*2.6. Expected General Features of the Jet Structure in GRBs*

Despite the complexity of the involved processes, the modeling and understanding of the birth and evolution of relativistic jets have been addressed since the late seventies, initially prompted by observations of radio galaxies [72]. A big deal of the understanding of jet launching and its evolution has been obtained through numerical simulations of the central engine (typically within general-relativistic magnetohydrodynamics, GRMHD) and of the jet propagation (usually within special-relativistic hydrodynamics–RHD–or magnetohydrodynamics–RMHD–framework, see [139] for a recent review). In the GRB context, a widely adopted approach (due in part to computational limitations) to the simulation of the propagation and breakout phase has been that of "injecting" a jet with properties based on an educated guess into a model of the progenitor vestige (in two dimensions, e.g., [30,140], and three dimensions, e.g., [116,123,141,142], but see e.g., [113,119,143]). While this helps in limiting the needed computational resources by leaving out the central engine region from the computational domain, it prevents a direct connection between the properties and evolution of the central engine and those of the jet at larger scales: in particular, this approach does not allow for a self-consistent description of: (1) the central engine variability (due, e.g., to the stochastic fluctuations in the accretion rate due to a turbulent disk); (2) the evolution of the jet luminosity (linked to that of the accretion rate and/or of the central compact object); and possibly (3) orientation; the (4) injected jet structure (angular distributions of kinetic luminosity and magnetization); and (5) the effects of the central engine on the vestige (e.g., gravity and the accretion disk winds). On top

of this, the idealized nature of the progenitor models employed in most of these studies can affect the results by introducing exact symmetries that are not present in nature. The steady advancement of computational methods and resources has led recently to many important works that investigated some of these limitations (e.g., [144–152]). These include three-dimensional GRMHD simulations that self-consistently cover jet launch (usually within the Blandford–Znajek paradigm), propagation and breakout [150–152], even though these still feature idealized initial conditions and do not include a treatment of neutrinos, whose contribution to cooling, transport of momentum and energy can have prominent effects on the central regions. Yet, these simulations currently constitute some of the most detailed investigations that can shed light on the GRB jet structure. Figure 4 shows the jet structures obtained from GRMHD simulations in the collapsar case (top panels-[151]) and in the case of binary neutron star mergers (bottom panels-[152]). In qualitative agreement with previous works, these investigations find a jet angular structure after breakout that broadly features a narrow *core* (with an opening angle of few degrees) with approximately uniform Lorentz factor and energy density (mostly containing jet material that crossed the collimation shock, but did not reach the head before breakout), surrounded by a wider structure (sometimes called the jet *wings*, and typically composed of an inner part of mixed jet and cocoon material—where the amount of mixing depends on the jet magnetization, e.g., [142]—surrounded by a wider, cocoon-dominated part) where both the average Lorentz factor and the energy density fall off relatively quickly with the angle (typically as steep power laws ∝ *θ <sup>a</sup>* with *<sup>a</sup>* . <sup>−</sup>3, or as Gaussians). A minority of the simulations find a "hollow" jet core with a lower energy density and Lorentz factor along the axis with respect to that at the core edge [150], but it is unclear whether this is a genuine result or a numerical artifact [153].

**Figure 4.** Jet structures resulting from GRMHD simulations representing collapsars (upper panels, adapted from [151]) and binary neutron star merger remnants (lower panel, adapted from [152]). Left-hand panels show the isotropic-equivalent energy *E*iso = 4*π*d*E*/dΩ from a late snapshot of the simulations (significantly later than the jet breakout), while right-hand panels show the distribution of energy in the four-velocity modulus *u* = Γ*β* space. Different colors refer to different initial conditions, as detailed in [151,152].
