# Instabilities in disc galaxies: from noise to grooves to spirals

## TL;DR

This paper demonstrates that phase-space grooves caused by finite-N noise can induce linear instabilities in otherwise stable disc galaxies, leading to the spontaneous formation of spiral patterns.

## Contribution

It introduces a linear theory showing how phase-space grooves trigger spiral eigenmodes, revealing a new mechanism for spiral formation in stellar discs.

## Key findings

- Grooves in phase space can excite two-armed spiral eigenmodes.
- Dominant mode is a cavity mode reflecting off corotation and grooves.
- Depletion of near-circular orbits is key to mode excitation.

## Abstract

Using the linearized Boltzmann equation, we investigate how grooves carved in the phase space of a half-mass Mestel disc can trigger the vigorous growth of two-armed spiral eigenmodes. Such grooves result from the collisional dynamics of a disc subject to finite-N shot noise, as swing-amplified noise patterns push stars towards lower-angular momentum orbits at their inner Lindblad radius. Supplementing the linear theory with analytical arguments, we show that the dominant spiral mode is a cavity mode with reflections off the forbidden region around corotation and off the deepest groove. Other subdominant modes are identified as groove modes. We provide evidence that the depletion of near-circular orbits, and not the addition of radial orbits, is the crucial physical ingredient that causes these new eigenmodes. Thus, it is possible for an isolated, linearly stable stellar disc to spontaneously become linearly unstable via the self-induced formation of phase-space grooves through finite-N dynamics. These results may help explain the growth and maintenance of spiral patterns in real disc galaxies.