The origin of spiral arms in galaxies is a longstanding problem in astrophysics. Although, by no means solved, here we summarise the progress of different theories and observations.
5.1. Quasi-stationary density wave theory
In the late 1960s and 1970s the problems of maintaining quasi-stationary spiral density waves were emerging, and the WASER mechanism/ swing amplification proposed to maintain standing waves in the disc. This approach has been developed further, for example investigating damping and gas dissipation to maintain a steady state, as described in Sections 2.1 and 4.2. As also described in Section 2.1, solutions and stability criteria for non-uniformly rotating discs have also been investigated. However as yet there has not been any demonstration that the WASER mechanism works, and that standing waves can develop. N-body simulations of galaxies were just developing in the 1970s and 80s, but the picture has remained largely unchanged. Instead, as discussed in Section 2.1.5, spirals in simulations appear to be dynamic features, more associated with the swing amplification mechanism for generating spiral features. Some simulations find longer lasting modes than predicted by swing amplification alone, but the overall spiral pattern is still transient, recurrent in nature (D'Onghia et al., 2013, Sellwood & Carlberg, 2014). Others specifically designed to support a standing wave between the ILR and OLR, still find a pattern that changes from m = 2 to m = 3 and is ultimately transient recurrent (Sellwood, 2011). The simulations of Salo & Laurikainen (2000b) also resemble the density waves proposed by density wave theory (Kalnajs, 1965, Lin & Shu, 1966). In this case, self gravity of the disc is high, and the tidally induced features in their models may indeed be sufficiently self-gravitating to allow propagating waves. However it is still not clear that these waves are maintained, or indeed any clear necessity that the density waves need to be maintained.
We note that the success of these models in reproducing density wave theory depends to some extent on the interpretation of quasi-stationarity, and whether current simulations satisfy quasi-stationarity. However for those simulations with longer lived spirals, it has not been shown that that the spirals satisfy global mode theory (e.g. Bertin et al. (1989a), Bertin et al. (1989b)) and do not exhibit a steady shape over their lifetime. Observationally we do not readily distinguish between very transient spiral arms, and spiral arms which are ultimately still transient, but survive multiple rotation periods.
5.2. Dynamic spirals
Spiral arm formation from swing amplified instabilities was demonstrated nearly 30 years ago in simulations by Sellwood & Carlberg (1984), and still remains a clear mechanism for producing spiral arms. Typically the dynamic spiral arms produced resemble multi-armed or flocculent galaxies, but as discussed in the previous section, it also possible to produce low m patterns. In recent work, as described in Section 2.2, more details of this mechanism have emerged, for example non-linear evolution, radial migration of stars, the behaviour of the arms and how they corotate with the gas. The simulations have also demonstrated that the predictions of the number and properties of spiral arms are in agreement with the theory. The simulations have recently shed light on a long-standing conundrum with regards the longevity of spiral patterns generated in this way. High resolution calculations (Fujii et al., 2011, D'Onghia et al., 2013) demonstrate that in fact the heating of the spiral arms due to dissipation is much less than previously thought. Thus it possible for such spiral patterns to last for much longer, up to ∼ 10 Gyr. Coupled to this, observations also demonstrate that spiral galaxies exist with little or no star formation (Masters et al., 2010), so there is no longer a need for a gas component, or cold accretion onto the galaxy.
5.3. Tidal interactions
Tidal interactions were certainly recognised as a means of producing spiral arms by the 1980s, but it was not clear whether the induced arms would correspond to kinematic density waves or stationary waves, and whether tidal interactions could produce spiral structure extending to the centres of galaxies. It is now clear from simulations that tidal interactions can readily reproduce grand design structure, although are unlikely to account for multi-armed or flocculent patterns. The dynamics of the arms is dependent on the self gravity of the disc. In the absence of self gravity, the arms are kinematic waves. With increasing self gravity, the arms become more rigid, less susceptible to winding, and with a higher pattern speed. In particular, the central parts of galaxies which are most dense are most susceptible to developing a more rigid pattern, and in some cases a bar. Simulations have shown that tidally induced spirals can last around a Gyr, thus certainly in galaxy groups interactions may well be frequent enough to explain the presence of m = 2 spirals.
5.4. Bar driven spirals
As described in Section 2.3, there are now numerous means by which bars can induce spiral arms, and consequently different behaviour of the spiral arms in relation to the bar. As yet however, there is no clear indication which scenario, whether manifold theory, bar induced spirals, different patterns for the bar and arms, or nonlinear coupling prevails. And, as discussed in Section 2.3, the behaviour of the spiral arms. Whether they have near constant pattern speeds, or are trailing in nature more similar to the swing amplified model of arm formation, is different between different simulations, and in any case is likely to evolve with time. The range of morphology in observed barred galaxies suggests that spirals in barred galaxies have multiple origins.
5.5. Other mechanisms
As we have stated in Section 2.5, the stochastic star formation mechanism has fallen out of favour. Self propagating star formation likely leads to structure in the gas and new stars in galaxies, which produces a much more irregular and flocculent appearance than the underlying old stars. However, simulations that adopt a smooth (structureless) stellar disc and follow the gas and new star formation with hydrodynamics do not find very realistic spiral patterns. At least some structure is required in the stars, for example from swing-amplified noise or perturbations.
Dark matter halos are certainly a plausible means of generating spiral structure but at present we have no way of telling where they are or what effects they are having (if any) on the dynamics of stellar discs.
As discussed in Section 4, current observational tests do not yet rule out any of the proposed mechanisms for determining spiral structure. However we note that now the resolution of observational data is such that tests on determining the origin of spiral arms are becoming feasible, and results increasingly reported in the literature. We emphasised that in the past, observational results have often been limited by the assumption of a constant pattern speed. Applications of the radially dependent Tremaine-Weinberg method have shown that the arms in both grand-design and flocculent galaxies exhibit radially decreasing pattern speeds. Mapping the ages of stellar clusters appears to be a useful test of distinguishing galaxies where gas does not flow through the spiral arms, as is the case for local swing amplified instabilities. Distinguishing the nature of pattern speeds in clear grand design galaxies may be a good way of testing the rigidity of spiral arms. Examining clusters in galaxies that appear to be isolated grand design galaxies (or multi-arm galaxies with a prominent m = 2 pattern), may be a good test of whether the arms originate from swing amplified instabilities, or are density waves.
Interestingly, the gas response seems to first order independent of the nature of the spiral arms (whereas bars for example induce such large shear that star formation appears to be suppressed). Gas and young stars dominate the observed structure, but the spiral potential merely gathers the gas together in the arms than change the gas properties or star formation rate. Thus, other processes in the ISM, such as turbulence, gravity and cloud collisions may have a greater role on the gas dynamics and star formation than spiral arms.
We would like to thank the referee for a very helpful, and thorough report. CLD acknowledges funding from the European Research Council for the FP7 ERC starting grant project LOCALSTAR. JB would like to thank Keiichi Wada, Masafumi Noguchi, Shugo Michikoshi, Shunsuke Hozumi, and Kana Morokuma-Matsui for their valuable comments. JB was supported by the HPCI Strategic Program Field 5 “The Origin of Matter and the Universe.”