The gravitational collapse of Plummer protostellar clouds

Abstract

The growing observational evidence that main-sequence and pre-main-sequence protostars are found in binary and multiple systems suggests that they are formed by a fragmentation of collapsing molecular cloud cores. In this paper we present the results of a set of numerical simulations aimed to study the gravitational collapse and fragmentation of a centrally condensed cloud with a nearly flat central density region and a surrounding gas envelope. In order to describe this cloud structure, we use the Plummer radial density profile which satisfies the observed fact that protostellar clouds have a flat central density profile in their innermost region. We consider the cloud to be made of molecular hydrogen and describe the thermodynamics with a single barotropic equation of state, which includes a critical density ρ crit as a unique free parameter that determines a thermodynamical change on the collapsing gas: from an isothermal to an adiabatic regime. In this paper we consider four different values for the initial radius R c of the cloud, ranging from 2675 to 19 913 AU. In the models, for each ratio R c /R 0 of the cloud to core radius, we use two critical density values: ρ crit = 5.0 × 10 −14 and 5.0 × 10 −12 gr cm −3 . When the adiabatic change regime starts earlier, we find interesting gas structures as a result of the collapse, although these structures are different according to the initial mass content of the envelope and the initial angular velocity of the cloud. When the thermodynamical change occurs later, i.e., for ρ crit = 5.0 × 10 −12 gr cm −3 , we observe that the previously found structure is almost erased to give place instead to a single clump of gas without any adorning spiral arms. In general, we find that as the extension of the envelope mass increases, the possibility of a model to produce a multiple system decreases. This is a result of the initial configuration of our models, namely that with bigger envelopes their cores have a lower ratio of rotational to gravitational energy β 0 , a lower ratio of thermal plus rotational to gravitational energy α 0 + β 0 , and a lower angular velocity Ω 0 , which induces a stronger collapse which in turn contributes to the destruction of the structure that is formed during the initial phases of the collapse. Thus in a sufficient quantity rotational energy is crucial for the fragmentation to occur and survive.

Experimental and Theoretical Advances in Fluid Dynamics

“…However, precise knowledge of the dependence of temperature on density at the transition from isothermal to nonisothermal collapse requires solving the radiative transfer problem coupled to a fully self-consistent energy equation. A similar result was found for Plummer models in Arreaga-García et al (2010). Therefore, it has been common to use instead a simple barotropic equation of state ) that clearly simplifies the computational problem and it turns out to be a good approximation for the dynamical collapse of the molecular clouds, see Arreaga-García et al (2007) and Arreaga et al (2008).…”

“…1a and 2. The fact that by diminishing the critical density the fragmentation enhances, found for Gaussian (Arreaga-García et al 2007;Arreaga et al 2008) and Plummer models (Arreaga-García et al 2010), seems to be reproduced for models G6A1 and G6B1. We now proceed to decrease the critical density, as shown in model G6B1.…”

“…The free fall time t ff % ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3p=ð32Gq c p Þ sets a characteristic time scale for the collapse of protostellar clouds which is given in terms of the central density and it is the same for all models, see for instance (Arreaga-García et al 2010).…”

Protostellar collapse and fragmentation using an MHD gadget

“…Rosswog 2009), so this approach is not used by many researchers, except when the system under consideration is strongly centrally condensed (e.g. Arreaga‐Garcia, Klapp‐Escribano & Gomez‐Ramirez 2010). For small perturbations, it is sufficient to slightly perturb the initial positions of the particles, in order to match the desired density distribution.…”

Scaled up low-mass star formation in massive star-forming cores in the G333 giant molecular cloud

“…The fall off in the density away from the central peak will follow a power law such that the cloud will be observed as a distinct feature. Again, inspired from low mass star formation, we adopt a Plummer sphere profile for the density (Arreaga- García et al 2010;Whitworth & Ward-Thompson 2001), which is a useful approximation to the more rigorous Bonner-Ebert sphere solution for a self-gravitating sphere in an environment with significant external pressure (Bonner 1956;Ebert 1955;Chandrasekhar 1967).…”