EFFECTS OF DUST GROWTH AND SETTLING ON THE IONIZATION BY RADIONUCLIDES. I. FORMULATION AND RESULTS IN A QUIESCENT STATE OF PROTOPLANETARY DISKS

Abstract

We investigate the evolution of the ionization rates by the decay of radionuclides in protoplanetary disks at the early stage of planet formation where size growth and settling of dust particles proceed extensively. Because most of the nuclides to ionize gas, such as short-lived nuclide 26Al and long-lived one 40K, are refractory elements, they are contained in the solid material of dust particles. Thus, the ionization by these nuclides is affected by the following three processes: (1) the change of the relative abundance of dust particles due to the settling toward the midplane of the disk, (2) the energy loss of emitted energetic particles inside the solid material of dust particles, and (3) the absorption of energetic particles by the other dust particles located nearby. In this series of papers we comprehensively investigate the basic physical processes, calculate the settling and size growth of dust particles numerically, and clarify the evolution of the ionization rates relative to their initial values in various disk models at this stage. In this paper we investigate the energy-loss processes concerning dust particles, formulate the coalescence equation for settling particles, and apply them to quiescent disk models that are similar to the solar nebula. For simplicity, dust particles are assumed to be compact spheres that remain perfect sticking for mutual collisions. Because the settling of dust particles is not appreciable in the first 103 yr, the ionization rate varies little except in the outermost part near the disk surface. As the settling proceeds, the rate around the midplane increases considerably. The maximum ionization rates by 26Al in the minimum mass solar nebula are about 100, 51, and 14 times larger than their initial values for the orbits R = 0.5, 1, and 5 AU, respectively, which are close to or exceed the ionization rate by cosmic ray in the interstellar medium. The rates by 40K also increase by factors of about 36, 19, and 5 at the same orbits. In the inner orbital regions, these rates exceed the rates by the attenuated cosmic rays by an order of magnitude. The rates in the residual parts decrease extensively as time goes by, because amounts of the floating dust particles decrease continuously.