Environmental Conditions of Moons

Much as with planets, the amount of stellar radiation received by a moon will help dictate some of its fundamental characteristics and potential habitability. The additional complication with moons lies in their range of masses, from tiny (e.g. Enceladus) to large (e.g. Ganymede or Titan) and how this relates to the retention of volatiles - which we discuss below.

In order to make an initial estimate of the orbital radius at which stellar insolation produces a given surface temperature, the classical prescription for estimating the equilibrium surface temperature of a fast-rotating body can be applied, namely:

where AB is the Bond albedo, L* the parent stellar luminosity, and d the distance from the parent star. The factor e is a crude, first-order, correction in the case where an atmosphere is assumed (for zero-atmosphere e = 1). It incorporates the infrared optical depth, and for a present-day Earth-type atmosphere e ~ 0.62. In Fig. 11.4 this expression is used to estimate the time-averaged surface temperature

100 150 200 250 300 350 Time averaged equilibrium surface temperature (K)

Fig. 11.4. Time averaged surface temperatures for hypothetical icy-moons (albedo 0.68 commensurate with Europa, no atmospheres) around a subset of 74 known exoplanets with orbital semi-major axes greater than 0.6 AU. Vertical dashed lines correspond to the water-ice sublimation temperature in a vacuum (170 K), and the water ice/liquid transition above the triple-point pressure (273 K).

100 150 200 250 300 350 Time averaged equilibrium surface temperature (K)

Fig. 11.4. Time averaged surface temperatures for hypothetical icy-moons (albedo 0.68 commensurate with Europa, no atmospheres) around a subset of 74 known exoplanets with orbital semi-major axes greater than 0.6 AU. Vertical dashed lines correspond to the water-ice sublimation temperature in a vacuum (170 K), and the water ice/liquid transition above the triple-point pressure (273 K).

for atmosphere-free water-ice mantled moons around a subset of known exoplanets - excluding those within 0.6 AU of their parent stars (Sect. 11.4). A significant fraction occupy the temperature range above 170 K - the sublimation temperature for pure water ice in a vacuum.

The rate of water sublimation for an ice mantled body can be estimated by considering the water vapor pressure over ice (e.g. Spencer, 1987). This is plotted in Fig. 11.5 as a function of temperature.

This plot assumes only sublimation, and does not account for re-deposition of material, which at ~ 170 K may be at rates approximately equal to those of sublimation - depending on local surface temperature variations (e.g. latitudinal variation on Galilean satellites, Spencer, 1987). For Teq > 170 K sublimation rates are extremely fast - with 100km depth of water ice sublimating in only a few 106 years at 170 K - if there is no re-deposition.

The escape velocity from the surface of a Europa mass moon 0.0082M®) is ~ 2 km s_1, compared to a mean velocity of a water molecule in a gas at 170 K of ~ 0.4 km s_1. Applying the thermal (Jeans) escape methodology (e.g. Lammer et al., 2004) then the typical flux of escaping gas particles at these temperatures is at least a factor 108 lower than that for gas in the exosphere of a large moon with 1000 K temps (e.g. similar to the Martian exosphere). Thus, pure thermal escape appears unlikely to be a dominant mechanism for material loss in cold moons beyond the sublimation line, and even up to the ice-line at 273 K. However, for moons harboring

Fig. 11.5. Water ice sublimation surface lowering rates (km per Myr) as a function of temperature, following (Spencer, 1987).

atmospheres, dissociation of molecular species can promote thermal loss for moons of mass < 0.12M© (Williams et al., 1997).

Sputtering by charged particles trapped within the magnetosphere of the giant planet host is likely to be a highly efficient atmospheric/volatile loss mechanism for moons of all masses (Williams et al., 1997). This is true unless a moon possesses an intrinsic magnetic field. A field such as that measured for Ganymede (0.03M©) (Kivelson et al., 1998) could prevent rapid particle loss. Finally, to represent a classical habitable environment a moon probably requires a climate stabilizing system such as the geophysical carbon-cycle on Earth (Kasting et al., 1993). In the absence of tidal heating (Sect. 11.3.1) Williams et al. (1997) estimate that a moon must exceed some 0.23M© in order to sustain plate tectonics.

Small (< 0.12M©) icy moons with mean surface temperatures in the 170-273 K range may therefore be likely to lose sublimated material and eventually all surface volatiles over relatively short timescales. By extension (based on Fig. 11.4) it appears that 15-27% (albedo ranging from 0.3 to 0.68) of all currently known exoplanets (i.e. including those within 0.6 AU of their parent star) might be capable of harboring small, ice-mantled moons with the potential for tidally heated subsurface oceans. The implications of volatile retention are also compared schematically to the theoretical population of exoplanets in Fig. 11.6. The criteria applied to produce the shaded zone described in Fig. 11.6 are likely overly conservative, but nonetheless there are 4 currently known exoplanet systems that fall within this zone - all with G-type parent stars (GJ 3021b, HD 80606b, HD 104985b, and 70 Vir b).

EU a

Fig. 11.6. The results of 3000 planet formation models are shown (adapted from Ida & Lin, 2004). Planet mass is plotted versus semi-major axis. The major planetary families are labeled. Vertical dashed lines correspond to (left to right): The vapor line - the distance from a 1 L0 star at which a planetary body of albedo 0.68 (commensurate with a reflective, icy, moon) and a terrestrial-type atmosphere and greenhouse effect could attain a surface equilibrium temperature of 273 K. The ice line corresponds to the same physical model, but for a surface temperature of 373 K. The sublimation line corresponds to an atmosphere-free body which attains a surface temperature of 170 K - corresponding to mean water ice sublimation in a vacuum. The horizontal solid line at 1000 M® corresponds to the giant planet mass that could yield a Mars sized (0.1 M®) moon according to the scaling suggested by Canup & Ward (2006) (Sect. 11.2). The shaded zone above this line between the vapor and ice lines therefore corresponds to the most probable region where an atmosphere retaining, "habitable", moon could be found (e.g. Williams et al., 1997)

Fig. 11.6. The results of 3000 planet formation models are shown (adapted from Ida & Lin, 2004). Planet mass is plotted versus semi-major axis. The major planetary families are labeled. Vertical dashed lines correspond to (left to right): The vapor line - the distance from a 1 L0 star at which a planetary body of albedo 0.68 (commensurate with a reflective, icy, moon) and a terrestrial-type atmosphere and greenhouse effect could attain a surface equilibrium temperature of 273 K. The ice line corresponds to the same physical model, but for a surface temperature of 373 K. The sublimation line corresponds to an atmosphere-free body which attains a surface temperature of 170 K - corresponding to mean water ice sublimation in a vacuum. The horizontal solid line at 1000 M® corresponds to the giant planet mass that could yield a Mars sized (0.1 M®) moon according to the scaling suggested by Canup & Ward (2006) (Sect. 11.2). The shaded zone above this line between the vapor and ice lines therefore corresponds to the most probable region where an atmosphere retaining, "habitable", moon could be found (e.g. Williams et al., 1997)

Fig. 11.7. Possible classes of moons as a function of mass and distance from the parent star (see Sect. 11.3)

In Fig. 11.7 a schematic is used to summarize some of the variations in moon characteristics that might be expected. The initial volatile composition of moons is assumed to increase with distance from the parent star (therefore host planet migration and sub-disk temperature structure is ignored). Low mass moons will have difficulty in retaining their initial complement of volatiles unless they are beyond at least the water ice sublimation line in a system. If they do retain volatiles then they are good candidates for tidally heated environments containing liquid water. More massive moons (i.e. those of at least 0.12-0.23 M®) may both retain volatiles and an atmosphere, as well as exhibit active tectonics (potentially boosted by tidal heating) which can provide climate stabilizing feedback (e.g. Kasting et al., 1993). Large moons that experience stellar irradiation commensurate with the classical circumstellar habitable zone may range from relatively "dry" to "wet". With tidal heating the potential for very wet, "ocean" moons is increased since these may form further from the star and therefore have a larger intrinsic volatile content. The most massive moons at large radii may resemble a class of objects akin to Titan, but with a potentially wide range in actual surface conditions.

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