# Effect of the Planet Shine on the Corona: Application to the Venusian Hot Oxygen

Jean-Yves Chaufray, Shane Carberry Mogan, Justin Deighan

► To cite this version:

Jean-Yves Chaufray, Shane Carberry Mogan, Justin Deighan. Effect of the Planet Shine on the Corona: Application to the Venusian Hot Oxygen. Journal of Geophysical Research Space Physics, 2025, 130 (5), pp.e2025JA033802. 10.1029/2025JA033802. hal-05107457

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Distributed under a Creative Commons Attribution 4.0 International License
RESEARCH ARTICLE

10.1029/2025JA033802

**Key Points:**

* We simulate the Venusian shine on the hot oxygen corona with a radiative transfer model with two populations

* We report a new hot oxygen density derived from Pioneer Venus Orbiter measurements reduced by a factor of ~1.6 compared to previous analysis

* This revised hot oxygen density provides constrains on the production rate or the thermalization by collisions of the hot oxygen atoms

**Correspondence to:**

J.-Y. Chaufray,
jean-yves.chaufray@latmos.ipsl.fr

**Citation:**

Chaufray, J.-Y., Carberry Mogan, S., & Deighan, J. (2025). Effect of the planet shine on the corona: Application to the Venusian hot oxygen. *Journal of Geophysical Research: Space Physics*, 130, e2025JA033802. https://doi.org/10.1029/2025JA033802

Received 30 JAN 2025

Accepted 6 MAY 2025

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# Effect of the Planet Shine on the Corona: Application to the Venusian Hot Oxygen

J.-Y. Chaufray¹ ID, S. Carberry Mogan² ID, and J. Deighan³ ID

¹LATMOS, IPSL, Sorbonne Université, Université Paris-Saclay, CNRS, Guyancourt, France, ²Space Sciences Laboratory, University of California, Berkeley, Berkeley, CA, USA, ³Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CA, USA

**Abstract** This paper presents a new derivation of the hot oxygen density in the Venusian upper exosphere (above 500 km) from Pioneer Venus Orbiter (PVO) ultraviolet spectrometer data, considering the effect of the solar photons backscattered by the oxygen atoms below ~300 km (Venus shine), not included in past analysis, with a resonant scattering radiative transfer model. The Venus shine increases the volume emissivity of the hot oxygen corona by ~60% compared to the direct solar illumination, and the O I 130.4 nm brightness measured by PVO is reproduced with a hot oxygen density reduced by 1.6 compared to the density deduced from past analysis. Therefore, this new hot oxygen density provides better constraints on the production rates of hot oxygen in the Venusian ionosphere or on the thermalization by collisions of the hot oxygen atoms.

## 1. Introduction

Venus' dense atmosphere drives its extreme climate, enveloping the planet in intense heat, crushing pressures, and thick clouds of corrosive acids that define its inhospitable surface conditions. At the surface of Venus, the atmosphere is predominantly composed of CO₂ at ~97% by volume, with N₂ making up ~2%, and trace amounts of other gasses, including water vapor (O'Rourke et al., 2023 and references therein). With increasing altitude, the CO₂-rich lower atmosphere transitions into a more rarefied upper atmosphere dominated by lighter, faster-moving species generated through photochemical processes; for example, solar extreme ultraviolet (EUV) photons dissociate CO₂, producing energetic CO and O (e.g., Martinez et al., 2023). In the upper thermosphere, above approximately 150 km, O becomes the dominant species. Solar EUV photons not only dissociate neutral molecules in the thermosphere but also ionize them, driving the formation of Venus' ionosphere. The interaction between the neutral thermosphere and the charged particles in the ionosphere establishes a dynamic system governed by photochemical reactions. For example, while CO₂ is the most abundant neutral species up to ~150 km, the dominant ion at these altitudes is O₂⁺ rather than CO₂⁺ (e.g., Fox & Sung, 2001). This arises from rapid reactions between CO₂⁺ and O, producing O₂⁺ (and more CO). The major sink of O₂⁺ is dissociative recombination (DR), which produces two energetic O atoms. Additionally, O⁺—produced either by direct ionization of O or by dissociative ionization of CO₂—can react with neutral CO₂ to produce yet more O₂⁺ (e.g., Fox & Sung, 2001), creating a feedback loop that sustains O₂⁺ and O as major species in the upper atmosphere. Above ~200 km, the frequency of these chemical processes diminishes, and O⁺ becomes the dominant ion species (Martinez et al., 2024), mirroring the dominance of atomic O in the neutral upper thermosphere. Whereas O⁺ is ultimately lost through Solar Wind pick up (Ma et al., 2023), Venus' gravity is sufficient to prevent the escape of O, resulting in the formation of an extended, gravitationally bound oxygen corona.

These processes, which regulate the composition and dynamics of Venus' upper atmosphere, have been extensively investigated through a combination of remote sensing, in situ measurements, and numerical modeling. Over decades of study, these efforts have illuminated the complex interplay of photochemistry, thermospheric circulation, and ionospheric physics. Among the in situ observations of Earth's "twin," the Pioneer Venus Orbiter (PVO) remains the most comprehensive mission to have explored the planet's upper atmosphere in detail.

The periapsis of PVO was actively controlled to remain within an altitude range of about 145–160 km from 1978 to 1980 until the necessary fuel supply was exhausted. After this period of active orbit control, the periapsis of PVO began to rise, reaching a maximum of ~2,200 km in 1986 prior to its final descent into the Venusian atmosphere, when it succumbed to its crushing pressure and disintegrated in 1992. The PVO Neutral Mass Spectrometer (NMS) sampled the neutral composition from 1978 to 1980 (Niemann et al., 1980) and in 1992, detecting CO₂, CO, O, N₂, N, and He over an altitude range of ~135–275 km covering a broad range of solar
zenith angles (SZA). While O was observed to be the dominant constituent of the atmosphere above ~155 and ~145 km on the day- and night-side, respectively, CO₂ was observed to be the predominant species below these altitudes. The PVO Ion Mass Spectrometer (IMS) operated from 1978 to 1992 (Taylor et al., 1980), detecting a range of ion species, including H⁺, C⁺, N⁺, O⁺, CO⁺/N₂⁺ (i.e., 28-amu ions), NO⁺, O₂⁺, and CO₂⁺. The IMS sampled Venus' ionosphere at higher altitudes than the NMS sampled the neutral atmosphere, extending from ~400 to 600 km, the region where the ionosphere transitions into the magnetosheath (Luhmann, 1986). However, between 1980 and 1992, the IMS observations primarily focused on the interaction between the solar wind and Venus' ionosphere, targeting regions well above the typical ionopause altitudes.

An extended O corona was also inferred from observations made by the PVO ultraviolet spectrometer (UVS, Nagy et al., 1981): PVO-UVS measured the OI resonance triplet near 1,304 Å at Venus' limb over a range of latitudes (19°S–19°N) and SZA (~30°–53°) at an altitude range of ~400–1,600 km, from which neutral O densities ranging from ~2 × 10³ to 4 × 10⁵ cm⁻³ were inferred. The inferred O densities were observed to be nearly independent of SZA at a given altitude on the day-side, and decrease rapidly beyond the terminator. As will be discussed in Section 4.2, several numerical models have since attempted to reproduce Venus' O corona inferred by Nagy et al. (1981) from PVO-UVS data. Indeed, this data set has provided a crucial constraint for several models of Venus' upper atmosphere, from which important features have been derived, such as ion outflow rates (Hodges, 2000) and interactions with the impinging solar wind (Ma et al., 2023). However, despite PVO performing hundreds of flybys of Venus throughout the course of the mission, the O corona inferred by Nagy et al. (1981) was from only a single flyby, and with no error bars provided. Moreover, Nagy et al. (1981) only considered direct solar illumination of the oxygen corona above ~400 km as the source of the OI 1304 emission. Conversely, Paxton and Anderson (1992) presented a more robust fit to PVO-UVS data averaged over 23 flybys (see Figure 53 therein), while also taking into account contributions to the detected emissions from planetary OI 1304 dayglow, that is, “planet shine.” However, unlike Nagy et al. (1981), they did not provide a density profile for the corresponding O corona that could be utilized as a constraint for models of Venus' upper atmosphere.

Here we explore a phenomenon that affects this inferred profile: planet shine, which serves to *reduce* the O densities inferred by Nagy et al. (1981) as a result of backscattering of the solar photons by the cold oxygen below ~400 km. These backscattered photons can excite the hot oxygen atoms, dominant at higher altitudes and then increasing the excitation frequency (g-factor) due to the only incoming solar photons. This process, called planet shine, has been studied at Mars, whose upper atmosphere is of essentially the same composition as Venus and has been extensively observed by several spacecraft, such as Mars Atmosphere and Volatile Evolution (MAVEN) and the Emirates Mars Mission. Similar to Venus, a hot O corona was detected at Mars via the IUVS instrument onboard MAVEN (Deighan et al., 2015). However, by applying a radiative transfer model, Chaufray et al. (2016) demonstrated that the planetary shine illuminating the hot corona could increase the volume emission rate of the hot oxygen atoms by ~1.1–2 (depending on altitude and solar zenith angle). Here we apply this same model to Venus' O corona to quantify the effect of the planetary shine on the hot oxygen brightness measured by PVO-UVS.

## 2. Model

In this study, we will only consider spherically symmetric cold and hot oxygen densities. Such an assumption is enough to estimate the effects of the scattered photons in the thermosphere/low exosphere (below ~300 km) on the hot oxygen corona. Considering the 3D structure of the upper atmosphere (e.g., the local time variations) would be needed only to study highly accurate observations of the spatial variations of the hot oxygen corona not currently available. This assumption, discussed in Section 4.1, was also done to study the shine effect on the Martian hot oxygen corona (Chaufray et al., 2016).

The cold and hot oxygen densities used in this study are displayed in Figure 1. The nominal cold oxygen density corresponds to the oxygen density at noon of the empirical model derived from the measurements of ONMS aboard PVO (Hedin et al., 1983). A sensitivity study of the shine effect with simply rescaled vertical profiles, also displayed in Figure 1 is performed. The nominal hot oxygen density profile is taken from the hot oxygen density derived by UVS aboard PVO (Nagy et al., 1981).

The CO₂ density and the temperature profiles at noon from the empirical model of Hedin et al. (1983) are used to compute the absorption and the local maxwellian velocity distribution of the cold oxygen below 250 km. An
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Cold oxygen density (solid lines) and Hot oxygen density (dashed lines) used to simulate the Venusian shine on the hot oxygen corona. The nominal profiles are given by the green profiles (the middle one). Other colors correspond to rescale densities by (0.2, 0.5, 2, and 5) for the cold oxygen densities and (0.5 and 2.5) for the hot oxygen densities, encompassing the hot oxygen density derived by Nagy et al. (1981) (black diamonds).</figcaption></figure>

isothermal profile is used for the temperature above 250 km while a Chamberlain's profile (Chamberlain, 1963) is used for the cold oxygen density. For the hot population, an isotropic Maxwellian velocity distribution at $T = 5,000$ K is used. This temperature corresponds to the temperature needed to fit the hot oxygen density profile derived by Nagy et al. (1981) with an hydrostatic profile (Figure 1).

The radiative transfer model used to compute the venusian shine on the hot oxygen corona is similar to the Martian model used by Chaufray et al. (2016) and is succinctly described here. More details about the simpler Martian version with only one cold oxygen population can be found in Chaufray et al. (2015).

Test particles representative of the solar photons in the 130.4 nm triplet (Gladstone, 1992) are followed inside the Venusian atmosphere between 100 and 50,000 km. The fine structure of the triplet (the ground state is divided in three fine levels corresponding to angular momenta, $J = 0, 1$, and $2$) is considered with a Boltzmann's distribution for the ground state for both populations (e.g., Meier & Lee, 1982). The probability $P$ for a photon to be scattered during a spatial step $ds$ is given by

$$P = 1 - \exp \left[ - \sum_j \sigma_j(\lambda, \vec{r}) n_j(\vec{r}) p_j(\vec{r}) ds \right] \quad (1)$$

where the sum over $j$ is the sum of the cold ($j = \text{cold}$) and hot population ($j = \text{hot}$); $n_j(\mathbf{r})$, $p_j(\mathbf{r})$ and $\sigma_j(\lambda, \vec{r})$ are the oxygen density, the relative population of the ground state able to be excited by the photon (e.g., a solar photon emitted inside the 130.217 nm line can only excite an oxygen atom in the $J = 2$ state) and the scattered cross section at the wavelength $\lambda$ of the photon at position $\mathbf{r}$, respectively. If a scattering occurs, the probability to have a scattering by a cold oxygen or by a hot oxygen is given by their relative optical thickness:

$$P_{\text{cold}} = \frac{\sigma_{\text{cold}}(\lambda, \vec{r}) n_{\text{cold}}(\vec{r}) P_{\text{cold}}(\vec{r})}{\sum_j \sigma_j(\lambda, \vec{r}) n_j(\vec{r}) p_j(\vec{r})} \quad (2)$$

$$P_{\text{hot}} = \frac{\sigma_{\text{hot}}(\lambda, \vec{r}) n_{\text{hot}}(\vec{r}) P_{\text{hot}}(\vec{r})}{\sum_j \sigma_j(\lambda, \vec{r}) n_j(\vec{r}) p_j(\vec{r})} \quad (3)$$
<figure><img src="image_4.png" /><figcaption>**Figure 2.** (left) Altitude profile for the single-scattering and multiple-scattering volume emission rate at solar zenith angle (SZA) = 0° of the cold oxygen for a simulation without hot oxygen and for a simulation with hot oxygen. The three horizontal black solid segments indicate, approximately, the altitude where the optical thickness at the center of each line of the O I 1304 nm triplet equals 1 (130.2 nm–280 km, 130.4 nm–250 km, and 130.6 nm–230 km). (right) Variations of the same volume emission rates with the solar zenith angle for an altitude near 300 km.</figcaption></figure>

The new emission line of the photon is computed from the transition probabilities (1/9 for $J=0$, 3/9 for $J=1$, and 5/9 for $J=2$) (Meier & Lee, 1982). The new propagation direction of the photon is computed considering the phase function of the line of the triplet (Chaufray et al., 2016). The wavelength of the scattered photon, considering the natural broadening of the lines and the angle-dependent partial frequency redistribution, is computed with the Monte Carlo method of J. S. Lee (1982). As in Chaufray et al. (2016), the spectral emission volume rate of each line $i$ of the 130.4 nm triplet is the sum of five terms:

$$ \varepsilon(\vec{r}, \lambda, i) = \varepsilon_{0,c}(\vec{r}, \lambda, i) + \varepsilon_{m,c}(\vec{r}, \lambda, i) + \varepsilon_{0,h}(\vec{r}, \lambda, i) + \varepsilon_{s,h}(\vec{r}, \lambda, i) + \varepsilon_{m,h}(\vec{r}, \lambda, i) \quad (4) $$

where $\varepsilon_{0,c}$ is the single scattering term for cold oxygen, $\varepsilon_{m,c}$ is the multiple scattering term for cold oxygen, $\varepsilon_{0,h}$ is the single scattering term for hot oxygen, $\varepsilon_{s,h}$ the “shine” term, and $\varepsilon_{m,h}$ the multiple scattering term for hot oxygen. These terms are exclusive, meaning that for each scattering, one and only one term is updated. The three lines of the triplet do not spectrally overlap, so that the spectral integration can be done separately for each line, and the volume emission for each line added to calculate the total volume emission rate for the five terms $X$:

$$ \varepsilon_X(\vec{r}) = \sum_{i=1}^{3} \int_{\lambda_{\min}}^{\lambda_{\max}} \varepsilon_X(\vec{r}, \lambda, i) d\lambda \quad (5) $$

The total volume emission rates calculated are normalized by the g-factor. Given the spherical symmetry used for the density, the total volume emission rates only depend on the altitude and SZA.

### 3. Result

The simulated volume emission rates for the cold population: $\varepsilon_{0,c}(\mathbf{r})$ and $\varepsilon_{m,c}(\mathbf{r})$ using the nominal density profiles for the cold and the hot oxygen are compared to those simulated with the same cold population but without hot oxygen (Figure 2). As with the Martian corona, we found that the presence of the hot oxygen does not change the volume emission rate of the cold population at the dayside, but does increase it at the nightside because the extended hot oxygen corona can scatter the solar photons toward the shadow, where these photons could not
<figure><img src="image_5.png" /><figcaption>**Figure 3.** (left) Altitude profile for the single-scattering (blue), multiple-scattering (red), and shine from the cold oxygen (green) volume emission rate at solar zenith angle (SZA) = 0° of the hot oxygen for a simulation, normalized by the g-factor. The hot oxygen density is also indicated by the black line. (right) Variations of the same volume emission rates with the solar zenith angle for an altitude near 600 km.</figcaption></figure>

access without scattering. The magnitude of this increase will vary with the spatial variations assumed for the hot oxygen density but an increase will be present whatever the hot oxygen density. Unfortunately, the nightside brightness has never been observed to study it in detail.

The simulated volume emission rates for the hot population: $\epsilon_{0,h}(\mathbf{r})$, $\epsilon_{s,h}(\mathbf{r})$, and $\epsilon_{m,h}(\mathbf{r})$, using the nominal density profiles, and normalized by the g-factor $g_{exc}$, are displayed in Figure 3. The normalized single scattering term is equal to the density as expected for an optically thin emission, except very close to the exobase due to the reduction of solar radiation by the cold oxygen. The multiple scattering is negligible, except on the nightside. The shine term, corresponding to solar photons backscattered by the cold oxygen and illuminating the hot oxygen corona, is similar to the single scattering term between ~500 and 1,000 km but decreases faster with altitude as simulated for Mars (Chaufray et al., 2016).

The sensitivity of the shine effect to the cold oxygen thermospheric density is studied by computing the ratio $G_c(\mathbf{r}) = \epsilon_{s,h}(\mathbf{r})/[g_{exc}n_{hot}(\mathbf{r})]$ for the five different cold oxygen density profiles presented in Figure 1. This ratio measures the relative importance of the shine term compared to the single scattering term, since $\epsilon_{0,h}(\mathbf{r}) \approx g_{exc}n_{hot}(\mathbf{r})$ and is less noisy than the simulated ratio $\epsilon_{s,h}(\mathbf{r})/\epsilon_{0,h}(\mathbf{r})$. The simulated vertical profiles at SZA = 60° and the simulated SZA variations at an altitude near 600 km of $G_c(\mathbf{r})$ are compared in Figure 4.

At a given altitude and SZA, $G_c$ increases with the cold oxygen density because a larger backscattered flux is able to illuminate the hot oxygen corona. $G_c$ decreases with altitude and becomes negligible (<0.1) above ~4,000 km for all cases, although the simulated values are very noisy at these high altitudes because of the poor statistics due to the low number of scatterings. $G_c(r)$ is expected to decrease as $1/r^2$ at high altitude due to the conservation of the flux of photons. As simulated on Mars, $G_c$ decreases also with SZA at a given altitude due to the decrease of the solar illumination. In the altitude range of the hot oxygen brightness observed by PVO, that is, below 1,600 km (Nagy et al., 1981), $G_c(r)$ varies between 0.2 and 0.8.

$G_c$ is expected to be independent of the hot oxygen density when the optical thickness of the hot oxygen population is much lower than 1 at all altitudes. The sensitivity of $G_c$ with the different hot oxygen densities presented in Figure 1 (using the nominal cold oxygen density), shows that the denser hot oxygen model is sufficiently dense to modify (reduce) $G_c$, while $G_c$ does not vary very much (the difference is lower than 10% and is neglected) between the two other density profiles (Figure 4). When the optical thickness of the hot population is not
<figure><img src="image_6.png" /><figcaption>**Figure 4.** (top left) Altitude profile of $G_c(r)$ at solar zenith angle (SZA) = 60° for the different cold oxygen density profiles, (top right) Variations of $G_c(r)$ with the solar zenith angle for an altitude near 600 km. The models of the cold oxygen are labeled by their scaling factors defined in Figure 1. Bottom: Same as above but for the three different hot oxygen density profiles, and the nominal cold oxygen profile. The hot oxygen density profiles are labeled by their scaling factors defined in Figure 1.</figcaption></figure>

negligible, the decrease of $G_c$ is due to a reduction of the solar flux reaching the lower exosphere and thermosphere by the hot oxygen population above.

As we will show, for the hot oxygen corona brightness measured by PVO, the linear variation between $\epsilon_{s,h}(\mathbf{r})$ and $n_{\text{hot}}(\mathbf{r})$, that is, the independence of $G_c$ with the hot oxygen density is valid, so that $G_c$, computed with the nominal hot oxygen population, can be used for any lower hot oxygen densities.

The brightness $I(z)$ at the tangent altitude $z$ is computed from the spectral volume emission rates by forward integration along the line of sight based on the geometry described in Nagy et al. (1981):
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Simulated brightness vertical profile, when the shine term is neglected (solid green line) and included (solid red line) obtained with the hot oxygen density from Nagy et al. (1981). The simulated profile including the shine term but with a hot oxygen density divided by 1.6 is represented by the red dashed line. The PVO-UVS data fit obtained by Nagy et al. (1981) is represented by the black diamonds and the fit from Paxton and Anderson (1992) is represented by the black triangles.</figcaption></figure>

$$I(z) = \sum_{i=1}^{i=3} \int_{\lambda_{\min}}^{\lambda_{\max}} \int_{s} [\varepsilon_{0,c}(\vec{r}(s), \lambda, i) + \varepsilon_{m,c}(\vec{r}(s), \lambda, i) + \varepsilon_{0,h}(\vec{r}(s), \lambda, i) + \varepsilon_{s,h}(\vec{r}(s), \lambda, i) + \varepsilon_{m,h}(\vec{r}, \lambda, i)] e^{-\tau_c(\vec{r}(s), \lambda, i) - \tau_h(\vec{r}(s), \lambda, i) - \tau_{CO2}(\vec{r}(s), i)} ds d\lambda \quad (6)$$

where, $\tau_c(r(s),\lambda,i)$ and $\tau_h(r(s),\lambda,i)$ are the optical thickness between the spacecraft and the distance $s$ along the line of sight for the wavelength $\lambda$ for the oxygen line $i$ of the cold population and the hot population respectively, $\tau_{CO2}(r(s))$ is the absorption optical thickness by CO$_2$ considered as constant for each line of the triplet. All these optical thicknesses are much lower than 1 for the lines of sight above 500 km. At the altitudes considered here, the volume emission rate of the cold oxygen is also negligible compared to the volume emission rate of the hot oxygen (see Figures 2 and 3), and if we also neglect the multiple scattering term of the hot population (Figure 3), the brightness can be approximated by

$$I(z) \approx \sum_{i=1}^{i=3} \int_{\lambda_{\min}}^{\lambda_{\max}} \int_{s} [\varepsilon_{0,h}(\vec{r}(s), \lambda, i) + \varepsilon_{s,h}(\vec{r}(s), \lambda, i)] ds d\lambda \\ \approx g_{exc} \int_{s} [1 + G_c(s)] n_{hot}(s) ds \quad (7)$$

The simulated brightnesses, using the nominal hot oxygen density from Nagy et al. (1981) and the nominal cold oxygen density, with and without the shine term, are compared to the observed brightness (the fit of the observed brightness derived by Nagy et al., 1981), showing that, in agreement with Nagy et al. (1981) the observed profile is reproduced when the shine term is not included with their hot oxygen density profile, but the brightness is overestimated when the shine term is included (Figure 5). Therefore, to fit the observed profile with the shine term, the hot oxygen density must be decreased by a factor ~1.6 (Figure 5) consistent with the value of $G_c \sim 0.6$ obtained with the nominal cold oxygen density (Figure 4). We used a hot

oxygen density profile that fits the brightness profile from Nagy et al. (1981) as input of our radiative transfer model (Figure 1). Because the profile retrieved from Paxton and Anderson (1992) is slightly different, we expect to better reproduce the profile from Nagy et al. (1981) than the profile from Paxton and Anderson (1992) (Figure 5). Both profiles correspond to fit of the observations and uncertainties are not added to these fits. While the difference below 800 km could be significant, the difference above 1,200 km should not be significant given the large uncertainty (~ few 10s Rayleigh) in the measured brightness (see for example Figure 53 in Paxton and Anderson (1992)).

# 4. Discussion

## 4.1. Discussing the Assumptions

The results show that the planetary shine illuminating the Venusian hot oxygen corona at high altitude is not negligible and can represent ~60% of the direct solar illumination, with large variations in altitude and solar zenith angle. Some simplifications have been done in this study to estimate this effect. One assumption is the spherical symmetry of the cold oxygen and hot density. Since the shine effect is important mostly on the dayside, the large dayside/nightside variations of the oxygen density measured by PVO/ONMS (Hedin et al., 1983) is not important to study this process. The dayside oxygen and carbon dioxide densities and temperature only present a few horizontal variations (Hedin et al., 1983) justifying this assumption. This assumption was also used by Nagy et al. (1981) and Paxton and Anderson (1992) considering a dayside average profile.

One other assumption, done mostly for numerical reasons, is the assumption of a Maxwellian velocity distribution for the hot oxygen population. This population is mostly produced by DR of $O_2^+$ ions which do not produce a continuum velocity distribution but several peaks depending on the electronic excitation state of the produced
oxygen atoms (Schunk & Nagy, 2009). The few collisions of the hot oxygen atoms with the atmospheric species can degrade this initial velocity distribution and generate a distribution closer to a Maxwellian distribution but with a temperature hotter than the atmospheric temperature at the exobase (see references in Section 1) thereby partly justifying our assumption.

The planet shine could impact the dayside hot hydrogen corona observed by both PVO/UVS and Venus Express/SPICAV (e.g., Anderson, 1976; Chaufray et al., 2012) but was found negligible by Anderson (1976). As it depends on the density of the cold population, the planetary shine contribution is expected to be more important at dawn than dusk and possibly noon, due to the hydrogen bulge density at dawn (e.g., Brinton et al., 1980; Grebowksky et al., 1996). The very large variations of the hydrogen density with local time, and its larger vertical extent compared to the cold oxygen could question the 1D assumption, better justified for the oxygen. Then, it would require at least a 2D model of radiative transfer with both cold and hot populations.

Finally, the momentum transferred from the photons to the atoms during a resonant scattering (radiation pressure) should deviate the atom's trajectory and modify the oxygen density in the exosphere. The acceleration by radiation pressure due to the solar photons is anti-sunward (in average) and given by $a = hg_{exc}/(m\lambda)$, where $h$ is Planck's constant and $m$ the mass of an oxygen atom (e.g., Bzowski, 1993). The shine effect on the dayside is expected to be roughly radial and its acceleration $\sim G_c \times a \sim 0.6$ a. Using $g_{exc} = 3.5 \times 10^{-5} \text{ s}^{-1}$, we find $a = 6.7 \times 10^{-6} \text{ m/s}^2$. This acceleration is much lower than the gravity at 1,000 km $g = 6.5 \text{ m/s}^2$ and therefore negligible.

## 4.2. Re-Evaluating Previous Models of Venus' O Corona

Several numerical models have been developed to characterize Venus' O corona, constrained by the observations of Nagy et al. (1981) using PVO-UVS data. Nagy et al. (1981) and Nagy and Cravens (1988) employed two numerical approaches—a 2-stream transport model and a diffusion equation—to simulate the production of hot O via DR of $O_2^+$. Their models included elastic collisions between hot O and a background atmosphere of cold $CO_2$, O, and H. These collisions both thermalized hot O and, through interactions between hot and cold O, generated additional hot O. The resulting exospheric O density distributions were compared to those inferred from PVO-UVS observations.

Hodges (2000) introduced a particle-based model that incorporated elastic collisions between neutrals and ions, as well as interactions with solar UV photons. This model accounted for O production via DR of $O_2^+$, ion-neutral charge exchange, and solar wind interactions, tracking hot O until it was thermalized via collisions or ionized. $O^+$ ions generated above the ionopause were assumed to escape through solar wind pickup.

Lichtenegger et al. (2009) simulated O diffusion through Venus' thermosphere, where particles underwent partial or complete thermalization via collisions with a fixed background of $CO_2$, CO, O, and $N_2$ before reaching an assumed exobase altitude. Their model introduced energy-dependent collision cross sections, departing from the constant values used in earlier studies, while also accounting for secondary hot O production. This approach predicted a less dense O corona, which the authors argued was consistent with the lack of observed energetic neutral atoms reported by Venus Express (Galli et al., 2008).

Building on the model of Lichtenegger et al. (2009), Gröller et al. (2010) incorporated inelastic collisions and used differential cross sections to calculate post-collision scattering angles. This refinement, favoring forward scattering in high-energy collisions ($>\sim 1$ eV), reproduced the O corona inferred by Nagy et al. (1981). However, when inelastic collisions were included, the modeled corona was more efficiently thermalized, resulting in lower densities than those inferred.

Most recently, Tenishev et al. (2022) applied a molecular kinetics model to simulate DR of $O_2^+$ and the diffusion of resulting hot O through a background of $CO_2$, CO, $N_2$, and O. Their model successfully reproduced the O corona inferred by Nagy et al. (1981) by including elastic collisions, secondary hot O production, and energy-dependent scattering angles.

The findings of this study reveal a ~60% reduction in the density of Venus' O corona compared to earlier constraints (Nagy et al., 1981), underscoring the need to revisit previous models with updated data and a refined understanding of thermo- and exospheric processes. While prior studies have significantly advanced our knowledge, the reduced density observed here highlights the importance of reassessing key assumptions, particularly the roles of elastic and inelastic collisions and their associated energy-dependent cross sections.
Gröller et al. (2010) demonstrated that inelastic collisions can lead to a more efficiently thermalized and reduced O corona, suggesting these interactions may be crucial for more accurately reproducing observed densities.

An additional factor that warrants consideration is the reciprocal effect of non-thermal collisions on the background atmosphere. While previous studies focused on how collisions degrade the energy of hot O, they did not account for how these same interactions would heat and expand the otherwise cold thermosphere, composed of CO₂, CO, O, and N₂. Such heating can elevate the exobase altitude, thereby increasing the altitude range over which collisions occur and influencing the overall density profile.

Future modeling efforts would benefit from incorporating these reciprocal effects by self-consistently treating the cold components of Venus' thermosphere, and further exploring the role of inelastic collisions with energy-dependent collision cross sections, such as those recently provided for O + CO₂, O + CO, and O + N₂ collisions (e.g., Gacesa et al., 2020; Kumar, Gacesa, et al., 2023; Kumar, Kumar, et al., 2023). Such efforts can provide a more comprehensive understanding of Venus' upper atmosphere and its broader implications for planetary exospheres.

## 5. Conclusion

We revised the hot oxygen density in the Venusian upper atmosphere derived from PVO Ultraviolet Spectrometer by using an updated radiative transfer model that includes the effect of the Venusian shine emission. This correction increases the excitation frequency of the hot atoms. Then, the oxygen density needed to reproduce the observations is reduced by 1.6 compared to the past derived density. This reduction requires reassessing key assumptions in exospheric models, particularly the roles of inelastic collisions of the freshly produced hot oxygen with the ambient atmosphere. Indeed, these collisions would increase the thermalization of the hot oxygen atoms and then reduce their density that could match better the new derived density.

## Data Availability Statement

No data was used in this study. The oxygen brightness profiles used in the manuscript are analytic fit available in the references: Nagy et al. (1981) and Paxton and Anderson (1992). Cold densities and temperature derived from PVO at noon and used as input can be found in Hedin et al. (1983).

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