The QSE-reduced \alpha Network

Examination of the process of silicon burning, the burning stage that leads to the production of the iron peak nuclei, reveals that the nuclear evolution is dominated by large groups of nuclei in mutual equilibrium. These quasi-equilibrium (QSE) groups form well in advance of the global Nuclear Statistical Equilibrium (NSE). We present an improved ``minimal'' nuclear network, which takes advantage of quasi-equilibrium in order to calculate the nuclear evolution and energy generation while further reducing the computational cost compared to a conventional \alpha-chain network. During silicon burning, the resultant \emph{QSE-reduced} \alpha network is twice as fast as the full \alpha network it replaces and requires the tracking of only half as many abundance variables, without significant loss of accuracy. When the QSE-reduced \alpha network is used in combination with a conventional \alpha network stretching from He to Si, the combined \alpha7 network provides an accurate approximation for all of the burning stages from He burning to NSE, while tracking only 7 abundances. These reductions in computational cost and the number of species evolved make the \alpha7 network well suited for inclusion within hydrodynamic simulations, particularly those in multi-dimension.