Six Decades of Spiral Density Wave Theory

Abstract

The theory of spiral density waves had its origin approximately six decades ago in an attempt to reconcile the winding dilemma of material spiral arms in flattened disk galaxies. We begin with the earliest calculations of linear and nonlinear spiral density waves in disk galaxies, in which the hypothesis of quasi-stationary spiral structure (QSSS) plays a central role. The earliest success was the prediction of the nonlinear compression of the interstellar medium and its embedded magnetic field; the earliest failure, seemingly, was not detecting color gradients associated with the migration of OB stars whose formation is triggered downstream from the spiral shock front. We give the reasons for this apparent failure with an update on the current status of the problem of OB star formation, including its relationship to the feathering substructure of galactic spiral arms. Infrared images can show two-armed, grand design spirals, even when the optical and UV images show flocculent structures. We suggest how the nonlinear response of the interstellar gas, coupled with overlapping subharmonic resonances, might introduce chaotic behavior in the dynamics of the interstellar medium and Population I objects, even though the underlying forces to which they are subject are regular. We then move to a discussion of resonantly forced spiral density waves in a planetary ring and their relationship to the ideas of disk truncation, and the shepherding of narrow rings by satellites orbiting nearby. The back reaction of the rings on the satellites led to the prediction of planet migration in protoplanetary disks, which has had widespread application in the exploding data sets concerning hot Jupiters and extrasolar planetary systems. We then return to the issue of global normal modes in the stellar disk of spiral galaxies and its relationship to the QSSS hypothesis, where the central theoretical concepts involve waves with negative and positive surface densities of energy and angular momentum in the regions interior and exterior, respectively, to the corotation circle; the consequent transmission and overreflection of propagating spiral density waves incident on the corotation circle; and the role of feedback from the central regions.

Spiral structure in barred galaxies. Observational constraints to spiral arm formation mechanisms

“…The observational results of our study, which are presented in the previous section, can be used to test some of the theories of spiral arm formation in barred galaxies (For a concise description of all theories, see the general review by Dobbs & Baba 2014). The quasi-stationary density wave theory (QSDW) developed by Lin & Shu (1964) assumes that spirals arms are density waves propagating within the galaxy disc where stars and gas are stacked while these components are passing through these dense regions (see Shu 2016, and references therein, for a detailed treatment). According to this theory, galaxies with m = 2 spiral structure are favoured contrary to disc galaxies with m ≥ 3 spiral arms, which are less likely.…”

A Consistent Set of Empirical Scaling Relations for Spiral Galaxies: The (vmax, MoM)–(σ0, MBH, ϕ) Relations

“…33 See the recent reviews on spiral structure in disk galaxies (Dobbs & Baba 2014) and spiral density wave theory (Shu 2016) for additional information and historical context. Figure 3.…”

The spiral pattern rotation speed of the Galaxy and the corotation radius with Gaia DR2

“…The Milky Way is a grand design galaxy, as revealed by its large scale spiral structure (Georgelin & Georgelin (1976), Levine et al (2006), Hou et al (2009), Hou & Han (2014), Reid et al (2014)). According to the classical theory (see Shu (2016) for a review), the arms are located between the inner and outer Lindblad resonances. The radius of corotation (Rc), where the velocity of rotation of stars coincides with the rotation velocity of the spiral arms (Ωp), is a fundamental parameter, which divides the Galactic disk in two regions.…”