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Published online by Cambridge University Press: 12 April 2016
The condition for homogeneous radiative stellar models to be marginally stable to convection at the centre is investigated for the family of models where the opacity к and energy generation ε are given by power laws in temperature and density κ = κo ρα T−β, ε = εo ρ Tη. The Naur-Osterbrock (1953) condition 6η > 6 + 10β − 15α is a necessary but not sufficient condition. A better estimate is obtained by taking the effective polytropic index n = dlogP/dlogT - 1 to be a linear function of temperature T throughout the model. This gives the condition
The predictions of this condition agree well with results for a set of stellar models 0 ≤ α ≤ 1, 0≤ β ≤ 5.