After more than two years in orbit still no Venus Express observations were published concerning the hot oxygen corona of Venus which could verify the corresponding controversial observations of Venera 11 and PVO, three decades ago. Based on recent energy and mass dependent collision cross sections, the energy distributions of hot atomic oxygen created via dissociative recombination of O2+ are calculated in the daytime thermosphere by means of a 3D Monte Carlo approach. The exosphere density is obtained from the corresponding energy density and angular distribution at 240 km altitude by using a test particle model which traces the ballistic trajectories of hot O atoms in the exosphere. Our study indicates that upon taking into account proper input parameters, the hot oxygen corona appears to be substantially less dense than suggested by previous simulations.
 The existence of a hot oxygen corona was first indicated by the 130.4 nm observations of the UV spectrometer aboard PVO [Nagy et al., 1981] and Venera 11 [Bertaux et al., 1981]. Using PVO measurements, Nagy et al.  obtained a density of a few times 104 cm−3 at ∼400 km altitude, while Bertaux et al. , based on a signal of 500 R observed by Venera 11, deduced an exospheric oxygen density of ∼1.6 × 103 cm−3. It should be noted, however, that similar emissions were not observed by Venera 12 during a Venus flyby 4 days later [Bertaux et al., 1981, 2007], prompting these authors to consider the Venera 11 observations as a result of a possible sporadic hot oxygen component.
 A first effort by Nagy et al.  to model these Venus exospheric oxygen densities resulted in values of about five times higher than those observed by PVO. Shortly after McElroy et al.  managed to reproduce the observed data quite well by assuming a larger collision cross section and a different dissociative recombination (DR) channel than Nagy et al. . By repeating their previous calculations and using updated ionospheric input parameters, Nagy and Cravens  also achieved results in good agreement with the preliminary analysis of the PVO data. These data points were also reasonably well reproduced by means of two different values of the O-O collision cross section in a 1-dimensional Monte Carlo model [Ip, 1988]. Finally, based on PVO data for the period of high solar activity in 1979–1981 in the atmosphere and ionosphere models, Hodges  also arrived at similar exosphere densities.
 However, the hot oxygen concentrations deduced from the UV spectrometer data appear to be based on early assumptions and have never been updated or confirmed by later measurements. Besides the brief discussions of these controversial observations of Bertaux et al.  and Nagy et al. , we are not aware of any publication focusing on a detailed analysis of the hot O observations in the exosphere of Venus. Moreover, the SPICAV instrument aboard Venus Express should be able to detect the hot oxygen corona and even its time variations if the number densities were in the order of the values mentioned above [Bertaux et al., 2007]. Evidence for a weaker hot oxygen corona is also suggested by the ASPERA-4/NPD analysis aboard Venus Express. Oxygen energetic neutral atoms (ENAs) should have been observed if the oxygen density were as dense as expected [Galli et al., 2008]. Yet no oxygen ENAs above the instrument threshold were registered. The failure so far to detect any signature for a permanent corona suggests that the former measurements could indeed indicate a sporadic feature of the corona or that the derived and modeled densities based on the OI resonant triplet measurements were overestimated. Hence, we do not consider these controversial data as a proper means to test the outcome of hot oxygen simulations.
 In order to obtain the hot oxygen exosphere density profiles the corresponding nonthermal energy distribution functions at the exobase must be known which in turn require information about the velocity distributions of the suprathermal source atoms as well as of the kinetics and transport characteristics of these particles along their stochastic way through the thermosphere. Thus a detailed calculation needs data of quite a number of physical parameters.
 All models of the Venus (and Mars) oxygen exosphere published so far used different assumptions and numerical values of these parameters. For instance, almost all previous models assumed a single constant cross section for the neutral collisions (between about 1 × 10−15 and 3 × 10−15 cm−2 s−1), whereas the DR-coefficient has been considered either as constant [e.g., Ip, 1988; Kim et al., 1998; Lammer et al., 2006] or dependent on the electron temperature [e.g., Nagy et al., 1981; Nagy and Cravens, 1988; Hodges, 2000; Valleile et al., 2009]. Only recently, an energy and mass dependent neutral collision cross section has been taken into account for a detailed calculation of the formation, collisions and transport of suprathermal oxygen in the upper thermosphere of Mars [Krestyanikova and Shematovich, 2005, 2006].
 In view of the lack of hot oxygen above the threshold of the SPICAV instrument, the former Venus hot oxygen coronae models have to be reinvestigated using the latest collision cross sections and other relevant input data. The aim of this brief report is to study the effects of the updated input parameters on the resulting hot oxygen corona of Venus and to compare the new results with previous models.
 For this reason we focus on the formation of a hot oxygen corona created via dissociative recombination of ionospheric O2+ ions with thermal electrons, which is considered as a major source of hot oxygen particles in the upper atmosphere of Venus. The energies of these newly created atoms distinctly exceed the mean energy of the background gas, thus the hot particles may become partially or fully thermalized via collisions with the main atmospheric constituents before possibly arriving at the exobase. In the following, the transport of hot atomic oxygen generated via DR through the venusian thermosphere up to the exobase is studied by means of a Monte Carlo model. A brief description of the model as well as of its input parameters is given and the effect of some critical parameters on the results is discussed.
2. Model Description
 Among the various nonthermal processes leading to the production of hot particles in the upper atmosphere, dissociative recombination of ionospheric O2+-ions with thermal electrons is considered as one of the major sources of suprathermal oxygen forming the exosphere of Venus [McElroy et al., 1982]. Dissociative recombination of O2+ ions produces energetic O atoms both in the ground O(3P) and metastable O(1D), O(1S) excitation levels according to the following channels
where the indicated excess energy is valid for non vibrationally or rotationally excited O2+. The branching ratios for the different channels are given in brackets according to the experimental results reported by Kella et al.  for O2+ ions in the ground vibrational level.
2.1. Atmospheric and Ionospheric Inputs
 In the present calculations, the ionosphere of Venus in agreement with observations is assumed to consist of molecular oxygen ions O2+ and atomic O+. The electron and ion temperatures and densities for low and high solar activity were taken from Fox and Sung . O, CO2, CO, and N2 are considered as the major constituents of the upper neutral atmosphere and represent the background gas in the simulations. The altitude profiles for these species and their common temperature were also adopted from Fox and Sung .
2.2. Production Rates of Hot Oxygen
 The temperature dependent rate coefficient of dissociative recombination of ground state O2+ is deduced from various experiments [Mehr and Biondi, 1969; Sheehan and St.-Maurice, 2004] and assumed to be given for Te < 1200 K by k = 1.95 × 10−7 (300/Te)0.7 cm3 s−1, where Te is the electron temperature. Although the O2+ ions in the experiments were contaminated by ions in metastable states, the above values are considered to be approximately valid for a beam of ions in the ground electronic and vibrational state [Sheehan and St.-Maurice, 2004]. Due to the lack of information about the distribution of vibrational states of the venusian ionospheric O2+ ions, we consider all of them in the v = 0 state so that their production rate can be estimated by the above relation. It should be noted, however, that this assumption is one of the major uncertainties concerning the outcome of the Monte Carlo model, since the initial ionic state plays a significant role in the DR process. The exclusive use of the expression given above may lead to an overestimation of the hot oxygen production rates since the DR rate of O2+ ions decreases for vibrationally excited ions [Sheehan and St.-Maurice, 2004].
 The velocity distributions of the newly created oxygen atoms were obtained by assuming that the ions and electrons can be represented by Maxwell distributions according to their altitude depending temperatures. Velocities from these distributions were taken at random and transformed into the center of mass system, where the velocity direction of the newly born oxygen atoms is supposed to be isotropically distributed. Because of the small electron mass with respect to the oxygen atom, the kinetic energy in the center of mass system is mainly due to the motion of the electron and is added to the dissociation energy of a specific branch. Upon assuming that the energy is equally shared among the two resulting oxygen atoms, the energy of these species is found by transforming back to the initial frame [Gurwell and Yung, 1993; Fox and Hac, 1997]. By taking a large number of randomly chosen velocity values for both O2+-ions and electrons, the initial energy distributions displayed in Figure 1 according to the four channels of equation (1) are obtained. At low altitudes, the distribution is highly non-Maxwellian and characterized by four peaks centered approximately at the energies corresponding to the energy released in the four dissociative recombination channels.
2.3. Collision Parameters
 After their production through DR, the hot oxygen atoms are subject to binary collisions with the main neutral atmospheric constituents, i.e. O, CO2, CO and N2. In this study the suprathermal particles are assumed to become thermalized via elastic collisions only. This may result in some underestimation of the thermalization rate due to the neglect of the excitation of rotational and vibrational levels of the molecules in inelastic collisions with hot O atoms [Krestyanikova and Shematovich, 2005]. The total cross section for elastic collisions between ground state oxygen atoms averaged over a statistical population of O(3P) fine structure levels can be represented by the semiclassical Landau-Schiff formula [Kharchenko et al., 2000] and is applied in the present calculations (Figure 2). The use of angular dependent differential cross sections would lead to a somewhat lower efficiency of the energy transfer from a hot to a thermal particle, since they are characterized by a large probability at small scattering angles [Kharchenko et al., 2000; Krestyanikova and Shematovich, 2005]. Due to the lack of data on cross sections for collisions between O and CO2, the constant O-O cross sections were also applied in previous models to simulate the O-CO2 interactions [e.g., Hodges, 2000; Ip, 1988]. In our calculations, however, the O-CO2 and O-CO collisions where modeled by using the energy dependent cross sections for O-N2 collisions given by Balakrishnan et al.  and illustrated in Figure 2. These values are expected to reflect the effect of different masses in O-CO2 and O-CO collisions in a more realistic way than those for the O-O interaction [Krestyanikova and Shematovich, 2005].
 In the present simulations, the interaction is treated via elastic collisions only, inelastic and quenching collisions are not included yet. According to Krestyanikova and Shematovich [2005, 2006], who studied the effect of inelastic and quenching collisions separately, the inclusion of these latter interactions is shown to modify the result with respect to pure elastic collisions only slightly.
2.4. Tracing of the Hot Oxygen Atoms
 Oxygen atoms produced via DR are launched randomly within thermospheric slices of 2 km altitude range linearly spaced in the radial direction between 100 and 300 km altitude. The initial velocity of these particles is taken randomly from the hot oxygen distributions shown in Figure 1 for the appropriate altitude. The initial velocity vector is assumed to point with equal probability in any direction and the trajectory of the hot atom through the thermosphere is followed by taking into account the gravity of the planet and collisions with the background atmospheric gas. Assuming a spherically symmetric atmosphere, the collision probability p for a hot particle travelling from a vector-point r1 to r2 is calculated via
where l(r) = 1/[n(r)σ(E)] is the mean free path, n(r) the altitude dependent atmosphere density, σ(E) the energy dependent collision cross section, and ds is the line element along the path of the particle, respectively. The limits of the integral are chosen within a sufficiently narrow interval so that the atmosphere density could be considered constant within this interval. Equation (2) allows to take into account different directions of hot particles travelling through the thermosphere. In case of a collision between two particles with masses m1 and m2, the velocities are transformed into the rest frame of m2, where the new post-collision velocities v1′ and v2′ are determined via
Here, v is the velocity of m1 with respect to m2 before the collision and θ is the rotation angle of the momentum vector in the center of mass frame. If the energy of the traced atom after the collision is less than the energy of the atmospheric species with which it collided, it is considered to be thermalized and its tracing is terminated. A new hot oxygen atom is launched at random within the simulation region according to the source function calculated from the distributions shown in Figure 1. If the energy acquired by the atmospheric O atom in a collision with a hot oxygen atom exceeds the local mean energy, then this particle is considered to be a secondary hot particle and followed in a similar way as the primary hot atoms originating in DR reactions. In order to limit the amount of calculation, a secondary particle is assumed to be produced only when its energy is above 0.05 eV which has an effect only on the low energy particle population which is not modeled here.
3. Results and Discussion
 In a first step we have tried to reproduce the results of Ip , who presented the model and input data in sufficient detail to allow a reasonable comparison. This was done by simplifying our code to approximate his model and simulating the energy distribution function (EDF) for the hot oxygen population of Venus by using the same input data. The resulting EDF obtained at an altitude of 240 km and displayed in Figure 3a agrees reasonably well with the original calculations by that author (his Figure 1). Figure 3a also shows the simulation results for low and high solar activity based on our model and input data discussed in the previous section. In addition, the result obtained with our model by using the same constant cross section for all collisions and a constant DR-coefficient, clearly shows that these input data have a strong effect on the EDFs. The higher values than those obtained by Ip  below ∼1 eV are due to the inclusion of secondary hot O atoms in our model which predominately contribute to the low energy domain. Above ∼1 eV, the reduction of the EDF is caused by an increased collision probability and hence more efficient thermalization since the hot particles can move in any direction and are not restricted to a radial motion as in the simpler model of Ip .
 It appears that the resulting energy distribution functions are very sensitive to the size of the cross section for the collision of the hot atoms with the ambient gas: in case of a higher collision probability less particles will arrive at the exobase and those entering the exosphere will exhibit on average smaller kinetic energies. Other properties of the collision cross sections, such as angular distribution, forward directed or isotropic scattering can also have an important effect on the energy transfer and escape probabilities of the hot O atoms. However, these questions deserve a more thorough study which is beyond the scope of the present paper.
 The exosphere density is obtained by calculating collisionless trajectories launched at 240 km altitude and using the corresponding energy and angular distributions as initial conditions for the velocities. The corresponding number densities of hot oxygen above the surface of Venus are illustrated in Figure 3b. The shaded area indicates the results calculated by Ip  for Venus using two different values for the collision cross section which closely corresponds to the PVO-UV data deduced by Nagy et al. . The two solid lines show the results according to our model for solar minimum and maximum conditions, while the dashed-dotted line is obtained by Hodges . In addition, the outcome of our model for a constant σ and α (corresponding to the dashed line in Figure 3a) is also shown. Although the production rate of hot O atoms is larger for high solar activity, the collision probability is also enhanced due to the increased neutral background density, eventually leading to lower exosphere densities at higher altitudes than in the case of low solar activity.
 According to the calculations of Barabash et al.  based on the hot oxygen corona model of Zhang et al.  for Mars, the corresponding O-ENA flux can be easily detected by modern ENA instrumentation. Since the hot oxygen corona densities modelled by Hodges  for Venus are comparable or even higher than those of Zhang et al.  for Mars up to about 2000 km altitude, at least a similar value of the oxygen ENA flux can be expected at Venus. This would be well above the ASPERA-4 threshold of 1 × 104 cm−2 sr−1 s−1 [Galli et al., 2008]. Our corona at 2000 km is almost two orders of magnitude less dense than that obtained in previous models [e.g., Ip, 1988; Hodges, 2000] and will result in O-ENA signals below the threshold of the ASPERA-4 instrument.
 This research has been supported by the Helmholtz Association through the research alliance “Planetary Evolution and Life” and through the joined Russian-Austrian project under the RFBR grant 09-02-91002-ANF-a and FWF grant I 199-N16. V. I. S. was partially supported by RFBR grant 08-02-00263.