The atmosphere of Io

ICARUS 29, 493--502 (1976)

The Atmosphere of Io S. H. G R O S S A:ND G. V. R A M A N A T H A N

Polytechnic Institute of New York, Route 110, Farmingdale, New York 11735 Received April 19, 1975; revised December 18, 1975 Observations of Io suggest that it may have an atmosphere in which sodium vapor, ammonia, and nitrogen are important constituents. Several atmospheric models consisting of these gases are treated here. These are tested as a function of total content against the Pioneer l0 observations and for stability against escape. The results suggest that the atmosphere is very tenuous and ~hat the interpretation of the ionosphere detected by Pioneer 10 by a static model may be inconsistent with the sodium cloud observations. It is postulated that ionization may also be escaping and that sodium may be comparable in content in the atmosphere with some molecular constituent such as NH3 or N 2. Sodium and this molecular component then dominate the atmosphere. It is also suggested that particle precipitation contributes to heating of the atmosphere and to the production of ionization; furthermore, the difference between day- and nighttime ionospheres and possible trailing and leading side effects may relate to the nature of the particle energy distributions. These distributions may be the l~sult of the peculiar interaction of Io with the Jovian magnetosphere. There is now evidence t h a t I o has some sort of an atmosphere. Pioneer 10 f o u n d it to have an ionosphere (Kliore et al., 1974) a n d detected a toroidal cloud of a t o m i c h y d r o g e n at its orbital radius a b o u t J u p i t e r (Carlson a n d J u d g e , 1974). E x t r a polation from the d a y t i m e ionospheric m e a s u r e m e n t indicates a v e r y thin atmosphere with a surface particle d e n s i t y between l0 t° a n d 1012 cm -3. G r o u n d observations have also detected an extended region of excited sodium a t o m s a b o u t it (Brown a n d Chaffee, 1974; T r a f t o n et al., 1974; Bergstralh et al., 1975). No constituents other t h a n sodium a n d h y d r o g e n have been detected as yet. Nevertheless, there is some belief t h a t its surface m a y be p a r t l y covered b y ice (Morrison a n d Cruikshank, 1974), which could provide v a p o r s to the atmosphere. Post-eclipse brightening has been observed on some occasions, a p h e n o m e n o n t h a t m a y be connected with the freezing a n d e v a p o r a t i o n of constituents, specifically a m m o n i a (Sinton, 1973). I o is also situated in the J o v i a n m a g n e t o sphere, and a dip in the flux of high e n e r g y particles at its orbital radius has been Copyright © 1976 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain

493

observed b y Pioneer 10 (Simpson et al., 1974), most likely implying the loss of such particles to the satellite. I t is also connected with decametric radio emission from J u p i t e r as observed from the E a r t h . U n d o u b t e d l y , all these various observations concerning I o are related in some fashion and a n y s t u d y of its a t m o s p h e r e m u s t necessarily consider them. M c E l r o y a n d Y u n g (1975) t r e a t several models for I o ' s atmosphere. Their models are purposely simple, consisting of N H 3, N2, or N a as main constituents. T h e y assume models with c o n s t a n t t e m p e r a t u r e s a n d neglect p h o t o c h e m i s t r y . Models are also p o s t u l a t e d b y others to explain sodium D line emission (Macy a n d Trafton, 1975a, b). I n t e r p r e t a t i o n of this emission led these a u t h o r s to postulate t h a t the sodium column c o n t e n t is of the order of 10 ~3 cm -2 and t h a t the surface sodium flux is ~107 cm -2 sec -~, with a sodium density of the order of 104 cm -3 at the base of the exosphere. Atmospheric temperatures, based on the observations, are deduced to be of the order of 500 to 1000°K. However, all of these n u m b e r s are still considered to be quite uncertain.

494

GROSS A ~ D R A M A ~ A T H A N

Here, we also t r eat several models using NH 3, N2, and Na as the main constituents. Of interest are the temperature profiles and the stability of the atmospheric models as a function of the total atmospheric content. Also included is altitudevarying gravitational acceleration which is essential in stability studies. The models are tested with respect to the Pioneer l0 daytime occultation measurement, particularly the scale height above the peak. However, since Pioneer l0 also measured the nighttime ionospheric profile (Kliore et al., 1975), we consider the possible relationship of these models to t h a t measurement. Simple models are assumed, each consisting of one main constituent; photochemical products and interactions are neglected. Though such models are a considerable simplification of what. is undoubtedly far more complex, their study still provides insight into major effects that, would dominate more precise models, at least for the neutral atmosphere. In view of the paucity of information on Io's atmosphere, it would appear t h a t such studies are essential prior to attacking more complex models. The stability of atmospheres about bodies with small gravitational pull is also of interest.. The Galilean satellites are unique for such considerations. Their locations within Jupiter's magnetosphere, and their proximity to Jupiter and the influence of its gravitational pull, make t h em even more unique. The studies described here are also usefnl in this respect. The various models are taken to be

sufficiently tenuous t h a t t hey may be treated as thermospheres. Consideration is given to heating by both solar UV and high energy magnetospheric particles. Gross (1975) has shown t h a t the surfaces of Io and the other Galilean satellites are warmer than t hey should be if t hey are heated only by the Sun's radiation. An additional heat source is required, and the most likely candidate is the high energy particles from the Jovian magnetosphere. I f such be the case, it would be difficult, to explain why these particles also do not contribute to the heating and ionizing of Io's atmosphere. These matters are discussed further. PHYSICAL

MEASUREMENTS ]~ONOSPHERE

AND

THE

The physical parameters of Io used in these studies are given in Table I. Table II contains the main parameters of [o's ionosphere as measured by Pioneer 1o. Measured infrared temperatures are given in Table I I I together with the blackbody and the equilibrium temperatures based on the Bond albedo suggested by Morrison and Cruikshank (1974). The occultation experiment's daytime measurement was for a region of the atmosphere and a time where the solar zenith angle was 81 °. The surface temperature for this region may be less than the infrared temperatures of Table III. Here, 100°K is arbitrarily used. The same temperature is used throughout the calculations for convenience, even though the actual values are not known. Any other appropriate value will not

TABLE

I

PI-I~'SICAL CHARACTERISTICS OF ~O Radius a

Massb Densityb Surface gravitational acceleration Orbit radius about Jupiter" Period of revolutiona a Morrison and Cruikshank (1974). b Anderson et al. (1974).

1820kin 9 × 102Sg 3.5gcm -a 181.2cmsec -2 4.21 × 10Skm 1.769days

495

THE ATMOSPHERE OF ~ 0

TABLE II IONOSPHERIC PARAMETERS FROM PIONEER 10

H e i g h t of i o n o s p h e r i c p e a k a b o v e surface Peak electron density E l e c t r o n d e n s i t y scale h e i g h t a b o v e p e a k M e a s u r e d e x t e n t of i o n o s p h e r e Z e n i t h a n g l e a t p o i n t of o c c u l t a t i o n

Dayside

Nightside

60-100 k m 6 × l04 e l / c m 3 220km a 750 k m 81°

50 k m 9 x 103 e l / c m a 60 k m 250 k m

T h i s scale h e i g h t is t h e figure q u o t e d in K l i o r e et al. (1974). I n K l i o r e et al. (1975) its v a l u e is c h a n g e d to 186 km.

TABLE III TEMPERATURES 8.0-8.8/~m t e m p e r a t u r e 10.0-12.0/~m t e m p e r a t u r o 17.0-28/~m t e m p e r a t u r e B l a c k b o d y t e m p e r a t u r e (slowly r o t a t i n g b o d y ) Phase integral Geometric albedo E q u i l i b r i u m t e m p e r a t u r e (slowly r o t a t i n g b o d y ) ( b a s e d o n a b o n d a l b e d o = 0.6)

151 ± 3°K ° 141 ± 3°K a 128 ± 5°K a 145°K 1 ± 0.3 b 0.62 ± 0.13 a II6°K

a V a l u e s listed b y M o r r i s o n a n d C r u i k s h a n k (1974). b M o r r i s o n (1973).

significantly affect the principal conclusions. ATMOSPHERIC CONSTITUENTS

Though others have suggested NH3, N2, and Na as constituents for Io's atmosphere, it is well to review the underlying arguments. I t is useful to consider only atmospheric constituents which relate in some way to sodium, although others may be present in various proportions. In this sense, N H 3 is an excellent solvent, and a solution of Na in NH 3 has very high electrical conductivity, possibly providing a source for triggering decametric radio emissions by the cyclotron mechanism of Piddington and Drake (1968) and Goldreich and Lynden-Bell (1969). Sodium, locked in solution in frozen NH3, m a y be released steadily to the atmosphere as a result of

sputtering by particle bombardment of the surface (Matson et al., 1974), which also heats the surface and excites sodium atoms, causing emission. NH 3 and Na, then, may be principal constituents of Io's atmosphere. Sinton (1973) has also suggested NH3, to explain post-eclipse brightening and the observed difference between 10 and 20 /~m radiation. He requires the atmosphere to have a temperature of 245°K, making it much warmer than the surface. Although ammonia would be frozen for the temperatures listed in Table I l I , its vapor pressure at these temperatures would still be sufficient to accommodate the Pioneer 10 results (for example, ~10 -s bars at llS°K, 10 -6 bars at 127°K). Either low temperatures < l 1 5 ° K or higher temperatures with less than saturation conditions would be consistent with the spectroscopic upper limit for the NH 3 vapor content of 0.5 cm-

496

GROSS A~TD RAMANATHAN

a m a g a t (Fink et al., 1973). T h e lower v a p o r pressure of h y d r a t e d a m m o n i a for the s a m e t e m p e r a t u r e s would also be sufficient. A m m o n i a photolysis suggests full dissociation of a m m o n i a b y solar U V to f o r m N2 a n d H 2 (Okabe a n d Lenzi, 1967; Anderson, 1968). Possible processes are shown in T a b l e IV. S e c o n d a r y products, such as N H , NH2, a n d hydrazine, are formed. T h e processes r e f o r m i n g N H 3 are limited a n d d e p e n d on the a b u n d a n c e of hydrogen. I n c o n t r a s t w i t h J u p i t e r , hydrogen, once formed, should r a p i d l y escape (Gross, 1974), leaving an a t m o s p h e r e m o s t l y of N 2 w i t h some N H 3 close to the surface. E x c i t e d N 2 m a y also excite N a (McElroy et al., 1974). T h e relationships b e t w e e n Na, N H 3, a n d N 2 a n d t h e e x p e r i m e n t a l observations, t h e n , lead to the consideration of the ibllowing three models: one t o t a l l y of N H 3, disregarding its dissociation, a second e n t i r e l y of N 2, a n d a third of Na. The neglect of dissociation of N H 3 m a y not be as serious a l i m i t a t i o n as m a y be expected, since diffusion m a y d i s t r i b u t e more N H 3 to higher altitudes t h a n would be t r u e for a chemical equilibrimn distribution. At:

higher altitudes, other p r o d u c t uents would d o m i n a t e .

SCALE H E I G H T AT A Z E N I T H A N G L E OF 81 °

W e t e s t the a t m o s p h e r i c models ~br 81 ° zenith angle conditions against Pioneer 10 d a y t i m e occultation d a t a as given in T a b l e I I , in p a r t i c u l a r the n e u t r a l scale height in t h e ionosphere relative to the p l a s m a scale height a b o v e t h e ionospheric peak. A s s m n i n g ion a n d n e u t r a l to be the s a m e species, the n e u t r a l scale height is h a l f t h e p l a s m a scale height if local t h e r m o d y n a m i c equilibrium applies. I f not, t h e n the n e u t r a l scale height is smaller t h a n onehalf t h e p l a s m a scale height, assu m i n t t h a t t h e electrons are h o t t e r t h a n the ions and t h a t t h e ion t e m p e r a t u r e is close to t h a t of t h e n e u t r a l particle t e m p e r a t u r e , i f the electron t e m p e r a t u r e is twice the ion a n d n e u t r a l t e m p e r a t u r e s , the n e u t r a l scale height is one-third of the p l a s m a scale height. W e t a k e the n e u t r a l scale height in the ionosphere to be b e t w e e n one-third a n d one-half t h e value for t h e p l a s m a [220 kin, according to Kliore et al., (1974)], so t h a t we seek a t m o s p h e r i c models with

TABLE IV PttOTODISSOCIATION OF AMI~ON[A

Primary dissociation NH3 hv > H + N H 2 hv > H 2 + N H hv > H + H + N H J

NH 2

hv > H +

A > 1600A t

NH

Secondary reactions formation of H2 and N2 NH2 + NH2 -~ NzH4 H + N2H, -~ H2 + NzH3 --> I ~ H 3 + NH2 NH2 + NzH, --> NH3 + NzH3 2N2Ha

-* N 2 H 4 -}- N2 + H2

NH a + NH H + NH3 H+H+M

--> ~ 2 -->

< 1600A < 2800A formation of hydrazine predominates ) destruction of less likely ) hydrazine

~- 2H2 ~'~2 -~-NH2

-+ H 2 + M

Reformation of ammonia Nz + 3Hz > 2NH 3 NH2 av > NH2(/~2AI) NH2 (~-2A1) + H2 > NH3 + H

constit-

requires heat or energy for the activation energy 4300-9000 A

THE ATMOSPHERE O]~ Io scale heights between about 75 and 110 km for a zenith angle of 81 °. [In Kliore et al. (1975) the plasma scale height is revised in value and quoted as 186 km. One-third to one-half this value would be 62 to 93 km instead of 75 to 110 kin. Here we use the higher values for judging the various atmospheres. The differences are not imp o r t a n t in view of the uncertainties in the measurements, the lack of fuller information, and the coarseness of the assumed models.] Smaller scale heights are still conceivable for hotter electrons, and some regard must be given to this possibility. The neutral particle scale heights at the altitudes where the neutral density is l0 s and 109 cm -3 are compared against this criterion. These neutral particle densities are appropriate for the region above the peak of the ionosphere. Suitable models are found by varying total content, or, equivalently, surface particle density. Computation of the neutral scale height requires the temperature and density profiles of each model. The atmospheres are thin and resemble thermospheres. The profiles are found by solving the thermal conductivity equation for a zenith angle of 81°:

dz ~ dz ]

(1) where K = thermal conductivity, approxim ated as A T s for each gas (see Table VI), T is the temperature, z the altitude, E the efficiency of heating (two values are used: 0.3 and 0.5), n(z) the number density, a(2) the absorption cross section of the gas to UV, ¢~(2) the solar flux per unit wavelength at the top of the atmosphere, A the wavelength ; 21 and 22 are the sensible wavelength limits for UV heating, and r(~, z) is the optical thickness = S~° a(~)n (z) dz. Infrared cooling due to atmospheric radiation is neglected in this expression. I t is regarded as unimportant, either because the constituent does not radiate or because the atmosphere is too thin to radiate much energy. A hydrostatic distribution with both temperature and gravi-

497

rational acceleration t h a t vary with altitude is used for calculating n(z), since there is only one main constituent in a model and mean mass motion is neglected. Solar ultraviolet flux at 1 AU is taken from Hinteregger (1970) for wavelengths below 1300 A and from Ackerman (1971) for longer wavelengths. These fluxes are scaled to Io's (Jupiter's) distance from the Sun. Absorption cross sections for N 2 and N H 3 are from Sullivan and Holland (1966), and for sodium, from Hudson and Carter (1967, 1968). The maximum wavelength absorbed by each species for heating the medium is given in Table V. Thermal conductivity is approximated by A T s, and the values of A and s for each gas are given in Table VI. The values for N2 and N H 3 are based on a least-squares fit to thermal conductivity data as given in the Purdue

University Thermophysical Properties Research Center Data Book, Volume 2, 1966. The temperature range of the fit is given in the table, as well as the maximum percentage error of the fit, an error which applies primarily at the extremities of this range. The values for sodium vapor are theoretical following the formulation in Chapman and Cowling (1961). Figure 1 is a plot of the neutral scale heights for sodium at two levels above the ionospheric peak. The graph is plotted against surface particle density. The upper pair of curves is for E = 0.5, whereas the lower pair is for 0.3. The lower of the two curves for each effÉciency is for the 109 cm -3 level and the upper is for the 10 s cm -3 level. The allowed range of scale height, 75 to 110 km, is shown as a crosshatched region. The scale heights increase as surface density increases. Where the curves intersect the cross-hatched region, sodium atmospheres fulfill the requirement TABLE V MAXIMUM WAVELENGTHS :FOR U V

Gas

AMax

N2 NH3 Na

796A 2150/~ 2412A

HEATING

498

GROSS A N D

RAMANATI-IAN

TABLE VI THERMAL CONDUCTIVITY Ka ~_ A T *

Gas

A

s

Nz NH3 Na

21.83 0.947 108.09

0.828 1.382 0.5

a Ill e r g s crn - I

scc -1

240

so%

/

2OO 160 F-

,T,

t20 [

i Ld a

80

~ 4c

~" 2 0 0 ~ -

.......",L, ::

O108

149 SURFACE

Maximum error (%)

100-1500°K 200-900°K (theoretical)

3 4

°K-L

based on the scale height m e a s u r e m e n t of the dayside ionosphere b y Pioneer 10. F o r E = 0.5, the surface density lies between 3 and 5 . 5 × 10 t° cm -3. F o r E = 0 . 3 , the range is a b o u t 5 to 9 × 10 ~° cm -3. The same c o m p u t a t i o n s for N 2 yield scale heights which are far less t h a n the 280

Temperature range

iO1-6 IO11 NUMBER DENSITY(crn-3)

-

FI~;. l. ~ ' e u t r a l p a r t i c l e scale h e i g h t v s s u r fact, n u m b e r d e n s i t y f o r a s o d i u m a t m o s p h e r e a b o u t Io. T w o sets of curves are shown, one for a s o l a r U V h e a t i n g efficiency E = 0.3 a n d t h e o t h e r for E = 0,5. T h e l o w e r a n d u p p e r c u r v e s o f e a c h s e t a r e f o r t h e scale h e i g h t s a t t h e h e i g h t w h e r e tile s o d i u m p a r t i c l e m u n b e r d e n s i t y is 10Vcm 3 a n d 10Scm -a, r e s p e c t i v e l y . T h e c r o s s - h a t c h e d a r e a r e p r e s e n t s t h e r a n g e (if n e u t r a l p a r t i c l e scale h e i g h t s a b o v e t h e i o n o s p h e r i c p e a k b a s e d on t h e P i o n e e r 10 o c c u l t a t i o n m e a s u r e m e n t .

required scale height even for surface densities as high as 1014 cm -3. [There is no point in including nitrogen surface densities greater t h a n 1014 cm -3, since such models are unstable against escape, and the height of the ionospheric peak for such models far exceeds the Pioneer l0 observation. F u r t h e r m o r e , such densities are inconsistent with surface densities extrapolated from the Pioneer 10 ionosphere m e a s u r e m e n t , 101° to 1012 cm -3 (Kliore et al., 1974).] McElroy and Y u n g (1975) also n o t e d this problem with nitrogen atmospheres. H o w e v e r , the nitrogen model m u s t reach higher t e m p e r a t u r e s if it is to a t t a i n the required scale height values. Such temperatures would be reached if the absorbed energy flux were increased, as, for example, b y heating b y particles precipitating from the J o v i a n magnetosphere. The e x t e n t of heating depends on the particle energy distribution, which as y e t is not known. I n the absence of this information, it is simpler to take the energy as a fraction. f, of the solar flux below 796 ~ , the maximum wavelength for ionization of N 2 (Table V). Values o f f between 0.1 and 0.5 are arbitrarily chosen, since t h e y seem appropriate. A set of graphs for f = 0.3 for nitrogen and E = 0.3 and 0.5 is shown in Fig. 2. Table V I I is a compilation for the various models of the ranges of surface densities t h a t satisfy the requirements of the P i o n e e r 10 occultation measurement. These ranges are obtained from graphs such as Figs. 1 and 2. Additional energy is inc o r p o r a t e d only for nitrogen models. Sodium and a m m o n i a models do not require additional energy, t h o u g h precipi-

T]tE ATMOSPHERE oF I o

I0

28(2

/

t a r i n g p a r t i c l e s m a y still w a r m t h e s e atmospheres. The corresponding surface d e n s i t i e s w i t h s u c h a d d i t i o n a l e n e r g y flux would h a v e to be lower t h a n those values g i v e n i n T a b l e V I I for t h e s e l a s t t w o cons t i t u e n t s . I n s o m e sense, t h e n i g h t t i m e i o n o s p h e r e m a y b e i n t e r p r e t e d as exh i b i t i n g the c o n t r i b u t i o n of p r e c i p i t a t i n g particles.

240 20C

12C

N 4o

~ 160 I-~

STABILITY

?

~ zoo

AGAINST

ESCAPE

Stability here refers to the onset of dynamic outflow. However, the outflux is computed on the basis of thermal escape. To determine the loss via escape, we determine the distribution of particles and

/

120

499

80

40 I

I

I

I

I

I

8

9

I0

It

12

15

Log n o

FIG, 2. Neutral particle scale heights vs surface number density (cm -3) for a molecular nitrogen atmosphere about Io. The two sets of curves and the cross-hatched areas are as described in the Fig. 1 caption, but for nitrogen. Additional heating above solar UV is represented by the parameter f = 0.3 for these curves (see text).

temperatures averaged over the hemis p h e r e for e a c h m o d e l , t a k i n g i n t o a c c o u n t the variation of gravitational acceleration w i t h a l t i t u d e . T h e loss v i a escape is t h e n determined using the exospheric temp e r a t u r e in the J e a n s escape formula ( J e a n s , 1925). T h e profiles are f o u n d f r o m t h e t h e r m a l c o n d u c t i o n e q u a t i o n (Gross 1972, 1974):

~i

dz] =

--o~en(z)f~itT(~)q~oo(,~)e-r"~'z'dA. (~)

TABLE V I I R A N G E S OF S U R F A C E D E N S I T Y ~O]¢ 8 1 ° ZENITI-I A N G L E AND L I F E T I M E AGAINST E S C A P E

Surface density range (cm -a)

Gas

•

f

Na

.3 .5 .3 .5 .3 .5 .3

0 0 0 0 .1 .1 .2

(5-9) × 101° (3-5.5) × 10 t° (3--8.5) × 109 (2--7) × l09 5 × 1012-1014 3 X 1012--1014 5 X 10H--1013

.5

.2

4 × 1 0 H - - 1 0 la

.3 .5 .3 .5

.3 .3 .4 .4

10H--2 × 1 0 1 2 8 × 10t0--2 X 1 0 1 2 4 X 1010--2 X 1012 4 X 1010--2 × 1012

NH3 N2

Lifetime against escape (years) lOXS-lO9 1014-109 1015--3 × 103 3 × 1010--10 5 × 106-10 5 X 10S--10 5 × 106--10 6 × 105--10 107--100 107--100 3 × 105--30 3 X 105--30

500

GROSS AND RAMANATHAN

E q u a t i o n (2) differs from (1) b y the introduction of the constant a which approximates the effects of rotation. H e r e it takes the value ½ for the hemisphere. E q u a t i o n (2) does not contain the see 81 ° modifying the optical thickness, because the formulation is for an average over the sunlit hemisphere. E q u a t i o n (2) is used for sodium and ammonia. The energy i n p u t for nitrogen is a u g m e n t e d b y including heating b y precipitation as well. P r e c i p i t a t i o n would be present e v e r y w h e r e a b o u t Io, u n d o u b t e d l y distributed nonuniformly. Such additional heating would also affect sodium or a m m o n i a atmospheres, l t s inclusion for nitrogen is based solely upon the scale height comparisons ibr the 81 ° solar zenith angle calculations. The J e a n s escape flux, F¢, from the base of the exosphere is given b y

Fe = rrReZn¢ (v} (1 + x)e -x,

(3)

where Re is the radius from the center of the satellite to the base of the exosphere, n¢ is the base density, .!v} is the m e a n t h e r m a l velocity at the base (8kT¢/=m) 1/2. T~ is the exospheric t e m p e r a t u r e , m is the escaping particle's mass, x :-R¢/H¢, and He is the scale height at the base of the exosphere. This outflux is applicable as long as R ¢ / H ¢ > I . 5 (Gross 1972, 1974).

W h e n R~/H~ < 1.5, loss is b y d y n a m i c outflow and the h y d r o s t a t i c distribution is invalid. The base of the exosphere is t a k e n as the level where the scale height He is equal to the m e a n free p a t h l = 1/(~/'2 rrnJZ). H e r e d is the molecular diameter. F r o m this equality ncH¢ = l/(~/2rrdZ), and, for d ~ 1.5 TT ~ 1 ~,,1 5 . The level where neH~ a , ncUe 10 ~5 is found from the c o m p u t e d profiles and the escape flux F~ is calculated from (3). A time t,o escape, r, m a y be defined as r .... 4rrR2sn~H~/F¢, (4) where Rs is the radius at the surface and n~ and H~ are the surface density and scale height, respectively, r is normally considered to be a lower limit for the escape time because of flow limitations arising fi'om diffusion. Here, however, we are concerned with the loss of the main constituent, and r would be more representative of the loss time. I f r is significantly less t h a n the age of the solar system, 4.5 × 10 9 years, we t a k e the constituent to be unstable against escape. Figures 3 and 4 contain profiles tbr sodium for all efficiency of 0.3, the first for the t e m p e r a t u r e and the second for the density. E a c h curve is labeled with it,s surt~ce density. The t e m p e r a t u r e profiles To

4000

5xlO II

SODIUM E =05

5200 I

E 240C

0 i I01t

~- 160C

80C

800

1600 24100 TEMPERATURE (°K)

3200

40100

F r o . 3. T e m p e r a t , u r e p r o f i l e s f o r s o d i u m a t m o s p h e r e s a,b o u t It) f o r d i f f e r e n t s u r f a c e n u m b e r d e n s i t i e s as g i v e n b y tile n u m b e r n e x t t o e a c h c u r v e . T h e s e p r o f i l e s are f o r a s o l a r U V h e a t i n g efficiency e = 0.3,

THE ATMOSPHERE OF I o

501

][o SODIUM

400(

=0.3

320( SxlO II

240C

1600

ION

t -

9

I010

7xlOlO

0 L

5

6

7

8

9

I0

il

Log n o

FIG. 4. N u m b e r d e n s i t y profiles for s o d i u m a t m o s p h e r e s a b o u t Io for • = 0.3 for v a r i o u s surface n u m b e r d e n s i t i e s as g i v e n b y t h e n u m b e r n e x t to e a c h curve. T h e s e d e n s i t y profiles c o r r e s p o n d t o t h e t e m p e r a t u r e profiles of Fig. 3. n o is in c m -a.

for surface densities o f 3 × 10 l° and l 0 II cm -3 in Fig. 3 exhibit an a s y m p t o t i c limit, t h e exospheric temperature. The profile for 3 × l 0 ll cm -3 has n o t quite reached its a s y m p t o t e at an altitude o f 3600 k m , t h e t e m p e r a t u r e increasing v e r y s l o w l y w i t h altitude. The profile for 5 × 10 II cm-3 reaches a t e m p e r a t u r e o f 4000°K at a b o u t 3000 k m and is still rapidly increasing at t h a t altitude. Ob-

400C

viously, this last case is highly unstable, the p a r a m e t e r x reaching values less t h a n 1.5; t h a t is, d y n a m i c outflow sets in. The corresponding density profiles in Fig. 4 exhibit s o m e w h a t the same characteristics. Figure 5 is a g r a p h of the t e m p e r a t u r e profiles of a m m o n i a for e = 0.3. The profiles for surface densities below 10 l° cm -3 are well behaved, b u t are unstable, in the

6xlO I0

8xiO I0

I0 II

3 x l O I°

3200

--~

5x]O 9 I0 I0 2400

J_l 1 6 0 0

AMMONIA

<

E: = 0 . 5

80O

0

800

r

I I 24100 1600 TEMPERATURE (°K)

I 3200

FIG. 5. T e m p e r a t u r e profiles o f a m m o n i a a t m o s p h e r e s a b o u t Io for c w i t h its c o r r e s p o n d i n g surface n u m b e r d e n s i t y .

~

----

[ 4000

0.3. E a c h c u r v e is l a b e l l e d

/,o,,

502

GROSS AND RAMA~NATHA1N 4000 l

5200~

1013

s

2800~-

ooo ilo,ol,o,, 2400t/

//

"~109

Io

f=02

0 IIZ,...F---'q I00

I 400

I

Z 700

L

1 IOOO

TEMPERATURE

I

L --A 1300

--J 1600

(~K)

]~'[u. 6. T e m p e r a t u r e p r o f i l e s o f n i t r o g e l l a t m o s p h e r e s a b o u t I o f o r e = 0 . 3 a n d f o r a d d i t i o n a l h e a t i n g above solar UV as represented by the parameter f = 0.2 (see te,xt). Each curve is labelled with its corresponding surface number density. sense of a continually increasing temperat u r e , for s u r f a c e d e n s i t i e s g r e a t e r t h a n 10 'o cm - s . F i g u r e 6 is a g r a p h o f t h e t e m p e r a t u r e profiles for n i t r o g e n f o r e 0.3 with additional heating by particle prec i p i t a t i o n a s specified b y t h e f r a c t i o n . f = 0.2. F o r s u r f a c e d e n s i t i e s as h i g h a s 1012 cm -3, t h e p r o f i l e s a r e well b e h a v e d . F o r s u r f a c e d e n s i t i e s g r e a t e r t h a n l 0 '2 c m -s, i n s t a b i l i t y is e v i d e n t . S i m i l a r p r o -

files m a y be d r a w n for all t h e r e m a i n i n g m o d e l s c o n s i d e r e d here. T h e e s c a p e flux a n d t h e l i f e t i m e r m a y be c a l c u l a t e d w i t h i n f o r m a t i o n as s h o w n in F i g s . 3 t o 6. T h e l i f e t i m e v s s u r f a c e n u m b e r d e n s i t y is p l o t t e d in F i g . 7 for s o d i u m , a m m o n i a , a n d n i t r o g e n ( f = 0, 0.2, a n d 0.3) as m a j o r c o n s t i t u e n t s . F o r all cases in F i g . 7, ~ = 0.3. S i m i l a r r e s u l t s , n o t s h o w n here, a r e o b t a i n e d for t h e o t h e r

IGr-

L r

X

o

#. Io F \

\\\

6k! 41 -

2!

oF

9

I0

II Log n o

12

13

14

FIG. 7. Logarithmic plot of lifetime ~ in years vs surface number density for ammonia sodium and nitrogen atmospheres about Io. All models shown are heated by solar UV with E = 0.3. Three nitrogen curves are shown, one heated only by solar UV, f = 0, and two b y solar UV augmented b y extra energy flux, possibly from precipitating high energy particles in Jupiter's magnetosphere, as represented b y the parameters f = 0.2 and.f = 0.3 (see text), no is in cm -3.

THE ATMOSPHERE OF I o

nitrogen models and for all cases with e = 0.5. I t may be seen t h a t the lifetime varies over a considerable range of values, decreasing very rapidly as surface density increases. For the same surface density, the lifetime of ammonia is smaller by a very large factor t han t h a t for sodium. The lifetime of nitrogen with f = 0.2 is greater th an t h a t of sodium for densities above 10~ 1 cm-3. For surface densities less t h a n l0 ~ cm -3, the lifetime of sodium is greater. This behavior is the result of the additional heat source included in the nitrogen calculations. (For f = 0, the lifetime of N2, as a major constituent, is far greater th an t h a t of sodium as a major, not minor, constituent for all surface densities above 109 cm-3.) The significance of the lifetime data is clear in Table VII, where lifetimes are listed next to the corresponding model. For each model the range of the surface density fulfilling the ionospheric scale height requirement is also given in the table. Although the surface densities arc for a location and for conditions at the point of occultation, we take these densiities as applying over most of Io. The lifetimes given in Table VII are for these densities and are based on calculations for a hemisphere. Figure 7 illustrates the type of curves used to obtain these lifetimes. Surprisingly (in view of the sodium clouds), Table VII[ illustrates t h a t the sodium models are the most stable timewise, against escape, their lifetimes being no lower th an 109 years. The ammonia models are stable, timewise, for the lower limits in their ranges of surface densities. The lowest densities correspond to the lower end of the scale height requirement, 75 km for a two to one electron-to-ion temperature ratio. The lifetimes of the ammonia models are very short at the other end of its surface density range, which corresponds to the l l 0 km scale height requirement for equal electron and ion temperatures. Thus, the density range for ammonia transcends the entire region from stable to unstable models. All the nitrogen models in Table V I I have lifetimes short compared with the age of the solar system. 19"

503

DISCUSSION

It is apparent from Figs. 3 through 6 t h a t an accumulating atmosphere will become unstable once the content, denoted by the surface density in the figures, exceeds certain values as indicated. All of these models are static models. The unstable profiles are for situations which would be more correctly treated by incorporating motion. It should be noted t h a t all models become unstable though still tenuous. F rom Fig. 7 it m ay be seen t h a t just a change in surface density of about onehalf order of magnitude for sodium and ammonia models results in a major shift from a long-lifetime model to a short-lived atmosphere. This change also indicates t h a t the analysis will be more correct if dynamic equations are utilized in place of static equations for media with the higher contents. The same is essentially true for nitrogen models. The uncertainties in the Hinteregger UV fluxes, which may actually be as much as 100% greater t han the flux given by Hinteregger (1970), or as much as 45% (Hinteregger, 1975), do not invalidate these results. The only effect of larger fluxes is to cause the onset of instability to occur for smaller contents, or surface densities, than indicated by the graphs of Figs. 3 to 6. One infers from the large sodium cloud about Io t h a t sodium is not very stable in Io's atmosphere. On the basis of the observations of Bergstralh et al. (1975), it wouhl appear t h a t the cloud is constantly being replenished. Yet, the calculations presented here and summarized in Table VII indicate t h a t a sodium atmosphere is the most stable of the models studied; t h a t is, it has the longest lifetime against escape while meeting the scale height requirement for the dayside ionosphere. Nevertheless, Macy and Trafton (1975a, b) and McElroy and Yung (1975) treat sodium as a minor constituent. They find t h a t a column content ~10 ~3 cm -2 of sodium is required for the D line emission. Furthermore, if sodium were a major constituent, its ionosphere would be entirely different from t h a t observed by

504

GROSS AND R A M A N A T H A N

Pioneer 10, in t h a t its m a x i m u m density would exceed the d a y t i m e m e a s u r e m e n t b y at least an order of magnitude, and the peak would be at or near the surface. The peak would be well above the surface only if the neutral density there is well in excess of 10 j2 cm -3. In addition, recombination of sodium ions is v e r y slow; lo's short lfight (~21 hours) would result in little difference between the peak elect r o n densities at, night and during the day. c o n t r a r y to observation. Maey and Trafton as well as MeElroy and Yung find t h e y are able to support their e s t i m a t e d t h e r m a l escape flux of sodium (~107 cnl-'- see -j) from the base of the exosphere, if it is a minor constituent. T h e y require a density of 104 cm -3 at this level with an exospheric t e m p e r a t u r e s o m e w h a t less t h a n 1000°K, a t e m p e r a t u r e t h a t is in accordance with the D line emission. Ionization is then supplied b y a m a j o r constituent which is p r o b a b l y molecular, such as NH 3 or N2, since sufficiently rapid recombination is required to explain the observed
content and e x t e n t t h a n t h a t of tile sodium clouds. The residence lifetime of such clouds would p r o b a b l y be a b o u t the same order of m a g n i t u d e as for sodium in spite of larger ionization cross sections, because of the lower solar ionization flux of their UV ionization bands. T h o u g h such a loss m a y indeed be tire case, we prefer not to accept it, because it requires a considerable imbalance ill the loss rate of the various species, whieti m a y e v e n t u a l l y lead to the dominance of sodium. P r o v i d e d tire sodium cloud is recent, this reasoning leads to tile conctusion t h a t the present atmosphere is either mostly of sodium or well on its way toward t h a t end, a conclusion t h a t appears c o n t r a r y to deductions from the measurements. In fact, it is hard to envision any other likely gas (CH 4, for example) a n d / o r its products as major constituents, excepting Argon and heavier gases, which would not be lost at rates exceeding t h a t of sodium as a minor constituent. There is a dilemma here; barring large losses of atmospheric constituents at rates far in excess of t h a t of sodium, deductions from analyses of sodium I) line measurements seem to be at odds with the Pioneer 10 ionospheric measurements. One m a y question the obserw~tions, particularly those for the ionosphere for which there are only two profiles, one at day and one at night. Certainly other measurements are essential to clarify these matters. It may also be t h a t the atmosphere alternates between stable and unstable periods with most gases driven off during the latter intervals and with the atmosphere accumulating during the former intervals. Gases emerging from the surface due to p a r t M e b o m b a r d m e n t and sputtering, v a p o r pressure equalization, and a n y other sources would provide the influx to the amassing atmosphere. The ionosphere occurs during the stable period. All evidence, however, seems to preclude such a split behavior. The nearly continual measurements of Bergstralh et al. (1975) and those made a b o u t the time ot' the Pioneer l I) e n c o u n t e r suggest t h a t the ionization measurements occurred under circmnstanees not distinctly different with

TI~E ATMOSI~RERE OF IO

respect to sodium clouds from those at other times. I t may also be t h a t we are dealing with an atmosphere t h a t is flowing out, away from the satellite into the Jovian magnetosphere. Neutrals as well as ionized particles may be involved in this flow. The ionization flux is not constant; it is the altitudeintegrated difference between production and loss. It is characteristic of certain dynamic outflows for the velocity to increase with altitudes up to some maximum value and then to decrease as altitude increases further. The electron density variation with altitude for such outflows need not vary inversely with the square of the radius, but may indeed decrease far more rapidly, as found during the day by Pioneer 10. This dynamic ionosphere has characteristics different from those of a static ionosphere (production equals losses); the peak density is reduced and its altitude is raised as a result of the outflow. Thus, sodium m a y contribute more significantly to the ionosphere than it would if the ionosphere were static. However, recombination of sodium ions would still be too long, and a molecular constituent must be involved. The net effect of outflowing motion is t h a t sodium may be comparable in content to the molecular constituent, in contrast with a static medium, to explain the observations. The relative losses of constituents would be more in balance; one would not forecast the buildup of a sodium atmosphere because of much higher losses of other constituents. The required column abundance of sodium, however, may exceed t h a t deduced from D line emission, but present uncertainties in those measurements do not rule out this possibility. Though this last explanation may be attractive, it is still highly speculative. Since the material presented here has utilized static models, outflowing models deserve further study to determine whether their characteristics fit the observations. The effects of particle precipitation on the atmosphere deserve some comments, particularly since such influx may be heating the surface (Gross, 1975) and causing sputtering (Matson et al., 1974).

505

High energy particles may ionize the atmosphere and heat it. The latter effect was used to augment the temperature of the nitrogen models to meet the scale height requirement. The ionization collision cross section may well exceed the UV cross section, and even a static sodium ionosphere may be feasible and in accordance with the daytime measurement. The effects of precipitation may also be more important on the trailing side of the satellite than its leading side, if thc magnetosphere corotates with Jupiter. However, if Io has considerable electrical conductivity due to its ionosphere and possibly its surface (sodium dissolved in ammonia, for example), the interaction with the magnetosphere may be complex; currents may be induced, and the energy distribution of particles may differ on the two sides. The measured nighttime ionosphere was on the trailing side with the reverse for the dayside. Yet, a smaller and colder ionosphere was found for the nighttime. This measurement may indicate t h a t incoming particles on the trailing side are not too effective as sources of ionization in spite of corotation effects. This lack of effectiveness may be due to magnetospheric interactions with Io. Though slowly recombining ions from the dayside could explain the nighttime ionosphere, a small influx of energetic particles may still be the source of the nighttime ionosphere. The relative contribution of energetic particles and UV is difficult to determine with the present state of knowledge. Some indication of the possible importance of energetic particles and of corotation may be obtained from future infrared temperature measurements of Io throughout its orbit. The trailing face is the dayside during part of its orbit and the nightside for the rest of its orbit, and similarly for the leading face. Any orbital effects in this respect may be significant. In summary, ionization and heating are probably due to both UV and particle precipitation. Streaming of gases from 1o necessitates treatment of the atmosphere and ionosphere in a dynamic model rather than a static model. Sodium and a molecu-

50(~

(1ROSS A N D ICAMANATHAN

]ar c o n s t i t u e n t , s u c h as N H 3 or N 2, m a y be o f c o m p a r a b l e i m p o r t a n c e in s u c h atmospheres, in spite of the n i g h t t i m e measurement of the ionosi)hcre and the estimated sodium column content. The p h o t o c h e m i s t r y o f N H 3 s h o u k l also be added to such models. More experimental o b s e r v a t i o n s are v i t a l t o p r o v i d e f u r t h e r information. O n e m a y also s u g g e s t t h e t b l l o w i n g o n t h e basis o f t h e l i m i t e d t r e a t m e n t h e r e : ( l ) N i t r o g e n s h o u l d be s o u g h t in t h e U V in l o ' s o r b i t a l p a t h ; (2) I t w o u l d be o f i n t e r e s t t o e s t a b l i s h w h e t h e r p o s t - e c l i p s e b r i g h t e n i n g m a y be due to energetic particle p r e c i p i t a t i o n t h a t produces broad emission, the sometime o c c u r r e n c e r e s u l t i n g f r o m t h e st~ructure o f t h e m a g n e t o s p h e r e , its i n t e r a c t i o n w i t h l o a n d I o ' s p o s i t i o n in o r b i t ~ b o u t J u p i t e r . ACKNOWLEDGMENT This research is i,he result of support un(hq' NASA Grant NGR 33-006-0(18.

(!ARI,SON, I~.. ~V., AND JVI)GE, 1). L.

(1974).

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R, EFEREN(~ES A(!|(ERMAN, M. (1971). Ultravi(d('t solar ra(lia,-

t ion rel~te(l t(~ mososphoric i)roe(~ss(,s, in Meso,s.pheric Model a~ul Related Experime,ts (G. Fioecii, Ed.). Springer Verlag, New York and D. llci(iel, Dor(lrecht, Hi)lla~nd, p. 149. A~,LEN, (!. ~V. (1963). Aa'trophysical Quantities, 2nd ed., University of London. The Atrhlono l)l*('SS. ANDERSON, A.

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C,ase,~'.

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T.,

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507

interaction with Io. J. Geophys. Res. 79, 35223544. SINTO)r, W~. M. (1973). Does Io have an ammonia atmosphere? Icarus 20, 284-296. SULLIVAN, J. O., AND HOLLAND, A. C. (1966). A congeries of ahsorption corss-sections for wavelengths less than 3000 A, NASA, CR-37 l, GCA Technical Report No. 64-20N. TRAFTON, L., PAXRKINSON, T., AND MACY, W., JR. (1974). The spatial extent of sodium emission around Io. Astrophys. J. 190, L85-89. TRAINOR, J. H., MCDONALD, F. B., TEEGARDEN, B. J., WEBBER, W. R., AND ROELOF, E. C. (1974). Energetic particles in J o v i a n magnetosphere. J. Geophys. Res. 79, 3600-3613. VAN ALLEN, J. A., BAKER, D. N., RANDALL, B. A., AND SENTMAN, D. D. (1974). The magnetosphere of Ju p i t er as observed with Pioneer 10: 1. Instrument and principal findings. J . Geophys. Res. 79, 3559-3577. DATA BOOK, Volume 2, Nonmetallic Elements, Compounds and Mixtures, Thermophysical Properties Research Center, Purdue University, Lafayette, Indiana, 1966.