Parametric study of the solar wind interaction with the Hermean magnetosphere for a weak interplanetary magnetic field
PParametric study of the solar wind interaction with theHermean magnetosphere for a weak interplanetarymagnetic field
J. Varela a,b , F. Pantellini b , M. Moncuquet b a AIM DSM/IRFU/SAp, CEA Saclay, France b LESIA, Observatoire de Paris, CNRS, UPMC, Universite Paris-Diderot, 5 place JulesJanssen, 92195 Meudon, France
Abstract
The aim of this study is to simulate the interaction of the solar wind withthe Hermean magnetosphere when the interplanetary magnetic field is weak,performing a parametric study for all the range of hydrodynamic values of thesolar wind predicted on Mercury for the ENLIL + GONG WSA + Cone SWRCmodel: density from 12 to 180 cm − , velocity from 200 to 500 km/s and temper-atures from 2 · to 18 · K, and compare the results with a real MESSENGERorbit as reference case. We use the code PLUTO in spherical coordinates andan asymmetric multipolar expansion for the Hermean magnetic field. The studyshows for all simulations a stand off distance larger than the Mercury radiusand the presence of close magnetic field lines on the day side of the planet, sothe dynamic pressure of the solar wind is not high enough to push the mag-netopause on the planet surface if the interplanetary magnetic field is weak.The simulations with large dynamic pressure lead to a large compression of theHermean magnetic field modifying its topology in the inner magnetosphere aswell as the plasma flows from the magnetosheath towards the planet surface.
Keywords:
Email address: [email protected] (telf: +33782822476) (J. Varela)
Preprint submitted to Journal of L A TEX Templates October 26, 2018 a r X i v : . [ a s t r o - ph . E P ] A ug . Introduction The analysis of MESSENGER magnetometer data revealed that the Her-mean magnetic field can be described as a multipolar expansion [1] with adipolar moment of 195 nT ∗ R M (with R M the planetary radius) as well as therelative small proportion between the strength of the interplanetary magneticfield (IMF) and the Hermean magnetic field α = B sw //B M [2, 3]. The rangeof α values oscillates from 0.3 during a coronal mass ejection ( B sw ≈
65 nT)to 0.04 for a period of low magnetic activity of the Sun ( B sw ≈ −
180 cm − ,velocity 200 −
500 km/s and temperature 2 · − · K [8, 9]. To minimizethe effect of the IMF in the Hermean magnetosphere we select as reference casea SW configuration with a weak IMF of 7 .
28 nT. The SW configuration duringcoronal mass ejections are excluded from this analysis because these events are2haracterized by plasma velocity larger than 500 km/s and a strong IMF mainlyoriented in the Southward direction (strong reconnection case). To isolate theeffect of a hydrodynamic SW parameters we perform the simulations fixing theother parameters to the same values than the reference case.We use the MHD version of the single fluid code PLUTO in the ideal andinviscid limit for spherical 3D coordinates [10]. The Northward displacement ofthe Hermean magnetic field is represented by a multipolar expansion [11]. TheIMF values are obtained from MESSENGER magnetometer data.This study is called to complement observational studies of the magne-tosheath plasma depletion [12, 13], including a comprehensive analysis of the SWhydrodynamic parameters effects, an extension of previous theoretical studiesdevoted to simulate the global structures of the Hermean magnetosphere usingMHD [14] and Hybrid [15, 16] numerical models.This paper is structured as follows. Section 2, we do a model descriptionincluding the code features, axisymmetric Hermean magnetic field, boundaryand initial. Section 3, we describe the results for the reference case. Section4, we show the results of the parametric study for the density, velocity andtemperature and the effect of the SW hydrodynamic parameters on the plasmaflows towards the planet surface. Section 5, conclusion, discussion and contextof the study.
2. Numerical model
We use the MHD version of the code PLUTO in the ideal and inviscid limitfor a single polytrophic fluid in 3D spherical coordinates. The code is freelyavailable online [10].The simulation domain is confined within two spherical shells, representingthe inner (planet) and outer (solar wind) boundaries of the system. Betweenthe inner shell and the planet surface (at radius unity in the domain) thereis a ”soft coupling region” where special conditions apply (defined in the nextsection).The shells are at 0 . R M and 12 R M ( R M is the Mercury radius).3he conservative form of the equations are integrated using a Harten, Lax,Van Leer approximate Riemann solver (hll) associated with a diffusive limiter(minmod). The divergence of the magnetic field is ensured by a mixed hyper-bolic/parabolic divergence cleaning technique (DIV CLEANING) [17].The grid points are 196 radial points, 48 in the polar angle θ and 96 in theazimuthal angle φ (the grid poles correspond to the magnetic poles).The planetary magnetic field is an axisymmetric model with the magneticpotential Ψ expanded in dipolar, quadrupolar, octupolar and 16-polar terms[13]: Ψ( r, θ ) = R M (cid:88) l =1 ( R M r ) l +1 g l P l ( cosθ )The current free magnetic field is B M = −∇ Ψ. r is the distance to the planetcenter and θ the polar angle. The Legendre polynomials of the magnetic poten-tial are: P ( x ) = xP ( x ) = 12 (3 x − P ( x ) = 12 (5 x − x ) P ( x ) = 12 (35 x − x + 3)the numerical coefficients g l taken from Anderson et al. 2012 are summarizedin the Table 1. coeff g (nT) g /g g /g g /g −
182 0 . . . g l for Mercury’s internal field.The simulation frame is such that the z-axis is given by the planetary mag-netic axis pointing to the magnetic North pole and the Sun is located in the XZplane with x sun >
0. The y-axis completes the right-handed system.4 .1. Boundary conditions and initial conditions
The outer boundary is divided in two regions, the upstream part (left inthe figure) where the solar wind parameters are fixed and the downstream part(right in the figure) where we consider the null derivative condition ∂∂r = 0 for allfields. In the inner boundary the value of the intrinsic magnetic field of Mercuryand the density are fixed. In the soft coupling region the velocity is smoothlyreduced to zero in the inner boundary, the magnetic field and the velocity areparallel, and the profiles of the density is adjusted to keep the Alfven velocityconstant v A = B/ √ µ ρ = 25 km/s with ρ = nm p the mass density, n theparticle number, m p the proton mass and µ the vacuum magnetic permeability.In the initial conditions we define a cone in the night side of the planet with zerovelocity and low density centered in the planet. The IMF is cut off at 2 R M .
3. Reference case
In this section we perform the analysis of the reference simulation showingthe global magnetosphere strucutres and the flows toward the planet surface.The solar wind parameters in the reference simulation are summarized in theTable 2. We assume a fully ionized proton electron plasma, the sound speed isdefined as c s = (cid:112) γ ∗ p/ρ (with p the total electron and proton pressure), andthe sonic Mach number as M s = v/c s with v the velocity.Date B field (nT) n (cm − ) T (K) β V (km/s) M s , ,
6) 60 58000 2 .
27 250 6 . . · R M further formthe planet surface and the magnetopause 0 . · R M . There is a magnetospherestructure (defined in the text as plasma stream) that links the back of the mag-6etosheath with the planet surface in the cusp region (transition between theopen/closed magnetic field lines near the planet poles). The graph C shows theregion with inflow/outflow (blue/red) and open magnetic field lines (cyan dots)on the planet surface. The largest inflows are observed at the South Hemispheredayside (at middle-high latitudes) although there is a local maximum too at theNorth Hemisphere near the pole. The local maximum of the inflow at bothHemispheres is correlated with the presence of the plasma stream and a regionof open magnetic field lines. The mass deposition at the North (D) and South(E) Hemispheres indicates stronger plasma flows at the South Hemisphere. Themass deposition at the North Hemisphere is located mainly near the poles whileat the South Hemisphere the deposition region is extended from the poles tomiddle latitudes.
4. Parametric studies
In the following we study the effect of different configuration of the SWhydrodynamic parameters in the magnetospheric global structures and plasmaflows towards the planet surface compared with the reference case.
The figure 3 shows the BS and magnetopause stand off distance at planesrotated θ = 0 o , 30 o , 60 o and 90 o respect to the equatorial plane at the NorthHemisphere day side for the parametric study of the density (A), velocity (B)and temperature (C). All the other simulation parameters are the same thanin the reference case (only one parameter is modified at the time). The mainmagnetospheric structures are located closer to the planet as the density or thevelocity increase because the dynamic pressure ( q = ρv /
2) of the SW increases,as can be expected from the balance between the SW dynamic pressure and themagnetic pressure of the Hermean magnetic field: R MP R M = (cid:18) B m p nµ v (cid:19) / R MP is the location of the magnetopause and B is the dipolar Hermeanmagnetic field module. There is no dependency of the magnetopause locationwith the temperature but a hotter SW leads to a reduction of the sonic Machnumber due to the increase of the sound speed c s = γT k B /m p , with T thetemperature and k B the Boltzmann constant. The drop of the Mach number iscorrelated with an expansion of the BS, located further from the planet as thetemperature increases, but no dependency between the magnetopause positionand the temperature is observed. The magnetopause is in all simulations is overthe Hermean surface so there are closed magnetic field lines on the day side of theplanet. For all the simulations the theoretical prediction of the magnetopauselocation in the equatorial plane (gray dashed line) is a 7 .
6% smaller in average(compared with the yellow dashed line), indicating that even for a low valueof the IMF module the slightly Northward orientation of the IMF leads to anenhancement of the Hermean magnetic field in the equatorial region, and themagnetopause is located further from the planet.Figure 4 shows the effect of the SW hydrodynamic parameters in the Her-mean magnetic field topology, plotting the magnetic field module and compo-nents at planes rotated θ = 0 o (A-D), 30 o (E-H) and 60 o (I-M) respect to theequatorial plane at the North Hemisphere for the simulations with ρ = 12 cm − , ρ = 180 cm − , v = 200 km/s, v = 500 km/s, T = 2 · K and T = 18 · K(the other values are the same than in the reference case). The module of themagnetic field shows the migration of the BS closer to the planet as the den-sity and the velocity increase, located further if the SW temperature is higher.There are two different regions in the magnetic field module: first the magneticfield module remains constant (along the magnetosheath) and beyond the mag-netopause where the magnetic field increases (inner magnetosphere). The innermagnetosphere shows a flattening of the profile between the magnetopause andthe closest approach related with the proximity of the reconnection betweenthe Hermean magnetic field and the IMF. If the density and velocity increaseor the temperature decreases, the flattening in the inner magnetosphere almostdisappears and both regions in the magnetosheath and inner magnetosphere are8lender. The magnetic field components show stronger rotations in SW config-uration with large dynamic pressure, driven by the compression of the magne-tosphere on the day side and the displacement of the cusp to lower latitudes,modifying the Hermean magnetic field topology in the inner magnetosphere.Different SW hydrodynamic parameters induce a dissimilar configuration ofthe magnetosheath, BS shape and Hermean magnetic field topology, pointingout that the plasma flows towards the planet surface change too. In the nextsection we analyse the properties of the plasma flows for the different configu-ration.
The figure 5 shows the density distribution in a polar cut for the simulationswith ρ = 12 cm − (A), ρ = 180 cm − (B), v = 200 km/s (C), v = 500 km/s(D), T = 2 · K (E) and T = 18 · K (F). The BS is more compressed andthe magnetosheath is thinner in the simulations with large dynamic pressureand low temperature. The magnetopause is closer to the planet and the plasmastream structures are shorter, particularly at the South Hemmisphere wherethe back of the magnetosheath reaches the planet surface for the ρ = 180 cm − and v = 500 km/s simulations. The region with closed magnetic field lines onthe planet day side decreases as the dynamic pressure increases, mainly locatednear the equator and at low latitudes of the North Hemisphere.The figure 6 shows the evolution of the density, temperature, magnetic andvelocity field modules as well as the component of the velocity along the plasmastream, from the magnetosheath (left on the graphs) to the planet surface (righton the graphs), for the simulations with ρ = 12 cm − (A), ρ = 180 cm − (D), v =200 km/s (B), v = 500 km/s (E), T = 2 · K (C) and T = 18 · K (F). Theplasma stream is originated at the magnetosheath, in the reconnection regionbetween the IMF and the Hermean magnetic field, observed as a local drop ofthe magnetic field module in the graphs. This region is correlated with a localmaximum of the plasma temperature and density as well as a local minimum ofthe velocity, indicating that the plasma is decelerated, heated and accumulated9efore precipitate along the open magnetic field line towards the planet surface.During the precipitation the plasma is accelerated, rarefied and cooled. In thesimulation with low dynamic pressure (plots A and B) and temperature (plotC), there is a second local maximum of the density nearby the planet surface,correlated with a local minimum of the temperature and a deceleration of theplasma, showing a region of dense and cold plasma accumulated over the Northpole before its precipitation on the planet surface. This structure is not observedin the simulations with large dynamic pressure (plots D and E) and temperature(plot F) because the plasma precipitates directly on the planet surface from themagnetosheath. The configuration with the most dense plasma stream is the ρ = 180 cm − simulation while the configuration with the fastest flows alongthe plasma stream (module and velocity components, in particular the V Z ) isthe v = 500 km/s simulation. These SW configurations are the main candidatesto drive the largest mass deposition on the planet surface.Figure 7 shows the regions on the planet surface with inflow/outflow (red/blue)and open magnetic field lines (cyan dots) for the simulations with ρ = 12 cm − (A), ρ = 180 cm − (D), v = 200 km/s (B), v = 500 km/s (E), T = 2 · K (C)and T = 18 · K (F). In the simulations with large dynamic pressure( plots Dand E), the flows are enhanced in both Hemispheres due to the magnetosheathcompression. The local maximum of the inflow is observed at lower latitudescompared with the reference case because the planet cusp is displaced towardsthe equator. If we compare the configuration with cold (plot C) and hot (plotF) SW, the inflow regions are similar, slightly enhanced in the case with largetemperature. The simulations with low dynamic pressure (plots A and B), showsmall inflow regions located at high latitudes at both Hemispheres. The regionswith open magnetic field lines are wilder in the simulations with larger dynamicpressure, correlated with the local maximum of the inflow, particularly in theSouth Hemisphere where the BS reaches the planet surface. In the simulationswith low dynamic pressure the magnetosphere is more sensitive to the IMForientation leading to a larger East-West asymmetry of the inflow and openmagnetic field lines regions. 10igure 8 shows the mass deposition distribution on the planet surface andthe table 3 the integrated value at each Hemisphere for the simulations with ρ = 12 cm − (A-N, A-S), ρ = 180 cm − (D-N, D-S), v = 200 km/s (B-N,B-S), v = 500 km/s (E-N, E-S), T = 2 · K (C-N, C-S) and T = 18 · K (F-N, F-S). The regions of mass deposition are wider for simulations withlarge dynamic pressure (plots D and E), particularly at the South Hemisphere.The mass deposition region is localized close to the poles on the planet dayside in the simulation with low SW density (pplots A-N and A-S) while it isdistributed on the night and day side for the slow SW configuration (plots B-Nand B-S). The mass deposition for cold and hot SW configurations (plots C andF) is similar, slightly smaller on the night side for a hot plasma. The integratedmass deposition indicates that the main part of the mass deposition takes placeat the South Hemisphere, a 50 % more compared with the North Hemisphere,except in the simulation with slow SW where the mass deposition is similar atboth Hemispheres. The mass deposition is more than 20 times larger compar-ing the configuration with high and low density, 2 times larger comparing thefast and slow SW simulation and almost the same for the hot and cold plasmasconfigurations. The mass deposition is enhanced at the North Hemisphere forthe cold plasma configuration because the magnetosheath is more compressedreinforcing the plasma stream at the North Hemisphere, the opposite scenariothan the hot plasma configuration where the mass deposition is enhanced atthe South Hemisphere due to the decompression of thmagnetosheath. The sim-ulation with high SW density shows a mass deposition a 15% larger than thesimulation with high velocity.
5. Conclusions
To perform a parametric study with a weak interplanetary magnetic fieldillustrates the effect of the solar wind hydrodynamic variables on the Hermeanmagnetosphere structure, minimizing the distortion driven by the reconnectionbetween the interplanetary and the Hermean magnetic field. The results indicate11odel North Hemisphere South HemisphereReference 0 .
034 0 . ρ = 12 cm − .
011 0 . ρ = 180 cm − .
146 0 . v = 200 km/s 0 .
086 0 . v = 500 km/s 0 .
130 0 . T = 2 · K 0 .
077 0 . T = 18 · K 0 .
056 0 . ρ = 12 cm − , ρ = 180 cm − , v = 200 km/s, v = 500 km/s, T = 2 · K and T = 18 · K.that the BS never reaches the planet surface in the equator if the SW dynamicpressure is smaller than 6 . · − Pa, the largest dynamic pressure for all thesimulations where the SW density is ρ = 60 cm − and the velocity is v = 500km/s. The forecast of the SW dynamic pressure in Mercury by the ENLIL +GONG WSA + Cone SWRC model usually expects values below 6 . · − Pa,pointing out that the erosion of the Hermean magnetic field by a Southwardoriented inteplanetary magnetic field is the main driver of the magnetopauseprecipitation on the Hermean surface.Another conclusion of the study is the evolution of the magnetopause andBS stand off distance with the hydrodynamic values, showing that an enhance-ment of the SW dynamic pressure leads to a more compressed magnetosheathand a more closed magnetosphere (triangular shape of the BS). Hot SW con-figurations show a decompression of the magnetosheath due to the increase ofthe SW sound velocity and the drop of the sonic Mach number. The BS frontis displaced 0 . · R M comparing the coldest to the hottest solar wind config-uration. The theoretical calculation considering only the dynamic pressure ofthe SW is slightly different than the values obtained in the simulations due tothe small but observable effect of the Northward IMF orientation, enough to12nhance the Hermean magnetic field in the nose of the bow shock and slightlydisplace further the magnetopause.The simulations with large SW dynamic pressure drives a strong compres-sion of the magnetic field lines on the day side and the magnetotail stretchingon the night side, changing the Hermean magnetic field topology of the innermagnetosphere. In consequence, the plasma flows and mass deposition on theplanet surface are altered by the different SW configurations.The inflow and open magnetic field lines regions on the planet surface arewider for configurations with large dynamic pressure. The magnetosheath deple-tion is more efficient in dense and fast SW configurations. The integrated massdeposition is a 15% larger in the ρ = 180 cm − simulation than in the v = 500km/s case, even if the dynamic pressure for the high density simulation is a 75%of the dynamic pressure of the high velocity case. On the other side, the config-urations with low SW density leads to integrated mass depositions much lowerthan the simulation with slow SW, almost 5 times smaller if we compare thesimulation with ρ = 12 cm − and v = 200 km/s, where the dynamic pressure ofthe low density simulation is only a 33% of the low velocity case. The integratedmass deposition is almost the same for hot and cold SW configuration, but theratio between Hemispheres changes; a 42% of the total deposition takes placeat the North Hemisphere for the T = 2 · K simulation versus a 31% for the T = 18 · K case, due to the larger magnetosheath compression in the coldplasma configuration. In summary, there is not a direct correlation between themass deposition and the dynamic pressure of the SW, it is required a furtheranalysis of the magnetosheath region where the plasma stream is originated tounderstand the effect of the SW hydrodynamic parameter in the flows towardsthe Hermean surface.The plasma stream is originated closer to the planet surface in the simula-tions with large dynamic pressure and the magnetosheath is slender comparedwith the low dynamic pressure cases. The influence of the reconnection regioncovers all the magnetosheath in the large dynamic pressure simulations leadingto an enhancement of the plasma precipitation.13he plasma stream is collimated by the Hermean magnetic field in the sim-ulations with low dynamic pressure, leading to small deposition region near thepoles. For the high dynamic pressure cases the flows are strong enough to over-come the collimation leading to a spread plasma stream that convers the dayand night side of the planet surface.In the configurations with low dynamic pressure and temperature there isa region near the planet North pole of cold and dense plasma. This structureis not observed in configurations with large SW dynamic pressure because themagnetopause is located too close to the planet surface. In the case of hot SWconfigurations, the magnetosheath decompression leads to a drop of the plasmaprecipitation on the North Hemisphere, avoiding a large accumulation of plasmanear the pole.The resolution of the model is not large enough to resolve the plasma de-pletion layer as a different structure than the magnetosheath, although thesimulation conclusion are similar to observational studies showing compatiblefeatures for the particles fluxes and magnetosheath depletion [13, 18]. The nu-merical resistivity of the code is several orders larger than the real plasma so nomagnetic field pile-up is observed on the day side [12], the reconnection is almostinstantaneous, but the simulation can reproduce the important effect of the re-connection in the origin of the plasma stream. The simulation conclusions agreeswith the last observations of proton precipitations from the magnetosheath to-wards the planet surface along the cusp, pointing out that there is not a directprecipitation of the SW at the North pole [19]. The present simulations sharesimilar magnetosphere global structures than other simulations performed withdifferent numerical schemes [15, 16]. Present research complements a recentcommunication of the authors devoted to study the effect of the interplanetarymagnetic field orientation on the fluxes toward the Hermean surface [20].14 . Aknowledgments
The research leading to these results has received funding from the Euro-pean Commission’s Seventh Framework Programme (FP7/2007-2013) under thegrant agreement SHOCK (project number 284515). The MESSENGER magne-tometer data set was obtained from the NASA Planetary Data System (PDS)and the values of the solar wind hydrodynamic parameters from the NASAIntegrated Space Weather Analysis System.
ReferencesReferences [1] B. J. Anderson, C. L. Johnson, H. Korth, R. M. Winslow, J. E. Borovsky,M. E. Purucker, J. A. Slavin, S. C. Solomon, M. T. Zuber, R. L. Mc-Nutt, Jr., Low-degree structure in Mercury’s planetary magnetic field,Journal of Geophysical Research (Planets) 117 (2012) E00L12. doi:10.1029/2012JE004159 .[2] D. N. Baker, D. Odstrcil, B. J. Anderson, C. N. Arge, M. Benna, G. Gloeck-ler, J. M. Raines, D. Schriver, J. A. Slavin, S. C. Solomon, R. M. Killen,T. H. Zurbuchen, Space environment of Mercury at the time of the firstMESSENGER flyby: Solar wind and interplanetary magnetic field mod-eling of upstream conditions, Journal of Geophysical Research (SpacePhysics) 114 (2009) A10101. doi:10.1029/2009JA014287 .[3] D. N. Baker, D. Odstrcil, B. J. Anderson, C. N. Arge, M. Benna, G. Gloeck-ler, H. Korth, L. R. Mayer, J. M. Raines, D. Schriver, J. A. Slavin, S. C.Solomon, P. M. Tr´avn´ıˇcek, T. H. Zurbuchen, The space environment ofMercury at the times of the second and third MESSENGER flybys, Plan-etary and Space Science 59 (2011) 2066–2074. doi:10.1016/j.pss.2011.01.018 . 154] B. J. Anderson, C. L. Johnson, H. Korth, M. E. Purucker, R. M. Winslow,J. A. Slavin, S. C. Solomon, R. L. McNutt, J. M. Raines, T. H. Zurbuchen,The Global Magnetic Field of Mercury from MESSENGER Orbital Obser-vations, Science 333 (2011) 1859. doi:10.1126/science.1211001 .[5] C. L. Johnson, M. E. Purucker, H. Korth, B. J. Anderson, R. M. Winslow,M. M. H. Al Asad, J. A. Slavin, I. I. Alexeev, R. J. Phillips, M. T. Zu-ber, S. C. Solomon, Messenger observations of mercury’s magnetic fieldstructure, Journal of Geophysical Research: Planets 117 (E12). doi:10.1029/2012JE004217 .[6] M. Fujimoto, W. Baumjohann, K. Kabin, R. Nakamura, J. A. Slavin,N. Terada, L. Zelenyi, Hermean Magnetosphere-Solar Wind Interaction,ssr 132 (2007) 529–550. doi:10.1007/s11214-007-9245-8 .[7] D. N. Baker, G. Poh, D. Odstrcil, C. N. Arge, M. Benna, C. L. Johnson,H. Korth, D. J. Gershman, G. C. Ho, W. E. McClintock, T. A. Cassidy,A. Merkel, J. M. Raines, D. Schriver, J. A. Slavin, S. C. Solomon, P. M.Tr´aVn´ıˇcEk, R. M. Winslow, T. H. Zurbuchen, Solar wind forcing at Mer-cury: WSA-ENLIL model results, Journal of Geophysical Research (SpacePhysics) 118 (2013) 45–57. doi:10.1029/2012JA018064 .[8] D. Odstrcil, Heliosphere at solar maximum modeling 3-d solar wind struc-ture, Advances in Space Research 32 (4) (2003) 497 – 506. doi:10.1016/S0273-1177(03)00332-6 .[9] A. Parsons, D. Biesecker, D. Odstrcil, G. Millward, S. Hill, V. Pizzo, Wang-sheeley-argeenlil cone model transitions to operations, Space Weather 9 (3). doi:10.1029/2011SW000663 .[10] A. Mignone, G. Bodo, S. Massaglia, T. Matsakos, O. Tesileanu, C. Zanni,A. Ferrari, PLUTO: A Numerical Code for Computational Astrophysics,apjs 170 (2007) 228–242. arXiv:astro-ph/0701854 , doi:10.1086/513316 . 1611] B. J. Anderson, M. H. Acu˜na, H. Korth, M. E. Purucker, C. L. Johnson,J. A. Slavin, S. C. Solomon, R. L. McNutt, The Structure of Mercury’sMagnetic Field from MESSENGER’s First Flyby, Science 321 (2008) 82. doi:10.1126/science.1159081 .[12] D. J. Gershman, J. A. Slavin, J. M. Raines, T. H. Zurbuchen, B. J. An-derson, H. Korth, D. N. Baker, S. C. Solomon, Magnetic flux pileup andplasma depletion in Mercury’s subsolar magnetosheath, Journal of Geo-physical Research (Space Physics) 118 (2013) 7181–7199. doi:10.1002/2013JA019244 .[13] G. A. DiBraccio, J. A. Slavin, S. A. Boardsen, B. J. Anderson, H. Korth,T. Zurbuchen, J. M. Raines, D. N. Baker, R. L. McNutt, S. C. Solomon,MESSENGER Observations of Magnetopause Reconnection at Mercury(Invited), AGU Fall Meeting Abstracts.[14] K. Kabin, M. H. Heimpel, R. Rankin, J. M. Aurnou, N. G´omez-P´erez,J. Paral, T. I. Gombosi, T. H. Zurbuchen, P. L. Koehn, D. L. DeZeeuw,Global MHD modeling of Mercury’s magnetosphere with applications tothe MESSENGER mission and dynamo theory, Icarus 195 (2008) 1–15. doi:10.1016/j.icarus.2007.11.028 .[15] P. M. Tr´avn´ıˇcek, D. Schriver, P. Hellinger, Structure of Mercury’s magneto-sphere for different solar wind beta: three dimensional hybrid simulations,AGU Fall Meeting Abstracts.[16] P. M. Tr´avn´ıˇcek, D. Schriver, P. Hellinger, D. Herˇc´ık, B. J. Anderson,M. Sarantos, J. A. Slavin, Mercury’s magnetosphere-solar wind interactionfor northward and southward interplanetary magnetic field: Hybrid simu-lation results, Icarus 209 (2010) 11–22. doi:10.1016/j.icarus.2010.01.008 .[17] A. Dedner, F. Kemm, D. Kr¨oner, C.-D. Munz, T. Schnitzer, M. Wesenberg,Hyperbolic Divergence Cleaning for the MHD Equations, Journal of Com-putational Physics 175 (2002) 645–673. doi:10.1006/jcph.2001.6961 .1718] R. Killen, G. Cremonese, H. Lammer, S. Orsini, A. E. Potter, A. L. Sprague,P. Wurz, M. L. Khodachenko, H. I. M. Lichtenegger, A. Milillo, A. Mura,Processes that Promote and Deplete the Exosphere of Mercury, ssr 132(2007) 433–509. doi:10.1007/s11214-007-9232-0 .[19] J. M. Raines, D. J. Gershman, J. A. Slavin, T. H. Zurbuchen, H. Korth,B. J. Anderson, S. C. Solomon, Structure and dynamics of Mercury’s mag-netospheric cusp: MESSENGER measurements of protons and planetaryions, Journal of Geophysical Research (Space Physics) 119 (2014) 6587–6602. doi:10.1002/2014JA020120 .[20] J. Varela, F. Pantellini, M. Moncuquet, The effect of interplanetary mag-netic field orientation on the solar wind flux impacting Mercury’s surface,Planetary and Space Science 119 (2015) 264–269. doi:10.1016/j.pss.2015.10.004 . 18igure 2: Density distribution for a polar (A) and equatorial (B) cuts. Weinclude the points along the trajectory where the satellite reaches the BS (SIand SO), magnetopause (MI and MO) and closest approach (CA). The red linesshow the magnetic field lines inside the magnetosphere. (C) Sinusoidal (Sanson-Flamsteed) projection of the inflow/outflow (blue/red) and open magnetic fieldlines regions (cyan dots) on the planet surface. Mass deposition at the North(D) and South (E) Hemisphere. 19igure 3: BS and magnetopause stand off distance at planes rotated θ = 0 o ,30 o , 60 o and 90 o respect the equatorial plane at the North Hemisphere day side.The graph (A) shows the results for the parametric study of the density, graph(B) for the velocity and graph (C) for the temperature (all the other simulationparameters are the same than in the reference case, only one parameter is mod-ified at the time). The gray dashed line indicates the theoretical position of themagnetopause in the equatorial plane from the balance between the solar winddynamic pressure and the magnetic pressure of the Hermean magnetic field.20igure 4: Magnetic field module and components at planes with angles of 0 o (A-D), 30 o (E-H) and 60 o (I-M) respect to the equatorial plane at the NorthHemisphere for the simulations with ρ = 12 cm − , ρ = 180 cm − , v = 200 km/s, v = 500 km/s, T = 2 · K and T = 18 · K (the other SW parameters arethe same than in the reference case). 21igure 5: Polar cut of the density distributions in the simulations with ρ = 12cm − (A), ρ = 180 cm − (B), v = 200 km/s (C), v = 500 km/s (D), T = 2 · K (E) and T = 18 · K (F). The red lines show the magnetic field lines insidethe magnetosphere. The white lines indicate the region plotted in the Figure 6.22igure 6: Density, temperature, magnetic and velocity field module, and veloc-ity field components along the plasma stream structure (see figure 5) for thesimulations with ρ = 12 cm − (A), ρ = 180 cm − (D), v = 200 km/s (B), v = 500 km/s (E), T = 2 · K (C) and T = 18 · K (F).23igure 7: Sinusoidal (Sanson-Flamsteed) projection of the inflow/outflow(blue/red) and open magnetic field lines regions (cyan dots) on the planet sur-face for the simulations with ρ = 12 cm − (A), ρ = 180 cm − (D), v = 200km/s (B), v = 500 km/s (E), T = 2 · K (C) and T = 18 · K (F).24igure 8: Mass deposition at the North and South Hemispheres for the simula-tions with ρ = 12 cm − (A-N, A-S), ρ = 180 cm − (D-N, D-S), v = 200 km/s(B-N, B-S), v = 500 km/s (E-N, E-S), T = 2 · K (C-N, C-S) and T = 18 ·4