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The equation of state of a self-gravitating gas sphere

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Abstract

In sequel to an earlier work (Mitra, 1984), I set out to find the appropriate equation of state of an isothermal (self-gravitating) cosmic gas sphere. It will be shown that because of self-gravitational interaction, a cosmic gas which is perfect otherwise, is destined to behave like an imperfect gas. It is found that for a cosmic gas in hydrostatic equilibrium the only mode of free expansion (or contraction) is by a homologous evolution. This theorem enables one to construct the equation of state in terms of the local thermodynamical parameters of the inhomogeneous medium in such a way that it is consistent with the boundary conditions at the centre and at the natural boundary of the system. This method can be extended even when there is a temperature gradient in the system. This analysis predicts that the density profile should be the same at least for all nondegenerate Newtonian stars having the same temperature profile and which can be considered to be in hydrostatic equilibrium. And the density profile will be that of a polytrope of indexn=3, modulated by a temperature profile.

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References

  • Chandrasekhar, S.: 1967a,Stellar Structure, Dover Press, New York, p. 155.

    Google Scholar 

  • Chandrasekhar, S.: 1967b,Stellar Structure, Dover Press, New York, p. 47.

    Google Scholar 

  • Chiu, Hong-Yec.: 1966, in R. F. Stein and A. G. W. Cameron (eds.),Stellar Evolution, Plenum, New York.

    Google Scholar 

  • Cox, J. P.: 1968a,Stellar Structure, Gordon and Breach, New York, p. 401.

    Google Scholar 

  • Cox, J. P.: 1968b,Stellar Structure, Gordon and Breach, New York, p. 408.

    Google Scholar 

  • Cox, J. P.: 1968c,Stellar Structure, Gordon and Breach, New York, p. 684.

    Google Scholar 

  • Cox, J. P.: 1968d,Stellar Structure, Gordon and Breach, New York, p. 713.

    Google Scholar 

  • Fowler, W. A. and Hoyle, F.: 1960,Astrophys. J. 132, 565.

    Google Scholar 

  • Mitra, A.: 1984,Astrophys. Space Sci. 107, 135.

    Google Scholar 

  • Munier, A. and Feix, M. R.: 1983,Astrophys. J. 267, 344.

    Google Scholar 

  • Munier, A. and Feix, M. R.: 1985,Astrophys. J. 293, 494.

    Google Scholar 

  • Schwarzschild, M.: 1958,Structure and Evolution of the Stars, Dover Press, New York, p. 251.

    Google Scholar 

  • Sengbusch and Temesvary: 1966, in R. F. Stein and A. G. W. Cameron (eds.),Stellar Evolution, Plenum Press, New York.

    Google Scholar 

  • Stein, R. F.: 1966, in R. F. Stein and A. G. W. Cameron (eds.),Stellar Evolution, Plenum Press, New York.

    Google Scholar 

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Authors and Affiliations

  1. Nuclear Research Laboratory, Bhabha Atomic Research Centre, Srinagar, India

    Abhas Mitra

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  1. Abhas Mitra
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Mitra, A. The equation of state of a self-gravitating gas sphere. Astrophys Space Sci 124, 295–303 (1986). https://doi.org/10.1007/BF00656041

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  • DOI: https://doi.org/10.1007/BF00656041

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