In Situ Heating of the Nightside Martian Upper Atmosphere and Ionosphere: The Role of Solar Wind Electron Precipitation

The solar extreme ultraviolet (EUV) and X-ray radiation are able to deposit a substantial amount of energy in the dayside Martian upper atmosphere, creating an ionosphere by ionizing ambient neutrals, initializing atmospheric and ionospheric chemistry, heating all atmospheric constituents, and driving both neutral and plasma escape (Fox et al. 2008, and references therein). The solar control of the dayside Martian ionosphere has been well established from the observed diurnal and solar cycle variations of peak electron density and altitude (e.g., Hantsch & Bauer 1990; Morgan et al. 2008; Withers 2009; Haider & Mahajan 2014; Yao et al. 2019). The dayside exospheric temperature on Mars has been observed to respond systematically with solar EUV and X-ray irradiance as well as solar zenith angle (SZA; e.g., Jain et al. 2015; Bougher et al. 2017; Zurek et al. 2017; Elrod et al. 2018). The dayside escape of important atmospheric neutrals such as O, C, and N, which occurs mainly via the dissociative recombination (DR) of ionospheric ${{\rm{O}}}_{2}^{+}$ and the photodissociation of atmospheric CO and N₂, has been found to be more intense under high solar activity conditions (e.g., Lillis et al. 2017; Cui et al. 2019b).

On the nightside of Mars where solar radiation is switched off, solar wind (SW) electron precipitation is generally thought to be the dominant driving force of the upper atmosphere. This process has been proposed to be responsible for the highly variable nightside ionosphere of Mars in terms of the thermal electron distribution (e.g., Verigin et al. 1991; Fowler et al. 2015; Cui et al. 2019a), a scenario that is also supported by the observation of enhanced densities of several important ion constituents such as ${{\rm{O}}}_{2}^{+}$, O⁺, and CO₂ ⁺ when the incident suprathermal electron flux is high (Girazian et al. 2017a). In general, the detailed pattern of electron impact ionization on the nightside of Mars has been well established (e.g., Lillis et al. 2009, 2011; Lillis & Brain 2013; Lillis & Fang 2015; Lillis et al. 2018), and found to be strongly modulated by the presence of crustal magnetic anomalies known to cluster over the southern hemisphere of the planet (e.g., Acuna et al. 1999; Connerney et al. 1999).

A notable feature of electron precipitation on the nightside of Mars is the sudden drop in electron intensity over a broad energy range (Mitchell et al. 2001), hereafter denoted as energetic electron depletion. A similar phenomenon has also been discovered in other solar system environments such as near comet 67P/Churyumov–Gerasimenko (Madanian et al. 2020). The occurrence rate of electron depletions on the nightside of Mars has been found to increase sharply toward lower altitudes and near strong crustal magnetic anomalies (e.g., Steckiewicz et al. 2015, 2017). Further studies have indicated that the occurrence of electron depletions shows a visible dawn-dusk asymmetry (Steckiewicz et al. 2019) and a strong dependence on the upstream SW condition (Niu et al. 2020). It has been proposed that the formation of electron depletions at low altitudes is due to CO₂ absorption as motivated by the observation of an apparent peak in electron intensity near 6 eV, coincident with the energy at which the electron-CO₂ collision cross section drops to a local minimum (Steckiewicz et al. 2015). However, Niu et al. (2020) has recently argued that this is more likely caused by magnetic shielding in response to a change in magnetic connectivity from open to closed.

Despite the existing efforts, our understanding of SW electron precipitation as a potential source of atmospheric heating is incomplete, partially because the historically available measurements of the nightside Martian upper atmosphere are extremely limited. The early morning orbits of the Mars Pathfinder provided the first opportunity to probe the atmospheric structure of Mars in darkness, revealing a peak temperature of 153 K at an altitude of 134 km (Magalhães et al. 1999). A large data set of nightside atmospheric density has been derived in an indirect manner (Lillis et al. 2010), but the associated uncertainties are large, and the upper atmospheric variability could thus be characterized only on timescales of weeks or longer. Meanwhile, existing model calculations of the Martian upper atmosphere have predicted a nightside thermal structure purely as a remnant of dayside solar EUV and X-ray heating, possibly strengthened by global circulation (e.g., Bougher et al. 1999, 2000; Angelats i Coll et al. 2005; González-Galindo et al. 2005, 2009a, 2009b, 2010; Bougher et al. 2015). None of these models have included SW electron precipitation as a potential source of nightside atmospheric heating. Whether or not such a source could be safely ignored or should be seriously considered remains to be validated by rigorously calculations.

With the arrival of the Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft at our sister world on 2014 September 21, knowledge of its nightside upper atmosphere and ionosphere has been substantially improved (e.g., Jakosky et al. 2015). Stone et al. (2018) reported that the nightside temperature in the Martian upper atmosphere was substantially lower than the subsolar temperature by a factor of two. The analysis of Pilinski et al. (2018) further revealed the presence of persistent nighttime temperature structures manifest as a local enhancement by 50–100 K at a local solar time of 4–5 hr relative to the surrounding environment. Such an enhancement was suggested to be a result of either nighttime dynamical heating caused by converging and downwelling winds or of a terminator wave originating in the lower atmosphere.

With the aid of the extensive in situ measurements made by several instruments on board MAVEN, here we attempt a detailed calculation of the neutral, ion, and electron heating rates associated with SW electron precipitation in the nightside Martian upper atmosphere and ionosphere. Channels of nightside heating considered here include various elastic and inelastic collisions (e.g., Bhardwaj & Jain 2009). We also evaluate the role of exothermic ion-neutral chemistry, which is at least partly driven by SW electron impact ionization and dissociation of atmospheric neutrals (e.g., Haider 1997). This is especially true for the deep nightside of Mars where horizontal plasma transport does not exert an appreciable influence (e.g., Withers et al. 2012; Chaufray et al. 2014; Cui et al. 2015a; Girazian et al. 2017b). The present study is complementary to that of Lillis et al. (2018) based on a similar multi-instrument MAVEN data set focusing on the nightside electron impact ionization rate. It is also complementary to the recent work of Gu et al. (2020) investigating in detail neutral heating of the dayside Martian upper atmosphere via photoelectron impact.

The structure of the paper is organized as follows. We describe in Section 2 different physical and chemical processes included in our energy term calculations. The multi-instrument MAVEN measurements used in the study are described briefly in Section 3. The available data motivate us to categorize the Martian nightside observations into two groups, one with substantial SW electron precipitation and the other one with clear evidence for energetic electron precipitation. We present the main results on various neutral, ion, and electron heating rates in Section 4 in the nightside mean sense, for both categories, with a special emphasis on the relative contributions from different heating channels. Finally, we discuss in Section 5 and provide concluding remarks in Section 6.

In general, the results presented here, along with those reported in previous studies (e.g., Girazian et al. 2017a; Steckiewicz et al. 2017; Lillis et al. 2018; Cui et al. 2019a; Niu et al. 2020), lay out the foundation for a thorough understanding of how the nightside Martian upper atmosphere and ionosphere respond to SW electron precipitation as an important external energy source. In particular, it remains to be seen whether nightside heating due to SW electron precipitation is really negligible or if it is (in the absence of solar EUV and X-ray energy input) strong enough to perturb the nightside Martian upper atmosphere and ionosphere.

2.1. Outline of Fundamental Physical and Chemical Processes

2.2. Neutral Gas Heating

2.2.1. Solar Wind Electron Impact Processes

We consider in this study both elastic and inelastic collisions of energetic electrons with atmospheric CO₂ and O, as the two most abundant species of the Martian upper atmosphere (e.g., Mahaffy et al. 2015). For CO₂, we include 12 channels of electronic or vibrational excitation and seven channels of (dissociative) ionization (Shematovich et al. 2008; Bhardwaj & Jain 2009), whereas for O, we include two channels of electronic excitation and three channels of ionization (Laher & Gilmore 1990). A comprehensive set of cross-sectional data recommended by Itikawa (2002) and Laher & Gilmore (1990) is adopted, which is nearly identical to that used in our previous modeling of photoelectrons in the Venusian ionosphere (Cui et al. 2011). All channels leading to highly excited fragments, multiple dissociation and ionization, as well as electron attachment are neglected according to Cicman et al. (1998).

The CO₂ (010) vibrational mode with an excitation energy of 0.083 eV is generally accompanied by radiative de-excitation via the well-known 15 μm line emission rather than collisional quenching, thus not contributing to local heating (e.g., Yelle et al. 2014). For the (100) mode with an excitation energy of 0.172 eV, Grofulović et al. (2016) showed that the cross sections of Itikawa (2002) were seriously overestimated. The above two modes are ignored in our calculations. As for the remaining (001) mode, a 100% efficiency for collisional quenching is assumed following Gu et al. (2020), which eventually deposits the corresponding excitation energy of 0.291 eV as local heat.

The electronically excited states of CO₂, including the 8.6, 9.3, 11.1, 12.4, 13.6, 15.5, 16.3, 17.0, and 17.8 eV states (e.g., Itikawa 2002; Bhardwaj & Jain 2009), are assumed to be fully dissociative (Flaherty et al. 2006), producing CO and O fragments in different states, ground or excited, as detailed in Table 8 of Fox & Dalgarno (1979a). According to Fox & Dalgarno (1979a), 1.0, 1.0, 1.4, 0.7, and 1.0 eV for the first five channels and 0.8 eV for the remaining four channels emerge as local heat (see also Gu et al. 2020; Zhang et al. 2020). In addition, CO₂ with excitation energy in excess of 15 eV generally experiences auto-ionization with a probability of 50% (Jackman et al. 1977), indicating that the neutral heating rates due to the last four channels of CO₂ electronic excitation should be multiplied by 0.5. Finally, the dissociative excitations associated with several intense emission features (O i 1356, C i 1329, O i 1304, C i 1657, C i 1561, and C i 1279) do not affect significantly the overall energy degradation due to the small cross sections involved (Fox & Dalgarno 1979b) and are consequently excluded from our calculations.

Electron impact ionization of CO₂ generally does not lead to neutral heating because most excited states of CO₂ ⁺, such as A²Π_u and ${{\rm{B}}}^{2}{{\rm{\Sigma }}}_{u}^{+}$ with excitation energies of 3.93 eV and 4.29 eV, radiatively decay to the ground X²Π_g state. This is not the case for the ${{\rm{C}}}^{2}{{\rm{\Sigma }}}_{g}^{+}$ state with an excitation energy of 5.6 eV, which is formed via the removal of inner shell electrons from CO₂ (Itikawa 2002) and predissociates with a probability near unity (Fox & Dalgarno 1979b; Itikawa 2002), thus contributing to local heating. Such a predissociation produces energetic ion and neutral fragments, both in ground states, with their kinetic energies assigned in proportion to their inverse molecular masses. The kinetic energy distributions of various charged fragments have been obtained by time-of-flight spectroscopy (e.g., Velotta et al. 1994; Locht & Davister 1995; Tian & Vidal 1998), and their contributions to both neutral and ion heating are discussed in Section 2.5. In contrast, the kinetic energy distributions of neutral fragments, which are generally not available from laboratory measurements (McConkey et al. 2008), are computed from the respective distributions of charged fragments.

For the two excited states of O (¹D and ¹S with excitation energies of 1.96 and 4.18 eV), they could decay to the ground ³P state either via radiative emission or via collisional quenching (e.g., Gu et al. 2020). The latter process releases the O excitation energy as local heat (see details in Section 2.2.4). In addition, the electron impact ionization of O has some probability to produce excited states of O⁺, such as ²D and ²P with excitation energies of 3.32 eV and 5.02 eV (Laher & Gilmore 1990), and these energies have a certain probability to be released as local heat via collisional quenching.

2.2.2. Ionospheric Chemistry

A complicated list of chemical reactions appropriate for the nightside Martian ionosphere is available from Haider et al. (2013). Two types of exothermic chemistry contributing to neutral heating are considered here: ion-atom interchange and DR (Rees et al. 1983). Here we calculate the excess kinetic energy for each product pair from the difference in enthalpy between the reactants and products. The kinetic energy delivered to each product is then obtained by assuming that it is inversely proportional to its molecular mass.

An important source of neutral heating in the Martian upper atmosphere is ${{\rm{O}}}_{2}^{+}$ DR (e.g., Fox 1988), with the weighted kinetic energy release calculated following Gu et al. (2020) and taking into account the population of ${{\rm{O}}}_{2}^{+}$ at different vibrationally excited states (Fox & Hać 2009). NO⁺ and HCO⁺ are two additional molecular ions following ${{\rm{O}}}_{2}^{+}$ that are relatively abundant in the nightside Martian ionosphere (Girazian et al. 2017a; Wu et al. 2019). We therefore also consider in our calculations NO⁺ and HCO⁺ DR, which are known to proceed via the following channels:

$$\begin{eqnarray}\begin{array}{lcc}{\mathrm{NO}}^{+}+e & \to {\rm{N}}{(}^{4}{\rm{S}})+{\rm{O}}{(}^{3}{\rm{P}})+2.75\ \mathrm{eV},\qquad & ({\rm{a}})\\ & \to {\rm{N}}{(}^{2}{\rm{D}})+{\rm{O}}{(}^{3}{\rm{P}})+0.38\ \mathrm{eV}, & ({\rm{b}})\end{array}\end{eqnarray} \tag{ 1 }$$

and

$$\begin{eqnarray}&&{\mathrm{HCO}}^{+}+e\to \mathrm{CO}+{\rm{H}}{(}^{2}{\rm{S}})+7.31\ \mathrm{eV},\end{eqnarray} \tag{ 2 }$$

where the respective exothermicities are provided, and the rate coefficients are taken to be $4.2\times {10}^{-7}{(300/{T}_{e})}^{0.85}$ cm³ s⁻¹ (Rees et al. 1983) and $3.0\times {10}^{-7}{(300/{T}_{e})}^{0.64}$ cm³ s⁻¹ (Geppert et al. 2005), with T_e being the electron temperature in units of kelvin. The neutral fragments produced from NO⁺ DR could be in different electronic states, ground or excited, with branching ratios also adapted from Rees et al. (1983). For HCO⁺ DR, CO as a product is assumed to be exclusively in its ground state, and the remaining channels leading to alternative fragments such as HC + O and HO + C are ignored because these channels have been measured to be of minor importance, with a total branching ratio of less than 10% (Korolov et al. 2009).

Although O⁺, as another relatively abundant species of the nightside Martian ionosphere (Girazian et al. 2017a; Wu et al. 2019), is not destructed via DR, it may contribute to local heating via two ion-atom interchange reactions

$$\begin{eqnarray}\begin{array}{lcc}{{\rm{O}}}^{+}+{\mathrm{CO}}_{2} & \to \ {{\rm{O}}}_{2}^{+}+\mathrm{CO}+1.20\ \mathrm{eV},\qquad & ({\rm{a}})\\ {{\rm{O}}}^{+}+{{\rm{N}}}_{2} & \to \ {\mathrm{NO}}^{+}+{\rm{N}}+1.41\ \mathrm{eV}, & ({\rm{b}})\end{array}\end{eqnarray} \tag{ 3 }$$

with respective rate coefficients of 9.4 × 10⁻¹⁰ cm³ s⁻¹ and 2.4 × 10⁻¹² cm³ s⁻¹ (McElroy et al. 2013). We also consider two extra ion-atom interchange reactions involving ${{\rm{O}}}_{2}^{+}$, which are

$$\begin{eqnarray}\begin{array}{lcc}{{\rm{O}}}_{2}^{+}+\mathrm{NO} & \to \ {\mathrm{NO}}^{+}+{{\rm{O}}}_{2}+2.81\ \mathrm{eV},\qquad & ({\rm{a}})\\ {{\rm{O}}}_{2}^{+}+{\rm{N}} & \to \ {\mathrm{NO}}^{+}+{\rm{O}}+4.17\ \mathrm{eV}, & ({\rm{b}})\end{array}\end{eqnarray} \tag{ 4 }$$

for which the rate coefficients are 4.6 × 10⁻¹⁰ cm³ s⁻¹ and 1.8 × 10⁻¹⁰ cm³ s⁻¹ (McElroy et al. 2013). Reaction 4(a) should be far less important than reaction 4(b) due to the relatively fast depletion of NO on the nightside of Mars via its reaction with ground state N in the ambient atmosphere (Cui et al. 2020). The products of all ion-atom interchange reactions included in our calculations are assumed to be in their ground states.

2.2.3. Maxwell Collisions with Ionospheric Plasma

While neutral heating via elastic collisions with ionospheric electrons is negligible, we evaluate in this study the neutral heating rate due to elastic Maxwell collisions, denoted as H_n,i and formulated following Rohrbaugh et al. (1979) as

$$\begin{eqnarray}&&{H}_{n,i}(z)={n}_{i}(z){n}_{n}(z)\displaystyle \frac{2.21\pi }{{m}_{i}+{m}_{n}}{\left({\alpha }_{n}{e}^{2}{\mu }_{{in}}\right)}^{1/2}3{k}_{{\rm{B}}}[{T}_{i}(z)-{T}_{n}(z)],\end{eqnarray} \tag{ 5 }$$

where z is the altitude, n_n and n_i are the neutral and ion densities, m_n and m_i are the neutral and ion masses, α_n is the neutral polarizability (3 × 10⁻²⁴ cm⁻³ for CO₂ and 0.8 × 10⁻²⁴ cm⁻³ for O), T_n and T_i are the neutral and ion temperatures, μ_in = m_i m_n /(m_i + m_n ) is the reduced mass, e is the fundamental electron charge, and k_B is the Boltzmann constant. To obtain the total neutral heating rate via such a mechanism, Equation (5) has to be summed over all neutral and ion species.

2.2.4. Collisional Quenching

Several processes described in Sections 5 and 6 lead to the formation of neutral and ionized products in their excited states. If the radiative lifetime of an excited state is sufficiently long, then the state is quenched via collisions with ambient neutrals, releasing the internal energy as local heat (Fox et al. 2008). In this study, we consider the collisional quenching of both excited state O and O⁺, as well as vibrationally excited CO₂, of which the last has been described in Section 2.2.1 and is thus not repeated here. In practice, excited state O could be produced in either the ¹D state or ¹S state via electron impact excitation, ${{\rm{O}}}_{2}^{+}$ DR, and predissociation of excited state CO₂, whereas excited state O⁺ could be produced in either the ²D state or ²P state exclusively via electron impact ionization. Collisional quenching of N(²D), which could be produced via NO⁺ DR, is ignored in our calculations because the respective production rate is lower than the O(¹D) production rate by at least two orders of magnitude. Predissociation of excited state CO₂ may also produce excited state CO, which is de-excited via radiative emission with a probability near unity (Slanger et al. 2008), thus also not considered here.

For O(¹D) with an excitation energy of 1.97 eV, the dominant quenchers are CO₂ and O. The corresponding quenching coefficients are $7.4\times {10}^{-11}\exp (133/{T}_{n})$ and $2.2\times {10}^{-11}{({T}_{n}/300)}^{0.14}$, both in units of cm³ s⁻¹, where T_n is the neutral temperature in units of K (Fox 2012). De-excitation via radiative emission is evaluated using a transitional probability of 8.604 × 10⁻³ s⁻¹ (Froese Fischer & Tachiev 2004) and is found to be unimportant for this metastable state. For O⁺(²D) with an excitation energy of 3.32 eV, a similar approach is used for calculating its contribution to local heat, and a similar conclusion is reached. The quenching coefficients for O⁺(²D) are assumed to be species-independent with a characteristic value of ∼1 × 10⁻¹⁰ cm³ s⁻¹ (Slanger et al. 2008).

For O(¹S) with an excitation energy of 4.18 eV, collisional quenching to the ground state is negligible as compared to radiative decay (Slanger & Black 1978; Capetanakis et al. 1993). Here we assume for simplicity that O(¹S) decays immediately to O(¹D) via spontaneous emission, and local heating occurs via O(¹D) collisional quenching. The situation for O⁺(²P) is quite different, in that the quenching timescale might be comparable to the radiative timescales to both O⁺(²D) and ground state O⁺. For the de-excitation of this metastable state, we include the effects of both collisional quenching and radiative decay, but the collisional quenching to excited O⁺(²D) is ignored since the corresponding quenching coefficient is unavailable. The quenching coefficient for O⁺(²P) to ground state O⁺ is taken to be species-independent with a characteristic value of ∼2 × 10⁻¹⁰ cm³ s⁻¹ (Slanger et al. 2008).

It is noteworthy that for the quenching of excited state neutrals or ions by CO₂, excess energy may be partially channeled into CO₂ vibrational excitation in addition to direct kinetic energy release. Unfortunately, the probability that this process occurs is not well known, but we may expect that the bulk of this energy is converted to local heat via further quenching of vibrationally excited CO₂ by ambient neutrals. For simplicity, we assume in our calculations that 100% of the vibrationally excited energy of CO₂ is deposited as local heat (e.g., de La Haye et al. 2008; Gu et al. 2020).

2.3. Electron Gas Heating

Suprathermal electrons in the nightside Martian upper atmosphere are able to heat ionospheric thermal electrons via Coulomb collisions (Stamnes & Rees 1983), with a heating rate, H_e , normally expressed as

$$\begin{eqnarray}&&{H}_{e}(z)=4\pi {n}_{e}(z)\underset{{E}_{c}}{\overset{\infty }{\int }}L(E,z)\displaystyle \frac{I(E,z)}{E}{dE}\end{eqnarray} \tag{ 6 }$$

where E is the suprathermal electron energy, n_e is the ionospheric electron density, I is the angularly averaged differential electron intensity, E_c is the crossover energy at which the thermal electron intensity is equal to the suprathermal electron intensity, and L is the electron stopping cross section. According to Swartz et al. (1971), the electron stopping cross section, in units of eV cm², is computed from

$$\begin{eqnarray}&&L(E,z)=3.37\times {10}^{-12}{n}_{e}{\left(z\right)}^{-0.03}{E}^{-0.94}{\left[\displaystyle \frac{E-{E}_{e}(z)}{E-0.53{E}_{e}(z)}\right]}^{2.36},\end{eqnarray} \tag{ 7 }$$

where E_e is given by 8.618 × 10⁻⁵ T_e in units of electronvolts with T_e in units of kelvin, and n_e is in units of cm⁻³. In previous studies, Coulomb collisions were treated as the principal heating source for ionospheric electrons on the dayside of Mars (e.g., Matta et al. 2014).

2.4. Ion Gas Heating

A portion of the energy deposition from precipitating suprathermal electrons to ionospheric electrons may be further delivered to ionospheric ions via Coulomb collisions (e.g., Cravens et al. 1979, 1980; Rohrbaugh et al. 1979; Matta et al. 2014). This process is much more important than direct heating of ions via Coulomb collisions with suprathermal electrons because the Coulomb collision cross section decreases with increasing electron energy. The corresponding heating rate, denoted as H_i,e , is given by

$$\begin{eqnarray}&&{H}_{i,e}(z)=\displaystyle \frac{{n}_{e}(z){m}_{e}{\nu }_{{ei}}(z)}{{m}_{e}+{m}_{i}}3{k}_{{\rm{B}}}[{T}_{e}(z)-{T}_{i}(z)],\end{eqnarray} \tag{ 8 }$$

where m_e is the electron mass, ν_ei is the electron-ion collision frequency, and all other parameters have been defined above. According to Cravens (1997), the electron-ion collision frequency can be computed from

$$\begin{eqnarray}&&{\nu }_{{ie}}(z)=54.5\displaystyle \frac{{n}_{i}(z)}{{T}_{e}{\left(z\right)}^{3/2}},\end{eqnarray} \tag{ 9 }$$

with ν_ei in units of s⁻¹, n_i in units of cm⁻³, and T_e in units of kelvin. To obtain the total ion heating rate via Coulomb collisions with ionospheric electrons, Equation (8) has to be summed over all ion species.

2.5. Neutral and Ion Gas Heating due to Energetic Ion Production

In the nightside Martian upper atmosphere, an energetic ion could be produced via either exothermic chemistry or CO₂ ⁺ predissociation, which could then deposit a portion of its kinetic energy to both neutrals and ions. The formulism used to split this energy is identical to that of Rohrbaugh et al. (1979) considering only elastic Maxwell and Coulomb collisions.

More specifically, the kinetic energy released from an energetic ion to an ambient thermal neutral or ion per unit time, denoted as _n,j and _i,j , can be expressed as

$$\begin{eqnarray}&&{\epsilon }_{n,j}(z)={n}_{n}(z)\displaystyle \frac{2.21\pi }{{m}_{j}+{m}_{n}}{\left({\alpha }_{n}{e}^{2}{\mu }_{{jn}}\right)}^{1/2}[2{E}_{j}-3{k}_{{\rm{B}}}{T}_{n}(z)],\end{eqnarray} \tag{ 10 }$$

and

$$\begin{eqnarray}&&{\epsilon }_{i,j}(z)=\displaystyle \frac{4\pi {n}_{i}(z){e}^{4}}{{m}_{i}{V}_{i}(z)}\mathrm{ln}{{\rm{\Lambda }}}_{{ji}}(z)F\left[\displaystyle \frac{{V}_{j}}{{V}_{i}(z)}\right].\end{eqnarray} \tag{ 11 }$$

In the above equations, E_j is the suprathermal ion energy, ${V}_{j}=\sqrt{2{E}_{j}/{m}_{j}}$ and ${V}_{i}=\sqrt{2{k}_{B}{T}_{i}/{m}_{i}}$ are the velocities of the suprathermal and thermal ions, Λ_ji is the dimensionless Coulomb logarithm given by

$$\begin{eqnarray}&&\mathrm{ln}{{\rm{\Lambda }}}_{{ji}}(z)=\displaystyle \frac{2{\mu }_{{ji}}{\left[{k}_{{\rm{B}}}{T}_{i}(z)\right]}^{3/2}}{1.78{m}_{i}{e}^{3}{\left[\pi {n}_{i}(z)\right]}^{1/2}},\end{eqnarray} \tag{ 12 }$$

with all parameters in Gaussian units, and F is an extra dimensionless parameter defined as

$$\begin{eqnarray}&&F(x)=\mathrm{erf}(x)/x-\left(1+\displaystyle \frac{{m}_{i}}{{m}_{j}}\right)\displaystyle \frac{2}{\sqrt{\pi }}{e}^{-{x}^{2}},\end{eqnarray} \tag{ 13 }$$

where $\mathrm{erf}$ represents the normalized error function. The desired neutral and ion heating rates could then be obtained from ∑_j E_j P_j ∑_{n n,j} /(∑_{n n,j} + ∑_{j i,j} ) and ∑_j E_j P_j ∑_{i i,j} /(∑_{n n,j} + ∑_{j i,j} ), respectively, where P_j is the altitude-dependent energetic ion production rate, and the summations are over all energetic ions (O⁺, C⁺, and CO⁺ from CO₂ ⁺ predissociation, ${{\rm{O}}}_{2}^{+}$ and NO⁺ from exothermic chemistry), neutrals (CO₂, O), and thermal ions (O₂ ⁺, NO⁺, HCO⁺, and O⁺) involved in our calculations.

Finally, we caution that neutral and ion heating via the different channels outlined above are species-dependent. For instance, heating via O(¹D) quenching by CO₂ collision is not necessarily identical to that by O collision, indicating that the in situ heating rates of atmospheric CO₂ and O, and consequently their respective temperatures, should in principle be different. However, we assume for simplicity that all neutrals and ions are thermally coupled at their respective common temperatures throughout the altitude range considered here. For neutrals, such an assumption is motivated by the 13-moment model calculations of Boqueho & Blelly (2005) revealing that the temperature difference between different neutrals becomes appreciable only at altitudes higher than 300 km, which is well above the upper boundary considered in this study. As for ions, the approximation of a common temperature essentially underlies the majority of existing calculations of ionospheric energetics on Mars (e.g., Chen et al. 1978) and on other planetary bodies as well (e.g., Cravens et al. 1980; Roboz & Nagy 1994). An exception is the modeling study of Matta et al. (2014), who took into account species-dependent ion temperatures but still assumed that all ions heavier than O⁺ share a common temperature (see their Figure 2).

For the purpose of this study, we use a combined MAVEN data set appropriate for evaluating the role of SW electron precipitation on atmospheric and ionospheric heating on the nightside of Mars. The MAVEN measurements used here were accumulated at SZA above 110°, which is beyond the EUV terminator up to a maximum altitude of 350 km (e.g., Lillis et al. 2018; Niu et al. 2020). We include a total number of 889 MAVEN orbits, covering the period from 2015 January 1 to 2018 November 14. Different MAVEN instruments relevant for this study include the Neutral Gas and Ion Mass Spectrometer (NGIMS; Mahaffy et al. 2015), the Langmuir Probe and Waves (LPW; Andersson et al. 2015), the Solar Wind Electron Analyzer (SWEA; Mitchell et al. 2016), as well as the Suprathermal and Thermal Ion Composition (STATIC; McFadden et al. 2015), which we describe briefly in turn below.

The NGIMS instrument is a quadrupole mass spectrometer capable of measuring the densities of both ambient neutrals and ions over the mass range of 2–150 Da and with a resolution of 1 Da (Mahaffy et al. 2015). Here we use the NGIMS level 2 data product providing CO₂ and O densities in the closed-source neutral mode (e.g., Mahaffy et al. 2015), as well as the ${{\rm{O}}}_{2}^{+}$, O⁺, NO⁺, and HCO⁺ densities in the open-source ion mode (e.g., Benna et al. 2015), respectively. Due to the well-known effect of adsorption or heterogeneous chemistry occurring on the NGIMS antechamber walls, only the inbound measurements are considered (Mahaffy et al. 2015). It is noteworthy that the NGIMS cannot distinguish among HCO⁺, HOC⁺, and N₂H⁺ due to their equality in mass per charge, but the dayside ionospheric model of Fox et al. (2015) predicted HCO⁺ to be the dominant one, and we assume that this is also the case on the nightside.

The LPW instrument provides information on the Martian ionospheric electron density and temperature from the measured current-voltage characteristics (Andersson et al. 2015). In general, the LPW electron density is consistent with the NGIMS total ion density, with an average discrepancy of ∼15% below 300 km. The LPW electron temperatures are used here to calculate the neutral heating rate via ionospheric DR (see Section 2.2.2), the ion heating rate via Coulomb interaction with ionospheric electrons (see Section 2.4), as well as the electron heating rate via Coulomb interaction with suprathermal electrons (see Section 2.3). It is known that the LPW temperatures are overestimated at relatively low altitudes due to surface resistance or capacitance on the instrument sensor (e.g., Ergun et al. 2015; Peterson et al. 2018). Following Cui et al. (2019a), we correct for the LPW-derived temperatures by assuming that the atmospheric neutrals and ionospheric electrons satisfy the condition of strict thermal coupling below a certain altitude (see below) and that a linear relation is sufficient for describing the altitude variation of electron temperature up to 200 km, above which the LPW temperatures are thought to be reasonable (e.g., Peterson et al. 2018).

The SWEA instrument is a symmetric hemispheric electrostatic analyzer that measures the differential electron intensity as a function of electron energy over the range of 3 eV to 4.6 keV with a resolution of ΔE/E ≈ 17%, and also as a function of the direction of arrival covering a field of view (FOV) of 360° × 120°, of which 8% is blocked by the spacecraft body (Mitchell et al. 2016). In this study, we use the SWEA level 2 data product that provides the differential energetic electron intensity averaged over the instrument FOV. A similar data set was used by Lillis et al. (2018) in their computations of the SW electron impact ionization frequency in the nightside Martian upper atmosphere. We caution that an electron spectrum measured by the SWEA may include the contributions of both SW origin and ionospheric origin, of which the latter could stem from photoelectrons produced on the dayside of the planet and populate the nightside via large-scale horizontal transport (e.g., Xu et al. 2016; Cao et al. 2020, 2021). To eliminate the effect of nightside photoelectrons, we adopt the procedure developed by Xu et al. (2017) that distinguishes SW electrons and photoelectrons via a pre-defined shape parameter. Any SWEA spectrum characterized by a shape parameter smaller than 1 is identified as a photoelectron spectrum and excluded from our subsequent analysis. Prior to our calculations, each SWEA spectrum has been corrected for the spacecraft charging effect with the appropriate shift in energy using the potentials estimated from the LPW current-voltage characteristics (e.g., Cui et al. 2018a). Background counts have also been subtracted following the procedure of Niu et al. (2020).

Finally, the STATIC instrument, consisting of a toroidal electrostatic analyzer and a time-of-flight velocity analyzer, can be operated to measure the distribution functions of mass-differentiated species in the Martian ionosphere over a broad energy range from 0.1 eV to 30 keV at a cadence of 4 s and covering an instrument FOV of 360° × 90° (e.g., McFadden et al. 2015). The low-energy portion of the measured distribution function, which characterizes cold ionospheric ions, can be used to derive the ambient ion temperatures (Fränz et al. 2006). Information on ion temperature is required to determine both the neutral and ion heating rates in the nightside Martian upper atmosphere and ionosphere (see Sections 2.2.3, 2.4, and 2.5). The STATIC also provides information on the densities of several ionospheric species such as ${{\rm{O}}}_{2}^{+}$, which have been reported to be different from the widely accepted NGIMS densities by a factor of three or more (Maes et al. 2020, see their Figure 2). Because of this and also because NO⁺ and HCO⁺ densities (required for evaluating heating via exothermic chemistry) are not available from the STATIC measurements, we use the NGIMS thermal ion densities throughout our calculations.

As an example, we show in Figures 1(a) and (b) the NGIMS-based densities of CO₂, O, ${{\rm{O}}}_{2}^{+}$, O⁺, HCO⁺, and NO⁺, as well as the LPW-based thermal electron density, all as a function of altitude from the inbound portion of MAVEN orbit #3637 on 2016 August 10 with a periapsis altitude of 146.4 km at SZA ≈ 1568. The CO₂ and O densities have been exponentially extrapolated to 285 km assuming constant density scale heights.

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In Figure 1(c), two electron temperature profiles are depicted, solid for the LPW-based profile and dashed for the corrected profile below 200 km (see also Fowler et al. 2015). The latter is obtained by assuming strict thermal coupling at an altitude of 125 km, which is set by considering that a common dayside temperature for all constituents is reached at 110 km where the CO₂ density is ∼1 × 10¹¹ cm⁻³ (Matta et al. 2014), about equal to the CO₂ density in Figure 1(a) exponentially extrapolated to 125 km and predicting the same collision frequency between neutrals and electrons. For comparison, both the STATIC-based ion temperature profile and the neutral temperature profile are superimposed, of which the latter is derived from the CO₂ distribution in Figure 1(a) by downward integrating the hydrostatic balance equation (e.g., Cui et al. 2018b; Stone et al. 2018). The figure reveals the expected behavior that all constituents tend to be thermally coupled toward the lower boundary, but their temperatures are significantly different at relatively high altitudes (e.g., Matta et al. 2014; Sakai et al. 2016; Peterson et al. 2018).

The SWEA-based mean differential electron intensity is displayed in Figure 1(d) as a function of altitude and energy, revealing the presence of energetic electron depletion over isolated regions of the nightside Martian upper atmosphere (e.g., Steckiewicz et al. 2015, 2017, 2019). This feature should in principle have an appreciable impact on the heating of the nightside Martian upper atmosphere and ionosphere because several heating mechanisms described in Section 2 depend critically on the intensity of precipitating SW electrons.

4.1. Categorization of the MAVEN Data Set

As motivated by Figure 1(d), we categorize the available MAVEN data set into two groups, one with substantial electron precipitation and the other one with clear electron depletion, where a depletion event is identified with the criterion that the electron energy flux integrated over the SWEA energy spectrum from 3 eV to 4.6 keV is below 10⁹ eV cm⁻² s⁻¹ according to Niu et al. (2020). Niu et al. (2020) also reported noticeable differences in thermal plasma density and temperature between the two categories. This further motivates us to compute for both categories the mean densities and temperatures of different thermal constituents, along with the mean differential suprathermal electron intensities, as compared in Figure 2. Despite that the suprathermal electron intensity is on average greatly reduced above 20 eV for the case with depletion, the low energy intensity is still substantial, and its contribution to local heating needs to be carefully evaluated.

Several features are immediately seen in Figure 2. First, both neutral species, CO₂ and O, show nightside density profiles that are irrespective of the presence of energetic electron depletion.

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Second, the ion distribution is clearly modulated by the precipitating electron intensity but in a pattern that is both species and altitude-dependent. In particular, the O⁺ density is substantially reduced at all altitudes during depletion, which is a natural result of reduced SW electron impact ionization (e.g., Girazian et al. 2017a; Cui et al. 2019a). A similar variation is also seen for ${{\rm{O}}}_{2}^{+}$ near and below 180 km. For ${{\rm{O}}}_{2}^{+}$ at higher altitudes as well as for HCO⁺ and NO⁺ over the bulk of the displayed altitude range, the nightside density is enhanced during depletion. This must imply that an alternative mechanism is responsible for ionospheric plasma formation in the deep nightside of Mars, presumably day-to-night transport (e.g., Withers et al. 2012; Chaufray et al. 2014; Cui et al. 2015a; Girazian et al. 2017b). The density enhancement during depletion is especially pronounced for NO⁺ with a relatively long chemical destruction timescale as noted by Girazian et al. (2017b). The scenario of enhanced plasma content due to day-to-night transport implies preferred magnetic field connectivity between the dayside and nightside regions of the Martian ionosphere (Cao et al. 2019), a situation that is also expected for the formation of energetic electron depletion (e.g., Xu et al. 2017; Niu et al. 2020).

Third, a substantial reduction in plasma temperature is observed during depletion, especially at high altitudes where the reduction in electron temperature reaches 35%, and the reduction in ion temperature reaches 50%. However, the neutral temperatures between the two cases are comparable, with a difference of no more than 10%.

4.2. Nightside Neutral Heating Rates

In Figure 3, we show the altitude profiles of various neutral heating rates, solid for cases with substantial SW electron precipitation and dashed for cases with energetic electron depletion. We compare in the figure the contributions from SW electron impact (Section 5), exothermic chemistry (Section 6), and Maxwell interaction with thermal ions (Section 7). Energetic ion production (Section 2.5) is included in either SW electron impact or exothermic chemistry depending on how the suprathermal ions are produced.

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In regions with substantial SW electron precipitation, neutral heating is dominated by SW electron impact processes, with a heating rate profile declining rapidly from 9 eV cm⁻³ s⁻¹ near 150 km to below 10⁻³ eV cm⁻³ s⁻¹ near 250 km. This is followed by elastic Maxwell interaction, with a heating rate ranging from 3 to 2 × 10⁻⁴ eV cm⁻³ s⁻¹ over the same altitude range. Heating via exothermic chemistry makes a comparable contribution as Maxwell interaction below ∼200 km but becomes less effective at higher altitudes, with a fractional contribution of less than 15% near 250 km.

The situation for cases with energetic electron depletion is to be distinguished. With substantially reduced electron intensity above 20 eV, the neutral heating rate due to SW electron impact is also reduced on average to about 2% of the respective heating rate when subject to significant SW electron precipitation. The Maxwell heating rate is reduced as well, a trend that is more pronounced at relatively low altitudes with a reduction of near 80% approaching 150 km. With increasing altitude, the difference in Maxwell heating between cases with and without depletion diminishes, possibly because the effect of ion density difference (see Figure 2(b)) is nearly counterbalanced by the inverse effect of ion temperature difference (see Figures 2(c)) according to Equation (6). The situation for exothermic chemistry during depletion is more complicated, which manifests as a reduced heating rate below 195 km but an enhanced heating rate at higher altitudes. Such a feature is closely related to the observed ${{\rm{O}}}_{2}^{+}$ and O⁺ density differences between regions with and without depletion. We show below that the chemical heating rate is most sensitive to the abundances of these two ion species. Considering the above observations, we note that the degree to which the neutral heating rate varies during depletion is channel specific. In particular, the variation of SW electron impact heating is much more pronounced than the variations of both chemical heating and Maxwell heating. Consequently, the latter two channels become the dominant ones in neutral heating when the nightside Martian upper atmosphere is shielded from SW electron precipitation.

Of equal interest is the neutral heating frequency, defined as the neutral heating rate divided by the total neutral density and characterizing the capability of an atmospheric neutral to be heated in situ. Various neutral heating frequency profiles are displayed in Figure 4 for reference, for both cases with and without depletion. Compared to the respective heating rate, Figure 4 indicates that the neutral heating frequency varies less prominently with altitude for all channels. In particular, the heating frequencies due to SW electron impact vary modestly by a factor of five to eight around 10⁻⁸ and 10⁻¹⁰ eV s⁻¹, respectively, throughout the displayed altitude range, when SW electron precipitation into the atmosphere is allowed or shielded. Elastic Maxwell interaction contributes to a heating frequency from 4 × 10⁻⁹ eV s⁻¹ at 150 km to 6 × 10⁻¹⁰ eV s⁻¹ at 250 km in regions with SW electron precipitation, and varies by a factor of two around 6 × 10⁻¹⁰ eV s⁻¹ in regions with depletion. For exothermic chemistry, the heating frequency varies from 5 × 10⁻⁹ eV cm⁻¹ at 150 km to 3 × 10⁻¹⁰ eV s⁻¹ at 250 km for the former case and is near constant around 7 × 10⁻¹⁰ eV s⁻¹ for the latter case.

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As described in Section 2.2.1, SW impact itself could induce a variety of processes that deposit heat locally. Therefore it is instructive to investigate further the relative contributions of these processes in order to identify the dominant ones. This is displayed in Figure 5, with the upper and lower panels standing for cases with and without depletion. In each panel, the neutral heating rate profiles for nine individual processes are compared, including elastic collisions between precipitating electrons and atmospheric neutrals, predissociation of excited state CO₂ via direct kinetic energy release or via subsequent collisional quenching if the fragments are in excited states, collisional quenching of vibrationally excited CO₂, production of energetic neutrals and ions from excited state CO₂ ⁺, as well as collisional quenching of excited state O and O⁺.

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Our calculations indicate that, despite the overall decrease in SW electron impact heating during depletion, the relative contributions of various processes remain roughly unchanged. For instance, irrespective of the presence of substantial SW electron precipitation, direct kinetic energy release from predissociation of excited state CO₂ makes the dominant contribution to SW impact heating below 210 km whereas collisional quenching of excited state O⁺ becomes the most important channel at higher altitudes. Energetic neutral production from predissociation of excited state CO₂ ⁺ is also important, especially at relatively low altitudes, whereas several SW impact channels such as elastic interaction of precipitating electrons with atmospheric CO₂ are completely negligible at all altitudes for both cases. However, the effect of collisional quenching of vibrationally excited CO₂ is somewhat different in that it makes a substantially larger contribution to SW impact heating in regions with depletion as compared to regions without. This is obviously a result of less pronounced variation in energetic electron intensity below 20 eV (see Figures 2(d) and (h)) where the electron impact cross section for CO₂ vibrational excitation is peaked (Itikawa 2002). For instance, the electron intensity at 10 eV averaged over the altitude range of 150–250 km is 4.5 × 10⁵ eV cm⁻² s⁻¹ sr⁻¹ eV⁻¹ in regions with depletion as compared to 9.8 × 10⁶ eV cm⁻² s⁻¹ sr⁻¹ eV⁻¹ in regions without, which is responsible for the reduction in neutral heating via this channel by a roughly altitude-independent factor of ∼25. At substantially higher energies, the difference in electron intensity is much larger, and accordingly neutral heating via more energetic channels of SW impact shows a more pronounced reduction in regions with depletion.

In Figure 3, we show that exothermic chemistry makes important contributions to in situ nightside neutral heating, irrespective of the presence of substantial SW electron precipitation. We now further show in Figure 6 the relative contributions of various chemical reactions in neutral heating, again with the upper and lower panels standing for cases with and without depletion. For both cases, the role of ${{\rm{O}}}_{2}^{+}$ DR is most effective at low and high altitudes, whereas the role of reaction O⁺ + CO₂ becomes dominant at intermediate altitudes. We note that for both cases, heating via ${{\rm{O}}}_{2}^{+}$ DR occurs mainly via direct kinetic energy release to O fragments rather than collisional quenching of excited state O as a DR product, whereas for heating via O⁺ + CO₂, the contribution from energetic CO production is much more important than the contribution from energetic ${{\rm{O}}}_{2}^{+}$ production followed by subsequent energy transfer from suprathermal ions to atmospheric neutrals via Maxwell collisions. The contribution from HCO⁺ DR also appears to be non-negligible for both cases. Two additional ion-atom interchange reactions quoted in Section 2.2.2 are the reactions of ${{\rm{O}}}_{2}^{+}$ with NO and N. The required NO and N density profiles are not available from the NGIMS measurements due to wall chemistry, but using the densities reported in Cui et al. (2020) at a reference altitude of 160 km, we may conclude that neutral heating via these two reactions can be safely ignored.

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4.3. Nightside Ion and Electron Heating Rates

We now move on to ion and electron heating as displayed in Figure 7. Ion heating in the nightside Martian upper atmosphere is dominated by energetic ion production at all altitudes, irrespective of the presence of substantial SW electron precipitation. The respective heating rate is reduced during depletion, by a factor of 25 near 150 km and by a factor of two near 250 km. For Coulomb interaction with ionospheric electrons, the ion heating rate during depletion is reduced below 180 km but enhanced at higher altitudes. Such a feature is closely related to the altitude-dependent difference in total ion or electron density between cases with and without depletion as displayed in Figures 2(b) and 2(f). We further obtain that in regions with significant SW electron precipitation, the electron heating rate via Coulomb interaction with suprathermal electrons decreases steadily from 0.12 eV cm⁻³ s⁻¹ near 150 km to 1.5 × 10⁻³ eV cm⁻³ s⁻¹ near 250 km. This is to be compared to regions with depletion, characterized by an electron heating rate ranging from 1.7 × 10⁻³ eV cm⁻³ s⁻¹ to 1.3 × 10⁻⁴ eV cm⁻³ s⁻¹ over the same altitude range.

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When SW electrons have access to the nightside Martian upper atmosphere, the ion heating frequency in Figure 8 declines modestly from 1.4 × 10⁻³ to 2 × 10⁻⁶ eV s⁻¹ for energetic ion production and from 8 × 10⁻⁶ to 5 × 10⁻⁸ eV s⁻¹ for Coulomb interaction, both over the altitude range of 150–250 km. These variations are less prominent than the variations in the respective ion heating rates when the altitude dependence of ion density is removed. For comparison, the ion heating frequency in regions with energetic electron depletion ranges from 1.4 × 10⁻⁴ to 5 × 10⁻⁷ eV s⁻¹ for energetic ion production and from 3 × 10⁻⁶ to 1 × 10⁻⁷ eV s⁻¹ for Coulomb interaction over the same altitude range. We also estimate that the electron heating frequency is roughly altitude-independent, being 3 × 10⁻⁶ eV s⁻¹ and 7 × 10⁻⁵ eV s⁻¹ for cases with and without depletion, respectively.

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We show above that ion heating on the nightside of Mars is predominantly contributed to by energetic ion production. A further demonstration of such a mechanism is presented in Figure 9 where we compare five different channels that all lead to the production of suprathermal ions in a range of forms. These channels include two exothermic reactions producing ${{\rm{O}}}_{2}^{+}$ (from O⁺ + CO₂) and NO⁺ (from O⁺ + N₂), as well as predissociation of excited state CO₂ ⁺ producing C⁺, O⁺, and CO⁺, respectively. The ion heating rate profile via Coulomb interaction with ionospheric electrons is also indicated for comparison. We note that in response to the vast difference in energetic electron intensity between regions with and without depletion, the relative contributions of different channels to nightside ion heating also present large differences. In particular, the effect of energetic O⁺ production is greatly suppressed due to the reduced production of excited state CO₂ ⁺ via SW impact ionization during depletion, making energetic ${{\rm{O}}}_{2}^{+}$ production from O⁺ + CO₂ the most important channel of ion heating. This is to be distinguished from the situation with substantial SW electron precipitation, for which the above two channels make comparable contributions at all altitudes. Ion heating via C⁺ and CO⁺ production is also significantly suppressed during depletion for the same reason, but becomes important when subject to significant SW electron precipitation. For both cases, the contribution from NO⁺ production from O⁺ + N₂ is negligible at all altitudes.

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We show in Section 4 that precipitating SW electrons likely deposit a substantial amount of energy in the nightside Martian upper atmosphere, except in regions shielded by closed magnetic loops, which tend to form near strong crustal magnetic anomalies (e.g., Steckiewicz et al. 2015, 2017; Xu et al. 2017; Niu et al. 2020). We should note that in this study, we assume electron depletions to be associated with magnetic shielding (Niu et al. 2020), rather than an after-effect of atmospheric heating. Since precipitating SW electrons cover a broad energy range (see Figure 1(d)), it would be instructive to examine, for a given heating mechanism, the relative contributions from precipitating electrons at different energies. This is displayed in Figure 10 for neutral heating via direct SW electron impact at two representative altitudes, 250 km in the upper panel and 150 km in the lower panel.

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Several interesting features can immediately be seen in the figure. At energies near and below 10 eV, neutral heating at relatively low altitudes occurs mainly via the collisional quenching of vibrationally excited CO₂ and electronically excited O. With increasing altitude, elastic collisions between precipitating SW electrons and atmospheric O atoms become more important in response to the increasing proportion of O in the ambient atmosphere. At higher energies, the occurrence of neutral heating is also altitude-dependent and characterized by different controlling processes as follows: (1) At relatively low altitudes, neutral heating is dominated by predissociation of excited state CO₂ (in terms of direct kinetic energy release), followed either by collisional quenching of excited state O produced via CO₂ predissociation below 30 eV or by predissociation of excited state CO₂ ⁺ from electron impact ionization of atmospheric CO₂ (in terms of direct kinetic energy release to neutral fragments) above 30 eV. (2) At relatively high altitudes, the importance of collisional quenching of excited state O⁺ produced via SW electron impact ionization is substantially enhanced and becomes the most important channel.

We further compare in Figure 11 the differential contributions of ionospheric electron heating via Coulomb collisions with precipitating SW electrons and ion heating via predissociation of excited state CO₂ ⁺, at a reference altitude of 150 km. The situation at higher altitudes is quite comparable and not shown. According to the figure, the peak of electron heating occurs at energies below 10 eV, whereas the peak of ion heating occurs at substantially higher energies because electron impact ionization of atmospheric CO₂ is required for such an ion heating channel. The possible role of SW electron precipitation on the Martian ionospheric electron temperature has already been noted by Cui et al. (2015b).

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Our data-driven calculations also indicate that the role of exothermic chemistry exerts an appreciable influence on neutral heating. The fact that nightside heating via chemistry is not reduced as much as nightside heating via direct SW impact processes suggests that SW precipitation cannot be fully responsible for the thermal plasma content observed in the nightside Martian ionosphere. Indeed, extensive studies have highlighted the role of day-to-night transport as an important source of nightside ionospheric plasma, especially in regions not too distant from the EUV terminator (e.g., Withers et al. 2012; Cui et al. 2015a; Girazian et al. 2017b; Adams et al. 2018; Cao et al. 2019). Such a process is especially important for shaping the nightside distribution of relatively long-lived ion species such as NO⁺ (González-Galindo et al. 2013; Girazian et al. 2017b). The importance of day-to-night plasma transport also implies that some of the neutral heating rates reported here are not strictly "in situ."

Collisional quenching is well acknowledged as a viable source of neutral heating in the dayside upper atmospheres of terrestrial planets (Fox et al. 2008, and references therein). In the nightside Martian upper atmosphere, collisional quenching is driven by the production of excited state O, O⁺, and CO₂ through a variety of ways including both SW electron impact (Figure 5) and exothermic chemical (Figure 9) processes. More specifically, the relevant processes are (1) vibrational excitation of atmospheric CO₂ by SW impact, (2) electronic excitation and excitative ionization of O by SW impact, (3) predissociation of electronically excited CO₂ from SW impact that produces excited state O, and (4) ${{\rm{O}}}_{2}^{+}$ DR that produces excited state O.

We compare in Figure 12 the production rate profiles of excited state O (left), O⁺ (middle), and CO₂ (right) from various channels averaged over the nightside Martian upper atmosphere when subject to strong SW electron precipitation. The figure indicates that more excited O atoms are produced in the ¹D state than in the ¹S state for SW impact on both atmospheric O and ${{\rm{O}}}_{2}^{+}$ DR. The only exception is CO₂ predissociation, which produces more excited O in the ¹S state due to a larger cross section for the respective dissociative channel (Bhardwaj & Jain 2009). Production of excited state O occurs mainly in the form of O(¹S) via CO₂ predissociation below 180 km and in the form of O(¹D) via SW impact excitation of atmospheric O at higher altitudes. The contribution from ${{\rm{O}}}_{2}^{+}$ DR is unimportant except near and below 160 km. For excited state O⁺, it is produced mainly in the ²D state via SW impact ionization of atmospheric O, whereas production in the higher ²P state is less effective by about 50%. For vibrationally excited CO₂, the production rate declines nearly exponentially from 3 cm⁻³ s⁻¹ at 150 km by five orders of magnitude to 3 × 10⁻⁵ cm⁻³ s⁻¹ at 250 km. Here we only include the production of vibrationally excited CO₂ in the (001) state (see Section 2.2.1).

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For some of the excited state species such as O⁺(²P), the internal energy is not entirely converted to local heat due to non-negligible radiative de-excitation. The neutral heating rates via different collisional quenching channels are shown in Figures 5 and 6, with notations terminated by "Q." For regions subject to strong SW electron precipitation, the contribution from collisional quenching to in situ heating of the nightside Martian upper atmosphere is important, as can clearly be seen in Figure 13(b), where we show the fractional contributions from collisional quenching of different excited state species to total heating. According to our calculations, such a fractional contribution increases systematically with increasing altitude from 10% near 150 km to 50% above 230 km. The bulk of neutral heating via collisional quenching is associated with O⁺(²D) production, except below 180 km, where it is surpassed by production of O(¹D) and O(¹S), as well as vibrationally excited CO₂.

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The situation for regions with energetic electron depletion is remarkably different, as depicted in Figure 13(a). Now the fractional contribution from collisional quenching appears to be unimportant at all altitudes, from 9% near 150 km to only 2% near 250 km. This demonstrates that the intensity of precipitating electrons is crucial for determining the role of collisional quenching in nightside atmospheric heating on Mars. For comparison, we note from the recent investigation of Gu et al. (2020) that the effect of collisional quenching in the dayside Martian upper atmosphere lies somewhat between the two nightside cases with and without depletion, and is characterized by a fractional contribution declining from 20% at 130 km to 5% near 250 km (see their Figure 3).

SW electron precipitation is generally acknowledged as an important external energy source in the nightside Martian upper atmosphere, creating a patchy ionosphere in the absence of solar EUV and X-ray radiation (e.g., Verigin et al. 1991; Fowler et al. 2015; Girazian et al. 2017a; Cui et al. 2019a). In principle, such an energy source may also affect the nightside thermal balance of various atmospheric species. However, none of the available model calculations have included SW electron precipitation as a potential source of nightside atmospheric and ionospheric heating (e.g., Bougher et al. 1999, 2000; Angelats i Coll et al. 2005; González-Galindo et al. 2005, 2009a, 2009b, 2010; Bougher et al. 2015).

With the accumulation of extensive measurements made by several relevant instruments on board MAVEN, we are able to, for the first time, evaluate the role of in situ heating via SW electron precipitation on the nightside of Mars. This serves as the main motivation of the present study. Our calculations are performed in a data-driven manner, which means that all of the controlling parameters required for the calculations are constrained as much as possible by realistic data, rather than being constrained by modeling results. This helps to reduce various sources of model uncertainty to minimum levels.

It is well known that precipitating SW electrons could be effectively shielded by closed magnetic loops preferentially formed near strong crustal magnetic anomalies (e.g., Steckiewicz et al. 2015, 2017; Xu et al. 2017; Niu et al. 2020), which causes a considerable variability in energetic electron intensity encountered on the nightside of Mars. To incorporate such a bimodality, we categorize the entire MAVEN data set into two groups, one for regions subject to strong SW electron precipitation and the other one for regions with clear electron depletion. Computations of various heating rates are performed separately for the two cases, with input atmospheric and ionospheric parameters (density, temperature, etc.) adopted by averaging over the respective regions.

Our calculations reveal some interesting characteristics as outlined below.

• (1)  
  In terms of nightside neutral heating, electron impact is more important than both exothermic chemistry and elastic Maxwell interaction with thermal ions, in regions subject to strong SW electron precipitation. In contrast, neutral heating via electron impact is substantially reduced in regions shielded from SW precipitation and could be safely ignored as compared to the other heating mechanisms.
• (2)  
  Among all SW electron impact processes, impact ionization of atmospheric O is dominant at high altitudes, but impact excitation of CO₂ followed by predissociation becomes the most important process at low altitudes. The contributions of these SW impact processes are substantially reduced during depletion. However, vibrational excitation of CO₂ is somewhat different in that it makes a substantially larger contribution to SW impact heating in regions with depletion as compared to regions without.
• (3)  
  Nightside chemical heating occurs mainly via ${{\rm{O}}}_{2}^{+}$ DR at low and high altitudes, but via O⁺ + CO₂ at intermediate altitudes. Such a feature is obtained for cases both with and without depletion.
• (4)  
  Excited state species in a variety of forms could be produced via either SW electron impact or exothermic chemistry, which could deposit energy locally via collisional quenching. This process is found to contribute substantially to nightside neutral heating in the presence of SW electron precipitation, dominated by O⁺(²D) quenching over the bulk of the altitude range considered here. During depletion, the contribution from collisional quenching is estimated to be negligible.
• (5)  
  Nightside ion heating is dominated by energetic ion production irrespective of the presence of electron depletion. In reality, this occurs mainly via reaction O⁺ + CO₂ and CO₂ ⁺ predissociation, respectively, for cases with and without depletion.
• (6)  
  In our calculations, nightside electron heating occurs exclusively via Coulomb interaction with precipitating SW electrons, thus presenting a large difference between regions with and without depletion.

The results presented here, along with those reported in previous studies (e.g., Girazian et al. 2017a; Steckiewicz et al. 2017; Lillis et al. 2018; Cui et al. 2019a; Niu et al. 2020), lay out the foundation for a thorough understanding of how the nightside Martian upper atmosphere and ionosphere respond to SW electron precipitation. The nightside neutral, ion, and electron heating rates that we estimate are indeed much lower than the respective dayside heating rates (e.g., Matta et al. 2014; Sakai et al. 2016; Peterson et al. 2018; Gu et al. 2020). Despite this, it remains to be verified by rigorous calculations whether SW electron precipitation is really negligible or if it is able to, in the absence of solar EUV and X-ray irradiance, cause in situ heating that is strong enough to perturb the nightside Martian upper atmosphere and ionosphere, especially in regions with open magnetic field lines. For instance, the ion temperature in the Martian ionosphere has been predicted to drop rapidly to a minimum level soon after sunset and remains there until sunrise when solar EUV and X-ray radiation is treated as the only external energy source (Matta et al. 2014). Such a minimum level was set by these authors as the imposed nightside neutral temperature due to the coupling between neutrals and ions via Maxwell collisions, characterized by a neutral heating rate or equivalently an ion cooling rate of 5 eV cm⁻³ s⁻¹ at a reference altitude of 150 km and in regions without depletion (see Figure 3). For comparison, our calculations predict an ion heating rate at the same altitude and in the same regions that is 50% of the above value (see Figure 7(a)), implying that in situ heating likely exerts an appreciable influence on the deep nightside ion temperature.

This work is supported by the B-type Strategic Priority Program No. XDB41000000 funded by the Chinese Academy of Sciences (CAS) and the pre-research project on Civil Aerospace Technologies No. D020105 funded by China's National Space Administration. The authors also acknowledge support from the National Natural Science Foundation of China through grants 42030201 and 41774186 to J.C., 41904154 to X.S.W., and 41774167 to M.Y.W., and from the CAS Institute of Geology & Geophysics through grant IGGCAS-201904. The data set used in this work is publicly available at the MAVEN Science Data Center (http://lasp.colorado.edu/maven/sdc/public/).