Bending instabilities of m=1 mode in disc galaxies: interplay between dark matter halo and vertical pressure

TL;DR

This paper presents a theoretical analysis of m=1 bending instabilities in galactic discs, showing how dark matter halos and disc thickness influence the growth and suppression of warps and other bending modes.

Contribution

It introduces a quadratic eigenvalue framework to analyze bending modes in realistic disc galaxy models with dark matter halos, highlighting the effects of disc thickness and halo mass.

Findings

Thinner discs exhibit faster-growing unstable bending modes.

Massive dark matter halos suppress bending instabilities.

Estimated growth timescales and wavelengths for Milky Way-like galaxies.

Abstract

A self-gravitating, differentially rotating galactic disc under vertical hydrostatic equilibrium is supported by the vertical pressure gradient force against the gravitational collapse. Such discs are known to support various bending modes e.g., warps, corrugation, or scalloping (typically, higher order bending modes) of which m=1 bending modes (warps) are the most prevalent ones in galactic discs. Here, we present a detailed theoretical analysis of the bending instability in realistic models of disc galaxies in which an exponential stellar disc is under vertical equilibrium and residing in a cold rigid dark matter halo. A quadratic eigenvalue equation describing the bending modes is formulated and solved for the complete eigen spectrum for a set of model disc galaxies by varying their physical properties such as disc scale-height, and dark matter halo mass. It is shown that the vertical pressure gradient force can excite unstable bending modes in such a disc as well as large scale discrete modes. Further, it is shown that the unstable eigen-modes in a thinner disc grow faster than those in a thicker disc. The bending instabilities are found to be suppressed in discs dominated by massive dark matter halo. We estimate the growth timescales and corresponding wavelength of the m=1 unstable bending modes in Milky Way like galaxies and discuss its implication.