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A. Arcones developed equilibrium bounds on the electron fraction in stellar matter with G. Martínez-Pinedo, L. F. Roberts and S. E. Woosley. Their 2010 study applied nuclear statistical equilibrium and beta equilibrium to obtain lower limits relevant to Type Ia supernovae and accretion-induced collapse.^[ref]

Beta equilibrium is a condition in which weak reactions interconverting neutrons and protons produce no net change of composition. For matter where neutrinos are thermally trapped, the reaction $n+{\nu }_e\rightleftharpoons p+e^{-}$ gives the chemical equilibrium conditionwhere each $\mu$ is the corresponding chemical potential. In cold neutrino-transparent neutron star matter, one usually takes ${\mu }_{{\nu }_e}=0$, giving ${\mu }_n={\mu }_p+{\mu }_e$. The escaping neutrinos do not form an equilibrated thermal bath in that approximation.^[ref]

Charge neutrality in matter containing only neutrons, protons and electrons additionally requires $n_p=n_e$. Given a total baryon density, these relations and an equation of state determine the composition. As an illustrative chemical-potential check, ${\mu }_n=1000$ MeV and ${\mu }_p=900$ MeV require ${\mu }_e=100$ MeV in the transparent approximation. At finite temperature, balancing emission and capture rates is the more general kinetic condition; nuclear statistical equilibrium under strong reactions alone does not impose beta equilibrium.

G. Martínez-Pinedo studied how nuclear composition constrains the electron fraction in stellar matter. With A. Arcones, L. F. Roberts and S. E. Woosley, he tested combined nuclear statistical equilibrium and beta equilibrium against presupernova models, rather than assuming every evolving plasma has reached equilibrium.^[ref]

L. F. Roberts helped calculate equilibrium constraints on the electron fraction in stellar matter. The 2010 study with A. Arcones, G. Martínez-Pinedo and S. E. Woosley sought limits less sensitive to uncertain weak-interaction rates, using nuclear statistical equilibrium together with beta equilibrium.^[ref]

S. E. Woosley investigated the electron fraction in stellar matter with A. Arcones, G. Martínez-Pinedo and L. F. Roberts. Their 2010 calculation combined nuclear statistical equilibrium with beta equilibrium conditions to constrain composition in presupernova and collapse environments.^[ref]