Secular Evolution of Spiral Galaxies. II. Formation of Quasi-Stationary Spiral Modes

摘要

In this second of a series of three papers, we demonstrate that the kind of spiral patterns in disk galaxies which can remain quasi-stationary on the timescale of a Hubble time are spontaneously formed spiral modes. The amplitude of the spiral mode is limited to a finite value, determined by the basic state characteristics, through a collective dissipation process, introduced in Paper I of this series. We show that the radial distribution of the total torque coupling integral of a spontaneously formed spiral mode must be (and is found to be) of a characteristic bell shape, with the peak of the bell located at the corotation radius of the mode. This distribution of the total torque coupling is concordant with the radial distribution of the phase shift between the potential and density spirals (Paper I). Whereas the existence and the sign of the total torque coupling imply that there is angular momentum being carried outward by a trailing spiral density wave mode, the bell shape further indicates that there is angular momentum being deposited on each annular ring of the galactic disk en route of this outward angular momentum transport. The amount of the deposited angular momentum is negative inside corotation and is positive outside corotation. Since a spiral mode has negative angular momentum density inside corotation and positive angular momentum density outside corotation, it follows that the bell-shaped torque coupling of a trailing spiral model leads to its own spontaneous growth in the linear regime. In going from the linear to the progressively nonlinear regimes, an increasingly larger fraction of the deposited angular momentum is channeled onto the basic state of the disk through a collisionless shock, rather than being used entirely for the wave mode growth. Finally, in the fully nonlinear regime (the quasi-steady state of the wave mode), all of the angular momentum deposited by the trailing spiral mode is given to the basic state. The spiral mode can then remain quasi-stationary on the order of a Hubble time, at the expense of a continuous dissipative basic state evolution. It is argued that the spontaneous formation and stabilization of a large-scale spiral mode in a disk galaxy is an example of a nonequilibrium phase transition.