# Mg Exosphere of Mercury Observed by PHEBUS Onboard BepiColombo During Its Second and Third Swing-Bys

Y Suzuki, Eric Quémerais, Jean-Yves Chaufray, R Robidel, G Murakami, François Leblanc, K Yoshioka, I Yoshikawa, O Korablev

► To cite this version:

Y Suzuki, Eric Quémerais, Jean-Yves Chaufray, R Robidel, G Murakami, et al.. Mg Exosphere of Mercury Observed by PHEBUS Onboard BepiColombo During Its Second and Third Swing-Bys. Journal of Geophysical Research. Planets, 2024, 129 (10), pp.e2024JE008524. 10.1029/2024je008524. insu-04741494

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Distributed under a Creative Commons Attribution 4.0 International License
# JGR Planets

## RESEARCH ARTICLE

10.1029/2024JE008524

**Key Points:**

* We established the calibration and background subtraction methods of the FUV channel of BepiColombo MPO/PHEBUS

* We analyzed the swing-by data and successfully obtained Mg exosphere distributions consistent with two theoretical models

* The lower energy of the Mg exosphere than that of Ca reflects the lower energy required for photodissociation from their parent molecules

**Correspondence to:**

Y. Suzuki,
suzuki.yudai@jaxa.jp

**Citation:**

Suzuki, Y., Quémerais, E., Chaufray, J.-Y., Robidel, R., Murakami, G., Leblanc, F., et al. (2024). Mg exosphere of Mercury observed by PHEBUS onboard BepiColombo during its second and third swing-bys. *Journal of Geophysical Research: Planets*, 129, e2024JE008524. https://doi.org/10.1029/2024JE008524

Received 29 MAY 2024
Accepted 23 SEP 2024

**Author Contributions:**

**Conceptualization:** Y. Suzuki,
E. Quémerais

**Data curation:** E. Quémerais, J.-Y. Chaufray, G. Murakami

**Formal analysis:** Y. Suzuki

**Funding acquisition:** Y. Suzuki,
I. Yoshikawa

**Investigation:** Y. Suzuki, E. Quémerais, J.-Y. Chaufray, R. Robidel, G. Murakami, F. Leblanc

**Methodology:** Y. Suzuki, J.-Y. Chaufray, G. Murakami, F. Leblanc, K. Yoshioka, I. Yoshikawa, O. Korablev

**Project administration:** E. Quémerais, J.-Y. Chaufray, G. Murakami

**Resources:** E. Quémerais, J.-Y. Chaufray, R. Robidel, G. Murakami, K. Yoshioka, I. Yoshikawa, O. Korablev

**Software:** Y. Suzuki, J.-Y. Chaufray, R. Robidel

# Mg Exosphere of Mercury Observed by PHEBUS Onboard BepiColombo During Its Second and Third Swing-Bys

<figure><img src="image_2.png" /></figure>

Y. Suzuki¹ ID, E. Quémerais² ID, J.-Y. Chaufray² ID, R. Robidel³, G. Murakami¹ ID, F. Leblanc² ID, K. Yoshioka⁴ ID, I. Yoshikawa⁴ ID, and O. Korablev⁵ ID

¹Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA), Sagamihara, Japan,
²LATMOS-IPSL, CNRS, UVSQ, Paris-Saclay, Sorbonne Université, Guyancourt, France, ³European Space Agency Centre (ESAC), European Space Agency (ESA), Madrid, Spain, ⁴Graduate School of Frontier Sciences, the University of Tokyo, Kashiwa, Japan, ⁵Space Research Institute of the Russian Academy of Sciences, Moscow, Russia

**Abstract** Mercury's exosphere is an important target for understanding the dynamics of coupled systems in space environments, tenuous planetary atmospheres, and planetary surfaces. Magnesium (Mg) is especially crucial for establishing methods for estimating the surface chemical composition distribution through observations of the exosphere because its distribution in the exosphere and on the surface is strongly correlated. However, owing to its low radiance, the Hermean Mg exosphere has only been detected by the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) onboard the Mercury Surface, Space Environment, Geochemistry, and Ranging (MESSENGER) spacecraft. Thus, we have few observation data for areas other than low latitude regions in addition to few detection cases of short-term or sporadic fluctuations, resulting in a poor understanding of ejection and transportation mechanisms of the Mg exosphere. In this study, we analyzed the distribution of the Hermean Mg exosphere by the Probing of Hermean Exosphere by Ultraviolet Spectroscopy (PHEBUS) onboard the Mercury Planetary Orbiter of the BepiColombo mission during its second and third Mercury swing-bys (MSBs). First, we constructed a calibration method including background subtraction and calibration using stellar observations. Mg light curves at two true anomaly angles were obtained, which were in agreement with the Chamberlain model and a three-dimensional numerical calculation. Comparing the Mg and calcium (Ca) radiances obtained by PHEBUS during the MSBs, the exospheric Mg atoms have a lower energy than the exospheric Ca atoms. This is consistent with the lower energy necessary for producing the Mg atoms produced by molecular photodissociation than for Ca atoms.

**Plain Language Summary** The tenuous atmosphere of Mercury helps us to understand how space environments, thin planetary atmospheres, and planetary surfaces interact. Magnesium is particularly important because its presence in Mercury's atmosphere can tell us a lot about the planetary surface composition. However, studying the magnesium atmosphere in Mercury is challenging because of its poor visibility. In this study, we used a new ultraviolet spectrometer installed on the BepiColombo spacecraft. Analyzing solar light scattered by magnesium atoms when the spacecraft was close to Mercury, we derived distributions of Mercury's magnesium atmosphere, which are aligned well with theoretical models. Furthermore, we compared the energies of magnesium and calcium in the atmosphere, both of which were measured by the same instrument. We found that magnesium has a lower energy than calcium in Mercury's atmosphere, which is consistent with our understanding that less energy is necessary for magnesium than calcium to break apart their original molecules in photodissociation. This study also demonstrates how to improve the quality of data obtained from the BepiColombo spacecraft.

## 1. Introduction

### 1.1. Surface-Bounded Exospheres

The atmospheres of Mercury and the Moon are sufficiently tenuous to be regarded as collisionless. These kinds of atmospheres directly connected to the planetary surfaces are called surface-bound exospheres (Stern, 1999). They are considered to reflect both the fluctuations of their space environment and the heterogeneity of the surface chemical compositions. Hermean exosphere has mainly been observed by ground telescopes and by the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) onboard the Mercury Surface, Space Environment, Geochemistry, and Ranging (MESSENGER) spacecraft. While for sodium (Na), being a volatile element, the photo-stimulated desorption is probably the dominant ejection mechanism (e.g., Cassidy et al., 2015), the

© 2024. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.
**Supervision:** E. Quémerais, G. Murakami, K. Yoshioka, I. Yoshikawa

**Validation:** E. Quémerais, J.-Y. Chaufray, R. Robidel

**Visualization:** Y. Suzuki

**Writing – original draft:** Y. Suzuki

**Writing – review & editing:** Y. Suzuki, E. Quémerais, J.-Y. Chaufray, R. Robidel, F. Leblanc, O. Korablev

major ejection process of refractories such as calcium (Ca) and magnesium (Mg) exospheres is micro-meteoroid impact vaporization (MIV) (Burger et al., 2014; Merkel et al., 2017). Although the Encke comet dust stream could also contribute to seasonal variability of the Ca exosphere (Christou et al., 2015; Killen & Hahn, 2015), no such components have been detected for Mg.

## 1.2. Mg Exosphere of Mercury

The Hermean Mg emission at 285.2 nm is not very bright because its g-factor and the Mg exospheric density are small (Killen et al., 2022). Therefore, it has never been detected from the ground or Earth-orbiting satellites. After its first detection by MESSENGER/MASCS (McClintock et al., 2009), its distribution and seasonal variability have been discussed based on MASCS data. The high energy of thousands of Kelvins and strong dawn/dusk asymmetry suggest that MIV is the primary source of Mg supply for the exosphere (Merkel et al., 2017). Chaufray et al. (2022) constructed a three-dimensional Mg, considering an MIV source only with spatio-temporal variations deduced from Ca, and including a non-uniform Mg distribution at the surface. This exospheric model reproduces the seasonal variations measured by MASCS at dawn. It has been pointed out that the Mg density is enhanced in accordance with surface Mg/Si ratios over the high-Mg region around 270°E (Merkel et al., 2018), which was the first evidence of a direct link between the exosphere and the surface of Mercury. On Mercury, the strong link has been confirmed only for Mg (Suzuki et al., 2023). Thus, the Hermean Mg exosphere is an especially important target for investigating the relationship between the exospheric distribution and the surface abundance map.

## 1.3. PHEBUS Onboard BepiColombo MPO

The BepiColombo mission consists of two spacecraft: the Mercury Planetary Orbiter (MPO), led by the European Space Agency (ESA), and Mio, led by the Japan Aerospace Exploration Agency (JAXA). It has already completed three Mercury swing-bys (MSBs) and is scheduled to perform them three more times before its Mercury orbit insertion in December 2025. The Probing of Hermean Exosphere by Ultraviolet Spectroscopy (PHEBUS) is an ultraviolet spectrograph onboard MPO (Quémerais et al., 2020) with two detectors covering the spectral range from 55 nm up to 315 nm (EUV and FUV channels) and two additional narrow windows at 404 and 422 nm (NUV channels). Instrumental field of view is 0.2 square degree with a slit and 6.1 square degree without a slit. PHEBUS aims to reveal the complex interaction between the Hermean exosphere and the surface and space environments by investigating the distributions and seasonal variations of atomic species such as Ca, helium (He), potassium (K), and Mg, and to realize the first detection of species such as carbon (C), nitrogen (N), and sulfur (S). It already measured the UV albedo of the surface (Chaufray et al., 2023) and the distributions of He and Ca density in the Hermean exosphere during the three MSBs (Quémerais et al., 2023; Robidel et al., 2023) of Mercury during the three MSBs. Because of instrumental constraints, the EUV or FUV channel detectors cannot be operated simultaneously. Observations were conducted using the EUV channel during the first MSB (MSB1) and the FUV channel during the second and third MSBs (MSBs 2 and 3).

In this study, we used an FUV channel with a wavelength range of 145–315 nm to investigate radiances of an emission line with a wavelength of 285.2 nm emitted by Mg atoms through solar resonance scattering. A micro-channel plate (MCP) was used to convert photons traveling through the optical system into electrons, which were then amplified. A four-pole resistive anode encoder was used to determine the position of the electron cloud. Ground measurements showed that the wavelength resolution was smaller than 1.5 nm with a slit and was approximately an order of magnitude higher without a slit.

## 1.4. Purpose of This Study

In this study, we investigated the spatial distribution and ejection process of the Hermean Mg exosphere using data obtained by PHEBUS during MSBs 2 and 3. Background subtraction and calibration methods developed in this study are also necessary for preparing the forthcoming observations.

# 2. Observations and Analyses

## 2.1. Fundamental Information of Second and Third Mercury Swing-Bys

Table 1 shows the time, true anomaly angles (TAAs) when BepiColombo reached the closest approach (CA) to Mercury, local times, longitudes, and latitudes of subspacecraft points at the time of CA, and the altitudes of the
<caption>**Table 1**</caption>

Conditions of CA to Mercury During MSBs 2 and 3

<table><thead><tr><th>Mercury swing by</th><th>Time (UTC)</th><th>TAA</th><th>Sub-SC<br>Local time (hr)</th><th>Sub-SC<br>Longitude</th><th>Sub-SC<br>Latitude</th><th>Altitude of SC (km)</th></tr></thead><tbody><tr><td>2</td><td>23/06/2022 09:44</td><td>265°</td><td>4</td><td>44°</td><td>-14°</td><td>199</td></tr><tr><td>3</td><td>19/06/2023 19:34</td><td>312°</td><td>2</td><td>25°</td><td>23°</td><td>236</td></tr></tbody></table>

Note. Times and true anomaly angles (TAAs) are when the spacecraft (SC) reached CA. Local times, longitudes, latitudes and altitudes are those of spacecraft's CA.

spacecraft at the time of CA. The orbits of the spacecraft are shown in Figure 1 in Mercury Solar Orbital (MSO) coordinates. The coordinates defined as +x<sub>MSO</sub>, +y<sub>MSO</sub>, and +z<sub>MSO</sub> being the sunward, duskward, and northward aligned with Mercury's spin axis, respectively. PHEBUS began observations at nightside and stopped them at dawnside. While the two swing-bys' orbits are similar, PHEBUS' lines of sight in MSBs 2 and 3 are opposite, pointing northward and southward, respectively. Observations were conducted without a slit, using an FUV channel, and with an integration time of 8 s every 10 s.

## 2.2. Obtained Data

Figures 2a and 2b display the spectra of dark and one of the standard stars, 9Alp CMA (Sirius), observed for sensitivity calibration, respectively. Both of them were taken during the cruise phase to Mercury. The spatial pattern of the dark was stable during the dark observations. Figures 2c and 2d show examples of the data collected

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Orbits of BepiColombo and lines of sight of PHEBUS during Mercury swing-bys 2 and 3. The red lines and the blue arrows represent the orbits of BepiColombo and lines of sight of PHEBUS, respectively. The dots indicate BepiColombo's positions every 10 min (a), (b), and (c) correspond to MSB2, and (d), (e), and (f) correspond to MSB3. (a) and (d) are views from the north pole, (b) and (e) are from the dawnside, and (c) and (f) are from the nightside.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Examples of observational data taken by PHEBUS. (a) Dark data obtained during the cruising phase. (b) 9Alp CMa (Sirius) data observed for sensitivity calibration. (c) Data at the time when Mg emission is expected to be detected during MSB2. (d) Data of last few minutes during MSB3.</figcaption></figure>

during the MSBs. Figure 2c displays the data obtained during MSB2 at the time when the Mg signals are expected to be detected. The region of the detector sensitive to the external source is between the 100th and 156th pixels in the spatial direction and the wavelength range of 145–315 nm. However, no clear features are visible around the wavelength of 285.2 nm. At the end of the observations, the count rate increased overall possibly due to reflected light from the Mercury surface (Figure 2d).

## 2.3. Background Subtraction

We assumed three types of background components. First, we prepared three types of data (Figure 3) that were unlikely to contain exospheric emissions: (a) the average of all the dark data obtained during the cruising phase; (b) the average of the five images around CA while BepiColombo was still in the shadow of Mercury; and (c) the average of the last five images before the end of the observations during two swing-bys. Note that (b) and (c) also contain a dark component. To avoid random noise affecting the results, a moving average was performed over ±3 nm in the wavelength direction and ±15 pixels in the spatial axis direction. The background component, which is calculated as the linear combination of the three components, was subtracted from the raw data. The weight of each background component at each time (Figures 3d and 3e) is calculated by performing least squares fitting for areas of the detector where the Mg emission line is not measured. Figures 3d and 3e show that the contribution of component (a) to the total background count increases during the swing-bys. It is possible that the dark signals increase due to the rising temperature of the electronics over time since the detector was switched on. Component (b) is thought to be a combination of dark and stray light. Its contribution decreases as the spacecraft moves away from Mercury. Component (c) has little contribution and a small fluctuation. It may not be a major background signal source or the assumed three background components may not be independent of each other and thus component (c) can be reproduced to some extent by the linear sum of components (a) and (b).
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Three types of the reference background component spectra were assumed in subtracting the background signals from observational data: the average of the dark data (a), the average of data around BepiColombo's closest approach (b), and the average of the last five images during the Mercury swing-bys (MSBs) (c). (d) and (e) are time series of the magnitude of each background component during MSBs 2 and 3, respectively, deduced from the calculation. The red, blue and green lines correspond to components (a), (b) and (c), respectively.</figcaption></figure>

## 2.4. Sensitivity Calibration

PHEBUS conducted several stellar observations to reconstruct the effective area. In this study, sensitivity calibration was conducted using five stellar observation data sets, whose observation start times, names of the observed stars, and positions of the stars on the detector are listed in Table 2. For these stellar observations, background subtraction was performed by fitting components (a) dark data, and (b) data around the CA, among the three components described in Section 2.3. The effective areas were calculated by dividing the number of detected photons by reference spectra obtained by the International Ultraviolet Explorer (IUE), the Solar Stellar Irradiance Comparison Experiment (SOLSTICE) and the Spectroscopy for Investigation of Characteristics of the Atmosphere of Mars (SPICAM) onboard Mars Express (Snow et al., 2013). Consequently, the effective area was shown to be dependent on the positions of the stellar images on the detector (i.e., the position of the star in the field of view of PHEBUS) and the time elapsed from the beginning of the observations (Figures 4 and 5). The blue dots in Figure 4 are the deduced effective areas normalized by observations with the star in the center of the field of view. The red line is a model of the instrument transmission from the entrance baffle to the slit as a function of the angular distance along the spatial axis to the center of the field of view. This transmission is not constant when the slit is removed because of vignetting between the primary and the slit. Dependency of the effective areas obtained from the stellar observations and from numerical calculations is consistent. Figure 5 shows the time series of the deduced effective area normalized by the first value. The blue dots represent the values obtained from

<table><caption>**Table 2**
List of Stellar Observation Conditions</caption><thead><tr><td>Observation start time (UTC)</td><td>Stellar name</td><td>Position of stars on the detector (pix)</td></tr></thead><tbody><tr><td>28/03/2022 15:00</td><td>9Alp CMa (Sirius)</td><td>138.2 ± 0.7</td></tr><tr><td>28/09/2022 22:04</td><td>67Alp Vir (Spica)</td><td>119.0 ± 0.6</td></tr><tr><td>08/03/2023 21:05</td><td>67Alp Vir (Spica)</td><td>116.9 ± 0.8</td></tr><tr><td>11/07/2023 03:42</td><td>Bet Cru (Mimosa)</td><td>127.7 ± 0.6</td></tr><tr><td>17/07/2023 08:42</td><td>9Alp CMa (Sirius)</td><td>136.7 ± 0.6</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Dependence of effective area at the pixel corresponding to a wavelength of 285.2 nm on the angle of incidence. The blue dots are deduced from observations, while the red line is from model calculation.</figcaption></figure>

observations. The red line corresponds to $S(t) = 0.55e^{-0.13t} + 0.45$, which is obtained by fitting $S(t) = Ae^{Bt} + C$ to observational data under the constraint condition of $S(0) = 1$, that is, $C = 1 - A$. Although the detailed cause of decreasing sensitivity over time remains unknown, it may be due to the gradual increase of the temperatures of the MCP and the electronics along the observations.

## 3. Results

### 3.1. Time Series of the Mg Radiances During the Two Swing-Bys

When the background signals are subtracted as described in Section 2.3, images such as Figure 6 are obtained. The Mg radiance can be calculated from the following equation:

$$I = \frac{p}{S} \times \frac{4\pi}{\Omega} \times 10^{-6} \quad (1)$$

where $I$ is Mg radiance in R (Rayleigh), $p$ is the number of detected photons in $s^{-1}$, $S$ is the effective area calculated in Section 2.4 in cm$^2$, $\Omega$ is the solid angle of the field of view in sr. After integrating the deduced radiances in a spatial

range of 128 ± 28 pix and a spectral range of 285.2 ± 7 nm, the time series of Mg radiances were obtained (Figures 7a and 7d). The errors were calculated by propagating the standard deviation of the dark data, a statistical fluctuation in the number of detected photons known as shot noise, and fitting errors of the sensitivity calibration. Soon after BepiColombo appears in the sun-lit regions, Mg radiances reach maximum, (7.4 ± 1.3) × 10$^2$ R and (5.2 ± 0.9) × 10$^2$ R (Figures 7a and 7d).

### 3.2. Mg Column Density Profiles

By combining information on time, BepiColombo orbit, and PHEBUS' line of sight, Mg radiance altitude profiles along the spacecraft trajectories were obtained (Figures 7b and 7e). The Mg column densities along the lines of sight of PHEBUS in cm$^{-2}$ were calculated as

$$N = \frac{I}{g} \times 10^{-6} \quad (2)$$

where $I$ in R is the Mg radiance when the spacecraft is outside the shadow of Mercury and $g$ is the atomic fluorescence efficiency, known as a g-factor (Figures 7c and 7f). G-factors during MSBs 2 and 3 are 3.25 × 10$^{-1}$/s and 4.20 × 10$^{-1}$/s, respectively (Chaufray et al., 2022). The g-factor was calculated considering the Doppler shift (Swings effect; Swings, 1942) associated with the radial velocity of Mercury with respect to the Sun. Dependence of the velocity of each particle (Greenstein effect; Greenstein, 1958) was ignored.

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

## 4. Discussion

### 4.1. Comparison of Data Obtained During Two Swing-Bys

First, we provide insights into the light curves (Figures 7a and 7d). In the shadow region, few counts should be detected, despite the possibility of Mg atoms present, as we observed emissions through solar resonance scattering. As the number of detected photons became proportional to the Mg illuminated column density along the line of sight (Equation 2), the number of detected photons rapidly increased when BepiColombo exited the shadow. Subsequently, as the spacecraft moved away from Mercury, the Mg signals gradually diminished because the Mg column density decreased with altitude. In MSBs 2 and 3, the time difference between the moment when

<caption>**Figure 5.** Dependence of the effective area at the pixel corresponding to a wavelength of 285.2 nm on the time elapsed from the beginning of observations. The blue dots are derived from observations, while the red line is $S(t) = 0.55e^{-0.13t} + 0.45$.</caption>
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Spectra during the Mercury swing-bys 2 (a) and 3 (b) after background subtraction. Signals originating from the Hermean Mg exosphere are visible around a wavelength of 285.2 nm.</figcaption></figure>

BepiColombo leaves the shadow regions and the observed Mg radiances reach their maximum slightly: 1 min for MSB2 and 2 min for MSB3. The cause of this is the difference in the timing at which PHEBUS' line of sight completely leaves the shadow region.

The scale height of the Mg exosphere was then estimated by fitting an exponential function and the Chamberlain model (Chamberlain, 1963) to the Mg column density profiles inferred in Section 3.2 (Figure 8). The Chamberlain model is an analytical exospheric model that solves the number density distribution in a steady state divided into three types of atomic orbits: ballistic, satellite, and escape orbits (see Equation 37 of

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Time variation of Mg radiances and profiles of Mg column densities. (a) and (d) show the time variation of Mg radiances during Mercury swing-bys 2 and 3, respectively. (b) and (e) are observed Mg radiances as a function of altitudes. The red and blue lines represent Mg radiances before and after closest approach, respectively. (c) and (f) are Mg column densities along the lines of sight of PHEBUS. The lighter color around each line indicates the 1σ error range.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Mg column density profiles fitted by an exponential function (a) and the Chamberlain model (b). Observations by PHEBUS are shown in dots with the 1σ error range displayed in lighter-colored shadows, and the fitted curves using an exponential function or the Chamberlain model are shown in lines. The results obtained from Mercury swing-bys 2 and 3 are shown in red and blue colors, respectively.</figcaption></figure>

Chamberlain, 1963), although the satellite component was ignored in this study. The benefit of adopting this model is that it requires only two parameters, number density and temperature at the exobase, when calculating the column density. We fitted the deduced Mg column density profiles along the lines of sight of PHEBUS, assuming that these two fitting parameters are spherically symmetric. Solar radiation acceleration was also included in the potential term (cf. Equation 4 of Cassidy et al., 2015), although it hardly contributed to the results for Mg. When fitted by a simple exponential function $N = N_0 \exp(-r/r_0)$ to the column densities $N$ as a function of altitude $r$, $r_0$ corresponding to the exospheric scale height was 970 and 560 km for MSBs 2 and 3, respectively (Figure 8a). Using the Chamberlain model, the number density $n_0$ and temperature $T$ at the exobase are $n_0 = (2.7 \pm 0.2) \times 10^1/cm^3$ and $T = (5.2 \pm 0.2) \times 10^3$ K for MSB2, and $n_0 = (6.7 \pm 0.8) \times 10^1/cm^3$ and $T = (3.2 \pm 0.1) \times 10^3$ K for MSB3 (Figure 8b). Therefore, exospheric production rates $S$, calculated from $S = n_0/2\sqrt{\pi m/2k_B T}$ (cf. Equation 5 of Merkel et al., 2017), are $(1.0 \pm 0.1) \times 10^6/cm^2/s$ and $(2.0 \pm 0.3) \times 10^6/cm^2/s$ for MSBs 2 and 3, respectively. $m$ and $k_B$ are the mass of a Mg atom and the Boltzmann constant, respectively. Although a direct quantitative comparison is difficult owing to differences in spacecraft trajectories and lines of sight, this is slightly larger than the results from MASCS (Figures 8c and 8d of Merkel et al., 2017). The exospheric production rate is approximately twice as large for MSB3 as for MSB2. This is consistent with the TAA dependence of the exospheric production rates obtained from MASCS (Figure 8f of Merkel et al., 2017).

## 4.2. Comparison With Numerical Calculation

Chaufray et al. (2022) numerically calculated a three-dimensional Mg exospheric number density distribution based on the MASCS knowledge at dawn, which is relevant for these two PHEBUS observations. This model sets Mg production rate distributions by multiplying the surface Mg/Ca abundance ratio based on Weider et al. (2015) and Ca production rates based on Burger et al. (2014). The distribution of micro-meteoroid flux is an angular e-folding width of 50° centered at a local time of 6 and latitude of 0°. The temperature of released Mg atoms is assumed to 6,000 K based on Mg exosphere observations done by MESSENGER/MASCS (Merkel et al., 2017). In order to compare the estimated Mg number density with the observations, we integrated it along PHEBUS' line of sight. Consequently, the model calculations and observations were in excellent agreement (Figure 9) without any parameter tuning. The local time range where exospheric Mg signals were detected in this study is from 4 to 9. Therefore, the consistency between the observations and the model indicates that our knowledge of micro-meteoroid flux distributions obtained from MESSENGER observations of the dayside Ca exosphere is valid up to local time 4.
<figure><img src="image_11.png" /><figcaption>Figure 9. Comparison of PHEBUS observations (red lines) and model calculation (blue lines) during the Mercury swing-bys 2 (a) and 3 (b).</figcaption></figure>

### 4.3. Comparison With Ca Density Profiles

During MSBs 1–3, PHEBUS also observed Ca exospheres using the NUV c422 channel. Fitting an exponential function and the Chamberlain model to the observational data showed that the scale height and temperature of the Ca exosphere were 2,555 km and >50,000 K for MSB1 and 2,777 km and >50,000 K for MSB2, respectively (Robidel et al., 2023). The scale factor and temperature were approximately 2.5–5 times and 10–15 times higher than those of Mg, respectively. This means that Mg atoms have much lower energy than Ca atoms because of their different forms when they are generated. As Mg- and Ca-bearing molecules, they are both ejected from the surface and quickly dissociate into atoms in the exosphere through photodissociation or shock-induced dissociation. The fact that Mg has a temperature of approximately 5,000 K is consistent with Mg atoms generated by photodissociation of MgO molecules ejected through MIV (Berezhnoy, 2018). On the other hand, it is hard to explain the high-energy Ca atoms, exceeding tens of thousands of kelvins by photodissociation from Ca-bearing molecules alone, and they are thought to be generated through neutralization of $Ca^+$ ions derived from shock-induced non-equilibrium dissociative ionization (Killen, 2016; Moroni et al., 2023).

## 5. Conclusion

In this work, we developed a calibration method for PHEBUS and unraveled the distributions of the Hermean Mg exosphere during BepiColombo's MSBs 2 and 3. We performed sensitivity calibration using stellar observation data and clarified the spatiotemporal dependency of the effective area. The obtained Mg light curves were consistent with the Chamberlain model with an energy of 3,000–5,000 K and a three-dimensional numerical calculation (Chaufray et al., 2022) with an energy of 6,000 K. Comparing the obtained Mg radiance profiles with Ca during MSBs 1 and 2 (Robidel et al., 2023), the Mg profiles are consistent with a lower release energy than the equivalent Ca exospheric profiles. This is consistent with the fact that Mg atoms might be produced with smaller energy when photodissociated from Mg-bearing molecules than in the case of Ca produced from Ca-bearing molecules.

Table 3 summarizes the dates and orbits of MSBs 4–6. MESSENGER/MASCS conducted limb scan observations from the southern hemisphere, resulting in a dramatic improvement in our understanding of the distribution of the Mg exosphere above the dayside equatorial regions. BepiColombo, on the other hand, will approach Mercury on an orbit from north to south and south to north in MSBs 4 and 6, respectively, although few exospheric signals will be detected in MSB5 due to the closest approach point too far from Mercury. Thus, exospheric Mg distribution not only in the longitudinal but also in the latitudinal directions will be able to be investigated. As the close approach point in MSB6 is close to the Caloris basin, where surface Mg abundance is low (Weider et al., 2015), it is expected that the direct link between the exospheric and surface Mg abundance will be clearly visible.
<caption>Table 3</caption>

Conditions of CA to Mercury During MSBs 4–6

<table><thead><tr><th>MSB</th><th>Time (UTC)</th><th>TAA</th><th>Sub-SC<br>Local time (hr)</th><th>Sub-SC<br>Longitude</th><th>Sub-SC<br>Latitude</th><th>Altitude of SC (km)</th></tr></thead><tbody><tr><td>4</td><td>05/09/2024 06:30</td><td>333°</td><td>6</td><td>-90°</td><td>39°</td><td>200</td></tr><tr><td>5</td><td>02/12/2024 23:52</td><td>331°</td><td>12</td><td>184°</td><td>3°</td><td>40,000</td></tr><tr><td>6</td><td>09/01/2025 01:07</td><td>150°</td><td>0</td><td>56°</td><td>45°</td><td>387</td></tr></tbody></table>

Note. Times and TAAs are when the spacecraft reaches CA. Local times, longitudes, latitudes and altitudes are those of spacecraft's CA.

## Data Availability Statement

The data are archived at Suzuki et al. (2024).

## Acknowledgments

This work was supported by JSPS KAKENHI Grant JP22J15382, JP24KJ2224, and JP21KK0056.

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