Similarity between the structure and stability of isothermal and polytropic gas spheres

Abstract

As shown by Chiéze, polytropic gas spheres imbedded in an ambient medium with a given pressure exhibit a relation between the mass and radius similar to isothermal gas spheres, providedn(polytropic index)>3 or <−1. Here, further investigation is made of the polytropic spheres. Not only the relation between radius and external pressure, but the relation between the central density (ρ c ) and the mass (M) is similar to isothermal spheres and neutron star models. Dynamical calculation shows that the stability of polytropic spheres is lost at the configuration which corresponds to the first peak in the ρ c M relation, as is the case for neutron star models in general relativity.

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References

  1. Bonnor, W. B.: 1956,Monthly Notices Roy. Astron. Soc. 116, 351.

    Google Scholar 

  2. Chandrasekhar, S.: 1957,An Introduction to the Study of Stellar Structure, Dover Publ., New York.

    Google Scholar 

  3. Chandrasekhar, S.: 1972, in O'Raifeartigh (ed.),General Relativity, Oxford University Press, Oxford.

    Google Scholar 

  4. Chiéze, J. P.: 1987,Astron. Astrophys 171, 225.

    Google Scholar 

  5. Larson, R. B.: 1981,Monthly Notices Roy. Astron. Soc. 194, 809.

    Google Scholar 

  6. Ledoux, P.: 1958,Handb. Phys. 51, 605.

    Google Scholar 

  7. Ledoux, P. and Walraven, T.: 1958,Hand. Phys. 51, 353.

    Google Scholar 

  8. McCrea, W. H.: 1957,Monthly Notices Roy. Astron. Soc. 117, 562.

    Google Scholar 

  9. Taff, L. G. and Van Horn, H. M.: 1974,Monthly Notices Roy. Astron. Soc. 168, 427.

    Google Scholar 

  10. Yabushita, S.: 1968,Monthly Notices Roy. Astron. Soc. 140, 109.

    Google Scholar 

  11. Yabushita, S.: 1975,Monthly Notices Roy. Astron. Soc. 172, 441.

    Google Scholar 

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Yabushita, S. Similarity between the structure and stability of isothermal and polytropic gas spheres. Astrophys Space Sci 193, 173–183 (1992). https://doi.org/10.1007/BF00643199

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Keywords

  • General Relativity
  • Neutron Star
  • Dynamical Calculation
  • Ambient Medium
  • Central Density