Density wave formation in differentially rotating disk galaxies: Hydrodynamic simulation of the linear regime

Most rapidly and differentially rotating disk galaxies, in which the sound speed (thermal velocity dispersion) is smaller than the orbital velocity, display graceful spiral patterns. Yet, over almost 240 yr after their discovery in M51 by Charles Messier, we still do not fully understand how they originate. In this first paper of a series, the dynamical behavior of a rotating galactic disk is examined numerically by a high-order Godunov hydrodynamic code. The code is implemented to simulate a two-dimensional flow driven by an internal Jeans gravitational instability in a nonresonant wave-“fluid” interaction in an infinitesimally thin disk composed of stars or gas clouds. A goal of this work is to explore the local and linear regimes of density wave formation, employed by Lin, Shu, Yuan and many others in connection with the problem of spiral pattern of rotationally supported galaxies, by means of computer-generated models and to compare those numerical results with the generalized fluid-dynamical wave theory. The focus is on a statistical analysis of time-evolution of density wave structures seen in the simulations. The leading role of collective processes in the formation of both the circular and spiral density waves (“heavy sound”) is emphasized. The main new result is that the disk evolution in the initial, quasilinear stage of the instability in our global simulations is fairly well described using the local approximation of the generalized wave theory. Certain applications of the simulation to actual gas-rich spiral galaxies are also explored.