Semi-analytical homologous solutions of the gravo-magnetic contraction

¹ Laboratoire de radioastronomie millimétrique, UMR 8112 du CNRS, École Normale Supérieure et Observatoire de Paris, 24 rue Lhomond, 75231 Paris cedex 05, France
² Department of Physics and Astronomy, Cardiff University, PO Box 913, 5 The Parade, Cardiff CF24 3YB, Wales, UK

Corresponding author: patrick.hennebelle@ens.fr

Received: 12 November 2001
Accepted: 17 July 2003

Abstract

We propose an extension of the semi-analytical solutions derived by Lin et al. ([CITE]) describing the two-dimensional homologous collapse of a self-gravitating rotating cloud having uniform density and spheroidal shape, which includes magnetic field (with important restrictions) and thermal pressure. The evolution of the cloud is reduced to three time-dependent ordinary equations allowing one to conduct a quick and preliminary investigation of the cloud dynamics during the precollapse phase, for a wide range of parameters. We apply our model to the collapse of a rotating and magnetized oblate and prolate isothermal core. Hydrodynamical numerical simulations are performed and comparison with the semi-analytical solutions is discussed. Under the assumption that all cores are similar, an apparent cloud axis ratio distribution is calculated from the sequence of successive evolutionary states for each of a large set of initial conditions. The comparison with the observational distribution of the starless dense cores belonging to the catalog of Jijina et al. ([CITE]) shows a good agreement for the rotating and initially prolate cores (aspect ratio 0.5) permeated by an helical magnetic field (G for a density of 10⁴ cm^-3).