Dayside magnetopause reconnection and flux transfer events: BepiColombo earth-Flyby observations

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 corresponds to a high plasma β (~ 8) and the IMF has a significant radial component. Six flux ropes are identified. The motion of flux rope together with the maximum magnetic shear model suggests that the reconnection X-line swipes BepiColombo near the magnetic equator due to an increase of the radial IMF. The flux rope with the highest flux content contains a clear coalescence 20 signature, i.e., two smaller flux ropes merging, supporting theoretical predictions the flux content of flux ropes can grow through coalescence. The secondary reconnection associated with coalescence exhibits a large normalized guide field and a reconnection rate comparable to the reconnection rate measured at the magnetopause (~ 0.1).


Introduction
Flux transfer events (FTEs) are frequently observed near the outer boundaries of planetary magnetospheres, 25 including at the Earth (e.g., Russell and Elphic, 1978;Saunders et al., 1984;Wang et al., 2005), Mercury Slavin et al., 2009;2012;Imber et al., 2014;Sun et al., 2020), Saturn (Jasinski et al., 2016; and Jupiter 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 30 reconnections in the magnetopause during intervals of significant magnetic shear across this current sheet (Lee and Fu, 1985;Raeder, 2006). As a result, the FTE-type flux ropes signal not only the occurrence of magnetic reconnection but their direction of travel can be used to infer the relative location of the reconnection X-lines at the magnetopause.
FTEs contribute to the transport of magnetic flux from the dayside to the nightside magnetosphere that drives the 35 Dungey cycle in dipolar planetary magnetospheres. In Mercury's magnetosphere, the FTE-type flux ropes transport majority of (>60%) the circulated flux (Slavin et al., 2010;Imber et al., 2014;Sun et al., 2020). In contrast, FTEtype 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). And 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 40 al., 2021).
FTEs at Earth are most frequent during periods of the southward interplanetary magnetic field (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, reconnections most likely occur on the magnetopause near the subsolar point 45 (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;. Magnetic reconnection is also thought to occur at the dayside magnetopause under the strong radial IMF (Bx dominate) (Belenkaya, 1998;Luhmann et al., 1984;Pi et al., 2017;Tang et al., 2013), but the strong radial IMF conditions are less well studied.
Coalescence events, which refer to the merging of neighboring flux ropes, are thought to be an important process in 50 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 at electron to ion scales.
This study investigates FTE-type flux ropes and reconnection at the Earth's dayside magnetopause during BepiColombo's flyby on 10 April 2020. The paper is arranged as follows. Section 2 introduces the BepiColombo 60 mission and the measurements during the dayside magnetopause crossing. Section 3 analyzes the distribution of magnetopause reconnection with a strong radial IMF component, and the properties of the flux ropes, including a coalescence event. Section 4 provides a summary of our results.

Spacecraft and Instrumentation
This study uses measurements collected by the magnetometer (MAG) onboard MPO (Heyner et al., 2021), the low energy electron by Mercury Electron Analyzer (MEA) (Sauvaud et al., 2010), which is part of the Mercury Plasma Particle Experiment (MPPE) onboard Mio (Saito et al., 2021). The MPO/MAG includes one outbound sensor and one inbound 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 75 minute.  Figure 1f). 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. The magnetosheath plasma 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 85 that the pressure balance existed across the dayside magnetopause and that the thermal pressure inside the dayside magnetosphere was negligible compared to the magnetic pressure.

Identification of FTE-type Flux Ropes
The FTEs were identified after the measured magnetic field was rotated into boundary normal coordinates (the LMN 90 coordinates). The minimum variance analysis (MVA) (Sonnerup and Cahill Jr., 1967;Sonnerup and Scheible, 1998) was performed on the magnetic field measurements across the magnetopause current sheet from 00:32:30 to the magnetopause was well determined [Sonnerup & Scheible, 1998].
The FTEs are identified with bipolar signatures in the normal magnetic field (BN) and clear magnetic field rotation (Russell and Elphic, 1978).

Reconnection X-lines from Maximum Magnetic Shear Model
To further investigate reconnection during BepiColombo's dayside magnetopause traversal, the maximum magnetic shear model (Trattner et al., 2007;  Although the maximum magnetic shear model faces challenges in determining the draping magnetic field lines in the magnetosheath during the intervals of the dominant Bx component (Trattner et al., 2007;2012), the model predictions were consistent with our observations during BepiColombo's crossing.

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This study employs 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) where ⃑ is the magnetic field vector, is the current density vector, and 0 is the magnetic permeability in the vacuum. Kivelson and Khurana (1995) The axial flux content (Φ ) is calculated by integrating the axial field (Bint) over the entire flux rope area, During the fitting, we assume that the traveling speed of flux ropes was 100 km/s, which corresponds to the average Alfvén speed in the sub-solar magnetosheath. The least-squares of the minimization of the magnetic field differences (Χ 2 ) is employed to define the best fit, which is calculated from where Bmax, Bint, Bmin, and Bt are the components and magnitude of the measured magnetic fields and ′ , ′ , 145 and ′ are the components from the model. The is the number of data points. We set up a threshold of Χ 2 < 0.1 to be the successful modeling.
Different from the circular profile of flux ropes resulted from the Lundquist force-free flux rope model (Lundquist, 1950), this force-free model gives a flattened profile of the flux rope. We use the semi-minor and semi-major to refer to the flatten features. This flux rope model is successfully applied for the flux ropes in the Earth's plasma 150 sheet (Kivelson and Khurana, 1995), Earth's magnetopause (Zhang et al., 2008), and in Mercury's plasma sheet (Zhao et al., 2019).
Out of the 6 FTE-type flux ropes, 4 were successfully modeled. The modeling results were summarized in Table 1.
In Figures 3a to 3d, the dashed lines overlapping with the solid measured magnetic fields represent the modeling curves from the flux rope model. The plasma density was ~ 10 cm -3 corresponding to an ion inertial length (di) of ~ 155 70 km. The two FTE-type flux ropes centered at 00:26:06 UT and 00:26:26 UT were in the scales of several di. The magnetic flux content of these two flux ropes was small (~ 20 kWb). In addition, these two flux ropes corresponded to the largest and smallest core fields.
The other two FTE-type flux ropes centered at 00:28:13 UT and 00:30:26 UT were in the scales of more than 10 di.
These two flux ropes contained much higher magnetic flux (~ 300 kWb and ~ 188 kWb). The analysis of the flux Figure 3 shows that the magnetic field measurements of the FTE-type flux rope centered at ~ 00:28:13 UT in the LMN coordinate. Figure 3c showed the BN included two successive bipolar signatures, which implied that two smaller scale flux ropes merging. Indeed, the hodogram in the Bmax-Bint plane in Figure 3f  It needs to note that the coalescence signature is only observed in this FTE-type flux rope. We did not see similar

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successive bipolar signatures of the BN in other 5 FTE-type flux ropes.

Magnetopause Reconnection and Secondary Magnetic Reconnection
In Figure 4, the reconnection properties of the secondary reconnecting current sheet in the coalescence event ( Figure   3) and the magnetopause current sheet are studied. For the secondary reconnecting current sheet, the ratios of / ~ 6.4, / ~ 11.0 resulted from MVA were both larger than 3 indicating the local coordinate of the 175 secondary reconnecting current was well built. 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 normal magnetic field component (Bnormal) to the reconnecting magnetic field (Binflow) in the inflow region (Sonnerup, 1974;Sonnerup et al., 1981;Fuselier and Lewis, 2011;Phan et al., 2001). In the secondary reconnecting current sheet 180 (Figures 4a to 4d), the Bnormal was ~ 5 nT (the Bmin averaged from 00:28:08.8 to 00:28:09.6 UT). Here the average Bt from 00:28:09.8 to 00:28:10.4 UT was taken as the Binflow (~ 36 nT). The dimensionless reconnection rate was ~ 0.14. Meanwhile, the intensity of the guide field (Bint, Figure 4b) was ~ 32 nT across the current sheet, which was ~ 0.89 when normalized to the Binflow. However, it needs to point out that the estimation of reconnection rate based on BN/Binflow could be imprecise. For example, the uncertainties of the normal direction and the fluctuations in the field 185 strength could influence the accuracy of the reconnection rates.
The Binflow in the magnetosphere side adjacent to the magnetopause was ~ 46.1 nT (average Bt from 00:33:06 to 00:33:15 UT, Figure 4h). Thus, the dimensionless reconnection rate was calculated to be ~ 0.18. The guide field across the magnetopause was ~ 13 nT, which was 0.28 normalized to the Binflow.  Third, the features of magnetic reconnection associated with the secondary reconnection in the coalescence event 205 and the magnetopause current sheet are investigated. The reconnection rate of the secondary reconnection (0.14) is comparable with the reconnection rate on the dayside magnetopause (0.18). However, the secondary reconnection corresponds to a larger normalized guide field (0.89) than the magnetopause reconnection (0.28).
The large guide field is likely a common feature for the secondary magnetic reconnection during the coalescence.
Using the MMS measurements, Zhou et al. (2017) reported a coalescence event with a strong guide field. We 210 suggest that the large guide field shall be considered in the simulations, which investigate the particle energizations due to the coalescence. For example, the large guide field may influence the reconnection rate as suggested by Pritchett and Coroniti (2004) and Ricci et al. (2004), and therefore influences 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).

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The FTE-type flux rope containing coalescence signature has a scale of ~20 di. Therefore, the secondary reconnecting current sheet embedded within the FTE-type flux rope is likely with scale much smaller than 20 di. We want to note that the secondary reconnection during the coalescence of flux ropes share some similarities with the electron-only reconnection the magnetosheath turbulence, whose reconnecting current sheet has scales (< 10 di) and a large guide field as revealed by MMS measurements (Phan et al., 2018;Stawarz et al., 2019) and simulations 220 (Califano et al., 2020). Therefore, it is likely that the secondary reconnection associated with coalescence is also electron-only magnetic reconnection, which certainly deserves a detail study.

Data availability
The measurements from Mio/MEA and MPO/MAG analyzed in this study are available in the supporting 225 information. The data archiving is underway. Mio/MEA data will be able to be accessed from the AMDA science