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Io: Energy constraints and plume volcanism
ICARUS 44, 234-239 (1980)
Io: Energy Constraints and Plume Volcanism* RAY T. REYNOLDS Theoretical and Planetary Studies Branch, Ames Research Center, NASA, Moffett Field, California 94035
STANTON J. PEALE 1 Joint Institute for Laborato~ Astrophysics, University of Colorado, National Bureau of Standards, Boulder, Colorado 80309 AND
PATRICK CASSEN Theoretical and Planetary Studies Branch, Ames Research Center, NASA, Moffett Field, California 94035 Received June 11, 1980: revised October 20, 1980 Observational and theoretical considerations, including near-surface energy constraints, suggest a model of Io that features a surface layer o f sulfur overlying an active silicate crust• Such a model would imply frequent contact b e t w e e n silicate m a g m a intrusions and the sulfur layer. This contact could produce volcanic plumes driven by high-temperature sulfur vapor. P l u m e s driven by sulfur vapor meet observational constraints for a wide range of possible conditions, in contrast to the special conditions required for plume generation by SO 2. Characteristics of the two models are c o m p a r e d , and it is suggested that high-spatial-resolution infrared radiometry could identify the driving volatile• • . . a fiery deluge, fed with ever-burning sulfur u n c o n s u m e d .
Paradise Lost, John Milton
Attempts to relate surface activity on Io to the near-surface thermal structure are frustrated by the fact that we cannot determine, at present, what fraction of the heat flow is delivered to the surface by dynamic processes (magma flows, plumes, explosive eruptions, and other phenomena involving rapid material transport), as opposed to simple thermal conduction. For inactive planets, such as the Moon and Mercury, it is certain that all of the internally generated energy escapes via conduction through a thick outer lithosphere. On the other hand, it is estimated that as much as 30% of the energy transported through the Earth's ocean floor is carried by hydrothermal circulations (Sclater et al., 1980), which thus * Presented at I A U Colloquium 57, "'The Satellites of Jupiter," K a i l u a - K o n a , Hawaii, M a y 1980. 1 P e r m a n e n t address: D e p a r t m e n t of Physics, University of California, Santa Barbara, Calif. 93106
account for about 20% of the Earth's total surface energy flux. Perhaps another 5% of the total escapes via the 7 kma/year of new crust produced by ocean ridge and continental volcanism (H. S. Yoder, 1976). Thus, energy transport via short-time-scale dynamic processes at the Earth's solid surface is important, and is likely to be even more so for Io. There are many indications from the Voyager images and data (Sagan, 1979; Nash and Nelson, 1979), as well as from ground-based observations (Wamstecker, et al., 1974; Nelson and Hapke, 1978), that sulfur is abundant on and near Io. This evidence suggests that sulfur layers hundreds of meters thick exist over much of the surface. For heat flux densities of the order suggested by the thin shell tidal heating model (Peale et al., 1979), approximately 500 ergs/cmZ-sec, such sulfur layers would probably be quite mobile and, therefore, 234
0019- 1035/80/I 10234-06502.00/0 Copyright © I980 by AcademicPress. Inc. All rights of reproduction in any form reserved.
PLUME VOLCANISM ON IO capable of providing considerable dynamic transport of heat. For instance, if an energy flux of 250 ergs/cm~-sec were conducted to the surface through a sulfur layer, the sulfur would be molten at 360 m (for thermal conductivity k = 3 x 104 ergs/cm-sec °K). In any event, a lower bound on Io's energy flux can be obtained by assuming that dynamic processes dominate the energy transport, and that these same processes are responsible for the resurfacing that must occur to obscure or obliterate all signs of impact craters (Johnson et al., 1979). The fact that sharp albedo markings, attributed to fluid flow, are clearly visible over much of the surface (Carr et al., 1979) suggests that resurfacing is primarily accomplished by the extrusion of molten material. Johnson et al. (1979) estimate a minimum resurfacing rate of the order of 0.1 c m / y e a r from consideration of the lack of craters, particularly in the diameter range of 1-5 km; the actual mean rate could be much higher. In fact, statistical variations from the time- and space-averaged values, both for impact fluxes and removal processes, would require much higher resurfacing rates to insure the removal of all craters. If resurfacing is accomplished by transport of liquids to the surface, the minimum energy requirement is h = ( d l / d t ) p (Hf + Cp AT),
where h is the average planetary heat flux density at the surface; d l / d t is the resurfacing rate; p is the density; H f is the heat of fusion; Cp is the heat capacity of the mobilized material; and AT is the difference between the melting point of the material and the surface temperature. This formula gives an extreme lower limit for h both because the value for d l / d t is only a lower limit and because it neglects all conducted heat. Resurfacing by silicates at a rate of 0.1 c m / y e a r (Hf = 4 × 109 ergs/g, Cp = 1.2 >( 10r ergs/g °K, AT = 1300°K, p = 3 g/cm a) would require h > 180 ergs/cm 2 sec.
235
If sulfur were the resurfacing agent (H e = 4.4 × 10a ergs/g, Cp = 0.7 × 107 ergs/g °K, AT = 300°K, p= 2 g/cma), h > 16 ergs/cm 2sec. These values should be compared with the value that would be expected if Io were heated only by radiactive elements in abundances comparable to chondritic or lunar abundances, h = 10-20 ergs/cm2-sec, and that suggested by a thin-shell tidal dissipation model, h = 500 ergs/cm2-sec. If resurfacing is accomplished by mobilization of sulfur, it can be presumed that molten sulfur must exist at relatively shallow depths. But note that a thermal gradient in sulfur that would result in melting closer to the surface than, say, 5 kin, would provide a c o n d u c t i v e flux greater than 20 ergs/cm2-sec in addition to the minimum 16 ergs/cm2-sec required for sulfur resurfacing. Therefore, even independently of observations of current thermal activity, it seems certain that Io's total heat flow must substantially exceed that corresponding to lunar or chondritic radioactive abundances. In fact, infrared data have been interpreted by Matson et al. (1980), Sinton (1980), and Pearl (1980) to indicate that the heat flux density from hot spots is of the order of 1000-3000 ergs/cm 2sec. These values exceed theroretical upper limits for tidal dissipation based on the current orbital configuration (C. F. Yoder, 1979). It is not clear whether more extensive infrared data, a more refined model for deriving heat fluxes from the data, or a fundamental revision in the theory of the orbital resonances is required to reconcile this inconsistency. In any event, such high heat flux densities could only be maintained by the upward movement of liquid. Although we cannot exclude either a silicate resurfacing mechanism with only a thin covering of sulfur on the one hand or resurfacing in a thick sulfur layer on the other, the fact that the energy estimates are minimum requirements strongly suggests that the resurfacing is primarily by sulfur. Nevertheless, the substantial relief observed in some calderas (Carr et al., 1979) and elsewhere implies the exis-
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REYNOLDS,
PEALE, AND CASSEN
tence of numerous volcanic silicate constructs. All of these considerations lead naturally to the suggestion that there will be frequent intrusions of silicate magma into an overlying sulfur-rich layer. Two types of volcanic events might be expected: (1) a melting in the outer few hundred meters could mobilize sulfur with little or no ejecta (this occurs when the subsurface temperature of sulfur exceeds the melting temperature and the molten region becomes unstable with respect to the overlying and denser solid layer); and (2) the intrusion of a silicate magma into the base of a sulfur layer, which would occur at temperatures near the melting range of silicates and could produce sulfur vapor. The sulfur vapor so generated could then drive the volcanic plumes, as suggested by Consolmagno (1979) and Hapke (1979). In the following, we analyze the energetics of plumes so produced. Smith et al. (1979a) have proposed that the plumes are driven by SOZ, and their model is compared with the one analyzed here. The maximum heights of the observed plumes range from 70 to 280 km (Strom et al., 1979), which, if plume particle trajectories are essentially ballistic, require surface velocities V of 0.5 to 1 km/set. Although the details of the environment and of the processes capable of producing such spectacular features cannot be ascertained at present, the observations that velocities of 1 km/set are maintained and that the plumes last for at least months impose nontrivial local energy constraints. Presumably the plumes are caused by the rapid expansion of gas from a subsurface chamber through a restricted pipe or vent to the surface, if supersonic velocities are to be sustained. If such an expansion occurs adiabatically, the change in specific kinetic energy between any two points along the flow is given by A(V2/2) = AH, where H is the change in specific enthalpy.
(Changes in gravitational energy during the flow to the surface are negligible.) Sulfur vapor consists of polymers ranging from S, to Ss, the fraction of each constituent being determined by the temperature and pressure. At low temperature near saturation, S,, S,, and S, dominate, but at the temperatures of molten rock (2 12OO’K), even the saturated vapor is dominated by SZ and S3 (Rau et al., 1973). Since SZ is very stable, the monomer is not an important constituent at the temperatures and pressures of interest here. For the superheated (i.e., unsaturated) vapor, S2 is even more dominant. We shall assume that the vapor produced when sulfur encounters molten rock is entirely S, and allow this gas to expand without condensation to the surface. The assumption of no condensation or polymerization means that no latent heat is released during the expansion, thereby minimizing H. Thus
AH= IT;c, dT, where (Rau et al.,
1973)
C, = 5.58 x lo6 + 183T - 5.16 x 1010T-2 ergs/g “K is an empirical formula for the specific heat at constant pressure for SZ vapor for 300°K < T < 1500°K. Table I gives the velocity V as a function of the temperature of the expanding vapor for initial temperatures of 1000, 1200, and 1500°K. (It was assumed that V = 0 at the silicate-sulfur interface.) The AH in this table is the change in enthalpy from the initial temperature to the given temperature. Velocities of 1 km/set are readily attained even for expansion to about 300°K for initial temperatures above 1200°K. (The calculations were truncated at 300°K because the expression for C, is not valid below this temperature.) Since expansion to lower temperatures no doubt occurs for the real plumes, we see that the observed plume
PLUME VOLCANISM ON IO TABLE I VELOCITY AND ENTHALPY CHANGES AS FUNCTIONS OF TEMPERATURE FOR EXPANDING S2 FLOWS T (°K)
H (10 s ergs/g)
V (km/sec)
Initial t e m p e r a t u r e 1000°K 975 950 900 800 700 600 500 400 300
1.42 2.85 5.70 11.4 17.0 22.6 28.1 33.5 38.6
0.168 0.239 0.338 0.477 0.538 0.672 0.749 0.818 0.879
Initial t e m p e r a t u r e 1200°K
237
the sulfur vapor through a nozzle can produce the observed plume heights without recourse to the extremely high temperatures that Gold (1979) suggested are necessary. Io's long-lived plumes require both a continuous supply of energy and volatilizable material. If the sulfur is already molten at the depth where contact with the silicates is made, an adequate supply of volatiles seems assured. It is then required that the magma intrusion heat liquid sulfur from its melting temperature of 395°K to a vapor at, say, 1200°K. The energy per gram of sulfur required is (Stull and Prophet, 1971), 1200 C~¢IT + Hv = 2.38 x 101°ergs/g, 95
1175 1150 1100 1000 900 800 700 600 500 400 300
1.44 2.88 5.75 11.5 17.2 22.8 25.8 34.0 39.5 45.0 50.2
0.170 0.240 0.339 0.479 0.586 0.676 0.754 0.825 0.889 0.948 1.00
Initial temperature 1500°K 1450 1400 1300 1200 i 100 1000 900 800 700 600 500 400 300
2.91 5.82 11.6 17.3 23.1 28.9 34.6 40.2 45.9 51.4 56.9 62.3 67.5
0.241 0.341 0.482 0.590 0.685 0.760 0.831 0.897 0.958 1.01 1.07 1.12 1.16
velocities are easily attained by sulfur vapor heated by silicate magmas. Considerable variations in the initial temperatures and pressures, departures from thermodynamic equilibrium, and frictional losses in naturally formed Laval nozzles do not alter this conclusion. Note that expansion of
where H v is the heat of vaporization. The mass flux in plume 1 observed by Voyager 1 was estimated to be more than 5x l06 g/sec (Johnson et al., 1979). Although this plume had ceased erupting by the time Voyager 2 arrived, let us suppose its lifetime was 3 months. If it was generated by a silicate magma intrusion into a sulfur deposit, more than 0.02 km a of sulfur was ejected at the expense of the solidification of 0.075 km a of silicates (assuming that all energy was derived from latent heat of fusion). The average power associated with such a plume would be more than 1.2 × 1017 ergs/sec. The total power for all observed plumes would be more than twice this value (Johnson et al., 1979). This is a small fraction of the satellite heat budget. In the Smith et al. (1979a) model of Io's volcanic plumes, SOz is heated to the melting point of sulfur (395°K) at a depth of approximately 1 km and allowed to expand isentropically through a vent to the surface. High- and low-entropy cases are considered in which the SO2 is initially in the gaseous and liquid states, respectively, at the start of the expansion, at an initial pressure of about 40 bars. Local thermodynamic equilibrium is assumed at all points during the expansion, which includes phase
238
REYNOLDS, PEALE, AND CASSEN
changes between gas, liquid, and solid forms of SO2. These phase changes are in fact an important feature of the model, since the resultant release of latent heat is used to obtain an enthalpy change sufficient to yield exit velocities of 1 k m / s e c . However, the onset of condensation in supersonic flow leads to the formation of shock waves which destroy isentropicity, decelerate the flow, and increase the ambient pressure (Howard, 1953). This effect is evident when air condenses in hypersonic wind tunnels (Daum and G y a r m a t h y , 1968). Hence, the calculated exit velocity of 1 k m / s e c should be regarded as an upper bound. Frictional losses would further tend to reduce this velocity. Thus the SO., model is energetically marginal. Also, because the heat of fusion per unit volume of sulfur is less than one-tenth that of silicates, a correspondingly greater volume of sulfur must be solidified or cooled to power an energetically equivalent SO., plume. Of course if the SO,, plume could be heated to high temperatures by contact with hot silicates, it too would have enthalpy to spare. But one would expect that a magma intrusion would encounter sulfur before SO.,, and that the sulfur plume would occur first. Since the vapor pressure of SOe exceeds that of sulfur at a given temperature, the latter can be retained at much greater depths than the former. In fact, for thermal gradients greater than that corresponding to a conductive heat flow through sulfur of only 100 ergs/cm2-sec, SO,, is explosively unstable at depths less than that at which sulfur would melt (see Fig. 1). Intrusion of molten sulfur to shallower depths could provide rapid heat transport to an SO,, layer, thereby possibly producing an event of the type discussed by Smith et a/. (1979a), which would be subject to the energy constraints discussed above. The positive identification of SO., frost on the surface (Hapke, 1979; Fanale et al., 1979; Smythe et al., 1979) and gas in the plumes of Io (Pearl et al., 1979) is consistent with the idea that the plumes are SO,,
1000 f
f
OVERBURDEN = VAPOR (S)
/ ~750
2 =<
~_ 500 250 100 ~ 0
OVERBURDEN
-
'~
/ ~ "
VAPOR (SO2) T M (SULFUR)
~
.2
TM (SO2 )
.4 .6 DEPTH, km
.8
1.0
FIG. 1. Curves a and b give temperature versus depth for a thermally conducting sulfur layer for two representative values of heat flux density, 100 and 500 ergs/cm2-sec, respectively. The dashed curves show the temperatures that would be required within this layer for the vapor pressure of sulfur and SO2, respectively, to equal the pressure of the overburden material. The melting temperatures of sulfur and SO._,are also shown.
driven. H o w e v e r , sulfur is clearly abundant on Io's surface, and the observed SO.) might be only a minor constituent of the plume flow, entrained during eruption, or even generated by the reduction of silicate magma by the sulfur vapor (Hapke, 1979). Thus, SO,, could be present in the plumes even though it was not the driving gas. Although the requirements for an SO,powered plume heated by liquid sulfur on Io are much more severe than those for a sulfur-vapor-driven plume, it is not possible to rule out these conditions from the data in hand. H o w e v e r , such an SO,, plume must emerge at very low temperatures (< 100°K for V = 1 km/sec) if the observed velocities are to be reached, whereas the sulfur vapor plume could emerge at temperatures considerably greater than the surface temperature (see Table I). Thus, high-resolution infrared radiometry could rule out the liquid-sulfur-heated-SO2 model for these plumes if the plume vents were warmer than the surrounding surface. The apparent correlation of the observation of an infrared excess (Sinton, 1980) with the formation of
PLUME VOLCANISM ON IO a plume signature on Io (Smith et al., 1979b) could imply a high vent temperature and therefore a sulfur-vapor driving mechanism for Io's plumes. Finally, Consolmagno and Lewis (1980) indicate that high (kbar) equilibrium partial pressures of SO., would be produced under the conditions obtaining at a sulfur-silicate interface for a silicate melt derived from C2 chondritic composition material. If it can be shown that the rate of production of SO., at such a boundary is high, this mechanism should be considered as a potential source for high-temperature plumes driven by both SO., and sulfur. ACKNOWLEDGMENTS We thank R. S. Hickman for helpful discussion of condensation phenomena in supersonic flow. We thank S. Kieffer and G. Consolmagno for several suggestions that improved the manuscript. The research by S.J.P. is supported by NASA Grant NGR05-010-062 and by Ames Research Center under interchange agreement NCA-2-OR680-805.
REFERENCES CARR, M. H., MASURSKY, H., STROM, R. G., AND TERRILE, R. J. (1979). Volcanic features of Io. Nature 280, 729-733. CONSOLMAGNO, G. (1979). Sulfur volcanoes on Io. Science 205, 397-398. CONSOLMAGNO, G., AND LEWIS, J. (1980). The chemical-thermal evolution of Io. Presented at IAU Colloquium No. 57, The Satellites o f Jupiter, KailuaKona, Hawaii. DAUM, F. L., AND GYARMATHY, G. (1968). condensation of air and nitrogen in hypersonic wind tunnels. AIAA J. 6, 458-465. FANALE, F. P., BROWN,R. H., CRUIKSHANK,D. P., AND CLARK, R. N. (1979). Significance of absorption features in Io's IR reflectance spectrum. Nature 380, 761-763. GOLD, T. (1979). Electrical origin of the outbursts on Io. Science 206, 1071-1073. HAPKE, B. (1979). Io's surface and environs: A magmatic-volatile model. Geophys. Res. Lett. 6, 799802. HOWARTH, L., et al., Eds. (1953). Modern Developments in Fluid Dynamics: High Speed Flow, pp. 219-221. Oxford Univ. Press, London. JOHNSON, T. V., CooK, A. F., SAGAN, C., AND SODERBLOM, L. A. (1979). Volcanic resurfacing
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rates and implications for volatiles on Io. Nature 280, 746-750. MATSON, D. L., RANSFORD, G. A., AND JOHNSON, T. V. (1981). Heat flow from Io (JI). J. Geophys. Res., in press. NASH, D. l . , AND NELSON, R. M. (1979). Spectral evidence for sublimates and adsorbates on Io. Nature 280, 763-766. NELSON, D., AND HAPKE, B. (1978). Spectral reflectivities of the Galilean satellites and Titan, 0.32 to 0.86/.tin. Icarus 36, 304-329. PEALE, S. J., CASSEN, P., AND REYNOLDS, R. T. (1979). Melting of Io by tidal dissipation. Science 203, 892-894. PEARL, J. (1980). The thermal state of Io on March 5, 1979. Presented at IAU Colloquium No. 57, The Satellites o f Jupiter, Kailua-Kona, Hawaii. PEARL, J., HANEL, R., KUNDE, W., MAGUIRE, W., FOX, K., GUPTA, S., PONNAMPERUMA, C., AND RAULIN, F. (1979). Identification of gaseous SO2 and new upper limits for other gases on Io. Nature 280, 755-758. RAU, H., KUTTY, T. R. N., AND GUEDES DE CARVALHO, J. R. F. (1973). Thermodynamics of sulfur vapor. J. Chem. Thermodyn. 5, 833-844. SAGaN, C. (1979). Sulfur flows on Io. Nature 280, 750753. SCLATER, J. G., JAUPART, C., AND GALSON, D. (1980). The heat flow through oceans and continents, Rev. Geophys. Space Sci. 8, 269-311. SINTON, W. M. (1981). The thermal emission spectrum of Io and a determination of the heat flux from its hot spots. J. Geophys. Res., in press. SMITH, B. A., SHOEMAKER, E. M., KIEEEER, S. W., AND COOK, A. F. (1979a). The role of SO2 in volcanism on Io. Nature 280, 738-743. SMITH, B. A., AND VOYAGER IMAGINGTEAM (1979b). The Galilean satellites and Jupiter: Voyager 2 Imaging Science Results. Science 206, 927-950. SMYTHE, W. D., NELSON, R. M., AND NASH, D. B. (1979). Spectral evidence for SO2 frost or adsorbate on Io's surface. Nature 280, 766-767. STROM, R. G., TERRILE, R. J., MASURSKY, H., AND HANSEN, C. (1979). Volcanic eruption plumes on Io. Nature 280, 733-736. STULL, O. R., AND PROPHET, H. (1971). J A N A F Thermochemical Tables 2nd ed. Office of Standard Reference Data, National Bureau of Standards, Washington, D.C. WAMSTECKER, W., KRUES, R. L., AND FOUNTAIN, J. L. (1974). On the surface composition of Io. h'arus 23, 417-424. YODER, C. F. (1979). How tidal heating in Io drives the Galilean orbital resonance locks. Nature 279, 767770. YODER, H. S., JR. (1976). Generation o f Basaltic Magma. National Academy of Sciences, Washington, D.C.
Io: Energy Constraints and Plume Volcanism* RAY T. REYNOLDS Theoretical and Planetary Studies Branch, Ames Research Center, NASA, Moffett Field, California 94035
STANTON J. PEALE 1 Joint Institute for Laborato~ Astrophysics, University of Colorado, National Bureau of Standards, Boulder, Colorado 80309 AND
PATRICK CASSEN Theoretical and Planetary Studies Branch, Ames Research Center, NASA, Moffett Field, California 94035 Received June 11, 1980: revised October 20, 1980 Observational and theoretical considerations, including near-surface energy constraints, suggest a model of Io that features a surface layer o f sulfur overlying an active silicate crust• Such a model would imply frequent contact b e t w e e n silicate m a g m a intrusions and the sulfur layer. This contact could produce volcanic plumes driven by high-temperature sulfur vapor. P l u m e s driven by sulfur vapor meet observational constraints for a wide range of possible conditions, in contrast to the special conditions required for plume generation by SO 2. Characteristics of the two models are c o m p a r e d , and it is suggested that high-spatial-resolution infrared radiometry could identify the driving volatile• • . . a fiery deluge, fed with ever-burning sulfur u n c o n s u m e d .
Paradise Lost, John Milton
Attempts to relate surface activity on Io to the near-surface thermal structure are frustrated by the fact that we cannot determine, at present, what fraction of the heat flow is delivered to the surface by dynamic processes (magma flows, plumes, explosive eruptions, and other phenomena involving rapid material transport), as opposed to simple thermal conduction. For inactive planets, such as the Moon and Mercury, it is certain that all of the internally generated energy escapes via conduction through a thick outer lithosphere. On the other hand, it is estimated that as much as 30% of the energy transported through the Earth's ocean floor is carried by hydrothermal circulations (Sclater et al., 1980), which thus * Presented at I A U Colloquium 57, "'The Satellites of Jupiter," K a i l u a - K o n a , Hawaii, M a y 1980. 1 P e r m a n e n t address: D e p a r t m e n t of Physics, University of California, Santa Barbara, Calif. 93106
account for about 20% of the Earth's total surface energy flux. Perhaps another 5% of the total escapes via the 7 kma/year of new crust produced by ocean ridge and continental volcanism (H. S. Yoder, 1976). Thus, energy transport via short-time-scale dynamic processes at the Earth's solid surface is important, and is likely to be even more so for Io. There are many indications from the Voyager images and data (Sagan, 1979; Nash and Nelson, 1979), as well as from ground-based observations (Wamstecker, et al., 1974; Nelson and Hapke, 1978), that sulfur is abundant on and near Io. This evidence suggests that sulfur layers hundreds of meters thick exist over much of the surface. For heat flux densities of the order suggested by the thin shell tidal heating model (Peale et al., 1979), approximately 500 ergs/cmZ-sec, such sulfur layers would probably be quite mobile and, therefore, 234
0019- 1035/80/I 10234-06502.00/0 Copyright © I980 by AcademicPress. Inc. All rights of reproduction in any form reserved.
PLUME VOLCANISM ON IO capable of providing considerable dynamic transport of heat. For instance, if an energy flux of 250 ergs/cm~-sec were conducted to the surface through a sulfur layer, the sulfur would be molten at 360 m (for thermal conductivity k = 3 x 104 ergs/cm-sec °K). In any event, a lower bound on Io's energy flux can be obtained by assuming that dynamic processes dominate the energy transport, and that these same processes are responsible for the resurfacing that must occur to obscure or obliterate all signs of impact craters (Johnson et al., 1979). The fact that sharp albedo markings, attributed to fluid flow, are clearly visible over much of the surface (Carr et al., 1979) suggests that resurfacing is primarily accomplished by the extrusion of molten material. Johnson et al. (1979) estimate a minimum resurfacing rate of the order of 0.1 c m / y e a r from consideration of the lack of craters, particularly in the diameter range of 1-5 km; the actual mean rate could be much higher. In fact, statistical variations from the time- and space-averaged values, both for impact fluxes and removal processes, would require much higher resurfacing rates to insure the removal of all craters. If resurfacing is accomplished by transport of liquids to the surface, the minimum energy requirement is h = ( d l / d t ) p (Hf + Cp AT),
where h is the average planetary heat flux density at the surface; d l / d t is the resurfacing rate; p is the density; H f is the heat of fusion; Cp is the heat capacity of the mobilized material; and AT is the difference between the melting point of the material and the surface temperature. This formula gives an extreme lower limit for h both because the value for d l / d t is only a lower limit and because it neglects all conducted heat. Resurfacing by silicates at a rate of 0.1 c m / y e a r (Hf = 4 × 109 ergs/g, Cp = 1.2 >( 10r ergs/g °K, AT = 1300°K, p = 3 g/cm a) would require h > 180 ergs/cm 2 sec.
235
If sulfur were the resurfacing agent (H e = 4.4 × 10a ergs/g, Cp = 0.7 × 107 ergs/g °K, AT = 300°K, p= 2 g/cma), h > 16 ergs/cm 2sec. These values should be compared with the value that would be expected if Io were heated only by radiactive elements in abundances comparable to chondritic or lunar abundances, h = 10-20 ergs/cm2-sec, and that suggested by a thin-shell tidal dissipation model, h = 500 ergs/cm2-sec. If resurfacing is accomplished by mobilization of sulfur, it can be presumed that molten sulfur must exist at relatively shallow depths. But note that a thermal gradient in sulfur that would result in melting closer to the surface than, say, 5 kin, would provide a c o n d u c t i v e flux greater than 20 ergs/cm2-sec in addition to the minimum 16 ergs/cm2-sec required for sulfur resurfacing. Therefore, even independently of observations of current thermal activity, it seems certain that Io's total heat flow must substantially exceed that corresponding to lunar or chondritic radioactive abundances. In fact, infrared data have been interpreted by Matson et al. (1980), Sinton (1980), and Pearl (1980) to indicate that the heat flux density from hot spots is of the order of 1000-3000 ergs/cm 2sec. These values exceed theroretical upper limits for tidal dissipation based on the current orbital configuration (C. F. Yoder, 1979). It is not clear whether more extensive infrared data, a more refined model for deriving heat fluxes from the data, or a fundamental revision in the theory of the orbital resonances is required to reconcile this inconsistency. In any event, such high heat flux densities could only be maintained by the upward movement of liquid. Although we cannot exclude either a silicate resurfacing mechanism with only a thin covering of sulfur on the one hand or resurfacing in a thick sulfur layer on the other, the fact that the energy estimates are minimum requirements strongly suggests that the resurfacing is primarily by sulfur. Nevertheless, the substantial relief observed in some calderas (Carr et al., 1979) and elsewhere implies the exis-
236
REYNOLDS,
PEALE, AND CASSEN
tence of numerous volcanic silicate constructs. All of these considerations lead naturally to the suggestion that there will be frequent intrusions of silicate magma into an overlying sulfur-rich layer. Two types of volcanic events might be expected: (1) a melting in the outer few hundred meters could mobilize sulfur with little or no ejecta (this occurs when the subsurface temperature of sulfur exceeds the melting temperature and the molten region becomes unstable with respect to the overlying and denser solid layer); and (2) the intrusion of a silicate magma into the base of a sulfur layer, which would occur at temperatures near the melting range of silicates and could produce sulfur vapor. The sulfur vapor so generated could then drive the volcanic plumes, as suggested by Consolmagno (1979) and Hapke (1979). In the following, we analyze the energetics of plumes so produced. Smith et al. (1979a) have proposed that the plumes are driven by SOZ, and their model is compared with the one analyzed here. The maximum heights of the observed plumes range from 70 to 280 km (Strom et al., 1979), which, if plume particle trajectories are essentially ballistic, require surface velocities V of 0.5 to 1 km/set. Although the details of the environment and of the processes capable of producing such spectacular features cannot be ascertained at present, the observations that velocities of 1 km/set are maintained and that the plumes last for at least months impose nontrivial local energy constraints. Presumably the plumes are caused by the rapid expansion of gas from a subsurface chamber through a restricted pipe or vent to the surface, if supersonic velocities are to be sustained. If such an expansion occurs adiabatically, the change in specific kinetic energy between any two points along the flow is given by A(V2/2) = AH, where H is the change in specific enthalpy.
(Changes in gravitational energy during the flow to the surface are negligible.) Sulfur vapor consists of polymers ranging from S, to Ss, the fraction of each constituent being determined by the temperature and pressure. At low temperature near saturation, S,, S,, and S, dominate, but at the temperatures of molten rock (2 12OO’K), even the saturated vapor is dominated by SZ and S3 (Rau et al., 1973). Since SZ is very stable, the monomer is not an important constituent at the temperatures and pressures of interest here. For the superheated (i.e., unsaturated) vapor, S2 is even more dominant. We shall assume that the vapor produced when sulfur encounters molten rock is entirely S, and allow this gas to expand without condensation to the surface. The assumption of no condensation or polymerization means that no latent heat is released during the expansion, thereby minimizing H. Thus
AH= IT;c, dT, where (Rau et al.,
1973)
C, = 5.58 x lo6 + 183T - 5.16 x 1010T-2 ergs/g “K is an empirical formula for the specific heat at constant pressure for SZ vapor for 300°K < T < 1500°K. Table I gives the velocity V as a function of the temperature of the expanding vapor for initial temperatures of 1000, 1200, and 1500°K. (It was assumed that V = 0 at the silicate-sulfur interface.) The AH in this table is the change in enthalpy from the initial temperature to the given temperature. Velocities of 1 km/set are readily attained even for expansion to about 300°K for initial temperatures above 1200°K. (The calculations were truncated at 300°K because the expression for C, is not valid below this temperature.) Since expansion to lower temperatures no doubt occurs for the real plumes, we see that the observed plume
PLUME VOLCANISM ON IO TABLE I VELOCITY AND ENTHALPY CHANGES AS FUNCTIONS OF TEMPERATURE FOR EXPANDING S2 FLOWS T (°K)
H (10 s ergs/g)
V (km/sec)
Initial t e m p e r a t u r e 1000°K 975 950 900 800 700 600 500 400 300
1.42 2.85 5.70 11.4 17.0 22.6 28.1 33.5 38.6
0.168 0.239 0.338 0.477 0.538 0.672 0.749 0.818 0.879
Initial t e m p e r a t u r e 1200°K
237
the sulfur vapor through a nozzle can produce the observed plume heights without recourse to the extremely high temperatures that Gold (1979) suggested are necessary. Io's long-lived plumes require both a continuous supply of energy and volatilizable material. If the sulfur is already molten at the depth where contact with the silicates is made, an adequate supply of volatiles seems assured. It is then required that the magma intrusion heat liquid sulfur from its melting temperature of 395°K to a vapor at, say, 1200°K. The energy per gram of sulfur required is (Stull and Prophet, 1971), 1200 C~¢IT + Hv = 2.38 x 101°ergs/g, 95
1175 1150 1100 1000 900 800 700 600 500 400 300
1.44 2.88 5.75 11.5 17.2 22.8 25.8 34.0 39.5 45.0 50.2
0.170 0.240 0.339 0.479 0.586 0.676 0.754 0.825 0.889 0.948 1.00
Initial temperature 1500°K 1450 1400 1300 1200 i 100 1000 900 800 700 600 500 400 300
2.91 5.82 11.6 17.3 23.1 28.9 34.6 40.2 45.9 51.4 56.9 62.3 67.5
0.241 0.341 0.482 0.590 0.685 0.760 0.831 0.897 0.958 1.01 1.07 1.12 1.16
velocities are easily attained by sulfur vapor heated by silicate magmas. Considerable variations in the initial temperatures and pressures, departures from thermodynamic equilibrium, and frictional losses in naturally formed Laval nozzles do not alter this conclusion. Note that expansion of
where H v is the heat of vaporization. The mass flux in plume 1 observed by Voyager 1 was estimated to be more than 5x l06 g/sec (Johnson et al., 1979). Although this plume had ceased erupting by the time Voyager 2 arrived, let us suppose its lifetime was 3 months. If it was generated by a silicate magma intrusion into a sulfur deposit, more than 0.02 km a of sulfur was ejected at the expense of the solidification of 0.075 km a of silicates (assuming that all energy was derived from latent heat of fusion). The average power associated with such a plume would be more than 1.2 × 1017 ergs/sec. The total power for all observed plumes would be more than twice this value (Johnson et al., 1979). This is a small fraction of the satellite heat budget. In the Smith et al. (1979a) model of Io's volcanic plumes, SOz is heated to the melting point of sulfur (395°K) at a depth of approximately 1 km and allowed to expand isentropically through a vent to the surface. High- and low-entropy cases are considered in which the SO2 is initially in the gaseous and liquid states, respectively, at the start of the expansion, at an initial pressure of about 40 bars. Local thermodynamic equilibrium is assumed at all points during the expansion, which includes phase
238
REYNOLDS, PEALE, AND CASSEN
changes between gas, liquid, and solid forms of SO2. These phase changes are in fact an important feature of the model, since the resultant release of latent heat is used to obtain an enthalpy change sufficient to yield exit velocities of 1 k m / s e c . However, the onset of condensation in supersonic flow leads to the formation of shock waves which destroy isentropicity, decelerate the flow, and increase the ambient pressure (Howard, 1953). This effect is evident when air condenses in hypersonic wind tunnels (Daum and G y a r m a t h y , 1968). Hence, the calculated exit velocity of 1 k m / s e c should be regarded as an upper bound. Frictional losses would further tend to reduce this velocity. Thus the SO., model is energetically marginal. Also, because the heat of fusion per unit volume of sulfur is less than one-tenth that of silicates, a correspondingly greater volume of sulfur must be solidified or cooled to power an energetically equivalent SO., plume. Of course if the SO,, plume could be heated to high temperatures by contact with hot silicates, it too would have enthalpy to spare. But one would expect that a magma intrusion would encounter sulfur before SO.,, and that the sulfur plume would occur first. Since the vapor pressure of SOe exceeds that of sulfur at a given temperature, the latter can be retained at much greater depths than the former. In fact, for thermal gradients greater than that corresponding to a conductive heat flow through sulfur of only 100 ergs/cm2-sec, SO,, is explosively unstable at depths less than that at which sulfur would melt (see Fig. 1). Intrusion of molten sulfur to shallower depths could provide rapid heat transport to an SO,, layer, thereby possibly producing an event of the type discussed by Smith et a/. (1979a), which would be subject to the energy constraints discussed above. The positive identification of SO., frost on the surface (Hapke, 1979; Fanale et al., 1979; Smythe et al., 1979) and gas in the plumes of Io (Pearl et al., 1979) is consistent with the idea that the plumes are SO,,
1000 f
f
OVERBURDEN = VAPOR (S)
/ ~750
2 =<
~_ 500 250 100 ~ 0
OVERBURDEN
-
'~
/ ~ "
VAPOR (SO2) T M (SULFUR)
~
.2
TM (SO2 )
.4 .6 DEPTH, km
.8
1.0
FIG. 1. Curves a and b give temperature versus depth for a thermally conducting sulfur layer for two representative values of heat flux density, 100 and 500 ergs/cm2-sec, respectively. The dashed curves show the temperatures that would be required within this layer for the vapor pressure of sulfur and SO2, respectively, to equal the pressure of the overburden material. The melting temperatures of sulfur and SO._,are also shown.
driven. H o w e v e r , sulfur is clearly abundant on Io's surface, and the observed SO.) might be only a minor constituent of the plume flow, entrained during eruption, or even generated by the reduction of silicate magma by the sulfur vapor (Hapke, 1979). Thus, SO,, could be present in the plumes even though it was not the driving gas. Although the requirements for an SO,powered plume heated by liquid sulfur on Io are much more severe than those for a sulfur-vapor-driven plume, it is not possible to rule out these conditions from the data in hand. H o w e v e r , such an SO,, plume must emerge at very low temperatures (< 100°K for V = 1 km/sec) if the observed velocities are to be reached, whereas the sulfur vapor plume could emerge at temperatures considerably greater than the surface temperature (see Table I). Thus, high-resolution infrared radiometry could rule out the liquid-sulfur-heated-SO2 model for these plumes if the plume vents were warmer than the surrounding surface. The apparent correlation of the observation of an infrared excess (Sinton, 1980) with the formation of
PLUME VOLCANISM ON IO a plume signature on Io (Smith et al., 1979b) could imply a high vent temperature and therefore a sulfur-vapor driving mechanism for Io's plumes. Finally, Consolmagno and Lewis (1980) indicate that high (kbar) equilibrium partial pressures of SO., would be produced under the conditions obtaining at a sulfur-silicate interface for a silicate melt derived from C2 chondritic composition material. If it can be shown that the rate of production of SO., at such a boundary is high, this mechanism should be considered as a potential source for high-temperature plumes driven by both SO., and sulfur. ACKNOWLEDGMENTS We thank R. S. Hickman for helpful discussion of condensation phenomena in supersonic flow. We thank S. Kieffer and G. Consolmagno for several suggestions that improved the manuscript. The research by S.J.P. is supported by NASA Grant NGR05-010-062 and by Ames Research Center under interchange agreement NCA-2-OR680-805.
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