Pkmet. Space Sci., Vol. 26 pp. 1063-1075

@I Per@mon Press Ltd., 1978. Printed in Northern Ireland

0032-0633/78/1101-1063$02.00/O

NON-THERMAL HYDROGEN IN THE VENUS EXOSPHERE: THE IONOSPHERIC SOURCE AND THE HYDROGEN BUDGET*

s. KUMAR

Jet Propulsion Laboratory, Pasadena, CA 91103, U.S.A.

D. M. BlUNTEN

Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, U.S.A.

A. L. BROADFOOT

Kitt Peak National Observatory, Tucson, AZ 85726, U.S.A.

(Received 20 January 1978)

Abshwt-A non-thermal, or “hot”, Venus oxona of H atoms has been observed by Mariners 5 and 10 and Venera 9. Of the sources investigated, reaction of Ha with ionospheric O’is still the strongest. It can explain the smaller densities but falls somewhat short of the largest (from Mariner 5). The subsequent recombination of OH+, supplemented by solar-wind processes, may give an escape flux of 10’ atoms cm-*s-i. The low density of thermal H atoms on the day side has previously been attributed to either a large eddy ditiirsion coefficient or an escape flux tenfold greater than this. We support an alternative mechanism, suggested by Hartle and Mayr: the hydrogen is swept to the night side by strong thermospheric winds. This process is analogous to the “Johnson pump” for the terrestrial winter helium bulge. Large nightside bulges of H and Ha are predicted; the night/day density ratio is estimated to be as large as 100 for each.

1. INl’RODUCTION: THE VENUS HYDROGEN PROBLEM

The first evidence of an unusual hydrogen corona on Venus was obtained from the Mariner 5 meas- urements of Lyman-o emission (Barth et al., 1967) which exhibited two components with scale heights differing by roughly a factor of two. Three possibilities were considered by Wallace (1969) and others to describe this effect: (1) H and D distribu- tions at 700 K (McElroy and Hunten, 1969; Donahue, 1969). (2) H and Hz distributions at 700K (Barth 1968) and (3) “thermal” H at = 350 K and “hot” H at 700-1000 K. The deuterium hypothesis was ruled out by a rocket experiment by Wallace et al. (1971) who did not find the D Lyman-a! component from Venus; (2) was ruled out by McElroy and Hunten (1969), as it required a very large production of H atoms which could not be eliminated from the exosphere. Until the rocket experiment, the deuterium hypothesis seemed

*Presented at the Third General Assembly of the International Association of Geomagnetism and Aeronomy (Seattle 1977), Session on the “Effect of non- thermal processes on escape and structure of atmospheres of planets and satellites” (Chairman G. E. Thomas, Uni- versity of Colorado) Monday 29 August.

plausible because the best estimates of the exos- pheric temperature indicated 700 K (McElroy, 1968). Moreover, McElroy (1969) obtained a good fit to the Venus ionosphere profile with a COz atmosphere at 700K. Kumar and Hunten (1974) subsequently reviewed the evidence and pointed out that (a) McElroy’s calculations yielded too high temperatures for Mars, about twice the tempera- ture of “-300 K deduced by Stewart (1972) from the Mars U.V. airglow data from Mariners 6 and 7, and that a similar correction could apply to Venus, and (b) an equally good fit to the ionospheric profile could be obtained with a cooler exosphere at 350 K with = 1% atomic oxygen in the ther- mosphere. On this basis, these authors concluded that a two-temperature exosphere with a “cold” main or inner component showed promise.

The two-temperature hypothesis was fumly sup- ported by the Mariner 10 observations of He 584 A and H 1216 A airglow emissions that were made simultaneously during the Venus flyby of this spacecraft; the 584 A data showed an exospheric temperature of 370* 105 K (Kumar and Broad- foot, 1975), consistent with a temperature of 400 K derived by assuming atomic hydrogen as the source of the inner Lyman-a component (Broadfoot et al.,

1063

1064 S. KUMAR, D. M. Hu~lw and A. L. BROADCAST

1974). These results agree well with the tempera- ture of the inner component from the Mariner 5 data (Wallace, 1969, Model 4; Anderson, 1976; and a re-examination of the heating efficiency in a CO* thermosphere (Dickinson, 1976) has shown that an exospheric temperature of 300400 K can be justified.

Further evidence for the “hot” hydrogen compo- nent is now available from Mariner 10 Lyman-a observations on Venus which indicate a thermal component at % 300 K and a secondary component at 31300 K (Kumar and Broadfoot, 1977) and from Venera 9 Lyman-a celI measurements on Venus which also show two components at -450 K&50 K and 900* 100 K respectively (Bertaux et al., 1977). An important conclusion from the Venera 9 data was that the altitude profile for the temperature strongly supported a nonthermal regime for the hot hydrogen component. There can be no doubt about the existence of a secondary nonthermal or “hot” component in the Venus exosphere in addition to the primary thermal component.

The source of nonthermal H atoms has always been a problem for the two-temperature hypothesis; indeed, inability to find an adequate source led to its rejection by McElroy and Hunten (1969). Kumar and Hunten (1974) pointed out two new canditates: reaction of Hz with COz+ or O’, followed by dissociative recombination. This sug- gestion is amplified in the present paper. A further issue has been to account for the extreme rarity of hydrogen in Venus’ exosphere. The solution of Kumar and Hunten (1974) was to adopt an eddy diffusion coefficient K= lo* cm2 s-l. Much more detailed discussions were given by Liu and Donahue (1975) and Sze and McElroy (1975). They too found that K needed to be lo* cm2 s-’ or somewhat greater, unless there was a nonthermal escape flux of nearly lo* crnm2 s-l, an order of magnitude greater than available from any mechan- ism so far conceived. Instead of a large K, it is worth considering the global thermospheric circula- tion of Dickinson and Ridley (1977) which trans- ports 0 and CO to the night side. In a similar study, Hartle et al. (1977) have found that a large transport of hydrogen also occurs. There is a close analogy with the “Johnson pump” mechanism that produces the terrestrial winter helium bulge (John- son and Gottlieb, 1969). We present estimates of the horizontal hydrogen flux that would be gener- ated by the Dickinson-Ridley flow field, and show that it is easily able to maintain limiting upward diffusion all over the day side, as required by the observations. There should be a large, but SO far

unobservable, H2 bulge on the night side. Extinc- tion by the corresponding H bulge may have been observed by Mariner 5 (Wallace, 1969).

2.CO-ONTHESOURCE OF NO- RYDROGRN

Atomic hydrogen densities derived from Mariner 5 data by Wallace (1969) and Anderson (1976) and from Mariner 10 data by Kumer and Broadfoot (1977) are summarized in Table 1. It is clear that hydrogen densities for the nonthermal component are a fac- tor of 3-4 lower at the time of Mariner 10 en- counter compared to those during the Mariner 5 encounter. It should be noted that Anderson (1976) used a g-value of 4.1 x 10e3 s-l in calculat- ing the Mariner 5 hot hydrogen density of 1.3~ lo3 cm-“, whereas if we use Vidal-Madjar’s (1975) analysis of solar Lyman-a variation with solar ac- tivity, the corresponding g-value should be 2.9X lo-‘s-l which would give a higher non-thermal hydrogen density of 1.8X 10’ cm-’ at the exobase, and enhances the difference between the Mariner 5 and Mariner 10 nonthermal hydrogen components. The “thermal” or “cold” component, however, ap- pears to be similar in the two cases although the error bar on density is large and a 30-50% varia- tion could very well be there. Nonetheless, it is important to note that the variation in the thermal component is certainly not as dramatic as it is in the nonthermal component. The comparison of abso- lute intensities is reliable since there is good agree- ment between the Lyman-a interplanetary back- ground measured by Mariner 10 (Broadfoot and Kumar, 1978) and that measured by Mariner 5 (Barth, 1970). In making this comparison, we allow for the variation in g-value with solar activity and include the factor of 0.73 reduction in Mariner 5 data required by Thomas and Krassa (1971) to normalize with OGO-5 Lyman-a interplanetary background data and by Anderson (1976) to fit the Venus Lyman-a altitude profile.

The hot H column density obtained from Table 1 is2~10”cm~~and6~10~~cm~~forMariner5and Mariner 10 conditions respectively, and the source of nonthermal atoms must be able to maintain these densities.

The sink of hot H atoms is determined by two factors, (1) their thermalization rate at the exobase, and (2) escape rate. Expanding on the arguments put forth by Kumar and Hunten (1974), the ther- malization rate at the exobase can be estimated as follows. The lifetime of hot H atoms depends criti- cally on how efficiently they lose energy during

Venus hydrogen exosphere 1065

TABLE 1. A COMPARISON OF HYDROGEN PE RAMETERS DERIVED FROM

MARINER 5 (WALLACE, 1969; ANDERSON, 1976) MARINJZR 10 (KUMAR AND BROADFUOT, 1977) AND VENERA 9 (BERTAUX et al., 1977)

Mariner 5 Mariner 10 Venera 9

Thermal component Temperature (K) H Exobase density (cnm3)

Non-thermal component

Temperature (K) H Exobase density (cme3) g-Value used (s-l) g-Value (s-l) from

Vidal-Madjar (1976) Solar 10.7 -CM flux Solar zenith angle

275+50 2*1x105

1020* 100 1.3x 103 4.1x1o-3

2.9x 1O-3 120 -0”

300 450*50 1.5 x l@

1300 900* 100 5x102

2.1 x lo-”

2.1 x10-3

6:’ -0”

collisions with CO2 molecules and 0 atoms. In Kumar and Hunten (1974), the densities of CO2 and 0 are practically equal at 200 km, the nominal exobase level. Collisions with 0 atoms can be approximated by assuming elastic collisions, but there may be some question of loss of H energy in vibrational excitation of C02(G. Thomas, private communication). No data exist to date on this process, although a study of energetic 0, (II-- 4 km/s) collisions with CO2 by Rahbee et al. (1977) shows that the vibrational excitation cross-section is small (< 10v2’ cm’). They argue, however, that this low probability of excitation can qualitatively be explained by Massey’s adiabatic hypothesis (Massey and Burhop, 1956) which states that in a collision with relative velocity 21, the chances of transition involving energy transfer AE will be small if the collision time (t = u/u, a -particle size) is much larger than the period (t, = h/AE) of the optically active electron, i.e. the collision is slow enough that the system has time to adjust itself. For mllision of O2 with C02, we have tJt. =L 30 for vibrational excitation of C02. The value for H at lOOOK is almost identical, since v is 4.6 kms-’ and a for H-CO, is only slightly less than for 0-C02, being the mean of the radii of the collision partners. The inelastic cross-section should, therefore, be simi- larly small.

Hence, a reasonable estimate of the hot H atom lifetime can be obtained by assuming elastic colli- sions. The average loss of energy per collision of a hydrogen atom is

KiZ= 2MM2

(A41+M2)2Eo (1)

if WC =curne isotropic scattering in the center of

mass system. Here MI = mass of hydrogen atom, M2 = mass of CO2 molecule or 0 atom, and E. is the initial energy of the hydrogen atom. Thus, it will take 23 or 9 collisions to reduce the H energy by l/e. For equal proportions of CO2 and 0, the mean number of collisions is 13 (obtained by av- eraging the hE). The flight time between collisions at the base is of the order of twice the time for free fall over a scale height, or approx 1000 s

for a velocity distribution represented by a temper- ature of 1000 K. Hence, allowing for the inefficient loss of energy per collision, the lifetime for hot hydrogen atoms is of the order of lo4 s. To main- tain a hot H column density of 6 X 10” cme2 re- quired for the Mariner 10 observations, we need a column production rate of -6X 10’ cmW2 s-l; a higher production rate of 1.7 X 10’ cme2 s-’ will be required to account for the Mariner 5 observations.

The main, and perhaps only, source of thermal H atoms is slowing of the nonthermal ones, some of which are thermalized before they reach the exos- phere. The source strength is, therefore, somewhat larger than estimated above. These atoms are even- tually removed either by downward eddy diffusion or by the planetary circulation, as discussed in Section 4.

3.THEsouRcEANDEscApEFLux OF NOB HYDROGEN

Basically two classes of source have been prop- osed for hot H production in the Venus exosphere: (1) ion-neutral reactions in the ionosphere (Kumar and Hunten, 1974; Sze and McElroy, 1975; Cham- berlain, 1977) and (2) momentum transfer by the solar wind to the atmospheric gases (Cloutier et al.,

6

1066 S. KUMAR, D. M. HUNTEN and A. L. BROADFOOT

1969; Stewart, 1972; Wallis, 1972; Sze and McEl- roy, 1975). We will review these models with re- spect to the constraints outlined above for the required source of hot hydrogen.

(1) The ionospheric source

Kumar and Hunten (1974) proposed that a sufll- cient supply of hot H could be provided by the reactions

O++H,+OH++H (2)

OH++e+O+H (3)

CO,’ + Hz --i, CO&I+ + H (4)

CO,H’ + e + CO* + H. (5)

Sze and McElroy (1975) argued that the charge exchange reaction

H++O*O+H (6)

would also be significant although a comparable contribution came from a combination of reactions (2,3), (4,s) and from

He++H*+ HeH++H (7)

HeH++e +He+H. (8)

However, the recent analysis of Mariner 10 data on He 584A emission from Venus (Kumar and Broadfoot, 1975) would rule out reactions (7) and (8) because the observed helium density is about a

factor of 20 lower than that assumed in the Sze and McElroy model.

Chamberlain (1977) recently treated charge ex- change of ionospheric hot H+ ions with ballistic neutral H atoms which works quite well for Earth because of the extensive plasmasphere, but appears inadequate on Venus for two reasons, (1) any plas- masphere on Venus is surely confined to the region below the ionopause, and (2) the model requires that the bulk of topside ionospheric density be due to H’, which is doubtful in light of current models of the Venus ionosphere.

The production rates of hot H by reactions (2)- (5) were computed with the Kumar and Hunten (1974) model after the completion of that paper, and are shown in Fig. 1. Although this model has its deficiencies (Nagy et al., 1975), they are not important for the present purpose, and there is an advantage in that the HZ prolile was calculated self-consistently with the rest of the model. (The very reactions that produce H atoms are also a significant drain on the HZ supply.) Other ionos- pheric models are used below for comparison, but the HZ has had to be “patched in” by analogy with our computed profile.

For comparison with the source requirements estimated above, it is convenient to use column production rates, integrated from each level to infinity. It is easy to see in Fig. 1 that photodissoci- ation of Hz and the plasmasphere charge-exchange

I lo* lo3 lo4 lo5 IO6 10' lo*

HOT H COLUMN PRODUCTION RATE (cm -2 ,-1

)

FIG. 1. COLUMN PRODUCTION RATES INTFKiRATED FROM ALITITJDE Z To m OF NON-THERMAL HYDROGEN

FOR VARIOUS PH- CAL REACTIONS IN THE IONOSPHERE OF VENUS.

The calculations are based on the ionosphere model of Kumar and Hunten (1974).

Venus hydrogen exosphere

TAEU 2. A SUMMARY OF SOURCES OF NON-THERMAL HYDROGEN

Flux contributing to non-thermal atoms observed Non-thermalt

Source of non-thermal H Atom* in the exosphere escape flux hydrogen atoms energy (eV) (ci@ s-l) (cm-2 s-1)

I. Tbe ionosphere source O++H,+OH++H 0.60 4X106

OH++e+O+H 838 4x106 CO,+ + H, + CO,H+ + H 1.17 1X106 <1x106

CO,H++e+CO,+H 7.97 1X106 H++O+O++H 1X106

II Photodissociation of Hz hv+H,+H+H < 104

III. Charge exchange with solar wind protons

H,+ + He,, +HL,+H 51x10” 4x106 H,++O+O++H S1X106

IV. Plasmasphere resonance charge exchange

H+ + Hoold -+ H& + H < 104

Total flux -1x10’ -1x10’

* For comparision, the escape energy on Venus is 0.56 eV for hydrogen atoms and equivalent mean energy for a hot component at 1300 K is 0.11 eV.

t For comparision, Jeans escape is 5 10’ cm-* s-l.

1067

reaction of H’ with 0 are insignificant. The major source above 200 km is the reaction of O+ with H, and subsequent recombination and below 200 km it is the reaction of CO*+ with Hz and the subsequent recombination. The exobase is at about 200 km.

Two different populations are produced from these reactions (see Table 2). Ion-molecule reac- tions provide “hot” atoms (Energy 5 twice the escape energy) whereas recombination reactions provide “very hot” atoms (Energy - 10 times the escape energy). In steady state the height integrals of the two components are equal. For comparison, the observed hot component from Mariner 5 and 10 could be produced by a hydrogen distribution with an average energy of 0.11 eV.

For convenience of description, the observed height distributions of L-a have been interpreted in terms of two temperatures rather than a continu- ous, non-Maxwellian energy distribution. The pro- cesses described here will naturally produce the latter, as the initially very hot atoms slow down in successive bounces from the exobase, and are even- tually thermal&d. Bertaux et al. (1977) interpret their resonance-cell transmission data to show a sudden rise of temperature above 3000 km. There is no obvious way of explaining such an effect in the present framework. Bertaux et al. suggest that they may be seeing the creation of satellite particles; but

it must also be pointed out that they cannot disting- uish a temperature rise from, for example, a net Doppler shift.

Ferrin (1976) has used the data of Fig. 1 in a Monte Carlo calculation of the altitude profile. He has also pointed out that the “very hot” atoms from reaction (3) will almost all escape; even those initially directed downwards will bounce with little energy loss. Because of their high velocities, these atoms will not contribute an observable density.

Ferrin’s altitude profile, starting with an energy of 0.31 eV from equation (2), reproduces the Mariner 5 observations very well if the energy loss per collision is as low as argued above. He actually preferred a much larger energy loss, which gives a similar height profile, but too low a density. J. Penner (private communication) has pointed out that the energy yield of reaction (2) is actually 0.6 eV, not 0.31. Fenin’s result may still be rescued if the OH’ is vibrationally excited. Indeed, this is very likely to be true, as it is normal for a large fraction of reaction energy to go into vibration of the newly-formed bond. Fortified by Ferrin’s suc- cess, we may, therefore, revert to a more general discussion of the various proposed sources of Table 2 as they appear in various model ionospheres. It is convenient to distinguish upper and lower ionos-

pheric sources (2,3) and (4,5), which contribute mainly above and below the exobase, respectively.

1068 S. KUMAR, D. M. HUNEN and A. L. BROADF~~T

TARLIZ 3. MODEIS USED FOR THE UPPER IONOSPHERE SOURCE (O++ H,) OF NON-THERMAL HYDROGEN

Neutral density at 145 km(cm-“) Peak O+ Exospheric Ion density temp. temperature Model fit References for

CO, 0 HZ (cm-3) T,(K) Ti (K) to data ionosphere model

Model 1 1.9x10” 1.9x109 2.5~10’ 6.0~10~ 350 1500 Mariner 5 Kumar and Hunten (1974) Model2 3.5~10~” 2.2~10~ 2.5~10~ 1.3x103 350 1500 Mariner 5 Nagy et aZ. (1975) Model3 3.5~10’~ 2.2~108 2.5~10’ 7.2~10’ 350 1500 Mariner 10 Nagy et al. (1975) Model4 1.8~10’~ 1.5~10~ 7.2~10~ 6.1~10~ 300 700 Mariner 5 Chen and Nagy (1978) Model 5 1.8~ 10” 1.5x lo9 7.2 x lo4 6.1 x lo3 300 350* Mariner 10 Chen and Nagy (1978)

Cloutier et al. (1969) Bauer and Hartle (1974)

* Here lower ion temperature is assumed to simulate “compressed” ionosphere observed from Mariner 10.

Upper ionospheric source ionospheric structure in general. Perhaps the most likely of these are the compositional changes, which

In Fig. 1, reaction (3) will give an escape flux of are sensitive to the transport processes discussed in - 4 x 10’ crne6 s-‘, as already discussed, and reac- the next section. Some idea of the possible variabil- tion (2) will contribute an equal amount to the hot ity can be obtained by adding Hz reactions to H density. Can we explain the factor of 3 variation various published models and computing the between Mariners 5 and lo? Possible causes could nonthermal broduction rates. The assumptions be changes of atomic-oxygen mixing ratio, Hz mix- made are shown in Table 3, and the column pro- ing ratio, exospheric temperature, and upper- duction rates illustrated in Fig. 2. It is seen that the

I 8 111111 1 I I I1llll I ,111,

1 IO5 lo6

HOT H COLUMN PRODUCTION RATE (cm -2

sac-‘)

I-

LL

10;

FIG. 2. VARIARILITV IN THE “UPPER” IONOSPHERE sOIJRClZ OF HOT HYDROGEN (O++HJ EXPECTED FROM VARIOUS IONOWHERR MODELS.

The parameters used in the five models are given in Table 3.

Venus hydrogen exosphere 1069

total range among these profiles exceeds the ob- ing the topside structure. Models l-3 assumed ion served factor of 3. We must therefore examine the temperatures of - 1500K and electron tempera- underlying assumptions and see if the variation tures about twice as great; Model 4 calculated them among models can plausibly represent changes in self-consistently, and obtained appreciably lower the planet Venus. values.

Although it is conventional to characterize the composition of a Venus thermosperic model by the mixing ratios at a standard height, this practice is a bit misleading for Model 1. Kumar and Hunten (1974) obtained an electron-density profile that peaked at least a scale height higher than the observations, and commented that a less-dense CO, profile would have been better. Model 4 has a much larger 0 mixing ratio, but this is almost entirely due to the lower CO* density. Experimen- tal information on the 0 mixing ratio is indirect, based on interpretation of U.V. airglow data. An upper limit of 10% is obtained from the rocket data of Rottman and Moos (1973) and the limb measurements by Mariner 10 of the 1304 8, triplet (Kumar and Broadfoot, 1976). Eddy-diffusion models (Sze and McElroy, 1975; Liu and Donahue, 1975) tend to favour a much lower mixing ratio, around 1%. Models l-3 follow this scheme, while Models 4 and 5 are based on the large-scale circu- lation scheme of Dickinson and Ridley (1977), discussed further in Section 4.

In fact, inspection of Fig. 2, especially with the 200 km location of the exobase in mind, shows that the principal variation is between Models 2 and 3 and the rest. Thus, what really seems to matter most is the amount of atomic oxygen in the model. It seems to us that Models 2 and 3 must be considered as extreme lower limits, and Models 1 and 4, with similar 0 densities, are to be preferred. They give a source strength of hot atoms of 7X ld crnw2 s-l, almost exactly equal to the require- ment derived in Section 2 for Mariner 10. For Mariner 5 the agreement is marginal at best.

Lower ionospheric source

Hz is an even more uncertain constituent; most of the isolation we have is based on interpreta- tions of Lyman-a data, working backward to a requirement on the Hz. Kurnar and Hunten (1974) adjusted the hydrogen to prevent the existence of a dense F 2 layer of O+ ions. Nagy et al. (1975), the source of Models 2 and 3, used a “hydrogen” density of 5 X 104cmw3 at 200km; since this is presumably atomic hydrogen, we have simply added our own I& profile to the model, ignoring any effects on the ion density profiles. Models 4 and 5 take their Hz directly from Fig. 1 of Chen and Nagy (1978).

The reaction of C02’ with Hz and the subs- quent recombination occur at a depth of some 7 scale heights below the exobase; the number of mean free paths is thus about 1000. To random- walk their way to the exobase, the H atoms must make of the order of lo6 collisions, which assures that they will have lost all memory of their original energy. The lower ionospheric source therefore contributes in a major way to the thermal H, (Liu and Donahue, 1975), but not to the nonthermal.

Charge exchange with solar wind

In regions where the solar-wind plasma is in contact with the hydrogen corona, the following charge exchange can take place:

The structure of the upper ionosphere, and its interface with the solar wind, are the least under- stood. Mariners 5 and 10 show features at 500 and 200 km, respectively, that are usually interpreted as ionopauses. If so, there must have been a major difference in conditions at the two times. For model 5, we have postulated that the ionosphere was not merely cut off, but compressed by entry of solar- wind ions (Cloutier at al., 1969; Bauer and Hat-de, 1974). We have therefore arbitrarily adjusted the topside scale heights of Model 4 to obtain Model 5. As can be seen in Fig. 2, the effect on the upper hot-H source is only a factor of 1.7. Electron and ion temperatures are important as well in determ-

I-&,,,++I&~+H+H+. (9)

The hot H atom can escape, either directly or by bouncing from the atmosphere with little energy 10s~. The slow ion can be picked up by the magnetic field of the solar wind (or, violently, accelerated by the electric field) for a net loss of planetary hydrogen. This loss depends therefore on the poorly-understood topology of the solar-wind flow (Bauer et al., 1977). However, it seems likely that the flow penetrates to the vicinity of the “ionopause”, only a few hundred kilometers above the surface. A typical rate for reaction (9) can be estimated as follows. The cross-section is not well known, but seems to lie in the range (l-2)x IO-” cm’ (Fite et al., 1960; Rapp and Francis, 1962). The solar-wind flux, scaled to Venus, is about 4X 10” rzr~-~s-* (Bame, 1972). The hot-H

1070 S. KUMAR, D. M. Huurnu and A. L. BROADFWT

production rate is therefore

P(hot H) = 2.4 x lo6 cm-* s-l above 500 km

= 4 X lo6 cane2 s-l above 250 km.(“)

For a low ionopause, as inferred from Mariner 10 data, there will also be a charge exchange with atomic oxygen:

&++O+H+O+. (11)

If the cross-section is the same as for equation (9), the rate could be as large as lo7 cm-*s-’ above 250 km. There is no net escape, because the escap- ing atoms came in as ions, but a fraction of the atoms could be slowed down and contribute to the nonthermal corona. According to the estimates in reaction (lo), the symmetrical charge exchange reaction (9) might contribute almost lo7 cmP2 s-’ to the escape flux.

4. ENJlROGFsNTRANSFORT

The H and H2 densities shown in Tables 1 and 3 can be converted to mixing ratios of total-H, that is H+2H2; they range from 3.5 to 20 ppm. At the cloud tops the corresponding value must be at least 2.6ppm, from 0.6ppm of HCl (Connes et al.,

1967) and 1 ppm of Hz0 (Fink et al., 1972). The presence of H2 in the stratosphere could raise the total still further. The enhancement of the total-H mixing ratio between the lower atmosphere and 145 km is therefore around a factor of 3: there is a remarkably small degree of difhtsive separation. As mentioned in Section 1, previous papers have taken the most likely explanation to be that the homopause is near 140 km, corresponding to an eddy diffusion coefficient somewhat greater than 10’ cm2 s-l. As an alternative, both Liu and

Donahue (1975) and Sze and McElroy (1975) found that an escape flux of about 10’ cmw2 s-l would give a similar effect. This is the “limiting flux” of Hunten (1973); see also Hunten and Donahue (1976). In limiting flow, the hydrogen mixing ratio can be maintained constant to heights far above the homopause. As Table 2 illustrates, no process has been found that can provide an escape flux of lo* cm-2 s-l, and it seems unlikely that the true value is greater than lo7 cmm2 s-l. We now discuss an alternative: that the limiting flux on the day side can be supported by a fast horizontal flow to the night side.

An alternative to the ad hoc hypothesis of eddy diffusion has been offered by Dickinson and Ridley (1977). In a detailed treatment of the thermal and mass balance of the thermosphere, they find a planetary wind blowing from the day side to the night side, with the return flow at a much lower level, in the mesosphere. They find day side temp- eratures and atomic-oxygen densities consistent with what is known: the unobserved night side is cooler and is strongly enriched in 0 and CO. Their model has been adopted for the successful ionos- pheric computation of Chen and Nagy (1977), which forms the basis of our Models 4 and 5. And the night side CO enhancement is seen in the 2.6 mm measurements of Kakar et al. (1977). The day side 0 mixing ratio at 145 km is 8%, and comparison with the eddy-diffusion treatment of Liu and Donahue (1975) suggests an equivalent K of 10’ cm2 s-l. Indeed, this result can be derived as follows by a simple scaling argument, suggested in conversation some years ago by G. Kockarts. In Fig. 3(a), u is the horizontal velocity, - 100 m s-r, derived by Dickinson and Ridley, for all heights above 110 km, and w is the upward velocity on the

(a) 4 1 I t t 1 1 1 I 1 I N (RETURN FLOW)

I I, , , , , , , , , , , , , , , , , ,

SUBSOLAR TERMINATOR ANTISOLAR

(b)

FIG. 3. (a) A SCHEMA TIC OF THE PJANETARY WIT-m IN THE THERMOSPHERE AND EXOSPHERE. (b) -l-HE NARROW SPHERICAL TRL4NGL.E FEtI2VAN-I TO THE FLOW FIELD.

Venus hydrogen exosphere 1071

day side. The eddy-diffusion time constant is

TE z I$&/& (12)

where Hi and H, are the scale heights of the minor constituent of interest and of the background at- mosphere [Hunten, 1975, equation (19)]. The time constant for the horizontal flow is

?f J rlu (13)

where r is the planetary radius. Equating (12) and (13), we find the effective values

~==uHi~r=2.6x107cm2s-’ for 0

=2.1x108cmzs-’ for Hz

= 4.2 x IO8 cm2 s-’ for H. (14)

Without this strong mass dependence of I<h, the Dickinson-Ridley model could not readily account for the behaviour of hydrogen; but now it seems that natural explanation is at hand. We are inde- pted to Dr. H. G. Mayr for a conversation in which this idea arose. The further discussion below is stimulated by his report of work in progress by Mayr and Hartle (cf. Hartle et al., 1977).

To account for the inferred hydrogen distribution on Venus, the horizontal flow above - 140 km should be able to carry away the hydrogen supplied by limiting upward flux all over the day side. A typical sector, extending from the subsolar point to slightly beyond the terminator, is shown in Fig. 3(b). The flow field is assumed to be that of Dickin- son and Ridley (1977), Fig. 8. The ratio of the shaded area to the width at solar zenith angle 2 is

AIW=r l-cosz Z

-=rtan!i* sin Z W)

The upward flow (molecules s-l) of H2 at the limiting flux 4l in the area A is (Hunten, 1973)

&A==* A, (16) a a*

where b = 1.1 x 10” cm-’ s-’ is the binary diffusion parameter, and no and &a are the densities of H,, and CO2 at 145 km. The corresponding horizontal flow at the chosen distance Z is

uH1 WnO, (17)

since the effective cross-sectional area for the flow is Ii, W, with H, the scale height for hydrogen. If the flow through W is to carry the flux up through

A at each solar zenith angle, equations (17) and (16) must be equal, or

b A br tan (Z/2) n”“=uw,H,*=H,H, u . (IS)

Scaling from Fig. 8 of Dickinson and Ridley, we find that the term tan (Z/2)/u is remarkably close to constant; its value at Z = 45” is 2.90 X lo+ cm-’ S, varying by -4% to 13% at 0“ and 90”. Within this small tolerance, naO = 1.41 x 10” cm3 for H2 and 2.82~ 10’“cm-3 for H. If these two forms are equally abundant, as suggested by Tables 1 and 3, a mean value, nao = 2 X 1O1’ cme3, is appropriate. The corresponding height in the Dickinson-Ridley model is about 145 km. The mixing ratio of total hydrogen all over the day side should remain nearly constant up to this height, in almost perfect agree- ment with the requirement.

Equation (17) embodies the principle of the “Johnson pump”, enunciated by Johnson and Got- tlieb (1969) to explain the terrestrial winter helium bulge. A minor constituent in a flow field is carried along at a rate pro~rtionai to its scale height, which in diffusive equilibrium can be very different from that of the major gas. A light gas can there- fore be greatly enriched in the downwind direction. Other workers (Mayr and Harris, 1977) use the term “wind-induced di@‘usion”. There should be a large “night side H2 and H bulge” on Venus, along with the analogous 0 and CO bulges already pre- dicted by Dickinson and Ridley.

The vertical distributions on the day and night sides are illustrated in Fig. 4, where we ignore the complication introduced by conversion of H2 to H. [A similar diagram has been given by Reber and Hays (1973), Fig. 25.1 On the day side the curve for limiting upward flux starts off with the same scale height as the rest of the atmosphere. At the height (145 km) derived above, the distribution switches to that of diffusive equilibrium. To give the down- ward flux on the night side, the distribution must have a slightly larger scale height than for diffusive equilibrium (Wallace and Hunten, 1973; Hunten, 1975). As Fig. 4 indicates, the day and night curves must join at some lower level, whose height is difficult to specify with present knowledge. It could be determined by mesospheric global circulation in a mode not modelled by Dickinson and Ridley, or by vertical eddy diffusion. Sze and McElroy (1975) have shown that an eddy coefficient Ks 3 X lo5 cm’s_’ in the mesosphere is required to account for the absence of detectable 02. Dickin- son (1976) finds that a value of lo6 cm’ s-l is permissible with no more than a small perturbation

1072 S. Kw, D. M. Hurrmn and A. L. BROADFOOT

I I I I

DAY NIGHT

REGLON OF LIMITING FLOW

IO5 lo6 10’ 108

NUMBER DENSITY (~tn-~,

F-IO. 4. -TIC tU.USI’RA~ON OF THR WROciRN F’ROFILES ON THE DAY AND NK3HT SIDES.

Limiting flow on the day side reduces the exospheric density there by a factor of 1000.

of a globally-averaged version of his model. The corresponding homopause is therefore near the level where n, = 2~ 1013 cmm3, and the density of total-H (at 2.5 ppm) is 5 X 10’ cm-j. Between this level (115 km) and 145 km, the density of hydrogen in downward flow remains essentially constant, while its mixing ratio increases by a factor of 1000. This is our estimate of the night/day ratio for the hydrogen bulge.

Dickinson and Ridley (Table 2) show an 0 de- nsity of 1.14 x 10’ cmw3 at 177 km, and a tempera- ture of 205.5 K, at a solar zenith angle of 150”. A density of 5 x lo7 cm-’ will be reached at 216 km; at greater heights the dominant constituents should be H and HZ in comparable amounts, falling off with sale heights of 200 and 100 km.

The question of the homopause could also affect the CO and 0 bulges, but just how is not clear. At the homopause adopted above, Dickinson and Rid- ley (1977) show a night/day ratio - 10. According to Sz.e and McElroy (1975), oxidation of CO occurs mainly befow 85 km, and (though their model treats a diurnal average), the reactions are effective only on the day side. The CO bulge may therefore survive to rather low altitudes, but this suggestion is sensitive to the details of horizontal and vertical mixing in the mesosphere and stratosphere. If the

mixing is rapid enough, the magnitude of the CO and 0 bulges could be reduced by nearly a factor of 10 from those shown by Dickinson and Ridley.

Hartle et al. (1977) have presented a similar analysis, from which the basic idea of the present treatment was taken. However, they suggest that the principal return flow for hydrogen occurs in the exosphere, and limits the magnitude of the bulge to less than a factor of 10 (cf. Reber and Hays, 1973). If this were so, we doubt that the mechanism couid maintain the thermospheric limiting flux that is essential to the whole explanation. However, we now give reasons to doubt that exospheric diffu- sion, or “lateral flow”, can overcome the thermos- pheric wind on a pianetary scale. We adopt a simplified model of the edge of the bulae. in which the density drops uniformly from n, to 0 over the distance L, which is to be determined. The height- integrated flux is given by Donahue and McAfee (1964), equation (6):

F a Hi’ ? (g Hi)“‘, (19)

where g is the acceleration of gravity. Equating this to the convective flux uHi%, we find

(20)

Venus hydrogen exosphere 1073

With w - 300 m/s-‘, the value near the terminator, I.- 1000 km for H and even less for HZ. As u drops, further into the night side, L will increase, but it does not seem that back-diffusion can carry either H or H2 across the terminator to the day side.

We must now address the question of why Reber and Hays (1973) reached the opposite conclusion for terrestrial helium, which at 800 K has the same scale height we used above for H. For a wind of -lOOm/s-’ they find a density ratio of only 10, not the 1000 we are suggesting. First, it is not clear from their paper how the exospheric diffusion was actually included; it is important to use a coordi- nate system moving with the wind. Second, their parameterized flow has a return cell in the middle thermosphere; they comment (p. 2986) that omis- sion of this cell results in a much larger decrease of helium near the summer pole, which corresponds to the day side for Venus. They rejected this case because it disagreed with observation. Since the Venus flow has no such cell, it is reasonable that we should obtain a much larger night/day ratio.

The night side Hz is very difficult to detect opti- cally (it is not much better on the day side!). The mass spectrometer on Pioneer Venus Orbiter (Colin and Hunten, 1977) will be able to measure ambient densities as low as 5 x 10’ cm-‘, and there- fore appears to have ample sensitivity. The atomic hydrogen might be detectable at Lyman-a, even though no direct solar radiation falls on it. Wallace (1969) noted a strange effect when the line of sight of Mariner 5 passed the dark limb: the drop of intensity corresponded almost exactly to the inter- planetary background, and did not seem to include the Venus airglow from beyond the limb. He suggested that “the atomic hydrogen near the night side of the planet was optically thick”. The quantity suggested here has a central optical depth, tangent to 145 km, of 5800, and remains optically thick to *2.9 Doppler widths. It would just nicely absorb the radiation scattered from the non-thermal corona, while transmitting nearly all the back- ground Lyman-a. On the other hand, Anderson (1976), from the Mariner-5 nightglow data, found a night/day ratio between l/3 and 3, very far from the 1000 suggested here. He remarked that he was unable to fit the change of intensity at the dark limb. It may be that his analysis is sensitive only to H atoms in the twilight zone; the dense bulge should begin to appear only 10-20” behind the terminator, judging from the Dickinson-Ridley (1977) results for 0 and CO. A thorough radiative- transfer analysis of both Mariner 5 and Mariner 10

data may help resolve this issue. There does seem to be some support for the idea of a major H bulge.

5. DISCUSSION

This paper has considered several aspects of the Venus hydrogen budget; they are now discussed in turn.

Source of hot H

The strongest source we have been able to iden- tify is still the upper ionospheric source, reaction (2) of Hz with 0’. The following reaction (3) contributes mainly to the escape flux. It is necessary to assume that hot H is thermalized at the minimum possible rate, corresponding to elastic collisions with 0 and CO*. No direct laboratory evidence is available, but a closely analogous ex- periment strongly supports this assumption. Our best estimates of nonthermal density still fall short of the observations by a factor of 2 or 3, which seems tolerable under the circumstances.

Variations of thermal and hot H

The differences between Mariners 5 and 10 seem most readily explained in terms of different solar- wind conditions, but a detailed mechanism is still not apparent. The same is true of the differences in ionospheric structure, if they are truly present. However, it is well to remember that the structure above 200 km was not well determined by either mission; the true magnitude (and even the reality) of the differences is not known.

Changes of 0 and H2 densities are another obvi- ous possibility, since the production of hot H by reaction (2) is proportional to their product. Again, a detailed mechanism is not at hand. The main circulation, discussed below, offers little scope for variability. The horizontal speed at the terminator is essentially the speed of sound, and presumably is insensitive to external conditions. The state of mo- tion of the mesosphere could perhaps be more variable, and permit some of the matter from the night side bulge to reach the day side thermos- phere.

Escape

According to Table 2, the dominant escape pro- cess is probably charge exchange with solar-wind protons, followed by re-acceleration of the newly- created thermal protons. The upper ionospheric source, reaction (3) is smaller but still significant. Together they deliver less than 10’ atoms cn~-~s-~, an order of magnitude less than the limiting flux.

1074 S. KUMAR, D. M. HU~EN and A. L. BROADFCKYC

As remarked by Walker et al. (1970), it is difficult to supply a large escape flux when the amount of hydrogen at high altitudes is so small.

The day side-to-night side circulation of Dickin- son and Ridley (1977) seems to account for the removal of H and Hz, as well as 0 and CO, from the visible part of the upper atmosphere. If rep- resented as an equivalent eddy coefficient, it yields a number proportional to the scale height of the constituent, thus permitting hydrogen to be de- pleted much faster than 0. An enormous night side bulge of H and Hz is predicted; it should be in a vertical distribution resembling diffusive equilib- rium. With a reasonable assumption on the location of a well-mixed lower boundary, the night day ratio in the exosphere is 1000.

The Hz bulge is probably detectable only by mass spectrometer, but extinction by the H may already have been observed by Mariner 5 (Wallace, 1969). Another analysis of the same data by Anderson (1976) does not show a bulge, but probably refers to the twilight region rather than the bulge proper.

Note ndded in proof: R. E. Hartle has pointed out that the nightside bulge cannot be as small as suggested in Section 4. because the downward diffusive flux, corresponding to the “night” curve in Fig. 4, is appro~ately e&al tothe uoward limit& flux &. If diffusion were the only sink of eiospheric hyd;ogen;‘the bulge would have to fill the whole night hemisphere. But, in fact, it is necessary to consider the vertical convective velocities of Dickinson and Ridley, which can greatly exceed the diffusive veloc- ity, contrary to the statement made just before equation (15). An upward velocity does not alter the “day” curve of Fig. 4, because it gives a constant mixing ratio up to some height, indistinguishable from the limiting-fiux line. For the night side, Dickinson and Ridley show, in their Fig. S(b), a vertical velocity at 130 km of about -25 ems-’ occupying about 30% of the night hemi- sphere, and not far bebind the terminator. The height was chosen to make the diffusive and bulk downward ve- locities esual. The hydrogen flux in this region should therefore be about 3_tim& the upward 3ux on the day side. or 3 X 10s cmd2 s-l, and the corresponding density is 10’ &nm3. By this estimate, the bulge oc&pies most of ihe night hemisphere, and has a density enhancement of about a factor of 100. As before, we suggest that H and H, may be comparably abundant. If a more efficient downward transport can be identified, the predicted en- hancement will be less.

Acknowledgements-We are indebted to H. G. Mayr for a conversat:on in which the idea of hydrogen transport to the night side arose. Stimulating discussions with G. Thomas and I. Ferrin are acknowledged.

This material is based upon research supported by the National ~en~Foundation under its contract No. AST

74-04129 with the Association of Universities for Re- search in Astronomy, Inc., for management, operation and maintenance of the Kitt Peak National Observatory. The work was also supported by NASA grant NAS-7- 100.

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