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Polytropic Gaseous Spheres

  • Rudolf Kippenhahn
  • Alfred Weigert
Chapter
  • 382 Downloads
Part of the Astronomy and Astrophysics Library book series (AAL)

Abstract

As we have seen in §9.1 the temperature does not appear explicitly in the two mechanical equations (9.1,2). Under certain circumstances this provides the possibility of separating them from the “thermo-energetic part” of the equations. For the following it is convenient to introduce once again the gravitational potential Φ, as it was defined in §1.3. We here treat stars in hydrostatic equilibrium, which requires [see(l.ll),(2.3)]
$$ \frac{{dP}}{{dr}} = - \frac{{d\Phi }}{{dr}}\varrho $$
(19.1)
, together with Poisson's equation (1.10)
$$ \frac{1}{{{r^2}}}\frac{d}{{dr}}\left( {{r^2}\frac{{d\Phi }}{{dr}}} \right) = 4\pi G\varrho $$
(19.2)
. We have replaced the partical derivatives by ordinary ones since only time-indenpendent solutions shall be considered.

Keywords

Radiation Pressure Hydrostatic Equilibrium Polytropic Index Comoving Frame Emden Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Rudolf Kippenhahn
    • 1
  • Alfred Weigert
  1. 1.GöttingenGermany

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