All Tables

Table 1: Properties of a radiative shock for gas with a ratio of specific heats, $\gamma =5/3$ .
Table 2: Cooling length of a radiative shock for gas with a ratio of specific heats, $\gamma =5/3$ , and cooling exponent, $\alpha =0$ . $L_{\rm c}'$ in appropriate units can be obtained by multiplying by the numerical values of $\bar{m} k/\Lambda_{0}$ (note that in this work we also specify that $\rho _{0}=1$ and v₀=1). There is convergence in the value of $x_{\rm b}$ as M increases.
Table 3: Critical value of $\alpha$ for damping of the fundamental mode, and angular frequency (when $\alpha =-1.5$ ) as a function of the Mach number. For $\alpha > \alpha _{\rm cr}$ the fundamental mode is damped, though the shock may still be unstable to higher order modes, such as the first overtone ( cf. Chevalier & Imamura 1982; Strickland & Blondin 1995).
Table 4: The initial behaviour of the M=5 and M=10 simulations shown in Fig. 9 can be determined from the solution to a Riemann problem, which yields the resulting wave velocities in the system ( $v_{\rm l}$ , $v_{\rm cd}$ , and $v_{\rm r}$ being the velocity into the left state, the velocity of the contact discontinuity, and the velocity into the right state). The left state is defined as the CDL, while the right state is defined as the pre-shock flow (see Fig. 3). While the values quoted are for the initial conditions, they should be a good representation of the conditions which exist at the exact moment that the cooling layer disappears when $\alpha \ll \alpha _{\rm cr}$ .
Table 5: Critical value of $\alpha$ for damping of the fundamental mode as a function of the Mach number and $\chi$ , the ratio of the temperature of the CDL to the pre-shock temperature. This table is an extension of Table 3 where $\alpha _{\rm cr}$ is listed for $\chi =1$ .
Table 6: Reflection coefficient, R, as a function of the Mach number and $\chi$ , the ratio of the temperature of the CDL to the pre-shock temperature.
Table 7: Approximate properties of SNR blast waves at the transition into the pressure-driven snowplough stage for different values of $T_{\rm ISM}$ and n₀, chosen to demonstrate the conditions under which SNRs in the pressure-driven snowplough stage have low Mach number forward shocks which are susceptible to the radiative overstability. The age of the SNR at the onset of shell formation, $t_{\rm tr}$ , the shock velocity, $v_{\rm s}$ , and the Mach number, M, at this time, are given. The values illustrate that overstable low Mach number radiative shocks in SNRs will exist. For $T_{\rm ISM} = 10^{6}\;$ K and $n_{0} = 3.5 \times 10^{-3}\;\hbox{${\rm{\rm\thinspace cm}^{-3}~}$ }$ the blast wave becomes subsonic before transition to the pressure-driven snowplough stage.