||Isamu Onishi, Minoru Sekiya, Planetesimal formation by an axisymmetric radial bump of the column density of the gas in a protoplanetary disk, Earth, Planets and Space, 10.1186/s40623-017-0637-z, 69, 50, 2017.04.
||Minoru Sekiya, Akihito Shimoda, An iterative method for obtaining a nonlinear solution for the temperature distribution of a rotating spherical body revolving in an eccentric orbit, Planetary and Space Science, 97, 23-33, 2014.07, An iterative method for determining the temperature distribution in a rotating spherical body
with an eccentric orbit around a star
The heating term is expanded into the Fourier series with respect the mean anomaly and the spherical harmonics with respect to the longitude and colatitude of a spherical body.
The obtained formula is suitable for the eccentricity less than about 0.7.
The remaining procedure to determine the temperature using an iterative method is same as that described in Sekiya and Shimoda (2013).
The method for determining the change rates of orbital elements due to the Yarkovsky effect is also developed.
Our method is applicable to any value of the rotation period of a body.
The errors of our results are less than 1%.
Our results can be used to test a grid-based numerical code..
||Minoru Sekiya, Akihito Shimoda, An iterative method for obtaining a nonlinear solution for the temperature distribution of a rotating spherical body revolving in a circular orbit around a star, Planetary and Space Science, 84, 112-121, 2013.08, We developed an iterative method for determining the time-dependent three-dimensional temperature distribution in a spherical body with smooth surface that is irradiated by a star.
In the method developed in our previous paper (Sekiya, Shimoda and Wakita, 2012), only the rotational motion is taken into account and the effect due to the revolution around the star is ignored.
The present work includes both the effects of the rotation and the revolution.
We take into account the cooling due to the surface radiation that is proportional to the fourth power of the temperature;
this is the difference of the present work from Vokrouhlicky (1999) that employs the linear approximation for the radiative cooling.
It is assumed that material parameters such as the thermal conductivity and the thermometric conductivity are constant throughout the spherical body.
We obtain a general solution for the temperature distribution inside a body by using the spherical harmonics and the spherical Bessel functions for space and the Fourier series for the time.
The term in the boundary condition that represents the heating due to the star is also expanded into the spherical harmonics and the Fourier series.
The coefficients of the general solution are fitted to satisfy the surface boundary condition by using an iterative method.
We obtained solutions that satisfy the nonlinear boundary condition within 0.1% accuracy.
The temperature distribution determined according to the iterative method is different from that according to the linear approximation; both the maximum and minimum temperatures at a given time after the summer solstice for an iterative solution are lower than those for a linear solution.
The maximum difference between rate of change of the semimajor axis due to the Yarkovsky effect according to the iterative solution and that according to the linear solution is about 20%.
Therefore current understanding of the Yarkovsky effect based on linear solutions is fairly good..
||Minoru Sekiya, Akihito A. Shimoda, Shigeru Wakita, An iterative method for obtaining a nonlinear solution for the temperature distribution of a spinning spherical body irradiated by a central star, Planetary and Space Science, 60, 304-313, 2012.01, We developed an iterative method for determining the three-dimensional temperature distribution in a spherical spinning body that is irradiated by a central star. The seasonal temperature change due to the orbital motion is ignored. It is assumed that material parameters such as the thermal conductivity and the thermometric conductivity are constant throughout the spherical body. A general solution for the temperature distribution inside a body is obtained using spherical harmonics and spherical Bessel functions. The surface boundary condition contains a term obtained using the Stefan?Boltzmann law and is nonlinear with respect to temperature because it is dependent on the fourth power of temperature. The coefficients of the general solution are fitted to satisfy the surface boundary condition by using the iterative method. We obtained solutions that satisfy the nonlinear boundary condition within 0.1% accuracy. We calculated the rate of change in the semimajor axis due to the diurnal Yarkovsky effect using the linear and nonlinear solutions. The maximum difference between the rates calculated using the two sets of solutions is 13%. Therefore current understanding of the diurnal.
||Shigeru Wakita and Minoru Sekiya, Numerical simulation of the gravitational instability in the dust layer of a protoplanetary disk using a thin disk model, The Astrophysical Journal, 675巻1559-1575ページ, 2008.03.
||Minoru Sekiya and Hidenori Takeda, Does the gas flow through a porous dust aggregate help its growth in a protoplanetary disk?, Icarus, 10.1016/j.icarus.2005.01.008, 176, 1, 220-223, 176巻 220-223ページ, 2005.01.
||Naoki Ishitsu and Minoru Sekiya, The effects of the tidal force on shear instabilities in the dust layer of the solar nebula, Icarus, 10.1016/S0019-1035(03)00151-9, 165, 1, 181-194, Vol. 165, No. 1, PP. 181-194., 2003.09.
||Minoru Sekiya, Masayuki Uesugi and Taishi Nakamoto, Flow in a Liquid Sphere Moving with a Hypersonic Velocity in a Rarefied Gas - An Analytic Solution of Linearized Equations -, Progress of Theoretical Physics, 10.1143/PTP.109.717, 109, 5, 717-728, Vol. 109, No. 5, PP. 717-728, 2003.05.
||Minoru Sekiya and Hidenori Takeda, Were planetesimals formed by dust accretion in the solar nebula?, Earth, Planets and Space, 55, 5, 263-269, Vol. 55, No. 5, PP. 263-269., 2003.05.
||Minoru Sekiya, Quasi-equilibrium density distributions of small dust aggregations in the solar nebula, Icarus, 10.1006/icar.1998.5933, 133, 2, 298-309, Vol.133, No.2, PP.298-309., 1998.06, The rotational velocity of a fluid element around the midplane of the solar nebula increased as dust settled toward the midplane. The Kelvin and Helmholtz instability due to velocity difference of a dust-rich region and a dust-poor region should have occurred and the dust layer became turbulent when the Richardson number decreased below the critical value. Then, dust aggregations stirred up due to turbulent diffusion and were prevented to settle further. In this paper, the sizes of dust aggregations are assumed to be equal to or smaller than the typical radius of chondrules (~0.3 mm). In this case, even very weak turbulence stirs up dust aggregations. Therefore a dust density distribution is considered to be self regulated so that the Richardson number is nearly equal to the critical value. The quasi-equilibrium dust density distribution is derived analytically by assuming that the Richardson number is equal to the critical value. The derived dust density at the midplane is much smaller than the critical density of the gravitational stability, if the solar composition of dust to gas ratio is assumed. On the other hand, the dust aggregations concentrate around the midplane and the dust layer becomes gravitationally unstable, if more than 97% (at 1 AU from the Sun) of the gaseous components have been dissipated from the nebula, leaving dusty components. Two alternative scenarios of planetesimal formation are proposed: planetesimals were formed by (1) mutual sticking of dust aggregations by nongravitational forces or by (2) gravitational instabilities in the nebula where the dust to gas ratio is much larger than the ratio with solar elemental abundance. Case (2) might be realized due to dissipation of the nebular gas and/or addition of dust by the bipolar outflow. In case (1), chondrule sizes do not indicate the maximum size of dust aggregations in the solar nebula. .