An inexpensive nuclear energy generation network for stellar hydrodynamics

We compare the nuclear energy generation rate and abundance levels given by an alpha -chain nuclear reaction network that contains only seven isotopes with a standard 13 isotope alpha -chain reaction network. The energy gener ation rate of these two small networks are also compared to the energy gene ration rate given by a 489 isotope reaction network with weak reactions tur ned on and off. The comparison between the seven isotope and ct-chain react ion networks indicate the extent to which one can be replaced by the other, and the comparison with the 489 isotope reaction network roughly indicates under what physical conditions it is safe to use the seven isotope and ct- chain reaction networks. The seven isotope reaction network reproduces the nuclear energy generation rate of the standard alpha -chain reaction networ k to within 30%, but often much better, during hydrostatic and explosive he lium, carbon, and oxygen burning. It will also provide energy generation ra tes within 30% of an alpha -chain reaction network for silicon burning at d ensities less than 10(7) g cm(-3). Provided there remains an equal number o f protons and neutrons (Y-e = 0.5) over the course of the evolution, and th at flows through alpha -particle channels dominate, then both of the small reaction networks return energy generation rates that are compatible with t he energy generation rate returned by the 489 reaction network. If Y-e is s ignificantly different from 0.5, or if there are substantial hows through n eutron and protons channels, then it is not generally safe to employ any al pha -chain based reaction network. The relative accuracy of the seven isoto pe reaction network, combined with its reduction in the computational cost, suggest that it is a suitable replacement for alpha -chain reaction networ ks for parameter space surveys of a wide class of multidimensional stellar models.