Main Manuscript for Mercury’s Ring Current: MESSENGER Observations and Test-Particle Simulations

Energetic protons can carry a longitudinal electric current via their gradient and curvature drift around a planet and form a current system known as the ring current. The ring current has been observed in the intrinsic magnetosphere of Earth, Jupiter, and Saturn. However, there is still lacking evidence of ring current in Mercury’s magnetosphere, which contains significantly weaker and oppressive “dipolar” magnetic field and the charged particles are thought able to efficiently escape the magnetosphere through magnetopause shadowing and/or directly hitting the surface. Here we present the first observational evidence of Mercury ring current with the measurement of MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER). The ring current is bifurcated under moderate solar wind forcing, which is caused by the off-equatorial magnetic minima on the noon side and tends to vanish during weak solar wind forcing. This morphology is validated by a test-particle simulation with a Mercury’s dynamic magnetic field model. The total energy stored in the ring current exceeds 5 × 10 10 J during active times, indicating that magnetic storms may also occur in Mercury’s magnetosphere.


Introduction
The ring current is a magnetospheric electric current mainly carried by ~keV to hundreds of keV ions trapped in a planetary magnetosphere. Chapman and Ferraro first proposed that the ring current, carried by energetic charged particles circling the Earth, causes geomagnetic depressions (i.e., geomagnetic storms) 1  Mercury's magnetosphere was discovered by Mariner-10 in the 1970s 3 . It has an intrinsic dipole field like Earth with a much smaller magnetic moment of ~190 nT ⋅ R M 3 (Mercury's Radius, i.e. 2440 km) 4,5, 6 . The subsolar magnetopause is located at ~1.5 R M during normal solar wind conditions 7,8 .
It has been shown that rapid, frequent, and intense ion injection and energization processes occurr in Mercury's magnetotail, which could supply energetic protons to the nightside magnetosphere 15 . However, this highly compressed magnetosphere was considered very hard to trap these energetic protons due to the strong magnetopause shadowing and surface absorption 16,17 . In-situ measurements in the magnetotail have revealed quasi-trapping regions with numerous energetic protons and their strong diamagnetic effect during some events 18 . Both global magnetohydrodynamic and hybrid simulations have also reproduced the quasi-trapping regions 18,19 . As for the dayside magnetosphere, the magnetic minimum deviates from the equatorial plane to the off-equatorial latitude due to the solar wind compression, which could result in a bifurcated ring drift shell (i.e., Shabansky orbit 20 ) . Test particle simulation suggested   that 34 keV electrons with specified initial position and pitch angle can completely drift around the planet   via Shabansky orbit 21 , which is consistent with the statistical result of low-energy (1-10 keV) or suprathermal electrons 22,23,24 . Through a case study, Jang et al also demonstrated the off-equatorial trapping of   energetic protons under strong solar wind compression based on MESSENGER observations 25 . Nevertheless, in-situ observations and simulations are still desired to determine whether energetic protons originated from the magnetotail can complete a full drift orbit and form the ring current, and if they are able to for a ring current, how they distribute and how strong they are.
In this study, we present conclusive evidence of Mercury's ring current based on 5-years in-situ observations of MESSENGER. First, we make two statements of Mercury's ring current-like structure under different solar wind conditions. We then apply a test-particle simulation to demonstrate the particle trajectories and to predict the ring current morphology. By superposing the long-term in-situ measurements, we present the spatial distribution of energetic protons and identify the ring current of Mercury. Further investigation of this spatial structure and the temporal variability is also provided.
Discussion and Conclusions are then followed. The dataset and method we used in this study are given in the Method section.   Figure S1 in Supplementary Information.

Dayside
The above observations demonstrate the existence of ~90 ∘ pitch angle protons with 1-10 keV energy in Mercury's dayside magnetosphere during both high and low p ram . Since localized energizations on the dayside (e.g., magnetic reconnection and centrifugal acceleration in the polar cusp) hardly produce ~10 keV protons, these protons are most likely transported from the magnetotail via gradient-curvature drift. Such inference is also consistent with the observed 90 ∘ -dominant pitch angle distribution and ~150 nT ambient magnetic field strength, which are similar to the characteristics of protons and the magnetic field strength in the near-Mercury magnetotail 27 . To validate this, we present more evidence from a test particle simulation and a statistical analysis in the following sections.

Test Particle Simulation
We use a test particle simulation with the latest dynamic magnetic field model (KT17) of Mercury to investigate the morphology of Mercury's ring current 28 . the subsolar distance is applied to a total of ~4000 MESSENGER orbits to keep a stable p ram and ring current morphology. The subsolar distance is estimated in the same way as the above two cases. Only dayside magnetopause crossings have been used to identify the subsolar distance since they are more sensitive to p ram than nightside crossings. Figure S3 presents the histogram of subsolar distances during ~2800 orbits with clear magnetopause crossings and complete particle measurements. These ~2800 orbits are classified into three groups with a similar sample size (low/moderate/high p ram ). In the following analysis, we use observations under moderate p ram (i.e., the subsolar distance between 1.35 R M and 1.49 R M ) to present the proton distribution.

Discussion and Conclusions
Observations and simulations of the energetic protons demonstrate the presence of Mercury's ring current, which is bifurcated on the dayside and different from Earth's. Such a bifurcation of ring current particles was first suggested by Shabansky in Earth's dayside outer magnetosphere 20 . The magnetopause current enhances the magnetic field inside it and this effect is focused on the equatorial plane. As a result, a local maximum in the magnetic field strength, , which prevents charged particles from crossing it, are produced in the subsolar equator. Therefore, these particles can be locally trapped near the off-equatorial minimum in one hemisphere and constitute a bifurcated particle distribution.
The bifurcation of the drift shell only occurs near the dayside magnetopause (L>7) in terrestrial magnetosphere and does not affect the ring current and the radiation belt 29 . However, due to the significantly weaker and oppressive "dipolar" magnetic field in Mercury's magnetosphere, this bifurcation is a fundamental characteristic of Mercury's ring current under moderate solar wind conditions.
Both simulations (Figure 2a) and observed statistical distribution (Figures 2b, 2c and 2d) suggest that the bifurcation spans from ~10 h local times to ~14 h local times and energetic protons are trapped near the off-equatorial minima at ~30 ∘ . In other local time sectors, the protons exhibit an Earth-like drift-bounce signature with a longer bounce-path on the dayside than that on the nightside.
The bifurcation tends to vanish when p ram decreases 18  The total energy carried by the magnetospheric ring current is estimated to be ~1 − 7 × 10 10 J.
Alternatively, the total current inside the ring current can be estimated to ~6kA − 43kA (I L = 3 2 2 | =1.5 ) 32 , which is comparable to the field-aligned current at Mercury. According to the DPS relation 33,34 , this proton ring current can cause a magnetic disturbance of ~0.7 − 4.9 nT, which is significant compared to the magnetic field strength of Mercury. The ~0.7 nT − 4.9 nT decrease (~0.4% − 2.5%) in the magnetic field strength is equivalent to a geomagnetic storm with Dst = from −110 nT to − 780 nT on Earth. Because of this relatively intense ring current, Mercury may also have magnetic storms in some sense. However, it is hard to detect this magnetic depression because the magnetopause current enhances the surface magnetic field, which is opposite to the ring current's contribution, and contribution from the magnetopause current could be even larger than that from the ring current during active times.
To summarize, in this study, we prove the existence of Mercury's ring current by providing both observational and simulation evidence. The ring current has a bifurcated morphology caused by the proton's Shabansky orbit. The estimated total energy carried by the ring current is ~1 − 7 × 10 10 J, which would trigger a magnetic storm with a magnetic field depression of ~0.7 − 4.9 nT. We also expect a series of drift-related phenomena in observations of the ongoing JASA-ESA Bepi-Colombo mission.

Instrumentation
Observational data used in this study are measured by the Fast Image Plasma Spectrometer (FIPS) and the Magnetometer (MAG) onboard MESSENGER.
MAG is a fluxgate magnetometer that measures the magnetic field vectors with a frequency of 20 Hz.

Aberrated MSM coordinates
In this study, we use the aberrated Mercury-Sun magnetospheric (aMSM) coordinate system. In traditional MSM coordinates, the X-axis and Z-axis point to the sun and north pole, respectively and the Y-axis completes a right-hand system. While in the aberrated coordinates, Mercury's orbital velocity is considered. The X-axis keeps anti-parallel to the solar wind direction in the rest reference frame of Mercury. The aberration angle varies between −5.5 ∘ and −8.4 ∘ assuming a solar wind speed of 400 km/s.

Superposed Analysis
As the dipole field and the ring current have axial symmetry to some extent, a 2-dimensional polar coordinate grid is used. The resolution of radial distance and polar angle is 0.05 R M and 3.75 ∘ , respectively. In the analysis of the distribution in the equatorial plane, the third axis (i.e., the Z-axis) is

Field Line Tracing
We include a 2-D field line tracing method in this section to trace the magnetic field line in the meridian plane. The third dimension, local time, is limited by the range of [11 h, 13 h] and [23 h, 01 h] for dayside and nightside, respectively.
Step 4: if ⃗ +1 is below the planetary surface of Mercury, break; else, return to Step 2.

Estimation of ring current energy
To estimate the total energy carried by the ring current, we numerically integrated the thermal pressure inside the grid boxes with radial distance less than 2 R M and magnetic latitude less than 60 ∘ using the following two equations. By choosing different quantiles of the thermal pressure inside each grid box, the quantile distribution of the ring current is presented in Figure 4g.