Polytropic Gaseous Spheres

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


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)]
$$ \frac{{dP}}{{dr}} = - \frac{{d\Phi }}{{dr}}\varrho $$
, together with Poisson's equation (1.10)
$$ \frac{1}{{{r^2}}}\frac{d}{{dr}}\left( {{r^2}\frac{{d\Phi }}{{dr}}} \right) = 4\pi G\varrho $$
. We have replaced the partical derivatives by ordinary ones since only time-indenpendent solutions shall be considered.


Radiation Pressure Hydrostatic Equilibrium Polytropic Index Comoving Frame Emden Equation 
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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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