Hidenori Takeda

Were planetesimals formed by dust accretion in the solar nebula

The growth of meter-sized bodies in the solar nebula by dust accretion is examined. The meter-sized bodies have velocity about 50 m/s relative to the gas and small dust aggregates. When a small dust aggregate hits a meter-sized body, the aggregate breaks into dust monomers. These monomers accrete onto the body after several bouncing as proposed by Wurm et al., Icarus (2001), if the mean free path of the gas molecules is larger than the radius of the body. On the other hand, the monomers never hit the surface of the body again, if the body is much larger than the mean free path of the molecules. The sizes of bodies would be limited to the order of 10 times the mean free path. Kilometer-sized planetesimals were hardly formed by dust accretion in the region within 5 AU from the sun where the mean free path is less than 1 m. The planetesimals were probably formed by the gravitational instabilities in this region.

Thermally driven flow in a gas centrifuge with an insulated side wall

A thermally driven steady axisymmetric flow of gas of small diffusivity in a vertical circular cylinder rotating rapidly about its axis of symmetry is studied. The side wall is a thermal insulator and the horizontal end plates are perfect conductors. The temperature of the top end plate is kept slightly higher than that of the bottom one. The boundary-layer method is applied to solve the linearized basic equations and the following results are obtained. The axial velocity in the inner core is fully controlled by the Ekman suction on the horizontal plates and is the same as that in the case of a perfectly conducting side wall. The closed circulation in the side-wall Stewartson E ½ layer is strongly suppressed compared with the case of a perfectly conducting side wall. This situation is reflected in the inner temperature field, which deviates from that in the case of a perfectly conducting side wall. The critical parameter governing the solution is found to be (γ − 1) PrG 0 E −1/3 /4γ, where Pr is the Prandtl number, γ the ratio of specific heats, E the Ekman number and G 0 the square of the Mach number based on the peripheral speed of the cylinder.

Dissipation of Primordial Turbulence and Thermal History of the Universe

The assumption that in the early stage of the universe there existed turbulence of photons and plasma dragged by them can explain the formation of galaxies plausibly. Using simple expressions to represent the decay law of the primordial turbulence, the thermal history of gas at the pre-galactic stage is followed and the residual ionization degree of hydrogen is computed. It is found that maximum temperatures attainable are about 104 oK for a wide range of heating paramaters. This is because a kind of thermostat that keeps gas temperature below 104 OK operates: the increase of temperature above 10 4 oK is prevented by the increase of the ionization degree and the resultant increase of cooling rate. Therefore, it can be concluded that galaxies cannot be formed through the thermal instability due to the heating by the primordial turbulence.

The structure of the Stewartson layers in a gas centrifuge. Part 2. Insulated side wall

The Stewartson E ½ - and E ¼ -layers in a rapidly rotating compressible fluid are considered within the framework of linearized equations and the boundary-layer method. The fluid is contained in a cylinder made of a thermally insulated side wall and conducting top and bottom end plates. The end plates and the side wall rotate with slightly different angular velocities. The case of an incompressible fluid was discussed by Stewartson, who found that the flow is restricted to the side-wall boundary layers. In the case of a compressible fluid, however, the solutions are strongly dependent upon the thermal boundary conditions assumed on the side wall. In particular, if the wall is insulated the fluid in the inner core is dragged along too since it is coupled strongly to the flow in the side-wall Stewartson layers. The critical parameter governing the solutions is found to be

On the Dissipation of Primordial Turbulence in the Expanding Universe

(\gamma -1) PrG_0 E^{-\frac{1}{3}}/4\gamma

Flows in a Rotating Cylinder with a Sloping Bottom

, where γ is the ratio of specific heats, Pr the Prandtl number, G 0 the square of the rotational Mach number and E the Ekman number.

Numerical Simulation of Viscous Flow by Smoothed Particle Hydrodynamics

The growth of primordial density contrasts and their separation from the general expansion of the universe are the first step in the course of galaxy formation, which has been attempted to describe by various mechanisms. The epoch of the separation depends on the amount of density contrasts at some epoch, which must be more than several billion years ago. In the case of ~ravitational instability there arises some lower limit for the initial density contrast which cannot be explained by the statistical origin.> It has been expected, on the other hand, that thermal instability may play an important role at an early stage of the growing of the density contrasts.),S) This mechanism can be effective, only if heating and cooling balance each other so as to keep matter at high temperature (at least higher than 10 °K) at the pregalactic stage. However, if no heating source of matter exists, the matter temperature Tm downs faster than the radiation temperature Tr after the epoch of the decoupling at Tr::::::4000°K. > The rotational and peculiar motions of the galaxies in the present state suggest us a possibility that enormous turbulent motions have existed at the pregalactic stage. Weizsacker> and Gamow> insisted upon its importance in the problem of galaxy formation. To meet with this, the theory of turbulence in the expanding universe has been developed by one of the authors (H. N.).>•*> On the basis of a more realistic picture for the hot universe motivated by the discovery of cosmic black-body radiation, Ozernoi and Chernin> have recently

Hydrodynamic calculations of axisymmetric accretion flow

An analytic solution of non-axisymmetric flow in a rotating cylinder with a sloping bottom and a flat top, which is rotating slightly farster than the other walls, is obtained for compressible fluid, and is compared with the imcompressible counterpart considered by Pedlosky and Greenspan. In the incompressible fluid the flow field is z -independent due to Taylor-Proudman theorem, and the phenomenon so called westward intensification is observed. In the compressible case, on the other hand, horizontal flow lines are circular, while non-axisymmetric weak z -motion is induced by the bottom slope.