On the structure and stability of a polytrope with an isothermal core.
Abstract
The structure is analyzed of a gaseous sphere containing an isothermal core and a polytropic envelope with an index of 1.5. The calculations show that if the transition from isothermal state to the polytropic one occurs at a given density and pressure, the mass vs central density plot will be similar to that for a neutronstar model and will have a mass maximum for dynamic stability. The equation of radial motion is used to investigate dynamic stability. It is found that if the adiabatic index attains a certain value (as calculated with the equation governing the unperturbed state), dynamic instability will occur precisely at the mass maximum. If, however, the adiabatic index in the envelope is increased, instability will set in beyond the mass maximum.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 August 1975
 DOI:
 10.1093/mnras/172.2.441
 Bibcode:
 1975MNRAS.172..441Y
 Keywords:

 Dynamic Stability;
 Polytropic Processes;
 Stellar Envelopes;
 Stellar Structure;
 Adiabatic Conditions;
 Astronomical Models;
 Equations Of State;
 Neutron Stars;
 Stellar Mass;
 Astrophysics