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Thermal Runaway During the Evolution of ONeMg Cores towards Accretion-Induced Collapse

We study the evolution of degenerate electron cores primarily composed of the carbon burning products oxygen, neon, and magnesium (hereafter ONeMg cores) that are undergoing compression. Electron capture reactions on A=20 and A=24 isotopes reduce the electron fraction and heat the core. We develop and use a new capability of the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution code that provides a highly accurate implementation of these key reactions. These new accurate rates and the ability of MESA to perform extremely small spatial zoning demonstrates a thermal runaway in the core triggered by the temperature and density sensitivity of the Ne-20 electron capture reactions. Both analytics and numerics show that this thermal runaway does not trigger core convection, but rather leads to a centrally concentrated (r < km) thermal runaway that will subsequently launch an oxygen deflagration wave from the center of the star. We use MESA to perform a parameter study that quantifies the influence of the magnesium mass fraction, the central temperature, the compression rate, and uncertainties in the electron capture reaction rates on the ONeMg core evolution. This allows us to establish a lower limit on the central density at which the oxygen deflagration wave initiates of $ρ_c > 8.5 \times 10^9\, \textrm{g cm}^{-3}$. Based on previous work and order-of-magnitude calculations, we expect objects which ignite oxygen at or above these densities to collapse and form a neutron star. Calculations such as these are an important step in producing more realistic progenitor models for studies of the signature of accretion-induced collapse.