# Dayside magnetopause reconnection and flux transfer events under radial interplanetary magnetic field (IMF): BepiColombo Earth-flyby observations

Weijie Sun, James A. Slavin, Rumi Nakamura, Daniel Heyner, Karlheinz J.

Trattner, Johannes Z. D. Mieth, Jiutong Zhao, Qiu-Gang Zong, Sae Aizawa, Nicolas Andre, et al.

► To cite this version:

Weijie Sun, James A. Slavin, Rumi Nakamura, Daniel Heyner, Karlheinz J. Trattner, et al. Day-side magnetopause reconnection and flux transfer events under radial interplanetary magnetic field (IMF): BepiColombo Earth-flyby observations. Annales Geophysicae, 2022, 40 (2), pp.217-229. 10.5194/angeo-40-217-2022. insu-03672031

HAL Id: insu-03672031

https://insu.hal.science/insu-03672031

Submitted on 19 May 2022

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# Dayside magnetopause reconnection and flux transfer events under radial interplanetary magnetic field (IMF): BepiColombo Earth-flyby observations

Weijie Sun<fnref n="1" />, James A. Slavin<fnref n="1" />, Rumi Nakamura<fnref n="2" />, Daniel Heyner<fnref n="3" />, Karlheinz J. Trattner<fnref n="4" />, Johannes Z. D. Mieth<fnref n="3" />, Jiutong Zhao<fnref n="5" />, Qiu-Gang Zong<fnref n="5" />, Sae Aizawa<fnref n="6" />,<fnref n="7" />, Nicolas Andre<fnref n="6" />, and Yoshifumi Saito<fnref n="8" />

**Correspondence:** Weijie Sun (wjsun@umich.edu)

Received: 20 October 2021 – Discussion started: 22 October 2021

Revised: 22 March 2022 – Accepted: 25 March 2022 – Published: 22 April 2022

**Abstract.** This study analyzes the flux transfer event (FTE)-type flux ropes and magnetic reconnection around the dayside magnetopause during BepiColombo's Earth flyby. The magnetosheath has a high plasma $\beta$ (~8), and the interplanetary magnetic field (IMF) has a significant radial component. Six flux ropes are identified around the magnetopause. The motion of flux ropes together with the maximum magnetic shear model suggests that the reconnection X-line possibly swipes BepiColombo near the magnetic equator due to an increase in the radial component of the IMF. The flux rope with the highest flux content contains a clear coalescence signature, i.e., two smaller flux ropes merge, supporting theoretical predictions that the flux contents of flux ropes can grow through coalescence. The coalescence of the two FTE-type flux ropes takes place through secondary reconnection at the point of contact between the two flux ropes. The BepiColombo measurements indicate a large normalized guide field and a reconnection rate comparable to that measured at the magnetopause (~0.1).

## 1 Introduction

Flux transfer events (FTEs) are frequently observed near the outer boundaries, i.e., magnetopause, of planetary magnetospheres, including on Earth (e.g., Russell and Elphic, 1978; Saunders et al., 1984; Wang et al., 2005), Mercury (Russell and Walker, 1985; Slavin et al., 2009, 2010, 2012; Imber et al., 2014; Sun et al., 2020a; Zhong et al., 2020), Saturn (Jasinski et al., 2016, 2021), and Jupiter (Walker and Russell, 1985; Lai et al., 2012). Some of the FTEs have magnetic flux ropes at their cores, which consist of helical magnetic field lines surrounding stronger magnetic fields paralleling their central axes (Paschmann et al., 1982; Lee et al., 1993). These FTE-type flux ropes are created by multiple X-line reconnections in the magnetopause during intervals of significant magnetic shear across the magnetopause current sheet (Lee and Fu, 1985; Raeder, 2006). As a result, the FTE-type flux rope signal the occurrence of magnetic reconnection its direction of travel, can be used to infer the relative location of the reconnection X-line at the magnetopause.

The FTEs usually include magnetic field lines with one end connecting to the interplanetary magnetic field (IMF) and the other to a magnetospheric cusp. They transport magnetic flux from the dayside to the nightside magnetosphere

<footnote n="1">¹Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109, USA</footnote>

<footnote n="2">²Space Research Institute, Austrian Academy of Sciences, Schmiedlstraße 6, 8042 Graz, Austria</footnote>

<footnote n="3">³Institut für Geophysik und extraterrestrische Physik, Technische Universität Braunschweig, 38106 Braunschweig, Germany</footnote>

<footnote n="4">⁴Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA</footnote>

<footnote n="5">⁵School of Earth and Space Sciences, Peking University, Beijing 100871, China</footnote>

<footnote n="6">⁶Institut de Recherche en Astrophysique et Planétologie, CNRS-UPS-CNES, Toulouse, France</footnote>

<footnote n="7">⁷Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Japan</footnote>

<footnote n="8">⁸Japan Aerospace Exploration Agency, Institute of Space and Astronautical Science, Kanagawa, Japan</footnote>
that drives the Dungey cycle in planetary magnetospheres with global intrinsic magnetic fields. Sun et al. (2022) recently reviewed the contributions of FTE-type flux ropes to the Dungey cycle in dipolar planetary magnetospheres. In Mercury's magnetosphere, FTE-type flux ropes transport the majority (> 60%) of the circulated flux (Slavin et al., 2010; Sun et al., 2020a). In contrast, FTE-type flux ropes are estimated to transport only a small portion (< 5%) of the circulated flux at Earth (Lockwood et al., 1995; Fear et al., 2017). For the giant outer planetary magnetospheres at Jupiter and Saturn, they appear to transport a negligible magnetic flux (< 1%) for the solar wind-driven portion of their internal convection (Jasinski et al., 2021).

The FTEs on Earth's magnetosphere appear most frequently during periods of the southward IMF when the magnetic shear angle across the magnetopause is larger than 90° (e.g., Rijnbeek et al., 1984; Kuo et al., 1995; Wang et al., 2006). The locations of magnetopause X-lines are closely related to the orientation of the IMF. For example, during the purely southward IMF, reconnection most likely occurs on the magnetopause near the subsolar point (Dungey, 1961). During the purely northward IMF, reconnections occur on the magnetopause tailward of the cusp (Dungey, 1961; Song and Russell, 1992; Shi et al., 2009, 2013; Gou et al., 2016). Magnetic reconnection is also thought to occur at the dayside magnetopause under the strong radial IMF ($B_x$ dominate) (Belenkaya, 1998; Luhmann et al., 1984; Pi et al., 2017; Tang et al., 2013; Toledo-Redondo et al., 2021), but the strong radial IMF conditions are less well studied.

Coalescence, which refers to the merging of neighboring flux ropes, is thought to be an important process in space plasma physics (Biskamp and Welter, 1980; Dorelli and Bhattacharjee, 2009; Fermo et al., 2011; Hoilijoki et al., 2017). The merging of flux ropes is associated with secondary reconnection, and changes in magnetic field configuration caused by this secondary reconnection can energize particles, especially electrons (Drake et al., 2006). Furthermore, several studies have suggested that FTE-type flux ropes are initially formed between electron and ion scales. They then grow through coalescence, thereby increasing their magnetic flux contents and scales (Fermo et al., 2011; Akhavan-Tafti et al., 2018). NASA's Magnetospheric Multi-scale (MMS) Mission (Burch et al., 2016) has provided several observations of secondary reconnections between neighboring flux ropes (see Zhou et al., 2017), between flux ropes and Earth's dipole magnetic field (Poh et al., 2019), and between interlinked flux tubes (Øieroset et al., 2016; Kacem et al., 2018).

This study investigates FTE-type flux ropes and reconnection at Earth's dayside magnetopause during BepiColombo's flyby on 10 April 2020. The paper is arranged as follows. Section 2 introduces the BepiColombo mission and the measurements during Earth's dayside magnetopause crossing. Section 3 analyzes the distribution of magnetopause reconnection with a strong radial IMF component and the proper-

ties of the flux ropes, including a coalescence event. Section 4 provides a summary of our results.

## 2 BepiColombo dayside magnetopause crossing

### 2.1 Spacecraft and instrumentation

BepiColombo is a joint mission by the European Space Agency (ESA) and Japan Aerospace Exploration Agency (JAXA), which consists of two spacecraft named the Mercury Planetary Orbiter (MPO) and Mercury Magnetospheric Orbiter (MMO or Mio). These spacecraft together aim to carry out detailed investigations of Mercury's interior, surface, exosphere, and magnetosphere (Milillo et al., 2020; Murakami et al., 2020; Benkhoff et al., 2010). The mission made its first planetary flyby maneuver at Earth on 10 April 2020 (Mangano et al., 2021), during which several instruments collected measurements. The MPO and the MMO were attached during the Earth flyby, and therefore their measurements could be deemed one observation point. The two spacecraft will be separated when they are scheduled to insert into Mercury's orbit by late 2025 or early 2026.

This study uses measurements collected by the magnetometer (MAG) onboard MPO (Heyner et al., 2021) and the low-energy electron by the Mercury Electron Analyzer (MEA) (Sauvaud et al., 2010), which is part of the Mercury Plasma Particle Experiment (MPPE) onboard MMO (Saito et al., 2021). The MPO/MAG includes one outboard sensor and one inboard sensor, and it has a sampling rate of 128 Hz. Mio/MEA has a sampling rate of 4 s. The IMF and solar wind conditions are obtained from the OMNI dataset (King and Papitashvili, 2005), which has a time resolution of 1 min.

### 2.2 Overview of the magnetosheath and magnetopause

Figure 1 shows an overview of the dayside magnetopause crossing during BepiColombo's Earth flyby. BepiColombo traveled from the magnetosheath into the dayside magnetosphere. It crossed the magnetopause at a distance of ~4.8 $R_E$ ($R_E$ is 1 Earth radius) dawnward from the subsolar magnetopause, which corresponded to a position of (11.2, -4.8, -0.3) $R_E$ in the geocentric solar magnetospheric (GSM) coordinate. During the 30 min interval around the magnetopause crossing (~00:05 to 00:35 UT) analyzed here, the IMF was southward with a strong radial component; i.e., the $B_x$ was the dominant component ($B_x/B_t > 0.7$ in Fig. 1h). The average electron density in the magnetosheath was estimated to be ~10 cm$^{-3}$ based on the onboard-calculated partial moment from Mio/MEA between 00:05 and 00:28 UT. The magnetosheath plasma $\beta$ was high, with a value of ~8.0, which was the ratio of the thermal pressure to the magnetic pressure. The thermal pressure in the magnetosheath was calculated by assuming that the pressure balance existed across the dayside magnetopause and that the thermal pressure in-
<figure><img src="image_3.png" /><figcaption>**Figure 1.** The electrons and magnetic field measurements of the dayside magnetopause during BepiColombo's Earth flyby. (a) The time-energy spectrogram of normalized electron counts from Mio/MEA, (b) magnetic x component $B_x$, (c) y component $B_y$, (d) z component $B_z$, (e) magnetic component normal to the magnetopause $B_N$, (f) magnetic field intensity $B_t$, (g) clock angle ($\theta$), (h) $B_x/B_t$ of the IMF, (i) solar wind number density ($n_p$), and (j) solar wind Alfvénic Mach number ($M_A$). All quantities are in the geocentric solar magnetospheric (GSM) coordinate. The green arrows in panel (e) indicate the six FTE-type flux ropes. “S” indicates southward traveling and “N” northward traveling. The $\theta$ in panel (g) is defined as $\arctan(B_y/B_z)$, ranging from 0 to 360°. In panel (g), the black line is from the measurements of MPO/MAG, and the blue line is from OMNI.</figcaption></figure>

side the dayside magnetosphere was negligible compared to the magnetic pressure.

# 3 Magnetopause reconnections and FTE-type flux ropes

## 3.1 Identification of FTE-type flux ropes

The FTE-type flux ropes were identified after the measured magnetic field was rotated into boundary normal coordinates (the LMN coordinate). The minimum variance analysis (MVA) (Sonnerup and Cahill, 1967; Sonnerup and Scheible,

1998) was performed on the magnetic field measurements across the magnetopause current sheet from 00:32:30 to 00:33:25 UT to obtain the LMN coordinate. The MVA results produced $L = [0.10, 0.24, 0.97]$ (maximum variance direction), $M = [0.12, 0.96, -0.25]$ (intermediate variance direction), and $N = [0.99, -0.14, -0.06]$ (minimum variance direction), and the eigenvalue ratios were $\lambda_{max}/\lambda_{int} \sim 54.3$ and $\lambda_{int}/\lambda_{min} \sim 3.9$. The $\lambda_{max}$, $\lambda_{int}$ and $\lambda_{min}$ are the maximum, intermediate, and minimum eigenvalues. Both of the ratios were larger than 3, indicating that the LMN coordinate of the magnetopause was well determined (Sonnerup and Scheible, 1998).
<table><caption>**Table 1.** List and properties of FTE-type flux ropes observed during BepiColombo's dayside magnetopause crossing.</caption><thead><tr><th>No.</th><th>Time</th><th>Duration (s)</th><th>Traveling direction</th><th>Core field intensity (nT)</th><th>Scale (km)<sup>b</sup></th><th>Flux content (kWb)</th><th>X<sup>2</sup></th></tr></thead><tbody><tr><td>1</td><td>00:11:04</td><td>~ 12</td><td>Southward</td><td>~<sup>a</sup></td><td>—</td><td>—</td><td>—</td></tr><tr><td>2</td><td>00:26:06</td><td>~ 7</td><td>Northward</td><td>~ 23.9</td><td>462, 388 (0.84)</td><td>~ 13.7</td><td>~ 0.04</td></tr><tr><td>3</td><td>00:26:26</td><td>~ 6</td><td>Northward</td><td>~ 60.8</td><td>565, 524 (0.93)</td><td>~ 22.5</td><td>~ 0.04</td></tr><tr><td>4</td><td>00:26:35</td><td>~ 4</td><td>Northward</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>5</td><td>00:28:13</td><td>~ 20</td><td>Northward</td><td>~ 41</td><td>1745, 1281 (0.73)</td><td>~ 300</td><td>~ 0.08</td></tr><tr><td>6</td><td>00:30:26</td><td>~ 15</td><td>Northward</td><td>~ 45.2</td><td>1853, 1745 (0.94)</td><td>~ 188</td><td>~ 0.08</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Figure 2.** The southward-traveling FTE-type flux rope centered at ~00:11:04 UT. (a) Magnetic field component in the L direction, $B_L$, (b) magnetic field component in the M direction, $B_M$, (c) magnetic field component in the N direction, $B_N$, and (d) $B_t$. This LMN is the local coordinate of the magnetopause. Panels (e) and (f) are the hodograms of the magnetic field measurements under the local coordinate of the flux rope. “B” and “E” indicate the beginning and end of the data points.</figcaption></figure>

The FTE-type flux ropes were identified with bipolar signatures in the normal magnetic field ($B_N$) and clear magnetic field rotation (Russell and Elphic, 1978). The identification of flux ropes also required the signature of a strong magnetic field along their central axis, i.e., the intermediate variance direction (see Fig. 2 for an example and, e.g., Slavin et al., 2009; Akhavan-Tafti et al., 2018). Six FTE-type flux ropes were identified in this manner in the magnetosheath just upstream of the dayside magnetopause and are marked with green arrows in Fig. 1e and listed in Table 1.

The first possible FTE-type flux rope shown in Fig. 2 was centered at ~00:11:04 UT when the IMF clock angle was ~210°, and $B_x/B_t$ was ~0.75. This flux rope traveled southward, as inferred from the polarities of the $B_N$ variation (negative to positive, Fig. 2c). The flux rope corresponded to clear

enhancement in $B_M$ (Fig. 2b) and field rotation in the plane of $B_{max} - B_{int}$ (Fig. 2e). However, the enhancement in the $B_t$ strength preceding the reversal in $B_N$ could indicate that the magnetic flux was piled up or that this structure was a magnetosheath structure other than a flux rope. About 2 min later, the clock angle increased to ~260°. This IMF orientation persisted for about 12 min, during which no FTE-type flux ropes were observed. At ~00:26:06 UT, the clock angle decreased from ~260° to ~210°, while the ratio of $B_x/B_t$ increased to ~0.90. At this point, five FTE-type flux ropes successively appeared up to the point where the magnetopause was crossed. The traveling direction for these five flux ropes was inferred to be northward, again based on the $B_N$ variations. The first flux rope traveled southward, indicating that the primary magnetopause X-line was initially located north-

<footnote><sup>a</sup> “-” indicates that the values are not determined by the flux rope model. See the text for more information on the flux rope modeling. <sup>b</sup> scale contains semi-minor and semi-major, and the ratio between semi-minor and semi-major refers to the flattened profile. See the text for more information.</footnote>
ward of the spacecraft. Later, the northward motion of the five flux ropes indicated that the primary magnetopause X-line(s) had shifted southward.

## 3.2 Reconnection X-lines from the maximum magnetic shear model

To further investigate reconnection during BepiColombo's dayside magnetopause traversal, the maximum magnetic shear model (Trattner et al., 2007, 2017) was employed to deduce the locations of reconnection X-lines. The magnetic shear angle plots during the intervals centered at 00:09, 00:20, and 00:28 UT are shown in Fig. 3. Figure 3a and b correspond to a distorted feature of the anti-parallel reconnection region, which has recently been termed a “Knee” event (Trattner et al., 2021). The bent shape of the anti-parallel reconnection region is associated with the field line draping in the magnetosheath during the dominant $B_x$ (significantly sunward) component in this period. Figure 3c did not provide the predicted X-line. This was because a continuous X-line along the maximum magnetic shear location was difficult to obtain under the situation of a $B_x/B_t \ge 0.9$, which was due to the lack of a comprehensive study on how the significant radial IMF draping around the magnetopause influences magnetic reconnection.

In Fig. 3a, BepiColombo was located southward of the predicted X-line. From Fig. 3a to b, the predicted X-line crossed the location of BepiColombo and was then located to the south of BepiColombo. The changes in X-line locations from Fig. 3a to b were due to the IMF clock angle decreasing around 10° together with the $B_x/B_t$ increasing from 0.78 to 0.86.

The traveling directions for the FTE-type flux ropes were consistent with the predicted locations of the reconnection X-line by the maximum magnetic shear model during the changing solar wind conditions for this magnetopause encounter. Figure 3a corresponded to the only southward-traveling FTE-type flux rope, while the other five northward-traveling FTE-type flux ropes were observed during the conditions shown in Fig. 3b and c. It needs to be noted that the FTE-type flux ropes and reconnection exhausts should correspond to strong lateral motion as the predicted X-lines were significantly along the north-south direction. The reconnection exhausts would correspond to a strong duskward component when the spacecraft was located southward of the X-line and a strong dawnward component when it was northward of the X-line. Although the maximum magnetic shear model faces challenges in determining the draping magnetic field lines in the magnetosheath during the intervals of the dominant $B_x$ component (Trattner et al., 2007, 2012), the model predictions are consistent with our observations during BepiColombo's crossing.

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

**Figure 3.** Magnetic shear angle plots on the magnetopause surface during BepiColombo's dayside magnetopause crossing, which are obtained through the maximum magnetic shear model (Trattner et al., 2007). Panels (a-c) correspond to the IMF averaged from 00:05 to 00:13 UT, 00:16 to 00:24 UT, and 00:24 to 00:33 UT, respectively. The black circle represents the terminator plane separating the dayside magnetopause from the tailward magnetopause. The grey line represents the predicted magnetopause reconnection line. White areas correspond to the magnetic shear angle within 3° of 180°. The black dots are the location of BepiColombo ("BC"). In panel (c), the predicted X-line is not provided. This is because a continuous X-line along the maximum magnetic shear location is difficult to obtain under the situation of a $B_x/B_t \ge 0.9$.
## 3.3 FTE-type flux rope modeling

This study employed a force-free flux rope model (Kivelson and Khurana, 1995) to fit the FTE-type flux ropes. This flux rope model starts from the periodic pinch solution (Schindler et al., 1973) of Ampere's law ($\nabla \times \mathbf{B} = \mu_0 \mathbf{J}$), where $\mathbf{B}$ is the magnetic field vector, $\mathbf{J}$ is the current density vector, and $\mu_0$ is the magnetic permeability in a vacuum. Kivelson and Khurana (1995) further include the axial magnetic field component ($B_{\text{int}}$) in the periodic pinch solution. The flux rope model introduced by Kivelson and Khurana (1995) does not consider the gradient of the magnetic field along the axis of the flux rope. The self-consistent solution of the flux rope model is

$$ \left\{ \begin{aligned} B_{\text{max}} &= \left(\frac{B_T}{\chi}\right) \sqrt{1 + \epsilon^2 \sinh\left(\frac{x_{\text{min}}}{T}\right)}, \\ B_{\text{int}} &= \left(\frac{B_T}{\chi}\right) \sqrt{1 + \left(\frac{B_{\text{int}0}\chi}{B_T}\right)^2}, \\ B_{\text{min}} &= \left(\frac{B_T}{\chi}\right) \epsilon \sin\left(\frac{x_{\text{max}}}{T}\right). \end{aligned} \right. \quad (1) $$

In the equation, $x_{\text{min}}$ and $x_{\text{max}}$ are the positions in the flux rope along the directions of $n_{\text{min}}$ and $n_{\text{max}}$. $n_{\text{min}}$, $n_{\text{int}}$, and $n_{\text{max}}$ refer to the local coordinate of the flux rope, which are determined from the MVA on the flux rope. $T$ is the vertical scale of the flux rope in the $n_{\text{max}}$ direction, and $B_T$ is the magnetic field intensity near the boundary of the flux rope along the $n_{\text{min}}$ direction. $B_{\text{int}0}$ is $B_{\text{int}}$ in the background. $\chi$ is

$$ \chi = \epsilon \cos\left(\frac{x_{\text{max}}}{T}\right) + \sqrt{1 + \epsilon^2} \cosh\left(\frac{x_{\text{min}}}{T}\right). \quad (2) $$

In this equation, the parameter $\epsilon$ is associated with the shape of the flux rope, i.e., from flattened to circular profiles. The axial flux content ($\Phi_{\text{axial}}$) is calculated by integrating the axial field ($B_{\text{int}}$) over the entire flux rope area:

$$ \Phi_{\text{axial}} = \int B_{\text{int}} dS. \quad (3) $$

During the fitting, we assume that the traveling speed of flux ropes was $100 \text{ km s}^{-1}$, which corresponds to the average Alfvén speed in the subsolar magnetosheath. The traveling speed is required in calculating the scales and magnetic flux content for the flux ropes. Least squares of the minimization of the magnetic field differences ($X^2$) is employed to define the best fit, which is calculated from

$$ X^2 = \frac{\sum_{i=1}^{N_{\text{point}}} \sum_{j}^{\text{max, int, min}} \left[ \left( B_j(i) - B'_j(i) \right) / B_t(i) \right]^2}{N_{\text{point}}}, \quad (4) $$

where $B_{\text{max}}$, $B_{\text{int}}$, $B_{\text{min}}$, and $B_t$ are the components and magnitude of the measured magnetic fields and $B'_{\text{max}}$, $B'_{\text{int}}$, and $B'_{\text{min}}$ are the components of the magnetic fields from the model. $N_{\text{point}}$ is the number of data points. We set up a threshold of $X^2 < 0.1$ to be the successful modeling.

Differently from the circular profile of flux ropes resulting from the Lundquist force-free flux rope model (Lundquist,

1950; Burlaga, 1988; Lepping et al., 1990), this force-free model can result in either flattened or circular profiles of flux ropes. We use “semi-minor” and “semi-major” to refer to the flattened features. Semi-major corresponds to the scale of flux rope along the $n_{\text{min}}$ direction, which is close to the L direction of the magnetopause. Semi-minor corresponds to the scale of flux rope along the $n_{\text{max}}$ direction, which is close to the N direction of the magnetopause. This flux rope model is successfully applied for the flux ropes in Earth's plasma sheet (Kivelson and Khurana, 1995), on Earth's magnetopause (Zhang et al., 2008), and in Mercury's plasma sheet (Zhao et al., 2019).

Out of the six FTE-type flux ropes, four were successfully modeled. As an example, the modeling curves of the flux rope centered at 00:28:13 UT are shown in Fig. 4a–d. In the figures, the dashed lines overlapping with the solid measured magnetic fields represent the modeling curves from the flux rope model. It can be seen clearly that the two curves are close to each other, and this flux rope is well fitted by the model. The modeling results for our flux ropes are summarized in Table 1. The plasma density of ~10 cm⁻³ in the magnetosheath corresponds to an ion inertial length ($d_i$) of ~70 km. The two FTE-type flux ropes at 00:26:06 UT and 00:26:26 UT are on the scales of several $d_i$. The magnetic flux contents of these two flux ropes are small (~20 kWb). In addition, these two flux ropes correspond to the largest and smallest core fields. The other two FTE-type flux ropes at 00:28:13 UT and 00:30:26 UT are on the scales of more than 10 $d_i$. These two flux ropes contain much higher magnetic flux (~300 and ~188 kWb). The analysis of the flux rope at ~00:28:13 UT corresponding to the highest magnetic flux content is shown in the next section. Moreover, the flux ropes at 00:26:06 UT, 00:26:26 UT, and 00:30:26 UT are close to circular profiles with the semi-minor slightly smaller than the semi-major. The flux rope at ~00:28:13 UT corresponds to the most flattened profile.

## 3.4 Coalescence event

Figure 4a–d show the magnetic field measurements of the FTE-type flux rope centered at ~00:28:13 UT in the LMN coordinate. This FTE-type flux rope corresponds to the fifth green arrow counting from the left-hand side in Fig. 1e. Figure 4c showed that the $B_N$ included two successive bipolar signatures, which implied that two smaller-scale flux ropes were merging. Indeed, the hodogram in the $B_{\text{max}}-B_{\text{int}}$ plane in Fig. 4f confirmed the field rotations of two flux ropes, named “FR#A” and “FR#B”. Figure 4e further illustrated the merging of the two flux ropes and the trajectory of BepiColombo. The magenta arrow and shaded region in Fig. 4e indicated the possible secondary reconnection between FR#A and FR#B. This FTE-type flux rope with the highest flux content possibly resulted from the coalescence of two smaller-scale flux ropes.
<figure><img src="image_8.png" /></figure>

**Figure 4.** Overview of the flux rope centered at ~00:28:13 UT with the coalescence feature. (a) $B_L$, (b) $B_M$, (c) $B_N$, and (d) $B_t$. The dashed lines are obtained from the flux rope model. This LMN is the local coordinate of the magnetopause. See the text for more information. (e) An illustration of the coalescence event and BepiColombo's trajectory. The secondary reconnection site is marked by the magenta region. Panels (f) and (g) are the hodograms of the magnetic field measurements under the local coordinate of the flux rope. “B” and “E” indicate the beginning and end of the data points. FR#A and FR#B indicate two flux ropes.

In order to study how well aligned FR#A and FR#B were, we applied the MVA to FR#A from 00:28:03 to 00:28:09 and FR#B from 00:28:09 to 00:28:16 separately. The eigenvalue ratios were $\lambda_{max}/\lambda_{int} \sim 1.91$ and $\lambda_{int}/\lambda_{min} \sim 21.7$ for FR#A. The eigenvalue ratios were $\lambda_{max}/\lambda_{int} \sim 3.34$ and $\lambda_{int}/\lambda_{min} \sim 12.6$ for FR#B. The large values of $\lambda_{int}/\lambda_{min}$ indicated that the $n_{min}$ were well determined for both flux ropes. $n_{min}$ was [-0.20, -0.58, -0.79] for FR#A, and $n_{min}$ was [0.23, -0.55, -0.80] for FR#B. The $n_{min}$ values were close to each other, with a separation angle of 25°. The $n_{min}$ obtained for the coalescence event was [-0.04, -0.49, -0.87], which was 12 and 17° away from the $n_{min}$ of FR#A and FR#B separately. The small separations of $n_{min}$ should indicate that FR#A and FR#B were well aligned. It needs to be noted that the coalescence signature was only observed in this FTE-type flux rope centered at ~00:28:13 UT. The successive bipolar signatures of $B_N$ were not found in the other five FTE-type flux ropes.

## 3.5 Magnetopause reconnection and secondary magnetic reconnection

In Fig. 5, the properties of the secondary current sheet in the coalescence event and the magnetopause current sheet are studied. For the secondary current sheet, the eigenvalue ratios were $\lambda_{max}/\lambda_{int} \sim 6.4$ and $\lambda_{int}/\lambda_{min} \sim 11.0$, resulting from the MVA. Both of the eigenvalue ratios were larger than 3, indicating that the local coordinate of the secondary current sheet was well established. The magnetic field measurements of the magnetopause current sheet were shown in the LMN coordinate.

In the reconnecting current sheet, the dimensionless reconnection rate can be determined from the ratio of the normal magnetic field component ($B_{normal}$) to the reconnecting magnetic field ($B_{inflow}$) in the inflow region (Sonnerup, 1974; Sonnerup et al., 1981; Fuselier and Lewis, 2011; Phan et al., 2001; Sun et al., 2020b). In the secondary current sheet (Fig. 5a–d), $B_{normal}$ was ~5 nT, which corresponded to $B_{min}$ averaged from 00:28:08.8 to 00:28:09.6 UT. Here the average $B_t$ from 00:28:09.8 to 00:28:10.4 UT was taken as the $B_{inflow}$ (~36 nT). The dimensionless reconnection rate was ~0.14
<figure><img src="image_9.png" /><figcaption>**Figure 5.** The magnetic field measurements under their separately local coordinate for the reconnecting current sheet of the coalescence event and the magnetopause current sheet. Panels (a) to (d) are for the secondary current sheet of the coalescence event. $n_{\text{min}}$, $n_{\text{int}}$, and $n_{\text{max}}$ refer to the local coordinate of the secondary current sheet. Panels (e) to (h) are for the magnetopause current sheet. The LMN local coordinate of the magnetopause current sheet is used. The eigenvalues and corresponding eigenvectors result from the MVA.</figcaption></figure>

if the reconnection occurred in the secondary current sheet. Meanwhile, the intensity of the guide field ($B_{\text{int}}$, Fig. 5b) was ~32 nT across the current sheet, which was ~0.89 when normalized to $B_{\text{inflow}}$. In the magnetopause current sheet, $B_{\text{normal}}$ was 8.3 nT, which corresponded to the averaged $B_N$ from 00:32:56 to 00:33:05 UT (Fig. 5g). $B_{\text{inflow}}$ on the magnetosphere side adjacent to the magnetopause was ~46.1 nT, which corresponded to the averaged $B_t$ from 00:33:06 to 00:33:15 UT (Fig. 5h). Thus, the dimensionless reconnection rate was calculated to be ~0.18. The guide field across the magnetopause was ~13 nT ($B_M$, Fig. 5f), which was 0.28 normalized to $B_{\text{inflow}}$.

However, it needs to be pointed out that the estimation of the reconnection rate based on $B_N/B_{\text{inflow}}$ could be imprecise. For example, the uncertainties of the normal direction and the fluctuations in the field strength could influence the accuracy of the reconnection rates. As noted by Sonnerup and Scheible (1998) and Khrabrov and Sonnerup (1998), there were uncertainties in the eigenvectors determined by the MVA, which could be either statistical error or error due to the magnetic structure not being perfectly stationary and one-dimensional. By employing the method introduced by Khrabrov and Sonnerup (1998), we obtained an uncertainty of ~0.93 nT for the $B_{\text{normal}}$ of the secondary current sheet and ~0.04 nT for the magnetopause current sheet.

Furthermore, it was not certain that magnetic reconnection was occurring in the secondary current sheet or the magnetopause current sheet when BepiColombo crossed them. There was no complementary evidence of the magnetic reconnection since the measurements from BepiColombo were limited during the Earth flyby. The low-energy electron measurements (Mio/MEA) were limited in the field of view,

and the time resolution was ~4 s. The MEA could not provide a complete distribution relative to the background magnetic field, and its time resolution was much longer than the timescale of the secondary current sheet. Therefore, the conclusions obtained about magnetic reconnection are tentative and further analysis about a similar event is needed, especially those measurements taken from the MMS.

## 4 Conclusions and discussions

Our analysis of the subsolar magnetopause observations during BepiColombo's Earth flyby has produced several conclusions.

First, BepiColombo's dayside magnetopause crossing took place during an interval when the magnetosheath had a high plasma $\beta$ (~8) and the IMF had a strong radial component ($B_x/B_t$ > 0.7). The traveling of the FTE-type flux rope suggests that the X-line crosses the location of BepiColombo. Although there is a possibility that the first and only southward-traveling FTE-type flux rope is a magnetosheath structure, the predictions of the maximum magnetic shear model suggest that the X-line crosses the location of BepiColombo as well. The X-line motion is associated with the rotation and the $x$ component increase in the IMF. BepiColombo crosses the magnetopause near the magnetic equator, and 10 April 2020 is close to the spring equinox, which indicates a small influence of Earth's dipole tilt. These observations of the possible crossing of the X-line provide clear evidence of magnetic reconnection occurrence near the magnetic equator under a strong radial IMF.
Second, the properties of the FTE-type flux ropes are ob-
tained by employing a force-free flux rope model introduced
by Kivelson and Khurana (1995). The FTE-type flux ropes
correspond to scales ranging from several $d_i$ to around 20 $d_i$,
and the FTE-type flux rope with a large scale and the highest
magnetic flux content exhibits clear coalescence signatures.
These observations strongly support the theories in which the
FTE-type flux ropes grow in scale and magnetic flux content
through coalescence.

Third, magnetic reconnection in the coalescence event and
the magnetopause current sheet is investigated. The recon-
nection rate of the secondary reconnection (0.14) is compa-
rable to the reconnection rate of the dayside magnetopause
(0.18). The secondary reconnection corresponds to a large
normalized guide field (0.89) and the magnetopause recon-
nection to a moderate guide field (0.28). However, there is
no complementary evidence that magnetic reconnection is
occurring in the secondary current sheet and magnetopause
current sheet. Therefore, the conclusions about magnetic re-
connection are tentative.

The large guide field of the secondary magnetic reconnection during the coalescence observed by BepiColombo is likely a common feature. For example, Zhou et al. (2017) reported a coalescence event with a strong guide field. We suggest that these large guide fields should be included in future simulations, which investigate the particle energizations due to coalescence. The large guide fields may influence the reconnection rate, as suggested by Pritchett and Coroniti (2004) and Ricci et al. (2004), and therefore affect the energization of particles during the coalescence. Furthermore, a recent investigation also suggests that a large guide field might limit the ability of Fermi acceleration during the coalescence (Montag et al., 2017).

Finally, the FTE-type flux rope containing the coalescence
signature has a scale of ~20 $d_i$. Therefore, the secondary
reconnecting current sheet embedded within the FTE-type
flux rope likely has a scale smaller than 20 $d_i$. We want to
note that the secondary reconnection during the coalescence
of flux ropes shares some similarities with the electron-only
reconnection associated with the magnetosheath turbulence,
whose reconnecting current sheet has scales smaller than
10 $d_i$ and is accompanied by a large guide field as revealed by
MMS measurements (Phan et al., 2018; Stawarz et al., 2019)
and simulations (Califano et al., 2020). Therefore, it is likely
that the secondary reconnection associated with coalescence
is electron-only magnetic reconnection, which certainly de-
serves a detailed study.

*Data availability.* The measurements from Mio/MEA and MPO/-MAG analyzed in this study are available in the supporting information. The data archiving is underway. Mio/MEA data are available in the Supplement of this article. MPO/MAG data is available in the supplement of this article. The OMNI dataset is publicly available at https://omniweb.gsfc.nasa.gov/ (King and Papitashvili, 2005).

*Supplement.* The supplement related to this article is available on-line at: https://doi.org/10.5194/angeo-40-217-2022-supplement.

*Author contributions.* WS led the work, identified the events, conducted the data analysis of the dataset, and wrote the manuscript. WS, JAS, and RN jointly designed the work. DH and JZDM provided knowledge of the MPO/MAG instrument and the MPO/MAG data. SA and NA provided knowledge of the Mio/MEA instrument and the Mio/MEA data. KJT provided Fig. 3 and the relevant descriptions. JZ performed force-free fittings of the flux ropes. All the authors discussed and contributed to the manuscript.

*Competing interests.* The contact author has declared that neither they nor their co-authors have any competing interests.

*Disclaimer.* Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

*Acknowledgements.* The BepiColombo project is supported by ESA and JAXA. MEA data analysis was performed with the CL software developed by Emmanuel Penou at IRAP and the AMDA science analysis system provided by the Centre de Données de la Physique des Plasmas (CDPP) supported by CNRS, CNES, Observatoire de Paris, and Université Paul Sabatier, Toulouse. Weijie Sun thanks Gangkai Poh for helpful discussions.

*Financial support.* This research has been supported by NASA grants NNX16AJ67G, 80NSSC21K0052, 80NSSC21M0364 and 80NSSC18K1137. The research at University of Colorado, Boulder (Karlheinz J. Trattner) has been supported by NASA grants NNG04EB99C and 80NSSC20K0688. Nicolas Andre and Sae Aizawa were supported by CNES for the BepiColombo mission.

*Review statement.* This paper was edited by Anna Milillo and reviewed by three anonymous referees.

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