After its launch, a GRB jet propagates through a dense medium prior to its breakout. The interaction of the jet with the medium gives rise to the formation of a complex structured outflow, often referred to as a "structured jet". This structure is essential for our understanding of GRBs as it ultimately dictates their emission signatures. However, to date, the underlying physics which sets the post-breakout jet morphology remained unexplored, and its modeling has been mainly done by assuming ad-hoc functions. Using a set of 3D simulations we follow the evolution of hydrodynamic long and short GRB jets after breakout and provide a physically motivated post-breakout outflow structure of GRB jets. Our simulations feature Rayleigh-Taylor fingers, which grow from the cocoon into the jet and destabilize it (for the video click here). The mixing of jet-cocoon material gives rise to a previously unidentified region between the two, which we denote the jet-cocoon interface (JCI). In lGRBs the mixing is strong, leading to most of the outflow energy to drift into the JCI. In sGRBs, where the medium is lighter, the mixing is weaker, and the JCI and the jet core hold a comparable amount of energy. Remarkably, the jet structure (core and JCI) in all systems can be characterized by simple angular power-law distributions of power and velocity, with power-law indices that depend solely on the level of mixing. This result supports the commonly used power-law angular distribution, and disfavors a Gaussian jet modeling. At larger angles, where the cocoon dominates, the structure is more complex including both an angular and a radial structure. The mixing shapes the prompt light curve and implies that typical afterglows of lGRBs are different from those of sGRBs. The predictions that we provide can be used to infer jet characteristics from prompt and afterglow observations.

The structure of weakly-magnetized γ-ray burst jets
The interaction of gamma-ray burst (GRB) jets with the dense media into which they are launched promote the growth of local hydrodynamic instabilities along the jet boundary. In a companion paper \citep{Gottlieb2020b} we study the evolution of hydrodynamic (unmagnetized) jets, finding that mixing of jet-cocoon material gives rise to an interface layer, termed jet-cocoon interface (JCI), which contains a significant fraction of the system energy. We find that the angular structure of the jet + JCI, when they reach the homologous phase, can be approximated by a flat core (the jet) + a power-law function (the JCI) with indices that depend on the degree of mixing. In this paper we examine the effect of subdominant toroidal magnetic fields on the jet evolution and morphology. We find that weak fields can stabilize the jet against local instabilities. The suppression of the mixing diminishes the JCI and thus reshapes the jet's post-breakout structure. Nevertheless, the overall shape of the outflow can still be approximated by a flat core + a power-law function, although the JCI power-law decay is steeper. The effect of weak fields is more prominent in long GRB jets, where the mixing in hydrodynamic jets is stronger. In short GRB jets there is small mixing in both weakly magnetized and unmagnetized jets. This result influences the expected jet emission which is governed by the jet's morphology. Therefore, prompt and afterglow observations in long GRBs may be used as probes for the magnetic nature at the base of the jets.

Jet propagation in expanding media
We present a comprehensive analytic model of a relativistic jet propagation in expanding media. This model is the first to cover the entire jet evolution from early to late times, as well as a range of configurations that are relevant to binary neutron star mergers. These include low and high luminosity jets, unmagnetized and mildly magnetized jets, time-dependent luminosity jets, and Newtonian and relativistic head velocities. Our model, which is tested and calibrated by a suite of 3D RMHD simulations, provides simple analytic formulae for the jet head propagation and breakout times, as well as a simple breakout criterion which depends only on the jet to ejecta energy ratio and jet opening angle. Assuming a delay time td between the onset of a homologous ejecta expansion and jet launching, the system evolution has two main regimes: strong and weak jets. The regime depends on the ratio between the jet head velocity in the ejecta frame and the local ejecta velocity, denoted as η. Strong jets start their propagation in the ejecta on a timescale shorter than td with η≫1, and within several ejecta dynamical times η drops below unity. Weak jets are unable to penetrate the ejecta at first (start with η≪1), and breach the ejecta only after the ejecta expands over a timescale longer than td, thus their evolution is independent of td. After enough time, both strong and weak jets approach an asymptotic phase where η is constant. Applying our model to short GRBs, we find that there is most likely a large diversity of ejecta mass, where mass ≲10−3 M⊙ (at least along the poles) is common.

A semi-analytical calculation of the jet propagation based on numerical simulations:
For the visual interface and a csv file for a given set of jet and medium parameters, click here.
For the python code, click here.
Link to the paper