Planet. Space Sci. 1971, Vol. 19. pp. 443 to 460. Pcroamon Press. Printed in Northern Ii-eland
J. R. HERMAN, R. E. HARTLE and S. J. BAUER Laboratory for Planetary Atmospheres, Goddard Space Flight Center, Greenbelt, Md. 20771, U.S.A. (Received infiMrform
12 October 1970)
~~~-Theoreti~l modeling of the daytime Venus ionosphere is used to augment the moments of Mariner V made during its 1967 flyby of Venus. The equations of heat transport for the electron, ion, and neutral gases are simultaneously solved along with the associated momentum and chemical equations for the ion and neutral gas densities. When solutions are constrained by the observations from Mariner V, the resulting temperature and density profiles can be used to estimate the possible magnetic field strength within the Venus ionosphere and concentration of neutral helium at 100 km altitude. Several alternate models are presented to account for the effects of eddy diffusion in the neutral atmosphere and solar wind heating. In all these models the resulting solutions lead to an approxi~tely horizontal magnetic field in the topside ionosphere of strength 10-20 y and a neutral helium density of order 10s cm-* at 100 km altitude. INTRODUCTION During the 1967 flyby mission, Mariner V obtained a single cross sectional profile of the day and night-time Venus ionosphere (Fjeldbo and Eshleman, 1969; Mariner Stanford Group, 1967). These data combined with in siiu measurements of the nightside by Venera IV can be used to construct additional features of the Venus ionosphere from theoretical models. The Mariner V occultation data clearly show that a sharp cutoff in the electron density (ionopause) occurred at about 500 km on the dayside and 3500 km on the nightside. As illustrated in Fig. 1, the location of these points was approximately 45” below the subsolar wind point and 135” above, respectively. It has been suggested (Dessler, 1968; Mariner Stanford Group, 1967; Johnson, 1968; Fjeldbo and Eshleman, ‘1969) that the observed electron density cutoff represents the interface between the solar wind and the Venus ionospheric plasma. Such an interface forms a natural upper boundary for the ionosphere where the requirement of continuity of the total pressure supplies one of the needed boundary conditions. Other data used to construct or confirm the models were the value of the electron density in the region just below the ionopause (~10~ cm--e), the large scale height in the topside suggesting a mixture of H, D and He at relatively high temperatures, the small scale height in the lower ionosphere corresponding to a CO* plasma at a neutral gas exospheric temperature about 600”K, and the observed electron density maximum of about 5 x lo5 cm-8 at 140 km altitude. The Venus ionosphere is quite sensitive to the amounts and relative composition of H, D and He and to the assumed magnetic field structure. Some estimates of H and D are available from the Lyman-a m~suremen~ made far from the planetary surface (Barth et al., 1969). However, neither the helium concentration nor the magnetic field structure have been measured beyond establishing an upper limit on the nightside of Venus (Dolginov et al., 1968) and therefore on a possible planetary magnetic moment. Estimates for helium have been based on assuming an earthlike model of the planetary crust (Knudsen and Anderson, 1969) and a lower limit on the nightside determined by assuming the topside ion composition to be pure He+ (McElroy and Strobel, 1969). The main features reIating to the solar wind interaction observed during the Mariner V encounter are summarized in Fig. 1. At the time of observation the solar wind speed was about 590 km/set with a density of 3 protons cm3 and a kinetic proton temperature of 3 x lo6 “K. The solar wind carried a small magnetic field of strength about 10 y and 443
J. R. HERMAN,
R. E. HARTLE
S. J. BAUER
WIND I \ &__I I I I
n=3 cm -3
I VENERA ORBITS
SOLAR WlND ENCOUNTER WITH [email protected]
SHOWING THE SHOCK
plane of the Venera and Mariner V orbits has been rotated into the plane normal to the Venus-Earth line.
oriented at 26” to the flow streamlines at the orbit of Venus (calculated from the usual spiral field model). A model of the solar wind interaction with Venus and its consequences for the ionosphere has been recently discussed (Bauer et al., 1970). In this model the streaming energy of the solar wind is converted to magnetic and thermal energy in the region inside the bow shock. The magnetic field strength is expected to rise from about 10 y in the solar wind to about 40 y in the vicinity of the ionopause. Between the bowshock and the ionopause the proton temperature increases to nearly 4 x lo6 “K. Within the ionosphere the inward solar wind pressure must be balanced by the sum of the ionospheric charged particle pressure and possible magnetic field pressure. In the ideal case of an intlnitely conducting ionosphere, the induced currents corresponding to the solar wind flow lie entirely in the ionopause surface and in the region above. The resulting magnetic field is excluded from the ionosphere. Even with a realistic finite conductivity the magnetic diffusion t, is so much greater than the reversal time for the interplanetary magnetic field, that magnetic diffusion into a quiet ionosphere should be negligible. Since t, is also much larger than a Venus day, the rotation effects and field reversal would have to be considered simultaneously to properly assess the degree of magnetic field penetration. However, if a magnetic field is present within the ionosphere, then it may arise from a weak planetary magnetic moment, from currents generated by large scale inhomogeneities or from enhanced magnetic diffusion. If the effective distance over which the magnetic field can be considered homogeneous is reduced from the order of a planetary radius to a much smaller value (thereby reducing ta), magnetic diffusion would become important. This may be possible if the likely turbulence in the topside ionosphere produces a wave structure with small characteristic lengths. ?he purpose of this work is to establish independent estimates of the neutral ionospheric composition and so infer the ionic composition and thermal structure based on computer modelling of the region between 100 km and the ionopause at 500 km altitude. Since the
THE DAYSIDE IONOSPHERE OF VENUS
thermal structure (electron, ion and neutral temperature) is very dependent on the strength and form of magnetic field assumed, the resulting models are used to characterize the likely magnetic field in the topside ionosphere. BASIS OF THE THEORETICAL
In order to assess the effects of solar control on the Venus ionosphere it was necessary to solve the heat transport equations for the electron, ion and neutral gases simultaneously with the momentum and chemical equations for their temperatures and densities. The equations and parameters used for this study are fully listed in the Appendix, and a detailed discussion of a similar set of equations as applied to the earth’s ionosphere has been given previously (Herman and Chandra, 1969). In addition to the pressure balance boundary condition needed at the ionopause, the values of the neutral densities at the lower boundary, 100 km, are among the most important
co2 1 5 1 5 1
x x x x x
10’2 lo’* 1018 10’3 10’4
4470 4380 4300 4350 4300
1380 1420 1440 1750 1510
1450 1490 1510 1550 1580
644 644 643 634 645
Ne, 521 523 5.21 5.33 5.51
x x x x x
2, 10” lo6 lo6 106 10”
120 130 130 140 145
parameters needed to characterize the ionosphere. In this connection we find that a CO% density of 5 x 1013cmJ with a small amount of N, (< O-1 per cent) in photochemical equilibrium with their ions reproduces the lower daytime ionosphere quite well. Varying the COZ density produces pronounced shifts in the altitude of the electron density maximum as shown in Table 1. That is, we find the calculated electron density maximum occurs at altitudes ranging from 120 to 145 km as the CO, density is varied from 1 x 10la cm-3 to 1 x 1014cm-3. The shift is in direct response to changes in altitude of the maximum solar EW absorption. Since the topside thermal structure is relatively insensitive to the COz concentration in the range indicated in Table 1, the observed electron density peak of 5.3 x IO5crnm3at 140 km can be used as an indirect boundary condition that fixes the density of CO, at 100 km at 5 x 1Ol3cm-3. The concentrations of hydrogen and deuterium at the 100 km base are determined by solving for all the temperature and density profiles simultaneously, and varying the base values of hydrogen and deuterium until the resulting densities are consistent with those inferred from Lyman-a measurements at great distances from the planet (Barth et al., 1968; Kurt et al., 1969). As is described elsewhere (McElroy and Hunten, 1969), one can obtain in this manner hydrogen and deuterium densities of 5 x IO8 and 2 x IO6cm-3 at 100 km, respectively. Molecular hydrogen, while possibly present in the lower ionosphere, is not thought to be an important constituent for the altitude range of interest because of its rapid photodissociation (Dalgarno and Allison, 1969). There is no experimental evidence concerning the quantity of helium in the atmosphere, although an estimate has been made based on an earthlike model of its radiogenic origin (Knudsen and Anderson, 1969). Accordingly, we have treated the neutral helium density at 100 km as a parameter of the problem, and have investigated its effect on the charged particle density and temperature distributions.
J. R. HERMAN,
R. E. HARTLE and S. J. BAUER
The boundary conditions for the heat transport equations are specified in terms of temperature gradients for each constituent at the upper boundary (500 km at the dayside Mariner V occultation point) and a common fixed temperature at the lower boundary (100 km). The use of a non-zero temperature gradient at the upper boundary implies a knowledge of the thermal structure above the boundary altitude. Based on a hydromagnetic analysis of the solar wind interaction with the Venus ionosphere (Spreiter et al., 1970), the maximum amount of thermal energy available for conduction into the ionosphere is less than 10 per cent of the energy deposited by energetic photo-electrons in the topside. At most this represents a small correction towards higher temperatures and pressures. Accordingly, we have used a zero temperature gradient at the upper boundary, z,, and have introduced a distributed source of thermal energy in the topside to simulate possible solar wind heating, Q*, = (crV/il)P8_ exp ((z - z,)/n). That is, a fraction a of the solar wind energy density P,, is deposited at each altitude z with a scale length R (where Vis the velocity at which energy from the solar wind interaction is propagated radially inward). We have also included the small amount of heating from the direct coulomb interaction between ambient charged particles and solar wind protons of which only -20 per cent are assumed to be able to penetrate the ionopause region (see Q,,, QaP, Q,, in the Appendix). Helium ions in the topside ionosphere are produced mainly by photoionization and lost by charge exchange with CO,, H, D and electron recombination. For an ionization rate approp~ate to Venus (+- 5 cm4 se&), the topside daytime electron density, as measured by Mariner V can be supplied in about 1000 set, and so maintained throughout the Venus day of about 10’ seconds unless the upward velocity of He+ exceeds O-5 km/set. A similar calculation for H+ including both photoionization and charge exchange yields a @ling time of IO6 set and an upper limit on the upward velocity of @Ol km/set. Since the Venus day is much longer than both filling times, H+, D+ and He+ are possible constituents of the topside ionosphere with He+, possibly the dominant ion. This conclusion depends upon the amount of neutral hydrogen and deuterium present in the topside. That is, H densities in excess of lo5 cm-a could lead to H+ as the dominant ion via charge exThe only requirements placed on the model by the change with He+ and photoionization. data are that the ion scale height be quite large (> 100 km) and that the electron density near the ionopause be l-2 x IO*cm *. This can be met by any combination of H+, D+ and He+, the sum of whose densities must equal the topside electron density. When the effects of even moderate upward flow are incorporated into our models, the requirements for pressure balance with the solar wind are drastically altered. Any horizontal components of the magnetic field within the topside ionosphere are carried with the flow and compressed into the region just below the ionopause (Banks and Axford, 1970). In this case we find that the electron and ion thermal conduction increases in the field free region thereby causing the temperatures and internal kinetic pressure to fall to somewhat less than half that needed for pressure balance with the solar wind, Fig. 2. An upward velocity of 05 km/set supplies only 1 per cent of the necessary upward pressure needed to support the topside ionosphere against the solar wind. Equivalently, a supersonic velocity of about 10 km/set is needed if the pressure balance is shared equally between kinetic and streaming pressure. However, such supersonic velocities are not likely to be obtained in a system with horizontal magnetic field lines at the ionopause preventing radial outflow from the planet. The resulting pressure deficit can be made up by adjusting the parameters aVand il in Q,, to supply a large amount of additional heating. These effects are discussed later. If the upward flow is limited by the need to maintain the observed electron density in the
THE DAYSIDE IONOSPHERE OF VENUS
iz t 2300
104 (‘K) ON THB IONOSPHERIC
Solid lines--Upward bulk flow compressesthe horizontal magnetic field into the region just below the ionopause (i.e. a field free ionosphere.).2. Dashed lines-A stationary ionosphere with a uniform topside magnetic field of strentgh 10~ and dip angle 45”. 1.
topside ionosphere, the radial density distribution of light ions is approximately given by a simple force balance with V, ‘v 0 (see Appendix). The solutions we obtain in this manner yield a large electric field in the region where the ionosphere changes from CO,+ to one of the light ions, Fig. 3 (E ‘v 20ma+e/g, where g = the acceleration of gravity). Newly created hydrogen ions would be accelerated by this large field creating an upward flux that might contribute significantly to the pressure balance. The result is that hydrogen ions would stream upwards at 6-8 km/set with a flux of about IO7cmw2se&. The flux is estimated by setting (nV) -P . L where the production rate P =G1 cm-3 set-l and L - 100 km. The resulting upward pressure from such a flux on the ionopause region is a maximum of 1 x lo-l1 dyn crnm2as compared to the solar wind pressure at the occultation point of 8 x 10es dyn cm- 2. Unless there is a more copious source of H+ in the vicinity of 200 km altitude than our computations indicate, it is the internal kinetic pressure and possible magnetic fields that supply the necessary pressure. DISCUSSION OF MODELS (a) No solar wind heating: Q,, = 0 In support of this view, we obtained a series of temperature and density profiles for both the neutral and charged particle gases. The neutral helium density at 100 km and the effective magnetic dip angles were varied as parameters while all the remaining boundary conditions and solar EW flux were held constant from model to model. From the resulting
J. R. HERMAN,
R. E. HARTLZ
S. J. BAUER
500 z Y x 2 F 2
IS THE DOMINANT ION
(kedd, = 0).
“11111’ “lllw’ “ltblll’ “111111’ “llJ 107
4. THEPRBSSURBOF THE CHARGED PARTICLES JUST BELOW THB IONOPAUSE LEVEL (500 AT THE MARINER V OCCULTATION POIM vs. THE NEUTRAL HELIUM DENSITY AT 100 km ALTITUDE.
The dashed lines represent the difference between the solar wind pressure and the magnetic pressure of the indicated field, P, - B,8/8a. The cases shown are for magnetic dip angles between 1 and lOa, and Keaay = lo6 cm2 xc-l.
sets of profiles the charged [He+] kT,,+, at the upper curves represent the kinetic solar wind pressure and the
particle pressure, P, = N,kT, + W+l kT,+ + P+l ki”,+ + boundary was obtained and is shown in Fig. 4. The solid pressure, PO, and the dashed lines the difference between the pressure of the horizontal component, Bta/87r, of any magnetic
a -7 ms
-5 14.0 -
5 E ; 12.0 In k w 5 10.0 -
-2 -1 -0
z 2 $
? % P 0
’ ’ “““’
’ ’ “““’
’ ’ “““’
’ ’ ““‘1’
’ ’ “““’
NEUTRAL HELIUM DENSITY AT 100 Km @mm3 ) FIG. 5. TOPS~ELE~~R~NANDIONTEM~~ATURES~S.THENE~~ALHELIUMDENS~~YAT ALTITUDE.
field that may be present in the Venus ionosphere. At low helium densities the pressure decreases slowly with increasing amounts of helium forming a pressure minimum in the vicinity of [He],,, = 5 x lo8 cm-3. Further increases cause the pressure to rise very sharply. The reasons for this behavior are illustrated in Fig. 5 where the temperature and pressure curves are given simultaneously. The topside density corresponding to each point on the pressure curve was l-2 x IO4cm- 3. It can be seen that the minimum in the pressure curve arises from decreasing ion temperatures as the ion thermal coupling to the neutral gas increases. Further increases in the neutral helium density cause the solar EUV heating of the electrons to increase at a much faster rate than the corresponding loss to the cooler ions and neutral gases. Therefore, at low neutral helium densities the pressure follows the ion temperature while at higher densities it follows the electron temperature. The solutions appropriate to Venus are where PC = P8, - Bt2/8rr (Fig. 4). Clearly, effective magnetic dip angles less than 4” are not possible since the resulting electron temperature and therefore P, are too high for any concentration of neutral helium considered. Solutions for effective dip angles greater than 5” are not explicitly ruled out except that they require a very high neutral helium concentration or stronger magnetic field than was measured on the nightside by Venera IV (Dolginov et al., 1968). If Venus has only a weak intrinsic magnetic field (less than 10 y above 100 km altitude) that is essentially horizontal in the vicinity of the occultation point, or if there exists an externally generated field of similar nature, then the neutral helium concentration at 100 km is likely to be in the vicinity of 5 x IO* cm3 (typical of the curve labelled dip = 4-l”). The total atmospheric content of He associated with this number density can be accumulated during 4.5 x log years, as long as the total escape flux of He is less than 10” cm-2 se+. In the absence of any experimental evidence for an induced field, the Venera IV measurements of about 10 y form an upper limit to any intrinsic field. The case B = 0 is not allowed since a pressure balance cannot be achieved (it is equivalent to the Dip = 90” case). The
g 400 = I g 300 ? F 2 200 -
dashed line labelled B = 0 should be interpreted as O-01 ZGB I O-05 y, a field strength suS%ient to reduce thermal conduction across field fines, yet small enough not to significantly affect the pressure balance (Leoutovich, 1965). As each point on the P, curves in Fig. 4 corresponds to a separate set of temperature and density proties, we show a typical example of one of the allowed solutions, Fig. 6, for a neutral helium density of 5 x 10’ cmq, P, I= 8.65 x 1O-Qdyn cmsa, and solar EW flux scaled by a factor of 2.68 to correct for distance and time of the solar cycle from the values given by Hinteregger et af. (1963). in this model the efectrou density has a peak of 5.2 x IO6 cm* at 140 km altitude in a region that is mainly CO %+=At 260 km the scale height rapidly increases as the ionic composition changes from CO,+ to the light ions He+ and H+. The proties for H+ and D+ have been combined by summing. At 500 km, the ionopause is indicated schematically by the dashed line P, = P,. A very similar set of proties is obtained when the quaatity of neutral hydrogen and deuterium is increased so that He+ becomes the minor ion. The only significant change is a further increase in scale height corresponding to the reduced average mass of the resufting ionosphere. These density profiles were computed seIf consistentIy with the temperatures shown in Fig. 6. Here the temperatures just below the ionopause are T,, = 640X, T, = 3670°K, T&+ = 216O’K, and TE+ = 2330°K. Because of the efficient transfer of thermal energy between the ions, T,, andT,,+ are closely coupled in the topside. In the lower region where the neutral helium density is much larger, the heat Ioss from He+ to He predominates over the heat input from the electrons via the large moments transfer cross section corresponding to the symmetric charge transfer reaction. Since the coupling of H+ to the neutral atmosphere is not as efficient as He+, T,+ tends to follow T,. An interesting feature af the Venus thermal structure is the relative stability of the
neutral gas temperature with respect to changes in neutral gas composition. An example of this is shown in Table 1 where the COz density is varied from 1 x 10la cm-a to 1 x 101* cm-3 with little change in T,. Unlike the similar case for the Earth’s ionosphere (Herman and Chandra, 1969) a single constituent, COz, is responsible for both the conversion of solar radiation into thermal energy and its subsequent reradiation in the infrared. Increasing the concentration of CO2 for a given solar energy input redistributes both the energy absorption and reradiation to somewhat higher altitudes without altering the exospheric thermal balance. (b) Solar wind heating: Q,, # 0 The picture of the dayside ionosphere presented so far is one where a static pressure balance is achieved as long as the solar wind streaming pressure remains constant. A decrease in the streaming pressure would require the ionopause boundary to move out a considerable distance from the planet to re-establish the necessary pressure balance. Since the solar wind streaming pressure is known to change quite frequently relative to the flux of solar radiation, the ionopause level would be constantly moving. This would mean the Mariner V data are merely a snapshot of a highly dynamic system. However, if the solar wind is responsible for about half of the charged particle heating within the ionosphere, for example by collisionless damping of fast mode hydromagnetic waves (Barnes, 1966) originating in the ionopause region, then reducing the solar wind streaming pressure leads to a corresponding reduction in ionospheric topside kinetic pressure. Using the previously defined expression Q,, = (aVP,,/~) exp ((z - z,)/il) to simulate solar wind heating as a function of the parameters aV and 1, the resulting electron temperatures are shown in Fig. 7 and the corresponding kinetic pressures in Table 2. When aV = lo3 cm/set, 600
g x z 2
TEMPERATURE (“K) FIG. 7. TIIEEFFECTOP A NONTHERMAL SOIJRCE OF HEATING, &,,ORIGINATING IN AND ABOVE THE IONOPAUSB REGION, ON THE ELECTRON TBMPERATURE (ked,,, = lOa, dip = 5”).
Q,, = (aVP,/jl) exp ((z - z,J/A). Solid lines represent rZ= 300 km and the dashed lines 1 = 100 km. T,, is the average of the neutral temperatures for all six cases shown with the spread indicated by the honzontal bars. l(r cm/set I a V I 10’ cm/set, where a is the heating efficiency and V is the energy transport velocity.
J. R. HERMAN,
TABLE2. THLZ EFFECT OF
R. E. HARTLE and S. J. BAUER WIND
100 km 3oOkm
4.88 x lo-* 4.83 x 10-O
5.77 x 10-o 5.21 x 10-O
I.10 x 10-e 8.51 x IO-*
2.80 x 10-a 2.15 x lo-+
results are approximately the same as the case where there is no solar wind heating (XV = 0). For example, if the heating mechanism were to arise from waves propagating at approximately the acoustic speed of about 5 x lo6 cm/set, then the overall heating efficiency a would have to be 0.001 for the effect to be negligible. The overall heating efficiency is that fraction of the solar wind streaming energy that propagates downward from the ionopause and dissipates over distances of order of the vertical extent of the ionosphere. As crV increases, the heating effect becomes very large, causing electron tem~ratures of 104“K when c# = lo6 cm/see. From Table 2, however, it can be seen that aV cannot exceed about 5 x lo4 without the internal kinetic pressure exceeding the solar wind pressure. The values in Table 2 and the profiles in Fig. 7 have been obtained for that density of neutral helium that produces a pressure minimum, see Fig. 4, dip = 5”. When aV = lo4 cm/see, Q,, is approximately half the total heat input to the electrons in the topside of the ionosphere. If V is about the ion-acoustic speed and 1 N 10’ cm, then an efficiency of a = 1-5 per cent would lead to a nearly stable ionopause and topside ionosphere. In the absence of a magnetic field in the topside ionosphere, the solar wind heating is insufficient to raise the electron and ion temperatures enough to maintain the ionopause. When an extreme upper limit for solar wind heating is used, aV = IO6cm/set and R = 100 km, the resulting charged particle pressure, PC, is only 4 x lO-s dyn cm-2, a factor of two too small. With more likely values for f&,, aV - lo4 cm se&, there must be an essentially horizontal magnetic field throughout a significant portion of the topside ionosphere. As mentioned earlier, moderate upward velocities will compress any horizontal components of a magnetic field into a restricted region below the ionopause. If the extent of this region, db, is about 100 km or larger, then sufficient heating occurs and a solution can be obtained. For a field of strength about 10 y and dip angle of 5”, aV = 104 cm [email protected]
and rZ= 100 km, a suitable solution is found with neutral helium densities at 100 km altitude in the vicinity of lo8 cm-s for 100 km 6 db G 400 km. At this time it is not possible to use the existing data to choose between the several models since each one leads to similar temperatures and densities for reasonable values of their parameters. The most likely choice should include a combination of all the effects we have discussed. (c) Eddy dijiision, thermal dijiision und thermal escape Since we have adopted the 100 km level as a boundary condition for our neutral atmosphere model, it becomes necessary to incorporate eddy and thermal diffusion effects and thermal escape for the light atmospheric constituents in a manner similar to that of McElroy and Hunten (1969). An example of the dependence of eddy diffusion for neutral helium is given in Fig. 8 for four values of &day (0, 5 x 106, 5 x lo6 and 5 x 10’ cm2 se&). The behavior of neutral helium is as expected; in the region dominated by CO,, the scale height for neutral helium is approximately that of CO,, while at higher altitudes the more usual scale height dominates. In the absence of eddy diffusion, Keaap = 0, the
8. THE NR~~~LI-~~~~~DENSI~FORVAL~RSOFT~EDDYDIFF~SION~OEFFI~~~RANGING FROMOTOS
The dashed line represents the CO, density for comparison with the neutral helium scale height for the case where T,, = 650°K. The heavy line shows the representative neutral H distribution for these cases.
reduced scale height effect persists since the effects of thermal diffusion are proportional to the strong temperature gradients in this region. Hydrogen, because of its high bulk velocity does not show substantial dependence on either eddy or thermal diffusion. Even in the absence of eddy diffusion the neutral hydrogen is strongly depleted relative to a simple hydrostatic density distribution by the upward flux escaping the planet. Thus, if Venus has a relatively non-turbulent atmosphere between the cloud tops and 150 km, helium and deuterium are likely to be enhanced relative to hydrogen in both the neutral and ionic forms above 100 km altitude. Although the He distribution in Fig. 8 corresponds to a He mixing ratio of - 1O-8, the shape of the curves for parametric values of Keaay are preserved and should be useful to define the mixing rate from a fit with upper atmosphere observations. Since neutral helium and deuterium are strongly affected by eddy diffusion, the thermal structure of the ionosphere must also show corresponding effects, Fig. 9. Above 200 km, increasing Keaas decreases the amount of neutral helium and deuterium present so that the ion-neutral thermal coupling is reduced and the ion temperatures rise. The effect on the electrons is quite different. Even though the heat loss to the ions and neutral gases is reduced, the heat input from the solar EUV is reduced even more to produce a net cooling effect. Since the electrons dominate the charged particle pressure, the upward pressure must also decrease. This means that the more turbulent the atmosphere, the more neutral helium will be needed to maintain the pressure balance under any fixed set of the other parameters. Since the degree of turbulence in the lower ionosphere may be small relative to the similar height range on Earth (McElroy and Hunten, 1969), a set of pressure curves is given for no eddy diffusion, Fig. 10. As expected, the minimum in the PC curves is shifted towards lower helium densities at 100 km (which become higher helium and deuterium 3
J. R. HERMAN,
K&Y T, 600 500 !
R. E. HARTLE
and S. J. BAUER
FIG. 9. THYELECTRONT~MPERATUREPORTKRBBVAL~ESOFTHEBDDYDIPFUSION~OBPFICIENT. P, is in units of 1O-9dyn cm-* and the listed helium densities are calculated at 500 km altitude
with a fixed value at the lower boundary (100 km), see Fig. 8.
8 = 20 Y_
IO5 IO6 lo7 lo8 109 NEUTRAL HELIUM DENSITY AT 100 KM (CM-3)
FIG. 10. CHARGED PAR~CLE PRESSURB JUST BELOW THE IONOPAUSB vs. em NEUTRAL ~~~nmi DENSITY AT 1~kIllINTW3ABSENCBOF EDDYDIFFUSION, Keaav= 0 (SEEFIG.4). The region below B = 0 defines the range of allowed ionospheric solutions for the indicated
magnetic field strengths.
250 km). In all other aspects the character of P, for no eddy diffusion is very similar to the case where Keday = lo6 cm2 set-l. For a fixed set of parameters, Bt = 10 y, ctV = 5 x 10s cm/set, and a sufficient ionization rate to maintain the topside electron density, turbulence in the bottomside ionosphere shifts the likely neutral helium density to one of the curves at 100 km from 1 x lo8 cm-3 to 5 x lo8 cm-3. Corresponding shown in Fig. 10 (dip = 4.19, the topside thermal structure is shown in Table 3. Except for the shift in neutral helium density necessary to maintain about the densities
TABLE3. TOPSIDETEMPERATURE vs. NEUTRAL. HELIUM DENSITY AT 1OOkm: &tidy = 0. Dip = 4.1 he 5 5 5 5 5 5
x x x x x x
104 106 10’ 10’ 108 100
3810 3800 3750 3870 5780 10,600
3310 3250 2840 1700 856 643
3360 3310 2960 1890 955 690
683 683 682 680 658 625
same topside temperatures and densities, the essential features are unchanged. For the same topside pressure, P,,the ion temperatures are slightly decreased and the electron temperature slightly increased in the absence of ionospheric turbulence. Therefore, while ultimately important for quantitative agreement with more detailed data, eddy diffusion does not alter the qualitative results concerning the charged particles in the ionosphere even though the topside ion composition and thermal structure depend strongly on the degree of turbulence. SUMMARY
Theoretical modeling of the daytime Venus ionosphere has been used in conjunction with the Mariner V data to help explain some of the observed features. The requirement of continuity in the total charged particle pressure across the ionopause (thermal, streaming, and magnetic), the observed value of the electron density just below the ionopause, 1.2 x 104 cm-s, the electron density maximum of 5.3 x IO6cm-s at 140 km, and the estimate of the exospheric neutral gas temperature, about 600”K, from the observed electron density scale height near 200 km altitude are the primary data used in constructing the models. Additional conditions were applied to satisfy either observational or theoretical considerations. These are, the neutral gas densities at 100 km ([NJ = lo* cm-s, [CO,] = 5 x 101scmW8,[H] = 6 x lo6 cm-s, and [D] = 2 x IO6cm-3), a common temperature for all species at 100 km (250°K), and vanishing temperature gradients at 500 km. Because of the lack of observational data there are at least two important free parameters, the neutral helium density distribution and the ionospheric magnetic field. Based on self-consistent solutions of the heat transport, momentum, and chemical equations, some restrictions can be placed on the possible values of these free parameters. In a relatively non-turbulent atmosphere, Keday< IO6cm2 set-l we find that the likely value of the helium density at 100 km is in the vicinity of 1 x 10s cm -a. The corresponding topside magnetic field strength is less than about 15 y with a dip angle between 4” and 5”. Once the degree of turbulence in the vicinity of 100 km is known, then the results of this study could be used to estimate the rate of effusion of helium from the planetary crust and the mixing ratio in the lower atmosphere. For one of the cases represented in Fig. 4 (Kedd, = lo6 cm2 set-l, B N 10y, dip = 4*2”, and [He] = 5 x lo8 cm-s) with a He mixing ratio of N lo”, we find that the nearly isothermal topside electron and ion temperatures are approximately 4000°K and 1300°K respectively at the location corresponding to the Mariner V occultation data. This case would imply a smaller rate of effusion of He4 than assumed by Knudsen and Anderson (1969) for Venus. The likely existence of a source of nonthermal heating, originating in the region of the solar wind interaction with the Venus ionosphere, provides a possible means of stabilizing the topside ionosphere. In the absence of this source of heating a relatively small change in the solar wind speed or density would cause large excursions in the ionopause
R. HERMAN, R. E. HARTLE and S. J. BAUER
altitude. With a solar wind heating efficiency a ranging between 1 and 5 per cent the topside ionosphere would be stable over the expected range of solar wind pressures PsuI. The quantitative description of the daytime Venus ionosphere is only tentative since most of the fundamental parameters, energy inputs and boundary conditions, are poorly known. In particular, a good quantitative model would require a knowledge of ionospheric turbulence, the degree of solar wind heating, the densitites of the light neutral constituents, H, D and He, and the effect on the dayside ionosphere of lateral transport of I-I+, D+ and He+ towards the nightside, which will have to be supplied by future measurement. BANKS,P. (1970). Private communication. BANKS, P. and AWORD, I. (1970).Nature, Land. 225, 924. BANKS, P. M. (1966). Annls Geophys 22,577. BANKS, P. M. (1967).J. geophys. Res. 72,3365. BARNES,A. (1966). Physics Fkiids 9,1483. BARTH, C. A., WALLKE,L. and PEARCE, J. B. (1968).J. geophys. Res. 73,254l. BAIJER,S. J., ~TL& R. E. and HERMAN,J. R. (1970). NutHre, f;ond. 225,533. BIONDI,M. A. (1964). An&s Geophys. 20,34. DALGARNO,A. and ALLISON,A. (1969). J. geophys. Res. 74,4178. DALOARO,A. (1969). Can. J. Chem. 47,1723. DESSLER,A. J. (1968). Atmospheres of Mars and Venus (Ed. J. C. Brandt and
M. B. McElroy), p. 241.
Gordon & Breach, New York. DOLGINOV,S. S., YEROSHENKO, E. G. and Zmzaov, L. N. Kosmich. 1968. Issled. 6,561. FJELDBO,G. and E~HLEMAN,V. R. (1969). Ra&o Sci. 4,879. HA=, R. R. and PIXEL=, A. V. (1967). Phys. Rev. 158,70. HASTFB,J. B. (1964).Physics of Atomic Collisions. Butterworth, London. HENRY, R. J. W. and MCELROY, M. B. (1968). Atmospheres of Mars and Venus (Ed. J. C. Brandt and M.
B. McElroy), p. 251.
J. R. and CHANDRA,S. (1969). Planet. Space Sci. 17,815. J. R. and CIUNDRA, S. (1969). Planet. Spuce Sci. 17,1247. HINTEREGGER, H., -L, L. and SCHMIDTKS, 0. (1965). Space Reseurch V, p. 1175. HIR%HFELR~R,J. O., Chms, C. F. and BIRD,R. B. (1954). Mo~ec~iar Theory of Gases and Ligti&. Wiley, HERMAN, HERMAN,
New York. Hoc~sn~, A. R. (1969). Kinetic Processes in Gases and Plasmas.
Academic Press, New York. JOHNSON,F.S. (1968). J. atmos. Sci. 25,658. KNUDSEN,W. C. and ANDERSON,A. D. (1969). J. geophys. Res. 74,5629. KURT, V. G., ~VALQW, S. B. and SHEFFER, E. K, (1969). The Venus Atmosphere (Ed. R. Jastrow and S. I. Rasool). p. 477. Gordon & Breach, New York. L~ONTOVICEX, M. A. (1964). Reviews of P&ma Physics, Vol. 1. Consultan&Bureau, New York.
Mariner Stanford Group (1967).Science158,1678. MCDANIEL,E. (1964). Co&ion Phenomenon in Zonized Gases. Wiley, New York. MCELROY,M. B. and HUNTEN,D. M. (1969). J. geophys. Res. 74,172O. MCELROY,M. B. (1967). Astrophys. J. 150,1125. PAULSON,J. F. (1964). Annls Geophys. 20,7S. SPRE~R, J. R. SUMMERS, A. L. and RIZZI, A. W. (1970). Planet. Space Sci. 18,128l.
APPENDIX The heat transport equations for the electrons, ions, and neutral gases are of the form
N, = density (cm-s),j = 1, 2,3,4,5, is &I, [CO,], @,I, [He], [HI, [D] k = Boltmann’s constant (ergs/%), C, = specific heat, Tf = temperature of speciesj, K, = thermal conductivity, Qj8 = solar heat production (ergs cm4 set-l), Q,9 = energetic particle heat production (ergs cm-s set-3, L,, = coefficient of the rate of energy exchange between gases, z = altitude (cm), t = time (set)
For the electron gas: Tb/2
K, = 1.8 x 10-beA
1 + 3.2 x lo4 g
z [email protected]
,, e 3
N, = density ofjth neutral species (cm-3), cr,!,?= ionization cross section for wavelength A (Hinteregger et al., 1965), cjj’ = absorption cross section for wavelength A (Hinteregger et al., 1965), sA = heating efficiency at altitude z, $A = solar EUV flux (cm-2 [email protected]
) (Hinteregger et al., 1965), x = solar zenith angle, e = electron charge, Ei = energy of incoming energetic ion (ergs), mi = mass (gm). &E,, z) = flux of incoming energetic ions (cm-2 set-l)
x‘d/Te+dt 2 60
= erf (X,)
Energy loss from electrons to neutrals L,, = 1.602 x lo-l2 n,(T, - T,) (l-77 x lo-l9 * N,(l -
1.21 x 104T,,)T,
+ 2.9 x 10-14N,T,-1’2 + 3 x 10-1aN2(1 - 4.8 x 10dT,‘2) + 5.8 x 10-14N2T;1’2 + 1.8 x lo-lbN3(1 + 4.3 x lOAT,) + 1.72 x 10-14N3T#-*‘2 + 2.46 x 10-17N4T;‘2 + 9.63 x lo--l6 N,(l + 4.82 x lo-r6N,(l
- 1.35 x 104Te)T,1’2
+ I.37 x lo-“N,exp + 6.43 x 10q(Te
1.35 x 104T,)T,1’2
(Banks, 1966; Dalgarno, 1969; McDaniel, 1964; Hake and Phelps, 1967). Energy Iossfrom electrons to ions Lez = 8.2 x lo-l9 n,nz(T, -
Tz)/(AzTf’2) In A =4,&
J. R. HERMAN,
R. E. HARnE
and S. J. BAUER
corresponding to the ionic species Na+, CO$, Hz+, He+, H+, D+, respectively. cases of interest 15 I In A I 20. ; UT,
- TJ = L,
+ z: &I. I
Zen gases. Only the light ions are assumed to have temperatures significantly different from the neutral gas temperature T,. KI = 7.37 x 1O-s T;‘2A~1’2
Qrs = 0 QrP = 2rre4 n, 2 -k (Ei) E 1nA. J j
Energy loss from He+ to neutral gases La,, = n,(T, -
T,) [l-21 x 10-26N,(T,
+ 5.78 x 10-28N, + 6.47 x 10-25N2
+ 1.28 x 10-25N, + 1.09 x 10-25N, + 1.17 x lo-s5N,] (Banks, 1967; McDaniel, 1964; Hasted, 1964). Energy loss from H+ to neutral gases L,,
= n,(T, - T,) [4078 x 10-2aN,(T5 + T,J’12 + 2.59 x 10-2sN, + 2.04 x 10-26N2
+ 1.41 x lo-=N,
+ 4.65 x 10-asN1 + 1.28 x 10-2sN6]
(Banks, 1967; McDaniel, 1964; Hasted, 1964). & = 5.35 x 10-16E P 6 = rate of heat exchange between ions 4 (He+) and 5(H+). ; L*G
- T,) = 4n + S,.z - L,.
Deuterium, D+, is assumed to have its temperature between T, and T,. This causes little error since T4 is close to T6 at all altitudes. Neutral gase$. All the neutral gases are assumed to have a common temperature T,,. 5 FY, = 8=1
Ji = 236, F, = 209, F3 = 1880, F4 = 875, F5 = 2080, Fs = 1470. (Hirschfelder,
and Bird, 1954)
Radiative energy loss from neutral gas L,, = 2.52 x 10-a2N2 2
- 82.8 Tn-l13 I
K = K&ray9 the coefficient of eddy diffusion. D,=
$!?-’ [ j b,j1
(McElroy and Hunten, 1966)
3 b,, = 8aij a, = -2
= thermal diffusion coefficient for H only. (McElroy and Hunten, 1969).
u 15= 3(Oi + ej) or = 3.68 x 1O-s,
CT2= 4.0 x 10-s,
cr* = 3 x 10-s,
CT,= 1.06 x 1O-s,
a, = 1.06 x 10”
v,,(z) = N,(z,,) G (z,,,)/N,(z) Vsb(zssC)= Jeans escape velocity for species s.
6.056 x 10s 2 g(z) = 877 6.056 x 108 + z
F JL(T, - TA = La, - 7
The momentum and continuity equations have the general form
api m,n,g + einiE - 2 Kij(Vi aZ
Because of the presence of the Venus plasmapause at an altitude of 500 km acting as a cap on the ionosphere, the vertical flow velocities are likely to be small. Specifically, for v, - V, < lo4 cm/set the Venus ionosphere can be well represented by the static equations (Vi ‘v 0) for the light ions.
minig + e,n,E = 0
J. R. HERMAN,
R. E. HARTLE and S. J. BAUER
and n, = 2
n, (charge neutrality)
Pi = n,kT,. The heavier ions, CO$ and Nz+ are assumed to be in photo-chemical throughout their region of importance. Nz+ + COz ki
kl = 9 x lo--lo
k, = 343 x lo-’
k, = 2.9 x lo-’
N, + CO,+
(Hinteregger et al. 1965). (Henry and McElroy, 1968).
Reactions with the light species The following table summarizes the charge transfer cross sections and electron recombination cross sections used in this work. A+B+-+A++B+hE Ionization potential
* (Hockstim, 1969) t k = 2se&&
k (cm-” see-l)
Hf He+ co*+ WZ+
0 10991 0.193 1.981
2.70(-9) 2*14(-9) 1*93(-9) 1*94(-9)
H+ He+ co*+ N*+
-10.991 0 - 10.798 -9.010
H” H H He He He He
:za co: CQ
-0.193 10.798 0 1.788
N8 N1 N* N*
H+ He+ co*+ N*+
-1.981 9.010 -1.788 0
e e e e
Hf He+ co+ N*+
13.595 24.586 13.788 15.576
Calc talc Calc
0 0 5*6(-11) 1*2(-9) 1*3(-9) 9*05(-10) 0 1*5(Dg) 5.(-12) q-12) 3*8(-7) 2.8( -7)
talc* Paulson (1963) Banks (1970) Calct Paulson (1963)
Biondi (1963) Biondi (1963) McElroy (1969) Biondi (1963)