A unified formalism for the core mass-luminosity relations of shell-burning stars

The luminosity evolution of stars with highly condensed cores surrounded by nuclear-burning shell(s) is analytically investigated with the aid of homo logy relations. With respect to earlier works using a similar approach (e.g . Refsdal & Weigert 1970; Kippenhahn 1981), the major improvement is that w e derive all the basic dependences (i.e. on core mass, core radius, and che mical composition) in a completely generalised fashion, then accounting for a large range of possible physical properties characterising the burning s hell(s). Parameterised formulas for the luminosity are given as a function of the (i) relative contribution of the gas to the total pressure (gas plus radiation), (ii) opacity source, and (iii) dominant nuclear reaction rates . in this way, the same formalism can be applied to shell-burning stars of va rious metallicities and in different evolutionary phases. In particular, we present some applications concerning the luminosity evolution of RGB and A GE stars with different chemical compositions, including the case of initia l zero metallicity. It turns out that homology predictions provide a good a pproximation to the results of stellar model calculations. Therefore, the proposed formalism is useful to understand the possible diff erences in the luminosity evolution of shell-burning stars within a unified interpretative framework, and can be as well adopted to improve the analyt ical description of stellar properties in synthetic models.