The virial theorem in stellar astrophysics
Abstract
This book provides a guided introduction to the use of the virial theorem in stellar astrophysics. The utility of the classical virial theorem is discussed, this theorem is derived in several ways, and the meaning of the ergodic theorem is elucidated. The tensor virial theorem is analyzed, and the development of higherorder virial equations is reviewed; the special and general relativistic versions of the virial theorem are developed separately. Complications due to magnetic fields, internal energy, and rotation are investigated, and results of applying the variational approach to the virial theorem are studied. An explicit form is obtained for the simple scalar theorem applicable to selfgravitating systems, the pulsational formula originally due to Ledoux is recovered, and the variational approach is expanded to include effects of magnetic fields and rotation. Some applications of the virial theorem to problems involving the pulsational stability of white dwarfs, effects of rotation and magnetic fields on the whitedwarf gravitational instability, and the stability of neutron stars are examined.
 Publication:

Astronomy and Astrophysics Series
 Pub Date:
 1978
 Bibcode:
 1978vtsa.book.....C
 Keywords:

 Astrophysics;
 Stars;
 Virial Theorem;
 Neutron Stars;
 Perturbation Theory;
 Radial Velocity;
 Relativity;
 Rotary Stability;
 Stellar Magnetic Fields;
 Stellar Rotation;
 Variational Principles;
 White Dwarf Stars;
 Astrophysics;
 VIRIAL THEOREM