Global lopsided instability in a purely stellar galactic disc

TL;DR

This paper demonstrates that purely stellar exponential galactic discs can support long-lived, slowly precessing lopsided modes, explaining observed asymmetries through a combination of linear theory and N-body simulations.

Contribution

It introduces a quadratic eigenvalue framework for lopsided modes in stellar discs and confirms their long-lived nature via simulations, advancing understanding of galactic asymmetries.

Findings

Lopsided modes precess very slowly with no preferred direction.

Ground-state modes are long-lived and either stationary or slowly growing.

N-body simulations support the spontaneous growth and stability of these modes.

Abstract

It is shown that pure exponential discs in spiral galaxies are capable of supporting slowly varying discrete global lopsided modes, which can explain the observed features of lopsidedness in the stellar discs. Using linearized fluid dynamical equations with the softened self-gravity and pressure of the perturbation as the collective effect, we derive self-consistently a quadratic eigenvalue equation for the lopsided perturbation in the galactic disc. On solving this, we find that the ground-state mode shows the observed characteristics of the lopsidedness in a galactic disc, namely the fractional Fourier amplitude A$_1$ increases smoothly with the radius. These lopsided patterns precess in the disc with a very slow pattern speed with no preferred sense of precession. We show that the lopsided modes in the stellar disc are long-lived because of a substantial reduction ($\sim$ a factor of 10 compared to the local free precession rate) in the differential precession. The numerical solution of the equations shows that the ground-state lopsided modes are either very slowly precessing stationary normal mode oscillations of the disc or growing modes with a slow growth rate depending on the relative importance of the collective effect of the self-gravity. N-body simulations are performed to test the spontaneous growth of lopsidedness in a pure stellar disc. Both approaches are then compared and interpreted in terms of long-lived global $m=1$ instabilities, with almost zero pattern speed.