Emergence of the<i>Gaia</i>phase space spirals from bending waves

Abstract

We discuss the physical mechanism by which pure vertical bending waves in a stellar disc evolve to form phase space spirals similar to those discovered by Antoja et al. in Gaia Data Release 2. These spirals are found by projecting Solar Neighbourhood stars on to the |$z$|–|$v$||$z$| plane. Faint spirals appear in the number density of stars projected on to the |$z$|–|$v$||$z$| plane, which can be explained by a simple model for phase wrapping. More prominent spirals are seen when bins across the |$z$|–|$v$||$z$| plane are coloured by median |$v$|R or |$v$|ϕ. We use both toy model and fully self-consistent simulations to show that the spirals develop naturally from vertical bending oscillations of a stellar disc. The underlying physics follows from the observation that the vertical energy of a star (essentially, its ‘radius’ in the |$z$|–|$v$||$z$| plane) correlates with its angular momentum or, alternatively, guiding radius. Moreover, at fixed physical radius, the guiding radius determines the azimuthal velocity. Together, these properties imply a link between in-plane and vertical motion that lead directly to the Gaia spirals. We show that the cubic R–|$z$| coupling term in the effective potential is crucial for understanding the morphology of the spirals. This suggests that phase space spirals might be a powerful probe of the Galactic potential. In addition, we argue that self-gravity is necessary to properly model the evolution of the bending waves and their attendant phase space spirals.