Evidence for Hydrostatic Equilibrium in the Extragalactic Molecular Clouds of M31

Abstract: Recent studies suggest that the density structure of turbulent molecular clouds in the Milky Way and the Andromeda galaxy, M31, aligns with expectations from hydrostatic equilibrium (HE) and virial equilibrium (VE). This study extends the study of the M31 clouds by matching their observed surface densities to a spatially-averaged solution of the Lane-Emden equation. The results affirm that the M31 molecular clouds exhibit density profiles expected from HE, further supporting the earlier conclusion that VE holds at all radii within the clouds. This study also discusses HE in the context of the turbulent interstellar medium, considering energy balance, cloud lifetimes, and the pressure of the interstellar medium. A comparison between the Galactic and extragalactic clouds indicates that both share similar dynamical states. These findings contribute to a broader understanding of the interplay between turbulence, gravitational stability, and cloud evolution in the molecular interstellar medium.