Chushiro Hayashi

Settling and growth of dust particles in a laminar phase of a low-mass solar nebula

Abstract It is considered that some vertical convection as well as possible turbulence in an early phase of solar nebula soon terminates owing to diminution of the temperature dependence of dust opacity due to rapid growth of dust particles. We reexamine settling and growth of dust particles in the subsequent laminar phase of the solar nebula in detail, treating a dust layer as a two-component fluid composed of the dust and the gas. We obtain analytic expressions for the settling path, the growing size, and the settling time. The settling process is divided into two phases, i.e., an early gas-dominant phase and a later dust-dominant phase. So far, only the former phase, where the particle path finally turns from vertical to radial, has been investigated. In the latter phase, dust particles drag the gas, rather than the gas does dust particles. Consequently, the particle path turns from radial to vertical. Dust particles grow most appreciably and rapidly in a radially sweeping phase. The final radii of dust particles at the onset of gravitational instability of the dust layer are 20, 5.9, and 0.60 cm in the Earths, Jupiters, and Neptunes zones, respectively. These values are much smaller than those obtained previously by S.J. Weidenschilling [1980, Icarus44, 172–189] and Y. Nakagawa et al. [1981, Icarus45, 517–528]. The total settling times are 1.9 × 103, 4.6 × 103, and 2.8 × 104 years in the above-mentioned three zones, respectively. These are somewhat smaller than those obtained by the previous studies. Most of the settling time is spent in the early vertically settling phase.

Earth's melting due to the blanketing effect of the primordial dense atmosphere

When the proto-Earth was growing by the accretion of planetesimals and its mass became greater than about 0.1 ME, where ME is the present Earths mass, an appreciable amount of gas of the surrounding solar nebula was attracted towards the proto-Earth to form an optically thick, dense atmosphere. We have studied the structure of this primordial atmosphere under the assumptions that (1) it is spherically symmetric and in hydrostatic equilibrium, and (2) the net energy outflow (i.e., the luminosity) is constant throughout the atmosphere and is given by GMM/R with M = M/106yr or M/107yr where M and R are the mass and the radius of the proto-Earth, respectively. The results of calculations show that the temperature at the bottom of the atmosphere, namely, at the surface of the proto-Earth increases greatly with the mass of the proto-Earth and it is about 1500°K for M = 0.25 ME. This high temperature is due to the blanketing effect of the opaque atmosphere. Thus, as long as the primordial solar nebula was existing, the surface temperature of the proto-Earth was kept high enough to melt most of the materials and, hence, the melted iron sedimented towards the center to form the Earths core.

Growth and sedimentation of dust grains in the primordial solar nebula

Abstract Of the formation processes in the solar system, the process of growth and sedimentation of dust grains in the primordial solar nebula is investigated for a region near the Earths orbit. The growth equation for dust grains, which are sinking as well as being in thermal motion, is solved numerically in the wide mass range between 10 −12 and 10 6 g. Any turbulent motions in the nebula are assumed to have already decayed when the sedimentation begins. The numerical simulation shows that the growth and sedimentation proceed faster than was found by Kusaka et al. (1970) but in accordance with the estimate of Safronov (1969) owing to a cooperative interaction of the growth and the sedimentation; that is, at about 3 × 10 3 years after the beginning of the growth and sedimentation a dust layer, composed of centimeter-sized grains, is formed at the equator of the solar nebula. Furthermore, the mass density of dust grains floating in the outer layers of the nebula is found to be of the order of 10 −5 after 10 5 years compared with that before the sedimentation. From these results, it can be estimated that at about 5 × 10 3 years after the beginning of sedimentation the dust layer breaks up owing to the onset of gravitational instability.

Accumulation of planetesimals in the solar nebula

Characteristic time scales relevant to the accumulation of planetesimals in a gaseous nebula are examined and the accumulation toward the planets is simulated by numerically solving a growth equation for a mass distribution function. The eccentricity and inclination of planetesimals are assumed to be determined by a balance between excitation due to mutual gravitational scattering and dissipation due to gas drag. Two kinds of mass motion in the radial direction, i.e., diffusion due to mutual scattering and inward flow due to gas drag, are both taken into account. The diffusion is shown to be effective in later stages with a result of accelerating the accumulation. As to the coalescent collision cross section, the usual formula for a binary encounter in a free space is used but the effect of tidal disruption which increases substantially the cross section is taken into account. Numerical results show that the gravitational enhancement factor (i.e., the so-called “Safronov number”), contained in the cross section formula, always takes a value of the order of unity but the accumulation proceeds relatively rapidly owing to the effects of radial diffusion and tidal disruption. That is, a proto-Earth, a proto-Jupiter, and a proto-Saturn with masses of 1×1027 g are formed in 5×106, 1×107, and 1.6×108 years, respectively. Also, a tentative numerical computation for the Neptune formation shows that a proto-Neptune with the same mass requires a long accumulation time, 4.6×109 years. Finally, the other effects which are expected to reduce the above growth times further are discussed.

Evolution of the Stars

Modern theories on the evolution of stars are extended to the phases of helium burning, carbon burning, and later burnings as far as possible, and the theoretical results are compared wth the Hertzsprung-Russell diagrams of star clusters. The topics discussed include nuclear generation and energy loss by neutrinos, quasi-static equilibrium, envelope,core, and surface solutions, stellar models with homogeneous chemical composition, hydrogen burning phase, helium burning phase, advanced phases of nuclear burning, iinal phase toward white dwarfs, and pre-mainsequence contricting phase. (C.E.S.)

Criteria for collapse and fragmentation of rotating, isothermal clouds

Isothermal collapse of a rotating interstellar cloud is computed three dimensionally with a so-called smoothed particle method. Initial clouds are rigidly rotating homogeneous spheres with small density fluctuations (..delta..rho/rho> or approx. =0.05). To find a condition for fragmentation of a cloud, we test a wide range of intial conditions in the ..cap alpha../sub 0/-..beta../sub 0/ plane, where ..cap alpha../sub 0/ and ..beta../sub 0/ are the initial ratios of thermal and rotational energies to gravitational energy, respectively.

Dissolution of the primordial rare gases into the molten Earth's material

Abstract We have shown in a previous paper that, if the primordial solar nebula existed when the Earth was formed, the Earth was once surrounded by a dense and massive primordial atmosphere, whose temperature and pressure were about 4000 K and 900 atm, respectively, at the bottom. We suppose that this hydrogen-rich atmosphere escaped from the Earth after the solar nebula itself disappeared, both phenomena probably being due to the effect of strong solar wind and radiation. Using the results of our previous and new calculations on the structure of the primordial atmosphere, we have investigated the amount of dissolution of the rare gases, which were contained in the primordial atmosphere, into the molten Earths material. The amount of the dissolved rare gases is found to be strongly dependent on the grain opacity of the atmosphere, i.e., on the amount of fine grains. However, their isotopic ratios and relative abundance are independent of the opacity and approximately equal to those in the primordial solar nebula, that is, to the present solar values. Especially, the dissolved neon is expected to have remained in the present mantle. Therefore, if a considerable amount of neon with nearly the solar isotopic ratio is discovered in present mantle material, this offers direct evidence for the proposition that the proto-Earth was once surrounded by the primordial atmosphere.

Dissipation of the rare gases contained in the primordial Earth's atmosphere

Abstract If the Earth was formed by accumulation of rocky bodies in the presence of the gases of the primordial solar nebula, the Earth at this formation stage was surrounded by a massive primordial atmosphere (of about 1 × 1026 g) composed mainly of H2 and He. We suppose that the H2 and He escaped from the Earth, owing to the effects of strong solar wind and EUV radiation, in stages after the solar nebula itself dissipated into the outer space. The primordial atmosphere also contained the rare gases Ne, Ar, Kr and Xe whose amounts were much greater than those contained in the present Earths atmosphere. Thus, we have studied in this paper the dissipation of these rare gases due to the drag effect of outflowing hydrogen molecules. By means of the two-component gas kinetic theory and under the assumption of spherically symmetric flow, we have found that the outflow velocity of each rare gas relative to that of hydrogen is expressed in terms of only two parameters — the rate of hydrogen mass flow across the spherical surface under consideration and the temperature at this surface. According to this result, the rare gases were dissipated below the levels of their contents in the present atmosphere, when the mass loss rate of hydrogen was much greater than 1 × 1017 g/yr throughout the stages where the atmospheric mass decreased from 1 × 1026 g to 4 × 1019 g.

Equilibria of rotating isothermal clouds

The effect of rotation on the equilibrium structure of an axisymmetric isothermal gas cloud embedded in a stationary external medium is investigated by means of numerical simulations. The underlying assumptions, basic equations, input parameters, and numerical approach are explained, and the results are presented in extensive tables and graphs and characterized in detail. The critical central density and rotation energy, beyond which clouds become unstable to global contraction/expansion and ring formation, respectively, are found to be 800 times the boundary-surface density (BSD) and 0.44 times the gravitational energy. Stable rotating clouds are shown to have maximum mass 31 times that of nonrotating clouds, maximum mean rotation velocity 2.7 times the sound speed, and maximum mean density 6 times BSD. An expression for the maximum height of the boundary surface above the equatorial plane is derived. 41 references.

Gas flow in the solar nebula leading to the formation of Jupiter

Three-dimensional gas flow in the solar nebula, which is subject to the gravity of the Sun and proto-Jupiter, is numerically calculated by using a three-dimensional hydrodynamic code - i.e., the socalled smoothed-particle method. The flow is circulating around the Sun as well as falling into a potential well of proto-Jupiter. The results for various masses of proto-Jupiter show that (1) the e-folding growth time of proto-Jupiter by accretion of the nebular gas is as short as about 300 years in stages where the mass of proto-Jupiter is 0.2 ~ 0.5 times the present Jovian mass, and that (2) proto-Jupiter begins to push away the nebular gas from the orbit of proto-Jupiter and form a gap around the orbit, when its mass is about 0.7 times the present Jovian mass. It is possible that this pushing-away process determined the present Jovian mass.