Origin of Mercury’s double magnetopause: 3D hybrid simulation study with A.I.K.E.F

Icarus 218 (2012) 666–687

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Icarus

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Origin of Mercury’s double magnetopause: 3D hybrid simulation study with A.I.K.E.F.

Joachim Müller a,⇑, Sven Simon b, Yung-Ching Wang f, Uwe Motschmann a,e, Daniel Heyner c, Josef Schüle d,Wing-Huen Ip f,g, Gero Kleindienst c, Gavin J. Pringle h

a Institute for Theoretical Physics, TU Braunschweig, Mendelssohnstrabe 3, 38106 Braunschweig, Germanyb Institute of Geophysics and Meteorology, University of Cologne, Zülpicher Str. 49, 50674 Cologne, Germanyc Institute for Geophysics and Extraterrestrial Physics, TU Braunschweig, Mendelssohnstr. 3, 38106 Braunschweig, Germanyd Gaub-IT-Centre, TU Braunschweig, Hans-Sommer-Strabe 65, 38106 Braunschweig, Germanye Institute for Planetary Research, DLR, Berlin, Germanyf Institute of Astronomy, National Central University, No. 300, Jhongda Rd, Jhongli City, Taoyuan County 32001, Taiwan, ROCg Institute of Space Science, National Central University, No. 300, Jhongda Rd, Jhongli City, Taoyuan County 32001, Taiwan, ROCh EPCC, The University of Edinburgh, James Clerk Maxwell Building, Mayfield Road, Edinburgh, EH9 3JZ, UK

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 August 2011Revised 8 November 2011Accepted 29 December 2011Available online 18 January 2012

Keywords:MercurySolar windMagnetospheresMagnetic fields

0019-1035/$ - see front matter � 2012 Elsevier Inc. Adoi:10.1016/j.icarus.2011.12.028

⇑ Corresponding author.E-mail address: [email protected] (J. Müller).

During the first and second Mercury flyby the MESSENGER spacecraft detected a dawn side double-cur-rent sheet inside the Hermean magnetosphere that was labeled the ‘‘double magnetopause’’ (Slavin, J.A.et al. [2008]. Science 321, 85). This double current sheet confines a region of decreased magnetic field thatis referred to as Mercury’s ‘‘dayside boundary layer’’ (Anderson, M., Slavin, J., Horth, H. [2011]. Planet.Space Sci.). Up to the present day the double current sheet, the boundary layer and the key processesleading to their formation are not well understood. In order to advance the understanding of this regionwe have carried out self-consistent plasma simulations of the Hermean magnetosphere by means of thehybrid simulation code A.I.K.E.F. (Müller, J., Simon, S., Motschmann, U., Schüle, J., Glassmeier, K., Pringle,G.J. [2011]. Comput. Phys. Commun. 182, 946–966). Magnetic field and plasma results are in excellentagreement with the MESSENGER observations. In contrast to former speculations our results prove thisdouble current sheet may exist in a pure solar wind hydrogen plasma, i.e. in the absence of any exo-spheric ions like sodium. Both currents are similar in orientation but the outer is stronger in intensity.While the outer current sheet can be considered the ‘‘classical’’ magnetopause, the inner current sheetbetween the magnetopause and Mercury’s surface reveals to be sustained by a diamagnetic current thatoriginates from proton pressure gradients at Mercury’s inner magnetosphere. The pressure gradients inturn exist due to protons that are trapped on closed magnetic field lines and mirrored between northand south pole. Both, the dayside and nightside diamagnetic decreases that have been observed duringthe MESSENGER mission show to be direct consequences of this diamagnetic current that we labelMercury’s ‘‘boundary-layer-current‘‘.

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1. Introduction

On 14 January 2008, the MESSENGER spacecraft detected a wideregion of decreased magnetic field inside Mercury’s dawn magne-tosphere (see Fig. 1) that was confined in between a double currentsheet. Such a double current sheet had never been observed before,neither in Mercury’s nor in any other planetary magnetosphere.Slavin et al. (2008) pointed out that both current layers are verysimilar in orientation and thickness, only the intensity of the innercurrent sheet is weaker. Consequently, the authors called this dou-ble current sheet Mercury’s ‘‘double magnetopause’’. Slavin et al.(2008) concluded that the outer current sheet separates the mag-netosheath and magnetosphere and that the region of decreased

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magnetic field in between the double sheet originates from en-hanced plasma pressure. This region in between both currentsheets was labeled Mercury’s ‘‘dayside boundary layer’’ (Andersonet al., 2011). The boundary layer could be observed in both flybysthat are abbreviated M1 and M2 in the following (Andersonet al., 2010). During the third flyby the spacecraft had been in se-cure mode and neither magnetic field nor plasma data has been re-corded for the respective region. MESSENGER’s orbital phase wassuccessfully initiated on 18 March 2011, but no measurementshad been available at the time of this writing.

Since both flybys M1 and M2 suggest the existence of theboundary layer and solar wind conditions have been very quietduring M1, it is very likely that the boundary layer is a stableand stationary region. Up to the present day the boundary layer it-self and the key processes of its formation are not well understood.Slavin et al. (2008) pointed out that different processes could cause

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Fig. 1. The sketch (a) illustrates the MESSENGER trajectory of the first flyby where the arrows indicate the spacecraft’s flight direction (red). The black dots mark from top tobottom the positions of outbound bow shock (BS), outbound magnetopause (MP), dayside boundary layer’s (D-BL) edge, closest approach (C/A) and nightside boundary layer’s(N-BL) edge. The corresponding magnetic field measurements are shown in (b).

J. Müller et al. / Icarus 218 (2012) 666–687 667

the layer’s formation: one explanation would be the diamagneticeffect of solar wind plasma that enters Mercury’s magnetospherealong open flux tubes. Alternatively exospheric ions that enterthe magnetosphere after being picked up by the solar wind andaccelerated in the magnetosheath could produce the diamagneticdecrease.

The present article intends to advance the understanding of theboundary layer and its formation. Since ion kinetic processes arebelieved to play an important role within Mercury’s magneto-sphere (Glassmeier et al., 2003; Slavin et al., 2008), the investiga-tion will be accomplished by means of three-dimensional hybrid(ion kinetic, electron fluid) numerical simulations. Plasma quanti-ties and magnetic field results will be compared to the measure-ments that have been provided in the initial, pre-orbital phase ofthe MESSENGER mission.

The article is organized as follows: In Section 2 we will brieflysummarize the measurements and knowledge about the boundarylayer that were available at the time of this writing. Since the pres-ent article proceeds the simulations of Müller et al. (2011), we willpoint out their major findings in Section 3. In Section 4 we will ex-plain the simulation setup of the present study. Numerical detailsare given in Section 5. Results will be shown in Section 6. Section 7discusses the simulation results with special emphasis on the dou-ble current sheet and dayside boundary layer. The major findingswill be summarized in Section 8.

2. On Mercury’s magnetospheric boundary layer

Based on Slavin et al. (2008), Anderson et al. (2011), Raines et al.(2011) we will summarize the available knowledge about Mer-cury’s boundary layer. A more detailed overview can be found inthe respective articles and references therein. During both, M1and M2, a region of depressed magnetic field and increased protonflux adjacent to it could be observed immediately after entranceinto Mercury’s dawn magnetosphere. This region of depressedmagnetic field was labeled the ‘‘dayside boundary layer’’ (D-BL).The M1 trajectory and corresponding magnetic field are shown inFig. 1. While interplanetary magnetic field (IMF) and Mercury’sdipole field were basically parallel at the sub-solar point duringM1, they had been anti-parallel during M2, resulting in notedly

increased sub-solar reconnection (Anderson et al., 2011). Sincethe existence of the D-BL does not seem to depend on the IMFdirection, Anderson et al. (2011) concluded that sub-solar recon-nection is unlikely to be responsible for the D-BL formation at Mer-cury. In contrast, the low latitude boundary layer (LLBL) at Earthsignificantly depends on the rate of sub-solar reconnection (Fuse-lier et al., 1999). Hence, it is unlikely that both layers are formedby the same process. Furthermore, the D-BL at Mercury occupiesa significant fraction of Mercury’s magnetosphere and is much lar-ger than the LLBL at Earth, at least on scales comparable to respec-tive magnetospheric dimensions.

During M1 the width of the D-BL was estimated to be 1000–1100 km and the magnetic field magnitude inside varied between60 nT and 70 nT (see Fig. 1b). According to Raines et al. (2011) theproton density was 16 cm�3, resulting in a proton inertia length ofabout 57 km. Hence, the D-BL itself is a macro scale phenomenonfor the protons. The width of the D-BL’s inner edge, on the otherhand, is comparable to proton gyration scale (see Fig. 1b at19:10:37 UTC). While the magnetic field intensity showed a sud-den decrease from 101 nT to 79 nT when crossing the inner edgeof the D-BL during M1, the direction of the magnetic field remainedbasically unchanged. This is consistent with a plasma pressure gra-dient that is directed outward and perpendicular to the magneticfield, as pointed out by Anderson et al. (2011). The magnetic fielddecrease inside the boundary layer was accompanied by an in-creased thermal pressure. The proton pressure inside the D-BL dur-ing M1 was estimated to be 0.4 nPa with a proton temperature of2 � 106 K during M1, whereas the values were 1.0 nPa and10 � 106 K during M2. A second magnetic field decrease, at Mer-cury’s nightside, was observed during M1 at 19:00 UTC and wentalong with an increased proton density of about 4–5 cm�3, duringboth M1 and M2 (Raines et al., 2011). The corresponding temper-atures were measured to 4–8 � 106 K during M1 and 8 � 106 Kduring M2. This region was labeled the ‘‘nightside boundary-layer’’(N-BL). Hence, solar wind protons should be considered to signifi-cantly impact on the boundary layer formation, even though heavyexospheric ions could play a role as well (Slavin et al., 2008; Ander-son et al., 2011). In particular, the results show that both flybysyielded qualitatively the same results in terms of magnetic fieldand plasma observations, despite the significant difference in IMFdirection.

Table 1The table lists the parameters of Mercury’s plasma environment. The values arechosen corresponding to Wang et al. (2010) and Alexeev et al. (2010). Simulationsthat use these parameters have been carried out by Müller et al. (2011), theirmagnetic field results are shown in Fig. 2.

Quantity Symbol Müller et al. (2011) Present study

Solar wind density n 32 cm�3 32 cm�3

Solar wind velocity v 430 km/s 430 km/sion temperature Tion 2 � 105 K 2 � 105 Kelectron temperature Telectron 2 � 105 K 2 � 105 Kplanetary radius RM 2440 km 2440 kmmagnetic moment M 200 nTR3

M 200 nTR3M

magnetic moment offset DM,z 405 km 0 kmIMF magnitude B 21.0 nT 12.6 nTIMF longitude angle /B �53� 90�IMF latitude angle kB 63� 0�

668 J. Müller et al. / Icarus 218 (2012) 666–687

3. Motivation and previous work

Both, the upstream plasma parameters during the MESSENGERflybys and Mercury’s intrinsic dipole field are not known exactly. Inthe literature, values for Mercury’s magnetic moment range from196 nTR3

M (Alexeev et al., 2010) to 340 nTR3M (Ness, 1979). Several

models for Mercury’s intrinsic magnetic field are discussed byAnderson et al. (2010). Corresponding to Anderson et al. (2008)Mercury’s dipole moment may exhibit an inclination of 5–12�against the rotational axis. The most recent dipole fit has been car-ried out by Alexeev et al. (2010) who estimate a dipole strength of196 nTR3

M , where the dipole center is shifted 405 km in northerndirection.

Previous simulations using the A.I.K.E.F. code have already beensuccessfully applied to model the magnetic field for the M1 and M2flybys (Müller et al., 2011). For these simulations a dipole of200 nTR3

M had been utilized with its origin shifted 405 km north-ward corresponding to Alexeev et al. (2010). Any inclination hadbeen neglected. Since upstream plasma measurements for theM1 and M2 flyby are not available the plasma parameters areadapted from Wang et al. (2010) who use typical values for Mer-cury’s plasma environment. Based on the MESSENGER observa-tions the M1 interplanetary magnetic field (IMF) was set to anlongitude angle of / = �53�, where we define / = 0� to be parallelto the x-axis, i.e. pointing downstream. A latitude angle of k = 63�was used, where we define k = 90� to be parallel to the z-axis, i.e.pointing in northern direction. The values are listed in Table 1.Using this definition, an arbitrary vector yields

x

y

z

0B@

1CA ¼ r

cosðkÞ cosð/ÞcosðkÞ sinð/Þ

sinðkÞ

0B@

1CA; ð1Þ

where r defines the distance to the origin.Fig. 2 illustrates the magnetic field results from Müller et al.

(2011) for the M1 flyby in red.1 In view of the unknown upstreamplasma parameters and the exact magnetic moment the results canbe considered in very good agreement with the MESSENGER obser-vations that are shown in blue. In particular a region of decreasedmagnetic field between t1 = 19:11 and t2 = 19:14 UTC could be ob-served, indicating that the model is capable of capturing the basicprocesses of the dayside diamagnetic decrease.

However, Müller et al. (2011) did not discuss the boundarylayer formation. Instead, they validated the newly developedA.I.K.E.F. simulation code. The analysis of Mercury’s magneto-sphere and boundary layer formation is subject to the presentwork. Even though the above results are in very good agreementwith the magnetic field that was recorded by MESSENGER, thesimulations are not well suited for the analysis of the physics in-volved in the boundary layer formation because the shifted dipoleand M1 IMF direction considerably complicate the analysis. Hence,we redid the simulations using a slightly simplified geometry andsuggest that the corresponding physical processes are valid for thereal M1 case as well.

4. Simulations setup

For the simulation presented in this article we will focus on theM1 flyby since Mercury’s dipole field and IMF were basically paral-lel in the sub-solar region, resulting in negligible dayside reconnec-tion. As the simulations of Müller et al. (2011) did show thedayside diamagnetic decrease even in a pure hydrogen plasma,we concluded that all physics seen in the data can be completely

1 For interpretation of color in Figs. 1–17, the reader is referred to the web versionof this article.

explained without the inclusion of sodium or any other exosphericspecies. Hence, at the current stage we decided to continue ourmodeling by using single species hydrogen plasma that is exclu-sively injected at the domain boundaries. A detailed study of theinfluence of exospheric ion species on the boundary layer will besubject to future studies. We only provide a brief outlook on thistopic in Appendix A. Furthermore we resign to consider doublecharged Helium He2+ which makes up less than 2% of the solarwind. It was shown in hybrid plasma simulations by Modoloet al. (2005) to be negligible for the solar wind interaction withthe induced magnetosphere at Mars. Compared to the inputparameters of Müller et al. (2011) we introduce the following mod-ifications that are also listed in Table 1:

1. Centered planetary dipole moment.2. M1 trajectory mapped to equatorial plane.3. IMF in y-direction, i.e. perpendicular to Mercury’s magnetic

moment.4. Improved model of Mercuries interior.

Each of the listed rearrangements is explained below:

1. According to Alexeev et al. (2010) the center of Mercury’smagnetic moment is shifted about 405 km in northern direc-tion. Fig. 3 shows the magnetic field of such a dipole along theM1 trajectory (red). As can be seen, both Bx and By are non-zero. However, we cannot see any physical reason why theexistence of the boundary layer should depend on this shift.Hence, we use a planetary centered magnetic moment inorder to simplify the analysis. The green line in Fig. 3 showsthe magnetic dipole field along the M1 trajectory that resultsfrom a centered magnetic moment.

2. The M1 Orbit is not exactly located inside the equatorialcross-section, but shows a rather small inclination. For thepresent simulation we neglect this inclination, i.e. we setz = 0 for each position while the x- and y-coordinates remainunchanged. Fig. 3 shows the corresponding magnetic field(blue). As can be seen, both the Bx and By components vanisheverywhere along the trajectory. However, we shall point outthat this simplification barely impacts the total magnetic fieldstrength: all three configurations show nearly the same mag-netic magnitude along the entire trajectory (see Fig. 3a).

3. In contrast to the simulations of Müller et al. (2011) that usethe real M1 and M2 magnetic field configurations, a simula-tion with simplified IMF is carried out for the present study.The IMF is set to BIMF = (0,12.6,0) nT, therefore being entirelydirected in y-direction. Like the Parker spiral field at Mercurythe latitude angle of this IMF is zero, i.e. the field is perpendic-ular to Mercury’s magnetic moment. Furthermore this choice

Fig. 2. (a–d) Shows the total magnetic field and its components of the simulations by Müller et al. (2011) in red. The simulation results are compared with the MESSENGER Imeasurements in blue. Due to lack of information on the upstream parameter and the precise magnetic moment the results can be considered in very good agreement withthe observations. In particular a region of decreased magnetic field strength between 19:11 and 19:14 UTC is visible, indicating that the model is capable of capturing theboundary layer formation. Animations of the magnetic field and plasma quantities are available online at: www.tu-braunschweig.de/theophys/people/jmueller.


simplifies the differentiation between Mercury’s intrinsicfield and the IMF: within the equatorial cross section weexpect to observe a zero Bz component within the magneto-sheath while inside the inner magnetosphere Bx and By areexpected to be zero. Hence, for the dayside boundary layerthat resides in between these regions it will be easy to distin-guish whether Mercury’s intrinsic dipole field or the IMFdominates.

4. Due to the small stand-off distance at Mercury that is about0.5RM above Mercury’s surface (where RM = 2440 km is theplanetary radius), current generation inside Mercury mayplay an important role (Glassmeier et al., 2007; Grosseret al., 2004; Hood and Schubert, 1979; Suess and Goldstein,1979). The A.I.K.E.F. simulation model self-consistently incor-porates obstacles of arbitrary conductivity profile into theplasma environment (Müller et al., 2011). This is accom-plished by solving for Ohm’s law inside the planetary interior.The ion velocity is set to zero within the entire obstacle. Thismethod has already been successfully applied to model fossilfields at Titan (Müller et al., 2010) and several other saturnianmoons (Roussos et al., 2008; Kriegel et al., 2009). For the Mer-cury simulations the resistivity profile of the planetary bodyis setup as visualized in Fig. 4.

Within a radius of 0.75RM that is marked by blue dashed verticallines a zero resistivity is specified, i.e. in this region Mercury’sintrinsic dipole field remains unaffected during the entire simula-tion, accounting for Mercury’s highly conducting ion core (Mililloet al., 2005) and therefore diffusion times of many thousand years.Formally this region can be referred to be the simulation’s ‘‘innerboundary’’. Assuming that electric properties of Mercury’s mantleare similar to those of Moon, Glassmeier (2000) concludes that val-ues of 10�2–10�9 S/m are reasonable to describe the mantle region.In terms of resistivity these values correspond to 0.1–106 kX m. Inour simulation we use values that are in between these estimates.We divide Mercury’s mantle into an inner region of lower resistiv-ity gi � 4 kX m that resides in between the blue and green verticalline (see Fig. 4a). An outer region of higher resistivitygo � 300 kX m is located in between the green and black verticalline. The black line coincides with Mercury’s surface. The highlyresistive outer region accounts for an isolating crust which con-fines any currents that are generated inside the mantle region fromMercury’s surface. Fig. 4b illustrates the resistivity profile in theequatorial cross section. To guarantee numerical stability the resis-tivity profile is slightly smoothed, which is visible at the smearedout edges near the surface. However, at C/A the resistivity has al-ready decayed to zero.

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Fig. 3. The images show the magnetic field and its components for an offset dipole (Alexeev et al., 2010) along the M1 trajectory (red). Both Bx and By are non-zero. As we donot see any physical reason why the boundary layer should depend on this shift we use a planetary centered dipole in order to simplify the analysis. The green line shows themagnetic field for a centered dipole along the M1 trajectory. Finally the blue line shows the field of a centered dipole along the M1 trajectory that is projected on theequatorial cross-section, i.e. the z-component of each coordinate is set to zero. We shall point out that any of the modifications barely affects the magnetic field magnitude inplot (a).


5. Numerical parameters

For a detailed description of the A.I.K.E.F. hybrid-model we referthe reader to Müller et al. (2011). The numerical parameters for thesimulation presented in this article are listed in Table 2. The simu-lation domain is visualized in Fig. 5a. A large simulation Box ofL = (12,20,20)RM is used in order to avoid any boundary effects.As argued before, the M1 trajectory is projected into the equatorialcross-section, which is shown by means of a blue frame. The trajec-tory is depicted in red where the arrows indicate the flight direc-tion of the MESSENGER spacecraft.

The simulation is carried out on 128 CPUs, the numerical meshincludes three levels of refinement: L0, L1 and L2. Fig. 5b illustratesan enlarged view on the plasma environment that is close toMercury and embedded inside refinement levels L1 and L2. The spa-tial resolution within the highest level of refinement isDx = (1.8,1.8,3.6)x0, where x0 = 40 km is the proton inertia length,i.e. the gyro radius at Alfvén speed with respect to the backgroundparameter of Table 1. Hence, the proton gyration is spatially re-solved inside the solar wind. Yet, the gyration of a proton that trav-els at background Alfvén speed is spatially not yet resolved in a100 nT magnetic field as at D-BL’s inner edge. However, as willbe seen later the thermal velocity at the D-BL’s inner edge reachesthree to four times the background Alfvén speed. Hence, the local

gyration radius in this region is about 1.2 times Dx in the equatorialcross section and therefore a reasonable spatial resolution is guar-anteed. Even more important, the kinetic treatment of the ions al-lows to accurately capture the proton temperature distributionwhich will show to be an important quantity for the boundarylayer formation (cf. Section 7).

Even though the code supports meshes that are also adaptive intime and may resolve dynamical features, we use a mesh that isstatic in time and fix the level of highest resolution within a spher-ical region of 3.5RM from the planetary center. In doing so, we re-sign to highly resolve the far downstream region and bow shockflanks. This saves computational resources that in turn are usedto increase the number of particles and resolution within theimmediate vicinity of Mercury. We shall point out that in particu-lar the following positions along the trajectory are embedded with-in this highest level of refinement L2: Outbound bow shockcrossing (BS), outbound magnetopause crossing (MP), daysideboundary layer crossing (D-BL), closed approach (C/A) and night-side boundary layer crossing (N-BL) (see Fig. 5b). Thus, we can ex-clude that any of these positions are influenced by refinementboundaries. Also we shall point out that the A.I.K.E.F. model is de-signed such that particle refinement is not required within thehighest level of refinement and therefore the phase space distribu-tion is not modified at all (Müller et al., 2011). However, as we do

Fig. 4. The plot (a) shows the resistivity profile by means of a one-dimensional cut along the x-axis. Within a radius of 0.75RM that is marked by blue dashed vertical line azero resistivity is specified, i.e. in this region Mercury’s intrinsic dipole field remains unaffected during the entire simulation. Mercury’s mantle is divided into an inner regionof lower resistivity gi � 4 kX m between the blue and green vertical line. An outer region of higher resistivity go � 300 kX m is located between the green and black verticalline. The black line coincides with Mercury’s surface. Plot (b) shows the resistivity profile in the equatorial cross-section.

Table 2The table lists the numerical parameters for the simulation presented in this article.

Quantity Symbol Value

Domain size L (12,20,20)RM

Origin O (4,10,10)RM

Mesh spacing L2 Dx (1.8,1.8,3.6)x0

Time step Dt 0.1 Xp,100nT

Particles each cell PPC 80Minimal proton density MPD 1.6 cm�3


not employ a time adaptive mesh the inbound bow-shock and in-bound magnetopause reside in coarse refinement levels. For thisreason we focus our analysis on the outbound passage between18:55 and 19:25 UTC that is entirely embedded in the highest levelof refinement.

The time step is chosen to be Dt = 0.1Xp,100nT, whereXp,100nT = 0.1 s is the proton gyration period inside a 100 nT field.This ensures that the proton kinetic motion is well resolved intime, even near the planetary surface where the magnetic field isstrongest. In some regions like the neutral sheet the proton densitymight drop to zero which cannot be handled within the hybrid

Fig. 5. The entire simulation domain is shown by means of the black cuboid in (a). All resuindicated by the blue frame. The brown sphere represents Mercury where the green aMESSENGER trajectory where the red arrows indicate the direction of flight. An enlarged vcan be seen the locations of interest from outbound bow shock (topmost red dot) to nirefinement.

approximation. We therefore set a lower threshold for the protondensity to 1.6 cm�3, that is 20 times below the solar wind density.The total number of macro particles involved in this simulation isabout 109.

6. Results

The simulation reaches the quasi stationary state after three do-main traversals, i.e. after the solar wind has traveled a distance of36RM. We shall point out that the physical quantities are quasi-sta-tionary, i.e. they are still subject to fluctuations. In order to elimi-nate high frequency and numerical noise, the visualized magneticfields and currents are averaged over 20 time steps. In order to ex-clude any start-up-effect, we let the simulation continue until thesolar wind has travelled a distance of 108RM. The magnetic fielddata along the M1 Orbit is recorded in regular time intervals andcompared against the M1 measurements.

Fig. 6 shows the magnetic field magnitude of the simulationalong the M1 orbit at simulation times t1 � 3 min (a), t2 � 5 min(b), t3 � 8 min (c) and t4 � 10 min (d) in red. For comparison theM1 measurements are visualized in blue. The five dashed verticallines indicate the outbound bow-shock (BS), outbound magneto-

lts discussed in this article have been taken from the equatorial cross section, that isrrow illustrates the direction of its magnetic moment. The red line illustrates theiew on the numerical mesh is shown in figure (b) for the equatorial cross-section. As

ghtside boundary layer (lowermost red dot) are located within the highest level of

Fig. 6. The images show the magnetic field magnitude along the MESSENGER1 trajectory (red) after the quasi-stationary state has been reached. The field is compared withthe MESSENGER measurements in blue for the simulation times t1 � 3 min (a), t2 � 5 min (b), t3 � 8 min (c) and t4 � 10 min (d). After 10 min the solar wind has traveled adistance of more than 100RM. As can be seen the magnetic field is stationary, yet not static. Several features such as the bow shock (BS), magnetopause (MP) and the daysideboundary layer (D-BL) are well visible at every time. However, the inbound diamagnetic decrease at 19:00 UTC is a rather transient structure. Over the observed time of10 min it dis- and reappears.


pause (MP), inner edge of the boundary layer (D-BL), closest ap-proach (C/A) and inner edge of the nightside boundary layer (N-BL). As can be seen the overall shape remains the same, eventhough the magnetic field jump at the D-BL’s inner edge does notshow a sharp step in each snapshot. Hence, we resign to state a va-lue for the magnetic field jump. However, a region of decreasedmagnetic field strength between MP and the D-BL’s inner edge isclearly visible and in agreement with the measured daysideboundary layer. The width of the D-BL is about 1100 km, whichis within the range estimated by Anderson et al. (2011). In contrastto this, the nightside diamagnetic decrease is a rather transientstructure that dis- and reappears with time (see Fig. 6d). However,we have reason to assume that this is due to numerical limitationsand will comment this behavior at the end of this section.

In order to gain an improved understanding of the magneticfield topology, the magnetic field magnitude and its componentsare visualized in Fig. 7a–h. The left column shows an enlargedtwo dimensional view of Mercury’s magnetosphere for the equato-rial cross-section while the right column shows the correspondingone-dimensional field along the M1 trajectory. Black dots withinthe 2D plots correspond to the vertical lines in the 1D plots, thatare from top to bottom: bow shock (BS), magnetopause (MP), inneredge of the dayside boundary layer (D-BL), closest approach (C/A)and nightside boundary layer (N-BL).

The magnetic field magnitude along the M1 trajectory in plot(a) shows the existence of four qualitative distinct regions: 1.undisturbed solar wind field (dark blue), 2. magnetosheath (lightblue), 3. dayside boundary layer (green) and 4. inner magneto-sphere (red). These regions are separated by sudden increases inmagnetic field intensity. While bow-shock and magnetopause arewell understood and have been observed in all magnetosphereswithin the Solar System, the differentiation between boundarylayer and inner magnetosphere is a feature exclusively related tothe Hermean magnetosphere. To the authors’ knowledge, theboundary layer has not been captured by any numerical model be-fore. We shall point out that this new simulation predicts the for-mation of a dayside boundary layer at Mercury even though thereare no heavy planetary ions included. However, we cannot con-clude at this point whether or not sodium or other heavy ion spe-cies play a role in the boundary layer formation at Mercury andwhether that role is minor or dominant.

The usage of a simple By IMF offers the unique opportunity todistinguish the regions by means of their magnetic field compo-nent. It is instructive to follow the simulation results from undis-turbed solar wind at outbound 19:25 UTC to the N-BL at 19:00UTC, that is the reverse direction of the MESSENGER1 spacecraftand from right to left within the 1D plots. The Bx component inFig. 7c/d vanishes within the undisturbed solar wind. At the BS it

Fig. 7. The figure illustrates the magnetic field and its components in the equatorial cross-section (left column) and along the MESSENGER trajectory (right column). Plot (a)shows the existence of four qualitatively different regions: 1. IMF (dark blue), 2. magnetosheath (light blue), 3. boundary layer (green) and 4. inner magnetosphere (red). Theinner edge of the dayside boundary layer is primarily visible in the Bz-component (h) rather than in the Bx or By-component (d)/(f).



exhibits a sudden increase, which is due to the draped and piled-upIMF within the magnetosheath. When crossing the MP it decays tovalues close to zero, i.e. it almost vanishes within the boundarylayer. The fact that it is not exactly zero might account for theslightly draped dipole field within the magnetopause. However,when crossing the inner edge of the D-BL and moving into the in-ner magnetosphere, Bx remains unaffected. Obviously, the bound-ary layer formation is controlled by Mercury’s intrinsic field,rather than by the IMF.

This conclusion is supported by the view on the By-componentin Fig. 7e/f: At BS, a sudden increase in field intensity can be ob-served, but when moving from the magnetosheath into the bound-ary layer the field strength decays below IMF intensity. The edge ofthe boundary layer is hardly visible within the By component.

A different behavior can be observed within Bz in Fig. 7g/h,which is zero within the undisturbed solar wind flow. It experi-ences some fluctuations in the magnetosheath, but remains basi-cally zero outside the magnetosphere. The reason is, that, in

Fig. 8. The figure illustrates the current density in lA m�2 in the equatorial cross-sectioshows the magnitude while the second illustrates the jx and the third the jy component

contrast to the Bx component, it does not contribute to the drapedmagnetosheath field. However, when crossing the MP into thedayside boundary-layer a sudden increase can be observed, i.e.Mercury’s intrinsic dipole field clearly dominates the boundarylayer region. Crossing the inner edge of the boundary layer intothe inner magnetosphere, the Bz component experiences anothersudden increase. Continuing to C/A, the Bz component exhibits adipolar behavior. In the inbound region of the trajectory, a suddendecrease can be observed denoting the nightside boundary-layer.

The magnetic field in Fig. 7 is consistent with a current densityj =r� B/l0 that is visualized in Fig. 8. Even though the currentdensity is quite noisy (which is inherent to particle mesh simula-tion codes), the basic current systems can be nevertheless identi-fied. Besides the current magnitude in Fig. 8a/b the jx and jy

components are visualized in Fig. 8c–f. The color scale of the jx

and jy components in Fig. 8c/e is arranged such that red indicatespositive, blue negative and green zero values. We resign to visual-ize the jz component that shows a single local maximum at the

n (left column) and along the MESSENGER trajectory (right column). The first row, respectively.


bow shock and therefore is only of minor interest for ourdiscussion.

The magnitude of the current density in Fig. 8a/b shows at leastfour local maxima above background noise: the maximum at 19:19UTC is consistent with the magnetic field jump at the bow shockwhile the peak at the MP accounts for the magnetopause current.As can be seen in Fig. 8d and f, this current is negative in jx andjy which is obvious if one follows the MP geometry in the 2DFig. 8c and e.

A third local maximum can be identified at 19:10:30 UTC inFig. 8b which coincides with the D-BL’s inner edge. This currentmainly points in negative x-direction and connects to the daysidemagnetopause current, which can be seen in Fig. 8a and c. Theorientation is very similar to the orientation of the MP currenteven though its intensity is weaker. The current extends to the

Fig. 9. The figure illustrates the proton velocity in km/s in the equatorial cross-section (lethe magnitude while the second illustrates the Ux and the third the Uy component, resp

nightside where the fourth local maximum at 19:00 UTC can beobserved in consistency with the presence of the nightsideboundary layer. Obviously, both, the inbound and outbound dia-magnetic decreases, are caused by the same current layer, whichwe will label boundary layer current in the following. Since theboundary layer current exhibits a semi-circle shape, it is mainlydirected in positive y-direction at the nightside that can be seenwell in Fig. 8e.

At about 18:55 UTC, close to the N-BL, the current’s direction isreversed into negative y-direction. This region can be clearly iden-tified with the neutral sheet current that extends from the dawn tothe dusk flank of Mercury’s magnetopause. It resides at about0.4RM above Mercury’s nightside surface.

As will be shown below, the regions and boundaries describedabove can be observed in the simulated plasma quantities as well.

ft column) and along the MESSENGER trajectory (right column). The first row showsectively.


Since a single species hydrogen plasma is used, any quantityshown below relates to protons. Their velocity is visualized inFig. 9a/b. The plasma is diverted at the bow shock and its velocitydecreases from 430 km/s in solar wind to about 280 km/s insidethe magnetosheath. At the magnetopause, the plasma velocity de-creases to nearly zero within the magnetosphere. In contrast to theterrestrial magnetosphere, the plasma does not co-rotate withinMercury’s magnetosphere. The reason is that Mercury itself doesnot rotate (at least not on time scales discussed here). Furthermore,neither curvature nor gradient drift play a noteworthy role nearMercury (cf. Section 7).

As we follow the direction from the magnetopause towards C/A,the velocity exhibits a sudden increase to about 80 km/s adjacentto the D-BL’s inner edge. However, the arrows in Fig. 9a and theUx-component in Fig. 9c/d show that the velocity is not directeddownstream, but sun-ward. The color scale of the Ux componentin Fig. 9c is arranged in such way that red indicates down-stream,

Fig. 10. The figure illustrates the proton density in cm�3 (top row) and the proton pressu(left plot) and the parallel proton temperature (right plot) in K.

blue sun-ward and green zero velocity. The sun-ward stream at theD-BL’s inner edge coincides with the sun-ward directed currentthat was shown in Fig. 8c/d.

The Uy-component at the N-BL in Fig. 9e/f shows a similarbehavior as the jy-component that was shown in Fig. 8e/f. Thenightside diamagnetic decrease resides between two opposingstreams where the planet-ward plasma stream is directed in posi-tive y direction at 60 km/s, while the flow points in negative y-direction at 160 km/s on the downstream side. Hence, the latterone accounts for the neutral sheet current while the planet-wardstream constitutes for the boundary layer current. The fact thattwo opposing plasma streams exist adjacent to each other at theN-BL within a narrow region results in a rather unstable configura-tion. This is why we observe strong fluctuations at the N-BL asmentioned at the beginning of this section. However, followingthe flow magnitude in Fig. 9a reveals that the flows at D-BL andN-BL are part of the same plasma stream.

re in nPa (second row). The third row shows the perpendicular proton temperature


While velocity measurements were not available at the time ofthis writing, density and temperature estimates have been pub-lished by Raines et al. (2011). In the following, we will compareour findings with these measurements. The proton number densityis visualized in Fig. 10a/b. In the two-dimensional plot Fig. 10a, thedensity is shown color coded on a logarithmic scale. The regionsmap to the colors in orange (solar wind), magnetosheath (red),boundary layer (yellow) and inner magnetosphere (green). Quanti-tative results along the M1 trajectory can be seen in Fig. 10b: At BSthe density experiences a jump from 32 cm�3 background value to118 cm�3, that is nearly a factor of four. Within the magnetosheathit undergoes strong oscillations with an average density of about80 cm�3. At the MP the density decays to about 20 cm�3, whichis comparable to the 16 cm�3 that have been estimated by Raineset al. (2011) for the density inside the D-BL. At the inner edge ofthe D-BL the density experiences a further decrease to about5 cm�3. After 19:08 UTC it finally decreases to nearly zero.

A small local maximum of about 10 cm�3 can be observed at19:01 UTC, coinciding with the N-BL. A comparable density in-crease of about 5 cm�3 at the N-BL has been estimated by Raineset al. (2011). Inside the plasma sheet the density resides at about2 cm�3 which is within the range of 1–10 cm�3 that was estimatedby Raines et al. (2011) for this region.

Raines et al. (2011) estimated the proton pressure inside theboundary to be 0.4 nPa during M1 and 1 nPa during M2. This iscomparable to the proton pressure in our simulation (seeFig. 10a/b) that is slightly above 1 nPa inside the D-BL. When cross-ing the D-BL’s inner edge into the magnetosphere the pressuredrops to nearly zero, which is expected for a classical magneto-sphere. At 19:01 UTC the proton pressure increases for a shortinterval, thereby causing the inbound diamagnetic decrease. Ascan be seen in Fig. 10a, the origin of this pressure increase is hotplasma that drifts towards the dusk side in the direction of theneutral sheet current. We reside to discuss the electron pressurewhich is pe = 5 � 10�3 nPa in our simulation inside the BL andtherefore negligible compared to the proton pressure.

By comparing Fig. 10b and d, it can be seen that the proton pres-sure pp = npkBTp inside the D-BL is only slightly smaller than insidethe magnetosheath, even though the density drops by nearly a fac-tor of four. The reason is the temperature increase inside the D-BLby more than a factor of three compared to the magnetosheath.However, while the parallel temperature Tp,k = 9 � 105 K remainsabout the same in both, magnetosheath and layer (see Fig. 10f),the perpendicular temperature increases to an average value ofabout Tp,\ = 2 � 106 K inside the boundary layer. A significantly in-creased perpendicular temperature near Mercury has already beenpredicted by the hybrid simulations of Trávnıcek et al. (2009,2010). Their results indicate that the perpendicular temperaturenear Mercury may be one order of magnitude above the solar windtemperature. The maximal perpendicular temperature inside theD-BL of Tp,\ = 2.5 � 106 K is reached at its inner edge. The valuesare comparable to the temperature of Tp = 2 � 106 K that was esti-mated by Raines et al. (2011) for the boundary layer.

At the N-BL the temperature increases to Tp = 7 � 106 K, whichis within the range of Tp = 4–8 � 106 K that was estimated by

Table 3The table shows a comparison of simulation results (left column) and MESSENGERobservations during the M1 flyby (right column) for the dayside boundary layerregion. The observations correspond to Anderson et al. (2011) and Raines et al. (2011).

Quantity Simulation Observations M1

Width 1100 km 1000–1400 km

jBj 60–70 nT 60–70 nT

nproton 20 cm�3 16 cm�3

Tproton 2.9 � 106 K 2 � 106 Kpproton 1 nPa 0.4 nPa

Raines et al. (2011) for this region. The key findings of our simula-tion for the dayside boundary layer region are summarized in Table3 and compared to the M1 observations. We choose the M1 obser-vations rather than the M2 observations for comparison since theformer configuration shows a sub-solar closed magnetospherewhich resembles the case in our simulations. Yet, both configura-tions are not identical and therefore differences are expected.

For the sake of completeness we shall place our simulation re-sults within the context of previous simulation studies. Similarsimulations have been carried out by Trávnıcek et al. (2007) whosesimulation model, like the A.I.K.E.F. simulation model, is based onthe hybrid schema by Matthews (1994). These authors studied theHermean magnetosphere for different solar wind pressures. Ineither case they found a drift driven proton belt at low latitudes.Trávnıcek et al. (2009) confirm the existence of the drift-drivenplasma belt and substantiate, that there is no uniform directionof the proton current circulating the planet. Trávnıcek et al.(2010) conclude that such a belt may account for the diamagneticdecreases observed on the inbound passes of both MESSENGER fly-bys. Even though we do observe a semi-circular shaped region ofincreased plasma density, the shape does not show a closeddrift-driven plasma belt. This might be due to the application ofdifferent magnetic moments or IMF orientations in the simula-tions. However, we can confirm the hypothesis that plasma istrapped on planetary field lines causing a diamagnetic decrease.We further agree with these authors that a circulating current, likethe ring current at Earth forming due to the gradient drift, shouldbe negligible at Mercury which we demonstrate by a simpleanalytical estimate:

According to Baumjohann and Treumann (1999) the magneticgradient drift reads:

vr ¼mv2

?

2qB3 B�rB: ð2Þ

Within the equatorial plane the cylinder symmetric dipole field de-cays by:

B ¼ l0M4p

1r3 ; ð3Þ

where M is Mercury’s magnetic moment. By using the gradient incylindrical coordinates and inserting the result and Eq. (3) into Eq.(4), the equatorial drift velocity reads

vr;equatorial ¼2pmv2

?ql0M

r2: ð4Þ

Even if we assume a 2 � 106 K plasma with a thermal speed ofv\ = 222 km/s, the drift speed near Mercury’s surface equatesvr,equatorial� 0.5 km/s, which is certainly negligible against any othervelocity observed in our simulation and thus the related current isnegligible.

Interestingly, the multi fluid simulations of Benna et al. (2010)show the formation of an equatorial drift belt as well: solar windparticles within this belt drift anticlockwise at a bulk speed of150 km/s. These authors conclude that this belt is neither inducedby curvature nor gradient drifts, and thus does not generate anynet current. Instead, it turns out to be an E � B drift which resultsfrom the radial electric field due to the electron pressureEp = �rpe/(e ne). Even though we can follow the argumentationof these authors, we cannot confirm this result as the electronpressure in our simulation turns out to be insignificant in this re-gion (cf. Section 6).

Further hybrid simulations have been carried out by Kallio andJanhunen (2003). These authors do not observe a closed drift belt,but report on regions of sunward plasma flow that can be foundeverywhere around the planet. Their simulations include planetary


Na+ ions in a self-consistent way that are injected by means of aspherically symmetric, exponentially decreasing profile. The totalproduction rate is chosen to be 10�24. Unfortunately these authorsdo neither comment on the influence of Na+ ions nor present re-sults related to Na+. In general, none of the above listed modelsdid analyze the influence of heavy planetary ions or the formationof Mercury’s dayside boundary layer or Mercury’s doublemagnetopause.

7. Discussion

In the following we will explain the physical processes that pro-duce the signatures shown above. In particular the boundary fill-ing, the origin of the temperature asymmetry and the formationof the boundary layer current will be discussed.

7.1. Boundary layer filling

At first we shall explore from the simulation where the plasmathat populates the boundary layer enters Mercury’s magneto-sphere. In order to understand this process, a volume of particlesthat enter the simulation geometry is marked at the inflow bound-ary and traced during its propagation. The initial size of this vol-ume is chosen to be V = (0.5RM,LY,LZ). Similar to a flip-book,Fig. 11 shows in real-time the motion of the marked protons bymeans of their normalized macroscopic density within the equato-rial cross-section. In order to understand the particle motion it isinstructive to account for the magnetic field topology, which isshown in Fig. 12. As the situation needs to be considered threedimensional, Fig. 13a/b illustrates the three dimensional shape ofthe proton density that drifts through the boundary layer. The grayplane in both figures is the equatorial cross-section of Fig. 11. Inaddition, we show a 3D view of the total plasma density inFig. 13c/d to explain how the marked particles are distributedwithin the magnetosphere.

We define t1 = 0 s in Fig. 11a to be the time when the markedparticles reach the bow-shock position of the M1 trajectory. Asthey enter the magnetosheath they are strongly compressed,heated and decelerated. The width of the magnetosheath at thisposition is 1700 km. At t2 = 20 s the protons arrive at the magneto-pause (see Fig. 11b). In the sub-solar region, the population is com-pressed to a narrow layer and deflected around the magnetopause.We did not observe a single proton that entered the magneto-sphere in the sub-solar region, which confirms the magnetosphereto be closed sub-solar. At t3 = 36 s the very first protons enter themagnetosphere in the equatorial cross-section along the dawnflanks, see Fig. 11c. Fig. 11d and e reveal that the downstreamdawn flank of Mercury’s magnetosphere is to some extent opento solar wind particles, as will be explained in the following.

Fig. 12 shows magnetic field lines that originate from both, Mer-cury and the IMF. The color indicates the Bx component: blue isnegative, i.e. pointing sunward, red is positive i.e. pointing down-stream and green indicates zero. As the draped IMF exhibits a po-sitive Bx component at Mercury’s dawn side, IMF and closed fieldlines are directed antiparallel in this region (see Fig. 12a, black ar-row). This topology is likely to trigger reconnection. Hence, Mer-cury’s magnetic field lines may connect to the IMF as can be seenin Fig. 12b and c. Fig. 12d shows the identical topology ofFig. 12c from Mercury’s dawn side. The field line that is markedby means of a black arrow connects to both, IMF and Mercury’ssouth pole. This type of reconnection where one end of a flux tubeconnects to the solar wind while the other roots in the planet hasalready been reported by Slavin et al. (2009) for the Hermean sys-tem. Fig. 12f shows by means of the density of the marked particlepopulation that solar wind protons enter Mercury’s magneto-

sphere in regions of exactly such open field lines. The yellow arrowindicates the direction of motion that is planet-ward. However,additional reconnection at higher latitudes may take place as well.The entire process can be observed best by means of animationsthat are available at: http://www.tu-braunschweig.de/theophys/people/jmueller/aikef/mercurybl.

We shall note that flux transfer events observed by MESSENGERduring M1 (Slavin et al., 2008) and analyzed in a subsequent study(Slavin et al., 2010) confirm that reconnection just tailward of thecusps was indeed taking place during M1 in agreement with oursimulation. However, additional mechanisms may likewise pro-mote the entrance of solar wind particles into the Hermean mag-netosphere, such as the protons’ gyro-kinetic motion as predictedby Trávnıcek et al. (2007, 2010). Another prominent candidate totransfer solar wind plasma into the Hermean magnetospheremight be the Kelvin–Helmholtz instability, which most likely is ex-cited at Mercury’s magnetospheric flanks (Glassmeier and Espley,2006). As pointed out by Sundberg et al. (2010), Mercury’s dawnmagnetospheric flank is shown to be less stable than the duskflank. This could explain the asymmetric entrance of solar windprotons into the magnetosphere as observed in our simulation inFig. 11.

After having shown that solar wind protons may enter Mer-cury’s magnetosphere at the downstream dawn flank we shall ex-plain why they drift planet-ward rather than downstream. At thedawn flank the neutral sheet current is present that flows fromdawn to dusk, i.e. basically in negative y-direction. However, itexhibits a positive x-component as well. For clarification this con-figuration is sketched in Fig. 14c by means of magenta arrows. Inconsequence, protons experience a Lorentz force that is:

F ¼ qpðEþ vp � BÞ; ð5Þ

where the electric field for a proton plasma in the hybrid approxi-mation reads:

E ¼ �up � Bþj� Bl0enp

� rpe

l0enp; ð6Þ

where up is the mean proton velocity, np the mean proton densityand pe the electron pressure. According to our simulations the elec-tron pressure gradient within the neutral sheet is significantlysmaller than the Hall term and may be neglected in the following.If we furthermore consider the drift direction of the particles toresemble the local bulk velocity (i.e. fluid behavior) we can assumevp � up. The resulting force on the guiding center of solar wind pro-tons then reads:

F ¼j� Bl0np

; ð7Þ

which is the j � B force known from MHD.As the magnetic field in this region exhibits a positive z compo-

nent (yellow circles in Fig. 14c), the resulting force points in nega-tive x and negative y direction (red arrows). Hence, protons areaccelerated sunward and towards the planet. Plots Fig. 11d–f showthat the particle population splits up as it approaches Mercury: Thelarger fraction moves in negative x-direction populating the D-BL.The smaller fraction propagates in negative y direction populatingthe N-BL and finally re-unites with plasma at the dusk flank of themagnetopause. We shall point out that the sequence describedabove indicates that D-BL and N-BL are part of the same boundarylayer that extends from Mercury’s dawn-dayside over the night-side to the dusk-dayside.

The sequence of Fig. 11f–i shows how the proton populationslowly drifts through the D-BL in sun-ward direction. By compar-ing Fig. 11f and i the drift velocity of the ions at the BL’s inner edgecan be estimated to vdrift = 1.2RM/62 s � 50 km/s. The density’s

http://www.tu-braunschweig.de/theophys/people/jmueller/aikef/mercurybl

http://www.tu-braunschweig.de/theophys/people/jmueller/aikef/mercurybl

Fig. 11. The figure shows a time sequence of solar wind protons that are marked immediately after being injected at the inflow boundary. This time sequence reveals wherethe solar wind protons enter the Hermean magnetosphere and how the boundary layer is populated.


Fig. 12. Shown are magnetic field lines that originate from Mercury and the solar wind. The M1 trajectory is the magenta line. The color indicates the Bx component: blue isnegative i.e. pointing sunward, red is positive, i.e. pointing downstream and green indicates zero. As the draped IMF exhibits a positive Bx component at Mercury’s dawn side,IMF and closed field lines are directed antiparallel in this region (see (a), black arrow). This topology is likely to trigger reconnection (b) and Mercury’s magnetic field linesmay connect to the solar wind (c). Protons that enter Mercury’s magnetosphere along such open field lines will arrive at the poles. Subsequently, they are trapped on closedplanetary field lines thereby populating the boundary layer (f). The equatorial altitude of closed magnetic field lines that connect to the poles is comparable with the altitudeof the boundary layer’s inner edge (e).


maximum is close to the boundary layer’s inner edge. Fig. 13a andb reveals that the motion must be considered 3-dimensional:While drifting through the boundary layer the protons are mir-rored between north and south pole on closed magnetic field lines.Hence, the boundary layer itself is a three dimensional region. Assketched in Fig. 14a that shows an enlarged view on the boundarylayer, the proton gyration coincides with the equatorial plane.

Furthermore, the time sequence Fig. 11 reveals that only a neg-ligible fraction of the protons enters the inner magnetosphere. Theinner magnetosphere is mainly devoid of protons (also sketched inFig. 14a). One reason for this behavior is that solar wind protonsmainly arrive at high latitudes at the poles before being trappedon closed field lines. Neighboring closed field lines extend to analtitude of about 0.4RM above Mercury’s surface in the equatorialcross-section (see Fig. 12e). Hence, protons that enter these closed

field lines near the poles will not underrun an altitude of 0.4RM

while bouncing from pole to pole and drifting sunward. This driftmotion is indicated by means of an yellow arrow in Fig. 12e.

However, protons still could drift planet-ward due to an j � B-force as stated to be the case near the magnetospheric flank. Aj � B-force exist at the boundary layer’s inner edge indeed but isoppositely directed: As sketched in Fig. 14c by means of green ar-rows and shown in the simulation results in Fig. 8c/d, a currentforms at the inner edge of the dayside boundary layer at about0.4RM above Mercury’s surface. This current is directed sunward.As the magnetic field in this region strictly points in positive z-direction (yellow circles in sketch Fig. 14c), the resulting j � B-force is directed outwards in positive y-direction (light blue ar-rows) thereby hindering protons from entering the inner magneto-sphere. This configuration sustains and enhances the devoid state

Fig. 13. Three dimensional view on the ions that populate the boundary layer at times t8 = 130 s in (a) and t9 = 162 s in (b). Mercury is illustrated by means of the whitesphere. Also shown is the MESSENGER trajectory where the dots indicate from left to right outbound BS, MP and inner edge of the D-BL. The protons move in sun-warddirection but remain inside the DB-L. The number of protons that arrive inside the inner magnetosphere, i.e. below the DB-L’s inner edge is negligible. Images (c) and (d) showthe total plasma density in front and back view, respectively. A logarithmic color scale is used. The yellow boundary layer region can be clearly distinguished from the redmagnetosheath and green inner magnetosphere. Animations are available online at: www.tu-braunschweig.de/theophys/people/jmueller.


of the inner magnetosphere and explains the rather steep densitydecay that can be observed in Fig. 10b at the D-BL’s inner edge.

More than 3 min after entrance into the D-BL the proton popu-lation arrives close to the sub-solar point. The drift velocity isnearly reduced to stagnation. Several ions that are close to themagnetopause are picked up and convected downstream, therebycompleting their 4 min-visit in the Hermean magnetopause (seeFig. 11k). The drift velocity of other ions is reversed and they driftback downstream again into the inner magnetosphere while theiraltitude is constantly decreased until they finally impact on Mer-cury’s surface. At t12 = 436 s, i.e. about 5.5 min after the populationhad reached the boundary layer, the density is reduced to less 1% ofthe initial density and can be considered negligible. During thesame time protons with background solar wind speed would havepassed a distance of 60RM.

From the three-dimensional view in Fig. 13a/b it can be wellseen that the location of the marked particles coincides with thelocation of the boundary layer that is visible in the total plasmadensity in Fig. 13c and d, i.e. the yellow layer that resides in be-tween the magnetosheath (red) and inner magnetosphere (green).Animations for both, the marked and total density are available on-line at: www.tu-braunschweig.de/theophys/people/jmueller.

7.2. Proton trajectories

Several studies exist on the proton dynamics and distributioninside Mercury’s magnetosphere with reference to different fo-cuses (Lukyanov et al., 2001; Delcourt et al., 2010). However, therequired electromagnetic fields are based on models such as Tsyga-

nenko’s model scaled for Mercury’s conditions and do not includethe diamagnetic decrease of Mercury’s dayside boundary layer. Wetherefore will analyze the ion motion with reference to the bound-ary layer formation in the following. In order to clarify the kineticmotion of the protons, the trajectories of three representativeprotons that enter the boundary layer are shown in Fig. 15. Whilethe particles A and B impact on Mercury’s surface, particle C mayescape the Hermean magnetosphere after having crossed theboundary layer.

Fig. 15 is arranged such that the left column illustrates the topview of the trajectories (from above Mercury’s north pole) whilethe right column shows the trajectories from the dawn side. Mer-cury is shown by means of a white sphere, the M1 trajectory isvisualized in magenta and the positions of BS, MP, D-BL, C/A andN-BL are marked by means of small magenta spheres from top tobutton. The z = const. cross-section shows the color-coded mag-netic field. The particle trajectories are colored in black. In additionclosed magnetic field lines are shown.

Particle A in Fig. 15a/b enters the magnetosheath in the sub-so-lar region, is subsequently deflected along the dawn-side magneto-pause but enters the magnetosphere downstream at x = 1.7RM. Aswas shown in sketch Fig. 14c by means of red arrows, it experi-ences a j � B-force in this region that is directed planet-ward.The particle drifts towards Mercury and is trapped on closed mag-netic field lines. While it is trapped inside the magnetic mirror con-figuration and bounces between north and south pole, it slowlydrifts in sun-ward direction. Again we shall point out that this driftis neither a gradient nor a curvature drift which firstly is negligiblein terms of magnitude and secondly would cause the particles to



Fig. 14. The sketch (c) illustrates the locations of the magnetopause current JMP

(blue), neutral sheet current JNS (magenta) and boundary layer current JBL (green)according to the simulation results of Fig. 8. Solar wind protons may enter themagnetosphere at the dawn flank (pink coloured region). There, the conjunction ofneutral sheet current and magnetic field (yellow circles) yields a j � B-force (redarrows) that accelerates protons planetward. However, at the inner edge of thedayside boundary layer the boundary-layer-current and magnetic field yield a j � B-force (light blue arrows) that prevents the protons from entering the innermagnetosphere. The enlarged view (a) explains the origin of the boundary-layer-current by means of the proton gyration (brown circles) and proton pressuregradient (brown arrow). Sketch (b) illustrates that the magnetic field related to theboundary-layer-current enhances the inner magnetospheric field but weakens theboundary layer magnetic field (yellow arrows), thereby causing the daysidediamagnetic decrease.


drift clockwise within the D-BL region, which is the contrary direc-tion. Particles like particle A account for the sun-ward plasma mo-tion that was shown by means of the macroscopic density in theprevious section (see Fig. 11). In the equatorial cross-section itstays off from Mercury’s surface at a distance of about 0.4RM, i.e.at the inner edge of the boundary layer. The magnetic field in-creases as it drifts further in sub-solar direction. Hence, while thegyro-frequency increases the gyro-radius decreases and the mirrorpoints move to lower latitudes since they depend on the particlespitch angle.

If the particle’s magnetic moment is conserved, the motion intoregions of increased field strength goes along with a gain in per-pendicular energy. This process is referred to as ‘‘adiabatic heat-ing’’, i.e. drift energy is converted into perpendicular energy. As aconsequence the perpendicular temperature increases while theparallel energy and temperature remain unaffected. This conclu-

sion is in agreement with the temperature profile in Fig. 10e/fwhere the perpendicular temperature increases inside the D-BLand experiences a local maximum at the D-BL’s inner edge. In con-trast to this the parallel temperature remains unaffected and ishardly showing any change, neither inside the D-BL nor at its inneredge. Another reason for a strong temperature asymmetry couldarise as argued by Trávnıcek et al. (2009), who observed asignificantly increased perpendicular temperature near Mercuryas well: the mirror points of protons that are heated parallel tothe magnetic field may be located below Mercury’s surface. As aconsequence, these protons will be lost by impacting on the plan-etary surface. In contrast, an increased perpendicular velocity en-hances the proton’s pitch angle and thus the probability to betrapped without impact.

The second particle B in Fig. 15c/d enters the magnetospherefurther upstream compared to particle A. It is accelerate sun-wardand traverses the D-BL at higher initial altitudes than A. Simulta-neously its altitude continuously decreases. Its guiding center mo-tion is reversed near the sub-solar point and for a short time theparticle drifts downstream again before it finally impacts on theplanetary surface. A close view on the density in Fig. 10a/b revealsthat this type of particle is responsible for the small densityenhancement observed at 19:08 UTC.

The third particle C that is shown in Fig. 15e/f enters Mercury’smagnetosphere downstream at about 1RM. Like particle B it tra-verses the D-BL at rather high altitudes. Its guiding center motionis decelerated while it drifts in sun-ward direction. However, incontrast to particle B its drift velocity is not reversed in the sub-so-lar region. Instead, it is reflected at high latitudes and may escapethe Hermean magnetosphere into the dusk magnetosheath whereit is picked up and convected downstream. We could observe manyparticles that are picked up into the dawn magnetosphere as well(not shown here). This behavior is consistent with the macroscopicdensity in Fig. 11j–l).

7.3. Origin of the boundary layer current

So far we have shown the existence of the boundary layer cur-rent in Fig. 8 and have argued that it gives rise to a j � B-force, pre-venting solar wind protons from entering the inner magnetosphere(see Fig. 14c). The density decrease in Fig. 10a/b is a direct conse-quence of this force. We will discuss the formation of the boundarylayer current below.

A first hint towards the current formation can be observedwhen comparing the macroscopic particle motion in Fig. 11 withthe macroscopic velocity in Fig. 9. As was argued above, the sun-ward drift velocity of the ion population was estimated to bevdrift � 50 km/s. In contrast to this, Fig. 9c showed the macroscopicion velocity in sun-ward direction to be about 80 km/s at theboundary layer’s inner edge. This might seem conflicting sincethe average drift velocity of the ion’s guiding centers should di-rectly translate into the macroscopic velocity. Hence the macro-scopic velocity appears to be overestimated by Du � 30 km/s.

However, the macroscopic velocity includes any particle andfluid drifts, where the latter does not necessarily require guidingcenter motion. In particular the diamagnetic drift is solely a resultof density and temperature gradients of a particle distribution thatgyrates with guiding centers at rest:

vdia ¼B�r?p?

qnB2 ; ð8Þ

where p\, q and n are the perpendicular thermal pressure, chargeand number density of the respective particle population. Sincethe drift direction depends on the sign of charge, the diamagneticdrift of an proton-electron plasma results into the current:

Fig. 15. The figure is arranged such that the left column illustrates the particle trajectories by means of a top view (from above Mercury’s north pole) while the right columnshows the trajectories from the dawn side view. The top row illustrates the trajectory of particle A, the second particle B and the third row particle C. See text for details.


jdia ¼B�r?p?

B2 ; ð9Þ

where p? ¼ p?hþ þ p?e� . As was argued above the electron pressureturned out to be negligible as it is at least one order of magnitudesmaller than the proton pressure inside the D-BL. Hence, the follow-ing analysis will be carried out solely for the proton population.

As was shown in Fig. 10c/d, the proton pressure experiences asudden decrease inside the inner magnetosphere at the D-BL’s in-ner edge. Fig. 10a and e reveals that this results from the decreasein density and perpendicular temperature. Hence, mainly the per-pendicular pressure is affected rather than the parallel pressure.The perpendicular gradient of the perpendicular pressure is shownin Fig. 16a. For technical reasons we assume r\ = (@x,@y,0) whichcan be justified by the observation Bx � By � 0 and Bz� 0 inside

the boundary layer region (see Fig. 7). However, this condition isnot met in other regions and the results of Fig. 16 may be consid-ered valid exclusively inside the boundary layer region. The direc-tion of the respective quantity within the boundary layer region isindicated by means of white arrows.

As has already been stated by Anderson et al. (2011) an outwarddirected plasma pressure gradient is expected at the D-BL’s inneredge in consistency with the change in magnetic field intensity.This conclusion is clearly confirmed by our simulation results, ascan be seen in Fig. 16a. Since the proton pressure gradient is per-pendicular to the magnetic field in this region, this yields a signif-icant proton diamagnetic drift velocity in negative x-direction atthe D-BL and positive y-direction at the N-BL, see Fig. 16b. In par-ticular the drift velocity at the D-BL is about 30 km/s that is super-imposed on the guiding center motion. This would explain the

Fig. 16. Shown is the perpendicular gradient of the perpendicular proton pressure (a). As the magnetic field points in z-direction at the location of this pressure gradient, asignificant diamagnetic drift velocity results of about 30 km/s that is shown in (b). The corresponding diamagnetic current is shown in (c). As the diamagnetic current isperpendicular to the magnetic field as well, this configuration yields a strong Hall electric field pointing radially outward. This field prevents protons from entering the innermagnetosphere and consequently maintains the pressure gradient.


deviation between macroscopic velocity and ion motion, as re-vealed at the beginning of this section.

The current related to the diamagnetic drift is shown in Fig. 16c.At the D-BL’s inner edge its magnitude can be estimated to about0.03–0.04 lA/m2, which is consistent with the current at the D-BL that was shown in Fig. 8. This in turn causes an increased Hallelectric field EHall = j � B/l0 enp that is directed outward (seeFig. 16d), thereby preventing the drifting protons from enteringthe inner magnetosphere.

For clarification the situation is sketched in the enlarged viewon the boundary layer in Fig. 14a. While protons populate theboundary layer (pink region) the inner magnetosphere is mainlydevoid of protons. This translates into a pressure gradient that isdirected outwards (brown arrow). For protons with guiding centersat rest the macroscopic velocity cancels to zero inside the bound-ary layer. However, Fig. 14a illustrates that this is not valid atthe boundary layer’s inner edge. The consequence is an enhancedproton velocity in negative x-direction at the boundary layer’s in-ner edge that superimposes with the proton drift motion and is re-ferred to as ‘‘diamagnetic drift’’. This conclusion is in agreementwith the simulation results in Fig. 9c. As the direction of the dia-magnetic drift depends on the rotational direction of the involvedgyrating particles, the diamagnetic drift of protons and electronsoccurs counterwards (compare Eq. (9)). Hence, a current forms thatin the case discussed here is the ‘‘boundary layer current’’ which issketched by means of a green arrow in Fig. 14a. The magnetic fieldwhich is consistent with the boundary layer current enhances theinner magnetospheric field while it causes the diamagnetic de-creases inside the boundary layer (see yellow circles in Fig. 14b).

In summary we conclude that the dayside boundary layer formsby means of the following sequence:

1. Protons enter the Hermean magnetosphere at its down-stream flank on open magnetic field lines. They are acceler-ated planet-wards and their perpendicular energy increasesas they move into regions of increased field strength.

2. Most open magnetic field lines connect to the planet at highlatitudes, i.e. near the poles.

3. Adjacent closed field lines extent to high altitudes within theequatorial cross section.

4. Hence, protons tend to complete their bounce motion atsimilar altitudes rather than immediately above Mercury’ssurface.

5. This causes an outward directed density gradient.6. In combination with the increased perpendicular energy an

outward directed perpendicular pressure gradient results.7. The conjunction of perpendicular pressure gradient and

dipole field initiates a diamagnetic current.8. The conjunction of diamagnetic current and dipole field

causes an outward directed j � B-force.9. This force enhances the initial state and steepens the pres-

sure gradient as protons are hindered to enter low altitudes,i.e. the inner magnetosphere.

10. Finally a self consistent quasi-stationary state is establishedwith the current being located at about 0.4RM above Mer-cury’s surface, thereby forming the inner edge of the daysideboundary layer.

Obviously the equatorial altitude of closed magnetic field linesthat connect to the poles seems to be an important property. In thisregard Mercury’s magnetic field very much differs from that ofEarth or any other planet within the Solar System. From initial testruns that are still in progress we can derive information on the


boundary layer’s distance to Mercury’s surface: As we increase thestrength of Mercury’s dipole field the size of the inner magneto-sphere increases and the boundary layer moves to higher altitudes.This might seem intuitively clear since closed magnetic field linesextend to higher altitudes. Hence, protons complete there bouncemotion at higher altitudes.

However, the influence of different core-mantle conductivitiesmight be less intuitive: As can be seen in Fig. 8c/e, the core–mantlecurrent is directed such that it enhances the inner magnetosphericfield. The magnitude of the corresponding generated magnetic fieldat the equatorial surface is about 13 nT and at the D-BL it is still6 nT. The effect is similar to an increased dipole field: closed mag-netic field lines extend to higher altitudes as without this fieldenhancement. As we decrease the core-mantle conductivity thecore-mantle current is suppressed. Consequently the inner magne-tospheric field diminishes and the boundary layer moves towardsMercury’s surface. Hence, current closure through Mercury’s inte-rior might play an important role, which has already been pro-posed by Janhunen and Kallio (2004). However, quantitativelyderiving the influence of different core-mantle conductivities or di-pole strengths is beyond the scope of this article and will be subjectto future studies.

8. Summary and outlook

We have carried out hybrid (ion kinetic, electron fluid) simula-tions in order to advance the understanding of Mercury’s daysideboundary layer. An idealized IMF and dipole field configurationhas been used to simplify the analysis but referring to previoussimulations of Müller et al. (2011) we are confident that the phys-ical processes involved are valid for the real configuration as well.The major findings are summarized below:

– The simulation shows a region of decreased magnetic fieldstrength that is consistent with the pre-orbital-phase MESSEN-GER observations for the dayside boundary layer in both, widthand field magnitude as discussed by Slavin et al. (2008) andAnderson et al. (2011). The proton plasma quantities such asdensity, pressure and temperature inside the dayside boundarylayer are very similar to what has been estimated by Raineset al. (2011) for the dayside boundary layer during the MESSEN-GER flybys.

– As a single species hydrogen plasma is used that is exclusivelyinjected at the domain boundaries, the simulation suggest thatthe dayside boundary layer may exist even in the absence of anyexospheric ions like sodium. The boundary layer is populated bysolar wind protons that enter Mercury’s magnetosphere down-stream and subsequently are accelerated planet-wards. The pla-net-ward acceleration is a consequence of the j � B-force thatresults from the configuration of neutral sheet current anddipole field.

– The dayside boundary layer region is confined by a double cur-rent sheet. Both current sheets are similar in orientation, butthe outer one is stronger in intensity. The occurrence of this‘‘double magnetopause’’ configuration is in agreement withthe MESSENGER observations discussed by Slavin et al. (2008).

– While the outer current sheet can be considered the classicalmagnetopause, the inner ‘‘boundary layer current’’ turns outto be a diamagnetic current sustained by solar wind protonsthat are mirrored between north and south pole. This boundarylayer current extends to Mercury’s nightside and dusk-sidecausing the nightside diamagnetic decrease. It exhibits asemi-circle shape and closes with the magnetopause current.

– The conjunction of boundary layer current and Mercury’s dipolefield causes a j � B-force that prevents the protons from

entering the inner magnetosphere, thereby enhancing the out-ward directed proton pressure gradient at the boundary layer’sinner edge.

One next step to further improve the quantitative results of theboundary layer is to increase the spatial resolution of the numeri-cal mesh. In particular for quantitative comparison of the magneticfield jump at the boundary layer’s inner edge an increased resolu-tion is desirable. The same applies for the nightside boundary layerwhich is still a rather transient structure in our simulations, mostlikely due to the limited resolution.

Secondly the influence of exospheric ions on the boundary layerformation should be tested. Corresponding to our simulations, thelayer may exist in the absence of exospheric ions, but the physicalprocesses involved might be modified when heavy ions are in-cluded. In particular Raines et al. (2011) found that there is insuf-ficient H+ thermal pressure in the MESSENGER plasma ionmeasurements to account for the decrease in the total magneticfield in the D-BL, implying that heavy ions like ionized sodiummust be contributing. Additionally Slavin et al. (2008) propose thatNa+ which is picked up in the dayside magnetosheath and pene-trates beyond the outer ‘‘proton’’ magnetopause might be thecause of the boundary layer. This has been motivation for us toredo the exact simulation discussed throughout this article byincluding ionized sodium. We documented some preliminary re-sults in Appendix A.

Finally further simulation results suggest that different conduc-tivity profiles for Mercury’s interior may influence the boundarylayer location. This should be investigated more precisely sincein doing so, it might be possible to derive information on Mercury’sinterior from the boundary layer’s shape and distance to the plan-etary surface.

Acknowledgments

J.M. would like to thank the VisIt-Team for their magnificentvisualization software (Childs et al., 2005) and reliable support.J.M. acknowledges helpful assistance from Bastian Koertgen(University of Cologne). We would like to thank Professor Karl-Heinz Glassmeier for his support. We acknowledge the ‘‘North-German Supercomputing Alliance’’ for computational resources.This work was partially carried out under the HPC-EUROPA2project (Project Number: 228398) with the support of the Euro-pean Commission Capacities Area – Research InfrastructuresInitiative.

Appendix A

In the following we show preliminary results for a simulation onthe influence of planetary sodium. Unfortunately it is rather diffi-cult to perform quantitatively reliable simulations as neither the to-tal Na+ production rate nor the Na+ distribution is known. Referringto the observations made prior to the MESSENGER orbital phase wemust base any simulation on an elaborate guess whose accuracy isquestionable. Thus, the following simulation should be considereda first test to obtain an approximate idea about the Na+ influencebut certainly shall not make claim to be complete.

According to Potter et al. (2002) the total production rate of neu-tral sodium is approximately 1024–1025 s�1. To obtain an upperestimate on the influence we choose a production rate of 1025 s�1.As Mercury’s exobase coincides with the planetary surface, neutralcollisions are neglected. We furthermore neglect gravitation as theneutrals leave Mercury’s surface. This results into a first approxima-tion by means of an isotropic neutral profile that decays by 1/r2. Wechoose the ionization rate equal to the production rate, i.e. 1025Na+

Fig. 17. Shown is the sodium pressure (a) and velocity (b) in the equatorial plane and the sodium velocity in the polar plane (c).


ions are placed each second into the simulation domain accordingto the profile specified above. In doing so we further overestimatethe real Na+ production as the real ionisation rate is certainly lower.Any initial velocity or temperature is neglected for the planetary so-dium, as both these values are small compared to the respectiveproton properties (Potter et al., 2002). All other input values arechosen corresponding to Table 1, i.e. the exact simulation discussedthroughout this article is repeated with the inclusion of Na+. After atime t ¼ 2000XHþ ¼ 87XNaþ the Na+ distribution of the self consis-tent simulation becomes stationary.

The thermal Na+-pressure is shown in Fig. 17a for the equatorialplane. Inside the D-BL it is pNaþ ; D-BL � 0:1 nPa, that is 10% of theproton pressure in this region (cf. Fig. 10a). However, the pressureinside the inner-magnetosphere is even higher pNaþ ; IM � 0:4 nPa.The reason is that heavy ions accumulate inside the inner magne-tosphere as the production is high and the convective electric fieldis close to zero. In fact, the sodium density peaks at 10 cm�3 at thedawn side inner magnetosphere (not shown), which is certainlyabove any realistic estimate. In contrast, the production in the D-BL is lower and the convective electric field causes the Na+-ionsto be picked up into the proton drift direction, i.e. sunward (seeFig. 17b). Consequently, Na+-ions can hardly accumulate insidethe D-BL. The sodium density inside the sheath is even lower.Based on this test we must conclude that the overall influence ofsodium to the magnetic field topology is firstly small (the magneticfield remains basically unchanged, not shown) and secondly, thesodium pressure distribution is inconsistent with an outwardpointing thermal pressure gradient at the D-BL which is requiredto explain the diamagnetic decrease.

Hence, by assuming a spherically symmetric 1/r2 profile and atotal production of 1025 s�1 sodium ions we cannot explain the rel-atively low proton pressure of pHþ ¼ 0:4 nPa observed by Raineset al. (2011) for the D-BL nor confirm the suggestions made by Sla-vin et al. (2008). From the sodium bulk velocity Fig. 17b we cannotdeduce ions that are picked up by the solar wind or inside the mag-netosheath and penetrate beyond the proton magnetopause. Onthe one hand sodium ions are more efficiently accelerated in direc-tion of the convective electric field (negative z-direction) ratherthan towards Mercury. This is due to the huge pick up cycloidsshown in Fig. 17c: the impinging sodium exhibits an ux;Naþ compo-nent that is five times smaller than the protons’ ux;Hþ component.Furthermore the sodium density is too low inside the magneto-sheath. Thus, even if magnetosheath sodium ions penetratethrough the proton magnetopause they hardly impact on the aver-age sodium bulk velocity as the by far largest fraction of sodiumions inside Mercury’s magnetosphere exhibits comparably smallvelocities. The simulation indicates that the mechanism, as pro-

posed by Slavin et al. (2008), may only operate if the majority ofsodium ions are produced outside Mercury’s magnetosphere. Wetherefore suggest for future studies to apply more advanced pro-files that, e.g. reduce the Na+-production inside the inner magneto-sphere and promote a higher production in the cusp regions,magnetosheath or Mercury’s magnetotail.

Appendix B. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.icarus.2011.12.028.

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