JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. E3, PAGES , MARCH 25, 2000

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. E3, PAGES , MARCH 25, 2000 Distributions of hot oxygen for Venus and Mars R. Richard Hodges Jr. William B. Hanson Center for Space Sciences, University of Texas at Dallas, Richardson Abstract. Hot atomic oxygen velocity distributions and corresponding profiles of density and temperature have been calculated for the Venus and Mars exospheres by Monte Carlo simulation. The Venus results are realistically based on well-established models of the Venus atmosphere and ionosphere that were derived from Pioneer Venus orbiter measurements near solar maximum. The confidence level is lower for Mars because the only viable data come from Viking entry measurements in daytime at solar minimum, and the global morphologies of the atmosphere and ionosphere are poorly understood. What is clear is that planetary differences arise because the exothermal velocities of hot oxygen created by dissociative recombination of 02 + are below satellite speeds on Venus and greater than escape on Mars. As a result, the distribution of velocities on Venus tends to be nearly isotropic, whereas it is grossly anisotropic on Mars, favoring the vertical with increasing distance from the planet. The calculated lower bound for the Martian oxygen escape rate indicates that the lifetime of CO2 in the Mars atmosphere is probably less than 10 Myr. 1. Introduction Exothermic ion-neutral reactions in planetary atmospheres tend to create supra-thermal neutrals that form extended coronae [cf. McElroy, 1972, Rohrbaugh and Nisbit, 1973; Wallis, 1978, Nagy and Cravens, 1988; Kim et al., 1998]. On Venus and Mars the most impor- tant of these reactions occurs when an 02 + ion collides with an electron, neutralizes, and dissociates into two fast neutral oxygen atoms with total kinetic energy (in the frame of reference of the parent ion) equivalent to the ionization potential of molecular oxygen minus the sum of the excitation energies of the atoms. The impor- tant branches of the dissociative recombination of 02 + are o(p) + o(p) o(p) e O(D) + O(D) o(q) + o('s) ev (.22) ev (.42) ev (.31) ev (.05), where parentheses enclose the measured branching ratios of Kella et al. [ On Mars the exothermic velocities of the first two branches exceed escape, but the fastest is only 63% of escape on Venus. However, the well-defined branch structure of this reaction is (1) suppressed by the addition of dissociation velocities to the generally high thermal velocities of the parent ions [Hodges, 1993]; the rotational and vibrational energies Copyright 2000 by the American Geophysical Union. Paper number 1999JE /00/1999JE of O +, which may add noticeably to the dissociation energy according to Fox and Had [1997], are neglected here. Owing to high ion temperatures ( K on Venus at night), a hot pseudo-thermal distribution of new, fast oxygen atoms is created by the charge exchange reactions [Nagy et al., 1981] O + + H O + H +, (2) O + + O - O + + O. (3) Reactions (2) and (3) are the major sources of hot O in the nighttime ionosphere of Venus, where there is very little O +. Since the peak densities of 02 + and O + tend to occur well below the neutral exobase on Venus and Mars, most hot oxygen atoms are created deep in the thermosphere, where the thermal background gas is abundant, collisional thermalization is rapid, and the hot component of O is negligible. Only the small fraction of new hot atoms that are created on the topside of the ionosphere, near or above the exobase, have an opportunity to avoid collisions, rise into the exosphere, and form a hot oxygen corona [Hodges, 1993]. The purpose of this paper is to elucidate the nature of the oxygen coronae and escape processes on Venus and Mars. To this end, realistic models of exospheric atomic oxygen have been calculated with a modified version of the Monte Carlo exosphere simulator that was previously developed by Hodges [1994, 1998, 1999] for planetary hydrogen studies. Pioneer Venus orbiter data for the period of high solar activity in provide the atmosphere and ionosphere models used in

2 6972 HODGES: DISTRIBUTIONS OF HOT OXYGEN FOR VENUS AND MARS the Venus exosphere simulation. Two essentially extreme versions of the Martian environment, based on global extrapolations of the daytime atmospheric and ionospheric conditions encountered by Viking entry vehicles in 1976, have been used to simulate limiting versions of the hot oxygen corona of Mars at solar minimum. Subsequent discussion will show that the rate of escape of hot oxygen is of geologic significance on Mars but not on Venus. 2. Oxygen Exosphere Simulation Table 1. Collision Cross Sections for Momentum Transfer and Charge Exchange Neutral-neutral O+O- O+O Encounter Cross Section, cm 2 O + CO2 - O + CO= Neutral-ion H H 0+H + --> 0 + H Hs+w --> 0 + +H Hodges [1990] assumption Hickman et al. [1997] Stebbings and Rutherford [1968] Hodges [1994]. 2 x 10-15" 2 x x 10 -ls c b 1.7 X d 3.4 X 10 -ls O 2 X e In the simulator, new oxygen atoms are created by volumetric integration of the rate of reaction (1), then (2), and finally (3), through the ionosphere, stopping when the integrand equals a random fraction of the total global rate for all three reactions. This process determines the reaction as well as its location within the ionosphere. Temperature and wind velocity at the point where the integration stops are used to generate random velocities for the reactants. If the reaction is dissociative recombination of 02 +, anotherandom number is compared to a successive sum of the branching ratios to determine the exothermic energy that is divided between the pair of new hot atoms. The trajectory of each hot atom is traced from col- The exosphere simulator described by Hodges [1994] calculates moments of the velocity distribution (e.g., density, flux, and temperature) by tracing the lives of a lision to collision until it escapes, ionizes in the ionoseries of test atoms, accounting for their random col- sphere, or becomes part of the thermosphere when its lisions with neutrals, ions, and solar photons in the energy falls below the mean energy of thermospheric upper thermosphere and exosphere by integrating col- oxygen. Escape occurs when an atom ionizes above the lision probabilities along ballistic trajectories to locate ionopause, that is, in the solar wind. The photoionizarandom collision events and by generating random scat- tion times at solar maximum and minimum are assumed tering parameters or reaction events for each collision. to be equivalent to 1.7 x 10 and 3.7 x 10 s, respec- Methods used to simulate basic physical processes that tively, at 1 AU. (These rates are derived from Bailey are essentially the same for all planets, such as ballistic and $ellek [1990]; they are approximately the same as transport, collisional scattering, and charge exchange, given by the EUV flux model of Richards et al. [1994].) are described by Hodges [1994, 1998]. The photoionization rates are significantly shorter than Ad hoc elements of the oxygen version of the exo- the time for charge exchange in the solar wind, which sphere simulator include the commonly used collision amounts to x 108 s (assuming that the solar wind cross sections listed in Table 1. Scattering collisions are proton flux is 3 x 108 cm - s - at 1 AU and the cross approximated as elastic, hard sphere encounters. Rate section for charge transfer at kev energies is 2 x 10-7 coefficients for source reactions (2) and (3) are assumed cm2). Atoms that reach distances of 1000 planet radii to vary as the square root of temperature, in accord with with superescape speeds are classified escaping ballisthe assumption of velocity-independent cross sections; tically. In reality these atoms are trapped in solar orbits these reactions are important on Venus and negligible that cross the orbit of the parent planet, but they eson Mars. The rate coefficient adopted for reaction (1) cape by ionization because orbital return times tend to is 1.6 x 10-?(300/Te) ø' cm 3 s - [Mehr and Biondi, be much longer than that for ionization. 1969]. Statistical data for each of the moments of the veloc- ity distribution are accumulated in a three-dimensional array of audit zones that gives complete global coverage and spans an altitude range from the middle thertoosphere to 10 planetary radii. Phenomenological parameters derived from these data are added to their hydrodynamic counterparts for thermospheric oxygen to obtain global distributions of density, flux, and temperature that are representative of the total oxygen gas. A discrete six-dimensional representation of the velocity distribution, with resolution of 0.5 km s -, is also included in the simulation for selected altitude ranges. To obtain usable statistics in reasonable computation times, the azimuthal variation of the distribution function about local vertical is represented by a first-order approximation of a Fourier series, that is, f fo + fssinx + fccosx, (4) where X is the local compass angle of the horizontal component of velocity. Equation (4) reduces the velocity grid to two dimensions, vertical and horizontal; each grid zone has three density accumulators (for f, rs, and

3 HODGES: DISTRIBUTIONS OF HOT OXYGEN FOR VENUS AND MARS 6973 fc)- These data are converted into elements of a velocity distribution function and added to the Maxwellian dis- tribution for thermospheric oxygen to give a complete representation of the distribution function, one that includes the nonthermal properties of the hot component as well as the anisotropies caused by vertical and lateral flow and by long-term satellite orbiters. Table 2 lists the basic parameters that were used in the simulations of the hot oxygen coronae of Mars and Venus. The exobase altitudes correspond to levels where the mean free path is equal to the effective scale height for the thermospheric mixture of O and CO2. Descriptions of the neutral and ion environments are given in sections 2.1 and Venus Thermosphere and Ionosphere Models Table 2. Model Parameters for Venus and Mars Parameter Venus Mars Base altitude, km Winds, m s- Corotation Diurnal tide Ionopause altitude, km Subsolar Terminator Nadir Exobase altitude, km Subsolar Terminator Nadir Oxygen lifetime, s Solar wind CE 8.4 x x 108 Photoionization 8.9 x 10 s 3.9 x 106 The Venusian hot O exosphere simulator uses the so- CE - charge exchange. lar maximum (F 0.7 = 200) backgroun distributions of thermal neutrals and ions compiled by ttodges [1999]. Neutral composition, density, and temperature are obin the present oxygen exosphere simulations. This aptained from the thermosphere model of ttedin et al. proach has the benefit of setting a reasonable lower limit [1983]. The proton distribution is taken from the ionofor the escape rate. sphere-exospher equilibrium calculations of Hodges. The global distributions of the atmosphere and iono- Global distributions of the other ionic constituents are sphere are heuristically approximated as being axisymapproximated as being symmetrical about the Sunmetric about the Sun-planet line and hence are func- Venus axis. The densities of the ion constituents are detions of the solar zenith angle (SZA). Thermospheric rived by lateral interpolation of profiles of the daytime winds near the exobase on Mars are assumed to have model calculations of Nagy et al. [1980], the nighttime the same pattern as those on Venus, that is, a 150 m model of Dobe et al. [1995], and the average night- s - tidal flow from day to night superimposed on corotime O + profile of Knudsen et al. [1986]. Ion temper- tarion, but the latter is at the Mars rotation rate. atures are interpolated from the Sun-referenced analy- Barotropic densities for neutral oxygen and CO2 in sis of retarding potential ion measurements of Miller et the daytime sector of the Mars atmosphere are derived al. [1980]; electron temperatures are from Theis et al. from the tabulated data of Nier and McElroy [1977] for [1984]. The ionopause is assumed to be an egg-shaped Viking 1. To extrapolate these data globally, the gas surface that has an altitude of 325 km at the subsodensities are assumed to be invariant at 120 km while lar point, 600 km over the terminator, and 1000 km at the temperature and scale heights decrease by 50% from nadir. the terminator to SZA ø and then remain constant Thermospheric winds on Venus are approximated, as for SZA > 120 ø. Figure I shows day and night profiles in the work of Hodges [1999], by the superposition of two for O and CO2, along with those assumed for O2 +, which wind components, one being corotation with a period are discussed below. of 4 days, and the other being a day-to-night diurnal Viking I ion measurements reported by Hanson et al. tide with a speed of 150 m s - across the terminators. The ion flow field is the same as neutrals below 200 kin, but the amplitude of the ion day-to-night component increases between 200 and 300 kin, reaching a speed of 2 km s - over the terminator; this approximates the terminator ion velocities reported by Knudsen et al. [1980] Mars Thermosphere and Ionosphere Models Most of what is known about the upper atmosphere and ionosphere of Mars was learned from experiments on two Viking entry vehicles in 1976, during a period of very low solar activity. Since solar cycle variations are uncertain, only solar minimum conditions are used [1977] indicate that 02 + is the dominant ion; these data are used to represent 02 + in the daytime ionosphere for $ZA < 60 ø. However, it should be noted that if Venus is a guide, the temporal variability of the ionosphere may be great, average conditions may be uncertain, and the present assumption may be only a crude approximation. Since the nature of the nighttime Martian ionosphere is even less certain, two extreme scenarios have been adopted. In one case, denoted Mars-H, the nighttime ionosphere (SZA > 120 ø) is represented by the upper limit model of Fox et al. [1993]; the other case, called Mars-L, is a Venus parody with no ions in the nighttime sector. In either case, linear interpolation with respect to the cosine of SZA is used to connect the transition region (60 ø < SZA < 120ø). Day and night profiles of

4 6974 HODGES: DISTRIBUTIONS OF' HOT OXYGEN F'OR VENUS AND MARS :5...,, "::"::::"',ii //,i :::'::::":: ' :..:, :.... %- 100,,,,I I... I... I... I... I... I l0 s ø Concentration (cm'3) Figure 1. Assumed vertical profiles O, C02, and O + for the subsolar and nadir regions on Mars. O + are included in Figure 1. The Mars-L scenario is essentially the same as the low solar activity model of Kim et al. [1998], the major exception being that the latter has much more O + above 200 km. 64% of dissociative recombination, exceed the escape velocity. The fractional data in Table 3 illustrate two interesting facets of the effects of exospheric processes on escape: first, the flux of escaping atoms at the exobase In daytime, reactions (2) and (3) are negligible sources is less important than the production of hot atoms in of hot O as compared to dissociative recombination of the exosphere, and second, exospheri collisions limit O +. This is also true at night in the Mars-H scenario the escaping fraction of hot atoms produced above the where the nighttime abundance of O + is substantial and as well for the negligible nighttime ionospheric abun- (lances of the Mars-L case. Hence reactions (2) and (3) are ignored in the Mars simulations. exobase to less than 32%, which is the upward going half of the superescape branches of reaction (1). The escape rate given in Table 3 for the Mars-L simulation is 6.6 times the rate derived for comparable conditions by Kim et al. [1998](i.e., low solar activity). 3. Planetary Escape However, the discrepancy is actually about twice the The difference in gravity on Venus and Mars is apparent in all of the simulation results but especially in the escape rate information summarized in Table 3 and in the axial distributions of solar wind mass loading shown in Figure 2. On Venus, where even the most energetic of the fast oxygen atoms created by recombination have subescape speeds, escape is limited to atoms in elongated trajectories that rise above the ionopause and then ionize in the solar wind. This process is confined to a region within 2Rv of the Sun-Venus axis, which makes the peak solar wind loading comparable to Mars even though the escape rate is significantly less. In the lower Martian gravity, ballistic escape dominates because the exothermic speeds of the two most energetic branches of reaction (1), which account for Table 3. Rates for Planetary Escape of Oxygen Parameter Venus Mars-H Maxs-L -1 Escape rate, s Solar wind CE 2.3 x X x 1023 Photoionization 2.9 X X X 1024 Ballistic x x 1025 Total 2.9 x X x 1025 Exobase flux/ escape flux Direct escape/ exosphere source

5 - - HODGES: DISTRIBUTIONS OF HOT OXYGEN FOR VENUS AND MARS 6975 l0 ; [,,, [ [ [ [ [ [ ] [ ] Venus - : Total Upstream - Mars-L O O.1 : Mars-H Figure 2. Fractional mass of 0 + added to the solar wind as a function of distance from the Sun-planet axis in units of the planetary radius Rp. The graph labeled upstream accounts for ionization on the sunward side of the terminator plane while that labeled total represents all ionization. ratio of the numbers, or roughly 13:1, because Kim et al. solved a one-dimensional problem and extrapolated a direct escape flux of 1.6 x 107 cm -2 s -, which is nearly 5 times the total escape flux given by Kim et al. the result over both the day and night hemispheres, whereas Mars-L has only daytime Major methodological differences preclude a quanti- 4. Oxygen Coronae: Densities and Temperatures tative determination of the causes of this discrepancy Altitude profiles of the density and temperature of in escape rates. However, a significant part of the disatomic oxygen in the upper atmospheres of Venus and crepancy can be traced to the way Kim et al. [1998] Mars are summarized in Figure 3. On both planets the treat the direct escape of the progeny of dissociative rebarometric decay of thermospheric oxygen yields to the combination of 02 + above their effectivexobase at 190 influence of hot O at a total oxygen concentration that kin. A simple calculation, using the ionosphere density is less than 105 cm -a and significantly less than the and temperature models of Kim et al. as well as their rate coefficient for dissociative recombination (which is essentially the same as that in the present simulations classical exobase density, which tends to be of the order of 108 cm -3. The low level of hot O production at night on Venus according to A. F. Nagy, private communication, 1999), and in the Mars-L scenario results in very large day-togives a hot O column production rate of 5 x 107 atoms night contrasts in exospheric oxygen density. On the cm -2 s -1 above 190 km. Since the exosphere of Kim et other hand, there is only a small diurnal variation of al. is postulated to be collisionless, -0 32% of these new hot O in the Mars-H simulation. atoms, that is, the fraction with upward, superescape velocities, should escape immediately. This amounts to Temperature in the hot O corona is ill defined because the velocity distribution of oxygen tends to have

6 6976 HODGES: DISTRIBUTIONS OF HOT OXYGEN FOR VENUS AND MARS t/venus ' ' I ' ' I ' ' I ' ' I ' ' I... I ' ' ' I I ' I ' I ' - x Venus \ ' X Noon "\/ - XX... Midnight -- I/ -.\ x... Sunrise "\ - x \\ - Sunset --, - : x x ' < looo o 0,, XX-r,,, - -- KX-. ' X t/mars T (103 K) Tr/T h Figure 3. Profiles the density, apparent temperature, and temperature anisotropy coefficient T,./Th for exospheric oxygen on Venus and for two Mars scenarios. a fast nonthermal component that surrounds the cold Maxwellian core of thermospheric gas. The kinetic energy of these nonthermal velocity distributions loosely represented in Figure 3 by the hydrodynamic tempera- ture T-.,(< v'" >-I < v > 12)/3k, where m is atomic mass, k is Boltzmann's constant, and the mean values of v and v 2 are simulator results. (No midnightemperature data are given for Venus or the Mars-L model, because the nighttime velocity distributions do not have significant thermal cores above 200 The parameter T,./Th that is plotted in the rightmost set of profiles in Figure 3 is a measure of the anisotropy of the velocity distribution. The T and Tu components are the apparent radial and horizontal temperatures:

7 HODGES: DISTRIBUTIONS OF HOT OXYGEN FOR VENUS AND MARS 6977 Venus Sunrise Noon Sunset 2100H Midnight 0300H m :::::::: km krn E (... W krn Figure 4. Venusian velocity distributions in the equatorial plane. Tick marks indicate velocity increments of 1 km s -1. White space corresponds to densities less than l0-16 cm -6 s -1. The outer contour level is l0 -t6 cm -6 s -t, and the contour level increment i,s one power of >2 )//½, (6) Tt, -m(< v > -1 < Vh > 1=)/2k, (7) where vr and Vh are the radial and horizontal components of velocity, respectively. Note that no data are given for nighttime in the Mars-L and Venus graphs. On Venus, where all hot O has subescape speeds, the profiles of Tr/Th are understandably near unity. This is also true for Mars-H in daytime, where horizontal velocities are supplied by long trajectories that begin on the nightside. Other Mars profiles of Tr/Ti show distinct anisotropies that favor the radial component of velocity. 5. Velocity Distributions Figure 4 shows a representative set of velocity distribution data for various local times and altitude ranges over the Venus equator. Analogous sets of data for the Mars-H and Mars-L exosphere simulations are given in Figures 5a and 5b, respectively. Each velocity distribution subgraph is an equatorial plane section through the center of the distribution function. The vertical axis points in the radial direction, and the right-hand end of the horizontal axis points in the direction of atmospheric rotation (west on Venus and east on Mars). Tick marks represent velocity intervals of 1 km s -1. Overlaid circles and hyperbolae in the Mars graphs guide the eye to distinct features of the data and relate them to families of trajectories with common attributes; these curves are explained in the specific discussion of the Mars data below. A contoured gray scale is used to elucidate the density variations of the distribution functions. White space corresponds to densities below 10-6 cm -6 s 3. The outer contour is also at cm -6 s 3, and contour levels increase in steps of one power of 10 toward the center. Much of the small-scale structure of the low level contours is due to statistical artifacts in the Monte Carlo accumulations. In analyzing the velocity distribution data for either planet, it is helpful to begin with the lowest altitude range where the cold oxygen of the thermosphere dominates the central part of velocity space (i.e., the darkest region). Corotation of the thermosphere accounts for the lateral offset of the thermal core at local noon

8 ,, HODGES: DISTRIBUTIONS OF HOT OXYGEN FOR VENUS AND MARS a Mars-H Sunrise Noon Sunset Midnight : : : : - :! - ::E km km km,, km Figure 5. Velocity distributions in the equatorial plane for (a) Mars-H and (b) Mars-L. Tick marks indicate velocity increments of 1 km s -. White space corresponds to densities less than 10-6 cm -6 s -. The outer contour level is 10-6 cm -6 s -, and the contour level increment is one power of 10. Dashed circles give the local escape speed; hyperbolae are velocities of atoms with periapses at 160 km. The cumulative effects of corotation and the day-tonight tide give a larger offset at sunset where the wind components add, and they give a smaller offset at sunrise where they cancel. At higher altitudes the thermospheric atoms are suppressed by barometric decay, and fast oxygen atoms dominate Venus The noon Venus velocity distributions shown in Figure 4 are essentially isotropic; that is, the contours are nearly circular. The same is true on the east side of each graph at sunrise and the west side of each graph at sunset; these are regions of velocity space that correspond to atoms traveling from day to night. On the other hand, there is a noticeable deficit of velocities in the terminator quadrants that face downward and toward the day hemisphere (i.e., toward noon). These missing velocities correspond to the descending ends of long trajectories that would start at night if 02 + were more abundant in the nighttime ionosphere. At night the Venus thermosphere is cold, its scale height is small, and thermospheric oxygen is negligible in the lowest altitude range of the velocity distribution data. Ballistic atoms in long trajectories that stem from dissociative recombination of 02 + in daytime or near the terminator create the horizontally elongated distribution of fast velocities near midnight and the distinctly one-side distributions in the evening and early morning sectors; these velocities tend to be downward because the atoms are suborbital [cf. Hodges, 1993].

9 HODGES: DISTRIBUTIONS OF HOT OXYGEN FOR VENUS AND MARS 6979 b Mars-L Sunrise Noon Sunset Midnight W., ß -' - -: :E krn krn km W km Figure 5. (continued) 5.2. Mars anisotropy of the temperature noted in the discussion of Figure 3. Above the ionopause the satellite velocities To better understand the Mars velocity distribution are near the hyperbolae and difficult to distinguish. data, it is important to keep in mind that at any al- In accord with traditional exosphere theory, supertitude there is a one-to-one correspondence of a velocescape velocities are concentrated in the upper hemiity and a Keplerian orbit. For example, all subescape sphere of velocity space (over areas where hot O producballistic trajectories have velocities within a sphere of tion occurs). However, the escape rate data discussed radius equal to the local escape speed; this sphere is above and the sheaf-like appearance of the oxygen verepresented by the dashed circle in each graph of Figlocity distributions argue against a classical explanation ure 5. In addition, all trajectories with periapses below of oxygen escape. The paucity of velocities outside the the mean exobase (160 km) have velocities in the inner hyperbola overlays in Figure 5 is a natural result of exregion of a hyperbola of revolution that is delimited by ospheri collisions, which have increasing probability as the pair of overlaid hyperbolae. the zenith angle of the velocity increases. Velocities of long-term satellite orbits are subescape, have periapses above the exobase, and hence are confined to the toroidal region within the escape velocity sphere and outside the hyperbolic surface of exobase 6. Conclusions periapses. These velocities are most apparent at lower altitudes, where their collisional residue causes a lat- Exospheric density distributions of hot 0 are closely linked to the ionosphere and thermosphere models used eral elongation of the inner contours and the horizontal in the calculations. Since Pioneer Venus orbiter data

10 6980 HODGES: DISTRIBUTIONS OF HOT OXYGEN FOR VENUS AND MARS have provided the calibration needed to establish the reliability of ionosphere and thermosphere models for Venus, the present Venus hot O results are fairly realistic for solar maximum conditions. These results support the argument of Hodges [1993] that collisional momentum transfer from hot O to H and D cannot have a significant effect on hydrogen escape and fractionation, because there is very little hot O in the early morning hydrogen bulge and most of what is there is going downward. There is a wide gap between the hot O models for Mars. These models represent extremes of the possible morphologies of the ionosphere and thermosphere at solar minimum. Nevertheless, the exospheric velocity distributions should be realistic in form. More important, the gross anisotropies in the velocity distributions suggest futility in the use of spheric approximations [cf. Hodges, 1993; Fox and Ha, 1997; Kim et al., 1998]. The Mars-L model provides a lower bound for the escape of oxygen from Mars at solar minimum. If Venus is a guide, the ion and electron abundances on Mars probably increase by a factor of 10 from solar minimum to maximum, and temperatures should increase as well [cf. Hartle et al., 1996]. Hence the hot O production and escape rates could increase by a factor of A conservative estimate of the solar cycle average escape rate for oxygen is at least 20 times the Mars-L escape rate, or 7 x 102a s -. It is important to note that each pair of escaping O atoms implies the photodestruction of one CO2 molecule and the escape of one carbon atom through an as yet unidentified process. This amounts to atmospheric mass loss of 8.1 x I0 TM kg Myr -x Since the total atmospheric mass of CO2 is 7.7 x 10 s kg [McElroy et al., 1977], the atmospheric lifetime for CO2 on Mars is probably less than 10 Myr. References Bailey, G. J., and R. 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11 HODGES: DISTRIBUTIONS OF HOT OXYGEN FOR VENUS AND MARS 6981 Theis, R. F., L. H. Brace, R. C. Elphic, and H. G. Mayr, New empirical models of the electron temperature and density in the Venus ionosphere with application to transterminator flow, J. Geophys. Res., 89, , Wallis, M. K., Exospheric density and escape fluxes of atomic isotopes on Venus and Mars, Planet. Space Sci., 26, , R. R. Hodges Jr., P.O. Box 4384, Frisco, CO , (Received July 8, 1999; revised December 8, 1999; accepted January 4, 2000.)