Effects of Resolution and Local Stability on Galactic Disks: I. Multiple Spiral Mode Formation via Swing Amplification

TL;DR

This work examines spontaneous multi-armed spiral formation in Milky Way–like disk–halo systems using high-resolution N-body simulations, focusing on how resolution, local stability, and a live halo influence mode growth and evolution. By tracking Fourier amplitudes for $m=1$–$6$ and analyzing angular momentum exchange, the authors uncover a robust mode cascade from higher to lower $m$ that propagates inward, modulated by swing amplification and long-lived mode interference. A central, centrally concentrated $m=3$ mode emerges as a key precursor to bar formation, driven by dynamical friction with the live halo, a process absent in fixed-potential models. The study highlights the crucial role of halo responsiveness and adequate particle sampling in preserving the natural evolution from transient spirals to a bar, with only small total angular-momentum transfer during the spiral phase but significant secular evolution thereafter.

Abstract

We investigate the formation of multiple spiral modes in Milky Way-like disk-halo systems without explicitly exciting perturbations. We explore how numerical resolution, the level of local disk stability, and the presence of a live halo influence both the initial appearance and the subsequent evolution of these modes. To characterize spiral structure, we compute Fourier amplitudes for modes $m=1$-$6$. In marginally unstable, lower-resolution disks ($N_\star=5\times10^6$, $N_{\rm DM}=1.14\times10^7$), faint features appear within the first $0.5$ Gyr due to numerical noise, in contrast to high-resolution models where perturbations emerge later. Across all sufficiently resolved, live-halo models with $m_{\rm DM}/m_\star \le 10$, the spirals exhibit a cascading sequence in both mode number and radius: higher-$m$ modes form and decay first, followed by the delayed emergence of lower-$m$ modes, with an inward drift of the activity's epicenter. This behavior reflects a combination of local swing amplification, which explains the initial growth of short-wavelength modes, and interference between coexisting long-lived spiral modes, which accounts for the recurrent short-timescale amplitude modulations. In contrast, models with a fixed halo potential or coarse halo resolution ($N_{\rm DM}=1.14\times10^6$ and $m_{\rm DM}/m_\star=100$) show strong early spirals but lack this coherent cascading behavior, owing to excessive shot noise and insufficient halo responsiveness. The $m=3$ mode plays a transitional role, marking the onset of angular-momentum transport in the inner disk that precedes bar formation, a process absent in fixed-potential models. Our results show that a live halo with appropriate mass resolution provides the gravitational response needed to sustain and regenerate multi-mode spiral structure, even though the total angular-momentum exchange remains small.

Figures (12)

• Figure 1: Face-on projections of surface density distribution in a $30\times30{\rm\,kpc}$ box at 0.5, 1.0, 1.5 and 2.0 Gyr (rows) and for model r2c14, r1c16, r2c16, r2c18, and r2c20 (columns).
• Figure 2: Comparison of radial profiles of individual Fourier modes and ${F_{\rm{sum}}}$ in r2c16 (left column) and r1c16 (right column). ${F_{\rm{sum}}}$ is the root-mean-square (RMS) sum of Fourier modes from 1 to 6. Each row is obtained from a snapshot at 0.5, 1.0, 1.5, and 2.0 Gyr.
• Figure 3: Temporal evolution of the radially averaged value of the RMS sum of Fourier modes, ${\langle F_{\rm{sum}} \rangle}$, in the r1 and r2 models, as labeled, for resolution comparison. The top panel is ${\langle F_{\rm{sum}} \rangle}$ inside $3{\rm\,kpc}$, and the bottom panel is the same within $15{\rm\,kpc}$.
• Figure 4: The same as Figure \ref{['fig:fmean1']}, but for the halo models.
• Figure 5: Fractional change of the total disk angular momentum divided by its initial angular momentum, $L_z/L_{z,0}$, over 2 Gyr. The top panel is for the r2 models with model r1c14 for reference, and the bottom panel is for the halo models with model r2c16 for reference, as they have the same halo concentration.