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The post main sequence expansion of a \(5 M_{\odot}\)-star is investigated by means of a simple composite configuration: a contracting He-core of Schoenberg-Chandrasekhar mass surrounded by an H-envelope of polytropic index \(n=3\). While the structure of the envelope is immediately obtained by solving the equations of hydrostatic equilibrium, the core requires some further simplification: if the actual non-local gravitational energy release due to contraction is replaced by its constant core-average, the equation of radiative energy transport may be easily integrated. Thus an explicit relation between pressure and temperature is obtained and the equations of hydrostatic equilibrium may be solved. Specifying \(M,M_{\mathrm{core}}\) and \(T_0\) (the temperature of the H-burning shell-source at the interface), a sequence of models follows with \(L_{\mathrm{core}}\), the gravitational energy released from the core per second, and hence with t , the contraction time, as the parameter. The resulting simple models show very rapid expansion, a consequence of the thermostatic action of the shell-source. Its fixed temperature prevents the shell-source from participating in the contraction of the core -thus causing the outer parts of the core and hence the adjoining envelope to decrease in density. Accordingly, the envelope must expand. This consequence of a fixed temperature \(T_0\) is clearly demonstrated by the distributions of the specific internal and gravitational energies. This characteristic behaviour is also found in stellar models obtained by elaborate numerical simulations.

On the post main sequence expansion of stars with contracting helium cores