The majority of astrophysics involves the study of spiral galaxies, and stars and planets within them, but how spiral arms in galaxies form and evolve is still a fundamental problem. Major progress in this field was made primarily in the 1960s, and early 1970s, but since then there has been no comprehensive update on the state of the field. In this review, we discuss the progress in theory, and in particular numerical calculations, which unlike in the 1960s and 1970s, are now commonplace, as well as recent observational developments. We set out the current status for different scenarios for spiral arm formation, the nature of the spiral arms they induce, and the consequences for gas dynamics and star formation in different types of spiral galaxies. We argue that, with the possible exception of barred galaxies, spiral arms are transient, recurrent and initiated by swing amplified instabilities in the disc. We suppose that unbarred m = 2 spiral patterns are induced by tidal interactions, and slowly wind up over time. However the mechanism for generating spiral structure does not appear to have significant consequences for star formation in galaxies.

In order to understand the physical mechanisms underlying non-steady stellar spiral arms in disk galaxies, we analyzed the growing and damping phases of their spiral arms using three-dimensional N -body simulations. We confirmed that the spiral arms are formed due to a swing amplification mechanism that reinforces density enhancement as a seeded wake. In the damping phase, the Coriolis force exerted on a portion of the arm surpasses the gravitational force that acts to shrink the portion. Consequently, the stars in the portion escape from the arm, and subsequently they form a new arm at a different location. The time-dependent nature of the spiral arms are originated in the continual repetition of this non-linear phenomenon. Since a spiral arm does not rigidly rotate, but follows the galactic differential rotation, the stars in the arm rotate at almost the same rate as the arm. In other words, every single position in the arm can be regarded as the co-rotation point. Due to interaction with their host arms, the energy and angular momentum of the stars change, thereby causing the radial migration of the stars. During this process, the kinetic energy of random motion (random energy) of the stars does not significantly increase, and the disk remains dynamically cold. Owing to this low degree of disk heating, the short-lived spiral arms can recurrently develop over many rotational periods. The resultant structure of the spiral arms in the N -body simulations is consistent with some observational nature of spiral galaxies. We conclude that the formation and structure of spiral arms in isolated disk galaxies can be reasonably understood by non-linear interactions between a spiral arm and its constituent stars.

It has been believed that spiral arms in pure stellar disks, especially the ones spontaneously formed, decay in several galactic rotations due to the increase of stellar velocity dispersions. Therefore, some cooling mechanism, for example dissipational effects of the interstellar medium, was assumed to be necessary to keep the spiral arms. Here we show that stellar disks can maintain spiral features for several tens of rotations without the help of cooling, using a series of high-resolution three-dimensional N -body simulations of pure stellar disks. We found that if the number of particles is sufficiently large, e.g., 3 × 10 6 , multi-arm spirals developed in an isolated disk can survive for more than 10 Gyrs. We confirmed that there is a self-regulating mechanism that maintains the amplitude of the spiral arms. Spiral arms increase Toomre's Q of the disk, and the heating rate correlates with the squared amplitude of the spirals. Since the amplitude itself is limited by Q, this makes the dynamical heating less effective in the later phase of evolution. A simple analytical argument suggests that the heating is caused by gravitational scattering of stars by spiral arms and that the self-regulating mechanism in pure-stellar disks can effectively maintain spiral arms on a cosmological timescale. In the case of a smaller number of particles, e.g., 3 × 10 5 , spiral arms grow faster in the beginning of the simulation (while Q is small) and they cause a rapid increase of Q. As a result, the spiral arms become faint in several Gyrs.

We propose a new dynamical picture of galactic stellar and gas spirals, based on hydrodynamic simulations in a 'live' stellar disk. We focus especially on spiral structures excited in a isolated galactic disk without a stellar bar. Using high-resolution, 3-dimensional N -body/SPH simulations, we found that the spiral features of the gas in galactic disks are formed by essentially different mechanisms from the galactic shock in stellar density waves. The stellar spiral arms and the interstellar matter on average corotate in a galactic potential at any radii. Unlike the stream motions in the galactic shock, the interstellar matter flows into the local potential minima with irregular motions. The flows converge to form dense gas clouds/filaments near the bottom of the stellar spirals, whose global structures resemble dust-lanes seen in late-type spiral galaxies. The stellar arms are non-steady; they are wound and stretched by the galactic shear, and thus local densities of the arm change on a time scale of ∼ 100 Myrs, due to bifurcating or merging with other arms. This makes the gas spirals associated with the stellar arms non-steady. The association of dense gas clouds are eventually dissolved into inter-arm regions with non-cirucular motions. Star clusters are formed from the cold, dense gases, whose ages are less than ∼ 30 Myrs, and they are roughly associated with the background stellar arms without a clear spatial offset between gas spiral arms and distribution of young stars.