*2.5. Jet and Cocoon Breakout*

When the jet head forward shock reaches the steep density gradient that characterizes the outer edge of the progenitor vestige, it starts accelerating in much the same way as a supernova shock does as it approaches the outer edge of the stellar envelope [77,128–131]. The main differences between the jet forward shock breakout and a supernova shock breakout are that the former is relativistic and highly anisotropic, both features having a strong impact on the resulting dynamics and emission [78,132–136]. As explained in Section 2.2, the head forward shock separates the shocked vestige material from the unshocked one (see Figure 2). Below the inner part of the forward shock, within an angle *θ*j,bo (the *jet angle at breakout*), is the head reverse shock: since the jet material crossing the latter is (by definition) faster than the head, its ram pressure ensures that the reverse shock keeps up with the accelerating forward shock. As a result, the head material remains dense and optically thick to Compton scattering during the breakout, and therefore its internal energy contributes to the expansion rather than being radiated. At angles larger than *θ*j,bo, on the other hand, the forward shock breakout is accompanied by the expansion of the underlying shocked material (which is part of the upper cocoon): the forward shock transitions from radiation-mediated to collisionless, liberating photons in what is sometimes called the "cocoon shock breakout emission" [79,137,138] (with a typical temperature of several tens of keV, [132]), and the underlying material becomes gradually transparent, giving rise to a "cooling" emission (typically peaking in the UV, [132]). The expansion of the cocoon after the shock breakout is sometimes called the cocoon "blowout" [74,114]. The entire breakout process is followed by a rearrangement of the jet and cocoon material into an inhomogeneous shell, which is what is most often referred to as the structured jet. In the following section, we focus on the structural properties of the latter, as found from numerical simulations.
