Icarus 206 (2010) 152–163
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Icarus
journal homepage: www.elsevier.com/locate/icarus
Oxygen ion escape at Mars in a hybrid model: High energy and low energy ions
Esa Kallio a,b,*, Kaijun Liu a, Riku Jarvinen a, Valter Pohjola a, Pekka Janhunen a
a
b
Finnish Meteorological Institute, Helsinki, Finland
University of Helsinki, Department of Physics, Helsinki, Finland
a r t i c l e
i n f o
Article history:
Received 15 November 2008
Revised 31 March 2009
Accepted 11 May 2009
Available online 2 June 2009
Keywords:
Mars
Planetary ionospheres
Planetary magnetospheres
Numerical modelling
Hybrid model
a b s t r a c t
We have studied the escape and energization of several Oþ populations and an Oþ
2 population at Mars by
using a hybrid model. The quasi-neutral hybrid model, HYB-Mars model, included five oxygen ion populations making it possible to distinguish photoions from oxygen ions originating from charge exchange
processes and from the ionosphere.
We have identified two high-energy ion components and one low-energy ion component of oxygen.
They have different spatial and energy distributions near Mars. The two high-energy oxygen ion components, consisting of a high-energy ‘‘beam” and a high-energy ‘‘halo”, have different origins. (1) The highenergy (>100 eV) ‘‘beam” of Oþ and Oþ
2 ions are originating from the ionosphere. These ions form a
highly asymmetric spatial distribution of escaping oxygen ions with respect to the direction of the convective electric field in the solar wind. (2) The high-energy (>100 eV) ‘‘halo” component contains Oþ
ions which are formed from the oxygen neutral exosphere by extreme ultraviolet radiation (EUV) and
by charge exchange processes. These energetic halo ions can be found all around Mars. (3) The low energy
Oþ and Oþ
2 ions (<100 eV) form a relatively symmetric spatial distribution around the Mars–Sun line.
They originate from the ionosphere and from charge exchange processes between protons and exospheric
oxygen atoms.
The existence of the low- and the high-energy oxygen components is in agreement with recent in situ
plasma measurements made by the ASPERA-3 instrument on the Mars Express mission. The analysis of
the escaping oxygen ions suggests that the global energization of escaping planetary ions in the martian
tail is controlled by the convective electric field.
Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction
The solar wind provides a non-thermal atmospheric escape
mechanism for martian ions where newly ionized atmospheric or
exospheric ions acquire energy from the electric field associated
with the flowing solar wind. The role of non-thermal atmospheric
processes is under intensive research because these processes provide escape mechanisms for an atmosphere and water in addition
to the thermal loss processes (Jeans and hydrodynamic escape) and
impact erosion (see, e.g., Hunten et al., 1989, for details for different escape processes).
Details of the ion escape at Mars have been under investigation
since the first indirect observations of the escaping oxygen ions
were made during the Mars-5 mission in 1974 (Vaisberg, 1976)
over 30 years ago. The most comprehensive set of data measuring
escaping planetary ions at Mars so far comes from the ASPERA-3
instrument on the Mars Express (MEX) mission. The ASPERA-3 particle instrument has detectors to measure ions (IMA sensor), elec* Corresponding author. Address: Finnish Meteorological Institute, Erik Palmenin
aukio 1, 01001 Helsinki, Finland. Fax: +358 9 1929 4603.
E-mail address: Esa.Kallio@fmi.fi (E. Kallio).
0019-1035/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved.
doi:10.1016/j.icarus.2009.05.015
trons (ELS sensor) and energetic neutral atoms (NPI and NPD
sensors) (see Barabash et al., 2006, for the details of the instrument). The ion mass analyzer, IMA, has a mass resolution good enough to distinguish heavy planetary ions (e.g., Oþ , Oþ
2 ) from the
light, predominantly solar wind origin Hþ and He2þ ions. The
IMA sensor was designed to observe ions in the energy range
10 eV/e–36 keV/e and it started to measure martian plasma environment in January 2004. By the end of year 2006, IMA has provided new data covering various aspects associated with
energetic ðE > 100 eVÞ escaping planetary ions (see, for example,
Fedorov et al., 2006).
A new phase in IMA observations started in May 2007 when
new energy settings made it possible for IMA to measure low-energy (10–100 eV) planetary ions (Lundin et al., 2008). The new
data set has reinitialized the discussion of the energy of escaping
planetary ions and the spatial distribution of escaping planetary
ions with different energies. Especially, the new IMA observations
have been interpreted to include (i) energetic ðE > 200 eVÞ escaping ions which are located asymmetrically with respect to the
Mars–Sun line, and (ii) low energy escaping ions which are located
relatively symmetrically about the Mars–Sun line (Lundin et al.,
2008).
E. Kallio et al. / Icarus 206 (2010) 152–163
Statistical analysis of the IMA ion escape observations is complicated by the fact that there is no magnetometer on MEX. This
limits to study of possible asymmetries associated with the direction of the interplanetary magnetic field, IMF, and with the direction of the convective electric field in the solar wind,
Esw ¼ Usw Bsw (Usw is the velocity of the undisturbed solar wind,
and Bsw is the IMF). The magnetometer on Mars Global Surveyor,
MGS, provided certain possibilities to estimate the direction of
IMF (see, e.g., Fedorov et al., 2006) but such estimations of IMF
have not been possible to perform after the loss of MGS in November 2006.
Computer simulations provide a tool to study possible asymmetries associated with the ion outflow and the energization of escaping ions. Magnetohydrodynamic (MHD) and quasi-neutral hybrid
simulations provide self-consistent global models to study the
Mars–solar wind interaction (Ledvina et al., 2008) and, indeed, several such global models have been used to study the ion escape at
Mars (Brain et al., in this issue).
The purpose of this paper is to study the escape of planetary Oþ
and Oþ
2 ions at Mars by a quasi-neutral hybrid model. The model,
referred to as the HYB-Mars model, is an advanced version of the
hybrid model which has been used to interpret ASPERA/Phobos-2
(Kallio and Janhunen, 2002) and preliminary ASPERA-3/MEX (Kallio et al., 2006) ion observations at Mars. The new model version is
tailored to study four Oþ ion populations and one Oþ
2 ion population which are produced either in the exosphere by Extreme Ultraviolet (EUV) radiation, by charge exchange processes, or by
escaping from the martian ionosphere.
The paper is organized as follows. First, the model is described
by emphasizing the improvements which has been made to the
HYB-Mars model to study ion escape at Mars in more detail than
described earlier. Then a HYB-Mars run is analyzed focusing on
the spatial distribution and the energy of various Oþ and Oþ
2 ions
near Mars. Finally the energization of Oþ and Oþ
2 ions are studied
by analyzing the electric field and by performing test particle
simulations.
2. Description of the model
The present study was carried out using the HYB-Mars
model, a Mars version of the three-dimensional quasi-neutral
hybrid model developed at the Finnish Meteorological Institute.
In the HYB-Mars model, plasma ions are treated as macro particles which represent ensembles of real plasma ions, while
electrons are treated as a massless, charge-neutralizing fluid.
The basic properties of the hybrid model have been described
earlier (see Kallio and Janhunen, 2002, 2003) and will not be
repeated here. Instead, we elaborate on the input parameters
used in this study and the recently developed new features
of the model.
2.1. The overview of input parameters
2.1.1. Simulation domain
A planet-centered Cartesian system, Mars Solar Orbital (MSO)
coordinate system, is employed in the HYB-Mars model. The x-axis
points from Mars towards the Sun. The z-axis points to the north
and is perpendicular to the orbital plane of Mars. The y-axis completes the right-handed coordinate system. The aberration caused
by the 24 km s1 orbital motion of Mars around the Sun is not expected to be significant and has been neglected in the present
study. The simulation box in the present study has the size:
and
6:4RM < y,
z < 6:4RM ,
where
4:2RM < x < 4:2RM
RM ¼ 3393 km is the Mars radius used in the simulation. A hierarchically refined grid is employed in the HYB-Mars model. The grid
153
size is 720 km where r > 3RM , 360 km where 2RM < r < 3RM , and
180 km where r < 2RM , respectively (r is the distance from the center of Mars). The time step is 0.02 s and the running time is 700 s in
the present study. The results are analyzed at the end of the run.
Limited by the available computational resources, there are about
30 macro particles in each cell. The model does not include martian
crustal magnetic anomalies because the limited spatial resolution
makes it impossible to include a realistic crustal magnetic field
model.
2.1.2. Solar wind parameters
The solar wind parameters are chosen to correspond to the input values in the community-wide solar wind–Mars interaction
modeling (SWIM) campaign (see Brain et al., in this issue, for the
details about SWIM): nsw ¼ 3 cm3 , Usw ¼ ½400; 0; 0 km s1 ,
Bsw ¼ ½ cosð57 Þ; sinð57 Þ; 0 3 nT ½1:6; 2:5; 0 nT, and T sw ¼
5 104 K which are the density, the bulk velocity, the IMF and
the temperature of the solar wind, respectively. Under this configuration, the convective electric field in the undisturbed solar wind,
Esw ð¼ Usw Bsw Þ, points towards the +z-direction. In the present
simulation, only Hþ ions are considered in the solar wind as suggested by the SWIM campaign. The solar wind Hþ ions are injected
in the simulation box at the front face of x ¼ 4:2RM .
2.1.3. Exosphere model
The exosphere model is adapted from Barabash et al. (2002).
The neutral oxygen is modeled by a Chamberlain density profile
with a scale height of 1:78135 104 km. The neutral hydrogen is
given by a similar Chamberlain density profile with a scale
height of 2:60674 104 km. The model contains exospheric Oþ
and Hþ ions. The exospheric Oþ and Hþ ions are generated in
the system by photoionization from their respective neutral density profiles. The total Oþ photoion production rate is
2:7 1023 s1 and the total Hþ photoion production rate is
1:8 1024 s1 . The photoion production is spherically symmetrical except that no photoionization takes place in the shadow
of Mars. In addition, the above neutral density profiles are used
in the simulation for consistency with our previous Mars–solar
wind interaction study (Kallio and Janhunen, 2002). The subject
of the exospheric density profiles is, however, under an extensive study because recent energetic neutral atom measurements
made by ASPERA-3 instrument seem to indicate that martian
hydrogen exosphere, and probably also the oxygen exosphere,
are much thinner than assumed earlier (Galli et al., 2006). The
role of the exospheric densities in the results presented in this
paper will be discussed in Section 4.
2.1.4. Ionosphere ion sources
The ionosphere ion sources in the HYB-Mars model contains
þ
and Oþ
Oþ and Oþ
2 ions. They are modeled by emitting O
2 ions
from a spherical shell at 3600 km from the center of Mars, which
mimics the top of the ionosphere. The reason of such a special
treatment is that the limited spatial resolution in the simulation
prohibits a self-consistent modeling of the ionosphere. The Oþ
and Oþ
2 ion emissions have the same solar zenith angle (SZA)
dependence: the SZA dependence factor is 0.1 on the nightside
and (0.1 + 0.9 cos(SZA)) on the dayside. The emitted ions have a
Maxwellian velocity distribution with the temperature of
100,000 K. The total emissions rates are set to be 1:4 1025 s1
for Oþ and 2 1025 s1 for Oþ
2 . As some of the emitted ions
can return to the obstacle and get absorbed, the total escape
rates of the ionosphere Oþ and Oþ
2 at t ¼ 700 s are found to be
2 1024 and 2:2 1024 s1 , respectively. The escape rate is
counted as the number of ions leaving from the six faces of
the simulation box in a unit time.
154
E. Kallio et al. / Icarus 206 (2010) 152–163
2.2. New features of the HYB-Mars model
Recently, three major improvements have been made to the
HYB-Mars model: (1) a fluid background ionosphere was introduced; (2) the electron pressure term was included; (3) the charge
exchange processes were implemented.
2.2.1. The fluid background ionosphere
A hierarchically refined grid is employed in the HYB-Mars model to allow a spatial resolution of 180 km around Mars, but the
resolution is still too coarse to model the martian ionosphere
self-consistently. In our previous work, a superconductive obstacle
was used to model the shielding effect of the ionosphere to the
magnetic field penetration. Recently, we introduced a fluid background ionosphere to mimic this effect. This improvement helps
to suppress the numerical noise caused by the previous sharp
superconductive obstacle boundary whereas it does not significantly change the overall fields and the ion pickup rates. The background ionosphere electron density profile used in this study is
given by Eqs. (1) and (2), which are derived from the Mars Thermospheric General Circulation Model (MTGCM) results (see Brain
et al. (in this issue) for the references to the MTGCM model):
ne;MTGCM ¼ a no expððr Ro Þ=ro Þ at r P Ro ;
ð1Þ
ne;MTGCM ¼ a no
ð2Þ
at r < Ro
where no ¼ 2:6 1011 m3 is the peak electron density,
Ro ¼ 3515 km (i.e., 125 km above the planet) is the peak density
altitude, ro ¼ 35:24 km is the scale height, and a is the SZA dependence factor. The a is 0.1 in the nightside and (0.1 + 0.9 cos(SZA)) on
the dayside. The total electron density in the HYB-Mars model is
then given by
ne ðrÞ ¼ ne;hybrid ðrÞ þ ne;MTGCM ðrÞ
ð3Þ
One should note that Eq. (6) includes the electron pressure
term, rðpe Þ=ðene Þ, which is also called the polarization electric
field. As the first step to include the electron pressure term into
the HYB-Mars model, isothermal assumption is used, that is, T e is
assumed to be a constant. This also implies that the polarization
electric field does not affect the propagation of the magnetic field
in Faraday’s law because r ðrðne Þ=ne Þ is zero. The isothermal
assumption is a very crude assumption as the electron temperatures in the martian ionosphere and solar wind are very different.
However, the isothermal assumption can still describe as least part
of the physics if the electron temperature is set to be close to the
observed electron temperature in martian ionosphere. Although
the electron temperature in the martian ionosphere is significantly
lower than the solar wind electron temperature, the electron pressure term is not expected to play a big role in the solar wind region,
at least for the present study. In the present simulation,
T e ¼ 4 103 K.
2.2.3. Charge exchange processes
The current HYB-Mars model includes four charge exchange
processes through which Oþ and Hþ ions are produced from the
neutral hydrogen and oxygen exospheres by solar wind and exosphere protons:
(i) Solar wind protons, Hsw , charge exchange with exosphere
oxygen neutral atoms ðOexo Þ,
Hþsw þ Oexo ! Hsw þ OþcxHþsw
ð8Þ
(ii) Protons from the exosphere charge exchange with exosphere oxygen neutral atoms,
Hþexo þ Oexo ! Hexo þ OþcxHþexo
ð9Þ
Hþ
sw ,
(iii) Solar wind protons,
charge exchange with exosphere
hydrogen neutral atoms ðHexo Þ,
where
ne;hybrid ¼ nðHþ Þ þ nðOþ Þ þ n Oþ2
þ
ð4Þ
þ
Oþ
2
as the analyzed run contains H , O and
ion species. Eqs. (1)–(3)
actually mean that the martian ionosphere is mainly described by a
static background ionosphere while ne;hybrid associated with the particle ions contributes the dynamic portion.
Eqs. (1) and (2) give only an approximation of the real MTGCM
output electron density profile which depends on both longitude
and latitude. However, this approximation does not affect the global simulation results. We found that the global results were not
very sensitive to the various ne;MTGCM profiles we tested.
2.2.2. The electron pressure term
In the HYB-Mars model, the ions are accelerated by the Lorenz
force:
F ¼ qi ðE þ vi BÞ
ð5Þ
where qi and vi are the electric charge and the velocity of the ion species i, B is the magnetic field, and the electric field E is calculated by:
E ¼ Ue B rðpe Þ=ðene Þ ¼ Ue B rðne kT e Þ=ðene Þ
ð6Þ
In Eq. (6), pe is the electron thermal pressure, ne is the electron density given by Eq. (3), T e is the electron temperature, k is the Boltzmann constant, and Ue is the electron bulk velocity derived from
the definition of the electric current:
Ue ¼ enðHþ ÞUðHþ Þ þ enðOþ ÞUðOþ Þ þ en Oþ2 U Oþ2 j =ðene Þ:
ð7Þ
In Eq. (7) j is the electric current derived from Ampere’s law, e is the
unit electron charge, UðHþ Þ, UðOþ Þ and UðOþ
2 Þ are the bulk velocity
of Hþ , Oþ and Oþ
2 ions, respectively.
Hþsw þ Hexo ! Hsw þ HþcxHþsw
ð10Þ
(iv) Protons from the exosphere, Hþ
exo , charge exchange with
exosphere hydrogen neutral atoms,
Hþexo þ Hexo ! Hexo þ HþcxHþexo
ð11Þ
The first two processes (Eqs. (8) and (9)) are the sources for the
new charge exchange-generated Oþ ions while the last two processes (Eqs. (10) and (11)) are the sources for the new charge exchange-generated Hþ ions. The model distinguishes the four new
ion populations in Eqs. (8)–(11) in order to study the influences
of the corresponding individual charge exchange process. For simplicity, the current model does not include the secondary charge
exchange, that is, the charge exchange of the newly generated Oþ
and Hþ ions in Eqs. (8)–(11) with the exosphere neutral atoms.
The simulation results also confirm that the secondary charge exchange is not significant to the present study, as the total numbers
of newly generated Oþ and Hþ ions in Eqs. (8)–(11) are significantly
smaller than the number of initial protons which drive the corresponding reactions. Charge exchange cross sections are energy
dependent but the energy dependencies are relatively weak for
the modeled processes in the analyzed energy region (see, e.g., Kallio et al., 1997, Fig. 3). Therefore, a constant cross sections of
1 1019 m2 is used in all the four charge exchange processes for
simplicity.
The model contains only two Oþ sources which result from the
charge exchange processes (Eqs. (8) and (9)) in order to limit the
number of different ion populations in the simulation. In reality,
for example, Oþ ions can also be formed and lost in a charge
E. Kallio et al. / Icarus 206 (2010) 152–163
exchange process Oþ þ O ! O þ Oþ . This process is not included
into the simulation because, although it decreases the momentum
and energy associated with oxygen ions, it does not increase the
total amount of Oþ ions. Another charge exchange process (see
Barabash et al., 2002) Oþ þ H ! O þ Hþ , which is a loss process
for oxygen ions, is neither included in the simulation.
After the charge exchange processes (Eqs. (8)–(11)) have been
included in the HYB-Mars model, the system has: (1) four Hþ popþ
þ
ulations: solar wind protons ðHþ
sw Þ, exosphere H photoions ðHhf Þ,
and
and two charge exchange-generated Hþ populations (Hþ
cxHþ
sw
); (2) four Oþ ion populations: ionosphere Oþ population
Hþ
cxHþ
exo
þ
photoion population ðOþ
ðOþ
iono Þ, exosphere O
hf Þ, and two charge
and Oþ
); (3) one
exchange-generated Oþ populations (Oþ
cxHþ
cxHþ
sw
exo
þ
population:
O
ions
from
ionosphere.
Oþ
2
2
Table 1 shows the total number of the macro particles of each
individual ion population in the system at t ¼ 700 s and the number of the real particles it represents. All ion populations are shown
in Table 1 for completeness, although only oxygen ion populations
is studied in detail in this paper. As one can see, we generally have
enough macro particles to derive plasma parameters statistically
þ
þ
þ
for Hþ
sw , Oiono , and O2 , but not for Ohf . In addition, the total number
þ
of Hsw ions in the system is almost two orders of magnitude larger
þ
than total number of Oþ ions and Oþ
2 ions. The total number of O
ions is about the same as total number of Oþ
ions
in
the
simulation
2
box. Recalling that the mass of Oþ ðOþ
2 Þ ions is 16(32) times larger
þ
than the mass of H ions, the total ion mass within the simulation
þ
box associated with Oþ
2 and O ions is roughly the same as the total
þ
mass of H ions.
Four Oþ ion populations means that the particle density of Oþ
ions, nðOþ Þ, the particle flux of Oþ ions, nUðOþ Þ, and the bulk velocity of Oþ ions, UðOþ Þ, are a sum of four populations:
nðOþ Þ ¼ n Oþiono þ n Oþhf þ n OþcxHþsw þ n OþcxHþexo
nUðOþ Þ ¼ nU Oþiono þ nU Oþhf þ nU OþcxHþsw þ nU OþcxHþexo
þ
þ
þ
UðO Þ ¼ nUðO Þ=nðO Þ
ð12Þ
ð13Þ
ð14Þ
Moreover, in order to decrease the number of different ion populations to be presented in this paper, the macroscopic parameters of
þ
Oþ
iono and Ohf are added together:
ð15Þ
nU Oþiono þ Oþhf ¼ nU Oþiono þ nU Oþhf
. þ
þ
þ þ
þ þ
U Oiono þ Ohf ¼ nU Oiono þ nU Ohf
n Oiono þ n Ohf
ð16Þ
3. Results
Fig. 1 gives an overview of the properties of protons near Mars
in the analyzed run. The macroscopic parameters are derived by
Table 1
The total number of the macro particles of each individual ion population in the
system at t ¼ 700 s and the number of the real particles it represents. Notice that the
simulations contains four Oþ ion populations and one Oþ
2 population. All ion
populations are shown in Table 1 for completeness, although only oxygen ion
populations is studied in detail in this paper.
Ion population
Total number of macro particles
Total number of real particles
Oþ
iono
0:7 106
3 1027
Oþ
hf
0:07 106
3 1025
Oþ
cxHþ
0:1 10
7 1025
Oþ
cxHþ
0:02 106
4 1023
Oþ
2
1:1 106
5 1027
Hþ
sw
9:8 106
1:7 1029
Hþ
hf
5:8 104
2:5 1026
1:3 10
6
2:3 1027
1:3 10
5
3:5 1025
sw
exo
Hþ
cxHþ
sw
Hþ
cxHþ
exo
6
155
taking into account all four Hþ ion populations (cf. Table 1). In
Fig. 1, as in all figures in this paper, the analysis is focused to a relatively small region near Mars ð5 103 km < x < 7 103 km;
15 103 km < y; z; < 15 103 kmÞ compared to the full
simulation domain where the grid size is in its minimum but
which is still large enough to study asymmetries in the y- and zdirections.
The density of protons, nðHþ Þ is enhanced and the speed of protons, UðHþ Þ, is decreased at the bow shock, as can be seen in Fig. 1.
The bulk velocity and the particle flux, nUðHþ Þ, are smaller near
Mars than in the solar wind. The bulk velocity and the particle flux
are also low in the martian tail. The magnitude of the magnetic
field, jBj, reaches its maximum downstream of the bow shock near
Mars. The z component of the IMF is zero in the analyzed run and,
therefore, the magnetic field is weak in the xz-plane near the location of the cross tail current sheet. A magnetic tail lobe is in the
y > 0 hemisphere and another lobe is in the y < 0 hemisphere
(see Kallio et al., 2006, for the details of the martian magnetotail
in the HYB-Mars model when the IMF z-component is zero and
the angle between the IMF and the x-axis is 55°). Although the
magnetic tail lobes cannot be fully seen on x ¼ 5000 km plane
in Fig. 1d because they are partly behind y ¼ 0 and z-planes, the
location of a magnetic tail lobe can be identified as a green oval
shape on the x ¼ 5000 km plane at y > 0.
The properties of the Oþ
2 ions near Mars are depicted in Fig. 2.
Notice that although all Oþ
2 ions in the model originate from a
spherical shell around Mars and that they were emitted in the
model axially symmetric about the x-axis (cf. Section 2), the overall
spatial distribution is highly asymmetric with respect to the direction of the convective electric field, Esw , (see the panels on the right
and on the left columns). In addition, a slight asymmetry between
the y > 0 and y < 0 hemispheres results from a non-zero IMF Bx
component.
Fig. 2 shows that the escaping Oþ
2 ions form two different components with respect to their energy and their spatial distribution
near Mars: (1) a high-energy component and (2) a low-energy
1
component. The high-energy Oþ
2 component ðU > 50 km s Þ is
þ
highly asymmetric about the x-axis. The high-energy O2 ions are
found only on the ‘‘upper” z > 0 hemisphere to where Esw points.
These ions form a relatively narrow layer (thickness RM ) around
the xz-plane (panels c, f and i). Notice also that in the analyzed run,
the IMF points toward +y-direction and the high-energy Oþ
2 ions
within the magnetotail are, therefore, located near the cross tail
current sheet where the magnetic field is weak (see panels c, f
and i in the upper half of the yz-plane).
The low-energy ðU < 50 km s1 Þ Oþ
2 component is, instead, located much more symmetrically about the x-axis than the high-enþ
ergy Oþ
2 ions. The low-energy O2 ions occupy the optical shadow
and the region near the optical shadow. The energy of these two
þ
Oþ
2 ion components and the comparison with O ions are studied
in detail later in this section.
An analysis of the total Oþ particle density, the particle flux and
the bulk velocity are given in Fig. 3. Notice that these macroscopic
parameters are a combination of four Oþ ion populations: Oþ
þ
photoions Oþ
ion from the
hf ,axially symmetrically emitted O
þ
ionosphere Oiono , the oxygen ions produced
in a charge exchange
process by the solar wind protons Oþ
, and the oxygen ions
cxHþ
sw
produced in a charge exchange process by protons originating from
Þ.
the hydrogen exosphere ðOþ
cxHþ
exo
The Oþ ions from the ionosphere form a high energy and asymmetric ion component, as well as a relatively symmetric low-enþ
ions formed
ergy Oþ component, much as Oþ
2 ions. However, O
from the hot oxygen corona by EUV radiation and by two charge
exchange processes, form an energetic ‘‘halo”-like Oþ component
all around in the simulation box. The halo component is not so
clearly visible in the density plot, nðOþ Þ, because of the chosen
156
E. Kallio et al. / Icarus 206 (2010) 152–163
Fig. 1. Properties of protons and the magnetic field near Mars in the analyzed hybrid model run. (a) The total density of protons, nðHþ Þ, in ½cm3 , from 0:1 to 20 cm3 . (b) The
bulk velocity of protons, UðHþ Þ, in ½km s1 , between 0 and 450 km s1 . (c) The particle flux of protons, nUðHþ Þ, in ½cm2 s1 , from 5 105 to 6 108 cm2 s1 . (d) The
magnitude of magnetic field, jBj, in nT, between 0 and 20 nT. In Fig. 1, as in Figs. 3–7, the values of the parameters are show on the x ¼ 5000 km, y ¼ 0 and z ¼ 0 planes, and
on the sphere around Mars with a radius of 3600 km. Note that in Fig. 1, as in all figures in this paper, the analysis is focused to a relatively small region near Mars
ð5 103 km < x < 7 103 km, 15 103 km < y; z; < 15 103 kmÞ compared to the full simulation domain where the grid size is in its minimum but which is still large
enough to study asymmetries in the y- and z-directions.
color scale, but these ions are clearly seen in the plot of particle
velocity, UðOþ Þ, and in the particle flux, nUðOþ Þ. The energetic
‘‘halo” Oþ component occupies the whole simulation box, as can
be seen in Fig. 3, panels (d–f). Notice also that the empty blue regions in panels (d–i) are artifacts resulted from the limited number
of ions used in the simulation (cf. Section 2).
Fig. 3 showed the properties of the sum of four Oþ ion populations while various oxygen populations are analyzed in detail in
þ
Figs. 4 and 5. Panels (a–c) in Fig. 4 show the sum of Oþ
hf and Oiono
densities. Panels (a–c) in Fig. 5 show the bulk velocity of these popþ
ulations calculated from Eq. (16). The Oþ
hf and Oiono populations can
be seen to form asymmetric high-energy ion component, and a
quite symmetric low-energy ion component about the x-axis, similar to the case of Oþ
2 ions (cf. Fig. 2).
The oxygen ions produced from the charge exchange process
between the solar wind protons and the hot oxygen neutral corona,
instead, form widely spread ion populations (Fig. 4, panels d–f).
with respect to the direction
Notice that the asymmetry in Oþ
cxHþ
sw
of Esw results partly from the asymmetry in nðHþ
sw Þ and partly beions are under the influence of an electric field
cause the Oþ
cxHþ
sw
which is non-axially asymmetric with respect to the x-axis (the
direction and the magnitude of the electric field will be discussed
ions form a widely spread energetic
later in this Section). The Oþ
cxHþ
sw
‘‘halo” ion component (Fig. 5, panels d–f) much like the Oþ
hf ions.
ions in the tail is
Note also that the maximum density of Oþ
cxHþ
sw
about two orders of magnitude smaller than the maximum density
þ
associated with Oþ
hf and Oiono ions. It is also worth noting that the
þ
velocity of OcxHþsw ions near the x-axis (Fig. 5, panel f) is much larger
that the velocity of the other oxygen populations (Fig. 5, panels c
and i). The high-energy halo oxygen ions, therefore, exist also within and near the optical shadow of Mars, simultaneously with the
oxygen ions from the ionosphere.
ions is
It is worth noticing that the total loss rate of Oþ
cxHþ
sw
8 1023 s1 . This is more than the total loss rate of Oþ
hf ions in
the analyzed run ð 2:5 1023 s1 Þ and comparable with the total
24 1
s Þ. The Oþ
ions are, however, a
loss rate of Oþ
iono ions ð2 10
cxHþ
sw
minor Oþ ion population in the martian tail region compared with
þ
ions are spread over a
the Oþ
iono ion population because the OcxHþ
sw
much
larger
volume
within
the
simulation
box
ions.
ð4:2RM < x < 4:2RM ; 6:4RM < y; z < 6:4RM Þ than the Oþ
iono
The oxygen ions formed by the exospheric Hþ ions form a very
minor oxygen ion population near Mars (Fig. 4, panels g–i). The
maximum density of these oxygen ions is about two orders of magions. The spanitude smaller than the maximum density of Oþ
cxHþ
sw
ions are
tial distribution (cf. Fig. 4) and the velocity of Oþ
cxHþ
exo
quite similar to the spatial distributions and the velocities of Oþ
hf
þ
and Oþ
ions is only
iono ions. The total loss rate of OcxHþ
exo
1 1021 s1 .
E. Kallio et al. / Icarus 206 (2010) 152–163
157
þ
3
2 1
Fig. 2. The Oþ
; (d–f) the particle flux, nUðOþ
s ; and (g–i) the bulk velocity,
2 ions near Mars in the analyzed HYB-Mars run. (a–c) The ion density, nðO2 Þ, in ½cm
2 Þ, in ½cm
1
Þ,
in
½km
s
.
The
view
directions
in
the
panels
on
the
left
(a,
d,
g),
in
the
middle
(b,
e,
h)
and
on
the
right
(c,
f,
i)
are
similar
to
that
in
Figs. 3–6 in this paper: view (left
UðOþ
2
panels) to the y-direction, (middle panels) to the z-direction, and (right panels) to the +x-direction. The direction of the undisturbed solar wind velocity ðUsw Þ, the direction
of the IMF ðBsw Þ, and the direction of the convective electric field in the undisturbed solar wind ðEsw ¼ Usw Bsw Þ for orientations in the three columns are showed at the
bottom of the corresponding column. In Fig. 2, as in all figures in this paper, the distance between the tick marks is 500 km. Notice the high velocity Oþ
2 component at z > 0 (g
and i), and the low velocity Oþ
2 component around the x-axis (g, h and i).
The energy associated with the bulk velocity of Oþ and Oþ
2 are
shown in Fig. 6. The low-energy ðE < 100 eVÞ ion component is
clearly visible near Mars and within the optical shadow. The
high-energy ðE > 100 eVÞ ‘‘beam” component is clearly visible
þ
plots (Fig. 6, panels d–f) the
in Oþ
2 plots (panels a–c). In the O
high-energy ‘‘beam” component is embedded with the high-energy
‘‘halo” component.
The planetary ions are accelerated in the simulation by the electric field given in Eq. (6). Fig. 7 depicts the value of the electric field
on the three analyzed planes. Notice the following characteristic
features concerning the magnitude and the direction of the electric
field which has its importance when the acceleration of the planetary ions is considered. First, the electric field is low, less than
1
1 104 V m1 ð¼ 0:1 V km 340 eV R1
M Þ behind Mars within
the high density planetary ion region (cf. Fig. 7). Therefore, if an ion
remains within the high density region in the tail and if it crosses
the high density region (with a diameter of RM ) along the direction of E, it receives energy of a few hundreds of eV, at maximum.
This energy estimation within the high density region is consistent
with the bulk energy seen in Fig. 6.
Second, the overall direction of E on the yz-plane is ‘‘upward”
(to the +z-direction), that is, in the same direction as Esw points.
158
E. Kallio et al. / Icarus 206 (2010) 152–163
Fig. 3. (a–c) The particle density ð½cm3 Þ, (d–f) the particle flux ð½cm2 s1 Þ and (g–i) the bulk velocity ð½km s1 Þ of Oþ ions near Mars in the hybrid model. Notice that the
parameters contain four oxygen ion populations. See Fig. 2 for the detailed description of the layout.
The planetary ions have to move to the +z-direction in order to increase their energy by the electric field. This explains why Oþ and
Oþ
2 ions from the exosphere had a high-energy component on the
z > 0 hemisphere near the xz-plane. Another interesting aspect
concerning the direction of electric field is that its direction has a
‘‘focusing” toward the high density region around the x-axis on
the z < 0 hemisphere (Fig. 6, panel c). Similar focusing toward
the xz-plane takes place on the z > 0 hemisphere where E points
away from the high density region. In addition to these ‘‘E-focusing” regions, there are ‘‘E-diverging” regions on the z > 0 hemisphere. The focusing/diverging regions occur because Ez is
predominantly positive, while Ey points toward the xz-plane almost everywhere on the z < 0 hemisphere. The same is also true
on the z > 0 hemisphere near the xz-plane. It should also be no-
ticed, that these trends of the direction of E may have consequences on the acceleration of Oþ ions that are formed in the
exosphere. Those ions are initially practically at rest and, consequently, the newly formed exospheric Oþ ions feel the Lorenz force
(eE) (see Eq. (5)) which points to the direction of the electric field.
Analysis of Fig. 7 illustrated how planetary ions may get energy
had they moved from one point to another. However, it does not
provide information about how the planetary ions really move,
for example, can they be energized, or avoid energization, in the
analyzed electric field and magnetic field configuration. This question is studied by Oþ test particle simulations. Fig. 8 illustrates the
motion of several oxygen ions near Mars. One can note the following. First, Fig. 8 shows that the high-energy oxygen ions have such
a large ion gyroradius on the z > 0 hemisphere near the xz-plane
E. Kallio et al. / Icarus 206 (2010) 152–163
159
þ
þ
Fig. 4. The density of Oþ populations near Mars. (a–c) The sum of the density ð½cm3 Þ of oxygen ions from the ionosphere, Oþ
iono , and the O photoions, Ohf . (d–f) The density
ð½cm3 Þ of the oxygen ions formed in a charge exchange process by the solar wind protons. (g–i) The density ð½cm3 Þ of the oxygen ions formed in a charge exchange process
by protons originating from the hydrogen exosphere. Note the different density color scales.
that they are practically non-magnetized. Those ions move long
distances toward +z-direction along the electric field and, therefore, become highly energized. The gyroradius of these energetic
ions on the nightside is also increased by the relatively weak magnetic field near the cross tail magnetic field.
Secondly, Fig. 8 shows that the relatively small gyroradius of Oþ
ions within the high density planetary ion region within the tail
prevents them from moving long distances along the +z-direction
and, consequently, from being highly energized by the electric
field. The ‘‘stagnation” of Oþ ions within the high density ion region
is a non-linear effect. When the velocity of the major ion specie is
low and their density is high, the electric field is small unless there
are strong electric currents (see Eq. (7) of how the electric current
enters into the electron velocity and Eq. (6) of how the electric current enters thereafter into the electric field). A weak electric field
(dark regions in Fig. 8a), in turn, cannot accelerate planetary ions
effectively. The ion velocities and the gyroradius of ions can, therefore, remain low. The planetary ions can then, consequently, remain within the high density region. The low ion velocity, the
relatively small ion gyroradius, and stagnation of the planetary
ions within the high density region can be clearly seen in Fig. 8a.
The Oþ ions are, in addition, ‘‘bounced” back to the low electric
field region as soon as they reach the high electric field region
(white regions in Fig. 8a) on the z < 0 hemisphere where the electric field ‘‘focuses” to the low jEj region. As can be seen in Fig. 7c, a
similar kind of focusing of the E-field toward low jEj (and high
160
E. Kallio et al. / Icarus 206 (2010) 152–163
Fig. 5. A comparison between the velocities of different oxygen ion populations. (a–c) The bulk velocity ð½km s1 Þ associated with the oxygen ions from the ionosphere, Oþ
iono ,
1
Þ of the oxygen ions formed in a charge exchange process by the solar wind protons. (g–i) The bulk velocity
and the Oþ photoions, Oþ
hf . (d–f) The bulk velocity ð½km s
ð½km s1 Þ of the oxygen ions formed in a charge exchange process by protons originating from the hydrogen exosphere. The velocity scales are identical for all ion
populations. Note that the ‘‘zero” velocity region near Mars seen in (a)–(c) indicates that the number of Oþ
hf ions in the simulation was so small near Mars in the small grid size
þ
region that many of the grid points do not have any Oþ
hf ions at all. If the number of Ohf had been larger in the simulation, the ‘‘zero” velocity regions would disappear.
density) regions can be seen all over on the z < 0 hemisphere. A
similar kind of movement of Oþ ions toward the low jEj region to
where E ‘‘focus” to, as seen in Fig. 8a, was, in fact, observed in test
particle simulations where Oþ ions were generated from the hot
oxygen exosphere far way from Mars (figures not shown).
4. Discussion
Our understanding of the Mars–solar wind interaction in the
20th century relies strongly on the plasma and magnetic field mea-
surements made by Mars Global Surveyor (MGS) and Mars Express
(MEX) missions.
The data set is, however, still relatively incomplete to study the
ion escape at Mars, for several reasons. MGS has a magnetometer
which observed martian magnetic anomalies and which made it
possible to study the magnetic configuration associated with localized martian intrinsic structures and the direction of the IMF. But
although MGS had a magnetometer and electron instrument onboard, it did not have an ion instrument onboard to directly measure escaping planetary ions. The ASPERA-3 mass spectrometer on
MEX, instead, makes direct observations of escaping planetary
E. Kallio et al. / Icarus 206 (2010) 152–163
161
þ
þ
þ
Fig. 6. The bulk energy ð½eVÞ of (a–c) Oþ
2 ions and (d–e) O ions near Mars in the hybrid model. Notice the high energy ðE > 100 eVÞ O and O2 ‘‘beam” components, the
2
high-energy ðE > 100 eVÞ Oþ ‘‘halo” component, and the low energy ðE < 100 eVÞ Oþ and Oþ
2 components. The bulk energy is calculated as E ¼ 0:5mi U i , where mi and Ui is
the mass and the bulk velocity of the ion species i (i ¼ Oþ or Oþ
2 ), respectively.
ions, but there is no magnetometer on board. This has limited the
possibility to perform a detailed analysis of how the interplanetary
magnetic field affects the escape of planetary ions. A deep analysis
of the response of the escape process to the upstream parameters
is also complicated because there are no monitoring spacecraft to
provide upstream solar wind parameters near Mars. It should also
be recalled, that ion escape measurements by a spacecraft are local
measurements and one has to make further assumptions to derive
a picture about the possible global ion escape processes near Mars.
The possibility to apply a global self-consistent model to derive
a global picture of the martian ion escape processes from a local
plasma and field measurements has arose increasing interests during the last ten years. There are at least eight different global models currently used to analyze martian plasma environment (see
Brain et al., in this issue). Both of the adopted self-consistent model
approaches, namely MHD models and hybrid models, have certain
obvious strengths but also certain limitations (see discussion in
Ledvina et al., 2008).
In this paper an advanced HYB-Mars model has been developed
to study the escape of planetary Oþ and Oþ
2 ions in detail. Inclusion
of four different Oþ ion populations makes it possible to distinguish Oþ ions formed in the ionosphere ðOþ
iono Þ, in the exosphere
by photoionization ðOþ
hf Þ, and in two charge exchange processes
Þ or by protons origcaused either by the solar wind protons ðOþ
cxHþ
sw
Þ. Includinating from the martian neutral hydrogen corona ðOþ
cxHþ
exo
ing the electron pressure term and an analytical electron density
profile based in MTGCM model formed another improvement to
the HYB-Mars model.
The power of the hybrid model is that different ions and different ion populations can have different velocities, both bulk and
thermal velocities. This is an important property of the model
when one wants to understand ion escape observations which include both high energy and low energy escaping planetary ions and
various ion species. Acceleration processes associated with the
martian magnetic crustal anomalies may also result in ions whose
properties differ from the average properties of escaping planetary
ions. Moreover, by a hybrid model one may also try to answer a
question motivated by the interpretation of ion escape measurements: Could we say something about the origin and/or different
acceleration processes while we are analyzing ion mass spectrometer measurements at a certain time from a given point in the
space?
The analysis presented in this paper indicates that one may, indeed, derive various conclusions about aforementioned issues
associated with ion escape processes: about the spatial distribution, the density, the velocity and the energy of various Oþ ion populations and Oþ
2 ions. Analyzing the strength and the direction of
the electric field, which finally increases the energy of planetary
ions, also shields light on why some of the ions are accelerated
to high energies while the other ions are not. Test particle simulations further clarified the picture derived by analyzing bulk plasma
properties.
162
E. Kallio et al. / Icarus 206 (2010) 152–163
Fig. 7. The magnitude of the electric field E ¼ ue B þ rðpe Þ=ne (see Eq. (6)) which energizes the planetary ions in the model. The vectors are normalized electric field
vectors, Eo ¼ E=jEj. The vectors shown on each panel are the components of Eo within that plane. Notice the low electric field region near the optical shadow. Notice also the
‘‘focusing” of the direction of Eo toward the xz-plane, i.e., toward the cross tail current sheet (c). The color on the x ¼ 5000 km, y ¼ 0 and z ¼ 0 planes show the magnitude of
the electric field in a linear color scale from 0 to 2:3 103 V m1 . The blue sphere of radius 3600 km is added to illustrate the approximate position of the martian exobase.
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. The motions and energization of Oþ test particles. The Oþ ions were launched at 3700 km from the center of Mars with the radial velocity of 5 km s1 . These ions
þ
represent Oþ
iono population in the hybrid simulation in which macroscopic plasma parameters were presented in details in Figs. 4 and 5a–c. The motion of O ions is calculated
from the Lorentz force (Eq. (5)) by using the electric field (Eq. (6)) and the magnetic field in the analyzed run. Colors on the trajectories show the ion velocity in km s1 . In (a)
the gray scale gives the magnitude of the electric field on the xz-plane (see Fig. 6 for the details of the electric field) and the vectors are normalized electric field vectors,
Eo ¼ E=jEj, as in Fig. 7. The electric field is strong in the white regions and low in the dark regions. In (b) the ion trajectories are viewed along the z-axis on the z < 0
hemisphere. Note that in (b) Mars is viewed on the z-axis in order to see clearly the orbits of the low energy oxygen ions. Therefore, +y-axis points up. In all other plots in
this paper, instead, z ¼ 0 plane is viewed on the +z-axis and the +y-axis points down. The black lines are magnetic field lines close to the xy-plane. Notice how the analyzed
ions remain near the xz-plane, that is, close to the cross tail current sheet.
Much more work, however, has to be done in order to understand ion escape processes at Mars with the HYB-Mars model thoroughly. The model does not include a self-consistent ionosphere or
the crustal magnetic fields. These limitations are partly related to
the minimum grid size in the simulation (180 km) which is too
coarse to model the ionosphere and small size magnetic anomalies
in detail. Electron impact ionization has to also been taken into account in the future work.
One may also anticipate that more detailed modeling of
the martian hydrogen and oxygen neutral exospheres will force
E. Kallio et al. / Icarus 206 (2010) 152–163
adjustment of the adopted neutral density profiles. For example,
the adopted hydrogen exobase density in this paper (Barabash
et al., 2002) may be about two orders of magnitude higher than
it is in reality during the solar minimum (see Galli et al., 2006). If
that is the case, the density of Hþ
exo ions would be two orders smaller than obtained in this simulation. Therefore, the density of Oþ
cxHþ
exo
ions produced from Hþ
exo ions by change exchange processes (Eq.
(9)) would also be two orders smaller than presented in this paper.
ions would, therefore, be even more of a minor Oþ ion
The Oþ
cxHþ
exo
specie than presented in this work (Fig. 4, panels g–i) and very difficult to be observed by a particle instrument. In addition, the denand Oþ
ions depends practically linearly on the
sity of Oþ
cxHþ
cxHþ
exo
sw
density of the oxygen exosphere. A factor of, say, one smaller density of oxygen in the exosphere would, therefore, result in a factor
and Oþ
densities than presented in this paof one smaller Oþ
cxHþ
cxHþ
exo
sw
per in Fig. 5, panels (d–i).
It should finally be noted that there is one ASPERA-3 data set
which provides information both about ions and the neutral coronas, but which has not been discussed in this paper: Energetic Neutral Atom (ENA) measurements. ENAs are measured by two ENA
detectors on the ASPERA-3 particle package (see Barabash et al.,
2006). The developed HYB-Mars model may provide new insight
to those issues, because the four implemented charge exchange
processes (see Eqs. (8)–(11)) result in hydrogen ENAs and hydrogen ENAs has been observed by ASPERA-3 instrument.
5. Summary
The escape of Oþ and Oþ
2 ions were studied quantitatively by a
hybrid model. These ions have formed two high-energy ion components and one low-energy ion component. (1) The low-energy Oþ
and Oþ
2 ion component was distributed relatively symmetrically
near Mars about the Mars–Sun axis. (2) The high energy Oþ and
Oþ
2 ion components originating from the ionosphere formed a
highly asymmetric and spatially localized oxygen ion ‘‘beam” component. (3) The Oþ ions formed in the exosphere, either by EUV
light or charge exchange processes, also formed high-energy ions
near Mars. These energetic ‘‘halo” Oþ ions were spread much more
symmetrically around Mars than the high-energy ions escaping
from the ionosphere. The existence of an asymmetric high-energy
escaping ion component and a relative symmetric low-energy ion
163
component is in line with the ASPERA-3/Mars Express plasma
measurements. The analysis of the magnitude and the direction
of the electric field near Mars indicated that low-energy planetary
ions are located in the region where the electric field is weak and
where they cannot be accelerated effectively. The high-energy
planetary ions are, instead, located in the high convective electric
field regions.
Acknowledgment
The authors thank Prof. Stephen Bougher for providing MTGCM
electron density profiles.
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