This document summarizes research predicting the long-term solar wind ion-sputtering source at Mercury using data from the Helios spacecraft. The key points are: 1) Maps of solar wind proton flux onto Mercury's surface were constructed using a magnetosphere model and solar wind conditions estimated from Helios data when it was in Mercury's orbit. 2) Analysis of Helios data in Mercury's orbital range found that solar wind density increases by a factor of 2.3 from aphelion to perihelion, while velocity is independent of distance. IMF Bz is more likely to be strongly southward at perihelion. 3) Model runs used solar wind parameters matching the most probable conditions identified

1. Planetary and Space Science 55 (2007) 1584–1595
Predicting the long-term solar wind ion-sputtering source at Mercury
Menelaos Sarantosa,Ã, Rosemary M. Killena
, Danheum Kimb
a
Department of Astronomy, University of Maryland, College Park, MD 20742, USA
b
GMV Space Systems, Rockville, MD 20850, USA
Accepted 10 October 2006
Available online 27 February 2007
Abstract
Maps of the precipitating solar wind proton flux onto Mercury’s surface are constructed using a modified Toffoletto–Hill (TH93)
model of the Hermean magnetosphere. Solar wind and IMF conditions around Mercury’s orbit near aphelion and perihelion,
respectively, were estimated by reanalyzing the Helios 40-s data for times when the spacecraft as in Mercury’s orbital range
(0.31–0.47 AU). Probability density estimates obtained in this way allow us to quantitatively predict the likely range of the ion-sputtering
source as a function of true anomaly angle of the planet. Results indicate that the sputtering source along open fieldlines increases
fourfold from aphelion to perihelion, and that significant precipitation along closed fieldlines is twice as likely at perihelion due to finite
Larmor radius effects. We conclude that ion sputtering is comparatively more important as a source for the Hermean exosphere at
perihelion.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: Mercury; Solar wind–magnetosphere interaction; Ion precipitation; Helios data
1. Introduction
Sputtering caused by precipitating solar wind ions has
been suggested as a source mechanism for the Hermean
exosphere (Potter and Morgan, 1990; Killen et al., 2001).
This ion-sputtering source, which is regulated by the
interaction of the magnetosphere with the solar wind,
may vary rapidly during transient events such as CMEs or
due to quasi-Alfvenic, small-scale turbulence in the solar
wind which increases at small heliocentric distances
(Marsch, 1991; Zurbuchen et al., 2004). In contrast, the
long-term precipitating flux onto Mercury’s low altitudes
and surface is expected to vary smoothly from the
Hermean aphelion (0.47 AU) to perihelion (0.31 AU)
following the general increase of plasma density and
magnetic field in the ambient solar wind. This variation
of the solar wind input at Mercury due to orbital effects
has not been properly reflected in simulations previously
performed. We derived probability density estimates of the
long-term particle and field environments of Mercury
obtained by the Helios I and II spacecraft to predict the
most likely configurations of southward IMF. With these
likely boundary conditions for the magnetosphere, we
analytically computed the injected ion flux that precipitates
onto Mercury’s surface along open field lines close to
perihelion (0.31 AU) and aphelion (0.47 AU). The distribu-
tion function (phase space density) of ions injected
along open field lines was reconstructed using the fieldline
geometry derived by a modified Toffoletto and Hill (1993)
model of the Hermean magnetosphere.
Four basic types of magnetosphere models have been
developed for Mercury and used to study the solar wind
interaction with the magnetosphere: three analytic models
(Luhmann et al., 1998; Sarantos et al., 2001, Delcourt
et al., 2002, 2003), a semi-empirical model (Massetti et al.,
2003; Mura et al., 2005), a quasi-neutral hybrid model
(Kallio and Janhunen, 2003, 2004), and two MHD models
(Kabin et al., 2000; Zurbuchen et al., 2004; Ip and Kopp,
2002, 2004). In broad terms their predictions agree: because
Mercury’s internal magnetic field is small, and its atmo-
sphere is tenuous, solar wind ions can hit Mercury’s surface
along open field lines (magnetic lines that have one end
connected to the solar wind). Large parts of the surface are
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ÃCorresponding author.
E-mail address: sarantos@astro.umd.edu (M. Sarantos).

2. thus exposed to the solar wind. The footprint of open
magnetic field lines (‘‘cusp’’) contracts or expands respond-
ing mainly to changes in the IMF. However, predictions of
different models regarding the extent of the cusps and the
amount of the plasma reaching the surface differ. These
differences arise partly because different models capture
different parts of the physical processes, and partly because
different input conditions were chosen.
It is very important to constrain boundary conditions
outside of the magnetosphere: the IMF and solar wind
conditions. For instance, although the IMF radial compo-
nent (Bx) is believed to be dominant at Mercury, many
models used do not incorporate the effects of the IMF Bx
(e.g., Luhmann et al., 1998; Delcourt et al., 2002, 2003;
Massetti et al., 2003; Mura et al., 2005). In such Bx-free
models it is necessary to apply high values of southward
IMF Bz to the magnetosphere to produce a realistically
open configuration. For example, Massetti presented cases
with IMF Bz ranging between À10 and À30 nT, while
Delcourt used a Bz ¼ À30 nT for his sodium photoion
tracings. All cases which have been modeled previously
tested either perihelion conditions ðN ¼ 60276 cmÀ3
Þ or
extreme, CME-like conditions (Nsw ¼ 100 cmÀ3
; vsw ¼
6002800 km=s) for the solar wind, and exploratory condi-
tions for the IMF. These conditions, although possible, are
not typical of the solar wind along the Hermean orbit, and
no realistic aphelion cases were modeled. Additionally,
previous papers have told us nothing about how often
these configurations occur. To complement these results, a
systematic approach was taken that establishes the most
probable ion-sputtering rate at Mercury’s extreme orbital
points.
2. Multivariate statistical analysis of Helios 40-s data in the
0.31–0.47 AU range
Probability estimates for input conditions for new
modeling runs of the Hermean magnetosphere and its
response to the solar wind were obtained by analyzing the
Helios I and II 40-s data within Mercury’s orbital range.
These spacecrafts explored the interplanetary medium
during the ascending phase of solar cycle 21 between
1975–1981. While previous work indicative of Mercury’s
space environment (Russell et al., 1988; Burlaga, 2001)
presented one-dimensional histograms of probability den-
sity functions for solar wind density, velocity, and IMF Bx,
By and Bz based on Helios data and investigated how these
parameters scale with heliocentric distance, our objective
was to visualize how these properties change concurrently
in the solar wind, i.e., evaluate multivariate probability
density estimates. For example, density and velocity in the
ambient wind are anti-correlated and therefore we must
select their most likely conditions simultaneously. How-
ever, with concurrent measurements missing in either the
plasma or magnetometer data, the high-dimensional data
are frequently incomplete: our sample size represents about
66 000 points at aphelion and 215 000 points at perihelion,
respectively. Thus, we did not have enough data for
adequate bin sizes in the five-dimensional space. Instead,
we treated the density–velocity and IMF Bx–Bz planes
independently. Our approach is essentially one of con-
structing bivariate histograms with the following bin sizes:
density, 1 cmÀ3
; velocity, 10 km/s; and IMF Bx, Bz, 1 nT.
More accurate probability density estimates can be
computed using an average shifted histogram method or
even a kernel density estimator (e.g., Martinez and
Martinez, 2002). However, for the purpose of choosing
self-consistent input conditions this present method will
suffice. The resulting probability density estimates of the
density–velocity plane appear in Figs. 1a (around Hermean
aphelion) and b (around Hermean perihelion), while those
for the IMF Bx–Bz plane are shown in Figs. 1c and d,
respectively. Also shown in Fig. 2 are one-dimensional
histograms describing probability densities at aphelion and
perihelion, respectively, for density, velocity, IMF jBxj and
IMF jBj.
As expected, the solar wind velocity was found to be
independent of orbital distance while the density varied
roughly as 1=r2
(Burlaga, 2001). A striking feature is that
the velocity distributions have modes around 342 km/s (see
Fig. 2b) for a wide range of likely density conditions
(20260 cmÀ3
at aphelion; 502120 cmÀ3
at perihelion).
Figs. 1a and b show that for the high-velocity cases, there
exists a small range of possible densities, but low density is
consistent with a wide range of velocity (400–700 km/s). In
spite of the extreme variability of the Hermean environ-
ment, the Helios data averaged over 40 s reveal that the
IMF Bx is the dominant component and that its variation
from aphelion to perihelion largely follows that of the total
field magnitude (compare Figs. 2c and d). The IMF Bx was
found to be directed towards the Sun (plus) as likely as
away from the Sun (minus). The distribution of IMF Bx is
bimodal (exhibiting towards and away sectors) but the
effect of its sign on the Hermean magnetospheric config-
uration is North–South symmetric (Sarantos et al., 2001).
For this reason, we only present the IMF jBxj in Figs. 1
and 2. Likewise, the IMF Bz was not preferentially directed
southward or northward as can be seen in Fig. 1.
Comparing Figs. 1c and d, the distribution function
(probability density) in the IMF Bx–Bz plane is signifi-
cantly wider at perihelion. Thus, strongly southward IMF
configurations ðBzo À 10 nTÞ are more likely at perihelion.
However, since the IMF Bx is seen to increase faster from
aphelion to perihelion than the IMF Bz, models that do not
incorporate Bx may be more descriptive of aphelion
conditions.
Consistent with this analysis of both the one-dimen-
sional and higher-dimensional data, we chose conditions
for comparative runs between aphelion and perihelion in
the following way: we sampled five velocities between 342
and 602 km/s, and chose self-consistent densities for which
the aphelion probability distribution function in the
density-velocity space is locally maximized. Three cases
with velocity 342 km/s were chosen reflecting the wide
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M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1585

3. range of densities consistent with low-velocity solar wind.
At perihelion, velocity choices remained the same, while
aphelion densities were increased by a factor of (0.47/
0.31)2
, or 2.3. The maximum density modeled at either
aphelion and perihelion is somewhat higher than the
respective nominal conditions (32 cmÀ3
at aphelion;
73 cmÀ3
at perihelion). We tested IMF Bz cases ranging
from À5 to À 10 nT (southward), keeping By ¼ 5 nT
throughout these runs, and readjusting Bx from the
aphelion mode of À16 nT to the perihelion most likely
value of À34 nT. These decisions reflect the increase in total
field magnitude and density from aphelion to perihelion.
Our choices were made so that we can separately study the
effects on the precipitating flux of increasing particle
pressure and of the IMF turning more southward.
Table 1 summarizes the input conditions used in our
simulations.
The reader should be reminded that inherent in these
data are effects of the solar cycle activity. During the solar
cycle 21 (1975–1986), solar activity minimum occurred late
in 1975 and through the first half of 1976, while solar
maximum was reached in 1979–1980. The solar wind and
IMF parameters analyzed in this work were collected by
Helios over the first half of solar cycle 21 (1975–1981). In
contrast, missing measurements during the declining phase
of solar cycle activity (1981–1986) would result in wider
distributions for the IMF Bx, By, Bz, and total magnitude
jBj as indicated by an analysis of Pioneer Venus Orbiter
ARTICLE IN PRESS
0 30 60 90 120 150 180 210
300
400
500
600
700
800
900
Density (cm )
Velocity(km/s)
Probability density (x10
−4
)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9Perihelion: 0.31−−0.34 AU
0 10 20 30 40
−30
−20
−10
0
10
20
30
IMFBz(nT)
Probability density (x10
−4
)
5
10
15
20
25
30
35
0 10 20 30 40 50 60
−30
−20
−10
0
10
20
30IMFBz(nT)
Probability density (x10 )
2
4
6
8
10
12
14
Perihelion: 0.31−0.34 AUAphelion: 0.44−0.46 AU
0 20 40 60 80 100
300
400
500
600
700
800
900
Density (cm )
Velocity(km/s)
Probability density (x10 )
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
IMF (nT) IMF (nT)
Fig. 1. Probability density of solar wind conditions at Mercury in the density- V (a,b) and IMF Bx–Bz (c,d) planes computed from Helios I and II 40-s
plasma and magnetometer data for times when the spacecrafts were within Mercury’s aphelion (a, c) (0.44–0.46 AU) and perihelion (b, d) (0.31–0.34 AU)
range, respectively. The bin sizes in these plots are the following: density, 1 cmÀ3
; velocity, 10 km/s; and IMF Bx, Bz, 1 nT. Note that while the distribution
of IMF Bx is bimodal (exhibiting towards and away sectors), a change in the polarity of Bx only reverses the hemisphere that is magnetically connected to
the solar wind. For this reason we only present the IMF jBxj in Figs. 1 and 2. Analysis of the high-dimensional data, along with the one-dimensional
probability densities shown in Fig. 2, allows us to quantify the likely range of the ion-sputtering source at Mercury using self-consistent solar wind input
for our magnetospheric model.
M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–15951586

4. (PVO) and IMP-8 data (Luhmann et al., 1993) taken at 0.7
and 1 AU, respectively, over the entire solar cycle 21.
Particularly wider are the distributions of By and Bz, as
they respond not only to the variable solar surface field (as
Bx does), but also to the solar wind velocity, whose
distributions also exhibit a strong solar cycle dependence:
at solar activity minimum, high-speed streams are more
likely since they are associated with coronal holes.
However, the most likely values for the magnetic field
predicted here will be only slightly shifted towards higher
values, as the high-field tail counts ðjBzj420 nTÞ in PVO
data comprise at most 3% of all measurements during the
declining phase of the solar cycle (see Luhmann et al., 1993,
Fig. 14). Another source of temporal variation is intro-
duced into our sample because the solar wind parameters
used in the multivariate analysis were not collected at the
same rates throughout the area of interest during solar
activity minimum and maximum periods. As is evident in
Fig. 3, the data around perihelion were collected mostly at
solar minimum and during the ascending phase of the
cycle, while at aphelion there is a marked lack of data
collected at solar minimum. This explains why the high-
velocity, low-density area of the density–velocity plane
is patchy at aphelion (Fig. 1a) but smooth at perihelion
(Fig. 1b): this is the regime of the high-speed solar wind
that is persistent around solar minimum. While some bias
is possible due to the aforementioned issues and to others
not discussed here (e.g., possible sampling of respective
heliocentric distances at different heliolatitudes each year
by separate spacecraft), it should be stressed that our
purpose is not to assess effects of the solar activity cycle,
but to provide reasonable estimates of the likely range of
conditions encountered at Mercury’s aphelion and perihe-
lion due to the inherent variability of the solar wind.
3. Modeling the effects of injected ions: the distribution
functions
We compute the solar wind ion flux precipitating onto
Mercury’s surface by analytically calculating the distribution
function of ions injected through the magnetopause along
open field lines. Our formulation is similar to that of
Massetti et al. (2003) with three key upgrades: (1) our model
(TH93) handles the critically important IMF Bx, while the
ARTICLE IN PRESS
30 90 150 210
1
2
3
Density (cm )
Prob.density(x10)
200 400 600 800
2
4
6
Velocity (km/s)
Prob.density(x10)
0 20 40 60
2
4
6
IMF |Bx| (nT)
Prob.density(x10)
0 20 40 60
2
4
6
8
IMF |B| (nT)
Prob.density(x10)
Perihelion
Aphelion
Perihelion
Aphelion
Perihelion
Aphelion
Perihelion
Aphelion
Fig. 2. (Clockwise from top left panel) Probability density plots of solar
wind density, IMF jBxj, IMF jBj, and solar wind velocity derived from
Helios 40-s data around Mercury’s aphelion (0.44–0.46 AU) and
perihelion (0.31–0.34 AU). The velocity is seen to be largely uncorrelated
to orbital distance, while the density responds as 1=r2
. The change in IMF
jBxj follows that of the increase of the total field magnitude from aphelion
to perihelion, which confirms the dominance of the Bx component of the
IMF. These observations, coupled with plots in Fig. 1 showing how
density and velocity, as well as IMF Bx and Bz, change concurrently in the
solar wind, help fine tune our input conditions (Table 1).
Table 1
Input conditions for cases 1–5
Case Aphelion Nsw ðcmÀ3
Þ Vsw (km/s) Perihelion
Nsw ðcmÀ3
Þ
1 9 602 21
2 16 532 37
3 22 342 50
4 27 342 62
5 35 342 80
In each case, scenarios of IMF Bz ¼ À5 nT and Bz ¼ À10 nT were tested.
We chose Bx ¼ À16 nT at aphelion and Bx ¼ À34 nT at perihelion and
kept By ¼ 5 nT throughout these runs. A total of 20 cases were thus
modeled to predict the likely range of the ion-sputtering source that is
consistent with the Helios data.
1975 1976 1977 1978 1979 1980 1981
10
12
14
16
18
20
Year
Relativesamplingfrequency(%)
Helios data used in multivariate statistics
Fig. 3. Temporal variation of the relative sampling rate of Helios 40-s
data around the Hermean aphelion and perihelion. It is seen that the solar
wind parameters used in the multivariate analysis were not collected at the
same rates throughout the area of interest during solar activity minimum
and maximum periods. Especially incomplete appears the coverage of the
solar min conditions around aphelion. Since high-speed streams prevail
around solar minimum, the high-velocity, low-density area of the
density–velocity plane is patchy at aphelion (Fig. 1a). In contrast, the
same area was well-covered at perihelion (Fig. 1b).
M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1587

5. model used in the previous work (T96) does not; (2) we vary
input conditions from aphelion to perihelion self-consistently
according to our analysis of the Helios 40-s data in the
0.31–0.47 AU range; and (3) we vary the Alfve´ n velocity in
the solar wind self-consistently with our input, while Massetti
et al. used a constant Alfve´ n speed of 120km/s.
In the open magnetosphere, magnetosheath plasma gains
access into the magnetosphere mainly through the cusp
region. Usually visualized in the plane which contains the
magnetic field and bulk velocity, injected magnetosheath ions
have a characteristic D-shaped distribution function (phase
space density) predicted theoretically as a result of magnetic
tension of fieldlines that have reconnected with the IMF
(Cowley, 1982; Cowley and Owen, 1989; Lockwood and
Smith, 1994; Lockwood, 1995) and observed both in the
Earth’s dayside low-latitude boundary layer (LLBL) (e.g.,
Fuselier et al., 1991) and, more recently, in the mid- and
high-latitude cusp by Interball-Tail (Fedorov et al., 2000),
POLAR (Fuselier et al., 2000), and Cluster (e.g., Bosqued
et al., 2001; Lavraud et al., 2004). Key features of terrestrial
cusp signatures, such as the cusp ion energy-latitude
dispersion and the mid-altitude energy-pitch angle V
signatures, have been successfully simulated (Onsager et al.,
1993, 1995; Xue et al., 1997) by assuming that ions near the
magnetopause are described by a truncated drifting bi-
Maxwellian (Hill and Reiff, 1977). Farther into the
magnetosphere, injected ion distribution functions evolve
away from a D-shaped to pancake or torus distributions as
parallel velocity is converted to perpendicular velocity due to
gradient and curvature drifts or as a result of convection
(e.g., Fedorov et al., 2000), and are usually accompanied by
populations of magnetospheric origin.
We may reconstruct the part of the ion distribution that
crosses the magnetopause (treated as a rotational disconti-
nuity) and eventually impacts the Hermean surface as
follows. The tangential stress balance on either side of the
rotational discontinuity requires that the plasma bulk flow,
~V
0
P;HT, in the de Hoffman–Teller frame (a frame that moves
with the discontinuity at the fieldline velocity, VHT) is field-
aligned at the Alfve´ n velocity, ~VA (Cowley, 1982; Cowley
and Owen, 1989). Thus, the peak velocity (bulk plasma
speed) in Mercury’s frame, ~VP;M, is ~VP;M ¼ ~VP;HT þ
~VHT ¼ ~VA þ ~VHT (1) (Wale´ n relation). Only magne-
tosheath ions having positive parallel (field-aligned)
velocities in the HT frame may enter the magnetosphere
in the northern hemisphere. In Mercury’s frame, this
corresponds to injected ions having a cutoff velocity Vmin
which is the projection of the fieldline velocity VHT along
the magnetospheric field direction:
Vmin ¼ VHT cos ySPH, (1)
while the peak and maximum velocities of the distribution
are given by
VP;k ¼ VHT cos ySPH þ VAÀSPH, ð2aÞ
VP;? ¼ VHT sin ySPH, ð2bÞ
Vmax ¼ VHT cos ySPH þ VAÀSPH þ VTH, (3)
where ySH and ySPH are the angles of the magnetic field on
the magnetosheath and magnetosphere sides with the local
tangent to the magnetopause (Fig. 4); , VTH is the thermal
velocity; and VAÀSH, VAÀSPH the Alfve´ n velocity in the
magnetosheath and magnetosphere, respectively. Last, the
fieldline (open flux tube) moves away from the reconnec-
tion site at the merging outflow velocity VHT:
VHT ¼ VSH À VAÀSH cos ySH. (4)
Thus, assuming Earth-like precipitation at Mercury, the
injected ion distribution function (phase space density) on
each open field line in a planet-centered frame can be
approximated as
f ðVÞ ¼ n
m
2pKTjj
1=2
m
2pKT?
exp À
mðVjj À VP;jjÞ2
2KTjj
À
mðV? À VP;?Þ2
2KT?
; VminpVjjpVmax,
f ðVÞ ¼ 0; VjjoVmin, ð5Þ
where n and m are the number density at the magnetopause
(sheath side) and mass of solar wind protons, respectively;
KTjj and KT? are the solar wind thermal energies parallel
and perpendicular to the local magnetic field; and Vjj and
V? are the particle’s velocity in the magnetosphere
immediately after injection. The differential particle flux
is then computed as
J ¼
2E2
m2
f ðVÞ. (6)
To compute (5) and (6) for each open fieldline, we need
(a) the magnetosheath plasma population at the injection
point, (b) an estimate of the anisotropy between KTjj and
KT? for sheath ions, (c) an assumption about what
percentage of sheath ions capable of transport actually
get reflected back into the magnetosheath, and (d) an
estimate of the loss cone angle at Mercury. The magne-
tosheath plasma density, velocity and temperature in (3)
are determined as polynomial fits derived from the
gasdynamic code of Spreiter and Stahara (1980). To be
consistent with the Massetti et al. (2003) formulation, we
ARTICLE IN PRESS
θSH
BSH
n
BSPH
t
θSPH
t
n
BSH
BSPH θSH
θSPH
LLBL Tail
Fig. 4. Schematic illustration of the angles ySH and ySPH in the Northern
hemisphere for (a) lines in the low-latitude boundary layer (LLBL) and (b)
lines stretched tailwards. BSH and BSPH are the magnetic field vectors in
the magnetosheath and magnetosphere, respectively; t is the tangent and n
the normal unit vectors at the magnetopause.
M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–15951588

6. used a fit for Mercury provided in that paper as follows:
n
nSW
¼ 3:3 À 3:22d þ 1:4d1:5
, ð7aÞ
T
TSW
¼ 1 þ 3ð1 À ðÀ0:249d þ 0:953d1=2
Þ2
Þ, ð7bÞ
V
VSW
¼ À0:249d þ 0:953d1=2
, ð7cÞ
where d ¼ dNOSE À dMP, the distance (measured along the
GSM X- axis) from the subsolar point ðdNOSEÞ to the point
where the field line crossed the magnetopause ðdMPÞ. Self-
consistent input for the asymptotic solar wind density and
velocity at Mercury is provided by our Helios analysis
(Table 1). The solar wind temperature TSW is regulated
self-consistently from aphelion to perihelion by employing
a relationship between the temperature and the speed for
the ambient solar wind developed by Lopez and Freeman
(1986):
TSW½Â103
KŠ ¼ ð0:0106VSW À 0:278Þ3
=R½AUŠ,
VSWo500 km=s,
TSW½Â103
KŠ ¼ ð0:77VSW À 265Þ=R½AUŠ,
VSWX500 km=s.
We assume that magnetosheath ions are anisotropic such
that the perpendicular thermal velocity is twice the parallel
thermal velocity, or T? ¼ 4Tjj, which is justified by global
hybrid simulations of ion velocity distributions in the
magnetosheath (Lin and Wang, 2002). In agreement with
Massetti et al. (2003), we assume that half of the
magnetosheath plasma on open fieldlines having the
required field-aligned velocity is pushed back into
the magnetosheath by the local Alfve´ n wave. Lastly, we
follow the above authors in their estimate that the loss cone
angle at Mercury is 351, and we map only those ions that
are injected with pitch angles up to 351off the local
magnetospheric field. However, we note that the loss cone
angle could be computed self-consistently by the model
from the field magnitude at the magnetopause and the
surface field footpoint of each open line.
In the way described above, we can map the injected
phase space density and particle flux along open field lines
at Mercury on the basis of the fieldline geometry (the
angles ySPH and ySH) predicted by an open magnetosphere
model. To this end, we have modified the Toffoletto and
Hill (1989, 1993) magnetosphere model as described in
results previously published (Sarantos et al., 2001; Killen
et al., 2001, 2004). Figs. 5 and 6 are an example of the field
line configuration computed with our model for an
aphelion configuration of the Hermean magnetosphere.
In this application we computed the precipitating flux onto
the Northern hemisphere, which is the hemisphere that
connects to the solar wind for the outward-directed Bx
chosen here. We are currently expanding our scheme to the
southern hemisphere, and will report those results along
with simulations of the resulting Hermean exosphere in a
future publication. For a dominant IMF Bx the total
precipitating flux is expected to be roughly twice as high on
the hemisphere that is magnetically connected to the solar
wind (Kallio and Janhunen, 2003).
We must note that the method of analytically computing
distribution functions of injected ions described above does
not accurately predict the latitudinal variation of the cusp
signatures. This is because, according to Liouville’s
theorem, the phase space density is conserved, not along
field lines, but along particle trajectories. Particles that
penetrate the magnetopause at the same injection point but
with different pitch angles or energies impact the surface at
different locations due to the velocity filter effect. A more
accurate approach, which was developed by Onsager et al.
(1993, 1995), requires particle tracing. However, the
advantages of our method are that it correctly determines
the integrated precipitating source along the entire open
area, without the need to know the electric field everywhere
in the magnetosphere, and that it has minimal computa-
tional cost (Lockwood and Smith, 1994). Thus, it allows us
to predict the long-term variation of the precipitating
source from aphelion to perihelion.
4. Results
Detailed maps of the precipitating solar wind flux for
likely aphelion cases are presented in Figs. 7a–d (cases 1
and 2). Comparative runs between aphelion and perihelion
ARTICLE IN PRESS
4
2
0
Z
–2
–4
2 0 –2
X
–4 –6
Fig. 5. Fieldline topology in the noon-midnight meridian plane produced
by the modified TH93 model of Mercury’s magnetosphere for a likely
aphelion configuration (density: 32 cmÀ3
; velocity; 430 km/s; IMF
½À16 5 À5Š nT). Note that, due to the dominance of the IMF Bx, open
fieldlines turn towards the solar wind in the North, but away from it in the
South for this antisunward-directed radial IMF.
M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1589

7. are presented in Figs. 8a–d (cases 3 and 5). These maps
show that the precipitating source is generally extended in
longitude (60–701). In all cases, the flux peaks within a
short latitudinal band at the LLBL ðySPHo90Þ but drops
off rapidly by two orders of magnitude or more within
15–201of latitude away from the open–closed boundary.
This is easily understood from cusp signatures in the
Earth’s magnetosphere: the resulting bulk flow in the
magnetosphere is primarily away from the planet’s surface
along fieldlines that map to the tail, but towards the surface
and more field-aligned for lines that cross in the dayside.
However, a unique feature of the Hermean magnetosphere
arises because the dominant Bx component introduces a
dawn–dusk asymmetry in the shape of the cusps: the cusp
is very asymmetric for the IMF Bz ¼ À5 nT cases, but
begins to straighten and become more symmetric as Bz
becomes comparable to Bx (e.g., compare Figs.7a, c with
Figs. 7b, d). The first open fieldline is typically located at
40–451Northern latitude, but the cusp may be pushed
further equatorward to 25–301 for high-velocity, high Bz
conditions that are likely at perihelion (cases 1 and 2).
Maps showing the effective open area (fieldlines that
cross the magnetopause within 2RM down the tail) and of
the integrated precipitating source for likely conditions of
the solar wind and IMF, including Bz ranging from À5 to
À10 nT, are presented in Figs. 9a, b. Up to 20% of the
entire northern hemisphere could be open to the solar wind
for strongly southward conditions at perihelion. Increasing
dynamical pressure within the high-velocity regime results
in substantial change in the precipitating area, while
pressure increases in the low-velocity regime affect the
area available to the solar wind rather weakly. On the other
hand, the precipitating flux seems to vary little within
aphelion conditions (Fig. 7) but clearly increases at
perihelion (Fig. 8) both in the dayside and in the tail. In
fact, Fig. 9b demonstrates that the integrated precipitating
source ðsÀ1
Þ increases by a factor of 4 for comparative
southward IMF Bz ¼ À10 nT conditions from aphelion to
perihelion. In contrast, photon-stimulated desorption
(PSD), which is believed to be the main source mechanism
for the Hermean exosphere (McGrath et al., 1986; Madey
et al., 1998), is expected to increase as the solar UV flux by
1=r2
(quiet Sun conditions), or by a factor of 2.3 from
aphelion to perihelion (Smyth and Marconi, 1995). Clearly,
the modeled ion-sputtering source increases faster than
PSD. This result implies that a larger fraction of the
Hermean exosphere is due to sputtering caused by the solar
wind at perihelion. Note that to determine the relative
importance of these mechanisms, one must account for the
sputter yield as well as the source rates (see Killen et al.,
2001, 2004; Lammer et al., 2003, and references therein).
Consequently, the determination of the relative importance
of each mechanism requires the coupling of the magneto-
sphere model to a model of the Hermean exosphere (e.g.,
Killen et al., 2001). We do not presently compare yields for
these two processes nor for impact vaporization, which is
also a possible source mechanism for the exosphere;
instead, we only identify trends.
A comparison with the Massetti et al. (2003) predictions
for a comparable case with VA ¼ 120 km=s, Pdyn ¼ 20 nPa
and Bz ¼ À10 nT shows that inclusion of a strong Bx ¼
À16 nT increases fluxes by a factor of 3. This is expected
because the IMF Bx leads to increased precipitation at the
LLBL: fieldlines turn forward, cross the magnetopause
closer to the subsolar nose, and the bulk flow is more field-
aligned. The same physical reasons explain the increase
of the precipitating flux from aphelion to perihelion.
ARTICLE IN PRESS
0 100 200
45
50
55
60
65
70
75
80
85
90
Longitude
Latitude
thetaSHEATH
(degrees)
20
40
60
80
100
120
140
160
−200 −100 0 100 200
45
50
55
60
65
70
75
80
85
90
Longitude
Latitude
theta
SPHERE
(degrees)
20
40
60
80
100
120
140
160
Fig. 6. (a) Variation of the angle ySH in the Northern hemisphere between
the magnetosheath field and the local magnetopause tangent as Hermean
fieldlines evolve away from the reconnection site for the configuration
shown in Fig. 5. Large angles ð490
Þ indicate lines turned towards the
solar wind while small angles ($201) map to the tail; (b) variation of the
angle ySPH between the magnetopause tangent and magnetospheric field at
different injection points. Small angles ðo90
Þ indicate the location of the
low-latitude boundary layer (LLBL); the cusp proper lies at 901. Based on
the topology of open field lines we may compute the distribution function
and flux of precipitating ions along the entire part of Mercury’s surface
that is open to the solar wind.
M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–15951590

8. Compared to aphelion conditions, the solar wind flux is higher
due to the higher density, the magnetopause is closer to the
surface, and the maximum energy, Emax, of the injected ions
along each open line is higher both in the LLBL and,
especially, in the cusp proper for perihelion configurations.
The picture of precipitation presented by the analytical
model is incomplete because it tells us nothing about
precipitation occurring along closed field lines. Since the
Hermean magnetosphere is small, the Larmor radius of
solar wind protons is often expected to be comparable to
the magnetopause and bow shock distances thus resulting
in significant precipitation along closed fieldlines. This
effect is evident in simulations of solar wind impact
performed with a hybrid model (Kallio and Janhunen,
2003) showing that solar wind ions penetrate a larger area
than that directly connected to open field lines. Using the
Helios 40-s data for Mercury, we modeled the distribution
of the predicted TH93 magnetopause nose distance under
this input (Fig. 10a) and computed the distribution of
observed proton gyroradius in the solar wind. This allowed
us to quantify the probability of substantial precipitation
occurring due to the finite Larmor radius effect. Using an
arbitrary threshold of rL=dnose ¼ 0:4 for significant pre-
cipitation on closed fieldlines, we find that the tail of the
distribution is wider at perihelion by about a factor of 2 in
probability space (Fig. 10b). These results point out that
the precipitating source may frequently increase by more
than a factor of 4 from aphelion to perihelion when one
accounts for the higher likelihood of high Larmor radii of
solar wind ions for conditions typical at perihelion.
ARTICLE IN PRESS
0 50 100 150 200
30
40
50
60
70
80
90
Longitude
Latitude
Log10
Flux (cm s )
7.5
8
8.5
9
9.5
0 50 100 150 200
30
40
50
60
70
80
90
Longitude
Latitude
Log10
Flux (cm s )
7.5
8
8.5
9
9.5
0 50 100 150 200
30
40
50
60
70
80
90
Longitude
Latitude
Log
10
Flux (cm s )
7
7.5
8
8.5
9
9.5
0 50 100 150 200
30
40
50
60
70
80
90
Longitude
Latitude
Log10
Flux (cm s )
7.6
7.8
8
8.2
8.4
8.6
8.8
9
9.2
9.4
9.6
a b
c d
Fig. 7. Precipitating flux (log scale) of solar wind ions impacting Mercury’s surface for aphelion cases 1 (a, b) and 2(c, d) outlined in Table 1. Two sets of
plots are produced with Bz ¼ À5 nT (a, c) and Bz ¼ À10 nT (b, d) while Bx ¼ À16 nT and By ¼ 5 nT. Vertical columns (a vs c; b vs d) address the effects
of increasing pressure on the cusp location and precipitation flux for the same IMF, while horizontal rows (a vs b; c vs d) illustrate the effects of a more
southward IMF for given pressure. The open-closed boundary exhibits a strong dawn-dusk asymmetry for the Bz ¼ À5 nT as a result of the dominant Bx.
In turn, the cusp becomes more symmetric as Bz grows comparable to Bx (cases with Bz ¼ À10 nT).
M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1591

9. 5. Conclusions
To quantify the systematic variability of the ion-
sputtering source between the Hermean aphelion and
perihelion, we reconstructed the distribution functions
and precipitating flux of solar wind protons in the open
field line region using a modified TH93 model of Mercury’s
magnetosphere. To determine realistic input conditions we
analyzed the Helios I and II 40-s data at times when the
spacecraft were within Mercury’s orbital range, and com-
puted multivariate probability density estimates (Fig. 1).
Consistent with these estimates, which are presented here
for the first time for Mercury, we modeled a wide variety of
conditions in velocity (342–602 km/s) and density space
(aphelion: 9235 cmÀ3
; perihelion: 21280 cmÀ3
) chosen
self-consistently (Table 1). For the IMF, we tested south-
ward conditions ðBz ¼ À5; À10 nTÞ coupled with the most
likely self-consistent IMF Bx measured by Helios (aphe-
lion: À16 nT; perihelion: À34 nT). We report that the
inclusion of the dominant IMF Bx component raised the
modeled precipitating flux by a factor of 3 over cases of
comparable density, velocity and IMF Bz but without Bx.
In addition, the likely range of the precipitating source is
amplified by a factor of 4 from aphelion to perihelion
conditions, while the area open to the solar wind increases
by a factor of 2. Therefore, we anticipate that ion
sputtering is a more important source for the Hermean
exosphere at perihelion.
Maps of the precipitation predicted by the analytical
model are simplified in three ways. First, they do not
ARTICLE IN PRESS
0 50 100 150 200
30
40
50
60
70
80
90
Longitude
Latitude
Log
10
Flux (cm s )
8.2
8.4
8.6
8.8
9
9.2
9.4
9.6
9.8
10
0 50 100 150 200
30
40
50
60
70
80
90
Longitude
Latitude
Log
10
Flux (cm s )
7.5
8
8.5
9
9.5
0 50 100 150 200
30
40
50
60
70
80
90
Longitude
Latitude
Log
10
Flux (cm s )
8.5
9
9.5
10
0 50 100 150 200
30
40
50
60
70
80
90
Longitude
Latitude
Log
10
Flux (cm s )
7.8
8
8.2
8.4
8.6
8.8
9
9.2
9.4
9.6
a b
c d
Fig. 8. Precipitating flux (log scale) of solar wind ions impacting Mercury’s surface for likely aphelion and perihelion conditions (cases 3 and 5 of Table 1).
These maps are produced with IMF Bz ¼ À10 nT and By ¼ 5 nT while at aphelion Bx ¼ À16 nT (a, c) and at perihelion Bx ¼ À34 nT (b, d). Responding
to the denser plasma and stronger field magnitude, the precipitating flux at perihelion clearly increases both in the dayside and in the tail.
M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–15951592

10. describe contribution by precipitating solar wind ions on
closed field lines due to finite Larmor radius effects. To
supplement our predictions, we investigated how the ratio
of the observed proton gyroradius over the TH93-modeled
magnetopause distance changes from aphelion to perihe-
lion according to the Helios data. Results indicate that
significant precipitation on closed field lines is twice as
likely at perihelion than at aphelion. Thus, the finite
Larmor radius effect will tend to further accentuate the
increase in precipitation from aphelion to perihelion.
Second, the simple magnetopause pressure balance per-
formed in the modified TH93 model does not include
induction effects caused by finite surface conductivity.
Surface-induced currents, which may contribute 10% of
the interior field, oppose the transfer of magnetic flux from
the dayside to the tail ðBzo0Þ and may substantially affect
the magnetospheric topology and dynamics (Glassmeier,
2000; Grosser et al., 2004; Janhunen and Kallio, 2004). A
more realistic magnetopause may resist extreme compres-
sion by the solar wind. As the dayside magnetic field
intensifies at low altitudes due to surface induction
currents, injected particle trajectories will be affected by
the added magnetic field, which may prevent penetration to
the planetary surface. It may be that only field-aligned
particles precipitate down to the low-altitude ionosphere
ARTICLE IN PRESS
1 2 3 4 5
6
8
10
12
14
16
18
20
22
Case index
EffectiveOpenArea
% of Northern Hemisphere
1 2 3 4 5
0
2
4
6
8
10
12
14
16
x 10
25
Case index
Precipitatingsource(s−1
)
Aphelion, Bz = −5nT
Aphelion, Bz = −10nT
Perihelion, Bz = −5nT
Perihelion, Bz = −10nT
Fig. 9. (a) Effective open area and (b) integrated precipitating source ðsÀ1
Þ
from the Hermean aphelion to perihelion for different conditions of the
solar wind and IMF. It is seen that when the IMF Bx is dominant, the
effect of IMF Bz is small provided that it is southward. The precipitating
source increases by a factor of 4 at perihelion, while the area available to
solar wind impact doubles.
0.5 1 1.5 2 2.5
0
5
10
15
20
Nose Distance from Center [Rm]
Frequency[%]
Helios 1 2 Data
Date: 1975 − 1981
Range: 0.31 − 0.46 AU
Weibull Fit
Dipole moment [nT R3
]
330
350
400
450
0.3 0.4 0.5 0.6 0.7
0
0.01
0.02
0.03
Probabilitydensity
High-end tail
0.1 0.2 0.3 0.4 0.5
0
0.05
0.1
Proton gyroradius/Magnetopause distance
Probabilitydensity
Main body of distribution
Aphelion
Perihelion
Aphelion: 2.4%
Perihelion: 5.6%
Fig. 10. (a) distribution of the modeled TH93 magnetopause nose
distance under the 40-s Helios input for different choices of magnetic
dipole moment consistent with the Mariner 10 data; (b) distribution
function of the solar wind Larmor radius to magnetopause distance for
dipole moment of 350 nT R3
. The tail of the distribution (upper panel) is
wider at perihelion by about a factor of 2. Thus, precipitation along closed
fieldlines due to the finite Larmor radius is expected to be twice as likely at
perihelion.
M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1593

11. and surface, much like the case in the Earth’s magneto-
sphere. Lastly, the extent to which possible pickup of heavy
exospheric ions (e.g., Naþ
, Kþ
, Oþ
) may alter the solar
wind flow and affect the bow shock and magnetospheric
boundaries has not been considered here. Thus, our
computations should be considered as only a first-step
towards quantifying the response of the magnetospher-
e–exosphere system to extreme solar wind environments at
Mercury’s aphelion and perihelion.
Acknowledgements
This work was supported by the NASA Geospace
Sciences Program Grant NNG04G195G. Helios 40-s data
were kindly supplied by R. Schwenn. The original version
of the TH93 model was provided by F. Toffoletto (Rice
University). The authors would like to thank H. Rosen-
bauer and F. Neubauer for making Helios data available to
the scientific community, and P. Reiff for numerous
discussions and helpful comments on this paper.
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