Effect of Rotation in Cloud Core Collapse

Abstract

The collapse of rotating clouds is investigated. At first, isothermal collapse of an initially uniform-density, uniform-rotating, molecular cloud core with pressure and self-gravity is investigated to determine the conditions under which a cloud is unstable to fragmentation. A semianalytic model for the collapse of rotating spheroids is developed with the . method of characteristics for inwardly propagating rarefaction waves. Three-dimensional self-gravitating hydrodynamical calculations are performed for the initially uniform-density rigid-rotating sphere. Both investigations show that the criterion for fragmentation is modified from the one in the literature if the property of the non-homologous collapse is taken into account. It is shown that the central flatness, that is, the axial ratio of the isodensity contour in the central region, is a good indicator for the fate of the cloud. We derive the criterion for the fragmentation considering the evolution of the flatness of the central core. If the central flatness becomes greater than the critical value ∼ 4π, a collapsing cloud with moderate perturbations is unstable for fragmentation, while if the central flatness stays smaller than the critical value, it does not fragment at least before adiabatic core formation. Warm clouds (α 0 ≥ 0.5) are not expected to fragment before adiabatic core formation almost independent of the initial rotation (β 0 ) and the properties of the initial perturbation. The effect of the initial density central concentration is also investigated. If it exists, distortion or flattening of a cloud core is suppressed even if α 0 ≤ 0.5 in small rotation cases due to stronger nonhomologous property of the collapse. We conclude that the binary fragmentation is difficult during isothermal stage if a core collapse had started from near spherical configurations with moderate thermal energy or small rotation. We suggest that the close binary fragmentation may be possible in the nonisothermal stage by rapid growth of a nonspherical first core. Second, to mimic fragmentation processes of primordial clouds, the equation of state is approximated by a simple polytropic relation with γ ∼ 1.1. A series of numerical and semianalytical calculations of the rotating collapse of an initially spherical cloud shows a criterion for fragmentation of rotating polytropic cloud cores with γ=1.1. Fragmentation during core collapse is not expected to take place if the cloud thermal energy is greater than 0.3 times its gravitational energy at the initial stage of runaway collapse. The collapse of the central small core will not be halted by centrifugal force since a nonaxisymmetric waves will appear and the flow will converge to a self-similar flow until γ exceeds 4/3. Finally, we take into account the detailed non-equilibrium chemical reactions for primordial gas that consists of pure hydrogen. The parameters of the collapse and the condition of the fragmentation are compared with those of isothermal clouds. It is shown that the geometrical flatness of the central region of the disc is a good indicator for predicting whether the clouds fragment or not. If the flatness is greater than the critical value, ∼ 4π,a cloud fragments into filaments and blobs.