We study the evolution of degenerate electron cores primarily composed of the carbon burning products \mathrm { { } ^ { 16 } O } , \mathrm { { } ^ { 20 } Ne } , and \mathrm { { } ^ { 24 } Mg } ( 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 ^ { 20 } Ne 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 \mathrm { { } ^ { 24 } Mg } 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 \rho _ { c } \ga 8.5 \times 10 ^ { 9 } \mathrm { 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 .