Abstract
A theory for the origin of the solar system, which is based on ideas of supersonic turbulent convection and indicates the possibility that the original Laplacian hypothesis may by valid, is presented.
We suggest that the first stage of the Sun's formation consisted of the condensation of CNO ices (i.e. H2O, NH3, CH4,...) and later H2, including He as impurity atoms, at interstellar densities to from a cloud of solid grains. These grains then migrate under gravity to their common centre of mass giving up almost two orders of magnitude of angular momentum through resistive interaction with residual gases which are tied, via the ions, to the interstellar magnetic field. Grains rich in CNO rapidly dominate the centre of the cloud at this stage, both giving up almost all of their angular momentum and forming a central chemical inhomogeneity which may account for the present low solar neutrino flux (Prentice, 1976). The rest of the grain cloud, when sufficiently compressed to sweep up the residual gases and go into free fall, is not threatened by rotational disruption until its mean size has shrunk to about the orbit of Neptune.
When the central opacity rises sufficiently to halt the free collapse at central density near 10−13 g cm−3, corresponding to a mean cloud radius of 104 R ⊙, we find that there is insufficient gravitational energy, for the vaporized cloud to acquire a complete hydrostatic equilibrium, even if a supersonic turbulent stress arising from the motions of convective elements becomes important, as Schatzman (1967) has proposed. Instead we suggest that the inner 3–4% of the cloud mass collapses freely all the way to stellar size to release sufficient energy to stabilize the rest of the infalling cloud. Our model of the early solar nebula thus consists of a small dense quasi-stellar core surrounded by a vast tenuous but opaque turbulent convective envelope.
Following an earlier paper (Prentice, 1973) we show how the supersonic turbulent stress\((\rho _t v_t ^2 ) = \beta \rho GM(r)/r\), where β is called the turbulence parameter, ρ is the gas density andM(r) the mass interior to radiusr causes the envelope to become very centrally condensed (i.e. drastically lowers its moment-of-inertia coefficientf) and leads to a very steep density inversion at its photosurface, as well as causing the interior to rotate like a solid body. As the nebula contracts conserving its angular momentum the ratio θ of centrifugal force to gravitational force at the equator steadily increases. In order to maintain pressure equilibrium at its photosurface, material is extruded outwards from the deep interior of the envelope to form a dense belt of non-turbulent gases at the equator which are free of turbulent viscosity. If the turbulence is sufficiently strong, we find that when θ→1 at equatorial radiusR e=R0, corresponding to the orbit of Neptune, the addition of any further mass to the equator causes the envelope to discontinuously withdraw to a new radiusR e>R0, leaving behind the circular belt of gas at the Kepler orbitR 0. The protosun continues to contract inwards, again rotationally stabilizing itself by extruding fresh material to the equator, and eventually abandoning a second gaseous ring at radiusR 1, and so on. If the collapse occurs homologously the sequence of orbital radiiR n of the system of gaseous Laplacian rings satisfy the geometric progression
analogous to the Titius-Bode Law of planetary distances, wherem denotes the mass of the disposed ring andM the remaining mass of the envelope. Choosing a ratio of surface to central temperature for the envelope equal to about 10−3 and adjusting the turbulence parameter β∼~0.1 so thatR n/Rn+1 matches the observed mean ratio of 1.73, we typically findf=0.01 and that the rings of gas each have about the same mass, namely 1000M ⊕ of the solar material. Detailed calculations which take into account non-homologous behaviour resulting from the changing mass fraction of dissociated H2 in the nebula during the collapse do not appreciably disturb this result. This model of the contracting protosun enables us to account for the observed physical structure and mass distribution of the planetary system, as well as the chemistry. In a later Paper II we shall examine in detail the condensation of the planets from the system of gaseous rings.
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References
Alfvén, H. and Arrhenius, G.: 1973 ‘Structure and Evolutionary History of the Solar System, III’,Astrophys. Space Sci.21, 117–176
Allen, C. W.: 1962Astrophysical Quantities, Athlone Press, London.
Babinet, M.: 1861, ‘Note sur un point de la cosmogonie de Laplace’,Comptes Rendus Acad. Sci. Paris 52, 481–484.
Bodenheimer, P. and Sweigart, A. V. 1968 ‘Dynamical Collapse of the Isothermal Sphere’,Astrophys. J. 152 515–522.
Cameron, A. C. W.: 1962, ‘The Formation of the Sun and the Planets’,Icarus 1, 13–69.
Cox, J. P. and Guili, R. T.: 1968,Principles of Stellar Structure, Vols 1 and 2, Gordon and Breach, New York.
Disney, M. J., McNally, D., and Wright, A. E.: 1969 ‘Collapse of Interstellar Gas Clouds—IV. Models of Collapse and a Theory of Star Formation’.Monthly Notices Roy. Astron Soc. 146, 123–160.
Duley, W. W.: 1974, ‘Comparison of Grain Mantles in Interstellar Clouds’,Astrophys. Space Sci. 26, 199–205.
Engvold, O. and Hauge, Ø.: 1974, ‘Elemental Abundances, Isotope Ratios and Molecular Compounds in the Solar Atmosphere’, Report No. 39, Institute of Theoretical Astrophys, Blindern-Oslo.
Ezer, D. and Cameron, A. G. W.: 1965, ‘A Study of Solar Evolution’,Can. J. Phys.,43, 1497–1517.
Freeman, J. W.: 1978., ‘The Primordial Solar Magnetic Field’, inThe Origin of the Solar System S. F. Dermott, ed.), John wiley&Sons, London (in press).
Grossman, L. and Larimer, J. W.: 1974, ‘Early Chemical History of the Solar System’,Revs. Geophys. Space Phys. 12, 71–101.
Hayashi, C.: 1961, ‘Stellar Evolution in Early Phases of Gravitational Contraction’,Publ. Astron. Soc. Japan 13, 450–452.
Hollenbach, D. and Salpeter, E. E.: 1971, ‘Surface Recombination of Hydrogen Molecules’,Astrophys. J. 163, 155–164.
Hoyle, F.: 1955,Frontiers of Astronomy, Heineman, London.
Hoyle, F.: 1960, ‘On the Origin of the Solar Nebula’,Quart. J. Roy. Astron. Soc. 1, 28–55
Hoyle, F. and Wickramasinghe, N. C.: 1968, ‘Condensation of the Planets’,Nature 217, 415–418.
James, R.: 1964, ‘The Structure and Stability of Rotating Gas Masses’,Astrophys. J. 140, 552–582.
Jeans, J. H.: 1928,Astronomy and Cosmogony, Cambridge University Press, Cambridge.
Kuiper, G. P.: 1951, ‘On the Origin of the Solar System’, inAstrophysics (J. A. Hynek, ed.), pp.357–424. McGraw-Hill, New York.
Laplace, P. S. de: 1796,Exposition du Système de Monde, Courcier, Paris.
Larson, R. B.: 1969, ‘Numerical Calculations of the Dynamics of a Collapsing Proto-Star’,Monthly Notices Roy. Astron. Soc. 145, 271–295.
Lewis, J. S.: 1974, ‘The Temperature Gradient in the Solar Nebula’,Science,186, 440–443.
Maxwell, J. C.: 1855, ‘On the Stability of the Motions of Saturn's Rings’, inScientific Papers of J. C. Maxwell (W. D. Niven, ed.), pp. 288–376, Dover, New York.
Mestel, L.: 1965a, ‘Problems of Star Formation—I’,Quart, J. Roy. Astron. Soc. 6, 161–198.
Mestel, L.: 1965b, ‘Problems of Star Formation—II’,Quart. J. Roy. Astron. Soc. 6, 265–298.
Monaghan, J. J. and Roxburgh, I. W.: 1965, ‘The Structure of Rapidly Rotating Polytropes’,Monthly Notices Roy. Astron. Soc. 131, 13–21.
Nieto, M. M.: 1972,The Titius-Bode Law of Planetary Distances: Its History and Theory, Pergamon Press, Oxford.
Penston, M. V.: 1966, ‘Dynamics of Self-Gravitating Gaseous Spheres. I. The Collapse of an Isothermal Gaseous Sphere’,Roy. Obs. Bull., No. 117.
Poincaré, H.: 1911,Leçons sur les Hypothèses Cosmogoniques, Herman, Paris.
Prentice, A. J. R. and ter Haar, D.: 1971, ‘On the Angular Momentum Problem in Star Formation’,Monthly Notices Roy. Astron. Soc. 151, 177–184.
Prentice, A. J. R.: 1973, ‘On Turbulent Stress and the Structure of Young Convective Stars’,Astron. Astrophys. 27, 237–248.
Prentice, A. J. R.: 1976, ‘Supersonic Turbulent Convection, Inhomogeneities of Chemical Composition, and the Solar Neutrino Problem’,Astron. Astrophys. 50, 59–70.
Prentice, A. J. R.: 1977, ‘Formation of the Satellite Systems of the Major Planets’,Proc. Astron. Soc. Australia 3, 172–173.
Reddish, V. C.: 1975, ‘Star Formation in Clouds of Molecular Hydrogen’,Monthly Notices Roy. Astron. Soc. 170, 261–280.
Reddish, V. C. and Wickramasinghe, N. C.: 1969,‘Star Formation in Clouds of Solid Hydrogen Grains’,Monthly Notices Roy. Astron. Soc. 143, 189–208.
Roxburgh, I. W.: 1966, ‘On the Fission Theory of the Origin of Binary Stars’,Astrophys. J. 143, 111–120.
Schatzman, E.: 1949, ‘On Certain Paths of Stellar Evolution., I—Preliminary Remarks’,Bull. Acad. Roy. Belgique 35, 1141–1152.
Schatzman, E.: 1967, ‘Cosmogony of the Solar System and the Origin of Deuterium’,Ann. Astrophys. 30, 963–973.
Schatzman, E.: 1971, inHighlights of Astronomy (C. de Jager, ed.), Vol. 2, p. 197, D. Reidel, Dordrecht, Holland.
Schmidt, M.: 1965, ‘Rotation Parameters and Distribution of Mass in the Galaxy’, inStars and Stellar Systems (A. Blaauw and M. Schmidt, eds.), pp. 513–530, University of Chicago Press, Chicago.
Spitzer, L.: 1968,Diffuse Matter in Space, Interscience, New York.
ter Haar, D.: 1948, ‘Studies on the Origin of the Solar System’,Proc. Roy. Danish Acad. Sci. 25, No. 3.
ter Haar, D.: 1950, ‘Further Studies on the Origin of the Solar System’,Astrophys. J. 111, 179–190.
ter Haar, D.: 1967, ‘On the Origin of the Solar System’,Ann. Rev. Astron. Astrophys. 5, 267–278.
ter Haar, D. and Cameron, A. G. W.: 1963, ‘Historical Review of Theories of the Origin of the Solar System’, inOrigin of the Solar System, (R. Jastrow and A. G. W. Cameron, eds.)., pp. 4–37, Academic Press, New York.
Urey, H. C.: 1951, ‘The Origin and Development of the Earth and Other Terrestrial Planets’,Geochim. Cosmochim. Acta 1, 209–277.
Weber, E. J. and Davis, L. Jr.: 1967, ‘The Angular Momentum of the Solar Wind’,Astrophys. J. 148, 217–227.
Whipple, F. L.: 1972,Earth, Moon and Planets, Harvard University Press, Cambridge Mass.
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Prentice, A.J.R. Origin of the solar system. The Moon and the Planets 19, 341–398 (1978). https://doi.org/10.1007/BF00898829
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DOI: https://doi.org/10.1007/BF00898829