Spontaneous generation of bending waves in isolated Milky Way-like discs

Abstract

We study the spontaneous generation and evolution of bending waves in N-body simulations of two isolated Milky Way-like galaxy models. The models differ by their disc-to-halo mass ratios, and hence by their susceptibility to the formation of a bar and spiral structure. Seeded from shot noise in the particle distribution, bending waves rapidly form in both models and persist for many billions of years. Waves at intermediate radii manifest as corrugated structures in vertical position and velocity that are tightly wound, morphologically leading, and dominated by the m = 1 azimuthal Fourier component. A spectral analysis of the waves suggests they are a superposition of modes from two continuous branches in the Galactocentric radius-rotational frequency plane. The lower-frequency branch is dominant and is responsible for the corrugated, leading, and warped structure. Over time, power in this branch migrates outward, lending credence to an inside-out formation scenario for the warp. Our power spectra qualitatively agree with results from linear perturbation theory and a WKB analysis, both of which include self-gravity. Thus, we conclude that the waves in our simulations are self-gravitating and not purely kinematic. These waves are reminiscent of the wave-like pattern recently found in Galactic star counts from the Sloan Digital Sky Survey and smoothly transition to a warp near the disc's edge. Velocity measurements from Gaia data will be instrumental in testing the true wave nature of the corrugations. We also compile a list of "minimum requirements" needed to observe bending waves in external galaxies.

Bending waves in the Milky Way’s disc from halo substructure

“…The correlation between bulk vertical motion and midplane displacement in simulations has been discussed by Gómez et al (2013), Gómez et al (2016), Chequers & Widrow (2017), and Gómez et al (2017). In both of our control and satellite simulations the bulk vertical motions follow the same general patterns as the displacements (c.f.…”

“…Our view is that immediately after the disc encounters a satellite the resulting vertical perturbation may well evolve kinematically, but that once sheared into an extended arc, it will behave as a self-gravitating wave. This picture is supported by the good agreement between the results from linear perturbation theory, which includes self-gravity (Hunter & Toomre 1969;Sparke 1984;Sparke & Casertano 1988;Nelson & Tremaine 1995), and simulations (Chequers & Widrow 2017). Eventually, the energy imparted to the disc by a passing subhalo or satellite is converted into random motions of the disc stars thereby vertically heating the disc (Lacey & Ostriker 1985;Toth & Ostriker 1992;Sellwood et al 1998).…”

“…The spectral methods developed by Sellwood & Athanassoula (1986) allow one to characterize density waves in terms of angular frequency and galactocentric radius. These methods provide valuable insight into disc dynamics and have been extended to the study of bending waves (see Chequers & Widrow 2017). Our spectral analysis for in-plane density waves and bending waves begins with the Fourier coefficients, Σ m (R, t j ) and Q m (R, t j ), for N snapshots at times t j = j ∆ t + t 0 , where ∆ t is the time between snapshots, j = 0 .…”

“…The challenge then is to see if one can disentangle these different processes. Adding to the complexity of the prob-lem is the realization that vertical bending waves are excited even in simulations where, apart from the shot noise of the N-body distribution, the halo is smooth and axisymmetric (Chequers & Widrow 2017). In what follows, we make direct comparisons between a control simulation, where the halo is smooth, and one run with a clumpy halo.…”

Emergence of theGaiaphase space spirals from bending waves

“…Further evidence for bending and breathing modes has been seen in both number counts and bulk motions of Solar Neighbourhood stars (see, for example, Widrow et al (2012); Williams et al (2013); Carlin et al (2013); Yanny & Gardner (2013); Gaia Collaboration et al (2018a); Bennett & Bovy (2018)). They can be excited by a passing satellite (Widrow et al 2012;Feldmann & Spolyar 2015;Gómez et al 2013Gómez et al , 2017, spiral structure or the bar (Debattista 2014;Monari et al 2015), or even shot noise in an N-body simulation (Chequers & Widrow 2017).…”