A Constraint on the Velocity Dispersion of the Missing Mass in the Solar Neighborhood

Abstract

The stability of an N-component stellar disk with finite thickness is examined with the gas dynamical approximation. The dispersion relation for marginal stability is obtained. This dispersion relation for N=2 is applied to the missing mass problem in the solar neighborhood, where two components represent the observed mass component and the miss­ ing mass component in the solar neighborhood. From the requirement that the Galactic disk should be locally stable, it is found that the velocity dispersion of the missing mass component should be greater than about 25km/sec. The stability of an infinitesimally thin disk is also investigated and compared with the disk of finite thickness. § l. Introduction It is well known that the observed mass density in the solar neighborhood is about a half of the dynamical mass density. 1l A solution to this problem has once been given by \Veistrop 2l and by Murray and Sanduleak. 3l They have claimed from their observations that the missing mass in the solar neighborhood consists of late .lYf-type dwarfs. However, recent controversies on this problem 4l, 5l have re­ vealed that their results are doubtful, and we must consider that the missing mass has not yet been identified. It may consist of fainter M-type dwarfs, white dwarfs and/or more exotic objects such as black holes. On the other hand, the density wave theory 6l prevails nowadays among the theories of spiral arms. According to this theory, unless the velocity dispersion is greater than Toomre's minimum dispersion,n the Galactic disk breaks into pieces and well-ordered spiral structures cannot be seen. 8l Usually the Galactic disk is considered to satisfy Toomre's criterion on the assumption that the velocity dispersion of the missing mass is the same as that of the observed stars. 6l However, as the velocity dispersion of the missing mass is unknown, the stellar disk of at least two components should be examined to check the stability of the Galactic disk. Here the two components represent the observed mass component and the missing mass component. Alternatively, the requirement that the Galactic disk should be locally stable will give a constraint on the velocity dispersion of the missing mass. To clarify this problem the local stability of an N-component stellar disk is studied in this paper. The N-component stellar disk is approximated as an N­ component gaseous system each component of which is isothermal and has a differ­ ent velocity dispersion from the others. Each component is assumed to interact