Appendix A – Extra

 
          Jopitar is modeled after the planet Jupiter, the dominant gas giant in our own solar system. Planetary scientists Andrew Ingersoll et al. have written an account of the dynamics of the accessible atmosphere of Jupiter [1]. This overview describes a range of Earth-based and spacecraft observations, and examines hypotheses proposed to explain the data.
          Marley and Fortney have published a book chapter that surveys our current understanding of giant planet interiors [2]. The structure adopted for Jopitar is an amalgam of configurations proposed for Jupiter by various researchers. [3][4][5][6]  In all cases, a molecular hydrogenous atmosphere envelops the planet, to a depth (measured from the top of the troposphere, or active weather layer) of about 14,000 kilometers, some 20% of the planet radius.
          Temperature and pressure both increase with depth through the troposphere, to balance the increasing weight of overlying material. The rate at which temperature increases with depth is known as the lapse rate, an important parameter in modeling any atmosphere. Assuming the fluid is well mixed by convection, the lapse rate is adiabatic, and determined by the local strength of gravity, the atmospheric composition, and the equation of state – the relationship between temperature, pressure, and density. [7]
          The elemental composition of the atmosphere used in the Jopitar model is over 92% (by number of atoms) hydrogen, 7% helium, and less than 1% heavier elements. The hydrogen is primarily in molecular form. The detailed abundances of important elements and molecules beneath the water clouds are generally close to values for Jupiter reported by Atreya and Wong [8] and by Wong et al. [9], respectively. An important exception applies to water (and hence, to oxygen), which is an order of magnitude more abundant in the Jopitar model. The published values largely derive from measurements by the Galileo space probe, which apparently descended through an atypical dry column in the Jupiter atmosphere, and may have grossly underestimated the actual deep abundance of water.
          At its upper levels, Jopitar's atmosphere is an ordinary gas. Yet because of the thermodynamic properties of molecular hydrogen, it becomes a supercritical fluid [10] at a depth of about 140 kilometers. The fluid becomes progressively more like a liquid and less like a gas at greater depths, with no abrupt transition from gas to liquid.
          The vertical distribution of the principal upper cloud layers (ammonia ice, ammonium hydrosulfide ice, water ice, ammonia-bearing liquid water) was modeled on work by Atreya and Wong [11] for Jupiter. Depths of lower, more exotic cloud layers (ammonium halide, alkali sulfide, alkali halide, silicate, magnesium-silicate, iron, etc.) are based on a publication by Fegley and Lodders [12]. Magnesium is assumed to be depleted with respect to silicon in Jopitar's lower troposphere (presumably, a larger proportion of magnesium is locked away in the planet's core). Otherwise most atmospheric silicon, crucial for jopian life, would condense there in magnesium-silicate clouds, and not be available at higher, more temperate levels.
          Pressure-temperature-density profiles from the top of the troposphere to below the water clouds were modeled with guidance from Jupiter data published by Seiff et al. [13] and by Sanchez-Lavega et al. [14]. Lapse rates were assumed to be dry adiabats (atmosphere not saturated with water vapor) in the former case, and moist adiabats (saturated atmosphere) in the latter. Profiles at progressively greater depths, to the base of Jopitar's molecular hydrogen envelope, were estimated using equations of state published by Slattery and Hubbard [15], Graboske et al. [16], and Kerley [17].
          Jopitar's two-layer upper- and mid-tropospheric convection systems derive from a paper by Showman and de Pater [18] for Jupiter. In the upper convection pattern, net upwelling occurs in the bright zones (leading to high, white ammonia ice clouds there), and net downwelling occurs in the darker belts. The situation is reversed in the mid-level convection pattern. Yet the net ascent at mid-tropospheric levels cannot be uniform across each belt, as this would produce thick zone-like stratus water clouds and a (moist adiabatic) temperature profile that inhibits thunderstorm formation. Powerful storms such as those observed in Jupiter's belts, and so crucial to the life cycle of the reys on Jopitar, would not be possible. Instead, ascending matter in belt thunderstorms must dominate over gradual subsidence between storms. Descriptions and models of moist convective storms, and analyses on how they might feed into large-scale flow structures, have been published by Hueso and Sánchez-Lavega [19] and by Li et al. [20].
          The existence of a weak radiative layer (where upward heat flow is carried mainly by radiation, rather than convection) at the base of the mid-tropospheric system was motivated by a paper by Guillot et al. [21]. The Jopitar layer is assumed to be much thinner than the one proposed for Jupiter, to enable hot convective plumes, rich in nutrients, to routinely break through from below. The existence of a lower-tropospheric convection system, beneath the radiative layer, is purely hypothetical.
          As described by Marley and Fortney [22], pressure and temperature would become so large toward the base of Jopitar's atmosphere that a phase transition occurs there. Electrons are squeezed out of hydrogen atoms, and the molecular hydrogen fluid becomes a metallic hydrogen liquid. The transition from molecular hydrogen may be gradual, and span a layer thousands of kilometers thick. Beneath this is an abyssal global ocean of metallic hydrogen, some 47,500 kilometers thick in the Jopitar model.
          At the heart of Jopitar is a rock/ice core with a diameter of 18,000 kilometers, containing the mass of 7.5 Earths. This mass value is typical of the referenced models for Jupiter, which range from 0 (no core) to about 15. The rock component in Jopitar's case is assumed to be concentrated in a central volume 13,000 kilometers across, which is sheathed by a layer of dirty molten ices (water, ammonia, methane). According to the accretion model of giant planet formation [23], a smaller, bare primordial core may have formed by accretion in the early yads of the suolar system. As this body accumulated mass, its gravitational attraction on the surrounding nebula grew, until it pulled in the huge quantities of gaseous material that now form the bulk of the planet.
 
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