Homology Relations

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


In physical problems it often happens that from one solution others can be obtained by simple transformations. When comparing different stellar models that are calculated under similar assumptions (concerning parameters or material functions), one therefore expects to find similarities in the solutions. It would be very helpful if we could find simple analytic expressions that transform one solution into another. It would then only be necessary to produce one numerical solution in order to find new ones by a transformation. There is indeed often a kind of “similarity” between different solutions, which is called homology, though the conditions for this are so severe that real stars will scarcely match them. There are a few cases, however, for which homology relations offer a rough, but helpful, indication for interpreting or predicting the numerical solutions. We indicate this in two examples, the main-sequence models and the homologous contraction. Except for this classical homology there is another type of homology, which applies to certain red giants (see §32.2.)


Material Function Stellar Model Homology Relation Simple Analytic Expression Polytropic Index 
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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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