Abstract
In this paper we develop a simple analytical criterion to investigate the
role of the environment on the onset of star formation. We will consider the
main external agents that influence the star formation (i.e. ram pressure,
tidal interaction, Rayleigh-Taylor and Kelvin-Helmholtz instabilities) in a
spherical galaxy moving through an external environment. The theoretical
framework developed here has direct applications to the cases of dwarf galaxies
in galaxy clusters and dwarf galaxies orbiting our Milky Way system, as well as
any primordial gas-rich cluster of stars orbiting within its host galaxy. We
develop an analytic formalism to solve the fluid dynamics equations in a
non-inertial reference frame mapped with spherical coordinates. The two-fluids
instability at the interface between a stellar system and its surrounding
hotter and less dense environment is related to the star formation processes
through a set of differential equations. The solution presented here is quite
general, allowing us to investigate most kinds of orbits allowed in a
gravitationally bound system of stars in interaction with a major massive
companion. We present an analytical criterion and some simple numerical and
observational applications to elucidate the dependence of star formation in a
stellar system on its surrounding environment. This criterion predicts the
threshold value for the onset of star formation in a mass vs. size space for
any orbit of interest. Moreover, we make evident for the first time the
theoretical dependencies of the different instability phenomena acting on a
system in a fully analytical way.
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