Abstract
Self-similar solutions describing the homogeneous, free, isothermal collapse of protostellar clouds are considered. One such solution correponds to the critical case of the propagation of a rarefaction wave near the time when it is focused in the central region of the cloud. The speed of the rarefaction front is finite and equal to three times the isothermal sound speed. The asymptotic distributions of gas-dynamical quantities in the central part of the collapsing cloud and the surrounding envelopes are considered at both early and late stages of compression, after the formation of an opaque core (protostar). These solutions are used in a magneto-kinematic approximation to study the geometry and evolution of the large-scale magnetic fields of collapsing protostellar clouds. All the solutions are verified using direct numerical simulations. It is shown that an initially uniform magnetic field acquires an “hourglass” geometry with time. The characteristic opening angles in the self-similar solutions are in satisfactory agreement with observations.
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