*2.2. Stages in the Life of a Relativistic Jet*

In order to understand the structure of gamma-ray burst relativistic jets, we need to have a global view of how a jet is formed and how it evolves throughout its life. For that purpose, let us briefly summarize the main stages of the jet evolution with reference to the scheme shown in Figure 2:


The above brief account should help in making clear that the jet structure evolves throughout the life of a GRB jet. Three crucial phases can be identified in such an evolution: (1) the jet *launch* where the initial energy breakdown (internal, kinetic, magnetic), its angular profile and time dependence (all of which could contribute in principle to determining the properties of the jet at later stages) is set by the central engine and its evolution; (2) the *interaction* of the jet with the progenitor vestige, comprising the *propagation* of the jet head, the formation of the cocoon and the jet *breakout*; (3) the *expansion* of the jet in the external medium, and the subsequent *deceleration*. The first phase sets the initial conditions of the problem and thus determines, along with the properties of the progenitor, the structure at later stages. On the other hand, it is possible that memory of the details of the initial conditions is lost along the evolution: for example, as the jet transitions from adulthood to seniority (i.e., when the external shock enters the self-similar blastwave phase) the radial structure of the jet is erased (over a time scale that depends on the presence or absence of a low-velocity tail).

Given the time-dependent nature of the system, no univocal definition of jet structure exists: the most useful definition must be determined depending on the particular application and on the observational or theoretical aspects under consideration. Yet, in modeling the prompt and afterglow emission, often the most relevant structure is that

corresponding to the jet's adulthood, i.e., during the free expansion following the breakout from the progenitor vestige. This is the phase during which the prompt emission is believed to be produced, and the structure during this phase also constitutes the initial condition for producing the afterglow emission.

**Figure 2.** Artist's impression of the different phases in the early evolution of a GRB jet (long and short GRBs schematically represented on the left-hand and right-hand side, respectively). The putative progenitors are depicted in the stamps on the top corners. The formation of a compact central object (BH or NS) accompanied by an accretion disk powers a relativistic jet, determining the properties at its base ("birth"). The jet expands within the progenitor vestige (stellar envelope—left—or merger ejecta and disk winds—right) and starts interacting with it ("infancy"). The cocoon formed by ambient and jet-shocked material produces an inward pressure that collimates the jet as it propagates ("childhood"). As the jet breaks out ("adolescence") its head accelerates and the cocoon blows out. The subsequent phases ("adulthood and seniority", described in the text) are responsible for the prompt and afterglow emissions. See Section 2.2 for the description of the phases through which a jet evolves.
