JournalofGeophysicalResearch: SpacePhysics

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1 JournalofGeophysicalResearch: SpacePhysics RESEARCH ARTICLE Key Points: Global effects of protons reflected from lunar crustal fields Magnetic fields and plasma compression outside the lunar wake Global effects persist independent of the ion reflection function Effects of protons reflected by lunar crustal magnetic fields on the global lunar plasma environment Shahab Fatemi 1,2, Mats Holmström 1, Yoshifumi Futaana 1, Charles Lue 1,3, Michael R. Collier 4, Stas Barabash 1, and Gabriella Stenberg 1 1 Swedish Institute of Space Physics, Kiruna, Sweden, 2 Department of Computer Science, Electrical and Space Engineering, Division of Space Technology, Luleå University of Technology, Luleå, Sweden, 3 Department of Physics, Umeå University, Umeå, Sweden, 4 NASA/Goddard Space Flight Center, Greenbelt, Maryland, USA Correspondence to: S. Fatemi, shahab@irf.se Citation: Fatemi, S., M. Holmström, Y. Futaana, C. Lue, M. R. Collier, S. Barabash, and G. Stenberg (2014), Effects of protons reflected by lunar crustal magnetic fields on the global lunar plasma environment, J. Geophys. Res. Space Physics, 119, , doi:. Received 18 FEB 2014 Accepted 29 JUL 2014 Accepted article online 4 AUG 2014 Published online 28 AUG 2014 Abstract Solar wind plasma interaction with lunar crustal magnetic fields is different than that of magnetized bodies like the Earth. Lunar crustal fields are, for typical solar wind conditions, not strong enough to form a (bow)shock upstream but rather deflect and perturb plasma and fields. Here we study the global effects of protons reflected from lunar crustal magnetic fields on the lunar plasma environment when the Moon is in the unperturbed solar wind. We employ a three-dimensional hybrid model of plasma and an observed map of reflected protons from lunar magnetic anomalies over the lunar farside. We observe that magnetic fields and plasma upstream over the lunar crustal fields compress to nearly 120% and 160% of the solar wind, respectively. We find that these disturbances convect downstream in the vicinity of the lunar wake, while their relative magnitudes decrease. In addition, solar wind protons are disturbed and heated at compression regions and their velocity distribution changes from Maxwellian to a non-maxwellian. Finally, we show that these features persists, independent of the details of the ion reflection by the magnetic fields. 1. Introduction The interaction of the solar wind plasma with the Moon is different than that of the Earth. The Moon, unlike the Earth, has neither a dense atmosphere nor a strong intrinsic magnetic field. Thus, the supersonic flow of the solar wind plasma is mostly absorbed on the lunar dayside, leaving a plasma wake downstream with a plasma cavity on the nightside [Lyon et al., 1967]. While the interplanetary magnetic field (IMF) convects through the nonconductive body of the Moon relatively undisturbed [Colburn et al., 1971; Halekas et al., 2005], the current system forming in the lunar wake enhances the magnetic fields in the wake cavity and depresses them in the surrounding expansion region [Colburn et al., 1967; Fatemi et al., 2013; Vernisse et al., 2013]. These perturbations of the magnetic field and plasma in the lunar wake are confined to a region bounded by a magnetosonic Mach cone [Whang and Ness, 1970; Holmström et al., 2012]. In addition to these regular perturbations, magnetic field enhancements often associated with plasma compressions have been observed outside the Mach cone sporadically [Siscoe et al., 1969;Lin et al., 1998]. They form downstream adjacent to the expansion region at the outer edge of the Mach cone [Barnes et al., 1971; Russell and Lichtenstein, 1975] and upstream above lunar crustal fields in the solar wind [Lin et al., 1998; Halekas et al., 2006a]. These compressions have clear association with solar wind interaction with lunar crustal magnetic fields [Mihalov et al., 1971; Lin et al., 1998]. Similar to the planetary bow shocks, one possible mechanism to compress the solar wind might be ion reflection from lunar crustal fields [Futaana et al., 2003]. Depending on density, velocity, and direction of reflected protons relative to the solar wind, they interact with the solar wind plasma and may form plasma instabilities and generate waves [Gary, 1991, and references therein]. Broadband whistler mode waves at low frequencies of about Hz near the Moon have been observed [Nakagawa et al., 2011] that are mainly generated by the solar wind interaction with lunar crustal fields [Halekas et al., 2006b; Tsugawaetal., 2011, 2012]. These waves are right-hand polarized in the solar wind reference frame and have similarities to waves often observed in the terrestrial foreshock [Halekas et al., 2013]. Nevertheless, forming a collisionless (bow)shock upstream the lunar crustal fields is still doubtful. This is mainly due to the small-scale size of the magnetized areas (interaction region) compared to the ion scale lengths [Halekas et al., 2011]. FATEMI ET AL American Geophysical Union. All Rights Reserved. 6095

2 Recent observations reveal that on average 10% of the incident solar wind proton flux to the Moon is reflected in charged form from lunar magnetic anomalies [Saitoetal., 2010; Lueetal., 2011]. Reflected protons have similar bulk velocity but higher thermal speed compared to those of the incident solar wind protons [Lue et al., 2011; Saito et al., 2012]. Lue et al.[2011] using the SWIM sensor on board the Chandrayaan-1 satellite provided a global map of the solar wind proton reflection ratio over the entire lunar farside. They showed that there is a geographical correlation between the areas with high proton reflection and the lunar crustal magnetic fields, but they did not indicate the direction of the reflected protons. The reflection ratio over the largest and strongest magnetic anomalies is 50%, while the reflection from unmagnetized (i.e., from surface scattering) and weakly magnetized regions is generally lower than 1% [Saitoetal., 2008]. It is also known that a fraction of reflected protons from the lunar dayside move downstream and enter the lunar wake [Nishino et al., 2009, 2013]. Holmström et al. [2010] studied the dynamics of the solar wind protons reflected from unmagnetized areas on the lunar surface using hybrid and test-particle models. They examined various reflection functions from the surface of the Moon and compared their simulation results with observations. They showed that a cos 2 -specular reflection function provides a good agreement to the observations compared to other reflection functions, such as specular and perpendicular. In this paper we use a three-dimensional hybrid model of plasma for resistive obstacles [Holmström, 2013] combined with a reflected proton map on the lunar farside observed by Chandrayaan-1. We examine various reflection functions to reflect protons from lunar magnetic anomalies. The aim of this study is to investigate the global effects of these reflected protons on the lunar plasma environment. In the following sections we first explain our simplified empirical model. Then we explain the global effects of reflected protons on the lunar plasma environment, and we show that the global effects endure regardless of the details of the particles reflection. Finally, we discuss the role of the reflected protons on the fields and plasma compression and the plasma wake infilling. 2. Model The hybrid simulation code used here is similar to that of Holmström [2013], where the ions are kinetic macroparticles and electrons are a mass-less charge-neutralizing fluid. Magnetic and electric fields are solved self-consistently, and the divergence-free condition of the magnetic field is satisfied over the entire simulation domain. The model is three-dimensional in both configuration and velocity spaces with periodic boundary conditions perpendicular to the solar wind flow direction. At the inflow boundary of the simulation box, kinetic macroparticles follow the Maxwellian velocity distribution function, and the upstream plasma conditions remain constant during simulations. The obstacle (here the Earth s Moon) is a resistive object, and its surface is assumed to be a plasma particle absorber. Thus, a plasma cavity region forms behind the Moon on the nightside. This cavity, to a first-order approximation, is considered as a vacuum with plasma density 0.1 cm 3 [Ogilvie et al., 1996; Halekas et al., 2005]. Handling such low-density regions is a challenge for hybrid plasma solvers since the evaluation of the electric field involves division by charge density [Holmström, 2010;Holmström et al., 2012]. Here, as proposed recently by Holmström [2013], we first assume that there is a large resistivity inside the obstacle, η obs, and in the low-density regions, η v. Then we solve a magnetic diffusion equation in these regions instead of the Faraday s law used in the general hybrid plasma equations. To numerically stabilize solving the diffusion equation, we also use a hyperresistivity, η h, in the electric field computation [Holmström, 2013]. By this algorithm, we handle the low-density regions in our model. A time step limit for stability is Δt <μ 0 Δx 2 2η, where μ 0 =4π 10 7 [H/m] is the permeability for the free space, Δx [m] is the simulation cell size, and η [Ωm] is the largest resistivity between η obs and η v Proton Reflection To model proton reflection from lunar crustal magnetic fields, we use the Chandrayaan-1 map of protons reflection ratio, shown in Figure 1. This map shows the ratio between the outflowing proton flux ( F r ) and the inflowing solar wind proton flux ( F sw ) over the lunar farside at 100 km altitude above the surface. We project this map on the lunar dayside such that the subsolar point locates at 0 longitude and latitude on this map. Note that this corresponds to 180 longitude and 0 latitude in the selenographic coordinate system. When the solar wind particles impact the dayside, a fraction of them will be reflected with the FATEMI ET AL American Geophysical Union. All Rights Reserved. 6096

3 Figure 1. Map of the ratio between reflected proton flux from the Moon ( F r ) and the solar wind proton flux ( F sw ) obtained from the SWIM sensor observations on board Chandrayaan-1 [Lue et al., 2011]. same speed as the incident particle speed with a probability corresponding to the reflection map shown in Figure 1. The rest is considered absorbed and removed from the simulation. The assumption of the same speed is consistent with Chandrayaan-1 [Lue et al., 2011] and Kaguya [Saito et al., 2010, 2012] observations of reflected proton bulk velocity. On the other hand, these observations as well as Nozomi flyby observations [Futaana et al., 2003] suggest rather high-velocity spread; thus, the assumption here may collimate the energy of reflected proton flows more than is observed. Since the directional velocity distribution of reflected protons from lunar crustal magnetic fields is unknown, we examined different reflection models, as explained by Holmström et al. [2010]. The employed reflection functions are specular (Figure 2a), cos 2 -specular (Figure 2b), and isotropic (not shown here). An incident proton at position r with velocity v is reflected at the same position with a velocity defined as follows: 1. Specular reflection: incident particle reflect with the same angle to the surface normal (θ) as that of the incident particle with velocity v = v 2(v r) r (see Figure 2a). 2. cos 2 -specular reflection: The angle between reflected proton velocity (v ) and the surface normal (β) is randomly chosen from a cos 2 β probability function (see Figure 2b). However, observations indicate that the lunar crustal fields are rather deflecting the solar wind plasma instead of reflecting it [Barnes et al., 1971; Lin et al., 1998;Lue et al., 2011]. Thus, in addition to the reflection functions defined above, we define a Gaussian velocity deflection function as a function of angle to the Sun with the mean of the distribution at 180 (antisunward) and a standard deviation σ<180. Figure 2c shows an example of this function for σ = 45. It shows that the reflected protons are mainly moving forward in the direction of the solar wind (forward deflection), instead of reflecting back and counterstreaming with the solar wind plasma. If the computed velocity vector for a deflected particle has a direction toward the Moon, the velocity vector is recalculated until it goes away from the Moon. In principle, we could self-consistently model the effects of crustal magnetic fields by including the actual crustal fields in the model. However, this requires extremely high spatial resolution and very small time steps, due to the high magnetic field strength near the surface (up to a few hundreds of nanotesla with a height scale of a few kilometers [Mitchell et al., 2008]) compared to the solar wind. Therefore, we follow an empirical approach of using the observed Chandrayaan-1 map of reflected protons. Using this method enables us to investigate the global effects of the observed reflected protons at a reasonable computational constant. The drawback is that the model lacks the complete physics below the lowermost 100 km altitude (Chandrayaan-1 altitude), though this is smaller than our simulation cell size. Figure 2. Illustration of (a) specular reflection function and (b) cos 2 -specular reflection function. The incident proton velocity vector (v) is shown by black arrows, and the reflected proton velocity vector (v ) is shown by red arrows. (c) A forward deflection function is shown by a Gaussian distribution as a function of angle to the Sun where the mean of distribution is at 180 (antisunward along the solar wind flow direction) with standard deviation σ = Coordinate System and Simulation Box Figure 3 shows the coordinate system we use here, which is a right-handed coordinate system centered at the Moon. The +x axis is toward the Sun, so the solar wind flows opposite to the +x axis. The +z axis is perpendicular to the ecliptic plane and points to the ecliptic north, and the y axis FATEMI ET AL American Geophysical Union. All Rights Reserved. 6097

4 completes the right-hand system. We assume that the IMF is in the xy plane, from now on denoted as the IMF plane. The convective electric field, E conv = v sw B sw,is perpendicular to both the solar wind flow direction and the IMF plane. Figure 3. Illustration of the coordinate system in units of the Moon radius (R L = 1730 km). The solar wind (red arrow) flows along the x axis, and the IMF (green arrow) creates a 45 angle to the solar wind flow in the xy plane without any component along the z axis. Then the solar wind convective electric field E conv = v sw B sw points along the +z axis. We assume that the solar wind plasma contains protons only, and we neglect the other solar wind ion species. We consider a resistive Moon with homogeneous interior resistivity η obs = 10 7 Ωm[Hood et al., 1982], and we assume the vacuum resistivity η v = 10 7 Ωm. Experimentally, we choose η h = Ωm 3 to stabilize solving the magnetic diffusion equation. We divide simulation domain into a Cartesian grid with cubic cells of size Δx = 150 km. We use 128 macroparticles per cell at the inflow boundary of the simulation box and advance the particle trajectories in small time steps (Δt = s) to satisfy the time step limit for stability. We show simulation results when numerical solution reached a steady state (60 s here). 3. Model Results Here we investigate the global effects of reflected protons from lunar crustal magnetic fields using the forward deflection function (Figure 2c). Then we compare the effects of various reflection functions on the global aspects of the interaction, and we show that the global effects persist independent of the reflection functions. We project the reflection map (Figure 1) on the Moon, and we assume that the lunar phase is the new Moon. Thus, the subsolar point is located at the center of the reflection map. Solar wind upstream parameters in our simulation are the typical solar wind conditions at 1 AU (astronomical unit) near the Earth [Kivelson and Russell, 1995, Table 4.1] that are summarized in Table 1. Upstream solar wind parameters at 1 AU are reasonably accurate indications of plasma and field conditions that interact with the Moon [Collier et al., 1998]. We assume that the IMF forms a 45 angle with the solar wind flow following the Parker spiral angle, shown in Figure 3. Figures 4a and 4b respectively show the relative magnitude of the magnetic field ( B B sw ) in the IMF plane at z = 0 and in the xz plane at y = 0 (we hereafter refer to this plane as the noon-midnight meridian plane). Magnetic field enhancement in the lunar wake and field reduction in the surrounding expansion region are evident in both planes. Typically, magnetic field and plasma perturbations in the lunar plasma wake and in the absence of particle reflection from the Moon are confined within a magnetosonic Table 1. Solar Wind Upstream Parameters at 1 AU Used in our Model Parameter Symbol Value Unit Solar wind speed v sw km/s IMF magnitude B sw 7.0 nt Number density n sw = n p = n e 7.1 cm 3 Proton temperature T p 10.3 ev Electron temperature T e 12.1 ev Proton thermal speed v th 44.5 km/s Proton gyroradius r g 66.3 km Proton gyrofrequency Ω g 0.1 Hz Sound speed c s 59.8 km/s Alfvén speed v A 57.3 km/s Sonic Mach number M s 7.5 Alfvén Mach number M A 7.8 Plasma beta β 1.3 Mach cone [Whang and Ness, 1970; Holmström et al., 2012]. The theoretical boundaries of the Mach cone are marked with dashed lines in Figures 4a 4d. In addition to the magnetic field disturbances inside the Mach cone, we see magnetic field compression in the lunar dayside. This compression extends up to 0.3 R L upstream from the lunar surface, and it reaches to nearly 120% of the undisturbed IMF over the largest cluster of the magnetic anomalies in the farside southern hemisphere. Moreover, Figure 4b shows magnetic field enhancement adjacent to the expansion region at the outer boundary of the Mach cone. This enhancement is an extension of the dayside compression that convects downstream with gradually decreasing magnitude. FATEMI ET AL American Geophysical Union. All Rights Reserved. 6098

5 Figure 4. Hybrid simulation results showing a map of (a, b) magnitude of the magnetic field normalized to the undisturbed upstream IMF ( B / B sw ); (c, d) proton number density, including both the solar wind and reflected protons, normalized to the upstream solar wind number density (n n sw ); and (e, f) normalized reflected proton number density (n r n sw ). Figures 4a, 4c, and 4e show cuts in the IMF plane (xy plane) at z = 0, and Figures 4b, 4d, and 4f show cuts in the meridian plane (xz plane) seen from the y axis at y = 0. The regions marked with cross and labeled with numbers in Figure 4b are the four places where we have shown proton velocity space distributions in Figure 7. The dashed lines in Figures 4a 4d approximately indicate the boundaries of the lunar Mach cone in the absence of reflected protons. Horizontal and vertical solid lines in Figure 4d show where we present our results in Figures 6 and 8, respectively. The white areas in Figures 4c 4f indicate zero number density. Black circles centered at the origin represent the Moon. All the axes are normalized to the radius of the Moon R L = 1730 km, and the IMF direction is only shown on the IMF plane in Figures 4a, 4c, and 4e with solid arrows. Some of the features displayed in the magnetic fields are also visible in proton density plots (Figures 4c and 4d). We see the presence of plasma compression coincide with magnetic field enhancement upstream in the dayside and downstream outside the Mach cone. The maximum proton density in the lunar dayside is nearly 160% of the ambient solar wind plasma. Figures 4c and 4d also show that the plasma void region behind the Moon is confined to x > 2.0 R L. We can compare this to previous simulations that showed in the absence of proton reflection from lunar dayside, and for approximately similar upstream solar wind Figure 5. Streamlines of particles velocity for (a, b) reflected protons from crustal magnetic fields and (c, d) all particles in the simulations domain. The colors show the normalized flux of protons to the upstream solar wind flux. Figures 5a and 5c show cuts in the IMF plane, and Figures 5b and 5d show cuts in the meridian plane. The geometry of the cuts are thesameasinfigure4. FATEMI ET AL American Geophysical Union. All Rights Reserved. 6099

6 Figure 6. Magnetic field and some of the moments of the velocity distribution along the horizontal solid line shown in Figure 4d upstream of the Moon. The quantities are taken along the x axis, where the selection area in the yz plane is km 2 (one simulation cell size), centered at y = 0 and z = 0.8R L. (a) Magnetic field magnitude. (b) Magnetic field azimuth angle. (c) Magnetic field elevation angle. (d) Total proton density including solar wind and reflected protons shown in black and the solar wind proton number density shown in blue. (e) Total protons bulk velocity shown in black and solar wind protons bulk velocity shown in blue. (f h) Nonreflected solar wind protons x-v phase space. conditions, the wake cavity extends beyond 2.0 R L [Kallio, 2005; Wang et al., 2011; Holmström et al., 2012; Xie et al., 2012]. Figures 4e and 4f show the normalized number density of the reflected protons only. They indicate that the wake cavity is filled in by the reflected protons from the lunar dayside, which is consistent with observations [Nishino et al., 2009, 2013]. In addition, we see asymmetries in the reflected protons density at the lunar dawnside to duskside in Figure 4e, as well as near the lunar poles in Figure 4f. These asymmetries are due to the IMF angle with respect to the solar wind flow and the uneven distribution of the magnetic anomalies with different strength and characteristics on the Moon. Figure 5 shows streamlines of proton velocity in the IMF plane (Figures 5a and 5c) and in the meridian plane (Figures 5b and 5d). The colors of streamlines indicate the normalized proton flux ( F F sw ). We calculated the flux as F = nv, where n and v are the protons number density and their bulk velocity vector, respectively. The magnitude of the upstream solar wind proton flux is F sw = n sw v sw m 2 s 1. Figures 5a and 5b show the flux of reflected protons only, while the flux of all protons (solar wind and reflected) are shown in Figures 5c and 5d. Figure 5a shows that large fluxes of reflected protons move away from the Moon upstream in the IMF plane as they gyrate around the magnetic field lines, while Figure 5b shows that most of the reflected particles are convected along the solar wind electric field upstream in the meridian plane and move into the wake. However, we cannot see the effects of these reflected protons on perturbing the total proton flux upstream, as shown in Figures 5c and 5d. Nevertheless, Figure 5d shows an enhanced flux of protons outside the lunar Mach cone in the meridian plane. However, such an enhancement is not seen FATEMI ET AL American Geophysical Union. All Rights Reserved. 6100

7 Figure 7. Velocity distribution functions for nonreflected solar wind protons (red dots) and reflected protons from lunar dayside (blue dots) at the four regions marked in Figure 4b. (a, b) Point 1 at x =+2.0 R L upstream. (c, d) Point 2, just above the largest cluster of the lunar magnetic anomalies. (e, f) Point 3, in the compression region outside the lunar Mach cone at x = 2.0 R L. (g, h) Point 4, at the center of the wake at x = 2.0 R L. The distribution functions are parallel to the IMF, v, shown in Figures 7a, 7c, 7e, and 7g, and the convective electric field, v E, and parallel to the v E and the E B drift, v E B, shown in Figures 7b, 7d, 7f, and 7h. in Figure 5b, indicating that they are only the solar wind protons accessing the compression region outside the lunar Mach cone. To investigate more details of this interaction and its influences on the solar wind plasma, we present magnetic fields and some of the moments of the velocity distribution upstream of the Moon. Figure 6 presents the results of this analysis along the horizontal line shown in Figure 4d in the meridian plane (along the x axis at z = 0.8R L ). Here the plasma incident on the Moon is absorbed by the lunar surface at x = 0.6R L. Figures 6a 6c show no magnetic field disturbances far upstream from the Moon (x > 1.5R L ). However, at close distances to the Moon (0.6R L 1.5R L ), magnetic fields pile up over the lunar crustal magnetic fields (Figure 6a) and their directions change toward more perpendicular to the solar wind flow direction (Figures 6b and 6c). Simultaneously, total (solar wind + reflected) proton number density, as shown in Figure 6d by a black line, increases to about 160% of the undisturbed solar wind plasma, while the total proton bulk velocity, shown in Figure 6e by a black line, slows down to nearly 70% of the undisturbed solar wind velocity. On the other hand, Figures 6d and 6e show that the solar wind proton number density and the magnitude of their bulk velocity (blue lines) remain relatively unchanged. Note that the hyperresistivity, η h, in our model smoothens the magnetic field solution and smears out magnetic field fluctuations in our simulations. Figures 6f 6h show the normalized solar wind proton x-v phase space. We see that v x slightly reduces at close distances to the Moon, while v z gradually increases to nearly 40% of the solar wind bulk velocity. This shows that the solar wind protons deflect over the crustal magnetic fields and move downstream. Most of these protons do not impact the Moon and thus enhance proton number density downstream outside the Mach cone. High flux of reflected protons may disturb the solar wind velocity space distribution and generate kinetic effects in the solar wind. To investigate such effects, we show the velocity space distribution of the solar wind and reflected protons in Figure 7 at four different regions marked in Figure 4b. We select all particles in a cube of one cell size (150 km) centered at each of the four regions and rotate their velocity vectors with respect to the IMF direction. Figures 7a and 7b show undisturbed solar wind protons upstream in the dayside. Figures 7c and 7d show the solar wind protons (red dots) and reflected protons (blue dots) just above the largest cluster of the lunar magnetic anomalies. The solar wind protons get slightly heated, and their bulk velocity component along convective electric field changes due to the interaction with reflected protons. Figures 7e and 7f show that the reflected protons do not access the compressed region outside the lunar Mach cone, while the solar wind protons have more spread in the velocity distribution function. The nonreflected proton temperature is 1.8 times higher than the undisturbed solar wind temperature. Additionally, their velocity distribution function is an anisotropic non-maxwellian with T T 1 1.4, where T and T are respectively the perpendicular and parallel temperature to the IMF direction. In contrast, the velocity distribution inside the wake (Figures 7g and 7h) shows absence of solar wind protons at x = 2R L, FATEMI ET AL American Geophysical Union. All Rights Reserved. 6101

8 Figure 8. Normalized magnetic field magnitude and total proton number density along the vertical solid lines shown in Figure 4d, (a, b) upstream of the Moon at x = 100 km and (c,d) downstream at x = 2 R L for forward deflection (black), cos 2 -specular (red), isotropic (green), and specular (blue) reflection functions. while the reflected protons from lunar dayside access the void and fill it in. The average energy of these protons is 800 ev, which is 75% of the undisturbed solar wind energy. In previous figures we showed the global effects of protons reflected from lunar crustal fields on the lunar plasma environment using forward deflection function. Figure 8 compares the effects of four different reflection functions (forward deflection, cos 2 -specular, isotropic, and specular) on the global lunar plasma environment. Figures 8a and 8c and Figures 8b and 8d compare normalized magnetic field magnitude and total proton number density for these different reflection functions in the meridian plane along the vertical solid lines shown in Figure 4d upstream and downstream of the Moon, respectively. These comparisons show that the global features of the interaction persist, regardless of the type of the reflection function. These global features include magnetic field enhancement in the lunar wake, magnetic field, and plasma density reduction at the expansion region, magnetic field, and plasma compression upstream over the lunar crustal magnetic fields and downstream outside the Mach cone, and plasma wake infilling by the expanding solar wind plasma and reflected protons from lunar dayside. However, the intensity of the magnetic field and plasma compressions clearly depend on the type of the reflection function. Figure 8 shows that the specular reflection (blue lines) predicts the highest and forward deflection function (black lines) predicts the lowest compression in fields and plasma upstream and outside the Mach cone among the presented functions. Moreover, we see from Figure 8c that the magnetic field compression and depression in the lunar wake are also influenced by the type of the proton reflection function. In addition, Figures 8c and 8d show that the angle between the compression region outside the Mach cone and the solar wind plasma flow, as well as the boundaries of the Mach cone, are altered by the type of the reflection functions. 4. Discussions We employed a three-dimensional electromagnetic hybrid model to study the global effects of protons reflected from lunar crustal magnetic fields on the lunar plasma environment. We examined different velocity reflection functions for the reflected particles over lunar crustal magnetic anomalies. Our simulations showed that the global effects of reflected protons on the lunar plasma environment is not very sensitive to the particular reflection function. The differences arise mostly in the magnitude of the fields and plasma perturbations, as shown by Figure 8. In this we considered nominal solar wind parameters at 1 AU, and we assumed that the lunar phase is the new moon. However, the global effects depend on upstream plasma parameters and the orientation of the Moon in its orbit (not shown here). Our simulations show clear signatures of field and plasma compressions in addition to the lunar wake disturbances. Such compressions have also been observed upstream at low altitudes ( 100 km) above lunar magnetic anomalies [Lin et al., 1998; Halekas et al., 2006a, 2008] and downstream adjacent to the lunar wake [Mihalov et al., 1971;Barnes et al., 1971; Russell and Lichtenstein, 1975]. Since we have chosen the upstream solar wind conditions in our simulations the same as those of Holmström et al. [2012], the results of these FATEMI ET AL American Geophysical Union. All Rights Reserved. 6102

9 two studies can be compared. Holmström et al. [2012] assumed that the Moon absorbs all the incident solar wind protons and no reflection was considered. They did not observe any sign of field or plasma perturbations upstream in the lunar dayside, nor outside the lunar Mach cone. Other simulations of the solar wind interaction with the Moon also did not observe extra signatures of fields and plasma compressions [e.g., Kallio, 2005; Wang et al., 2011; Xie et al., 2012]. Thus, the extra signatures we see in our simulation results are due to proton reflection from lunar crustal magnetic fields. Here we only discussed proton reflections from lunar crustal magnetic fields. Nevertheless, observations indicate that protons also reflect from unmagnetized areas with reflection flux ratio lower than 1% [Saitoetal., 2008; Lue et al., 2014]. This can be neglected compared to the 10% reflection from lunar crustal fields. In addition, Holmström et al. [2010] using hybrid simulations showed that the reflected protons from unmagnetized regions do not considerably perturb upstream fields and plasma. In many situations reflected ion beams interact with the solar wind plasma. Examples include ion beams from planetary bow shocks [Behannon et al., 1985;Hoppe and Russell, 1982] and interplanetary shocks [Tsurutani et al., 1983]. This interaction is primarily electromagnetic, generating plasma waves, and instabilities [Winske and Gary, 1986;Gary et al., 1986]. The existence of instabilities may rapidly consume the free energy of the reflected ion beams and assimilate them into the solar wind [Wu and Hartle, 1974]. Considering the relative drift of the reflected ion beams and the background solar wind plasma as the only source of free energy, the right-hand polarized resonant and nonresonant electromagnetic ion/ion instabilities may form, which result in magnetic and plasma fluctuations [Gary, 1991]. Similarly, reflected protons from lunar crustal fields interact with the solar wind and generate electromagnetic waves [Halekas et al., 2006b, 2008; Tsugawaetal., 2011, 2012]. These waves interact with the solar wind and reflected particles, piling up the magnetic fields and compressing plasma upstream, and deflecting the solar wind flow around magnetized areas [Halekas et al., 2006a, 2013], as shown in Figures 4 6 in our simulations. Figures 6a and 6d show that the interaction between reflected protons and the solar wind upstream is a fast magnetosonic mode. The fast magnetosonic waves propagate upstream into the solar wind, perturb magnetic field and plasma (Figures 6a 6d), and deflect the solar wind particles around crustal magnetic fields (Figure 6h). Since the solar wind Mach number is much larger than unity at 1 AU, as listed in Table 1, these fast magnetosonic waves are blown backward and convect downstream by the solar wind. The downstream convected fast-magnetosonic waves form the compression region outside the lunar Mach cone, as shown in Figure 4. They interact with particles and give their energies to them, resulting in plasma heating and changing the particles velocity distribution function from a Maxwellian to a non-maxwellian, as shown in Figures 7e and 7f. In addition, expansion of the compression region may also be another mechanism that results in decreasing of the waves energy density downstream. Therefore, the waves are moderately damped as they move downstream. This is consistent with our simulation results, shown in Figures 4b and 4d, and as was also predicted by Barnes et al. [1971]. Furthermore, the non-maxwellian distribution of the solar wind can perturb the fields and plasma even more as an additional free source of energy to the energy of the reflected protons [Gary, 1991]. Plausibly, this additional energy source, which can trigger proton cyclotron or mirror instabilities, also interacts with the solar wind plasma and heats it up upstream and during its downstream convection. Recent observations show that the magnetic field and plasma compressions upstream of the Moon and their associated generated waves have similarities to the disturbances from the terrestrial foreshock [Halekas et al., 2013]. Moreover, our simulations in Figures 7c and 7d show that the reflected protons upstream the lunar crustal magnetization have broader energy distributions compared to the undisturbed solar wind. This is similar to the so-called intermediate foreshock ion distribution upstream the Earth and Venus [Russell and Hoppe, 1983;Eastwood et al., 2005]. The intermediate ion distributions are an intermediate distribution between the field-aligned reflected particles, which mainly occurs at quasi-perpendicular shocks, and diffuse ions during quasi-parallel shocks [Russell and Hoppe, 1983;Eastwood et al., 2005]. This is, however, due to the IMF angle with respect to the normal vector to the largest cluster of the magnetic anomalies in the southern hemisphere of the lunar farside ( 45 ), which is the main source of the particle reflection in our global simulations. Reflected particles from lunar crustal fields deflect the solar wind, drap the magnetic fields around the Moon, and form a tail-like structure downstream. This analogy is similar to what a bow shock does upstream planets and most of the comets, yet we do not see formation of a bow shock upstream FATEMI ET AL American Geophysical Union. All Rights Reserved. 6103

10 of the Moon. A bow shock could have been formed if the density of the reflected protons were sufficiently higher, and/or if there was a higher rate of mass loading into the interaction region. Similar to the foreshock ion region upstream of the terrestrial planetary bow shocks, we expect to observe right-hand polarized ULF waves in the solar wind rest frame with the frequency of the order of proton gyrofrequency propagating upstream into the solar wind in our simulations. Although observations have confirmed existence of such waves upstream of the Moon [Halekas et al., 2006b; Tsugawaetal., 2012; Halekas et al., 2013], but identification of the wave modes from our simulations are left for future studies. In addition, the time period that the waves are in contact with the reflected protons is also an important factor to determine which type of wave mode (resonant or nonresonant) will dominate the interaction [Onsager et al., 1991]. Since our model does not include the mechanisms by which the proton reflection occurs, it does not consider the effects of those mechanisms in our simulations, i.e., the whistler waves that might be generated at the shocked plasma. In addition, the assumption of fluid electrons in the hybrid models may neglect the effects of reflected electrons. This may result in ignoring the production of VLF emissions associated with these electrons in our simulations. Recently, Fatemi et al. [2013] and Vernisse et al. [2013] using hybrid simulations explained the current system in the lunar Mach cone. They assumed the Moon as a plasma absorber without any proton reflection. Fatemi et al. [2013] assumed a resistive Moon, and they did not detect any signature of magnetic field and plasma compressions outside the Mach cone. Though Vernisse et al. [2013] showed magnetic field enhancement in the lunar dayside which was due to the lunar conductivity in their simulations. However, our simulations here show that the magnetic field perturbations outside the Mach cone result in forming an additional current system to those described previously. Moreover, influences of the reflected protons from lunar magnetic anomalies on the lunar wake magnetic disturbances have impact on the current systems forming inside the Mach cone. However, studying the current systems and the effects of reflected protons on them are left for future investigations. Acknowledgments The work of Shahab Fatemi was supported by the National Graduate School of Space Technology (NGSST), Luleå University of Technology, the Swedish National Space Board (SNSB), and the National Graduate School of Scientific Computing (NGSSC), Uppsala University, Sweden. This research was conducted using resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North (HPC2N), Umeå University, Sweden. 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