Size Distribution of Grains Growing by Thermal Grain-Grain Collision

Abstract

The time variation in the size distribution of dqst grains is. investigated for the case where the grains are in thermal motion under the impact of ambient gas molecules and they are growing by sticking in grain-grain collisions. The growth of grains in this manner may be expected to occur in .highly dense interstellar .clouds (or protostars) and, especially, in the primordial solar nebula. · · The growth equation for the grains is formulated and some features of its solutions are studied analytically. Furthermore, for some initial condition the equation is numerically solved with a result that the mass spectrum of the grains tends to have a peak and the peak mass itself increases continuously with time. Finally, the shap~ of the spectrum approaches that given by a similarity solution of the equation. The final spectrum has a shape such that with increasing mass it rapidly rises to a peak and for large mass it decreases nearly exponentially. The peak mass is 8.8 times smaller than the mean mass. The analysis of the origin and composition of interstellar dust grains has so . far been made by many people, mainly on the l,o,asis of . the optical properties of the grains known from studies of the visible, infrared and ultraviolet spectrum of light from distant stars. The origin of the grains is not yet clear, but it is generally believed that they are formed somewhere by the condensation of vapor molecules of graphites, silicates and ices at temperatures between 2,000 and 100°K. For the condensation to proceed, high gas density is favorable. As possible places of the grain formation which requires relatively low temperatures and high densities, we can consider the cool atmospheres of red supergiants, planetary nebulae, expanding shells of novae and supernovae and very dense interstellar clouds (see, for example, a ·recent article of Salpeter 1'). After the condensation of grains from the vapor phase has been completed in the objects mentioned above, the grains ~ill further grow by sticking in grain­ grain collisions. The growth of this. type may be expected to occur in objects of high gas densities such as Q.ense interstellar clouds and, especially, in a rotating gaseous disk of the primordial solar nebula as studied by Kusaka, Nakano and Hayashi. 2' The motion of a grain in a dense gas will be thermalized relatively easily by the collisions of ambient hydrogen molecules and helium atoms, unless the gas is in a state of violent turbulence. In this paper, we shall study the change in the size distribution of grains