New Results on the Vishniac and Ryu – Vishniac instabilities in astrophysics and laboratory astrophysics

Serge Bouquet (CEA)

A supernova remnant (SNR) results from the propagation in the interstellar medium of a spherical blast wave created by the explosion of a massive star (supernova). After the ejecta-dominated stage, the SNR enters a decelerated regime and its radius obeys the well-known Sedov-Taylor power law of time with the exponent 2/5.
Old SNRs exhibit however large deviations to sphericity with messy structures thought to arise due to the Vishniac (1983, V83) and Ryu-Vishniac (1987, RV87) instabilities.
These instabilities have not been, nevertheless, yet clearly evidenced numerically and V83 and RV87 disagree when the adiabatic index is close to 1 and these points are clarified.
First, analytical calculations confirm that the linear perturbation varies as a power of time and we derive the growth rate of the perturbation in terms of the mode number and the adiabatic index. As a result, a unification between V83 and RV87 is obtained.
Second, numerical simulations performed with the 2D radiation hydrodynamics code HADES developed by C. Michaut and coll. at LUTH are presented. In a first step, adiabatic blast waves are studied and the oscillation process (called initially “overstability” by Vishniac) is observed but no growth happens : the perturbation is smoothed out by expansion. More realistic simulations have been carried out by including cooling in the SNR over more than 100 thousands years. As expected a dense shell forms and complex structures are observed deep inside the SNR. In the late nonlinear evolution, simulations show that the expansion of the SNR passes from the exponent 2/5 to 0.3 and, in addition, the mode of the late instability is twice the mode of the initial perturbation. Finally, considerations about laboratory astrophysics experiments are given.

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