Stability of SN Ia progenitors against radial oscillations

We analyze the possible existence of a pulsational instability excited by the $\epsilon$-mechanism during the last few centuries of evolution of a Chandrasekhar mass white dwarf prior to its explosion as a Type Ia supernova. Our analysis is motivated by the temperature sensitivity of the nuclear energy generation rate ($\sim T^{23}$) in a white dwarf whose structural adiabatic index is near 4/3. Based upon a linear stability analysis, we find that the fundamental mode and higher order radial modes are indeed unstable and that the fundamental mode has the shortest growth time scale. However, the growth time scale for such instability never becomes shorter than the evolutionary timescale. Therefore, even though the star \emph{is} pulsationally unstable, we do not expect these radial modes to have time to grow and to affect the structure and explosion properties of Type Ia supernovae.