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Release processes of exospheric particles from Mercurys surface

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Release processes of exospheric particlesfrom Mercury`s surface

H. Lammer, and C. Kolb

136

December 2001

Space Research Institute, Dept. for Extraterrestrial Physics,Austrian Academy of Sciences,

Schmiedlstr. 6, A-8042 GrazAustria

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Contents

1 Introduction 3

2 Origin of Mercury 4

3 Mercury’s planetary parameters 5

4 ESA’s Planetary Mercury Orbiter (MPO) 6

5 Surface composition of Mercury 6

6 Mercury’s exosphere 7

6.1 Simulation of particle velocity distributions by random numbers 9

6.2 Velocity distributions of photon-stimulated desorption and particlesputtering 10

6.3 Micrometeoroid driven velocity distributions of Na and K atoms 11

7 Particle energy and ejection angle distributions as function ofaltitude 13

7.1 Ejection angle dependence of surface sputtered particles 14

8 Results 15

8.1 Energy and ejection angle distributions of photon-stimulateddesorption processes 16

8.2 Energy and ejection angle distributions of micrometoritevaporised particles 18

7.3 Energy and ejection angle distributions of surface sputteredparticles 19

9 References 20

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1 Introduction

A detailed investigation of Mercury`s exosphere-surface interaction by the MercuryApparatus for Ions and Atoms (MAIA) on the planned Neutral Particle Analyzer (NPA)instrument on board of ESA`s Mercury Planetary Orbiter (MPO) will give the scientificcommunity for the first time the change to study in detail the efficiency of various gasrelease processes from a planetary surface. Particle ejection processes like, photon-stimulated desorption, electron stimulated desorption, thermal desorption and particlesputtering of surface constituents depend mainly on mineralogical and geochemicalproperties of Mercury`s surface, the incoming solar UV radiation flux, X-ray fluxes, aswell as galactic cosmic ray and energetic solar-wind particle exposure.

Our study investigates energy and ejection-angle distributions of H, He, O, Na andK atoms as a function of altitude in Mercury’s exosphere. The particles involved inenergetic processes are released from the planetary surface with a Mote-Carlo simulatedvelocity distribution which resembles the velocity distribution for photon-stimulateddesorption (H, He, O, and Na), induced surface sputtering of O and Na atoms andparticles released from micrometeoroid vaporization (Na and K) very well.

We found that H, He, O, Na and K atoms will reach altitudes up to MPO`speriherm and apoherm of 400 km and 1500 km. Heavy particles like O, Na and K canonly reach the spacecraft altitude if they originate by energetic source processes likeparticle sputtering or micrometeoroid vaporization. The NPA/MAIA instrument willtherefore have the possibility to separate particles which are released from the surfaceinto Mercury`s exosphere via low energetic thermal desorption processes from moreenergetic exospheric populations who have their origin in charged particle sputteringprocesses and micrometeoroid vaporization.

Since the heavy exospheric particles which are ejected from Mercury`s surface havetheir origin from the surface material, the NPA investigation will give us not only adetailed knowledge of the chemical composition of Mercury`s exosphere, we will getalso information about the planetary surface composition and the mineralogy of thesurface material.

A comparison of core sizes between Venus, Earth and Mars show that Mercury`sinterior consist only of a very tiny mantle and an extremely large iron core with a radiusof 70 to 80 % of the whole planet. Recent studies on isotope anomalies in planetaryatmospheres (Bauer, 1983; Lammer et al., 2000, Lammer et al., 2001), meteoroids andX-ray observations by the ROSAT, ASCA and CHANDRA satellites of solar-like G-typestars with various age, indicate that our early Sun may have underwent a very activeperiod over the first 600 million years where the solar-wind mass flux and the soft X-ray flux was hundreds to thousand times larger than at present (e.g. Güdel et al. 1997;Guinan, Ribas, Harper, 2002). Additionally the solar irradiance was also higher thantoday. Since Mercury is the closest planet to the Sun its surface was exposed more thanall the solar system bodies by such an enhanced early solar-wind and radiation flux. Adetailed analysis of photon-stimulated particle desorption processes and charged particlesputtering in the frame of ESA`s BepiColombo mission will give us the opportunity toinvestigate the possibility if such an early active Sun was responsible for enhancedsublimation processes and blow off of Mercury`s silicates.

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A confirmation by MPO of these erosion effects related to an early active Sun wouldhave important consequences for the evolution of planetary paleoatmospheres, as wellas to the particle and radiation exposure to organic molecules in early planetary systems.

2 Origin of Mercury

Mercury is one of the four terrestrial planets whose detailed study will enhance ourknowledge concerning the evolution of the inner part of the solar system, particularlybecause Mercury is seen as a so called “end-member-planet” with astonishing features.One of these features is its large iron core, resulting in a Fe/Si-ratio in the range from66:34 to 70:30 and an uncompressed bulk density of around 5.3 g cm-3. Several modelswere deduced since the second half of the last century. Three of these are able to explainthe unusual Fe/Si-differentiation without considerable inconsistencies. The first twoscenarios consider Mercury’s proximity to the center of the solar system.

• Iron/silicate-fractionation during accretion

This model considers scenarios involving differences in the physical properties ofmetallic iron and silicates (density, ferromagnetism, mechanical strength) during theaccretion phase of the planet (Harris and Tozer, 1967; Orowan, 1969; Weidenschilling,1978; Smith, 1979). Weidenschilling, (1978) proposed that Mercury is special in thisregard due to the higher gas density and shorter dynamical time scales in proximalregions of the ancient accretion disk.

• Thermal sublimation, physical abrasion and blow off of Mercury’s silicatemantle due to the activity of the young Sun

It is known that young stars undergo an intensive phase of activity which results in amuch higher solar flare activity and in some cases huge ultrasonic gas bursts and X-rayreleases during a so called post T-Tauri phase. Extreme solar-winds could introducethermal shock-waves into the due to accretion still heated proto-planets which leads to ahigher temperature level and gas density in the early solar system. The molten silicate-mantle may not be able to withstand the solar force and remains as a refractory richresidual.

Several works were done to employ the Suns heat to proto-Mercury (Bullen, 1952;Ringwood, 1966; Sagan, 1974; Cameron, 1985; Fegley and Cameron, 1987 andCameron et al., 1988). By studying the “Sun in time” it is possible to apply new modelsof solar evolution on Mercury – this represents an advantage of verifying both models.

• Huge planetary impacts

It is assumed that major planetary impact could drove off much of Mercury’s silicatemantle (Smith, 1979; Wetherill, 1985; Benz et al., 1986a, 1986b, 1987a, 1987b andCameron et al., 1988). Cameron et al., (1988) showed that an iron-cored projectile(0.38 times the mass of present Mercury), centrally colliding a target (2.25 times themass of present Mercury) at 20 km s-1, could produce the present planet and its Fe/Si-ratio. The target was assumed to be of chondritic composition. Most of the ejected massshould be vaporized and finally collected by the Sun.

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Two features of Mercury speak for the last two models: The globally distributedintercrater-plains seem to be of volcanic origin (Strom, 1977) and their age isdetermined to around 4.2 – 4.0 Gyr. This plains could be the remnants of a globalresurfacing event during the time of the “late heavy bombardment” (Spudis and Guest,1988 and Strom and Neukum, 1988). Abundant lobate scarps are possibly formedbetween 4.0 and 3.85 Gyr (Strom et al., 1975; Solomon, 1977; Strom, 1984; Leake et al.,1987; Spudis and Guest, 1988 and Strom and Neukum, 1988) and could be evidence of aglobal compression phase after cooling of the molten silicate-mantle.

To explain the origin, it is important to obtain the chemical properties of Mercury.Owing to meteoritic impacts over billions of years, the surface is contaminated withmeteoritic material - only the intercrater-plain-bedrocks may represent unmodifiedregolith. Hence, to explain the forming process of the planet, it is necessary not only toanalyze the surface-mineralogy, but also to reveal the detailed internal constitution withseismic studies. Phase transitions could indicate changes in chemical and mineralogicalcomposition, leading to a better understanding of the processes which have formed it.

3 Mercury`s planetary parameters

Mercury looks like our Moon, but this planet had a complete different evolution and isquite different in many aspects. Mercury differs also from all the other terrestrial planetslike Venus, Earth and Mars. Distinctive features include the:

• Resonance of Mercury`s spin and orbital periods.• Composition and density.• The state of its core.• The planetary magnetic field.• The topography of its surface.• The origin of the thin exosphere.

The planetary bulk and orbital parameters of are shown in Table 1.

Bulk parameters Orbital parametersMass: ≈ 0.3302 × 1024 kg Semi-major axis: 57.9 × 106 kmVolume: ≈ 6.085 × 1010 km3 Perihelion: 46 × 106 kmEquatorial radius: 2440 km Aphelion: 69.8 × 106 kmMass density: 5.427 g cm3 Eccentricity: 0.2056

Surface gravity: 3.8 m s-2 Inclination: 7.0°Escape velocity: 4.3 km s-1 Mean orbital velocity: 47.89 km s-1

Siderial orbit: 87.969 days

Synodic rotation period: 115.88 days

Solar irradiance atperihelion: 14490 W m-2

aphelion: 6290 W m-2Siderial rotation period: 1407.6 h

Table 1: Marcury`s bulk and orbital parameters.

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4 ESA`s Planetary Mercury Orbiter (MPO)

ESA`s BepiColombo Mercury mission is an ESA cornerstone consisting of twospacecraft, a Planetary Mercury Orbiter (MPO) and a Magnetospheric Mercury Orbiter(MMO) and one landing unit which is called Mercury Surface Element (MSE). Thescientific objectives of this mission are summarized in Table 2.

Scientific objectives of ESA`s BepiColombo missionStudy the origin of a terrestrial planet close to the parent star

Planetology: form, interior structure, geology, composition, cratersStudying the origin of Mercury`s intrinsic magnetic fieldStudy of Mercury`s exosphere, composition and origin

Magnetospheric structure and dynamics

Test of Einstein`s theory of general relativity

Detection of potentially Earth-threatening asteroids

Table 2: The table shows the main scientific objectives of ESA`s mission to Mercury.

The planetary orbiter is a three-axis stabilized spacecraft and will play the main role inthe investigation and study of Mercury`s exosphere. The spacecraft payloads carriesinstruments devoted to:

• Close range studies of Mercury`s surface;• Measurements of the planetary gravity field and rotational state;• Tests for general relativity;• The observation of dangerous near Earth Objects.

The orbit is polar to facilitate global scanning and as low as possible for optimizing thespatial resolution. The periherm and the apoherm are at altitudes of 400 and 1500 km.Many of the remote sensing instruments have their apertures in the base of the body andpoint constantly along the nadir direction for a continuous observation of Mercury`ssurface. The total data volume collected by MPO is 1550 Gb for a lifetime of about oneyear. The MPO spacecraft data and an illustration are summarized in Table 3.

Stabilization 3-axisOrientation Nadir pointing

Mass 357 kgEnergy power 420 WAntenna 1.5 m diameterOrbit altitudes 400 to 1500 kmLifetime > 1 yearData volume 1550 Gb / yearAverage bit rate 50 kb / s

Table 3: The table summarizes the MPO data and the illustration of the right side showsthe MPO spacecraft orbiting above Mercury`s surface.

5 Surface composition of Mercury

Up to now, only reflectance spectroscopy and visual albedo studies were obtained todetermine the surface composition of Mercury (McCord and Adams, 1972; Hapke et al.

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1975; Vilas 1988). This spectra fit very well to the lunar highland-soils - indicatingsimilar weathering processes. The lunar soils consist of abundant Fe- and Ti-bearing,agglutinitic glasses (Adams and McCord, 1973). Submicroscopic metallic iron formscoatings on soil particle surfaces and inside agglutinates. McCord and Adams (1972)found evidence for a weak Fe2+-orthopyroxene absorption feature. However Hapke etal. (1975) related it to incomplete removal of telluric H2O. Weathering effects on theregolith of Mercury have been discussed by Hapke (1977), Rava and Hapke (1987) andHapke (2001). Although it is very similar to that on Moon, there are particulardifferences.

Melting due to micrometeoritic impact is important for both celestial bodies. Cintala(1992) showed that on Mercury the impact-rate is 5.5 times greater and the meanimpact-velocity is more than 60% higher than it is on Moon. This leads to almost 14times more impact melt production per unit time. Therefore, Mercury soils might alsoconsist more of glassy components.

The sunward portion of Mercury is heated between 590 to 725 K, much more as it ison the Moon (~300 K). Killen (1989) demonstrated that the diffusion of alkali-elementsout of glassy material under Mercury`s conditions is very efficient. In contrast to this onthe Moon sodium is concentrated on the rims of glassy agglutinates. Obviously thealkalis condense on the hot glass-spherules (Kurat and Keil, 1972). For both bodiesdiffusion alone is inadequate to explain the high Na and K content of the exospheres(Killen, 1989).

Already Wehner (1961) proposed that darkening of lunar soils is due to unattenuatedexposure to the solar-wind. For example, protons with energies of around 1 keV areable to sputter atoms out of the crystal lattice. The released neutral particles condenseon the grain surfaces or escape to the exosphere, depending on their vapor pressure.While metallic iron is known to form nanocrystalline adsorbates, alkali-elements andoxygen are released easier to the exosphere. Metallic iron accounts for the darkening ofthe soils and their magnetic properties (Hapke, 1973, 2001).

Although surface sputtering and impact vaporization are different processes,numerous experiments showed that the results are quite similar (for example Wehner,1964; Hapke, 1966, 1973; Hapke et al., 1975; Moroz et al., 1996 and Yamada et al.,1999). On the Moon surface sputtering due to the solar-wind particles is an importantprocess (Hapke, 1973). Mercury possesses an intrinsic magnetic field, therefore solar-wind sputtering may be less important than impact vaporization (Hapke, 2001). Cintala(1992) estimated the impact vapor production and concluded that more than 20 timesmore vapor is generated per time unit on Mercury than it is on the Moon.

6 Mercury’s exosphere

The existence of H, He, O, Na and K particles were established by EUV spectroscopicobservations on Mariner 10 for the first three and Earth based telescopic observationsfor the last two species with column contents of the orders of 1012 or less. Such columncontents qualify the gaseous envelope of Mercury as an exosphere (exospheric columncontents are per definition ≤ 1014 cm-2). The light constituents H and He are thought tobe solar-wind ions, which impinge on the daytime surface, become neutralized and thenre-enter the exosphere with the average exospheric daytime temperature of about 540 K.The heavier constituents can arise from photon-stimulated desorption (Madey andYakashinskiy, 1998; Yakashinskiy and Madey, 1999) particle sputtering (Lammer andBauer, 1997) and micrometeoroid vaporization (Morgan et al., 1988) of Mercury`ssurface materials.

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Observations by Potter and Morgan (1986) of sodium atoms indicate that Na extends toaltitudes which are higher than 700 km above the surface at the subsolar-point, implyingthe existence of a non-thermal sodium corona (Lammer and Bauer, 1997). Figure 1shows the particle surface release processes, their estimated Na source rates and theestimated surface number densities of various exospheric constituents.

Fig. 1: Main particle surface release processes and estimated source rates for Na in s-1

on Mercury. One can see that the source rate values are very uncertain for photonstimulated desorption and particle sputtering processes. The surface number densitiesfor the heavy p articles correspond in this table to low energetic particle releaseprocesses and are related to their column densities. If a more energetic process likeparticle sputtering is more important than thermal processes than the surface numberdensities of the released particles may be lower but the particles are extended tohigher altitudes above Mercury`s surface.

there is a great uncertainty in the estimation of the particle release processes fromMercury`s surface. Particle sputtering of Mercury’s surface caused by bombardment ofsolar-wind protons, alpha particles and heavy ions in the auroral zones was firstdiscussed by McGrath et al. (1986), by Cheng et al. (1987) and by Killen (1989).

McGrath (1986) suggested that photon-stimulated desorption processes may bemore likely than charge particle sputtering and estimated the photon desorption fluxesfor Na to be of the order of 2 × 107 - 2 × 108 cm-2s-1. Killen and Morgan (1993)however argued that these fluxes are optimistic since they were based on data for alkali

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halides. The photon-stimulated desorption yield depends critically on the low energycut-off of photons capable of ejecting Na. Sodium can only ejected from the surface bylight with energy larger than the band gap (Townsend and Elliot, 1970).

Killen et al. (1990) therefore assumed that photons beyond this band gap (for NaCL≈ 10 eV) can release Na atoms and obtained an average Na flux of only about 2 × 105cm-2 s-1, by assuming a lunar Na abundance. Shemansky and Morgan (1991), on theother hand etimated an Na flux caused by photon-stimulated desorption of only about 2× 104 cm-2 s-1 atoms. One can see the discrepancy between the estimated productionrates of exospheric Na by photon-stimulated desorption of nearly 4 orders ofmagnitude.

The study of Mercury`s exosphere-surface interaction by the NPA-MAIAinstruments on board of MPO is essential for the determination for the efficiency of thevarious particle ejection processes of Mercury’s surface constituents.

6.1 Simulation of particle velocity distributions of by random numbers

We assume in this study that the particles involved in surface release processes areejected from Mercury’s surface with a Monte-Carlo simulated velocity distribution(Hodges, 1973) which resembles the velocity distribution for photon-stimulateddesorption (H, He, O, and Na), induced surface sputtering of O and Na atoms andparticles released from micrometeoroid vaporization (Na and K) very well.

Figure 2 shows angular relationships used to describe the points of origin, thetrajectory and the impact point of an ejected particle. The coordinate systems on theright side correspond to the particle velocity vectors as function of their direction.

Fig. 2: Definition of angles and locations that specify points of origin and impact and thedirection of departure of particles ejected from Mercury`s surface. ΘΘΘΘ0 in equations (2) and(3) corresponds to the definition of the planetary location where the particle has its origin,which will be relevant for future studies .

α0

z,z

vx x

vy

y

xv0vz0 = vz0

vx0

α: ejection anglev: particle velocityvx, vz: velocity components

in x and z direction

•point of origin

F

Mercury

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We use for the calculation of the particle trajectories the projection in the x – z area. α0is the surface ejection angle of the released particle. A set of three Gaussian deviates isgenerated to determine the velocity from the distribution. The Gaussian deviates,denoted Xi are found by using a relation given by Hodges (1973):

Xi = [ -2 ln(R1i) ]0.5 cos(2πR2i) (1)

where R1i and R2i are random numbers between 0 and 1. The variance of each Xi is 1.Therefore, the identification can be made by:

Xi = ( m/kT )0.5 [vi - δi1 ωRM sin(Θ0)] (2)

vi = Xi ( m/kT )-0.5 + δi1 ωRM sin(Θ0) (3)

where m is the particle mass, vi the velocity components in x, y and z direction (i=1=x;i=2=y; i=3=z), k is the Boltzmann constant.

6.2 Velocity distributions of photon-stimulated desorption and particlesputtering

T is the temperature at the point of origin (Mercury’s average dayside surfacetemperature is about 540 K), or in the case of particle sputtering, the temperaturecorrespond to the energy of the majority of the sputtered particles (TO ≈ 11600 K; TNa ≈19740 K). RM is the radius of the planet, ω is Mercury’s angular rotation rate and δi1 theKronecker delta function. The particle velocity v0 at the point of origin on Mercury’ssurface is:

v0 = [v12 + v2

2 + v32]0.5 (4)

Figure 3 shows the velocity distribution of particles released by low energetic photon-stimulated desorption processes.

Fig. 3: The figure shows the velocity distribution of Na, O, He and H atoms in km/sreleased to Mercury’s exosphere via photon-stimulated desorption calculated by themodel described above. The shape of the velocity distribution of heavy Na atoms agreeswell with the Na velocity distribution obtained by Yakashinskiy and Madey (1999) vialaboratory experiments.

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Where Eb is the surface binding energy and Ei the energy of the incident particles.Although the surface composition of Mercury is not well known, Na is likely to bebound to O with a binding energy of about 2 eV, as for example in NaAl2Si3O8(McGrath et al., 1986; Cheng et al., 1987). Oxygen atoms are themselves tightly boundto the molecule, their overall binding energy Eb is about 3 – 4 eV (Johnson, 1995),where the incident solar-wind protons have energies around 1 KeV. Figure 4 shows theparticle velocity distribution simulated via the Monte-Carlo technique described above.

Fig. 4: The figure shows the velocity distribution of heavy Na and O atoms which are producedby particle sputtering. The velocity distribution is a result of our Monte-Carlo simulation andagrees well with the calculated energy distribution function of Lammer and Bauer (1997).

6.3 Micrometeoroid-driven velocity distributions of Na and K atoms

Micrometeoroids may contribute Na and K atoms to Mercury’s exosphere, since themeteoroid population in the inner solar system is not so rich on water like populations inthe outer solar system, which is more cometary like and supplied from comets whichhave their origin in the Kuiper Belt. On the other hand, the impact of micrometeoroidswill also evaporate particles from Mercury`s surface which are incorporated to theproduced vapor in general.

The number of Na and/or K atoms added to Mercury`s atmosphere via impact-driven supply each second depends on the mass of the infalling material pro second andon the meteorite impact velocity. It should also be noted that the elemental abundanceof Na and K in the surface regolith and in the micrometeoroid population regulate thenumber of Na or K atoms that are added to the exosphere. Table 4 shows variousparameters related to micrometeoroid vaporization scaled to Mercury, including thegravitational effect of the Sun.

Perihelion AphelionAverage impact velocities [km s-1] 27.2 22.3Vaporized regolith [kg s-1] 4.9 1.3

Fraction of meteoroid vaporized 0.59 0.4

Table 4: Various parameters related to micrometeoroid vaporization inMercury`s exosphere.

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Eichhorn (1977) studied the velocities of impact ejecta parameters during hypervelocityprimary impacts. He found that the velocity of the ejecta in creases with increasingimpact velocity and decreasing ejection angle. The ratio of the maximum ejecta velocityto the primary impact velocity decreases with increasing impact speed. Important forour study is that the velocities of particles which are vaporised via the impact is muchsmaller than the meteoroid-impact velocity. The measured temperature of ejectedparticles via this process is in a range between 2500 K up to 5000 K. This temperatureis much higher than the exospheric temperature, but lower than for ejected particles whohave their source in ion sputtering. Figure 5 shows an illustration of the micrometeoroidvaporisation process.

Fig. 5: Illustration of a vaporised micrometeoroid on Mercury`s surface. It isimportant to note that the gas inside the vapour has a temperature between2500K and 5000K, which is much higher than Mercury`s average daysideexospheric temperature of about 540 K.

We can therefore use our Monte-Carlo generated random distribution – similar than asfor the photon-stimulated particles – but with a higher energy related to about 3000 K.The vaporised particles are not dependent on their ejection angle, like particle sputteredparticles (Figure 6).

Fig. 6: The figure shows the velocity distribution of heavy sodium atoms which areproduced by micrometeoroid vaporization. The velocity distribution is a result of ourMonte-Carlo method.

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7 Particle energy and ejection angle distributions as afunction of altitude

The particles released from the surface are moving on ballistic trajectories. One can seefrom Figure 2 that we can calculate the ejection angle α from v and vz:

α0 = arc sin(vz0/v0) (6)

We neglect in this study the influence of radiation pressure effects and the slow rotationof the planet on the velocity components (vxi, vyi, vzi) of the particles. Therefore, weconsider the red coordinate system in Figure 2 for the calculation of vi and αi asfunction of altitude zi (i=0,1,2,3,4…):

z = v0 t sin (α0) – ½ g t2 (7)

where g is Mercury’s surface acceleration of 2.78 m/s and t is the flight time of theparticles. Since the altitude steps are known in the simulation (z1=10 km) one cancalculate the flight time t for a particle which is released from the surface up to variousaltitudes by:

t = v0 sin (α0) / g ± [ (v0 sin (α0) / g)2 – (2 z1 /g)]0.5 (8)

The second solution by subtracting (-) the root makes physical sense and is thereforechosen. After knowing the flight time from the surface to the first altitude step one cancalculate the new vzi, vi and αi corresponding to the new altitude zi above the surface byusing the following relations (Figure 7):

vi = v0 – g ti and vzi = vz0 – g ti (9)

Fig 7: This figure shows the velocity vectors related to ballistic trajectories and ejection anglesof particles which are released from Mercury`s surface.

x

v0

vz0

z

x

v0

vx

αααα0z1 = 10 km

z2 = 20 km

αααα1 vz1

v1

vx1

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7. 1 Angle dependence of surface sputtered particles

For a binary collision with a stationary atom, like atoms or molecules on Mercury’ssurface, the relationship between energy transfer and deflection angles of collidingparticles is:

cos Θ1= [ 1- ( E / E1 ) ( M1+M2 ) / 2 M1 ] / ( 1 – E / E1 )1/2 (10)

and

cos Θ2 = ( E / Emax )1/2 (11)

where Θ1 and Θ2 are the angles of particles one and two with respect to the initialdirection of motion of the incident particle (Figure 8), where:

• Θ2 the ejection angle of the sputtered particle;• M2 is the mass of the stationary atom;• M1 is the mass of the incident atom or ion;• Emax is the maximum energy transfer between both atoms – incident and

stationary.

Emax = [ 4 M1 M2 / ( M1 + M2 )2 ] E1 (12)

E is the energy of the particle which is ejected from the surface and E1 is the incidention energy of about 800 eV (≈ solar-wind energy). The incident ion is assumed totransfer energy in close binary collisions with one of the atoms of mass M2 in themolecule of mass M1. In this case the incident particle deflection angle is the same.Also, the direction of motion of the center of mass of the scattered molecule, whether itis dissociated or whole, is equal to Θ2 as determined for a collision with the free atomequation (11).

Fig. 8: The illustration shows the incident (i) and ejected (e) and angles during the sputtering process.

From the total energy transfer E an amount (M2 / M1) E goes into motion of the centerof mass of the molecule, and an amount [( M1 – M2 ) / M1] E goes into relative motionof the component atoms. If [(M1 - M2) / M1] E < D, where D is the molecular

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dissociation energy of the struck atom, then the molecule remains bound and this energygoes into molecular rotation and vibration.

If [( M1 - M2) / M1 ] E >> D, then the struck atom is, essentially, ejected from themolecule with an energy of approximately (E – D), and its direction of motionapproaches Θ2 in the limit of large E. The equations fail in the region where E ≈ D M1 /(M1-M2) and for some collisions of interest the distances of closest approach arecomparable to the bond lengths.

Table 5: Energy range, particle fluxes and ejection agles for two cross sections(Sieveka and Johnson, 1984).

Table 5 shows particle energies, fluxes in percent and ejection angles related to crosssections for hard sphere and Thomas-Fermi processes. One can see that the particleswhich are ejected via particle sputtering have a dentency to ejection angles larger than70 degrees.

8 Results and discussion

One can see from Figures 9, 10, 11 and 12 from this study that a neutral particleanalyser on board of BepiColombo`s MPO should have the capability to detect thermalH and He atoms, as well as heavy particles like Na, O and K. The heavy atoms willhave their origin only in surface release processes which are more energetic thanphoton-stimulated or thermal desorption. A future study will investigate the radiationpressure effects on the velocity components (vx, vy, vz) of the particles, the solar UVirradiance during one Mercury orbit, surface temperature variations and the directionand point of impact of particles which are falling back to Mercury’s surface. The studyof the energy and ejection angle distributions is included in a new comprehensiveexosphere model which is developed by Dr. Peter Wurz (PI-MAIA) from theDepartment of Physics at the University of Bern, Switzerland.

Hard sphere Thomas-FermiEnergy range[eV] Flux [%] α0 Flux [%] α0

0.5 - 50 19.5 76 90.5 82

50 - 100 18.7 58 4.7 61

100 - 150 16.9 48 2.1 52

150 - 200 13.9 40 1.2 43

200 - 250 10.7 33 0.66 37

250 - 300 7.8 27 0.38 32

300 - 350 5.2 22 0.21 27350 - 400 3.2 20 0.12 23400 - 450 2.0 15 0.06 20450 - 500 1.1 12 0.03 17

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8. 1 Energy and ejection angle distributions of photon-stimulateddesorption processes

Fig. 9: Shows the energy and angle distribution as function of altitude above Mercury’s surface.In our first study only the gravitational effect is included. Future studies will include the effectof the radiation pressure, planetary rotation, and local surface temperature variations. Thesimulations were done with 100 randomly produced particles for H, with 200 for He atoms.One can see that a large fraction of H and He atoms will reach an altitude where they can bedetected by the NPA/MAIA instrument on board of BepiColombo`s MPO.

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Fig. 10: The figure show simulations with about 800 randomly produced particles for Na andO atoms. The simulation show that nearly no O and Na atoms reach BepiColombo’s perihermof about 400 km, if they have their origin by photon-stimulated desorption. A simulation with500 particles for O and Na showed no difference. This is an interesting result, since it shows thatheavy particles like O and Na detected by the orbiter should have their origin from particle

sputtering and / or micrometeoroid impact vaporization processes.

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8. 2 Energy and ejection angle distributions of micrometeoroidvaporised particles

Fig. 11: The figure show a simulation with a few hundred randomly produced Na and K particles,who have their origin in a micrometeoroid vaporized cloud. The simulation show that the heavyparticles who have their origin in this process can reach altitudes which are higher thanMPO`s periherm of about 400 km and will therefore be detected.

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8. 3 Energy and ejection angle distributions of surface sputteredparticles

Fig. 12: The figure show a simulation with a few hundred randomly produced Na and O particles,who have their origin in surface sputtering. The simulation show that heavy particles who havetheir origin in this process can easy reach altitudes which are higher than MPO`s perihermof about 400 km and will therefore be detected.

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