The collapse and fragmentation of molecular cloud cores is examined numerically with unprecedentedly high spatial resolutions, using the publicly released code GADGET-2. As templates for the model clouds we use the ''standard isothermal test case'' in the variant calculated by Burkert & Bodenheimer in 1993 and the centrally condensed, Gaussian cloud advanced by Boss in 1991. A barotropic equation of state is used to mimic the nonisothermal collapse. We investigate both the sensitivity of fragmentation to thermal retardation and the level of resolution needed by smoothed particle hydrodynamics (SPH ) to achieve convergence to existing Jeans-resolved, finite-difference ( FD) calculations. We find that working with 0.6Y1.2 million particles, acceptably good convergence is achieved for the standard test model. In contrast, convergent results for the Gaussian-cloud model are achieved using from 5 to 10 million particles. If the isothermal collapse is prolonged to unrealistically high densities, the outcome of collapse for the Gaussian cloud is a central adiabatic core surrounded by dense trailing spiral arms, which in turn may fragment in the late evolution. If, on the other hand, the barotropic equation of state is adjusted to mimic the rise of temperature predicted by radiative transfer calculations, the outcome of collapse is a protostellar binary core. At least, during the early phases of collapse leading to formation of the first protostellar core, thermal retardation not only favors fragmentation but also results in an increased number of fragments, for the Gaussian cloud.

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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.

In this paper we continue the investigation reported by Arreaga (2016) concerning the morphology of binary configurations obtained via the collapse of rotating parent gas structures with total masses in the range of M T = 1 to 5 M . Here we extend the mass range and consider the collapse of two uniform gas clumps of M T = 50 and 400 M , so that they also rotates rigidly in such a way that its approximate virial parameter takes the values of 0.5, 1.5, and 2.5 and their collapse is induced initially by implementing an azimuthal mass perturbation. To assess the effects of the total mass of the parent gas structure on the nature of the resulting binary configurations, we also consider the collapse of two cores of M T = 1 and 5 M . We calculate the collapse of all these parent gas structures using three values of the ratio of thermal energy to potential energy and for two values of the mass perturbation amplitude. We next calculate the binary separations, masses and integral properties of the binary fragments and present them in terms of the total mass of the parent structure. For most of our models, we finally calculate the β extreme value, so that a model with a slightly higher β value would no longer collapse.

In this paper we present a set of numerical simulations designed to study the interaction process of H II molecular clouds. For the initial conditions we assume head-on and oblique collisions of binary identical clouds placed adjacent to one another, with their surfaces just in contact. The colliding initial clouds are uniform density molecular gas spheres with rigid body rotation. The cloud initial conditions are chosen to favor its gravitational collapse as an isolated system. To study the effect of the self-gravity of the cloud in the collision process, we consider several models in which the approaching speed of the colliding clouds increases from zero up to several times the initial sound speed of the barotropic gas. We present the outcome of these collision models for several values of the impact parameter b, which depends on the initial radius of the cloud. We have explored the parameter space of the approaching velocity Vapp of the colliding clouds for configurations that may result in seeds for the formation of more complex systems. Such systems are expected to include filaments and gas clumps, where the star formation process is still possible despite the occurrence of the collision. We show hereby that collisions may have a major and favorable influence on the star formation process.