Self-similar dynamics of radiative blast waves

The self-similar study of cooling blast waves (BWs) is performed for the case of a homogeneous self-similar cooling of the gas. This analysis is crucial to better understand its internal structure and global evolution when the BW loses a significant amount of energy due to cooling processes. The evolution of the shock front radius R-sh follows the law R-sh(t) proportional to t(alpha) where the decelerating parameter alpha covers the range 1/4 <= alpha <= 2/5 depending on the magnitude of the cooling rate. When the cooling is negligible, alpha = 2/5, and we recover the analytical solution of Sedov-Taylor (ST) where the total BW energy is conserved. For the internal structure of the cooling BW, we demonstrate that there exist two types of solutions. The first type is the ST-type solution, which is smooth until the center of the BW and only exists for 1/4 < alpha ' <= alpha <= 2/5, where alpha ' is a specific value of alpha. This special solution is determined through an eigenvalue problem. The second type is a shell-type solution where a thin cooled shell is bounded by a contact discontinuity separating the shell from a hot rarefied interior bubble where the pressure is homogeneous. The shell becomes thinner and denser when the cooling rate increases. For a strong enough cooling rate, the density inside the shell can diverge at the contact discontinuity while the temperature goes to zero.