On the stability of nonisothermal Bonnor-Ebert spheres

II. The effect of gas temperature on the stability

¹ Max-Planck-Institute for Extraterrestrial Physics (MPE), Giessenbachstr. 1, 85748 Garching, Germany
e-mail: osipila@mpe.mpg.de
² Department of Physics, PO Box 64, 00014 University of Helsinki, Finland

Received: 27 May 2014
Accepted: 23 August 2015

Abstract

Aims. We investigate the stability of nonisothermal Bonnor-Ebert spheres in the context of a model that includes a self-consistent calculation of the gas temperature. In this way, we can discard the assumption of equality between the dust and gas temperatures and study the stability as the gas temperature changes with the chemical evolution of the cooling species.

Methods. We use a gas-grain chemical model to calculate the chemical evolution. The model includes a time-dependent treatment of depletion onto grain surfaces, which strongly influences the gas temperature as the main coolant molecule CO depletes from the gas. The dust and gas temperatures are solved with radiative transfer calculations. For consistent comparison with previous work, we assume that the cores are deeply embedded in a larger external structure, corresponding to visual extinction A_V^ext = 10 mag at the core edge. We also study the effect of lower values of A_V^ext.

Results. We find that the critical nondimensional radius ξ₁ derived here, which determines the maximum density contrast between the core center and the outer boundary, is similar to our previous work where we assumed T_dust = T_gas. Here, the ξ₁ values lie below the isothermal critical value ξ₀ ~ 6.45, but the difference is less than 10 %. We find that chemical evolution does not notably affect the stability condition of low-mass cores (< 0.75 M_⊙), which have high average densities and a strong gas-grain thermal coupling. In contrast, for higher masses the decrease in cooling due to CO depletion causes substantial temporal changes in the temperature and in the density profiles of the cores. In the mass range 1−2 M_⊙, ξ₁ decreases with chemical evolution, whereas above 3 M_⊙, ξ₁ instead increases with chemical evolution. We also find that decreasing A_V^ext strongly increases the gas temperature, especially when the gas is chemically old, and this causes ξ ₁ to increase with respect to models with higher A_V^ext. However, the derived ξ₁ values are still close to ξ₀. The density contrast between the core center and edge derived here varies between 8 and 16 depending on core mass and the chemical age of the gas, compared to the constant value ~14.1 for the isothermal BES.