# X-ray morphology due to charge-exchange emissions used to study the global
structure around Mars

G.Y. Liang  CAS Key Laboratory of Optical Astronomy, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, China  Institute
for Frontiers in Astronomy and Astrophysics, Beijing Normal University,
Beijing 102206, China  T.R. Sun  National Space Science Center, Chinese
Academy of Sciences, Beijing, China  H.Y. Lu  School of Space and Environment,
Beihang University, Beijing 100191, China  X.L. Zhu  Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  Y. Wu  Key
Laboratory of Computational Physics, Institute of Applied Physics and
Computational Mathematics, Beijing 100088, China  S.B. Li4 H.G. Wei1, D.W.
Yuan1 J.Y. Zhong2 Department of Astronomy, Beijing Normal University, Beijing
100875, China  W. Cui  Department of Astronomy, Tsinghua University, Beijing
100084, China  X.W. Ma5, G. Zhao1

###### Abstract

Soft x-ray emissions induced by solar wind ions that collide with neutral
material in the solar system have been detected around planets, and were
proposed as a remote probe for the solar wind interaction with the Martian
exosphere. A multi-fluid three-dimensional magneto-hydrodynamic model is
adopted to derive the global distributions of solar wind particles.
Spherically symmetric exospheric H, H2, He, O, and CO2 density profiles and a
sophisticated hybrid model that includes charge-exchange and proton/neutral
excitation processes are used to study the low triplet line ratio
$G=\frac{i+f}{r}$ (0.77$\pm$0.58) of O VII and total x-ray luminosity around
Mars. We further calculate the emission factor $\alpha$-value with different
neutrals over a wide ion abundance and velocity ranges. Our results are in
good agreement with those of previous reports. The evolution of the charge
stage of solar wind ions shows that sequential recombination due to charge-
exchange can be negligible at the interaction region. This only appears below
the altitude of 400 km. The anonymous low disk $G$ ratio can be easily
explained by the collisional quenching effect at neutral densities higher than
1011cm-3. However, the quenching contribution is small in Mars’ exosphere and
only appears below 400 km. Charge-exchange with H2 and N2 is still the most
likely reason for this low $G$-ratio. X-ray emissivity maps in collisions with
different neutrals differ from each other. A clear bow shock in the collision
with all the neutrals is in accordance with previous reports. The resulting
total x-ray luminosity of 6.55 MW shows a better agreement with the XMM-Newton
observation of 12.8$\pm$1.4 MW than that of previous predictions.

atomic processes – solar wind: individual: Mars-x-rays

##  1 Introduction

Solar wind ion–induced charge-exchange (SWCX) x-ray emissions have been
detected from most planets in the solar system, e.g., Earth (Snowden et al.,
2004)), Mars (Dennerl et al., 2006), Saturn (Branduardi-Raymont et al., 2010),
Jupiter (Branduardi-Raymont et al., 2007; Hui et al., 2009). A review of SWCX
emission in the solar system was presented by Dennerl et al. (2012). This kind
of x-ray emission was further suggested as a probe for remote monitoring of
the magnetosheath and magnetopause of the planets and the solar wind by
Snowden et al. (2009); Sun et al. (2019) for Earth. Gunell et al. (2004)
estimated the SWCX total x-ray luminosity (1.8 MW) to be consistent with the
Chandra 2001 observation for Mars that used a hybrid model for the solar
wind–Mars interaction and a test particle simulation of heavy ion trajectories
near Mars, where a constant cross-section for H and O atoms and a simplified
two-step cascade model were adopted. Later, Koutroumpa et al. (2012) performed
a three-dimensional (3D) multi-species hybrid simulation model, and reproduced
the solar wind–Martian interfaces well by using x-ray morphology, and
confirmed its feasibility for the remote probing to the interaction between
the solar wind and the Martian exosphere. However, the estimated luminosity of
$\sim$0.7–2.0 MW is far smaller than the total observed luminosity of
12.8$\pm$1.4 MW (Dennerl et al., 2006). Koutroumpa et al. (2012) included
three neutral profiles of H, O, and CO2 in the Martian environment and
constant cross-sections with H and H2O without the H2 and He components.
Additionally, an anonymous low line intensity ratio $(i+f)/r$ of O VII in disk
observation cannot be explained by the charge-exchange process.

In this work we incorporate recent progress on solar wind ions distributions
from a multi-fluid magneto-hydrodynamic (MHD) simulation comparing with the
Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft data. Furthermore,
we include more neutral components in the Martian exosphere to re-study the
x-ray luminosity. In section 2 we describe the MHD model for solar wind ions,
the neutral profile, as well as a sophisticated hybrid atomic model for x-ray
emission. In section 3 we present the temperature- and velocity-dependent
$\alpha$-value, the evolution of charge-stage of solar wind ions, the
collisional quenching effect on line ratios of O VII, and the x-ray emissivity
maps in the XZ plane. Finally, a summary and conclusion are outlined in
section 4.

##  2 Simulation model

In this interaction of solar wind ions with Martian neutrals (including H, H2,
He, O, CO2), the local volume emission rate $P(r)$ from $X^{q+}$ charged ion
is given by Cravens (1997); Koutroumpa et al. (2009),

$\displaystyle P^{q+}(r)=N^{q+}(r)\sum_{ij,k}\epsilon^{k}_{ij}(v),$ (1)

where $N^{q+}$ is number density of solar wind ions $X^{q+}$ at given location
($r,\theta$, $\phi$), respectively. $\epsilon^{k}_{ij}(v)$ is the $i\to j$
line emissivity at a relative collisional velocity
$v=\sqrt{v_{sw}+3k_{B}T/m_{p}}$ between solar wind ion and $k$-th neutral.
Here $v_{sw}$ is the bulk velocity of the solar wind and the second term is
the general thermal velocity. The number density of different charged ions
$X^{q+}$ is a self-consistent solution to the differential equation:

$\displaystyle\frac{dN^{q+}(r)}{dr}$
$\displaystyle=-N^{q+}\sum_{k}\sigma_{k}^{q+}(v)n^{k}_{\rm neu}$
$\displaystyle+N^{(q+1)+}\sum_{k}\sigma_{k}^{(q+1)+}(v)n^{k}_{\rm neu}$

that describes the evolution of solar wind charged ions in the radial
direction, where the initial $X^{q+}$ ion number density
$N^{q+}(r_{\infty})=Ab*n_{\rm sw}$ is defined by its abundance in the solar
wind before interaction.

###  2.1 Neutral atmosphere and exosphere

The Martian neutral environment is composed of CO2, O, H, H2, He, and N2 as
shown in Fig. 1. The density profiles of CO2, and O are fit to results from
the Mars thermosphere global circulation model (MTGCM) as reported by
Koutroumpa et al. (2012). The hydrogen density profile is fit to results from
Anderson & Hord (1971) and Krasnopolsky (2002) and can be written by

$\displaystyle n_{\rm H}$ $\displaystyle=10^{3}{\rm exp}\left[9.25\times
10^{5}\left(\frac{1}{z+3393.5}-\frac{1}{3593.5}\right)\right]$ (3)
$\displaystyle+3.0\times 10^{4}{\rm exp}\left[1.48\times
10^{4}\left(\frac{1}{z+3393.5}-\frac{1}{3593.5}\right)\right]$

For the H2 and He density profile we adopt the results of Krasnopolsky
(2010)with a similar fitting formula as H but with different fitting
parameters as given by

$\displaystyle n_{\rm H_{2}}$ $\displaystyle=1.59\times 10^{4}{\rm
exp}\left[1.48\times
10^{6}\left(\frac{1}{z+3384.1}-\frac{1}{3548.2}\right)\right]$ (4)
$\displaystyle+5\times 10^{4}{\rm exp}\left[4.8\times
10^{4}\left(\frac{1}{z+3384.1}-\frac{1}{3548.2}\right)\right],$

$\displaystyle n_{\rm He}$ $\displaystyle=1.79\times 10^{4}{\rm
exp}\left[1.38\times
10^{6}\left(\frac{1}{z+3381.1}-\frac{1}{3549.2}\right)\right]$ (5)
$\displaystyle+9\times 10^{4}{\rm exp}\left[8.5\times
10^{4}\left(\frac{1}{z+3381.1}-\frac{1}{3549.2}\right)\right].$

The fitting values at low altitudes are consistent with the results of
Krasnopolsky (2010).

Recently, these neutral profiles below 500 km have been measured by the
Neutral Gas and Ion Mass Spectrometer (NGIMS) on the Mars Atmosphere and
Volatile EvolutioN (MAVEN) mission (Mahaffy et al., 2015; Stone et al., 2022;
Wu et al., 2021). The hydrogen profile was measured via the 1216 Å Lyman alpha
line covered by the Imaging Ultraviolet Spectrograph (IUVS) on the MAVEN
mission (Chaffin et al., 2018). Stone et al. (2022) further investigated their
horizontal variations with local time, latitude and season. The magnitude of
variation is very large, and even more than an order of magnitude for H2 and
He (Stone et al., 2022, see Fig. 6 there). For comparison, the MAVEN
measurements during the orbit period of DD2 (Wu et al., 2021; Stone et al.,
2022) and similar fitting as above are presented in the bottom panel of Fig.
1. Since there are not in-situ measurement data for the neutral density above
1000 km, we still can not calibrate the uncertainty of this extrapolation. Yet
it approximately follows the relation of $\sim 1/r^{3}n^{{\dagger}}_{\rm H}$
(here $n^{{\dagger}}_{\rm H}$ is the hydrogen density near Mars). Although
their proportional relation to the x-ray emission as shown in Eq.(2), the low
neutral density at distant halo region makes the resultant total X-ray
luminosity to be affected smalle by the uncertainty of this extrapolation. By
using the two different groups of the neutral profiles, we will estimate the
uncertainty of the total luminosity from neutrals, that will be discussed in
the following discussion section.

Figure 1: Neutral density profile of different species in the Martian
atmosphere. Upper: For H2 and He neutrals, a fitting procedure was used to
extend the available data (symbols) from Krasnopolsky (2010) to a higher
altitude. For N2 gas, the density profile is from the work of Bougher et al.
(2015). Bottom: The MAVEN measurement at the period of DD2 (Wu et al., 2021)
and the corresponding fitting.

###  2.2 Global distribution of solar wind ions around Mars

The interaction of the solar wind with the Martian atmosphere and ionosphere
results in the formation of two distinct boundaries, i.e., bow shock and
magnetic pileup (or magnetic pause). Modolo et al. (2005, 2006) investigated
the global structure around Mars using a three-dimensional multi-species
(proton and He2+) hybrid model, where complicated substructures were
demonstrated in density maps of protons and $\alpha$-particles. Using the
MAVEN spacecraft data and an algorithm of automated region identification,
N${\rm\check{e}}$mec et al. (2020) derived an empirical model for both the bow
shock and magnetic pileup boundary locations around Mars. By assuming
cylindrical symmetry, a parabolic model with a focus on the subsolar standoff
location ($x_{0}=C~{}p^{\beta}_{sw}F^{\gamma}B^{\delta}$) in the $x$-axis
(Sun-Mars center line) can well fit the two boundaries, i.e.,

$\displaystyle\rho^{2}=$ $\displaystyle\alpha(x-x_{0}).$ (6)

Here, $\rho$ and $x$ (in $R_{\rm M}$) are aberration-corrected cylindrical
coordinates of a given point at the bow shock and magnetic pileup boundary.
$C$, $\alpha$, $\beta$, $\delta$, and $\gamma$ are parameters fit to the MAVEN
spacecraft data for the bow shock and magnetic pileup boundary. $p_{sw}$ is
dynamic pressure in nPa, $F$ refers to the solar ionizing flux in mW m-2, and
$B$ denotes the magnitude of the magnetic field in n$T$. The best-fit result
for the bow shock and magnetic pileup boundary are illustrated by thick black
curves in Fig. 2.

In this work a multi-fluid 3D MHD model is adopted to derive the global
distributions of the solar wind particle (H+) density and velocity surrounding
Mars, where the Navier-Stoker equations for five significant ion species
(i.e., proton in solar wind, H+ from Mars, O${}_{2}^{+}$, O+, CO${}_{2}^{+}$)
in the Martian ionosphere were used to describe the physics. The equations
include conservation equations for the plasma flow with respect to continuity,
momentum, and energy. The Navier-Stoker equations for each species are
augmented by the interaction of the electromagnetic effects. The physical
detail for this 3D MHD model can be found in the studies of Li et al. (2020,
2022).

The computational domain is -24$R_{\rm M}\leq x$ $\leq 8R_{\rm M}$, -16$R_{\rm
M}\leq y/z$ $\leq 16R_{\rm M}$, where $R_{\rm M}$ is the radius of Mars
($R_{\rm M}=3396$ km). Because the general curvilinear coordinate system is
adopted, a high resolution for the region with the most intense variations of
physical parameters is achieved by refining the physical grid, and the
smallest grid size can approach 60 km. The solar wind density and velocity are
chosen to be 4 cm-3 and 500 km/s, respectively. The interplanetary magnetic
field (IMF) is chosen to be 3 nT.

The solar wind density and velocity profiles in the XZ-plane show a clear bow
shock with its position being excellent agreement with that from MAVEN
spacecraft data (N${\rm\check{e}}$mec et al., 2020), see Fig. 2.

Figure 2: Left: Density map of the solar wind H+ species reproduced from a 3D
five species multi-fluid magnetohydrodynamic (MHD) simulation by Li et al.
(2020). Right: Velocity map of the solar wind ions reproduced from the 3D
multi-fluid MHD simulation by Li et al. (2020, 2022). The thick solid curves
represent the locations of bow shock and magnetic pileup boundary from the
formula derived by N${\rm\check{e}}$mec et al. (2020) based on the MAVEN
spacecraft data.

###  2.3 Emission model

To calculate the line emissivity $\epsilon$ of $X^{q+}$ at a given location
($r,\theta$, $\phi$) due to charge-exchange electron captures with neutrals,
and to calculate subsequent radiative decays, either directly to the ground
and lower excited states or via cascades, we obtain the density $N^{q+}_{i}$
of an ion $X^{q+}$ at a given $i$-th level state by solving the following rate
equation assuming equilibrium:

$\displaystyle\frac{d}{dt}N_{i}^{q+}(r)=\sum_{j>i}N_{j}^{q+}(r)A_{ji}-\sum_{j<i}N_{i}^{q+}(r)A_{ij}$
$\displaystyle+\sum_{k}n^{k}_{\rm
neu}(r)N_{0}^{(q+1)+}\left[C^{k}_{0i}(v)+\eta^{2\to 1}C^{2,k}_{0i}(v)\right]$
(7) $\displaystyle+n_{\rm H}\sum_{j\neq i}\left[N_{j}^{q+}(r)Q_{ji}(T_{\rm
e})-N_{i}^{q+}(r)Q_{ij}(T_{\rm e})\right]$ $\displaystyle=0,$

where $N_{i}^{q+}$ is the number density of $q+$ charged ions at $i$-th level
state, while $n^{k}_{\rm neu}$ corresponds to the number density of $k$ kind
of neutrals, e.g. H, H2, He, O, and CO2. $n_{\rm H}$ refers to the density of
H. $C^{k}_{ij}\equiv<v\sigma^{k}_{\rm cx}(v)>$ and
$C^{2,k}_{ij}\equiv<v\sigma^{2,k}_{\rm cx}(v)>$ are the single and double-
electron capture rate coefficients, respectively. $A_{ij}$ is the radiative
decay rate for a given transition line $i\to j$. $Q_{ij}(T_{\rm e})$ are the
proton impact excitation rates at a given temperature $T_{\rm e}$ that are
used to account for neutral impact excitations due to high density at lower
altitudes, and are only considered for O VII triplets at disk observation. $v$
is the relative collision velocity between $X^{(q+1)+}$ and $k$ kind of
neutrals, while $\sigma^{k}_{\rm cx}(v)$ and $\sigma^{2,k}_{\rm cx}(v)$ are
the cross-section of single- and double-electron transfer processes.
$\eta^{2\to 1}$ refers to the ratio of ionic fraction between $(q+2)+$ and
$(q+1)+$ charged ions before electron capture. Furthermore, the line
emissivity $\epsilon_{ij}=N^{q+}_{i}A_{ij}$ can be obtained.

The atomic data of level energies and radiative decays have been reported by
Liang et al. (2014, 2021). Here the charge-exchange cross-sections are from
the Kronos v3.1 database 111www.physast.uga.edu/research/stancil-group/atomic-
molecular-databases/kronos  that is implemented by Stancil research group in a
series of studies (Cumbee et al., 2014, 2018; Mullen et al., 2016, 2017) that
use multiple methods, including multichannel Landau-Zener (MCLZ), atomic-
orbital close-coupling (AOCC), molecular-orbital close-coupling (MOCC), and
classical trajectory Monte Carlo methods. For the collision of O7+ with the O
atom, there are no data available. Hence, the MCLZ CX cross-section of O7+
with water (H2O) is used because of their similar weight. For the double-
electron capture cross-section, we adopt those available data that are
explained in the study by Liang et al. (2021). Since the data availability
from AOCC/MOCC method are in the Kronos database, we adopt cross-sections from
the AOCC/MOCC method for bare- and H-like ion collisions with the hydrogen or
helium atom, while data from the MCLZ method will be used for collisions with
other neutrals. This means the velocity-dependent CX cross-section is used in
this work, not the constant cross-section used in the work of Koutroumpa et
al. (2012). For example, Fig. 3 shows the cross-section of H-like oxygen O7+
ion collisions with different neutrals in the Martian exosphere. For
comparison the values used by Koutroumpa et al. (2012) are also plotted; these
values have a smaller cross-section with H and a larger cross-section with O
than the accurate calculation in Kronos v3 database by $\sim$40% and
$\sim$300% respectively, and were used by Koutroumpa et al. (2012). Therefore,
the x-ray emissions would be under-/over-estimated in this previous work. In
the collision with H, Zhang et al. (2022) measured the absolute cross-sections
at collisional velocities covering the typical solar wind velocities; see
symbols with error bars in Fig. 3. Thus, these experimental data in the
collision with H are used in this work. There is an obvious difference between
the experimental results and the theoretical calculations including those from
Kronos database and from Gu’s fitting below 200 km/s. This illustrates that a
sophisticated method and laboratory measurements are still required for the
velocity-dependent cross-sections in the collisions with other neutrals, even
the best available cross-sections are used in this paper. This kind of
uncertainty has a significant effect on spectral analyses for observations
with high-resolution by using the charge-exchange model, and has been pointed
out by Gu et al. (2022) for advanced theoretical calculations for especially
the low collision energy regime, in combination with more laboratory
measurements.

Figure 3: Charge-exchange cross-section of O7+ with H, H2, He, O and CO2,from
the Kronos v3.1 database ${}^{\ref{ft_kronos}}$. For the collision with the H
atom, the data are from MOCC calculation, and Gu’s fitting (Gu et al., 2016).
Symbols refer to the values used by Koutroumpa et al. (2012) for collisions
with H (open circle) and O (filled square). Symbols with error bars are from
recent experiments by Zhang et al. (2022).

##  3 Results and Discussion

###  3.1 Velocity and temperature dependence of $\alpha$ value

The $\alpha$-value combined with MHD modeling is extensively used by the space
physics community. This is a proportional factor based on a combination of the
relative abundances and the cross-section of each possible interaction between
a solar wind ion and a neutral particle $k$ causing line emissions as defined
by Cravens (1997) and Whittaker et al. (2016) as follows:

$\displaystyle\alpha_{k}(X)=\sum_{q+}\alpha_{k}(X^{q+})=\sum_{q+}\left[\frac{X^{q+}}{O}\right]\left[\frac{O}{H}\right]\epsilon_{k}(X^{q+}),$
(8)

where ion emissivity $\epsilon_{k}(X^{q+})$ of a $q+$ charged ion is obtained
by summing the line emissivity $\sum_{ij}\epsilon_{k,ij}(X^{q+})$ with the
neutral particle of $n^{k}_{\rm neu}=1.0$ for a given transition $i\to j$. The
line emissivity of one solar wind species $\epsilon_{k,ij}(X^{q+})\equiv
N^{q+}_{j}A_{ij}$ can be obtained from Eq. (7) at the collision with the $k$
neutral by multiplying by the radiative rate $A_{ij}$. In previous works
(Schwadron & Cravens, 2000; Cravens, 1997; Whittaker & Sembay, 2016), the line
emissivity $\sum_{ij}\epsilon_{k,ij}(X^{q+})$ in Eq. (8) is replaced by
$\sigma_{ij}\Delta E_{ij}$, which means cascading effects to the upper atomic
states $j$ of the $\Delta E_{ij}$ transition have been neglected.

Eq. (8) shows that the $\alpha$-value is highly variable depending on the
ionic fraction of a given element and its abundance. Due to the extreme low
electron density in inter-planetary space, the charge state distribution of
solar wind ions will freeze-in after leaving the solar surface (Landi et al.,
2012). This distribution in the solar wind provides insight into its origin
with the characteristic temperature from the Sun. Thus, we adopt the
temperature in collisional equilibrium to represent the relative ionic
fraction in solar wind. Figure 4 shows the $\alpha$-values (in eV cm2) of
oxygen in collisions with different neutrals (e.g., H, H2, He, O and CO2) as a
function of solar wind velocity and logarithmic temperature (in the unit of
K). Here, the solar abundance of Lodders et al. (2009) is adopted with oxygen
to hydrogen abundance ratio of [O/H]=6.05$\times 10^{-4}$, which is slightly
higher than the mean values ranging from 2.03$\times 10^{-4}$ to 4.76$\times
10^{-4}$ from the ACE SWICS data for fast and slow solar winds (Whittaker &
Sembay, 2016), but consistent with the reported mean [O/H] ratio of
3.94$\times 10^{-4}$ with a standard deviation of 3.01$\times 10^{-4}$ by
Whittaker et al. (2016) from the OMNI data 222https://omniweb.gsfc.nasa.gov/.
By using the ACE (Advanced Composition Expoloer) data (including the ion
density of O7+,8+, oxygen abundance [O/H], and solar wind velocity) obtained
over 13 years (1998–2011) and the charge-exchange cross-sections from Bodewits
(2007), the resulting $\alpha$-value has a modal peak at $6\times 10^{-16}$ eV
cm2 when colliding with hydrogen (Whittaker & Sembay, 2016, see Fig. 2). To
compare with empirical methods Whittaker et al. (2016) derived an
$\alpha$-value of 7.6$\times 10^{-16}$ eV cm2 by using [O/H]=1.1$\times
10^{-3}$, an O7+ abundance of 0.28, and an O8+ abundance of 0.05. The present
calculation (7.3$\times 10^{-16}$ eV cm2) shows an excellent agreement with
the value measured at the temperature corresponding to the O7+,8+ abundance
ratio at equilibrium. The present calculation of log($T_{e}$)/K=6.1 shows a
good agreement with that of Whittaker & Sembay (2016) at a typical solar wind
velocity of 300–600 km/s, where in-situ ACE data including velocity, O7+,8+
abundance, and abundance ratio [O/H], were used. Both the present calculations
and previous work from ACE data demonstrate that there is a strong dependence
on the ionic fraction or temperature between log($T_{e}$)/K=6.0 and 6.5.

Figure 4: Top: Present $\alpha$-value of oxygen in collision with hydrogen at
three temperatures (log($T_{e}$)/K=6.0, 6,1 and 6.2), along with calculated
ones from the work of Whittaker & Sembay (2016)) based on parameters
(velocity, O7+,8+ fraction and abundance ratio [O/H]) from ACE data. Contour
plots for $\alpha$-values (eV cm2) of oxygen in collisions with H, H2, He, O
and CO2 in the temperature range log($T$) = 5.0–7.0 and velocity range of
50–2000 km/s with grid of 0.1 and 20 km/s, respectively. Here the solar
abundance for oxygen [O/H]=6.05$\times 10^{-4}$ is used. The horizontal solid
lines refer to the typical solar wind velocity range of 200–500 km/s and the
temperature (log($T)=6.3$ K) with O7+ and O8+ abundances of 0.28 and 0.05 in
collisional ionization equilibrium, respectively.

Hydrogen gas (H2), He, O, and CO2 are also important components in the Martian
neutral environment. Both the multi-fluid 3D MHD computation performed by Li
et al. (2020) and MAVEN data demonstrate that the bow shock and magnetic
pileup boundary are approximately 1.55 $R_{M}$ (corresponding to the altitude
of 1868 km 333In the unit of the Martian radius $R_{\rm M}$, this value is
relative to Mars’ center, otherwise it refers to the altitude relative to the
Martian surface.) and 1.3 $R_{M}$ (1018 km) in the direction of Sun to Mars,
respectively, see Fig. 2. Below this altitude the number densities of H2 and
He become dominant and are higher than those of atomic hydrogen, see Fig. 1.
We also present the $\alpha$-value in collision with other Martian neutrals.
An obvious dependence on solar wind velocity appears below $\sim$200-300 km/s.
Large decrease of solar wind velocity after bow shock as shown in Fig 2
reveals that the constant $\alpha$-value adopted in previous works should
generate large uncertainties (Whittaker & Sembay, 2016; Whittaker et al.,
2016). The present $\alpha$ calculation will help improve the estimation of
x-ray emission in the interaction region. In the calculated temperature and
velocity grids the $\alpha$-value with H2, O, and CO2 is systematically higher
than the value in the collision with H.

We further calculate the $\alpha$-value of carbon, nitrogen and neon in the
collisions with H, H2, He, O, and CO2, see Fig. 5. Compared to the
$\alpha$-value of oxygen, the carbon $\alpha$-value is lower than that of
oxygen, while the nitrogen $\alpha$-value is even lower. This is mainly
resultant from the higher abundance of oxygen than carbon and nitrogen in the
solar wind. According to the mean abundance from ACE data of highly charged
oxygen ions (O8+/0.28, O7+/0.05, Whittaker et al. (2016)) and carbon ions
(C6+/0.13, C5+/0.37, Koutroumpa et al. (2012)), the calculated $\alpha$-values
in the collisions with H are about 7.9$\times 10^{-16}$ eV cm2 (O) and
4.4$\times 10^{-16}$ eV cm2 (C), respectively. With the similar temperature of
log$(T)=6.1\pm 0.1$, the nitrogen $\alpha$-value is $\sim 3.5\times 10^{-16}$
eV cm2. We also notice that there is a sudden decrease around 900 km/s for the
$\alpha$-value of N in the collision with H. This is due to the recommended
$nl$-selective cross-section used (Wu et al., 2011, see Fig. 5 there), and its
complicated $nl$-distribution along the collisional velocity.

Figure 5:  Contour plots for $\alpha$-values (eV cm2) of carbon (left) and
nitrogen (right) in collisions with H, H2, He, O and CO2 in the temperature
range log($T$) = 5.0–7.0 K and velocity range of 50–2000 km/s with grid of 0.1
and 20 km/s, respectively. The horizontal white solid lines corresponding to
temperature (log$(T)=6.0$ K) with C5+ and C6+ abundance of 0.37$\pm$0.03 and
0.13$\pm$0.06 are from ACE data; see Table 1 in Koutroumpa et al. (2012).

###  3.2 Evolution of charge stage of solar wind ion

To examine the validity of the $\alpha$-value that comes from a specified ion
abundance at the interaction region, we calculate the evolution of charge
stage of solar wind ions of carbon, nitrogen, and oxygen as defined by Eq.
(2). Here, the initial ion abundances are from published literature, for
example, Schwadron & Cravens (2000) for oxygen, and Koutroumpa et al. (2012)
for carbon. Because the evolution profile of nitrogen ions are similar to
those of carbon and oxygen ions, only bare and H-like carbon and oxygen ions
in the solar wind are given. For this we considered the resulting soft x-ray
emissions within a photon energy range of 200–1000 eV, see Fig. 6. This figure
shows that the charge stage distribution of solar wind ions does not change
over the interaction region between the bow shock (1.57$R_{\rm M}$) and
magnetic pileup boundary (1.3$R_{\rm M}$). This indicates that there is no
sequential recombination due to charge-exchange when the solar wind ion passes
through this interaction region. At an altitude of $\sim$400 km the relative
ion abundance of solar wind carbon and oxygen ions starts to change, and
reaches a peak ion abundance for H-like ions at the altitude of $\sim$230 km;
in other words solar wind ions move slowly, captured H-like ions accumulate
and then further sequential recombination take places below $\sim$400 km. By
using MAVEN DD2 data for the neutral density (Wu et al., 2021), such rising
does not appears, that is ion accumulation and sequential recombination do not
take place. This is probably due to the lower oxygen density below 300 km in
the MAVEN DD2 data. The evolution behavior of highly charged solar wind ions
also indicates that the general fixed $\alpha$-value for a given ion abundance
is still valid in the interaction region, but it fails below $\sim$400 km of
Mars.

Figure 6: Evolution of charge state of oxygen and carbon ions with initial ion
abundance of slow solar wind from the work of Schwadron & Cravens (2000) for
O8+/0.07 and O7+/0.20, as well as from the work of Koutroumpa et al. (2012)
for C6+/0.13 and C5+/0.37. Dashed-dot-dot lines refer to calculation with the
inclusion of double electron capture (DEC).

###  3.3 Collisional quenching effect on He-like triplet ratio of O VII

The triplet-to-single line intensity ratio ($G=\frac{(f+i)}{r}$, here $i,f,r$
is inter-combination, forbidden, and resonance line, respectively) of He-like
ions is an important probe for the charge-exchange and/or coronal emissions of
astrophysical plasmas, and is used extensively by those who appy astrophysical
x-ray spectroscopy with high-resolution (Katsuda et al., 2012; Zhang et al.,
2014) to study the interface of hot outflows and cold interstellar (or
intergalactic) medium. From the high-resolution XMM-Newton observations of
Mars, Dennerl et al. (2006) and Koutroumpa et al. (2012) extracted out these
line fluxes for disk and halo regions with $G$ ratios of 0.77$\pm$0.58 (disk)
and 5.36$\pm$5.82, respectively. The mean value of the $G$ ratio for the halo
is significantly higher than value for the disk. Many charge-exchange emission
models have been setup to explain the large $G$ ratio. Mullen et al. (2017)
and Cumbee et al. (2018) listed such velocity-dependent ratios of O VII for
collisions with different neutrals. For comparison, we also plot these ratios
in the left panel of Fig. 7. The present calculation for collisions with H
shows a favorable agreement with the halo mean value and theory from Bodewits
et al. (2007). Due to the low signal-to-noise ratio, the halo $G$ ratio has
large error bars (Fig. 7). This will be clarified by next-generation X-ray
missions, e.g., XRISM 444https://heasarc.gsfc.nasa.gov/docs/xrism/about/,
Athena 555https://www.cosmos.esa.int/web/athena and HUBS
666http://hubs.phys.tsinghua.edu.cn/en/index.html.

Figure 7: Left: The $G=\frac{i+f}{r}$ ratio of He-like oxygen. Different
charge-exchange (CX) model calculations (Mullen et al., 2017; Cumbee et al.,
2018, and the present work) are compared along with XMM-Newton observations
for Mars’s disk and halo from the work of Koutroumpa et al. (2012). Right: The
$G$ ratio as the function of neutral density from a pure charge-exchange model
(filled symbols) at typical solar wind velocity of 500 km/s and hybrid one
(open symbols) with charge-exchange plus proton/neutral impact excitation
(PIE) in collisions with H, H2, and He. Here, the solar wind temperature of
log($T_{e}$)/K=6.1 is based on the previous analysis of the $\alpha$-value of
oxygen.

For the disk $G$ ratio of 0.77$\pm$0.58 the charge-exchange model from Mullen
et al. (2017) when colliding with nitrogen and hydrogen gases (N2 and H2)
gives ratios ranging from 1.0 to 1.7, which is consistent with disk
observations within error bars. Koutroumpa et al. (2012) suggested this low
ratio is due to the quenching collisions with neutrals, that will remove
excited electrons from the long-lived metastable states, then suppress the $f$
line intensity. Their qualitative analysis for the collisional effect is clear
below 150 km, and they estimated the contribution from below 150 km to be less
than 15%. In this work we performed a detailed calculation by including
excitations from heavy particles in Eq. (7). However, neutral impact
excitation data of highly charged ions are very scarce, even the proton impact
excitation of highly charged ions is available for just a few cases. Seaton
(1955, 1964) presented the theory of proton impact excitation, and applied it
to the green coronal line of Fe13+for the $3p_{3/2}\to 3p_{1/2}$ transition.
When the excitation energy $\Delta\ E$ is much smaller than the plasma
temperature $kT$, the proton excitation rate would be greater than the
electron impact by a factor of order $\sqrt{M_{p}/m}$, $M_{p}$ being the
proton mass and $m$ the electron mass (Dalgarno, 1983). The excitation energy
of O VII from metastable level (1s2s ${}^{3}S_{1}$) to 1s2p levels is
$\sim$10–16 eV, which is far smaller than the plasma temperature of $\sim$110
eV. Thus, we derived the proton (neutral) impact excitation (PIE) rates from
the metastable level of O VII by using the electron impact excitation rates in
the sasal database (Liang et al., 2014; Takabe et al., 2008).

According to Eq. (7) we calculate the $G$ ratio of O VII with a pure charge-
exchange model and a hybrid one (e.g. CX plus proton impact excitation) in the
collisions with H, H2, and He, respectively. From the right panel of Fig. 7,
we see that the $G$ ratio from the hybrid model starts to deviate from the
pure CX one when above the neutral density of 106 cm-3, and becomes more
obvious as the neutral density increases. According to the neutral profile
presented in Fig. 1, the collisional quenching effect appears below the
altitude of $\sim$400 km through the collisional excitations by neutral oxygen
and/or CO2. Figure 7 also indicates that the $G$ ratios from the pure CX
calculation with different neutrals disperse strongly, for example, 5.3 (H),
2.7 (He), and 0.98 (H2). However, the disk observation of Mars reported by
Dennerl et al. (2006)) covers the photons within 10${}^{{}^{\prime\prime}}$,
that is below altitude of 2180 km. Above $\sim$400 km and below $\sim$2000 km
altitude H2, He, and O are dominant components in the Martian atmosphere with
density of $\sim 10^{4}$—2$\times 10^{5}$ cm-3. From Fig. 9 and Fig. 10
discussed in next subsection, we can see that the disk observation (white
dotted circle) covers more than $\sim$86% of the emission energies, where the
emissivities from H2 and O are comparable to or higher than those from H at
lower altitudes. Both their contributions can be up to $\sim$43% and
$\sim$65%, respectively. Thus, we suggest the pure CX with H2 and O may be the
part of the reason for the low disk observation of 0.77$\pm$0.58.

By including all the neutral components in Eq.(7) we can further calculate the
map of triplet line ratios $G$ with a pure charge-exchange and a hybrid one as
illustrated in Fig. 8. Here, only the hybrid calculation is presented due to
both maps have basically the same distribution except for data below $\sim$200
km which show small differences. Hence, the proton impact excitation may not
be the main reason for the low disk observation of 0.77$\pm$0.58. In this
figure, the nearly spherical symmetry of the $G$ ratio follows the neutral
profiles used in this work. It is obvious that the G ratio decreases with
decreasing altitude, and it reaches a low value of $\sim$2.8 at altitude of
$\sim$700 km. Within the main region of disk observation reported by Dennerl
et al. (2006), the $G$ ratio is approximately 2.8–3.4, which is still higher
than the disk observation. By using the in-situ MAVEN measurements for
neutrals shown in the bottom panel of Fig. 1, the $G$ ratio changes slightly
to $\sim$2.2–3.0. This decreasing trend of the $G$-ratio indicates that the
contributions from H2 and O steadily increase and become significant, but
still not absolutely dominant. This is consistent with the x-ray luminosity
profiles shown in Fig. 10, which will be discussed in the next subsection.
When the solar wind bulk velocity is used, the $G$-ratio can reach a low value
of $\sim$0.9 at the altitude of $\sim$400 km. The higher cross-section below
100 km/s in the collision with H2 (see Fig. 3) and the low bulk velocity
($\leq$100 km/s, see Fig. 2), is the reason for the low calculated $G$-ratio
of $\sim$0.9. Therefore, we suggest that the charge-exchange with H2 gas may
still be the possible reason for the low disk observation. Such dependence of
the $G$ ratio on the altitude can be explored by future deep observations with
next generation x-ray missions with high efficiency (e.g. XRISM ${}^{\ref{ft-
xrism}}$, Athena ${}^{\ref{ft-athena}}$ and HUBS ${}^{\ref{ft-hubs}}$). We
also notice that there is a tail-like feature for the $G$-ratio by using the
bulk velocity of the solar wind, that is consistent with the tail-like feature
in the bulk velocity map shown in Fig. 2. Then we think this tail-like feature
in the $G$-ratio is resultant from the low bulk velocities and relative higher
cross-sections at low collisional velocities with the multiple-electron
neutrals (e.g. H2, He and O) as shown in Fig. 3. By considering the observed
$G$ ratio derived from the observed flux in the line of sight, the $G$ ratio
map is weighted by projected flux in different direction of line of sight
(LOS) discussed in Sect. 3.5, then we obtain the expected $G$ ratio of
$\sim$1.6–1.8 in the disk observation, see Table 1. That is slightly higher
than the disk observation of 0.77$\pm$0.58. It should be noted that the
present charge exchange cross sections are the best ones available, but not
the best ones qualified to use for high-resolution spectroscopy; these need
more elaborate benchmark measurements for the $nl-$selective cross section for
its extensive application in the near future.

Figure 8: Map of $G=\frac{i+f}{r}$ ratio of He-like oxygen with charge-
exchange and proton impact excitation (namely, the hybrid model) for all
neutrals in cases of average collisional velocity $v$ (left) and solar wind
bulk velocity $v_{\rm sw}$ (right). Solid curves refer to the bow shock and
magnetic pileup boundary from the work of N${\rm\check{e}}$mec et al. (2020).
Black dotted and red solid circles indicate regions of disk observation in
Dennerl et al. (2006) and Mars’s position, respectively. Note: Both the pure
and hybrid calculation are basically the same except for values below
$\sim$200 km.

###  3.4 Contribution of different neutrals on x-ray emissivity distribution
in the XZ plane

In view of the different neutral profiles as shown in Fig. 1 and different
charge-exchange cross-sections as shown in Fig. 3, we begin by investigating
the contribution from different neutrals to the x-ray emissivity distribution
in the XZ-plane (Fig. 9). The spatial distribution of x-ray emissivities shows
obvious differences in collisions with different neutrals. On the whole the
x-ray emissivity distribution for the collisions with H shows an obvious bow
shock in the XZ-plane, consistent with that derived from MAVEN spacecraft data
(N${\rm\check{e}}$mec et al., 2020, solid white curves) and the density map
from the MHD simulation. Weak x-ray emissions extend toward the solar
direction in the longer region and toward the far region in magnetosheath.
However, the bright x-ray emissions in the collisions with H2 (with peak value
of 1.5$\times 10^{-14}$ erg cm-3s-1) concentrate in the region near the
magnetic pileup boundary with less extension toward the magnetosheath, and are
higher than those from the H collision between $\sim$1.15–1.32$R_{\rm M}$
(Fig. 10). The contributions of the He collision are mainly below
$\sim$1.17$R_{\rm M}$ with emissivity values much smaller than those of the H
and H2 collision. Since the oxygen and carbon-dioxide become the dominant
components of the Martian atmosphere below the altitude of $\sim 1.16R_{\rm
M}$ (550 km), the main x-ray contribution is from the collision with O with
emissivity values comparable to those of H collisions, as shown by the dark-
blue curve in Fig. 10. For a clear inspection we further present the profile
of x-ray emissivities at four different directions (0∘, 30∘, 60∘ and 90∘)
relative to the Sun-to-Mars line (Fig. 10). Basically, the contributors to
x-ray emissivity profiles follow the neutral profiles in the Martian
environment with some difference in detail.

Figure 9: X-ray emissivity (with photon energies of 0.2—1.0 keV) map in XZ-
plane of highly charged ions (O) in collisions with neutrals of H, H2, He, O,
CO2 and all around the Martian atmosphere. The spatial units are in terms of
the martian radius $R_{\rm M}$. Solid curves refer to the bow shock and
magnetic pileup boundary from the work of N${\rm\check{e}}$mec et al. (2020).
White dotted and red solid circles indicate regions of disk observation in
Dennerl et al. (2006) and Mars’s position, respectively. Notes: For the
collision with CO2, the emissivity is too weak to be manifested, see Fig. 10
for details.  Figure 10: X-ray emissivity profile of oxygen in XZ-plane at
different directions (0∘, 30∘, 60∘ and 90∘) relative to solar-Mars center
line. Vertical solid and dashed lines mark the positions of bow shock and
magnet pileup boundary from the fitting formula based upon MAVEN satellite
data (N${\rm\check{e}}$mec et al., 2020) .

By considering the consistency of x-ray emissivity distribution with the
structure of solar wind interaction with the Martian exosphere, the present
work confirms again that x-rays can be used to probe the global structure of
solar wind interaction with planets (Snowden et al., 2004, 2009; Sun et al.,
2019). The different contribution profiles and line features in x-rays with
different neutrals suggest that x-ray spectroscopy can probe the neutral
components with future deep observations with spatial and energy resolutions
that can be achieved by next generation x-ray missions, such as XRISM
${}^{\ref{ft-xrism}}$, Athena ${}^{\ref{ft-athena}}$ and HUBS ${}^{\ref{ft-
hubs}}$.

###  3.5 X-ray morphology of Mars

The same procedure is used for carbon and nitrogen emissions with ion
fractions of 0.13 (C6+)777From real-time measurement of ACE-SWICS, see Table 1
in the work of Koutroumpa et al. (2012) , 0.37 (C5+)${}^{\ref{ft-k12}}$, 0.006
(N7+), and 0.058 (N6+). We calculate the x-ray emissivities in the energy
range between 200—1000 eV for the three-dimensional distribution of carbon,
nitrogen, and oxygen ions within 8.3$R_{\rm M}$ (55${}^{{}^{\prime\prime}}$)
of Mars. Since there are not emission lines from captured H- and He-like
carbon, nitrogen and oxygen ions in the ranges of 200–300 eV and 900–1000 eV
(Koutroumpa et al., 2006; Liang et al., 2021, see Table 1 and Fig. 10 there,
respectively), the present energy range is consistent with that (300–900 eV)
in the XMM-Newton observation and previous works (Koutroumpa et al., 2012). We
obtain the x-ray morphology and total x-ray luminosity around Mars (Fig. 12)
by integrating along the $y$-direction (Martian motion) and summing in this
projected plane as following:

$\displaystyle L(xz)=\int\sum_{ele,q+}P^{q+}(xyz)dy,$ (9) $\displaystyle
L_{tot}=\int\sum_{ele,q+}P^{q+}(xyz)dV,$ (10)

where $L(xz)$ refers to the projected emission flux (in the unit of erg cm-2
s-1) in $y$-direction with integration range between -8.3$R_{\rm M}$ and
$+$8.3$R_{\rm M}$, yet those emissions from the $y<0$ region with
$\sqrt{x^{2}+z^{2}}\leq R_{M}$ are blocked by Mars in this projection plot.
The summations $\sum_{ele,q+}$ are for above listed elements, as well as H-
and He-like captured ions that emits x-ray photons. $L_{tot}$ is the total
SWCX luminosity by integrating the emissivity $\sum_{ele,q+}P^{q+}(xyz)$
within a cubic box with the size of 16.6 $R_{\rm M}$ (or $\pm 8.3R_{\rm M}$).
The emission rate $P^{q+}(xyz)$ or $P^{q+}(r,\theta,\phi)$ of one charged ion
is defined by Eq.(1) in the previous model section.

The resulting total SWCX x-ray luminosity is 6.55 MW (O: 3.01, C: 2.69 and N:
0.85 MW, respectively) in this work, showing a better agreement with the XMM-
Newton observation of 12.8$\pm$1.4 than previous predictions. Koutroumpa et
al. (2012) made some estimations for the additional x-ray luminosity, e.g.,
larger simulation box ($\sim$8 $R_{\rm M}$) with an additional 5%, average
abundance of solar wind which is three times higher than their usual value,
with He and H2 contributions in the disk region. After these additional
contributions their simulated x-ray luminosity can reach between 1.2 and 2.0
MW. They also pointed out a halo coronal mass ejection (CME) event on
2003/11/18 as perhaps a possible explanation. A strong ion flux on average 18
times real-time values in their simulation could yield a total luminosity of
$\sim$6.3 MW, that is in better agreement with, but still quite lower than,
the observed value of 12.8$\pm$1.4 MW.

In this observed luminosity, assumptions of isotropic emission and optically
thin were used by multiplying the observed fluxes of emission lines with
$4\pi\Delta^{2}$ (here $\Delta=0.77$ AU is the distance between Earth and
Mars) (Dennerl et al., 2006; Koutroumpa et al., 2012). Contribution from
fluorescent scattering of solar x-rays has not be included (Dennerl et al.,
2006). By using the observed fluxes of the fluorescence lines from
$1\pi_{g}\to 1s$ and $3\sigma_{u}\to 1s$ transitions of CO2 around $\sim$525
eV, the fluorescent luminosity was derived to be 3.4$\pm$1.4 MW by Dennerl et
al. (2006), being approximately 27% of the total SWCX luminosity of
12.8$\pm$1.4 MW.

We further calculate total SWCX luminosity contributions at different layers
(with a step of 0.5 $R_{\rm M}$) by using the oxygen emissivity with all
listed neutrals, see Fig. 13. The contribution from the interaction region
($<2R_{\rm M}$) is the largest emission source ($\sim 21\%$) with the minimum
emitting volume. While the emissivities shown in Fig. 9 become smaller with
increasing altitude, the emitting volume increases as $R^{2}_{\rm M}$,
resulting in the luminosity contributions to increase again after $\sim
4.5~{}R_{\rm M}$. The luminosity contribution between
43${}^{{}^{\prime\prime}}$ ($\sim 7R_{\rm M}$) and 50${}^{{}^{\prime\prime}}$
radius ($\sim 8R_{\rm M}$) is $\sim 16\%$, being higher than the crude
estimation (5%) of Koutroumpa et al. (2012). This illustrates that the
uncertainty of neutrals at high altitude has a non-negligible effect on the
total luminosity. However, the absence of in-situ measurement for the hydrogen
density at higher altitudes limits the examination for the present
calculation.

By using a different group of neutral densities, e.g. in-situ MAVEN
measurement at the orbit period of DD2 (Stone et al., 2022; Wu et al., 2021),
we re-calculate the total CXE luminosity to be 5.93 MW being smaller than the
former calculation by 10%. Although there are large differences for the
neutral densities at low altitude shown in Fig. 1, the resultant total SWCX
luminosity does not change a lot. Figure 1 illustrates that SWCX emission is
dominantly from the collision with hydrogen at $\gtrsim 2R_{\rm M}$, where the
hydrogen density is very close between the fitting to MAVEN DD2 data and the
fitting given by Eq. (3). The small difference of the calculated luminosities
indirectly indicates that the emission from distant halo regions with large
volume around Mars plays an non-negligible role on the observed luminosity,
that is consistent with the discussion for the radial distribution of the
luminosity, as shown in Fig. 13.

By using the in-situ solar wind data from ACE Science Center Level 2 database
888https://www.swpc.noaa.gov/products/ace-real-time-solar-wind, we estimate
the time delay ($dt$) of the solar wind to be about $\sim$45–53 hours between
the L1 point (ACE position) and Mars by using $dt=\Delta/v_{\rm sw}$ with
$v_{\rm sw}$ of $\sim$600–710 km/s and $\Delta$=0.77 AU (Koutroumpa et al.,
2012). This corresponds approximately to the window between 2003/11/18 05:00
UT and 2003/11/19 10:00 UT for the solar wind event around Mars, during the
XMM-Newton observation (Dennerl et al., 2006), see Fig. 11. The solar wind
velocity decreases from $\sim$710 to 530 km/s, yet the density holds basically
a constant value of 2.7 cm-3 till 2003/11/19 00:00 UT, then increases to
$\sim$5.0 cm-3 at the end of above window. By considering the difference
between the in-situ ACE measurements and the values used in this work, the
total SWCX luminosity varies in the range of 6.28–8.68 MW. When the solar wind
density is further scaled to Mars’ heliocentric distance (1.43 AU) by
$1/r^{2}$, the total luminosity decreases to $\sim$3.1–4.3 MW. During this
period, the solar wind state changes slightly at Mars, see gray shadow region
in the third panel of Fig. 11. By using the ACE measured oxygen abundance and
the charge state (Bonamentel et al., 2021), we further calculate the
$\alpha$-value of oxygen, that shows a mean value of (1.4–6.6)$\times
10^{-16}$ eV cm2 from the beginning till the end of the event window at Mars,
that is slightly lower than the value of 7.3$\times 10^{-16}$ eV cm2 adopted
in our work, see the discussion at Sect.3.1. That is the resultant total
luminosity should be decreased again slightly.

Figure 11: Solar wind properties (proton density $n_{\rm H}$, bulk velocity
$v_{\rm sw}$, ion abundance ratio of O7+/O6+ and O8+/O7+) as measured by ACE
during 2003/11/17–23, and $\alpha$-value of oxygen in the collision with H
(bottom) at a velocity of 500 km/s by using the in-situ ACE data. Red shadow
region marks the window of XMM-Newton observation, while gray shadow region
marks the window at Mars. The filled star symbol in the bottom panel is the
$\alpha$-value of 7.3$\times 10^{-16}$ eV cm2 discussed in Sect.3.1 with
O7+,8+ abundances of 0.28 and 0.05, respectively. Notes: $n_{\rm H}$ and
$v_{\rm sw}$ are binned by 12-min, while ion abundance ratio is binned by 2-hr
from the ACE Science Center Level 2 database.

Another possible reason is the assumption of isotropic emission used to derive
the observed luminosity by Dennerl et al. (2006). The projected x-ray flux
shown in the left panel of Fig. 12 illustrates that there is an obvious non-
isotropic feature for the dayside and nightside. By considering the observed
flux from a specified phase angle ($\phi\approx 40^{\circ}$) adopted to derive
the luminosity, we calculate the mean value for the projected x-ray emission
flux within the disk region (15${}^{{}^{\prime\prime}}$ radius) at different
phase angles, see Table 1. It shows that the mean projected flux varies within
4.5–5.7$\times 10^{-6}$ erg cm-2 s-1. Then we suggested the observed
luminosity of 12.8$\pm$1.4 might be overestimated by $\sim$20%.

Table 1: Mean projected x-ray emission fluxes within disk region at different phases. Phase |  $G$ ratio | Projected flux
---|---|---
angle |  |  $10^{-6}$ erg cm-2 s-1
90∘ | 1.75 | 5.60
60∘ | 1.63 | 4.52
40∘ | 1.75 | 5.61
0∘ | 1.68 | 4.79
120∘ | 1.64 | 4.49
140∘ | 1.74 | 5.66
180∘ | 1.68 | 4.76

In summary, the total SWCX luminosity is closely related to the solar wind
condition and the planetary environment, that can be used to study the neutral
density when the real-time information is available for the solar wind.

Figure 12: Left: Projection in Martian motion direction ($y$) of three-
dimensional x-ray emissivity distribution of solar wind oxygen ions with all
neutrals. Right: Total luminosity around Mars from observations of XMM-Newtron
(Dennerl et al., 2006) and Chandra (Dennerl et al., 2002), and from previous
predictions and this work.  Figure 13: Radial distribution of the total
luminosity in the Martian exosphere with an grid step of 0.5$R_{\rm M}$.

##  4 Summary and conclusion

In this study, using the newest charge-exchange cross section in Kronos v3.1
and experimental measurements, we calculate the emission factor $\alpha$-value
of carbon, nitrogen, and oxygen with different neutrals (H, He, H2, O, and
CO2) in the Martian environment over wide temperature and velocity ranges. The
$\alpha$-value is highly variable over a temperature range of
log($T_{e}$)/K=5.9—6.4 for oxygen, which shows an obvious dependence on
velocity below 200–300 km/s. Both the MHD simulation and in-situ MAVEN
measurements reveal that the bulk velocity of solar wind decreases to below
100 km/s after the bow shock. Then the general single $\alpha$-value is not
valid again. Overall, the $\alpha$-value in collisions with O and CO2 is
higher than with others, e.g., H and He. The present $\alpha$-value of oxygen
agrees well with previous reports in the collisions with H at the temperature
of log($T_{e}$)/K=6.1 and typical solar wind velocity of 300–600 km/s. The
evolution of charge stage of solar wind ions shows that there is not a
sequential recombination from charge-exchange across the interaction region;
H-like ion pileups and sequential recombination appear below the altitude of
400 km. This indicates again that the general fixed $\alpha$-value is not
valid below this altitude.

By considering the excitation energy ($\sim$10–16 eV) from the metastable
level to higher $1s2p$ levels, we obtain the proton impact excitation cross
sections from electron impact excitation data based on the theory of Seaton
(1955). Then we incorporate them into a sophisticated hybrid emission model.
Furthermore, the anonymous low disk $G=\frac{i+f}{r}$ ratio (0.77$\pm$0.58)
was explored, and can be directly explained by the collisional quenching
effect due to proton/neutral collisions. However, the quenching contribution
is small for the disk observation and only appears below 400 km. Hence, we
suggest that charge-exchange with H2 and N2 may be the most likely reason for
this low mean $G$-ratio with large error-bars.

We also presented x-ray emissivity maps from solar wind ions impinging on
different neutrals in the Martian exosphere, which is in accordance with bow
shock derived from in-situ MAVEN solar wind ion density and velocity mapping.
The contributions from different collisional neutrals are explored, which are
shown to differ from each other. The resulting total x-ray luminosity of 6.55
MW shows a better agreement with the XMM-Newton observation of 12.8$\pm$1.4 MW
than previous ones. Its dependences on solar wind variation and neutral
density profile around Mars are discussed.

We present a detailed study for x-rays due to charge-exchange around Mars.
This reconfirms that x-rays represent a good remote sensor for the global
interaction of solar wind with a planetary atmosphere. This study illustrates
an example of charge-exchange emissions in space physics, and shows a
requirement for benchmarks for data of $nl-$selective velocity-dependent
charge-exchange cross-section.

This work was supported by National Key R&D Program of China, Nos.
2017YFA0402400, 2022YFA1603200 and National Natural Science Foundation of
China under grants U1931140 and 42074214, as well as Key Programs of the
Chinese Academy of Sciences (QYZDJ-SSW-SLH050, QYZDJ-SSW-JSC028). We are
grateful to Xiaoshu Wu from Sun Yat-sen University for providing MAVEN data.
We thank LetPub (www.letpub.com) for its linguistic assistance during the
preparation of this manuscript.

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