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Interstellar-ice residue model

  This model assumes that cometary ice was formed in the course of the formation of the solar system from the interstellar-cloud stage to the planetesimal-formation stage as described in §2. For simplicity the formation of cometary ice is divided roughly into two stages.

The first stage is the parent interstellar cloud stage. At this stage, gaseous molecules in the cloud condensed onto grain surfaces to form icy mantles on them. The grain temperature in dense regions of the cloud is as low as tex2html_wrap_inline1256 K, so that even very volatile gaseous species such as N tex2html_wrap_inline1146 and CO could condense onto the grain surfaces. The mantle composition reflects the interstellar molecule composition, apart from positive ions. The grains in dense molecular clouds have been characterized by Greenberg (1982). Namely, the volatile mantle is composed of a mixture of oxidized and reduced species. It should be pointed out that the chemical composition of the gas and mantles are far from the composition expected in chemical equilibrium. This is because the chemistry prevailing in interstellar clouds is not thermal chemistry as is in the primordial solar nebula, but is rather based on ion-molecule reactions in the gas phase because of the low density and temperature of the cloud as well as because of the irradiation by UV and cosmic rays (see papers by Strazzulla and Pirronello in this volume).

The second stage occurs when and after the solar nebula formed from the interstellar cloud. The important physical quantities are the temperature distribution of the solar nebula and its time variation, which, however, are not well clarified at present. In the inner region, most of the grains would have sublimed completely, and as the gas cooled down subsequently, grains would have recondensed. In the outer solar nebula where the temperature rise was not much, on the other hand, there must have been a region where the the grains coated with ice mantles survived. Since the solar nebula was warmer than the interstellar cloud because of heating by solar radiation, however, very volatile species would have been lost by sublimation from the ice mantles. The degree of sublimation would depend upon the distance from the sun. The formation region of comets is the region where the observed volatile abundances are realized. Comets are regarded as planetesimals accreted from grains in this region.

On the basis of this scenario, Yamamoto et al. (1983) and Yamamoto (1985) deduced the following results:

  1. The observed molecular abundances in comets are roughly reproduced from the interstellar abundances except for N tex2html_wrap_inline1146 and CO.
  2. N tex2html_wrap_inline1146 and CO in comets are depleted by more than one order of magnitude compared with the interstellar abundances of N tex2html_wrap_inline1146 and CO. Note that both species are very volatile species (see Fig. 6), which are expected to be the species lost from the grains by sublimation.
  3. From (1) and (2), the formation temperature is estimated to be between the sublimation temperatures of tex2html_wrap_inline1266 and tex2html_wrap_inline1268 .

The sublimation temperature for each molecular species is defined by the gas temperature at which the sublimation rate from a grain surface equals the sticking rate of the molecules from a gas phase. The sublimation rate tex2html_wrap_inline1270 of molecular species X of molecular weight tex2html_wrap_inline1272 per unit surface area of a grain of temperature tex2html_wrap_inline1274 is expressed by

  equation103

where tex2html_wrap_inline1276 is the vapor pressure of the molecular species X, tex2html_wrap_inline1278 mass of an hydrogen atom, and k the Boltzmann constant. On the other hand, the sticking rate tex2html_wrap_inline1282 of the molecules X in the gas (mainly of H tex2html_wrap_inline1146 in the solar nebula conditions) of temperature T and density n onto grain's unit surface area is given by

equation113

where tex2html_wrap_inline1290 is abundance of molecular species X relative to H tex2html_wrap_inline1146 , and tex2html_wrap_inline1294 is the mean thermal velocity of molecules X. At tex2html_wrap_inline1296 , both sticking and sublimation balance, i.e. tex2html_wrap_inline1298 , and we have

  equation120

The relation between the gas temperature T and the grain temperature tex2html_wrap_inline1274 is determined from energy balance of a grain in the solar nebula. It is assumed that grains settle toward the midplane in the solar ne bula just before formation of a cometary nucleus by gravitational fragmentation of the dust layer (see §2). The grains are heated by collisions of gaseous molecules in the solar nebula; heating by solar radiation may be ignored since the dust layer is optically thick for the solar visible and UV radiation. Gaseous molecules contributing most to the grain heating are H tex2html_wrap_inline1146 molecules in the solar nebula. Ignoring other molecular species, the heating rate tex2html_wrap_inline1306 for a grain of radius a is given by

  equation130

where tex2html_wrap_inline1310 is mean thermal velocity of H tex2html_wrap_inline1146 molecules, and tex2html_wrap_inline1314 is the accommodation coefficient of H tex2html_wrap_inline1146 , which is an efficiency of energy transfer at collisions. On the other hand, grains cool by thermal emission with temperature tex2html_wrap_inline1274 . The cooling rate tex2html_wrap_inline1320 of a grain of radius a and emissivity tex2html_wrap_inline1324 is given by

  equation137

where tex2html_wrap_inline1326 is the Stefan-Boltzmann constant, and tex2html_wrap_inline1328 is a background radiation temperature. The grain temperature tex2html_wrap_inline1274 is obtained from the energy balance

  equation146

The sublimation temperature tex2html_wrap_inline1332 and the grain temperature tex2html_wrap_inline1274 corresponding to tex2html_wrap_inline1332 obtained by solving simultaneously eqs. (3) and (6) with putting tex2html_wrap_inline1296 in eq. (6).

Figure 6 shows tex2html_wrap_inline1332 and corresponding tex2html_wrap_inline1274 thus calculated for molecular species relevant to cometary ice, together with the temperature-gas density profiles of the radiative equilibrium (Hayashi, 1981) and adiabatic (Cameron, 1978) models of the solar nebula.

The formation distance of cometary nuclei corresponding to the formation temperature of tex2html_wrap_inline1344 K is estimated to be 14 to 15 < r < 80 to 110 AU, depending upon the temperature distribution of the solar nebula (these values assume a radiative equilibrium (Hayashi, 1981), or adiabatic distribution, (Cameron, 1978). It must be mentioned that there remain ambiguities in translating the formation temperature into the formation distance, since the latter depends upon the actual temperature distribution in the solar nebula and its time variation, and upon the degree of radial transport of the nebular materials.


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Next: Examination of the assumptions Up: Theories on the Origin Previous: Quenching model

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Mon Sep 16 16:23:29 JST 1996