V Shock-cloud collisions

In Chapter I different physical mechanisms to account for the alignment effect in radio galaxies were discussed. Whatever the physical mechanism responsible for this effect, it seems that shock waves (Best et al., 2000) are the most important mechanism for producing the observed radiation, at least for the cases of the small double radio sources.

These shock waves might be due to different causes, but the obvious one is the interaction of the shock at the leading edge of the expanding jet of the radio source with cold clouds embedded in the intergalactic medium. In order to describe these collisions, the simplest model is the one described by the interaction of a plane shock wave with a self gravitating cloud in which magnetic fields and relativistic effects may be present. This problem requires unattainable computer power in three dimensions and has not been achieved so far. The best simulation that has been carried out to date is the one in which a plane parallel shock hits a two dimensional spherical cloud of constant density (Klein et al., 1994) in which relativistic effects and magnetic fields are not taken into account. This is of course a very simplified version of the problem, but has a very important conclusion: the cloud is destroyed due to instabilities after the interaction.

In this chapter we describe a simplified solution to the problem as compared with that described by Klein et al. (1994). We analyse the interaction of a one dimensional plane parallel shock which collides with a cold high density region bounded by two tangential discontinuities (a cloud). Magnetic fields and self gravity of the cloud are not taken into account. This oversimplification has made it possible to give a complete analytic description of the interaction.