An analytical model for the evolution of starless cores – I. The constant-mass case

Abstract

We propose an analytical model for the quasi-static evolution of starless cores confined by a constant external pressure, assuming that cores are isothermal and obey a spherically symmetric density distribution. We model core evolution for Plummer-like and Gaussian density distributions in the adiabatic and isothermal limits, assuming Larson-like dissipation of turbulence. We model the variation in the terms in the virial equation as a function of core characteristic radius, and determine whether cores are evolving towards virial equilibrium or gravitational collapse. We ignore accretion on to cores in the current study. We discuss the different behaviours predicted by the isothermal and adiabatic cases, and by our choice of index for the size–linewidth relation, and suggest a means of parametrizing the magnetic energy term in the virial equation. We model the evolution of the set of cores observed by Pattle et al. in the L1688 region of Ophiuchus in the ‘virial plane’. We find that not all virially bound and pressure-confined cores will evolve to become gravitationally bound, with many instead contracting to virial equilibrium with their surroundings, and find an absence of gravitationally dominated and virially unbound cores. We hypothesize a ‘starless core desert’ in this quadrant of the virial plane, which may result from cores initially forming as pressure-confined objects. We conclude that a virially bound and pressure-confined core will not necessarily evolve to become gravitationally bound, and thus cannot be considered pre-stellar. A core can only be definitively considered pre-stellar (collapsing to form an individual stellar system) if it is gravitationally unstable.