Dynamics of solar wind protons reflected by the Moon
M. Holmstrom, M. Wieser, S. Barabash, Y. Futaana, A. Bhardwaj
DDynamics of solar wind protons reflected by the Moon
M. Holmstr¨om ∗ , M. Wieser ∗ , S. Barabash, Y. Futaana, and A. Bhardwaj † October 27, 2018
Abstract
Solar system bodies that lack a significant atmosphere and significant internal magnetic fields, such as theMoon and asteroids, have been considered as passive absorbers of the solar wind. However, ion observationsnear the Moon by the SELENE spacecraft show that a fraction of the impacting solar wind protons are reflectedby the surface of the Moon. Using new observations of the velocity spectrum of these reflected protons by theSARA experiment on-board the Chandrayaan-1 spacecraft at the Moon, we show by modeling that the reflectionof solar wind protons will affect the global plasma environment. These global perturbations of the ion fluxesand the magnetic fields will depend on microscopic properties of the object’s reflecting surface. This solar windreflection process could explain past ion observations at the Moon, and the process should occur universally atall atmosphereless non-magnetized objects.
Traditionally, bodies that lack a significant atmosphere and internal magnetic fields, such as the Moon and asteroids,have been considered passive absorbers of the solar wind (Cravens, 2004). The solar wind ions and electrons directlyimpact the surface of these bodies due to the lack of atmosphere, and the interplanetary magnetic field passes throughthe obstacle relatively undisturbed because the bodies are assumed to be non-conductive. Since the solar wind isabsorbed by the body, a wake is created behind the object. This wake is gradually filled by solar wind plasmadownstream of the body, through thermal expansion and the resulting ambipolar electric field, along the magneticfield lines (Farrell et al., 1998), This picture of the interaction between the Moon (and asteroids) and the solar wind,is based on in-situ observations of ions, electrons, and magnetic fields by many missions (Schubert and Lichtenstein,1974; Ogilvie et al., 1996; Halekas et al., 2005; Nishino et al., 2009b).However, there have been observations that do not easily fit into this picture of atmosphereless bodies as thepassive absorbers of the solar wind.On the Moon, the Apollo 12 and 14 Suprathermal Ion Detector (SIDE) observed energetic ion fluxes at thenightside surface (Freeman, 1972). Also, Nozomi observed non-thermal ions at large distances from, and upstreamof, the Moon (Futaana et al., 2003). Such ions are not easily explained in the traditional picture of the Moon–solarwind interaction.Recent observations at the Moon by the SELENE (Selenological and Engineering Explorer) mission (Saito et al.,2008) and by the Chandrayaan-1 mission (Goswami and Annadurai, 2009) might provide a clue to many of theseunexplained observations. Ion detectors on-board SELENE observed that some of the solar wind protons (around0.1%) are reflected by the Lunar surface, which was unexpected, since it has been assumed that all solar windprotons are neutralized on impact with the Lunar surface (Crider and Vondrak, 2002).Also, the ion detector (SWIM) of the SARA experiment on-board the Chandrayaan-1 mission (Bhardwaj et al.,2005; McCann et al., 2007; Barabash et al., 2009; Wieser et al., 2009) observes these reflected solar wind protons,and in Fig. 1 we show the energy spectrum of one such observation. The sunward sectors of the detector see anundisturbed solar wind, while the surface looking sectors see reflected protons with a broader energy distribution.These observations show that the simplified picture of atmosphereless bodies as passive absorbers of the solar windis incomplete.The reflection of solar wind ions on solar system bodies that lack a significant atmosphere affects the solar windinteraction, where the microphysical properties of the reflecting surface will perturb the global ion and magneticfield environment near the object. We illustrate this effect on the solar wind interaction by modeling results forions near the Moon. In particular, we show that this model can explain the SARA/Chandrayaan-1 ion observations(Fig. 1) and the observations of non-thermal ions by the Nozomi mission (Futaana et al., 2003). ∗ Swedish Institute of Space Physics, PO Box 812, SE-98128 Kiruna, Sweden. ([email protected]) † Space Physics Laboratory, Vikram Sarabhai Space Center, Trivandrum, India a r X i v : . [ phy s i c s . s p ace - ph ] O c t igure 1: Ion observations on February 19, 2009, by the SWIM sensor, of the SARA instrument, on Chandrayaan-1. In (a) and (b) we show ion energy spectra from different directions, and in (c) the observation geometry isillustrated. The view directions are approximately in the equatorial plane, and they are labeled by the angle, Θ, tothe nadir direction. The spectra in (a) show the undisturbed solar wind from 106 and 116 deg, while the spectrain (b) show the protons reflected from the surface. The spectra are averaged over 30 minutes, and are from twelveof the 16 sectors (the remaining four sectors show only background values). The plane of the illustration in (c) isapproximately the equatorial plane. Chandrayaan-1 is in a circular polar orbit at 100 km altitude (Goswami andAnnadurai, 2009). The SWIM sensor has a total field of view of 7 . ◦ FWHM × ◦ divided into 16 sectors, anda time resolution of 8 seconds (McCann et al., 2007). The energy resolution is dE/E = 0 . − .
08, depending onviewing direction. 2
Model
We present a model of the surface reflection of solar wind protons at the Moon and its effects on the global iondistribution in the vicinity of the Moon. Reflection (or back scattering) of solar wind protons on the surface of asolar system body is a process where some of the solar wind protons that impact the surface will recoil on atoms inthe top atomic layers of the regolith, with only a slight reduction in velocity.We assume that there are three basic parameters that characterize the reflection process, (1) the fraction of theprecipitating protons that are reflected, f r , i.e. the probability that a proton is reflected. We assume here thatit is a constant, independent of impact velocity. (2) the speed of a reflected protons, as a fraction of the impactspeed, f v , and (3) the directional (angular) distribution of the reflected protons. The first published observationof reflected protons was by SELENE at the Moon (Saito et al., 2008). Their estimate is that the reflected fraction f r = 0 . − .
01 (this is consistent with estimates from SWIM observations), and that the velocity magnitude ofthe reflected protons is 80% of the solar wind velocity magnitude, f v = 0 .
8. Regarding the angular distributionof the reflected protons, Saito et al. (2008) find that it is much broader than that of the solar wind ions, thusthe observed ions are not specularly reflected but rather scattered at the lunar surface. Since the exact angulardistribution is unknown, we have used four different reflection models for determining the velocity direction of thereflected ion. • Specular. For specular reflections, the protons’ velocity vector before and after the reflection are in the sameplane, and the angle to the surface normal is the same. So, an ion inside the spherical obstacle at the position r , with velocity v , is reflected by updating the velocity to v (cid:48) = v − v · ˆr ) ˆr , where ˆr = r / | r | . • Perpendicular, v (cid:48) is perpendicular to the surface of the spherical obstacle (parallel to the surface normal). • cos -perpendicular. The angle between v (cid:48) and the surface normal, θ , is randomly drawn from a cos θ proba-bility distribution. • cos -specular. The angle between v (cid:48) and the direction of specular reflection (see above), θ , is randomly drawnfrom a cos θ probability distribution.These different reflection models are illustrated in Fig. 2d. If not noted otherwise, we have used the cos -specularreflection model since that gave the best fit to the observations.When a solar wind proton has reflected, it will travel in a cycloid motion, gyrating around the magnetic fieldlines. The motion of the ion with charge q i and velocity v i = v i ( t ) is governed by the Lorentz force, q i ( E + v i × B ) = q i ( v i − v sw ) × B sw since the solar wind convective electric field is E sw = − v sw × B sw . Here v sw and B sw is the solar wind velocity,and the IMF, respectively. We have assumed constant solar wind conditions.For an ion with zero initial velocity, this lead to the classical trajectory of a pick-up ion as illustrated in Fig. 2a.Since the reflected protons have non-zero velocity in a coordinate system where the reflecting body is stationary,the trajectory will be different, as shown in Fig. 2b. In addition to the cycloid motion perpendicular to the IMF,the ion will also drift with a constant velocity along the IMF, if the initial velocity of the ion had a non-zero velocitycomponent along the IMF. The trajectories of five ions, launched perpendicular to the Lunar surface at (lng,lat)= (0,0) and (+-30,+-30) degrees with velocities of 175 km/s in a 350 km/s solar wind are shown in Fig. 2c as anillustration of this combined cycloid and drift motion. The solar wind magnetic field has a magnitude of 3 nT andis directed along ( − , , x -axis from the center of the Moon toward the Sun, the y -axis in the ecliptic plane, and the z -axis in thenorthern ecliptic hemisphere.Previous investigations of ion trajectories near the Moon have considered ions produced by photoionization ofexospheric neutrals (Manka and Michel, 1970, 1973), not reflected ions. Neither has previous global models ofthe Moon’s interaction with the solar wind included reflected solar wind protons (Kimura and Nakagawa, 2008;Tr´avn´ıˇcek et al., 2005; Kallio, 2005; Harnett and Winglee, 2003). However, in a more general setting, Shimazu(1999) saw acceleration of reflected ions in hybrid simulations of plasma flow around a generic obstacle.For the modeling of reflected protons at the Moon we have used a test particle approach, where the trajectory ofeach proton is computed by integrating the Lorenz’ force for constant solar wind conditions, i.e. constant solar windconditions throughout the simulations domain. In what follows, the coordinate system used is centered at the Moonand has its x -axis toward the Sun, a z -axis perpendicular to the ecliptic plane, in the northern hemisphere, and a3igure 2: (a) The cycloid trajectory of a pick-up ion where the initial velocity is zero, and a solar wind of velocity v is inflowing from the right. The solar wind magnetic field, B sw , is directed out of the page. The solar windconvectional electric field is E sw = v × B sw . The ion velocity vary between 0 and 2 v along the trajectory. (b)The trajectory of an ion injected into the solar wind with velocity − v . This is equivalent to a pick-up ion withzero velocity in a solar wind of velocity 2 v , as seen by an observer moving with velocity − v . In the frame of theillustration, where the plasma flow to the left with velocity v , the ion velocity will vary between − v and 3 v alongthe trajectory. (c) Sample trajectories of protons launched perpendicular to the lunar surface. (d) Illustration ofsome different reflection models, i.e. different ways of selecting the direction of the velocity vector of a proton thathas reflected on the planetary surface. 4 -axis that completes the right handed system. The outer boundary of the simulation domain is a box centeredat the Moon with sides of length 8000 km. The inner boundary is a sphere of radius 1730 km. At the start ofthe simulation the domain is empty of particles. Before each time step we fill the x -axis shadow cells (cells justoutside the simulation domain) with proton meta-particles with weight N m = 7 . · (number of real protons permeta-particle). The proton meta-particles are drawn from a Maxwellian distribution with a specified temperatureand bulk velocity. After each time step the shadow cells and the obstacle region are emptied of protons. A fraction, f r , of the protons found inside the obstacle are selected to be reflected, randomly, with a velocity magnitude that isreduced by a fraction f v . The boundary conditions in the y - and z -directions are periodic. We have N I (meta-)ionsat positions r i ( t ) [m] with velocities v i ( t ) [m/s], mass m i [kg] and charge q i [C], i = 1 , . . . , N I . Using a Leap-Frogintegrator, the trajectories of the ions are computed from the Lorentz force, d r i dt = v i , d v i dt = q i m i ( E + v i × B ) , i = 1 , . . . , N I where E = E ( r , t ) is the electric field, and B = B ( r , t ) is the magnetic field, and time is stepped forward by 0.05 sIn Fig. 3 we show results for a model run with a solar wind with a velocity of 350 km/s, a temperature of 48000 K,and a magnetic field that is ( − . , . ,
0) nT, at time 20 s (when the solution has reached a steady state). Thevelocity of the reflected protons is reduced by f v = 0 .
5. Note that this is for the case of complete reflection of allprecipitating protons ( f r = 1), but this can be scaled for other reflection fractions, e.g., by 1/100 for a 1% reflection.In reality the solar wind flow is affected by the presence of the Moon and the reflected protons. To correctlymodel this a self-consistent model is needed, at a considerable computational cost. Also, since this is a first attemptto model the effects of reflected protons, and the details of the reflection process is not known, a fully self consistentmodel of the process would not add much to the investigation. To justify the use of the test particle approach wedid a self-consistent hybrid model (Holmstr¨om, 2009) run using the same parameter values as used in Fig. 3. Theresult is shown in Fig. 4. We see that the morphology of the reflected ion fluxes are similar, although the maximumflux is smaller in the test particle case (0.065 times the solar wind flux, i.e. 1.3 times the reflection of 0.05 usedin the hybrid model) compared to the hybrid model (0.08), probably due to statistical fluctuations in the hybridsimulation. In the hybrid simulation we also see the wake refill behind the Moon, which is not present in the testparticle simulation, but that is acceptable, since we are mostly interested in the dayside dynamics of the reflectedsolar wind protons. We now investigate in more detail the general morphology of the reflected ions. The proton flux, in directionsperpendicular to the solar wind flow direction, around the Moon is shown in Fig. 3a. The global effects of thereflected protons are clearly visible. The reflected solar wind protons create a plume of ions that initially areaccelerated along the solar wind electric field direction, then drift along the IMF direction, and gyrate perpendicularto the IMF. The density of reflected ions is highest near the sub solar point, then decrease tailward from dispersiondue to different initial velocities. At the cusps of the cycloid motion there is however a density increase, as seen inthe lower left corner of the middle plot of Fig. 3a. The maximum density is 1.3 times the solar wind density whenall protons are reflected. So if 1% of the solar wind protons are reflected the maximum density would be 0.013times the solar wind density.In Fig. 3b is shown the meta-particles that correspond to the reflected ions. The cycloid motion, and accelerationalong E sw is again clearly visible. The velocity spectrum of all protons in the simulation domain in Fig. 3c, showsthe solar wind population, and the much broader distribution of reflected ions. This broadening of the spectrumis consistent with the broadening of the observed spectrum for look direction toward the lunar surface, as shownin Fig. 1b. The similarity between the observed and modeled spectrum is even better if we only include protons inthe model that are close to the position of Chandrayaan-1 at the observation time. In Fig. 5 we show the spectraof reflected protons in three latitude bands, with Fig. 5b corresponding closest to the observation position in theecliptic plane. Only protons with velocities away from the Moon are included, to approximate the SWIM viewconditions. The observed spreading of the solar wind spectrum to lower and higher energies is seen in the modelspectrum. That the peak of the model spectrum is so much lower in energy than the solar wind (not seen in theobserved spectrum), might indicate that the model reduction in velocity ( f v = 0 .
5) is too large. This is consistentwith the SELENE observation that f v = 0 . yz -component of the proton numberflux (number density times average velocity) around the Moon, relative to the magnitude of the solar wind protonnumber flux. This is for the case of 100% reflection ( f r = 1) of the precipitating protons, but can be scaled for anyother value of f = 1. Shown are cuts through the planes x = 0 (left), z = 0 (middle), and y = 0 (right). (b) Thereflected proton meta particles, colored by velocity magnitude (relative to the solar wind velocity). (c) The velocityspectrum of all protons in the simulation domain. The x -axis unit is km/s, and the y -axis scale is logarithmic inarbitrary units. The solid line is the reflected protons, and the dashed line is the solar wind protons.6igure 4: Solar wind proton reflection using a hybrid model. Shown is the magnitude of the yz -component of theproton number flux, as in Fig. 3a. The test particle run is the same as in Fig. 3. The additional parameters forthe hybrid run is n sw = 5 cm − , T e = 10000 K, γ = 5 /
3, ∆ t = 0 .
08 s, five subcycles per time step, f r = 0 . − . , . ,
0) nT. However, there areuncertainties in this IMF estimate since the direction was obtained from the observed temperature anisotropy inthe electron velocity spectrum, and Futaana et al. (2003) estimate the uncertainty in IMF direction to 20 ◦ . Dueto this uncertainty, and since the trajectories of reflected protons are sensitive to the IMF, we tried different IMFsand found a best fit for ( − . , . ,
0) nT, i.e. about 25 ◦ away from the estimate by Futaana et al. (2003). In Fig. 6we compare velocity space plots of the test particle model with Nozomi’s ion observation (Fig. 5 in Futaana et al.(2003)).We see clear similarities in the observed and modeled velocity space distributions. This shows that reflectedprotons is a possible explanation for the observed nonthermal ions. The discrepancies in distributions could be dueto a change in the IMF between the two observation times. For an illustration of the observation geometry, seeFig. 2 in (Futaana et al., 2003). This show that the Nozomi ion observations, even upstream of the moon, can beexplained by reflected solar wind ions.To illustrate the global effects of different assumptions for the local reflection process, Fig. 7 show the effect ofperpendicular reflection, and of no velocity loss at reflection, f v = 1. The perpendicular reflection model give lessvelocity dispersion of the reflected ions, and lead to more than three times the solar wind number flux (assumingall protons are reflected). No velocity loss at reflection on the other hand lead to a larger velocity dispersion, anda more diffuse plume of ions, with only 0.7 times the solar wind flux.To illustrate the sensitivity of the reflected protons to the microphysics of the reflection process, we show inFig. 8 how the velocity space distributions of the reflected protons change when we assume a cos perpendicularand a specular reflection model. We can compare the surface reflected ions with pick-up ions, observed at comets, Mars and Venus. In a framefollowing the reflected ions, the situation is similar. So a reflected proton behaves as a pick-up ions seeing a fastersolar wind (from different directions for all reflected ions). This will create a ring distribution in velocity space,as was observed at the Moon (Futaana et al., 2003). The cycloid trajectory of these reflected ions can take themdeep into the wake of the Moon, which has been observed by SELENE (Nishino et al., 2009a), giving a possibleexplanation for the Apollo observations of solar wind energy ions at the night side surface of the Moon (Freeman,1972). These were bursts of ions in the keV range, with fluxes of the order 10 cm − s − sr − , and mass per unitcharge less than 10 amu/q, and hence thought to be of solar wind origin.7igure 5: Energy spectra of reflected protons (solid lines) and solar wind protons (dashed lines). Corresponding tothe spectrum in Fig. 3c, but instead of including all protons in the domain, each spectrum is for selected regions ofthe simulation domain. The included protons are those on the dayside ( x >
0) at altitudes less than 200 km with z coordinates in the ranges (a) z >
500 km, (b) -500 < z <
500 km, and (c) z < −
500 km. The solid line is thereflected protons, and the dashed line is the solar wind protons. The y -axes are logarithmic in arbitrary units.8igure 6: The reflected protons in velocity space. Comparison of (a) test particle model at time 120 s, with (b)Nozomi observations. Top row is the velocity space distribution projected along B sw (left) and perpendicular to B sw (right). Shown are all simulation meta-particles in a cube with side of 500 km, centered at the positions of theobservations, (2500,-3700,-900) km and (-600,-5500,-1400) km, respectively. These positions are shown in Fig. 4.In gray are the solar wind protons, and in black are the reflected protons. The plots in (b) are from Futaana et al.(2003, Fig. 5). The solar wind conditions used in the simulation has a velocity of 350 km/s, a temperature of48000 K, and a magnetic field that is ( − . , . ,
0) nT. The reflection model is cos specular.Figure 7: Different reflection processes. Here it is illustrated how the global solar wind interaction is perturbedby changes in the local microphysics of the reflection process. Shown is the magnitude of the yz -component of theproton number flux, relative to the magnitude of the solar wind proton flux, in the plane x = 0, when the reflectedprotons are (a) perpendicular to the lunar surface with f v = 0 .
5, and (b) reflected according to the cos -specularmodel, without losing velocity ( f v = 1). The different reflection processes are illustrated in Fig. 2d and the colorscale is the same as in Fig. 3a. All other parameters for these two simulation runs are the same as for that in Fig. 3.9igure 8: The reflected protons in velocity space from the test particle model for the same Nozomi comparison asshown in Fig. 6. This is a comparison of two different reflection models. (a) cos perpendicular, and (b) specular.Both cases has the same solar wind conditions as in Fig. 6.It is interesting to note that a local process (surface reflection) can perturb the global interaction of the Moonwith the solar wind. Also, the character of this global interaction depends on the details of the local process, e.g.,the velocity distribution of the reflected protons. Thus, it is possible to infer properties of the local reflection processfrom far away observations of the ion distributions.If we consider the energies involved in the reflection process, the kinetic energy density of the reflected ions is W r = f r n sw m p ( f v v sw ) / m p is the proton mass, and the magnetic field energy density is W B = B sw / (2 µ )where µ is the magnetic constant. Using f r = 0 . n sw = 5 cm − , f v = 0 . v sw = 350 km/s, and B sw = 3 nT,we get that W r /W B = 0.35. Thus, the kinetic energy density of the reflected ions is a significant fraction of thesolar wind magnetic field energy density, and the reflected ions should be a strong source of wave activity.We can compare these reflected protons with the protons reflected by Earth’s bow shock. There, in Earth’sforeshock region, these ion beams propagate upstream in the solar wind. It is a classical case of an electromagneticcounter-streaming beam situation, with the beam density around 1% of the solar wind density. This causes waveactivity, and has been studied for a long time in great detail, see e.g. Tsurutani and Rodriguez (1981).The reflection of solar wind ions should be a universal process that occur at all bodies without a significantatmosphere, e.g., at asteroids, and at the Martian moons Phobos and Deimos. Acknowledgments
This research was conducted using the resources of the High Performance Computing Center North (HPC2N),Ume˚a University, Sweden, and the Center for Scientific and Technical Computing (LUNARC), Lund University,Sweden. The software used in this work was in part developed by the DOE-supported ASC / Alliance Center forAstrophysical Thermonuclear Flashes at the University of Chicago.
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