Stability of Gas Clouds in Galactic Nuclei: An Extended Virial Theorem

TL;DR

This paper develops an extended Virial theorem incorporating external pressure and tidal forces to accurately assess the stability of gas clouds in galactic nuclei, challenging traditional criteria and providing new insights into their masses and stability.

Contribution

It introduces a novel extended Virial theorem that accounts for external pressure and tidal forces, improving stability analysis of gas clouds near supermassive black holes.

Findings

Derived smaller cloud masses than traditional Virial estimates.

Proved stability of gas clumps in AGN tori and galactic centers.

Challenged the adequacy of the Roche limit for stability assessment.

Abstract

Cold gas entering the central $1$ to $10^2$ pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulate a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to include an external tidal field, crucial for the stability in the region of interest -- in dense star clusters, around SMBHs. We apply our extended Virial theorem to find the correct solutions to practical problems that until now were controversial, namely, the stability of the gas clumps in AGN tori, the circum-nuclear disk in the Galactic Center, and the central molecular zone of the Milky Way. The masses we derive for these structures are orders of magnitude smaller than the commonly-used Virial masses (equivalent to the Jeans mass). Moreover, we prove that these clumps are stable, contrary to what one would naively deduce from the Roche (tidal) limit.