SECULAR EVOLUTION OF SPIRAL GALAXIES. Ⅰ. A COLLECTIVE DISSIPATION PROCESS

摘要

A collective dissipation mechanism responsible for the secular evolution of the disks of spiral galaxies is proposed and analyzed. The key element in this process is the outward transport of angular momentum. Although it has been previously shown by Lynden-Bell & Kalnajs (1972) that a trailing spiral pattern transports the angular momentum outward, it has also been claimed by them that the exchange of angular momentum between the disk stars and the spiral density wave happens only at the wave-particle resonances. This implies that for the majority of the disk stars there is no secular orbital decay or increase, and, as a result, there is little redistribution of disk surface density over the lifetime of a spiral galaxy. In this paper, we demonstrate that such a conclusion results from the fact that Lynden-Bell & Kalnajs had solved the problem locally and considered only the orbital response of stars to an applied spiral potential. They did not incorporate the constraint for a self-sustained global spiral solution. It is shown that this constraint is in the form of a phase shift, which exists between a self-consistent, open spiral potential and density pair. A phase shift between the potential and density spirals indicates that there is a torque applied by the spiral potential on the spiral density, and a secular transfer of energy and angular momentum between the disk matter and the spiral density wave. For the actual density distribution of a spiral wave mode, it is shown that the sense of this phase shift is such that for a trailing spiral, the disk matter inside the corotation radius should lose energy and angular momentum to the density wave and accrete inward, and the matter outside corotation should gain energy and angular momentum from the wave and excrete. As a result, the disk surface density should -become more and more centrally concentrated, together with the buildup of an extended outer envelope. This trend is consistent with the direction of entropy evolution in self-gravitating systems (Antonov 1962; Lynden-Bell & Wood 1968) and is also consistent with the trend found in the recent N-body simulations of stellar disks (Donner & Thomasson 1994; see also the simulation results in this paper). It is further demonstrated that a local physical mechanism can be found to account for the secular dissipation as is revealed and required by the phase shift. This mechanism takes the form of a temporary local gravitational instability of the streaming disk material at the spiral arms. The presence of this instability, coupled with the fact that a phase shift appears to cause a finite amplitude, open spiral wave to steepen until there is sufficient dissipation in the spiral instability to offset the steepening tendency, indicate that the nature of the large-scale spiral density waves are large-scale spiral gravitational shocks. The typical width of the spiral gravitational shock is on the order of 1 kpc, the same as the effective mean free path of stars in the spiral-arm local gravitational instability. As a result of the instability condition at the spiral arms, a single disk star, when crossing the spiral arms, experiences many small-angle scatterings produced by the combined potential of its neighboring stars, besides experiencing the smooth axisymmetric potential and the smooth spiral potential. The is leads to a secular decay in the mean orbital radius for those stars inside corotation, as well as a secular increase in the mean orbital radius for stars outside corotation.