The dark matter wake of a galactic bar revealed by multichannel Singular Spectral Analysis

TL;DR

The paper tackles how galactic bars exchange angular momentum with their dark halos by analyzing a high-resolution, isolated barred-disc N-body simulation with an adaptive Basis Function Expansion (BFE) representation. It applies multichannel Singular Spectral Analysis (mSSA) to the BFE coefficient time series $A_{nlm}$ for the disc, bulge, and halo, isolating explicitly coupled dynamical modes such as the central shadow bar and the trailing dark wake. The study quantifies growth rates, pattern speeds, and phase lags, showing that the bar slows approximately as $\Omega_p \sim t^{-1}$ during most of its evolution, with later stages approaching $\Omega_p \sim t^{-0.7}$ as resonance-driven angular-momentum exchange saturates. Overall, the work demonstrates a non-parametric, data-driven framework to disentangle complex coupled structures in galaxies and highlights the potential for extending the approach to varying disc/halo parameters and cosmological environments.

Abstract

The Milky Way is known to contain a stellar bar, as are a significant fraction of disc galaxies across the universe. Our understanding of bar evolution, both theoretically and through analysis of simulations indicates that bars both grow in amplitude and slow down over time through interaction and angular momentum exchange with the galaxy's dark matter halo. Understanding the physical mechanisms underlying this coupling requires modelling of the structural deformations to the potential that are mutually induced between components. In this work we use Basis Function Expansion (BFE) in combination with multichannel Singular Spectral Analysis (mSSA) as a non-parametric analysis tool to illustrate the coupling between the bar and the dark halo in a single high-resolution isolated barred disc galaxy simulation. We demonstrate the power of mSSA to extract and quantify explicitly coupled dynamical modes, determining growth rates, pattern speeds and phase lags for different stages of evolution of the stellar bar and the dark matter response. BFE & mSSA together grant us the ability to explore the importance and physical mechanisms of bar-halo coupling, and other dynamically coupled structures across a wide range of dynamical environments.

Figures (14)

• Figure 1: Upper row: Face on number density of stellar particles as a function of time (increasing left to right). Lower row: Face on dark matter particle number density within $\mid z_{\mathrm{DM}}\mid<3$ kpc in the initial condition (left panel) and the relative number density over time compared to the initial condition (remaining panels) which show the evolution of the dark bar.
• Figure 2: Upper row: Edge on number density of stellar particles as a function of time (increasing left to right). Lower row: Edge on dark matter particle number density in the initial condition (left panel) and the relative number density over time compared to the initial condition (remaining panels) which show the evolution of the dark bar. The color bar is the same as Figure \ref{['fig:evo']}.
• Figure 3: Upper row: Basis function expansion coefficients for $m=2,\ n=0-15$ for the vertically symmetric disc basis functions (left) and $l=2,\ m=2,\ n=0-15$ for the spherical basis functions representing the stellar bulge (middle) and dark matter halo (right). The radial scale increases with decreasing values for $n$, i.e. low $n$ represents the largest scales. The $m=2$ disc and bulge coefficients primarily show the growth and subsequent evolution of the bar, while the halo coefficients show the response of the dark matter halo. Lower row: Absolute value of the coefficients showing the expected exponential growth in the bar instability at early times, while losing phase and pattern speed information.
• Figure 4: Upper: Growth rate of the $m=2$, $n=0$ coefficients for the disc (red) and the $l=2,\ m=2$, $n=2$ coefficients for the halo (black) as a function of time during the early formation of the bar. The growth rate at these times increases exponentially with $\mathrm{e}^{6t}$. Lower: Growth rate from $2\leqslant t\leqslant3$ Gyr, for radial nodes $n=0-10$. Growth rates are defined as the change in coefficient amplitudes over time.
• Figure 5: Pattern speed of the disc $m=2,\ n=0-5$ coefficient series (left) and the halo $l=2,\ m=2,\ n=0-5$ coefficient series (middle) as shown in Figure \ref{['fig:coefs']}. The right panel shows the disc $m=2,\ n=0$ series vs. the halo $l=2,\ m=2,\ n=0$ series, which are clearly coupled.