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Problems on gravitational collapse of interstellar gas clouds

II. Caustic and critical times for a one-dimensional hydrodynamic model

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Abstract

The gravitational collapse of a spherically symmetric interstellar gas cloud has been investigated following the non-linear discontinuity waves propagation theory. It has been pointed out that macroscopic phenomena, such as the process of fragmentation, can arise (shock wave formation)-even in the case of spherical symmetry- at times smaller than the free-fall timet ff, provided the initial data of the Cauchy problem be discontinuous within a sphere of radius\(\bar R< R_{ cloud} \) (caustic cases). It has also been proved that strong discontinuities outside the mentioned sphere may generate critical timest cr<t ff (depending on the typical non-linear structure of the differential system). The cooling-heating function plays an important role in contrasting the formation of shock waves.

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Authors and Affiliations

  1. Institute of Mathematics, University of Rome, Italy

    F. Ferraioli

  2. Institute of Mathematics, University of Bologna, Italy

    T. Ruggeri

  3. Rome Astronomical Observatory and Institute of Mathematics, University of Rome, Italy

    N. Virgopia

Authors
  1. F. Ferraioli
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  2. T. Ruggeri
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  3. N. Virgopia
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Ferraioli, F., Ruggeri, T. & Virgopia, N. Problems on gravitational collapse of interstellar gas clouds. Astrophys Space Sci 56, 303–321 (1978). https://doi.org/10.1007/BF01879562

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  • DOI: https://doi.org/10.1007/BF01879562

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