Jovian ionospheric models

IcJmus

20, 200-212 (1973)

Jovian Ionospheric Models L. A. C A P O N E AND S. S. P R A S A D

Department of Physics and Astronomy University of ~'lorida, Gainesville 32601 R c c e i v e d N o v e m b e r 16, 1972; revised May 4, 1973 This p a p e r r e p o r t s rcsults o b t a i n e d on ionosphere f o r m a t i o n in t h e J o v i a n u p p e r a t m o s p h e r e with special reference to seine of t h e r e c e n t l y available reaction rates, a n d to recent modcls o f t h e J o v i a n n e u t r a l a t m o s p h e r e based on t h e possibility o f a w a r m c r m c s o p a u s e . W e find t h a t t h e role o f t h e h y p o t h c t i c a l r a d i a t i v e association o f 14 + to H 2 to form Ha +, as b r o u g h t to light in our earlier s t u d y , is still i m p o r t a n t , even with a reaction rate as low as 10-1Scnt3sec-t. In t h e lower regions o f t h e ionosphere t h r e e - b o d y processes leading to t h e f o r m a t i o n of l t z + and H s + ions, which h a v e very flint dissociative r e c o m b i n a t i o n rates, p r o d u c e u d r a m a t i c r e d u c t i o n in t h e electron d e n s i t y . W h e n no r a d i a t i v e association t a k e s place, a n d t h e H + ions are lost by r a d i a t i v e r e c o m b i n a t i o n alone, we confirm t h a t t h e p h o t o c h e m i c a l e q n i l i b r i u m profile is also t h e diffusive equilibrium profile. H o w e v e r , w i t h collisional-ra(tiativc r e c o m b i n a t i o n , whose rate becomes a l t i t u d e d e p e n d e n t , diffusion t e n d s to [)ring a b o u t some rcdistriburion of the ionization. Inclusion of r a d i a t i v e association e n h a n c e s t h e role of diffusion. I n this case, diffusion brings a b o u t all t h c cxt)ected changes. I n particular, t h e ttifferetmes in t h e electr(m d e n s i t y profile, originated in t h e lower-middle ionosphere by r a d i a t i v e association, are p r o p a g a t e d up to all higher a l t i t u d e s by diffusion. T h e r a t e c o n s t a n t of r a d i a t i v e association is, however, u n k n o w n . ] t is h o p e d t h a t the, critical i m p o r t a n c e of this reaction for the J o v i a n ionospher(, will be an incentive t o w a r d s a careful l a b o r a t o r y d(~termination of its r a t e (:oefficien|. I n the older models o f t h e J o v m n ionosphere the m a j o r ions were H + which were lost only by pure radiative r e c o m b i n a t i o n . This led to high clcctrt)n densities and practically no diurnal change. In contr~ust, our new models h a v e relatively mttch stnaller electron densities, especially in lower regions, a n d m a y be susceptible to significant d i u r n a l variation. INTRODUCTION

In the past twclve years or so, there have been several studies of the Jovian ionosphcre: by Zheleznyakov (1958), Rishbeth (1959), Zabriskic (1960), Gross ant| Rasool (1964), Hen r y and 3'lcElroy (1969), Shimizu (1971), and Prasad anti Caponc (197 I). Some of these studies were ofi~hoots of the researches pertaining to the structure of the neutral atmosphere, whilc others were stimulated by the discovery of" the Jovian radio emissions. Ionosphcric conductivitics as well as day to night changes in the ionosphere enter as parameters in the models for the role e r i e in the stimulation of the radio emission (Goldrcich and Lyden-Bel}, 1969). Photochemical equiCopyright ,(~ 1973 by AcademicPress, Inc. All rightsof reproductionin any form reserved. Printed in Great Britain

200

librium was assumed by all authors, although it was always realized t hat the influence of diffusion could be important. This tendency of ignoring details in the model studies referred to above, may be ascribed to the lack of observational data. Thc situation with respect to the amount and variety of observational data is expected to improve in the near future due to the combined efforts of NASA's Pioneer F/G fly-by missions and ground- as well as OAO spacecraft-based radio and optical observations. Therefore, it seems worthwhile to give some more thought to the Jovian ionospheric formation. This has been one motivation behind this paper, ill which we discuss models for the Jovian ionosphere in relation to plasma diffusion

JOVIAN IONOSPHERIC MODELS

effects and the degree of solar activity. Almost all of the previous modeling of the ionosphere utilized the "cold mesopause" model for the neutral atmosphere. Recently, however, it has been realized t h a t there may be a temperature inversion in the Jovian stratosphere. This would result in a considerably warmer mesopause and higher molecular hydrogen densities in the ionospheric region. This situation would enhance the role of all three-body association processes resulting in the formation of H3 + and H5 + ions (Prasad and Capone, 1971). Also, the radiative association of H + ions with H 2, which is already quite important even in the "cold mesopause" condition may be more important in the "warm mcsopause" models. Recent laboratory determinations of the rate coefficient of dissociative recombinations of H3 ~ and H5 ~ ions (Lew et al., 1973) have vicldcd large values. This eouhl result in a considerable decrease in the electron densities. These considerations constituted another incentive for the present studies. THE MODEL NEUTRAL ATMOSPHERE

The structure of any planetary ionosphere is vcry much dependent upon the nature of the neutral atmosphere. For the purpose of our study, therefore, we need to know the neutral atmosphere of Jupiter. But this knowledge is currently in a very uncertain stage. The thermal structure of the atmosphere above the cloud top is still a matter of debate. According to a study by Trafton (1967), the temperature decreases from a value of 158°K at the cloud top to 95°K in the mesosphere where it is constant. In this study, the infrared opacity was assumed to be due, mainly, to the pressure-broadened H: lines. In a more recent study Hogan et al. (1969) considered the contributions of CH4 and NH 3 to the infrared opacity. Their radiativeconvective computations yielded results favorable to the temperature inversion theory suggested from the observed infrared (Gillet et al., 1969), and microwave (Wrixon and Welch, 1970) brightness temperatures. In this case the atmospheric temperature in the mesosphere may reach

201

more than 140°K. This "warm mesopause," with Tm¢~ = 140°K, has been the basis of a few model neutral atmospheres constructed by Shimizu (1971 ). Similarly uncertain is the state of our knowledge about the helium and molecular hydrogen relative abundances. The ionospheric studies are not greatly dependent upon the exact value of this relative abundance, so long as the H z is the most abundant, and its number density is known fairly reliably. But knowledge of the altitude profile of atomic hydrogen is quite important. Unfortunately, this knowledge is shrouded with uncertainty due to ignorance about the appropriate valuc of the eddy diffusion coefficient. Recently, Hunten (1969) estimated this coefficient to be 5 × 106cm2/see by fitting the integrated number of hydrogen atoms above the mesopausc to that obtained from the UV airglow measurements by Moos el al. (1969). But this conclusion may not be unique. Shimizu (1971) has discussed this point more fully and has ascribed this lack of uniqueness to primarily two causes: Firstly, the hydrogen amount above the mesopause depends seriously on the uncertain temperature distribution. Secondly, the airglow spectrum used by Hunten (1969) had a strange feature at 1310~. This presents some problem, as pointed out by Wallace (1969). Consequently, the altitude profile of the atomic hydrogen is still quite uncertain. Since the ionospheric structure is dependent upon the atomic hydrogen profile, the above uncertainty propagates into the ionospheric models also. In situations such as these, the sensible way to make progress is the one in which models are constructed corresponding to the various possible values of the atmospheric parameters. In this spirit, we have adopted two main atmospheric models: a "cold mcsopause" model in which Tm¢~o= 95°K, and a "warm mesopause" model with Tmcso .... 140°K. The H 2 density at the mesopausc was taken as 2.9 × l()Zacm-3. The altitude distribution of atomic hydrogen was taken from the calculations of Huntcn (1969) for the "cold mesopause" and Shimizu (1971) for the "warm mcso-

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Fr~. 1. Models for t h e a t o m i c h y d r o g e n d i s t r i b u t i o n a n d t h e n e u t r a l t e m p e r a t u r e in t h e u p p e r a t m o s p h ( ' r e o f J upiter. T h e left h a l f of t h e figure d e p i c t s lho n u m b e r d e n s i t i e s of t h e a t o m i c hydrogerl for t h e "cold m e s o p a u s e " (eurw~ 1), a n d " w a r m m e s o p a u s e " (curves 2---5) c o n d i t i o n s . T h e n u m b e r s 0 or 106 by t h e side of each c u r v e in(tick,re t h e e(tdy (liffusion eoeffi(,ients used in o b t a i n i n g l h e m . Similarly, J : : 1 an(l J = 3 i n d i c a t e t h e level of flux. T h e r i g h t h a l f of t h e figure gives t h e n e u t r a l t e m p e r a t u r e profile for t h e " c o l d " ((:urve a), a n d " w a r m " (curves b a n d c) me.sopause eon(titions. T h c sour(:t,s ()f t h e s e figures arc H u n t t , n (1969) a n d S h i m i z u (1971).

pause." We have used their profiles approl)riatc to the value of the eddy d i f fusion coefficient equal to zero and l06 cm2/sec. In the "warm mesopause" case, two levels of solar activity were considered. In the lower level the assumed solar fluxes were the same as those given by Hinteregger et al. (1965) for solar minimum. The other level, the level of maximum activity, was obtained by multiplying these Hintcrcggcr et al. (1965) fluxes by a factor of 3. This arbitrary procedure was adopted hecause we had a neutral atmospheric model available from the calculations of Shimizu (1971). The hydrogen atom distribution, adopted in our present study is shown in Fig. 1 together with the temperature distribution. Following Shimizu (1971), the two levels of solar activity will bc henceforth labeled by J : l, and J =: 3, respectively. THE FORMATION OF THE IONOSPItERE To study the tbrmation of the J o v i a n ionosphere, one has to first consider ion

production by absorption of the XUV solar radiation in the neutral atmosphere. After its ibrmation by the photoionization, an ion may become neutralized by various recombination processes. Alternatively, it may change its identity through ion-atom or ion-molecule reactions. It may be noted t hat a chemical reaction, such as the reaction (a) in Table I, may be a loss p r o c e s s f o r one ion and a source for another. As the altitude incrcascs, the neutral number density decreases and the lifetime of an ion against destruction by chemical reactions becomes increasingly larger. When plasma transport is neglected, the equilibrium number density of a given ion is determined by the competition between the production and loss processes. The assumption of this photochemical equilibrium, or in other words the neglect of the plasma transport, is justified whenever the chemical reaction time constant is small compared with the time constant involved in the process responsible for the transport. This situation is expected to prevail in the lower, denser regions of the

203

J O V I A N I O N O S P H E R I C MODELS

TABLE I IONIC REACTIONS

Process Chargetransfiw and ion molecule reactions

(a) (b) (c) (d) (e) (f)

(g) (h) (i) (j) (k) Recombination

Reaction Rate (cm a see- l )

Reaction He + + H 2 -> Hz + + He He + -~-H 2 -> H e l l + {- H H2 + -~ H 2 -> Ha + ~- H Ha + -~ H -~ H + - H2 H2 + ÷ He -+ HcH + + H H + = 1-[2 -> H3 + -k- hu He + + H 2 -:.- I-ieH2 + -.- }Iv H3 + + H 2 + H 2 -~- Hs + + H2 H + + H 2 + H 2 --> Ha + + H 2 He + + H2 ~ H + -!- H + He H e l l + + H2 -> Ha + + He

(1) H2 + + e (m) H e l l + + (n) He + + c (o) ]13 + ~- e

~ H -~ H e -÷ He + H --> Hc ÷ ]iv -> H2 ~ ]1

(p) H + - e

->H-"

(q) H + H

• M->H2+M

1.0(--13) 1.0(-13) 2.9(-09) 1.0(-10) 1.0(-13) 0, 1 . 0 ( - 1 5 )

1.0( 15) 6.0(-29)cm6sec -1 3.2(- 29)em6sec -t 1.0(-13) 3.5(-- i l ) 1.0(-07) 1.0(-07) 6.25(- 12) 3.:1(-07)

hv

(r) Hell2 + + e -~ He - H2 (s) H~ + -: e -+ Neutrals

3.0(-32) era6 see -1 4.0(-07) 3.6(--06)

Sources of the ratesa

Gross and Rasool (1964) Gross and Ra.sool (1964) Estimated Estimated Estimated

Estimated Estimated Hunten (1969) Lew et al. (1973) Bates and Kingston (1965) Estimate(t Lew et al. (1973)

° Unless otherwise indicated the rates arc from McDaniel et al. (1970). ionosphere. I n the upper ionosphere, therefore, the photochemical e q u i l i b r i u m is n o l o n g e r v a l i d , a n d t h e c o m p u t a t i o n o f e q u i l i b r i u m n u m b e r (tensitics of t h e ions m u s t take into a c c o u n t the divergence of t h e fluxes. W e shall d i s c u s s these p o i n t s in ,the following subsections.

Absorption of the Solar X U V Production Rates

and Ion

T h e t e c h n i q u e of c o m p u t i n g t h e solar XUV absorption and the consequent p h o t o i o n i z a t i o n r a t e s is n o w a v a i l a b l e in n u m e r o u s o r i g i n a l p a p e r s a n d t e x t s (e.g., ~ i c o l e t a n d Swider, 1963) in c o n n e c t i o n w i t h t h e t e r r e s t r i a l i o n o s p h e r e . T h e s e are r e a d i l y a d a p t e d for t h e J o v i a n a t l n o s p h e r e . For a given model atmosphere the comput a t i o n s r e q u i r e a k n o w l e d g e of" t h e r e l e v a n t solar fluxes a n d t h e a b s o r p t i o n a n d i o n i z a t i o n cross sections. W e used t h e e s t i m a t e s o f fluxes i n t h e v a r i o u s (62) w a v e l e n g t h b a n d s a n d lines as g i v e n b y H i n t e r e g g e r et al. (1965), a f t e r s c a l i n g t h e m d o w n b y a

f a c t o r of 1/27 to t a k e i n t o a c c o u n t t h e larger S u n - t o - J u p i t e r d i s t a n c e a n d a f a c t o r of l / 2 to t a k e a n a v e r a g e o v e r o n e r o t a t i o n ( d a y - t o - n i g h t change). T h e r e h a v e b e e n some r e c e n t m e a s u r e m e n t s o f t h e solar X U V flux ( H i n t e r e g g c r , 1970), b u t t h e r e are d o u b t s a b o u t t h e i r v a l i d i t y ( R o b l e a n d I ) i c k i n s o n , 1973). P a r t l y for this r e a s o n , a n d p a r t l y for r e t a i n i n g c o n s i s t e n c y w i t h the neutral models constructed by Shimizu (1971 ), we h a v e used t h e o l d e r ( [ f i n ~ r e g g e r et al., 1965) e s t i m a t e s of t h e solar X U V fluxes. T h e a b s o r p t i o n a n d i o n i z a t i o n cross s e c t i o n s were t a k e n from a n u m b e r o f s o u r c e s : Cook a n d M e t z g e t (1964) for H2, S t e w a r t a n d W e b b (1963) for He, a n d M a r r (1967) for H. I o n i z a t i o n of" m e t h a n e a n d a m m o n i a was i g n o r e d . T h e s o l a r Z e n i t h a n g l e used was 60 °.

The Ionic Reactions T h e r e a c t i o n s c o n s i d e r e d in this work are listed in T a b l e I. Most o f these [(a-c) a n d (l-o)] were from t h e p r e v i o u s w o r k o f

204

CAPONE AND ]'RASAD

Gross an(l Rasool (1964). The additional features t h a t have been introduced consist, tirstly, in considering the loss of H" and H e ions through radiative ass<)ciatioll (suggested also by Dalgarno, see H u n t e n , 1969).

H " + H 2 --+ H3 * + hr.

(1)

The implication of this radiative association process was examine(1 in some detail b y Prasad and Capone (1971), in the c o n t e x t of the ibrmation of the J o v i a n ionosphere. The rate constant of this reaction is not known. In their study, therefore, Prasad and Capone (1971 ) used various plausible rates. For a rate coefficient as low as 10-J3cm3/sec, the effect of this process was found to be quite significant. In the present, study, we have adopted an even more conservative estimate fi)r this rate coefficient, viz. 10 -j5 cm3/sec, since prirna facie this process could be slow. The neutral density in the lower ionosphere is quite h i g h . . H e n c e , following our earlier work (Prasad and Caponc, 1971) we have also include(1 the ibrmation of the heavier H3 ~ and Hs + ions by the t h r e e - b o d y association process. F o r the t h r e e - b o d y a t t a c h m e n t of H to H 2 resulting in the formation of H3 +, we used the rate coefficient as determined by Miller et al. (1968). B u t for the H5 + formation b y the a t t a c h m e n t of H3 + to H2, we had to a d o p t estimated rate coefficients. Electrons and positive ions m a y unite by collisional-radiative recombination. This is a complex process tending to pure radiative recombination in the low plasma density-limit, and to pure collisional recombination in the high plasma densitylimit (Bates and Dalgarno, 1962). In all previous studies of the J o v i a n ionosphere only the pure radiative recombination was taken into account. However, the collisional-radiative recombination becomes quite i m p o r t a n t for even tenuous plasmas ( n p ~ 103 or 104cm -3) if the t e m p e r a t u r e is low (Bates and Kingston, 1965). Since the t e m p e r a t u r e s in the J o v i a n ionosphere are h)w ( T < 250°K), it appeared proper to include the collisionalradiative recombination also. The coefficient for collisional-radiative recombin-

ation depen
(R, -+- R~ + R, + Rl)n(Hz)--~- R,n(e)

(2)

n ( H 2 +) =

q(H: +) + R . n ( H e + ) n ( H 2 ) R~n(H 2) + Ban(H) + Ren(He) + B l n(e

(a) n(H +) _: q ( H - ) - - - R a n ( H z - ) n ( H ) t Rjn(He+)n(H:)

Ri n(Hz) z + Rf-n(H2) + Rv-n-(e)

(4) n ( H e H +) = R b n ( H e - ) n ( H z ) - R,.n(H 2 ')n(He) --Rkn(H2) + R.,n(c)

(5)

n(H 3') =

Rcn(H2+)n(Hz) + R~n(H+)n(H2) 2 + R ~ n ( H + ) n ( H 2 ) + Rkn(HeH~)n(H2) Rhn(H2) 2 -t Ri, n(e )

(6) n ( H e H 2 +)

Rgn(He+)n(H2)

.....

~ r n ( e ) ....

(7)

n(Hs +) - Rhn(H3')n(Hz) 2 R~n(e) . . . .

(8)

In the a b o v e equations, n(X) represents the n u m b e r density o f the ionic or neutral species X, R, is the rate coefficient of reaction (n) in Table I and q(X) the photoionization production rate of the ions m e n t i o n e d in the parentheses. These equations are readily solved by a n y standard numerical method. The N e w t o n - R a p h s o n m e t h o d was found to be easily adaptable for this purpose, giving an economical (computer-timewise) solution.

JOVIAN I()NOSPIIER1C MODELS

Inclusion of Plasma Transport

As pointed out earlier, at higher altitudes the lifetime of an ion against destruction b y chemical reactions or recombinations becomes large. At these altitudes the contribution to the production or loss by net m o v e m e n t of the ionization in and out of a given e l e m e n t a r y volume under consideration m a y become important. The cquilibrium n u m b e r density, therefore, will t)e governed b y thc following c o n t i n u i t y equation, appropriate for a horizontally stratified ionosphere,

0 (n~v~)

Onj

(9)

~t = % - / ~ -- ~z where: qi, li, v j, and n j are, rcspcctivcly, the i)roduction rate, loss rate, vertical t r a n s p o r t velocity, and the equilibrium n u m b e r density of the j t h ion. In our case we have two ions ( j = 1,2); namely, H + and H3 +. In the absence of a n y detailed knowledge a b o u t the electric fields, or the neutral winds at the J o v i a n ionospheric heights, we have assumed t h a t the transport vclocity vj is due entirely to the plasma diffusion process. Under this assumption, the vertical c o m p o n e n t of the t r a n s p o r t velocity for the j t h ion is given b y (Stubbe, 1970) sin 2 I

V 1 = _ ~;

J_~ Vii f t J l l

;~

0~

" +~;~

0~

j +m~g

(lO)

where 1 is the dip angle; vjr, the collision f r e q u e n c y of the j t h ion with the lth neutral species ; tx~, the ion-neutral reduced mass, T,, and Ti; the electron and ion t e m p e r a t u r e ; m j, the mass of the j t h ion; g, the acceleration due to g r a v i t y and n~ and nj the n u m b e r densities. The summation extends over all of the neutrals. The collision frequencies were t a k e n from recent studies b y Banks (1966). T h e y are, I/H+,H

=

1.9 × 1 0 - ' 2 n ( H ) % / ~

[ 1 4 . 4 - 1.15 log~oX/2T] 2

(11)

Vn+, H2 = 2 . 8 8 × 10 -9 n ( H z )

(12)

205

VH3+.jf = 2.46 X 10-gn(H)

(13)

Vn3-.n z = 2.15 × 10-gn(Hz)

(14)

If" the radiative a t t a c h m e n t of H " to H 2 is ignored, then the J o v i a n upper ionosphere, where only the diffusion is important, consists entirely of protons. We then have only one ion, and the expression tor the diffusion velocity simplifies to - 2 s i n 2 1 [l

0

] J

(15) In the general case, when the radiative association is i m p o r t a n t , we have two ions to consider, and two simultaneous secondorder differential equations have to bc solved. The lmmerical analysis problem thus posed is of common occurrcnce, and various methods, as discusscd in m a n y t e x t books on numerical analysis, are available to solve it. We adoptcd a t i m e - d e p e n d e n t apI)roach towards the equilibrium densities; the full c o n t i n u i t y equations were solved till On/~t became exceedingly small. An implicit Crank-Nicholson m e t h o d was used. The b o u n d a r y conditions were: (a) photochemical equilibrium at the lowest level, and (b) diffusive equilibrium at the upper boundary. A coarse grid of 8km in altitude and 60see in time was used to start the procedure. The final results from this were inputs into a n o t h e r calculation where the altitude and time grids were 4kin and 15scc, respectively. This saved c o m p u t a t i o n time without sacrificing accuracy. I t soon became obvious t h a t the simultaneous solution of both the H + and H 3" ion continuity equations was unnecessary. In the region where the H 3 ~ ion is important, its (lensity changes v e r y little b y the inclusion of the t r a n s p o r t term. The H ~ ion becomes i m p o r t a n t in the region where diffusion is dominant. B u t in this altitude range the H 3" n u m b e r density decreases progressively. Hence, the H + profile remains mostly unaffected by the slight diffusive redistribution in the H 3 ~ profile. Our computations indicated t h a t so far as the H + ion profile is concerned, it is a d e q u a t e to hold the H~ + ion density

206

CAPOI~E A N D I'RASAD

profile fixed at its photochemical equilibrium value. However, it is very importa n t to keep the terms belonging to both the ions in the expression for the diffusion velocity of the H - ion. This is so, because in the region where H - ion diffusion starts to become i m p o r t a n t , this ion is still a minor ion. F o r a correct description of its diffusion velocity, the terms belonging to the Hs + ion m u s t be retained, irrespective of the fact t h a t the H34 ion density is held fixed at its photochemical cquilibrium value. Most of our diffusive equilibrium profiles have been c o m p u t e d on this basis.

this, in as much as we have c o n s t r u c t e d diurnal average model ionospheres for the region of the J o v i a n globe lying at the foot of the magnetic tube of force connecting J u p i t e r to its satellite Io. We shall discuss our results in various steps. Lct us first consider the results pertaining to the lower regions, up to a b o u t 400kin, where photochemical equilibrium is a valid assumption. Let us first consider the effect of the t h r e e - b o d y reactions (h) and (i). To simplify the considerations, we m a y set R f , the rate coefficient of radiative association of H ~ to H,, as zero, an(l compare the results obtained with and w i t h o u t the t h r e e - b o d y processes. The results obtained are shown in Fig. 2 for the ease of " w a r m mesopause" and h)wer solar activity. I t is obvious t h a t the t h r e e - b o d y association of H- and Hs + ions to H , resulting in the formation of H 3 ~ and Hs ~ ions is quite d o m i n a n t in the lower ionosphere. The very lower ionosi)here is d o m i n a t e d by hcavier ions. F u r t h e r m o r e , the electron densities are considerably reduce(l in these regions because of the

R.ESULTS AND DISCUSSIONS I n all the previous studies, only J o v i a n global average ionospheric models were presented. This was achieved arbitrarily b u t conveniently, by cutting down the solar radiation b y a factor of 1/2 to take into a c c o u n t the d a y - n i g h t average and a n o t h e r factor of 1/2 to achieve the global average. Our present stu(ty departs from 800

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D-_-NSII Y (cm-3) Fro. 2. Altitude profile of photochemical equilibrium densities of H + and Ha + ions in the case of "warm mesopause" and low solar activity (d == 1) and eddy diffusion eoeftieient K = I 0~'. The curves belonging to the various species are, labeled. The flHl lines ( .... ) represent lh(, ease when no threebody attachments are allowed to take place. The dashed curves (.... ) represent the (.t~e when I hreebody attachments with H 2 result in 113+ and Hs + ions. No radiative association of 11+ to ~H2 wtm allowed in either ease.

207

J O V I A N I O N O S P H E R I C I~IODELS 800

E y.

700

WARM MESOPAUSE

v

03 600

J =5

o

K= 106

2,~

.._1 (D 5 0 0 LLI

> © pn < L~ d~

L

40o

3oo

D F200

_J ,,, lOglo I

. . . . . . . . . . . . . .

~o 2

,

,o 3

......

;,,

,o 4

....

. .... ,

,o5

.......

~o6

DENSITY (cm -3) Fx(;. 3. A l t i t u d e p r o f i l e s o f e l e c t r o n d e n s i t y . F u l l l i n e s ( ) for p u r e r a d i a t i v e r e c o m b i n a t i o n , a n d d a s h e d l i n e s (. . . . . . ) f o r c o l l i s i o n a l - r a d i a t i v e r e c o m b i n a t i o n . N o r a d i a t i v e a s s o c i a t i o n w a s allowed.

rapid dissociative recombination of the heavier ions. Next, in Fig. 3 we have shown the effect of collisional-radiative recombination. As pointed out earlier, the rate coefficient is altitude d e p e n d e n t t h r o u g h the local electron density. So the e x t e n t of the modifying effect is also altitude dependent. At high altitudes the plasma density is so low t h a t the collisional-radiative recombination attains the limiting value of the pure radiative recombination. In these regions, therefore, inclusion of collisional-radiative recombination does not produce a n y change in the n~(z) profile. In the vicinity of the peak electron density, however, the collisional effects do produce a reduction in the electron density b y a factor of 1.5. At altitudcs below a b o u t 400km, again, the electron densities obt~ined with or w i t h o u t collisional effects are the same. B u t this effect is due to the prcponderencc of the t h r e e - b o d y loss mechanism in these lower altitude regions. I n t r o d u c t i o n of radiative association of H + to H 2 to form H3 +, even with a rate coefficient of 10-15cm3sec -~ produces interesting changes in the ionospheric structure. Firstly, the region which in the

absence of radiative association was the region of maxim u m electron density suffers a great reduction in the electron concentration. The altitude of the m a x i m u m electron density, therefore, moves very high up. This prominence of the H3 ~ ions continues up to greater altitudes. The heights at which H~ ~ and H~ ions are both 50% of the total density are respectively 330, 520, and 330kin in the three mo(lels considered here. These featurcs are clearly seen in the Figs 4, 5 and 6, where we have plotted the H ÷ and H3 + densities in photochemical equilibrium with v,~rious neutral atmospheric models. The reduction in the electron density is seen to be larger for higher level of solar activity. This is readily understood in terms of higher molecular hydrogen densities at an), given altitude as wc go from colder to the w a r m e r mcsopause, and from low to high solar activity. As the altitude increases, the importance of the radiativc associa.tion decreases progressively duc to the decrease in the molecular hydrogen n u m b e r density. So at the higher levels of photochemical equilibrium electron densities are the same with or without the radiative association. I f the radiative association of H + with

CAPONE

208

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I

''':'1

AND

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'

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I

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; I Ill

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1

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500

1

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1 I

7

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.u

H

fe

I T I;,,, I ','0 z

0 r

.03 2/z_.NS

104 " Y

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si

F r o . 4. A l t i t u d e p r o f i l e s (,f t h e e q u i l i b r i u m t t +, H 3 + i o n s a n d e l e c t r o n d e n s i t i e s p e r c i n 3, in t h e e a s e o f t h e " c o l d m e s o p a u s c " c o n d i t i o n s w i t h low s o l a r a c t i v i t y ( J = 1) a n d e d d y d i f f u s i o n c o e f f i c i e n t /~ = 10 6. T h e c u r v e s b e l o n g i n g t o t h e v a r i o u s s p e c i e s a r e l a b e l e d . ])a.~hed l i n e s (. . . . ) a n d full l i n e s ( - - - - . ) p e r t a i n t o r a d iativ(, a s s o c i a t i o n r a t e c o e f f i c i e n t s (]~s) o f 10-~s a n d 0 e m s s e e -1 r e s p e c t i v e l y .

tt 2 resulting in the formation of H3 + is ignored, then in the upper regions, where diffusion alone can be important, H ~ ions are lost by radiative recombination only. 800

l

I

::ill;

I

I

....

Rf = 10-~5

- -

Rf:O

I

il

;i

This is a very slow loss process. At first glance, therefore the effect of plasma transport by diffusion may be thought to be important in this case. In actuality, I

I

i ii

i

I

,

illll,

i

, ::~

l

i ,i

WARM MESOPAUSE

700 d=;

K = 106

600

g 500

400

300

H

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200 I00

i

i0 ~

I

'1

, [

102

i

'

i

,

; I!I::'

IO 3

i

104

I

105

i06

DENSITY (cm "3)

F r o . 5. A l t i t u d e profiles o f e q u i l i b r i u m ]-I +, H a + i o n s a n d e l e c t r o n d e n s i t i e s p e r c m 3, in t h e c a s e o f " w a r m m e s o p a u s e " c o n d i t i o n s w i t h low s o l a r a c t i v i t y (J = 1) a n d e d d y d i f f u s i o n c o e f f i c i e n t K = 106. T i l e c u r v e s b e l o n g i n g t o t h e v a r i o u s s p e c i c s a r e l a b e l e d . D a s h e d l i n e s (......... ) a n d flfll l i n e s (- ---) p e r t a i n t o r a d i a t i v e a . s s o c i a t i o n r a t e eoefl3eients (Ry) o f 10 -~5 a n d 0 e m 3 s e c -~, r e s p e c t i v e l y .

JOVIAN

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I

J

IONOSPHERIC

t It~tt~

- . . . . Rf -- i(J 5 ----,Rf--O

.... E70°

I

t

209

MODELS

t ittro:

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I

WARM M E S O P A U S E J--5 K =10 ~

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t

I llJl

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.

.

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.

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1 Iltltl[

lO s

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I I trill]

I IO s

I I III 10e

D E N S I T Y (cm 3 )

FIe. 6. Altitude profiles of equilibrium H +, Hs + ions and electron densities per cm s, in the e~meof "warm mesopause" with high (J = 3) solar activity and eddy diffusion coefficient K = 106.The curved belonging to the various species are labeled. Dashed lines (. . . . ) and full lines ( ) pertain to radiative association rate coefficients (R/) of l0 -is and 0cmSsec -1, respectively. however, allowance for the plasma diffusion did not produce a n y changes in the electron density distribution. This results from the fact t h a t in the region where diffusion is i m p o r t a n t , the photochemical distribution has already a scale height which is twice the scale height of the I-Iion, provided t)ure radiative recombination is the only loss process. In the case of thermal equilibrium, which of course prevails in the J o v i a n ionosphere ( H e n r y and McElroy, 1969; P r a s a d and Capone, 1971), a scale height of this magnitude would also bc the scale height for plasma distribution in diffusive equilibrium. Hence, allowing for plasma diffusion (lid not pro(iuce any additional change over the photochemical equilibrium profile obtained with altitude independent pure radiative recombination. With collisional-ra(liative recombination, however, the situation is slightly different. Inclusion of diffusion I)roduccs slight redistribution of the ionization, as ean be seen from our Fig. 7. The situation changes considerably when the radiative association of H ~ with H 2 is allowed to proceed. The plasma diffusion

does produce significant change in the H ÷ density distribution. However, as already explained above (in the section Inclusion of Plasma Transport), the effect of plasma diffusion was negligible in the case of the Hs + ion distribution. On the H + ion density profile the diffusion had several effects. These can be seen in Fig. 7. The peak of the distribution was b r o u g h t down b y several kilometers. R o u g h l y speaking, the new" peak is situated at a level where the loss due to diffusion is comparable to t h a t due to chemical reactions. This is analogous to the situation in the terrestrial ionosphere. The t ~ a k electron density is also reduced slightly. At the higher altitudes, the plasma diffusion produced a general reduction in the densities. In the lower region, a general increase was b r o u g h t about. Such a change is the manifestation of the fact t h a t plasma diffusion transported the ionization from the highcr region to the lower region. All other factors equal, the plasma diffusion effect starts at a lower altitude, and is more pronounced if the atmospheric t e m p e r a t u r e s are lower. H a v i n g discussed the relative roles of the various processes t h a t control the

210

CAPONE A N D PI~ASAD

8OO

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.

i,

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" PHOTOCHEMICAL E 7oo

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DIFFUSIVE

,

i

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I

i

,

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LIJ > 0qq 400

J=l

,

,111

i

i

i

,,

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WARM MESOPAUSE

500

o

i

EQUILIBRIUM ", ..~-~,,~ Rf : I 0 -15

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i

EQUILIBRIUM

K

I =O

6 O~

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f

Ld 30( i-1~20( <:[ iOCloi

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,

, , , , , , I

~o2

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,

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r

t,,Itll

DENSITY

~o4

t

I

Jt

....

J

jo s

. . . . . . .

~o6

(cm -3)

Fro. 7. H + ion density profiles for the ease of " w a r m mesopause" and high ( J - 3) solar activity. B o t h the photochemical and diffusive equilibrium distributions are shown for 1¢s = 0 and ] 0 - I s c n P s e e -l. F o r the H+-e recombination eollisionM-radiative reeombinati(m was used. Tim solid lines ( - - - ) and the dashed lines (. . . . ) represent the photochemical and diffusive equilibrmm, respectively.

Jovian ionosI)here, we now present in Fig. 8 our model J o v i a n ionospheres, correspon(ling to the various neutral atmospheric models and the reaction rates listed in Table I. Since the plasma diffusion 800,

•

,

,

• ,i

,

.

,

,.

• ,

. . . . . . . .

i

,

has been taken into account, these models should be valid up to high Mtitudes. Intercomt)arison of the electron density p r o f i l e s in p u r e p h o t o c h e m i c a l e q u i l i b r i u m ( F i g s . 4 - 6 ) a n d in d i f f u s i v e e q u i l i b r i u m

.....

,

. . . . . .

(a) COLD MESOPAUSE

i

....

.,,.

. . . . .

(b) WARM MESOPAUSE

i

:

,

\ ,~

70£

U3

© L)

5Oq

,i >

0 40C ~C <% LJ 30C !-

7_ aoc

.-----'"

--

Rf = 0

/

15

fO. . . . . . . I OCIc

2

:

iO 3

iO 4

iO 5

iO 2

i

iO 3

i

i

,,,.,,i

. . . . i O 4.

,,

:1 iO 5

10 6

DENSITY (cm -3) 1,'Iu. 8. E l e c t r o n density profiles obtained when all the reactions of Table 1, and diflkrsion arc allowed to operate. Two pairs of curves have been shown fi~r the " w a r m mesopause" e,mdition. The pairs m a r k e d 1 and 2 belong t.o low solar activity. The remaining pair is fi~r high solar a c t i v i t y . In each pair the dashed (. . . . . ) and fllll () lines represent R s = 10 -~s and 0creSset -1, respectively.

JOVIAN IO.NOSPHERIC MODELS

(Fig. 8) is quite instructive. In pure photochemical equilibrium, the electron densities for the two cases, with or without radiative association, merge together above some altitude depending upon the model. With diffusion taking place, however, such is not the case. The (tifferences in the electron density profiles, originated in the lower regions by the radiative association, are propag~tte(l up to all the higher altitudes. The consideration of diffusion, as introduced in this present study, therefore, accentuatcs thc conclusions about the role of the radiative association process as reached in the earlier stu(ly of Prasad and Capone (1971 ).

(30.'~CLUDINO REMARKS W e r e e m p h a s i z e t h e fact t h a t t h e r a t c coefficients of t h e r a d i a t i v e or t h r e e - b o d y a s s o c i a t i o n s (f a n d h in T a b l e I), whose roles h a v e b e e n s h o w n to be of i m p o r t a n c e , are u n k n o w n . T h e r a t e s a d o p t e d in t h i s s t u d y were s i m p l y p b m s i b l e guesses. I t is hoI)cd t h a t t h e i r i m p o r t a n c e in t h e J o v i a n i o n o s p h e r i c f o r m a t i o n , as b r o u g h t to l i g h t b y thin stu(ty, will be a n i n c e n t i v e tbr t h e theoretical and laboratory atomic physicists a n d c h e m i s t s to shed some d e f i n i t i v e light on these reactions. T h c t h r e e - b o d y a s s o c i a t i o n proccsscs r e s u l t i n g in h e a v i e r H s ) a n d H5 ~ ions w i t h v e r y thst d i s s o c i a t i v e r e c o m b i n a t i o n prod u c e s d r a s t i c r e d u c t i o n s in t h e lower ionosI)heric e l e c t r o n (tensities. T h i s m a y h a v e i m p o r t a n t bearing upon the expected values of the ionospheric conductivities w h i c h e n t e r i n t o t h e t h e o r y o f I o aN u n i polar i n d u c t o r (Gohlreich a n d Lyn(tenBell, 1969). F u r t h e r m o r e , o u r n e w e r ionos p h e r i c m<)dels m a y he s u b j e c t to large (lay to night wu'iation. This wouht produce d i u r n a l c h a n g e in t h e i o n o s p h e r i c cond u e t i v i t i e s , which is o f some i m p o r t ~ m c e in t h e n a t u r e of t h e J o v i a n d e c a m e t r i c b u r s t s ( G o h l r e i c h a n d L y n d e n - B e l l , 1969).

ACKNOWLEDGM ENTS It is ~t ph,asure to thank Professor A. E. S. Green for his kind continued interest in this

211

study, Professor M. A. Biondi fi)r the rates of dissociativc recombination used in this study, and Profcssor A. Dalg~rno for his comlnents. This research has been supported by the National Aeronautics and Space Administration through its grant NGL- 10-005-008. I~EFERENCES BA:X'KS, P. (1966). Collision fi'equencies and energy transfi'r ions. l'lanetNpaceNci. 14, 1105. BATES, 1). H., AND ])AL(IAENO, A. (1962). Electron l/ecolubination. In "Atomic and Molecular Processes" (D. R. Bates, ed.), p. 245. Ac~demic Press, New York. BATES, D. R., AND KINGSTON, A. E. (1965). "Collisional-radiativc recombination". Preprint. GILLET, F. C., Lo~,v, F. d., AND STI'HN, '~V. A. (1969). Tltc 2.8-14/zm spect rum of Jupiter. Astrophy,'. J . 157, 925. GOLI)ICEICH, P., AND LVNI)EN-BEI,T,, D. (1969). 1o, ~ ,h)vian unipolar inductor. Astrophys. g. 165, 621. (~'OOK, G. 1~,., AND ~IETzGER, l). 1t. (1964). Photoionizt~tion and absorption cross sections of H 2 and D 2 in the vacuum nltr~violet region. J . Opt. Noc. A mer. 54, 968. GItOSS, S. H., aND RASOOL, S. i. (1964). The upper atmosphere of Jupiter. Icarus 3, 311. HENRY, [4. ,1., ,aND McEL~oY, M. B. (1969). Tile absorption of extreme ultraviolet solar ra(liation by Jupiter's upper ~tmosplwre. J. A trees. Nci. 26, 912. HI NTERECf'ER, -]-1. U., HAl,l,, L. z~k., AND SCIIMIDTKE. G. (1965). Solar XUV radiation and neutral particle distribution in ,hlly 1963 thermosphere. Npace Res. 5, 1175. I-[INTERE(:GEI¢, H. E. (1970). Tile extreme ultraviolet solar spectru,n and its variation during a solar cycle. A n n . (/eophys. 26, 547554. HOGAN, J., I~.ASOOL, S. I.. AN-D ENt'REN'EZ. T. (1969). The thermal structure of the ,lovian atmosphere. J . ,4tmon. ,%'ci. 26, 898. HU~Z'I'E.~,D. hi. (1969). The upper atmosphere of Jupiter. J. Alines. ,~'ci. 26, 827. Li.:w, M. T., BIONDt, 3[. A., A.','D .JOItNSON, Px. Dissociative recoml)inatioll of Its + ions, to be pllblished. MAI¢R, G. (1967). "Photoioniza! ion Processes in Gases." Acatlemic Press. New Y(Jrk. 5'I('I)A.~.'[EL,E. "~V., (:ERMAK, V.. DAl.(;Att.~.'O,i . . FER(;VSON, E. E., AND FRIE1)I~AN, a. (1970). "lon-Moh,cuh, Reactions." a,Viley-hlt erscience. New York. 5'[II.I,ER, T. ,'~1., ~IOSnl,Y, ,]. T., .~[AR'rIN, l). ~,¥., ANl) MCDANIl.:l,, E. ~,V. (1968). Reactions ofH +

212

CAPONE A N D P R A S A D

ill H 2 a n d D + in D2; mobilit.ies of h y d r o g e n a n d alkali ions ira H 2 a n d I)2. Phys. Rev. 173, 115. MOON, 1-[. ~V., FASTIE, ~V. G., AND BOTTEMA, M. (1969). R o c k e t m e a s u r e m e n t (if u l t r a v i o l e t s p e c t r a (if V e n u s a n d J u p i t e r b e t w e e n 1200 a n d 1800,-~. Astrophys. J. 155, 887. NICOLI=:T, M., AND SWIDER, ~¥. (1963). I o n o spheric c(indit ions. Planet. ,b'pace Nci. 11, 1459. ])nASAD, S. S., Axo CAPONE, L. A. (1971). T h e , h i v i a n i(inosph('re: c o m p o s i t i o n a n d t e m p e r a t m'es. Icarus 15, 45. RIsHm.:'t'~, H . (1959). T h e i o n o s p h e r e of J u p i t e r . Austral. J. Phys. 12. t/OnLE, t t . (;., A.,4r) DICKL~-SON, 1~. E. (1973). Is t h e r e e n o u g h u l t r a v i o l e t r~utiation to m a i n t a i n t h e ghibal m e a n t e m p e r a t u r e ? J. Geophy*'. Ices. 78, 249. SnIl~nzt:, M. (197]). T h c u p p e r a l m o s p h c r e of ,lupit(~r. Icar~s 14, 273. STE'~VAR'r, i . I,., AND ~VEBB, T. (~. (1963).

P h o t o i o n i z a t i o n o f h e l m m anti ionized l i t h i u m . Proc. Phys. Soc. 82, 532. STUBBI':, P . (1970). S i m u l t a n e o u s s o l u t i o n of t h e tim(' d e p e n d e n t coupled c o n t i n u i t y e q u a t i o n s , h e a t c o n d u c t i o n e q u a t i o n s , a n d e q u a t i o n s of m o t i o n for a s y s t e m consisting of a n e u t r a l gas, Sill ehmtron gas, S),II(IIt follr COlllpOn(,nt ion gas. d. Atmos. Terr. Phys. 32, 865. TI~AFTO.~, L. M. (1967). Model a t m o s p h e r e s of t h e m a j o r p l a n e t s . Astrophys. d. 147, 765. WALLAC}:, L. (1969). AnMysis of t h e L y m a n A l p h a o b s e r v a t i o n s of V e n u s m a d e from M a r i n e r 5. J. Geophys. ICes. 74, 115. %VurxoN, O. T., Axr) WELt,n, ~V. ,I. (1970). T h e millim(,tcr w a v e s p e c t r u m of S a t u r n . Icarus 13, 16:1. ZAm~rsK;~;, F. 11. (1960). D i s s e r t a t i o n , P r i n c e t o n University. ZUT,:L~:ZXYAKOV, V. V. (1958). On t h e the(iry of S p o r a d i c radio cmission from J u p i t e r . No~,'. Astron. A J . 2, 206.