Linear analysis of the secular gravitational instability in protoplanetary discs
I discuss briefly about various mechanisms which may lead to the concentration of dust particles in the protoplanetary discs (PPDs). When the dimensionless stopping time of dust particles is less than unity, it seems that da kind of the rag-driven instability is effective in accumulation of dust particles in PPDs which is know as secular gravitational instability (SGI). Most of the previous studies generally do not consider dust size distribution and the magnetic field. In this talk, I will discuss about role of dust size distribution on the growth rate of the SGI in PPDs. An extreme case is considered in which the population of dust particles is consisted of two grain species. By analyzing the obtained dispersion relation, it is found that once a certain amount of large dust particles is formed, even though it is much smaller than that of small dust particles, the dust layer becomes more unstable and dust clumping is accelerated. I then extend this analysis by considering the effect of magnetic field on the growth rate of SGI. Based on a linear analysis, I discuss that magnetic field is able to amplify the instability more or less irrespective of the dust-gas coupling. I then conclude by the astrophysical implications of the results in the linear regime and the possible directions for the future works. For example, our linear analysis is restricted to the axisymmetric modes. It would be interesting to extend the model to the non-axisymmetric modes either for a system consisting of single-size particles or for a system including dusts with different sizes.