Saturation of spiral instabilities in disk galaxies
Abstract
Spiral density waves can arise in galactic disks as linear instabilities of the underlying stellar distribution function. Such instabilities grow exponentially in amplitude at some fixed growth rate $\beta$ before saturating nonlinearly. However, the mechanisms behind nonlinear saturation, and the resulting saturated spiral amplitude, have not received much attention. Here we argue that the most important nonlinear saturation mechanism is likely trapping of stars near the spiral's corotation resonance. Under these circumstances, we show analytically that an $m$armed spiral will saturate when the libration frequency of resonantly trapped orbits reaches $\omega_\mathrm{lib} \sim 3\, m^{1/2} \beta$. For a galaxy with a flat rotation curve this implies a maximum relative spiral surface density $\vert \delta\Sigma/\Sigma_0\vert \sim \mathrm{a\,\,few} \times (\beta/\Omega_\mathrm{p})^2 \cot \alpha$, where $\Omega_\mathrm{p}$ is the spiral pattern speed and $\alpha$ is its pitch angle. This result is in good agreement with recent Nbody simulations of isolated stellar disks, and is consistent with observed trends from spectroscopic surveys.
 Publication:

arXiv eprints
 Pub Date:
 February 2023
 DOI:
 10.48550/arXiv.2302.06602
 arXiv:
 arXiv:2302.06602
 Bibcode:
 2023arXiv230206602H
 Keywords:

 Astrophysics  Astrophysics of Galaxies;
 Physics  Plasma Physics
 EPrint:
 6 pages