Formation of internal shock waves in bent jets

We discuss the circumstances under which the bending of a jet can generate an internal shock wave. The analysis is carried out for relativistic and non–relativistic astrophysical jets. The calculations are done by the method of characteristics for the case of steady simple waves. This generalises the non–relativistic treatment first used by Icke (1991). We show that it is possible to obtain an upper limit to the bending angle of a jet in order not to create a shock wave at the end of the curvature. This limiting angle has a value of ∼ 75 ◦ for non–relativistic jets with a polytropic index κ = 4/3, ∼ 135 ◦ for non–relativistic jets with κ = 5/3 and ∼ 50 ◦ for relativistic jets with κ = 5/3. We also discuss under which circumstances jets will form internal shock waves for smaller deflection angles.