  The study presents a theoretical framework for understanding the role of dark
matter on the stability of the galactic disc. We model the galaxy as a
two-component system consisting of stars and gas in equilibrium with an
external dark matter halo. We derive the equations governing the growth of
perturbations and obtain a stability criterion that connects the potential of
the dark matter halo and the gas fraction with the stability levels of the
galaxy. We find that a two-component disc is more susceptible to the growth of
gravitational instabilities than individual components, particularly as gas
fractions increase. However, the external field, due to the dark matter halo,
acts as a stabilizing agent and increases the net stability levels even in the
presence of a cold gas component. We apply the stability criterion to models of
the Milky Way, low surface brightness galaxies, and baryon-dominated cold
rotating disc galaxies observed in the early universe. Our results show that
the potential due to the dark matter halo plays a significant role in
stabilizing nearby galaxies, such as the Milky Way, and low surface brightness
galaxies, which would otherwise be prone to local gravitational instabilities.
However, we find that the baryon-dominated cold disc galaxies observed in the
early universe remain susceptible to the growth of local gravitational
instabilities despite the stabilizing effect of the dark matter halo.
