On the Neutral Cloud Distribution in the Saturnian Magnetosphere

ICARUS

126, 42–57 (1997) IS965618

ARTICLE NO.

On the Neutral Cloud Distribution in the Saturnian Magnetosphere W.-H. IP Max-Planck-Insitut fuer Aeronomie, D-37191 Katlenburg-Lindau, Germany E-mail: [email protected] Received March 25, 1996; revised September 9, 1996

theoretical studies were subsequently carried out to model the structure and density distribution of the neutral ring cloud in the wake of the Voyager 1 and 2 encounters with the saturnian system (see Ip 1984, 1995, Pospieszalska and Johnson 1991). Because of the collisional absorption effect of the magnetospheric plasma by the ring particles, meteoroid bombardment at hypervelocity is the main agent in the generation of water vapor clouds. The ionization by photoionization and electron impact of this ring cloud could play an important role in maintaining the thermal plasma population of heavy ion composition (Ip 1984, Eviatar et al. 1981). Because of the uncertainties in the meteoroid influx at 10 AU solar distance and the meteoroid impact vapor yield, very different estimates have been obtained for the number densities of H2O, OH, O, and H near the ring system. If the meteoroid-impact gas production rate of the rings is assumed to be Qm 5 5 3 1027 molecules sec21, the maximum density of the H2O molecules near the B ring would be about n(H2O) P 100 molecules cm23 (Ip 1995). Furthermore, because of the Keplerian motion of the particles emitted at relatively low speed (p2–3 km sec21 ), the ring atmosphere is highly confined such that n(H2O) , 10 cm23 beyond the A ring. On the other hand, the maximum value of the ring gas production rate of Qm,max P 5 3 1029 molecules sec21 given by Northrop and Connerney (1987) will mean a neutral gas content a factor of 100 larger. An important implication of the large value of Qm,max is that the age of the ring system must then be extremely young (,5–60 myr). In the absence of direct observations of the neutral gas population, the measurements of the corotating II1 and O1 ions by the Plasma Science (PLS) instrument on Voyager (Bridge et al. 1981, 1982, Richardson and Sittler 1990) have been used to constrain the source strength of the neutral atoms and molecules (Richardson et al. 1986, Richardson, 1992). The ion source strength near the ring edge was ˙ L2 P 8 3 1025 to 8 3 1026 ions sec21, which assumed to be N could be translated to a neutral gas density of n $ 8.8 3 103 molecules cm23, if the ionization time scale is as long as 3 3 108 sec (see Appendix).

Recent spectroscopic observations of the saturnian system by the Hubble Space Telescope have shown the surprising results that the icy satellites and the rings are copious sources of neutral gas as a result of magnetospheric particle sputtering and meteoroid bombardment. Not only are the composition and structure of the saturnian magnetosphere significantly influenced by the continuous injection of water-group neutrals and ions, but the dynamics and mass distribution of the main ring as well as the tenuous E ring are also subject to the physical processes occurring in this unique plasma–dust–gas complex. By coupling the orbital motion of the neutral gas cloud with the photochemical effects and plasma chemistry, a numerical scheme is developed to analyze the possible contributions from different source mechanisms to the OH emission detected by the Hubble Space Telescope. It is found that, even if the maximum ion sputtering rate estimated by M. Shi, A. Baragiola, D. E. Grosjean, R. E. Johnson, S. Jurac, and J. Schou (1995, J. Geophys. Res.100, 26387–26395) is used, the number density of the hydroxyl molecules still falls short by a factor of about 2. The discrepency can be partially elevated if additional source from meteoroid-impact vapor production at Enceladus is introduced. The collisional interaction of Enceladus with the E-ring particles of micron size first proposed by D. P. Hamilton and J. A. Burns (1993, Nature, 365, 498) is of particular promise. One corollary of the present model consideration is that the impact of the E-ring particles in highly eccentric orbits with the A ring could lead to a dense ring atmosphere.  1997 Academic Press

1. INTRODUCTION

The ring system and icy satellites of Saturn have long been considered to be an important source of its magnetospheric plasma. For example, Dennefeld (1974) suggested that meteoroid bombardment and surface sublimation of the ring particles could lead to the formation of a tenuous atomic hydrogen cloud in the vicinity of the ring system. On the report of Lyman-a emission with a brightness of 200 6 100 R from the saturnian ring system (Weiser et al. 1977), it was proposed that the neutralization of the ionospheric H1 ions by the ring particles might contribute to this neutral hydrogen population (Ip, 1978). Several 42 0019-1035/97 $25.00 Copyright  1997 by Academic Press All rights of reproduction in any form reserved.

NEUTRAL CLOUD DISTRIBUTION IN SATURNIAN MAGNETOSPHERE

Because the radial diffusion coefficient essential to the plasma model calculations is not accurately determined, the above inferred value of the ion source strength could be significantly smaller than considered in Richardson’s (1992) model. Nevertheless, the high concentration of neutral gas in the vicinity of the ring system seems to be supported by the preliminary result of the Hubble Space Telescope (HST) detection of OH emission associated with the rings during the ring edge-on viewing condition (Hall et al. 1996). If the reported value of a number density of a few hundred molecules per cubic centimeter is confirmed by further study, the whole issue of the ring atmosphere, and in fact the evolutionary history of the ring system, would have to be reconsidered anew. Another major surprise has also to do with the earlier HST observation of OH emission in the radial distance at L P 4.5RS (saturnian radius) (Shemansky et al. 1993). The observational value of n(OH) P 160 molecules cm23 is much higher than the previous estimates of 2 to 3 molecules cm23 by Richardson et al. (1986) and n(OH) P 20 molecules cm23 by Ip (1985) and Johnson et al. (1989) on the basis of simple chemical calculations using the argument of ionization source balance. Shemansky et al. (1993) suggested that one possible explanation for such discrepency might have to do with the possibility that the meteoroid-impact vapor yield at the icy satellites and the E ring could have been significantly underestimated. In defense of the energetic ion sputtering effect, Johnson et al. (1989) and Shi et al. (1995) have used new laboratory data to recompute the production rate of neutral gas from energetic ion bombardment of the E-ring particles and the icy satellites. They found that the E-ring sputtering source alone could account for about 40 to 80 OH cm23 at L P 4.5. If the neutral gas productions from Enceladus and Tethys via ion sputtering and meteoroid bombardment are included, the HST value of n(OH) P 160 molecules cm23 might be explained. As will be discussed later, there appears to be no strong reason to discard meteoroid bombardment as a potential contributor to the neutral gas cloud. Hamilton and Burns (1993) were the first to point out the possible link to the impact effect of the E-ring grains as a source. The very interesting work by Horanyi et al. (1992) and Hamilton and Burns (1994) has further presented important argument that a significant amount of impact vapor could be generated by the surface collision of the E-ring particles with Enceladus and the mutual collisions among themselves. Electron-impact processes and ion–molecule reactions as a result of chemical interaction with the corotating thermal ions all play significant roles in the dissociation and ionization of the H2O molecules emitted from the icy satellites or ring particles. The number densities of the neutral gas molecules and their ratios, i.e., n(H2O)/n(OH) and n(O)/n(OH), therefore depend very much on the details

43

of the magnetospheric plasma environment and the spatial distribution of the source objects, be they the E ring or the icy satellites. It is quite possible that a significant amount of oxygen atoms (and water molecules to a lesser extent) can exist in the saturnian system. The inference of the neutral gas production rate from the measurements of n(OH) would hence require the development of a self-consistent model capable of describing the radial distributions of different neutral species. The measured value(s) of n(OH) can in turn be used to ‘‘normalize’’ the absolute values of other neutral components. Taking advantage of the published values of the plasma parameters that have been derived from the Voyager PLS measurements (Richardson and Sittler 1990, Richardson 1995), we can build a numerical simulation model incorporating the following elements: (1) the magnetospheric plasma environment with the ion number densities (H1 and O1 ), cold and hot electron number densities, ion temperature, and cold and hot electron temperatures given in tabular forms; (2) a comprehensive database of electron-impact rates as functions of electron temperature and ion–molecule reaction rates of importance; (3) a database describing the ion chemistry network involving the water-group neutrals and ions: (4) a Monte-Carlo scheme to compute the spatial distribution of neutral particles after emission from a parent object. The first three steps are combined to compute the spatial variations of the loss and production rates of H2O, OH, O, H2 , H, and O2 (if injected as parent molecule) in a twodimensional saturnian magnetosphere of azimuthal symmetry (see Section 2). In the computation, the saturnian magnetosphere is divided into a system of grid points of small spatial and angular intervals in which the contributions from different neutral species are binned. More details of the numerical method concerning step 4 are given in Section 3. The numerical results of the compositional distribution of the saturnian neutral clouds are described in Section 4, which is followed by the final Discussion section. 2. PLASMA CHEMISTRY

Laboratory experiments have shown that the sputter yield of water vapor from surface bombardment of heavy ions on low-temperature ice is very large (Johnson et al. 1982, 1983, Brown et al. 1984; Reimann et al. 1984, BarNun et al. 1985). According to these experiments, significant yields of H2 and O2 are also found in addition to water molecules: the hydrogen and oxygen molecules are supposedly the products of chemical recombination of the sputtered H and O atoms in the subsurface lattices. These

44

W.-H. IP

TABLE I Photolytic Effects Reaction H2O H2O H2O H2O H2O H2O H2O OH OH O2 O2 O2 H2 H2 H2 O H a b

1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv 1hv

R R R R R R R R R R R R R R R R R

H 1 OH H2 1 O H1H1O OH1 1 H 1 e H1 1 OH 1 e O 1 1 H2 1 e H2O1 1 e O1H OH1 1 e O1O O1 1 O 1 e O21 1 e H1H H1 1 H 1 e H21 1 e O1 1 e H1 1 e

b (sec21)

Reference a

Remark b

9.5E-8 1.3E-8 5.5E-9 5.0E-10 1.2E-10 1.0E-10 3.0E-9 4.6E-8 3.0E-9 5.5E-10 4.7E-10 4.8E-9 3.2E-10 8.8E-11 5.0E-10 2.0E-9 6.8E-10

SWH SWH SWH SWH SWH SWH SWH SWH SEVR SWH SWH SWH SWH SWH SWH SWH SWH

1.1 1.2 1.3 1.4 1.5 1.6 1.7 2.2 2.1 3.1 3.2 3.3 4.1 4.2 4.3 5.1 6.1

SWH, Schmidt et al. (1988); SEVR, Schreier et al. (1993). Notations for indices used in the computer program.

recombined molecules are subsequently purged by thermal diffusion process and hence the corresponding ejecta should consist of a thermalized population with the ejection speed determined by the surface temperature of the ice. The thermalized particles which are not able to escape the surface gravity of the icy satellite will execute ballistic motion before surface impact. The oxygen atmosphere of Europa recently detected by HST (Hall et al. 1995) is likely

to be of such sputtering origin (see Johnson et al. 1982, Eviatar et al. 1981, Ip 1996a); however, because of the small masses of the saturnian icy satellites, most of the directly sputtered particles can escape into planetocentric orbits while only a small fraction of the thermalized molecules would be recycled to the satellite surfaces after ballistic motion. (The structures of the exospheric coronas of the saturnian icy satellites, i.e., Enceladus, will be pursued in a future study. Our focus here is the formation of the neutral gas cloud surrounding Saturn.) The parent molecules, once injected into the saturnian magnetosphere, will be subject to ionization and dissociation effects of the solar UV radiation and electronimpact collision. Interactions with the corotating thermal ions via charge exchange and ion–molecule reactions are also important in the loss process. A comprehensive chemical model, therefore, will require the inclusion of many different reaction rates. The photolytic rates listed in Table I are from the work of Schmidt et al. (1988) [see also Huebner and Carpenter (1979) and Huebner and Giguere (1980)]. The electron-impact rates of the H 2O, OH, O2 , and H 2 molecules are obtained partly from the published values in the literature (Kieffer 1969, Richardson et al. 1986, Schreier et al. 1993) and partly from the computation by D. E. Shemansky (personal communication, 1995). The electron-impact rates corresponding to four different electron temperatures are given in Table II. While photoionization, photodissociation, and electron-impact effects serve as loss mechanisms for the parent molecules (H2O and O2 ), they also lead to the production of hydroxyl radicals

TABLE II Electron Impact Rates (cm3 sec21)

H2O H2O H2O H2O H2O OH OH OH OH O2 O2 H2 H2 H2 O H a b

1e 1e 1e 1e 1e 1e 1e 1e 1e 1e 1e 1e 1e 1e 1e 1e

R R R R R R R R R R R R R R R R

Reaction

a (0.5 eV)

a (1.0 eV)

a (5.0 eV)

a (10.0 eV)

a (50.0 eV)

Reference a

Remark b

H2 1 O 1 e OH 1 H 1 e H2O1 1 2e O1 1 H2 1 2e OH1 1 H 1 2e O1H1e OH1 1 2e O1 1 H 1 2e H1 1 O 1 2e O1O1e O21 1 2e H1H1e H21 1 2e H1 1 H 1 2e O1 1 e H1 1 e

0.250E-14 0.392E-10 0.319E-19 0.213E-18 0.267E-28 0.108E-17 0.671E-20 0.691E-25 0.322E-25 0.558E-12 0.337E-18 0.139E-15 0.337E-18 0.129E-26 0.337E-18 0.337E-18

0.612E-11 0.917E-9 0.252E-13 0.144E-15 0.747E-18 0.511E-13 0.148E-13 0.353E-16 0.164E-16 0.204E-9 0.229E-13 0.208E-11 0.643E-14 0.774E-18 0.229E-13 0.186E-13

0.347E-8 0.240E-7 0.117E-8 0.201E-9 0.505E-10 0.140E-8 0.237E-8 0.366E-9 0.169E-9 0.305E-7 0.126E-8 0.372E-8 0.126E-8 0.126E-10 0.126E-8 0.794E-9

0.894E-8 0.333E-7 0.681E-8 0.160E-8 0.571E-9 0.598E-8 0.120E-7 0.312E-8 0.144E-8 0.617E-7 0.797E-8 0.104E-7 0.633E-8 0.216E-9 0.797E-8 0.397E-8

0.363E-7 0.501E-7 0.628E-7 0.236E-7 0.141E-7 0.306E-7 0.750E-7 0.349E-7 0.160E-7 0.124E-6 0.549E-7 0.388E-7 0.436E-7 0.320E-8 0.549E-7 0.246E-7

SEVR DES(R98) DES(R91) DES(R96) DES(R94) DES(R114) DES(R109) DES(R112) DES(R113) DES(R102) RES SEVR RES DES(R106) RES RES

1.9 1.11 1.10 1.12 1.13 2.3 2.4 2.5 2.6 3.4 3.5 4.4 4.5 4.6 5.2 6.2

DES, D. E. Shemansky (personal communication, 1995); RES, Richardson et al. (1986); SEVR, Schreier et al. (1993). Notations used in the computer code.

45

NEUTRAL CLOUD DISTRIBUTION IN SATURNIAN MAGNETOSPHERE

and H and O atoms in the extended neutral cloud region. In the case of ion–molecule reactions and charge exchange processes like O1 1 H R H1 1 O*, however, the neutralized products always tend to escape the saturnian system in ballistic orbits because of the high initial speed of the thermal ions in corotational motion. The ion–molecule reactions (see Table III) therefore act mainly as a sink for the neutral cloud. In the present calculations we have neglected the probable contribution of the N1 (and possible C1 also) ions emitted from Titan. We believe that the carbon and nitrogen ions picked up in the vicinity of the gas torus of Titan should be accelerated to suprathermal energy by the time they reach the orbital regions of Tethys and Enceladus. The major thermal ions are therefore mostly H1 and O1 which are of ionospheric and satellite/ring origins. As discussed by Richardson et al. (1986) more complex watergroup molecular ions (i.e., OH1, H2O1, and H3O1) could exist; however, in the present model only the chemical effects of H1 and O1 ions are computed. The rate equation of the neutral gas species can be written as







dn, 5 o [a n ]n 2 n o [a n ] ,9 ,9, , e ,9 , ,9 ,, ,9 e dt electron-impact terms

photolytic terms

(1)

n, o ,0 c,0 n,0

  

2







1 o,9 b,9, , n,9 2 n, ? o ,9 b,,,9

ion-neutral terms. where n, , n, , and n,0 are the ,2 and ,9th neutral species and the ,0th ion species, respectively, ne is the electron number density, a ,9, , is the electron-impact ionization or dissociation rate for the formation of neutral species , from neutral species ,9 (the inclusion of both cold and hot electrons is denoted by the [...]), b ,9, , represents the photoionization and photodissociation rates for forming neutral species , from neutral species ,9, and finally, c,0, , represents the ion–molecule reaction rate involving the neutral species , and the ion species ,0. Using the tabulated values of the plasma temperatures and the number densities of the ions, cold electrons, and hot electrons at the equator as given in Richardson (1995), the rates of different chemical reactions can be computed. From these, the production and loss rates for all neutral species (H2O, OH, O, H2 , O, and H) at the equator (z 5 0) can be calculated. Some sample values are given in Fig. 1. Between the outer edge of the ring system and 5RS , where the dense plasma disk of heavy ions [with n(O1 ) P

TABLE III Ion–Molecule Reaction Rates Reaction H2O H2O H2O H2O H2O H2O H2O H2O OH OH OH OH OH OH OH OH OH OH O2 O2 O2 O2 O2 O2 O2 O2 O2 H2 H2 H2 H2 H2 H2 H2 H2 H2 O O O O O O O H H H H H

1H1 R H 1 H2O1 1H21 R H3O1 1 H 1H21 R H2O1 1 H2 1O1 R H2O1 1 O 1OH1 R H3O1 1 O 1OH1 R H2O1 1 OH 1H2O1 R H3O1 1 OH 1O21 R H2O1 1 O1 1H1 R OH1 1 H 1H21 R OH1 1 H2 1H21 R H2O1 1 H 1O1 R OH1 1 O 1O1 R H1 1 O2 1OH1 R H2O1 1 O 1H2O1 R H3O1 1 O 1O21 R O1 1 O1 1 H 1O21 R O1 1 H1 1 O 1O21 R O1 1 OH1 1H1 R H 1 O21 1H21 R H 1 O2H1 1H21 R H2 1 O21 1O1 R O21 1 O 1OH1 R O21 1 OH 1H2O1 R O21 1 H2O 1O21 R O2 1 O21 1O21 R O1 1 O1 1O21 R O1 1 O21 1H1 R H21 1 H 1H21 R H31 1 H 1H21 R H21 1 H2 1O1 R OH1 1 H 1OH1 R H2O1 1 H 1H2O1 R H3O1 1 H 1O21 R O2H1 1 H 1O21 R O1 1 H1 1 H 1O21 R O1 1 H21 1H1 R O1 1 H 1H21 R OH1 1 H 1O1 R O1 1 O 1OH1 R O21 1 H 1H2O1 R O21 1 H2 1O21 R O1 1 O1 1O21 R O11 1 O 1H1 R H21 1H1 R H1 1 H 1H21 R H2 1 H1 1O1 R H1 1 O 1O21 R O1 1 H1

Rate (cm3 sec21)

Remark

8.2E-9 3.4E-9 3.9E-9 3.2E-10 1.3E-9 1.6E-9 2.1E-9 6.0E-10 2.1E-9 7.6E-10 7.6E-10 3.6E-10 3.6E-10 7.0E-10 6.9E-10 6.8E-10 6.8E-10 3.4E-10 1.2E-9 1.9E-9 8.0E-10 1.9E-11 5.9E-10 4.3E-10 1.3E-8 1.4E-9 3.4E-10 1.0E-10 2.1E-9 3.6E-9 1.7E-9 1.0E-9 8.3E-10 2.5E-9 1.0E-9 2.4E-10 7.0E-10 1.0E-9 1.8E-8 7.1E-10 4.0E-11 2.0E-11 5.0E-9 2.0E-20 3.5E-8 6.4E-10 6.8E-10 1.2E-9

1.15 1.16 1.17 1.19 1.20 1.21 1.22 1.25 2.7 2.8 2.9 2.11 2.12 2.13 2.14 2.15 2.16 2.17 3.7 3.8 3.9 3.11 3.12 3.13 3.14 3.18 3.19 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.20 4.21 5.3 5.4 5.6 5.7 5.8 5.16 5.19 6.3 6.4 6.5 6.6 6.10

Source. Data from Schreier et al. (1993).

115 cm23 ] is located, the loss of the hydrogen and oxygen atoms against charge exchange with the O1 ions is rapid. The minimum loss time scales are P 106 sec when L P 4RS . The imprints of the ion–molecule reactions can also be seen in the curves of other species even though the

46

W.-H. IP

FIG. 1. Radial variations of the loss time scales against dissociation and/or ionization of different neutral species including H2O, OH, and O. The plateaulike structures A, B, and C at L . 12 are caused by the plasma bubbles in the Richardson (1995) model of the saturnian magnetosphere.

effects are not as marked. Beyond the dense cold plasma region the loss of water molecules is driven mostly by electron-impact dissociation via H2 O 1 e R OH 1 H 1 e (D. E. Shemansky, personal communication, 1995). As a result, the water molecules can be quickly converted into OH daughters. In Richardson’s (1995) plasma model, the formation of detached plasma bubbles in the outer magnetosphere for L . 10 is represented by the insertion of several low-plasma-density regions. Because of the reduction in the plasma loss rates, the loss process is determined only by photolytic effects in these magnetospheric bubbles; hence the appearance of the plateaus in Fig. 1. As pointed out by a referee, the formation of plasma bubbles in the saturnian magnetosphere is characterized by strong local time dependence. The electron and ion measurements from the PLS experiment in fact did not detect such detached plasma structures on the outbound passes of Voyager 1 and 2 through the morning side of the outer magnetosphere (Sittler et al. 1983). The extrapolation of the loss time scales to the vertical direction requires an additional step of calculating the ion density along the dipole magnetic field line. In lieu of the digitized values as presented in contour plots in Richardson and Sittler (1990) and Richardson (1995), this is done by using the simplified formula (Hill and Michel 1976),

F S DG

n,0 (s) 5 n,0 (0) exp 2

s H,0

2

(2)

with the centrifual scale height H,0 5

S

D

2KBT,0 3m,0 V2

1/2

.

(3)

In the above equation, s is the distance along the magnetic field line (s 5 0 at the equator), KB is the Boltzmann constant, T,0 and m,0 are the temperature and mass of ion species ,0, respectively, and V is the angular frequency of the planetary rotation. In our azimuthally symmetric magnetospheric model, the saturnian system is divided into a number of grid points with a radial interval dr 5 0.05RS (saturnian radius) and a vertical interval dz 5 0.05RS . The lower left corner of the rectangular grid (i, j ) is defined by the values ri 5 i dr and zj 5 j d z. With this convention, two sets of n,0 (0) for ,0 5 1 (H1 ) and ,0 5 2 (O1) are computed at discrete grid points along the radial direction (between r 5 2RS ) at z 5 0. They are then mapped along individual field lines to obtain the ion number densities n,0 (i, j ) at various grid points. The same method can then be used to obtain the production and loss rates of different neutral species in different magnetospheric regions. The numerical values are stored in lookup tables for later use. 3. ORBITAL DYNAMICS

In laboratory experiments, it was found that the energy dependence of the sputter yield of water molecules can be

NEUTRAL CLOUD DISTRIBUTION IN SATURNIAN MAGNETOSPHERE

47

approximated by a collision cascade model (Reimann et al. 1984, Johnson 1990) Y (E) 5

2UE (E 1 U )3

(4)

with an empirical value of 0.055 eV for the binding energy (U ). In a planetary environment, the microstructure of the surfaces of the satellite or ring particles such as porosity and chemical composition might be very different from the laboratory conditions. Caution must therefore be exercised in the application of the experimental results to the problem of magnetospheric particle sputtering. Even larger uncertainties exist in the velocity distribution of the water vapor from meteoroid bombardment. There exists practically no information. The general approach so far is to assume a Maxwellian velocity distribution for the impact vapor gas or to fit a collision cascade model to the ejecta velocity distribution (Ip 1984, 1995, Pospieszalska and Johnson 1991). This is one critical area where laboratory experiments and computer simulations are urgently needed. Before the situation is improved we will use the collision cascade distribution as the working model in the calculations below. Once the ejecta velocity distribution is chosen, the next step is to follow the orbital distribution of the neutral gas particles by using a standard Monte-Carlo method (see Ip 1995). The ballistic emission from a satellite surface is assumed to be isotropic and the initial velocity is chosen at random according to the assumed velocity distribution. The equation of motion is solved in the rotating coordinate system of the satellite written as (Danby 1989) x¨ 5 2 y˙ 1 x 2

(1 2 e)(x 2 x1 ) e 2 3 (x 2 x2 ), r 31 r2

y¨ 5 22 x˙ 1 y 2 z¨ 5 2

S

(1 2 e) y e 2 3 y, r 31 r2

(5) (6)

D

(1 2 e) e 1 3 z, r 31 r2

with e 5 ms /(ms 1 mp ), x1 5 e, x2 5 1 2 e,

(7)

r1 5 [(x 2 x1 )2 1 y 2 1 j 2 ]1/2, and r2 5 [(x 2 x2 )2 1 y 2 1 j 2 ]1/2. In the above equations, ms is the satellite mass, mp is the planetary mass, and the unit of time is Ts /2f (where Ts is

FIG. 2. Rotating coordinate system used in the orbital integration. In the center-of-mass frame Saturn is located at x1 and the source satellite at x2 .

the orbital period of the satellite) and the length scale is normalized to the distance between the planet and the satellite (see Fig. 2). No radiation pressure effect is included in the computation because of the relatively short lifetimes (pa few 106 sec for OH). The momentum-transfer process during ion–molecule impact is also neglected since all such collisional interactions are assumed to be loss effect for the neutral gas. The numerical integration is performed with a Runge Kutta subroutine of variable time step (Dt). We start the integration at t 5 0 by assigning Dt 5 Dto (5 1023 ? Ts ). Along the trajectory of the test particle, an account will be kept of the gradual statistical loss of the parent molecules and the production of the daughter molecules and atoms. This is done by constructing yet another grid system with an angular interval in the azimuthal direction taken to be Du 5 38 and the radial and vertical intervals set to be Dr 5 Dz 5 0.1RS . Thus, a volume element can be identified as V (i, j, k) with ri 5 i ? Dr, zj 5 j ? Dz, and uk 5 k ? Du. In the Monte-Carlo calculation the particle trajectories are traced with the positions marked as rn at time step tn . At the start of each run, the test particle (i.e., H2O) is given a weighting factor f0 (H2O) 5 1 while the weight factors of the daughter species are assigned to be f0 (OH) 5 f0(O) 5 f0(H2 ) 5 f0 (H) 5 0. In the subsequent time step, the weighting factor of the parent molecule will be reduced because of photolytic loss, electron-impact dissociation and ionization, and ion–molecule reactions in the interim interval. At the same time, a certain amount of

48

W.-H. IP

OH, H2 , and H will be created. Along the particle beam, the number densities of H2 O and O2 (if injected as parent molecule) will gradually diminish, while those of the daughter species will first increase and then decrease. The global structure of the distributed neutral cloud is composed of an ensemble of such particle beams of different time histories with trajectories going through different regions of the saturnian magnetosphere. Note that the time histories of individual test particle beams under fixed plasma condition are assumed to be independent of each other. This approach is different from the time-relaxation method in which the incremental effect from runs at successive time steps must be incorporated in the time evolution of the system. By the same token, the statistics of the numerical results are controlled by the number of test particle beams (and hence computation time) used. The optimization was achieved by trial and error. At the next level of calculation, the rate equation given in Eq. (1) is then solved in finite difference form to obtain the weight factors ( f ) for different species as functions of time. The contributions from individual neutrals are recorded by adding the respective f values to the particular bin with volume element V (i, j, k) where the test particle is located. When a particle beam intercepts the ring plane, the corresponding f value will be reduced by a factor of exp(2t ), where t is the local value of the ring optical depth. A trajectory run is terminated when the sum of the f values at this time step is less than a preset value of 0.01 (the run will be terminated if the test particle hits the planetary surface). In matrix form the sum of the weighting factors for H2O, say, from the mth run can be written as Fml (i, j, k) 5 o fml (i, j, k), where l is an index identifying different neutral species. This procedure is repeated M times with the Fm values of individual species accumulated in the three-dimensional grid system. The total value of the weighting factors for H2O, OH, O, and O2 , respectively, is F Fl (i, j, k) 5

OF M

ml (i,

j, k).

(8)

m51

Under the assumption of steady-state condition, these values can be used to estimate the absolute number densities of the neutral gas if the total production rate of the H2O molecules (and oxygen molecules) is given. A scaling factor c can then be used to relate Q to the emission rate of test particles: Q 5 c ? M/Dt.

(9)

The number density is hence n, (i, j, k) 5 c ? FF, (i, j, k)/V (i, j, k),

(10)

where the volume element at grid point (i, j, k) is defined as V (i, j, k) 5 2f (r 2i11 2 r 2i )Dz/120.

(11)

Note that the factor of 2 in the numerator in the above equation comes from the fact that in our calculation we have added all the particle points into the upper half of the grid system with z $ 0 because of the assumption of mirror symmetry. For photodissociation and electron-impact dissociation it is generally true that the fragments will carry a certain amount of excess energy (DE P 0.5–2 eV). Because of conservation of momentum, the light fragments usually get the major share of the DE and hence will be ejected at relatively high velocity. For example, in the case of the photodissociation of H2O with DE P 1.9 eV (Huebner and Carpenter 1979), the hydrogen atom could have an ‘‘ejection’’ velocity as high as 19 km sec21. The atomic fragments so produced will quickly decouple from the neutral gas cloud characterized by the heavy molecules. For this reason we have not considered the spatial distributions of both H atoms and H2 molecules here. Also, we have omitted the effect of the excess kinetic energy on the orbital motion of the oxygen atoms and OH. In other words, these heavy fragments are supposed to co-move with the H2O or the O2 particle beam. We intend to implement the inclusion of the extra velocity components from the photolytic processes in a future study. This point is mentioned here because it might have some interesting consequence on the global distribution of neutral hydrogen atoms in the inner saturnian magnetosphere (Shemansky and Hall 1992, Ip 1996b). 4. RESULTS

As an example, Fig. 3 shows the contour plots of the average number densities of H2 O, OH, and the oxygen atoms in the neutral cloud emitted from Enceladus. It can be seen that the hydroxyl radicals are the most abundant with n(OH)/n(H2O) p 3. This is basically caused by the fast electron-impact dissociation effect in the plasma environment of this satellite. Even though the oxygen atoms are the end product of the dissociation chain of the H2 O and OH molecules, their number density is kept low relative to those of H2 O and OH because of the rapid charge exchange loss in the inner magnetosphere. The global density distributions can be obtained by the superposition of the neutral clouds from all four major saturnian satellites (Enceladus, Tethys, Dione, and Rhea). Note that in the model calculation the most crucial parameters have to do with the gas production rates from different icy satellites. Once the Q values are known, the corresponding c values can be computed and hence the neutral density distributions. Different source mechanisms yield different patterns

49

NEUTRAL CLOUD DISTRIBUTION IN SATURNIAN MAGNETOSPHERE

FIG. 3. Two-dimensional distributions of the number densities of (a) H2O, (b) OH, and (c) O neutrals emitted from Enceladus.

of Q values. Therefore, a comparison of theoretical models with observations from remote-sensing measurements (or in situ investigations by the Cassini Orbiter) would be able to tell us which production effect is more important. In this section, we consider several different possible scenarios, so that the pros and cons of the ion sputtering mechanism versus meteoroid impact can be evaluated.

Using new laboratory data Shi et al.. (1995) recalculated the gas production rates from charged particle sputtering (Qs ) for different icy satellites of Jupiter and Saturn. Their estimates of the minimum and maximum values of Qs for the saturnian satellites are summarized in Table IV together with the corresponding scaling coefficients, c. The factor of 4 difference in the minimum and maximum values

TABLE IV Neutral Gas Source Models Sputtering rate (H2O/sec) Satellites Enceladus Tethys Dione Rhea

Orbital period (sec) 1.18 1.63 2.36 3.90

3 3 3 3

105 105 105 105

Semimajor axis (cm) 2.38 2.94 3.77 5.27

3 3 3 3

1010 1010 1010 1010

(a) 3.0 2.8 5.3 3.2

3 3 3 3

1023 1025 1025 1026

(a) Minimum value and (b) maximum value of sputtering rate according to Shi et al. (1995).

(b) 1.2 1.1 2.1 1.3

3 3 3 3

1024 1026 1026 1026

Conversion factor, c 3.20 4.16 1.14 1.14

3 3 3 3

1026 1025 1024 1024

50

W.-H. IP

FIG. 4. Two-dimensional cross sections of the neutral OH clouds emitted from the saturnian satellites Enceladus, Tethys, Dione, and Rhea. In this example, the production rates of H2O molecules are assumed to be Qs(En) 5 1.2 3 1024 sec21, Q(Te) 5 1.1 3 1026 sec21, Q(Di) 5 1.2 3 1026 sec21, and Q(Rh) 5 1.4 3 1026 sec21. A composite of all four separate neutral clouds is shown in the bottom panel.

of the gas emission rates comes from the considerations of the impact geometries and surface structures. In the following, the maximum Qs values will be used to assess the relative importance of charged particle sputtering. Figure 4 depicts the two-dimensional cross sections of the neutral OH clouds associated with magnetospheric particle sputtering of individual source satellites. The combined distribution is also shown. This result indicates that n(OH) P 60 cm23 at L P 4.5 and there are density peaks near the orbits of different satellites with the corresponding values given in Table IV.

As a summary, Fig. 5 illustrates the composite number density distributions of H2O, OH, and O in the framework of the magnetospheric particle sputtering mechanism [case (a)]. It is noteworthy that because of the small gas production rate of Enceladus, the bulk of the neutral cloud is actually located between the orbits of Tethys and Dione. In fact, because of the small gas production rate of Enceladus, the density of OH at L P 4.5 comes mainly from the neutral cloud of Tethys according to this scenario. When the model value of n(OH) at this distance is compared with the HST results of Shemansky et al. (1993), a large discrepancy

NEUTRAL CLOUD DISTRIBUTION IN SATURNIAN MAGNETOSPHERE

still remains. To overcome this difference by a factor of 2.5 (at least), an additional source would be required. As discussed before, besides charged particle sputtering, another potential source mechanism of the neutral gas cloud is micrometeoroid bombardment. In addition to the interplanetary meteoroid population, the E ring might have a lot to do with this impact process (Hamilton and Burns 1993). The dynamical calculations by Horanyi et al. (1992) and Hamilton (1993) have shown that this ring feature, which has a brightness peak at the orbit of Enceladus and a very narrow size distribution (radius rg P 1 em), could be self-generated by collisional interaction with Enceladus (see also Hamilton and Burns 1994). The reason is that a combination of the solar radiation pressure force, the J2 term from the oblateness of the planet, and the Lorentz force on the charged dust grains leads to periodic variations of the orbital eccentricities of particles of differ-

51

ent sizes. For a surface potential of approximately 25 V, which is the predicted value according to the Voyager plasma data (Horanyi et al. 1992, Jurac et al. 1995), the maximum eccentricity (P0.65) is reached by dust grains with rg 5 1 em. Numerical simulations indicated that the theoretical distribution of the charged grains of rg 5 1 em matches the observed brightness profile of the E ring reasonably well (Horanyi et al. 1992, Hamilton 1993). The maximum eccentricity of these particles will permit them to have collisional interaction with Enceladus, Tethys, and the A ring at high speed. The corresponding dynamical time scales have been estimated to be on the order of 20 years against collision with Exceladus to 100 years against collision with Tethys (Hamilton and Burns 1994). It is consequently the recycle of these impact ejecta that leads to continuous injection of a population of micron-sized dust particles into the E ring.

FIG. 5. Two-dimensional projections of the composite density distributions of (a) H2O, (b) OH, and (c) O neutral clouds from ion sputtering of the four major icy satellites. The assumed gas production rates are given in Table 4.

52

W.-H. IP

Taking the normal optical depth of the E ring to be (Showalter et al. 1991)

t 5 1.5 3 1025

S D

, for L , 3.9,

t 5 1.5 3 1025

S D

, for L . 3.9,

15

L 3.9

(12)

and L 3.9

27

(13)

we can calculate the total mass of the micrometer-radius particles to be M 5 1.5 3 1012 g if the particle density is assumed to be r 5 1 g cm23. To maintain a steady-state ˙ P structure, the required mass injection rate would be M 3 21 2.5 3 10 g sec for a collisional loss time of about 20 years. Suppose 60% of this dust particle population reimpacts Enceladus, 20% impacts Tethys, and 10% impacts the outer edge of the A ring, we could henceforth estimate the corresponding mass erosion rates of the satellites and the ring particles. For target surface of icy water composition, a fraction of the impact energy at hypervelocity will be consumed in vaporization while a large quantity of solid ejecta would be produced as well (Eichhorn and Gru¨n 1993, Koschny and Gru¨n 1995a, b). The mass ratio of the impact vapor to the particulate ejecta depends on the kinetic energy of the projectile. There exists only scant information from laboratory work. From a consideration of the surface binding energy of water molecules on ice (Hobbs 1974), Eichhorn and Gru¨n (1993) suggested the conversion formula of 0.5 eV for each H2O molecule to relate the vapor pressure pulses detected in their ice-impact experiments to the masses of the vapor clouds. This also implies that a large fraction of the impact energy is consumed in the generation of vapor gas cloud. (The exact distribution of the kinetic energy of the projectile is still uncertain, however.) If we follow this assumption and use vi 5 5 km sec21 for the collision speed in the case of satellite impact and vi 5 10 km sec21 in the case of ring impact, we find the following vapor gas production rates due to the E-ring dust-impact process [e.g., case (b)]: Qm P 1.5 3 1026 H2O molecules sec21 at A ring, Qm P 3.7 3 1026 H2O molecules sec21 at Enceladus, Qm P 7.6 3 1025 H2O molecules sec21 at Tethys. The most dramatic effect occurs for Enceladus; the introduction of the dust-impact yield could enhance the corresponding gas production rate by a factor of 300! This is followed by Tethys of which the total value of Q(5 Qm 1 Qs ) could nearly double the gas production

rate from the ion sputtering mechanism alone. (As mentioned earlier, our focus in this study is on the OH and other neutral gas density distribution in the region between the orbits of Enceladus and Tethys. The contribution of the highly confined ring atmosphere is therefore not specifically modeled here.) The introduction of this hypothetical meteoroid-impact source leads to very significant changes of the density distributions of the neutral gas clouds. Most important, as shown in Fig. 6, the number densities of H2O, OH, and O now peak at the orbit of Enceladus. This is because of the artificial assumption of allocating some 60% of the E-ring particle flux to Enceladus. As a consequence, the value of n(OH) is as much as 1.7 3 104 cm23 at L P 4 and about 4.6 3 103 cm23 at L P 4.5. This is clearly inconsistent with the HST observations (Shemansky et al. 1993). The origin of this excess appears to lie in the previous assumption that a large fraction of the E-ring dust particles will reimpact Enceladus under the influence of electrodynamic effects and the orbital perturbation of the J2 term. This might not necessarily be the case. A reexamination of the time evolution of the charged dust particles of different sizes has been carried out by Ip and Richter (1996, manuscript in preparation) by using a value of 0.5 for the radiation pressure coefficient Qpr , which is more appropriate for water icy grains (H. Ishimoto, personal communication, 1995). It is found that the basic feature that the orbital eccentricity of the charged grains would reach a maximum value of about 0.7 for rg P 1 em remains unchanged except that the periods of the cyclic variations of the orbital elements will be lengthened. Dust particles with radii between 1.0 and 1.05 em can reach the outer edge of the A ring at aphelia. Because of the nature of grazing incidence at ring plane crossing, these dust grains have a high probability of colliding with the ring particles. Thus, they will tend to be lost in the first half-cycle with a time scale of about 18 to 20 years. For this reason, the majority (say 60%) of the dust particles in the extended E-ring structure will impact the A ring instead of Enceladus. This would mean that the impact vapor production rate at the outer edge of the A ring could be as much as 8 3 1026 H2O sec21. This, however, is not to say that Enceladus would not be a source of neutral gas as a result of meteoroid impact. This is because dust grains with radii outside the ‘‘resonant’’ range will still collide with it, albeit with smaller impact speed. Without a detailed calculation (and eventually in situ measurements by the Cassini Orbiter) it is not certain what should be the appropriate impact-generated gas emission rate. We have computed the neutral density profiles with different values of Qm at Enceladus as inputs and have found that n(OH) P 300 cm23 for Qm P 6 3 1025 H2O sec21. Figure 7 shows the two-dimensional distributions of the number densities of H2O, OH, and O for

NEUTRAL CLOUD DISTRIBUTION IN SATURNIAN MAGNETOSPHERE

53

FIG. 6. Two-dimensional projections of the composite density distributions of (a) H2O, (b) OH, and (c) O neutral clouds from ion sputtering and meteoroid impact. The assumed meteoroid-impact vapor production rates are Qm P 1.5 3 1026 H2O sec21 at the A ring, 3.7 3 1026 H2O sec21 at Enceladus, and 7.6 3 1025 H2O sec21 at Tethys.

this example [case (c)]. It is important to note that the azimuthally averaged density of OH at L P 4 is as high as 2880 cm23. Because of the time dependence of the dissociation/ionization effect, there is also a certain degree of longitudinal asymmetry which might be observable as far as the H2O cloud is concerned. As for OH, the presence of a high-density region in the vicinity of the icy satellite will imply the direct generation of hydroxyl molecules in the impact vapor. Besides Enceladus, the gas emission of other icy satellites is mostly driven by charged particle sputtering. Density peaks of smaller amplitudes are found near the orbits of Tethys, Dione, and Rhea. The background value of the OH gas decreases from about 300 cm23 at L P 4.5 to about 5 cm23 at L P 10, while the total density of the ‘‘heavy’’ neutrals changes from approximately 4000 cm23 to about 10 cm23 over the same distance. This cloud of oxygen-bearing molecules and oxygen atoms

coexists with the hydrogen atomic halo produced by the dissociation of the water molecules and Titan’s hydrogen cloud. The saturnian magnetosphere is therefore highly enriched in neutral gas. Figure 8 compares the radial variations of n(OH) for three different emission source mechanisms. It can be seen that the introduction of a modest meteoroid-impact source [case (c)] at Enceladus will produce a neutral cloud distribution with the highest concentration near Enceladus’ orbit. Such a profile is distinctly different from that of sputtering origin [case (a)]. 5. DISCUSSION

In this work we have combined the orbital dynamics of the neutral gas particles with a model of the plasma chemistry in the saturnian system to simulate the density distribu-

54

W.-H. IP

tions of the water and hydroxyl molecules and the oxygen atoms. Several possible scenarios of source mechanisms are examined. These vary from sputtering-dominated models to meteoroid bombardment-dominated models. The assessment by Shi et al. (1995) that charged particle sputtering processes (at maximum yield) can maintain an OH density of about 60 cm23 at L P 4.5 is confirmed by our calculations [case (a) in Fig. 7]. The difference between this theoretical value and the observed value of 160 cm23 reported by Shemansky et al. (1993) can be accounted for by invoking meteoroid-impact vaporization at Enceladus’ surface (Hamilton and Burns 1993, 1994); however, the idea that most of the E-ring dust particles should reimpact Enceladus would probably lead to an excessive amount of OH gas. This discrepency can be elevated by noting that a large fraction of the E-ring particles in highly eccentric orbits should actually collide with the A ring instead of Enceladus. [The exact probability and radial location of

ring impact depend on the orbital inclination of the E-ring particles and, hence, the pointing direction of the rotation axis of Saturn (M. Horanyi, personal communication, 1996).] Such orbital interception effect could, on the one hand, lead to a more favorable value of n(OH) between the orbits of Enceladus and Tethys and, on the other hand, ensure the generation of a dense ring atmosphere. The required meteoroid-impact-related gas production rate at Enceladus amounts to about 6 3 1025 H2O molecules sec21 and about 8 3 1026 H2O sec21 at the A ring. In comparison, the maximum production rate from ion sputtering at Enceladus is only 1.2 3 1024 sec21 according to Shi et al. (1995). One major assumption we have adopted in the present calculations is that the parent molecules from meteoroidimpact vaporization and ion sputtering are mostly H2O. It is quite possible that the impact vapor cloud contains a certain amount of OH molecules as a direct product. If this is the case, the ratio of n(OH) to n(H2O) for L # 5

FIG. 7. As in Fig. 6 but with the following values of the meteoroid-impact vapor production rates: Qm P 8 3 1026 H2O sec21 at the A ring,

6 3 1025 H2O sec21 at Enceladus and at Tethys.

NEUTRAL CLOUD DISTRIBUTION IN SATURNIAN MAGNETOSPHERE

55

FIG. 8. Comparison of the radial variations of the average values of the number densities of OH at the equatorial plane for case (a) with pure ions puttering source, case (b) with maximum meteoroid bombardment source at Enceladus, and case (c) with an intermediate meteoroid-impact source at Enceladus.

should be further enhanced. As for the oxygen molecules, a significant amount of O2 molecules could be generated by heavy ion sputtering as discussed earlier (Reimann et al. 1984, Bar-Nun et al. 1985). We therefore expect the formation of O 21 ions in the saturnian magnetosphere. Our model calculations are only the first step toward a quantitative description of the source and transport of the neural gas and magnetospheric plasma in the saturnian system. As discussed above, the basic results are subject to several major uncertainties in the input parameters. These include the ion composition of the thermal plasma, with the heavy species assumed to be O1 ions in the plasma model of Richardson (1995). The introduction of H2O and OH molecules into the plasma system means that the water-group ions like H3O1 and H2O1 will likely play a role in the plasma chemistry (cf. Richardson et al. 1986). Second, the electron temperature profile, which is vital to the computation of the electron-impact rates (i.e., H2O 1 e R OH 1 H 1 e), may be subject to modification as a result of the time variability of the saturnian magnetosphere. The influence of the cooling effects of H2O and OH on the thermal budget of the magnetospheric plasma might also be very significant (Shemansky and Hall 1992). The interrelation between the neutral cloud and the corotating plasma will be investigated by coupling the radial diffusive model of magnetospheric plasma with the distributed neutral cloud computational scheme. It is hoped that an iterative approach will eventually permit the development of a selfconsistent model in describing the plasma–dust–gas complex in the Saturnian magnetosphere.

Finally, the neutral cloud associated with the ring system must be included in the global picture at a later stage. There are two issues to be clarified. The first one concerns the meteoroid-impact process at the A ring and at Enceladus. Because the dust population of the E-ring complex is a most important link to the neutral gas cloud, a clear understanding of the mass budget of the neutral gas and magnetospheric plasma of water-group ions will require a precise knowledge of the orbital distribution and size distribution of the E-ring particles near the orbit of Enceladus and in the saturnian system. With the changing orientation of the planetary rotation axis as Saturn revolves around the Sun, the variations of the eccentricities and inclinations of the micron-sized particles might be modulated, hence leading to a change in the impact source strengths of the ring system and icy satellites. A comprehensive model of the density and orbital distributions of the E-ring particles of different sizes is urgently needed to address this interesting problem. The second issue has to do with the structure of the ring atmosphere. The recent HST observations of the OH emission at edge-on viewing condition (Hall et al. 1996) in the vicinity of the ring system suggest that the neutral gas distribution within L P 2RS might be largely determined by the ring material. A preliminary model calculation shows that a neutral number density of n P 1–2 3 103 cm23 can be maintained at the outer edge of the A ring if the corresponding impact vapor production rate is of the order of 8 3 1026 molecules sec21. This would mean that about 50% of the expanding vapor

56

W.-H. IP

is probably composed of dissociated products like OH. (This is because photodissociation of H2O is too inefficient in producing enough OH against the ring absorption effect.) The HST ring observations thus have interesting implications on the general structure of the distributed neutral cloud in the saturnian system. APPENDIX If the radial distance (L) at the equator is given in units of the planetary radius (RS ), the number density of ions, n0 , is related to N, the ion content per unit L, by the relation (Siscoe et al., 1981) N 5 2fLR 2S

E

y

nj (z)dz P 2f 3/2 LR 2S n0 H,

REFERENCES BAR-NUN, A., G. HERMAN, M. L. RAPPAPORT, AND YU. MEKLER 1985. Ejection of H2O, O2 , H2 and H from water ice by 0.5–6 keV H1 and Ne1 ion bombardment. Surf. Sci. 150, 143–156. BRIDGE, H. S., J. W. BELCHER, JR., A. J. LAZARUS, et al.1981. Plasma observations near Saturn: Initial results from Voyager 1. Science 212, 217–224. BRIDGE, H. S., F. BAGENAL, J. W. BELCHER, et al. 1982. Plasma observations near Saturn: Initial results from Voyager 2. Science 215, 563–570. BROWN, W. L., W. M. AUGUSTYNIAK, K. J. MARCANTONIO, E. H. SIMMONS, J. W. BORING, R. E. JOHNSON, AND C. T. REIMANN 1984. Electronic sputtering of low temperature molecular solids. Nucl. Instrum. Methods B 1, 307–314.

(A1)

DANBY, J. M. A. 1989. Fundamentals of Celestial Mechanics, 2nd ed. Willmann–Bell, Richmond, VA.

where n0 is the number density at the equator and H is the scale height. A similar expression can be derived for NL2 and the corresponding source ˙ L2, strength N

DENNEFELD, M. 1974. Theoretical studies of an atmosphere around Saturn’s rings. In IAU Symposium No. 65: Exploration of the Planetary System (A. Woszcyk and C. Iwaniszewska, Eds.), pp. 471–481.

˙ L2 5 2f 3/2L3R 2S n0 H/ti N

EICHHORN, G., AND E. GRU¨ N 1993. High velocity impacts of dust particles in low-temperature water ice. Planet. Space Sci. 41, 429–433.

2y

(A2)

where ti is the ionization time scale. In the calculation of the nominal value of the ionization time scale (ti ), we find that electron-impact ionization of H2O with a rate of a P 10213 cm3 sec21 at an electron temperature of Te P 1 eV (Richardson and Sittler, 1990) is competitive against photoionization with a time scale of 3 3 108 sec only when ne P 104 cm23. Since this is much above the observed values, we have ti P 3 3 108 sec. Therefore, we have

S S DS

D

?

D

(A3) 0.1RS ti 23 ? molecules cm . H 3 3 108 sec

This shows that a value of ˙ L2 P 8 3 1025 ions sec21 would imply n0 P 3 3 103 neutral molecules cm23 N (A4) near the ring system! The application of Eq. (A3) to the orbital region between Enceladus and Tethys, e.g., L P 4.5, could also yield an estimate of the expected neutral gas density in this region. Using ne P 50 cm23, Te P 5 eV, and hence a P 1.2 3 1029 cm3 sec21 and ti P 1.7 3 107 sec. Thus we have

S S

D

HALL, D. T., D. F. STROBEL, P. D. FELDMAN, M. A. MCGRATH, AND H. A. WEAVER 1995. Detection of an oxygen atmosphere on Jupiter’s moon Europa. Nature 373, 677–679.

DS D

HAMILTON, D. P., 365, 498.

AND

J. A. BURNS 1993. OH in Saturn’s rings. Nature,

HAMILTON, D. P., AND J. A. BURNS 1994. Origin of Saturn’s E ring: Selfsustained, naturally. Science 264, 550–553. HILL, T. W., AND F. C. MICHEL 1976. Heavy ions from the Galilean satellites and the centrifugal distortion of the jovian magnetosphere. J. Geophys. Res. 81, 4561–4565. HOBBS, P. V. 1974. Ice Physics, pp. 38–39. Clarendon press, Oxford. HORANYI, M., J. A. BURNS, AND D. P. HAMILTON 1992. The dynamics of Saturn’s E ring particles. Icarus 97, 248–259. HUEBNER, W. E., AND C. W. CARPENTER 1979. Solar Photo Rate Coefficients.. Los Alamos National Laboratory, Informal Report LA-8085MS. HUEBNER, W. F., AND P. T. GIGUERE 1980. A model of comet comae: II. Effects of solar photodissociative ionization. Astrophys. J. 238, 753–762.

˙ L2 N 0.5RS ? n0 (L P 4.5) P 12 ? 8 3 1025 ions/sec21 H ?

HALL, D. T., P. D. FELDMAN, J. B. HOLBERG, AND M. A. MCGRATH 1986. Fluorescent hydroxyl emissions from Saturn’s ring atmosphere. Science 272, 516–518.

HAMILTON, D. P. 1993. Motion of dust in a planetary magnetosphere: Orbit-averaged equations for oblateness, electromagnetic, and radiation forces with application to Saturn’s E ring. Icarus 101, 244–264.

˙ L2 N n0 (L P 2.5) P 8 3 10 ? 8 3 1025 ions/sec21 3

EVIATAR, A., G. L. SISCOE, T. V. JOHNSON, AND D. L. MATSON 1981. Effects of Io ejection on Europa. Icarus 47, 75–83.

(A5)

ti molecules cm23. 1.7 3 107 sec

ACKNOWLEDGMENTS I thank D. E. Shemansky for useful discussions and information on the electron impact rates, M. Horanyi and an anonymous referee for useful comments, F. Both for assistance in the production of the graphics, and M. Steinmetz and H. Reuter for assistance in preparing the manuscript. This work is supported in part by DARA under grants WE 1-50 QS 9401 (GLL/IDS) and WE 1-50 OH 95011 (CAS/INMS).

IP, W.-H. 1978. On the Lyman-alpha emission from the vicinity of Saturn’s rings. Astron. Astrophys. 70, 435–437. IP, W.-H. 1984. The ring atmosphere of Saturn: Monte Carlo simulations of the ring source model. J. Geophys. Res. 89, 8843–8849. IP, W.-H. 1985. Titan’s hydrogen torus. In The Atmospheres of Saturn and Titan, ESA SP-241, pp. 129–144. IP, W.-H.1986. Plasmatization and recondensation of the saturnian rings. Nature 320, 143–145. IP, W.-H. 1995. The exospheric systems of Saturn’s rings. Icarus 115, 295–303. IP, W.-H. 1996a. Europa’s oxygen exosphere and its magnetospheric interaction. Icarus 120, 317–325.

NEUTRAL CLOUD DISTRIBUTION IN SATURNIAN MAGNETOSPHERE IP, W.-H. 1996b. The asymmetric distribution of Titan’s atomic hydrogen cloud as a function of local time. Astrosphys. J. 457, 922–932. JOHNSON, R. E. 1990. Energetic Charged-Particle Interactions with Atmospheres and Surfaces. Springer-Verlag, Berlin/Heidelberg. JOHNSON, R. E., L. J. LANZEROTTI, AND W. L. BROWN 1982. Planetary applications of ion induced erosion of condensed gas frosts. Nucl. Instrum. Methods 198, 147–158. JOHNSON, R. E., J. W. BORING, C. T. REIMANN, L. A. BARTON, E. M. SIEVEKA, J. W. GARRETT, K. R. FARMER, W. L. BROWN, AND L. J. LANZEROTTI 1983. Plasma ion-induced molecular ejection on the Galilean satellites: Energies of ejected molecules. Geophys. Res. Lett. 10, 892–895. JOHNSON, R. E., D. E. GROSUEAN, S. JURAC, AND R. A. BARAGIOLA 1993. Sputtering, still the dominant source of plasma at Dione? EOS Trans. 74, 569–573. JOHNSON, R. E., M. K. POSPIESZALSKA, E. C. SITTLER, JR., A. F. CHENG, L. J. LANZEROTTI, AND E. M. SIEVEKA 1989. The neutral cloud and heavy ion inner torus at Saturn. Icarus 77, 311–329. JURAC, S., R. A. BARAGIOLA, R. E. JOHNSON, AND E. C. SITTLER, JR. 1995. Charging of ice grains by low-energy plasmas: Application to Saturn’s E ring. J. Geophys. Res. 100, 14821–14831. KIEFFER, L. J. 1969. Low-energy electron collision cross section data: I. Ionization, dissociation, vibrational excitation, At. Data 1, 19–89. KOSCHNY, D., AND E. GRU¨ N 1995a. Impacts into ice–silicate mixtures: Crater morphologies, volumes, depth-to-diameter ratios, and yield. Icarus, submitted. KOSCHNY, D., AND E. GRU¨ N 1995b. Impacts into ice–silicate mixtures: Ejecta mass and size distributions. Icarus, submitted. NORTHROP, T. G., AND J. E. P. CONNERNEY 1987. A micrometeorite erosion model and the age of Saturn’s rings. Icarus 70, 124–137. POSPIESZALSKA, M. K., AND R. E. JOHNSON 1991. Micrometeorite erosion of the main rings as a source of plasma in the inner saturnian plasma torus. Icarus 93, 45–52. REIMANN, C. T., J. W. BORING, R. E. JOHNSON, J. W. GARRETT, AND K. R. FARMER 1984. Ion-induced molecular ejection from D2O ice. Surf. Sci. 147, 227–240.

57

RICHARDSON, J. D. 1992. A new model for plasma transport and chemistry at Saturn. J. Geophys. Res. 97, 13705–13713. RICHARDSON, J. D. 1995. An extended plasma model for Saturn. Geophys. Res. Lett. 22, 1177–1180. RICHARDSON, J. D., AND G. L. SISCOE 1983. The problem of cooling the cold Io torus. J. Geophys. Res. 88, 2001–2009. RICHARDSON, J. D. AND E. C. SITTLER, JR. 1990. A plasma density model for Saturn based on Voyager observations. J. Geophys. Res. 95, 12019– 12031. RICHARDSON, J. D., A. EVIATAR, AND G. L. SISCOE 1986. Satellite tori at Saturn. J. Geophys. Res. 91, 8749–8755. SCHMIDT, H. V., R. WEGMANN, W. F. HUEBNER, AND D. C. BOICE 1988. Cometary gas and plasma flow with detailed chemistry. Comp. Phys. Comm. 49, 17–59. SCHREIER, R., A. EVIATAR, V. M. VASYLIUNAS, AND J. D. RICHARDSON 1993. Modeling the Europa plasma torus. J. Geophys. Res. 98, 21231– 21243. SHEMANSKY, D. E., AND D. T. HALL 1992. The distribution of atomic hydrogen in the magnetosphere of Saturn. J. Geophys. Res. 97, 4143– 4161. SHEMANSKY, D. E., P. MATHESON, D. T. HALL, H.-Y. HU, AND M. TRIPP 1993. The hydroxyl radicals in the Saturnian magnetosphere. Nature 363, 329. SHI, M., A. BARAGIOLA, D. E. GROSJEAN, R. E. JOHNSON, S. JURAC, AND J. SCHOU 1995. Sputtering of water ice surfaces and the production of extended neutral atmospheres. J. Geophys. Res. 100, 26387–26395. SHOWALTER, M. R., J. N. CUZZI, AND S. M. LARSON 1991. Structure and particle properties of Saturn’s E ring. Icarus 94, 451–473. SISCOE, G. L., A. EVIATAR, R. M. THORNE, J. D. RICHARDSON, F. BAGENAL, AND J. D. SULLIVAN 1981. Ring current impoundment of the Io plasma Ions. J. Geophys. Res. 86, 8480. SITTLER, E. C., JR., K. W. OGILVIE, AND J. D. SCUDDER 1983. Survey of low-energy plasma electrons in Saturn’s magnetosphere: Voyager I and 2. J. Geophys. Res. 88, 8847–8870. WEISER, H., R. C. VITZ, AND H. W. MOOS 1977. Detection of Lyman a emission from the saturnian disk and from the ring system. Science 197, 755–757.