by the Lorentz forces—not just forcing the structure to be circular, but also preventing the structure from expanding, which it is consistent with the in situ observations. However, in the interpretation of the remote sensing observations, the observational structure is far to be considered circular in the core. In the case of the EC model results, the in situ reconstruction and remote sensing visual inspection are consistent with the interpretation of an elliptical cross section shape. The results suggest that the Lorentz forces remain dominant from 12 solar radii (COR2 FOV) to ~54 solar radii (PSP solar distance). According to the in situ reconstruction, the spacecraft is crossing along the maximum distortion, where the Lorentz forces are more significant. In this scenario, the Lorentz forces would balance the thermal forces also preventing the expansion in the major radius direction. Note that the solar wind temperature from the in situ observations is low, as compared to the surrounding ambient solar wind, which could be indicative of an expanded structure.

The scenarios described previously correspond to a combination of the results from two different techniques, and some important assumptions have been made. For the in situ reconstruction, the CC or EC models assume a single flux rope geometry and a specific internal topology. In the case of the Mishra & Wang (2018) model, the results are very sensitive to small variations in the measurements, as well as in the assumed kinematic profiles. However, this analysis paves the way to reconcile both techniques in order to understand the dynamics of the coupling between the large structures in the solar wind and its consequences in the change of the internal structure.

## 6. Brief Discussion and Conclusions

A large magnetic structure was observed on (2018) November 11 during the outbound leg of PSP at first perihelion, at a distance of 0.25 au from the Sun. The FIELDS magnetometer measured an increase of the magnetic field strength and a coherent change in the magnetic field direction. The magnetic field components indicate a deviation from the expected smooth rotation of a helical magnetic flux rope. Simultaneously, SWEAP displayed signatures of confined magnetized plasma, i.e., low proton temperature and low proton beta plasma. The structure was embedded in the slow solar wind in the vicinity of the IMF sector boundary, but not enclosed in the HCS. It barely exhibited any signatures of expansion. The partial bidirectionality of the electron PAD indicates two-thirds of the structure remains connected to its solar source region. The rear third part of the structure depicts a sharp change in the electron PAD profile with a flux dropout. Thus, our preliminary visual inspection of the internal transient structure magnetic and plasma properties suggests high complexity, with deviations from an ideal flux rope 3D topology.

The conjunction with STA enabled remote observations of a streamer blowout in the FOV of the SECCHI suite of instruments. The solar source of the slow and well-structured flux-ropes was identified in an overlying streamer, the details of which are described in Korreck et al. (2020). Indeed, as we have shown, the rising and expansion of the streamer in COR1
evolves into the flux rope observed in COR2. Thanks to this unique opportunity, we have performed a comprehensive analysis of the internal CME–SBO magnetic structure in the context of the initiation and evolutionary processes by combining the remote and in situ observations.

The detailed 3D reconstruction of the internal structure was carried out using three well-established models and a fitting technique: the CC and EC models by Nieves-Chinchilla et al. (2016, 2018b), and the Grad–Shafranov reconstruction technique by Hu & Sonnerup (2002). The comparative analysis of the structure orientation and physical parameters is inconclusive. This is partly due to the current limitations in stereoscopic views (e.g., STEREO B was lost in 2014) that have prevented us from extrapolating the global shape of the SBO, but also is also a result of our limited understanding of such internal structures without further analysis.

As such, the focus of this paper was to review the observations available and attempt to reconcile them with our current understanding of this CME internal magnetic structure. Therefore, our analysis led us to consider three possible scenarios that may explain the structure.

1. A single flux rope transient. This is the traditional scenario. We consider the structure as a whole magnetic flux rope. The in situ reconstruction determines that the flux rope is highly distorted along the spacecraft trajectory and the propagation direction. This is very consistent with remote sensing observations, which exhibit an elongated shape, as well as with initiation mechanisms for SBOs. For this scenario, we could argue that the flux rope structure may be parceled with different magnetic and plasma properties, and therefore in situ measurements would display different signatures of the core and the outer layers (e.g., Owens et al. 2017). The back magnetic field compression could also be justified by an internal poloidal plasma motion due to evolutionary processes such as deflection or rotation (e.g., Wang et al. 2015).

2. Two internal flux rope transients. This scenario is supported by the double-ring substructure observed in the STA-COR2 FOV (see Figures 8(h)–(i)). The in situ reconstruction techniques still indicate a highly distorted structure that is aligned with the propagation direction and consistent with the observations. These cases have already been reported in previous studies (e.g., Oshervich et al. 1999; Hu et al. 2003). However, this scenario does not explain why the second part of the structure displays a different electron PAD profile with a sharp change from bidirectionality to a “flux dropout.”

3. A combination of a flux rope and open magnetic field lines. This scenario is based on the combination of the flux rope disconnection with interchange reconnection that was proposed by Crooker et al. (2002). Thus, the magnetic structure would be a mixed topology of a traditional flux rope, where the electron counterstreaming combines with an adjacent bundle of interchanged and disconnected flux. The sketch shown in Figure 3(c) and the reconstruction illustrated in Figure 7 exemplify this scenario. It should be noted, however, that the real nature of the structure could be even more complex—see, for instance, the sketches in Gosling (1999)—with multiple topologies having different coronal connectivities, even in a structure that appears to be a coherent magnetic flux

rope. Therefore, the different connectivities may also explain the penetration of energetic particles within the magnetic structure as observed by ISoS Epi-Lo instrument. After complementing PSP observations with the remote sensing observations, we can justify this scenario with the plethora of structures observed in EUVI data in the hours preceding the SBO evacuation.

In the last part of this study, we took advantage of the unique observations from PSP, which allowed us to explore the first stages of the effects of coupling with the solar wind and the evolutionary processes in the magnetic structure. The appearance of the asymmetry, after considering the whole structure as a single flux rope, can be interpreted as a signature of erosion and magnetic reconnection. However, the ambiguity in the orientation of the flux rope axis prevents us from concluding as to whether the structure is eroded. In the case of magnetic reconnection, we found evidence of bifurcated current sheets in the structure boundaries that may suggest this, but the lack of sufficient temporal resolution in the plasma observations also puts a damper on this conclusion.

In terms of coupling with the ambient solar wind and the effects on the internal structure dynamics, we have carried out a preliminary study based on remote sensing observations, as proposed by Mishra & Wang (2018). Our results suggest that the internal Lorentz forces would dominate over the thermal forces decreasing from 20% to 5% in the COR2 FOV. Thus, the Lorentz forces would act to balance the magnetic tension due to the strong distortion observed in the STA-COR2 FOV. These results are confirmed by our in situ analysis of the internal Lorentz distribution; an analysis we based on the studies carried out by Nieves-Chinchilla et al. (2016, 2018b). We have demonstrated that the inward forces are more significant along the major radius or maximum distortion. This preliminary analysis of the internal force imbalance will widen current understanding of the distortion as a consequence of the coupling of the structure with the solar wind. Further studies that follow this direction are needed, not only to improve the techniques for reconciling the remote sensing with observations, but also to evaluate the impact of other force components in CME dynamics.

At this stage in our analysis, we cannot definitively identify which of the scenarios described above is the most reliable. In addition to the ever-present question of whether or not all CMEs are flux ropes, one other important question to pose is whether all flux ropes are topologically alike, i.e., are the internal structures of CMEs originating from active regions the same as those of “stealth” CMEs and/or those of streamer-blowout CMEs? What we can say is that PSP brings the opportunity to be closer than ever to the Sun, and provides a uniquely advantageous perspective to observe these transients in a more “pure” stage of development before the effects of its evolution. The PSP spacecraft is thus providing an opportunity to validate the ideas, sketches, cartoons, models, and theories that have dominated the literature for many decades, but have yet to be observed with confidence.

Parker Solar Probe was designed, built, and is now operated by the Johns Hopkins Applied Physics Laboratory as part of NASA’s Living with a Star (LWS) program (contract NNN06AA01C). Support from the LWS management and technical team has played a critical role in the success of the Parker Solar Probe mission.
## ORCID iDs

Teresa Nieves-Chinchilla https://orcid.org/0000-0003-0565-4890

Adam Szabo https://orcid.org/0000-0003-3255-9071

Kelly E. Korreck https://orcid.org/0000-0001-6095-2490

Nathalia Alzate https://orcid.org/0000-0001-5207-9628

Laura A. Balmaceda https://orcid.org/0000-0003-1162-5498

Benoit Lavraud https://orcid.org/0000-0001-6807-8494

Kristoff Paulson https://orcid.org/0000-0002-5699-090X

Samantha Wallace https://orcid.org/0000-0002-1091-4688

Lan K. Jian https://orcid.org/0000-0002-6849-5527

Janet G. Luhmann https://orcid.org/0000-0003-0626-9353

Huw Morgan https://orcid.org/0000-0002-6547-5838

Aleida Higginson https://orcid.org/0000-0003-1380-8722

Charles N. Arge https://orcid.org/0000-0001-9326-3448

Stuart D. Bale https://orcid.org/0000-0002-1989-3596

Anthony W. Case https://orcid.org/0000-0002-3520-4041

Thierry Dudok de Wit https://orcid.org/0000-0002-4401-0943

Keith Goetz https://orcid.org/0000-0003-0420-3633

Peter R. Harvey https://orcid.org/0000-0002-6938-0166

Shaela I. Jones-Melosky https://orcid.org/0000-0001-9498-460X

J. C. Kasper https://orcid.org/0000-0002-7077-930X

Davin E. Larson https://orcid.org/0000-0001-5030-6030

Roberto Livi https://orcid.org/0000-0002-0396-0547

David J. McComas https://orcid.org/0000-0001-6160-1158

Robert J. MacDowall https://orcid.org/0000-0003-3112-4201

David M. Malaspina https://orcid.org/0000-0003-1191-1558

Marc Pulupa https://orcid.org/0000-0002-1573-7457

Nour E. Raouafi https://orcid.org/0000-0003-2409-3742

Nathan Schwadron https://orcid.org/0000-0002-3737-9283

Michael Louis Stevens https://orcid.org/0000-0002-7728-0085

Phyllis L. Whittlesey https://orcid.org/0000-0002-7287-5098

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