Structure and Stability of Prestellar Cores

Following an approach initially outlined by McKee & Holliman [5], we investigate the structure and stability of dense, starless molecular cloud cores. We model those as spherical clouds in hydrostatic equilibrium and supported against gravity by thermal, turbulent, and magnetic pressure. We determine the gas pressure by solving for thermal equilibrium between heating and cooling, while the turbulent and magnetic pressures are assumed to obey polytropic equations of state. In comparing the models to observed cloud cores we find that the observed peak column densities often exceed the limit for stable equilibria supported by thermal pressure alone, suggesting significant non-thermal pressure if the cores are to be stable. Non-thermal support is also needed to stabilize cores embedded in molecular clouds with high average pressures. Since the observed molecular linewidths of cores suggest that the turbulent pressure is lower than the thermal pressure, magnetic field are likely a dominant pressure component in many such cores. 1 Hydrostatic equilibrium models To model a gas cloud in hydrostatic equilibrium we make the simplified assumption that the gas pressure consists of the sum of thermal (subscript “th”), turbulent wave (“w”), and magnetic (“m”) pressure components, P = Pth + Pw + Pm . (1) We compute the thermal pressure through a detailed thermal equilibrium calculation, but the wave and magnetic pressures are assumed to obey a polytropic equation of state, Pw ∝ ̺ γP,w , Pm ∝ ̺ γP,m , (2) i.e. the pressure only depends on density, and γP , the polytropic exponent, is constant in a given object. Given the thermal and non-thermal gas pressure, it is possible to construct hydrostatic equilibria for any surface pressure 2 Jens Kauffmann and Frank Bertoldi and central to surface density contrast. We assume spherical symmetry for simplicity. Whether a given hydrostatic equilibrium model cloud is gravitationally stable depends on its response to perturbations in pressure or density. Different equations of state apply for such perturbations. For example, if the perturbation occurred on a time scale shorter than the cooling time, the scaling of the thermal pressure with density would be stiffer than if the perturbation would be allowed to reach thermal equilibrium. To analyze the stability we make the simple assumption that the perturbation obeys a polytropic equation of state, but with some different “adiabatic index”, γ: δPw/Pw,0 ∝ (δ̺/̺0) , δPm/Pm,0 ∝ (δ̺/̺0) , (3) where δ are infinitesimal perturbations, and the subscript “0” refers to values before the perturbation. A hydrostatic equilibrium cloud is stable against spontaneous contraction or expansion when at any point in the cloud, the pressure increases during a compression or decreases during an expansion, i.e.,