Conductive Heating

Momentum is transfered to the cloud from the blast wave and from the streaming material. But thermal energy is also transferred by conduction. The exterior gas is diffuse and hot while the cloud gas is relatively dense and cold. Thermal conduction will heat the cloud gas and cause evaporation. This process was investigated by McKee & Cowie (1975) in great detail.

In general, the collisional mean free path for a post-shock particle is very long and thus conduction is particularly inefficient. However even a very weak magnetic field can give ions a gyroradius much shorter than the diameter of a typical ISM cloud. Heat conduction then possible.

As the cloud is immersed in hot gas (for instance, after the main blast wave has passed by) a conduction front moves into the cloud at v_cond. V_cond depends strongly on the efficiency of radiative heat loss. If radiative losses in the front are large, v_cond < c_s. If radiative losses are minor compared with the heat flux (non-radiative), v_cond > c_s and a shock-like set of jump conditions develops. It appears that older SNRs (Cygnus) have radiation-dominated conduction fronts while younger SNRs (CasA) are non-radiative (McKee & Cowie 1975).

It should be pointed out that for any reasonable set of astrophysical conditions, thermal conduction is a very slow process and thus probably does not play a major role in shaping SNR morphology. The time scale for cloud shocks and conduction fronts are related by

$$\frac{t_{cond}}{t_{shock}} = \frac{n_{cloud,preshock}v_{shock}}{n_{cloud,postshock} v_{cond}}$$

If the conduction front is radiation dominated, the time scale is even longer. In any case, the conduction time scale is much longer than the shock crossing time scale and probably longer than the lifetime of the SNR itself (McKee & Cowie 1975).