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We propose an analytical model for the quasistatic evolution of starlesscores confined by a constant external pressure, assuming that cores areisothermal and obey a spherically-symmetric density distribution. We model coreevolution for Plummer-like and Gaussian density distributions in the adiabaticand isothermal limits, assuming Larson-like dissipation of turbulence. We modelthe variation in the terms in the virial equation as a function of corecharacteristic radius, and determine whether cores are evolving toward virialequilibrium or gravitational collapse. We ignore accretion onto cores in thecurrent study. We discuss the different behaviours predicted by the isothermaland adiabatic cases, and by our choice of index for the size-linewidthrelation, and suggest a means of parameterising the magnetic energy term in thevirial equation. We model the evolution of the set of cores observed by Pattleet al. (2015) in the L1688 region of Ophiuchus in the 'virial plane'. We findthat not all virially-bound and pressure-confined cores will evolve to becomegravitationally bound, with many instead contracting to virial equilibrium withtheir surroundings, and find an absence of gravitationally-dominated andvirially-unbound cores. We hypothesise a 'starless core desert' in thisquadrant of the virial plane, which may result from cores initially forming aspressure-confined objects. We conclude that a virially-bound andpressure-confined core will not necessarily evolve to become gravitationallybound, and thus cannot be considered prestellar. A core can only bedefinitively considered prestellar (collapsing to form an individual stellarsystem) if it is gravitationally unstable.

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