Convective instability of radiatively cooling self-similar implosions

The linear convective instability of imploding gaseous masses is investigated with a self-similar solution, which takes radiation heat conduction into account. The solution shows that the implosion process continuously transits from initial adiabatic regime to consequent non-adiabatic regime, where the mechanical compression work and the radiation loss balance such that the Peclet number of the system is kept constant. The transition accompanies the decrease in the polytropic index, Gamma equivalent to d(logp)/d(log rho) where p and rho are respectively the pressure and density, with the adiabatic index gamma(greater than or equal to Gamma) as its initial value. As a result of the radiative cooling, the fluid becomes unstable to convective modes, when the criterion for instability, d(p/rho (Gamma))/dr < 0, is fulfilled in the core. The spatial and temporal dependence of the perturbations are presented.