The propagation of choked jet outflows in power-law external media

Abstract

Observations of both gamma-ray bursts (GRBs) and active galactic nuclei (AGNs) point to the idea that some relativistic jets are suffocated by their environment before we observe them. In these 'choked' jets, all the jet's kinetic energy is transferred into a hot and narrow cocoon of near-uniform pressure. We consider the evolution of an elongated, axisymmetric cocoon formed by a choked jet as it expands into a cold power-law ambient medium ρ ∝ R −α , in the case where the shock is decelerating (α < 3). The evolution proceeds in three stages, with two breaks in behaviour: the first occurs once the outflow has doubled its initial width, and the second once it has doubled its initial height. Using the Kompaneets approximation, we derive analytical formulae for the shape of the cocoon shock, and obtain approximate expressions for the height and width of the outflow versus time in each of the three dynamical regimes. The asymptotic behaviour is different for flat (α ≤ 2) and steep (2 < α < 3) density profiles. Comparing the analytical model to numerical simulations, we find agreement to within ∼ 15 per cent out to 45 degrees from the axis, but discrepancies of a factor of 2-3 near the equator. The shape of the cocoon shock can be measured directly in AGNs, and is also expected to affect the early light from failed GRB jets. Observational constraints on the shock geometry provide a useful diagnostic of the jet properties, even long after jet activity ceases.

Broad-line type Ic SN 2020bvc

“…considerable amount of kinetic energy into the cocoon, which expands at mildly relativistic velocities once it breaks out of the progenitor star (Ramirez-Ruiz et al 2002;Bromberg et al 2011a). A choked jet, which fails to escape its progenitor star, transfers all its energy into the cocoon component (Bromberg et al 2011b(Bromberg et al , 2012Irwin et al 2019). The cocoon emission is expected to be detectable a few hours after the collapse of the progenitor star (Ramirez-Ruiz et al 2002), and once it breaks out it starts to expand into the interstellar medium.…”

How Dense of a Circumstellar Medium Is Sufficient to Choke a Jet?

“…While jets do not appear to ever be rapidly "choked" in the CSM for observed CSM densities, non-choked jets can still have their opening angle widened slightly as they propagate out due to the normal spreading process typical of GRB afterglow jets. We define the distinction between "choked" and merely "spreading" by the evolution of the opening angle with time; choked jets evolve as in Irwin et al (2019) (such jets should be roughly isotropic by the time they emerge from the dense CSM), whereas jets that are merely "spreading" evolve like GRB afterglow jets, as in Zhang & MacFadyen (2009), Granot & Piran (2012), and Duffell & Laskar (2018). In the case of jet spreading, the final opening angle has nothing to do with the duration of the engine.…”

“…The high-pressure cocoon then crushes the jet core, contaminating it with baryons and quickly thermalizing the jet kinetic energy. The flow from that point on mostly resembles a nonrelativistic blastwave, which rapidly evolves toward a spherical explosion (Irwin et al 2019). Jet choking is typically seen in calculations of a jet drilling through a star when the engine is shut off before breakout from the stellar surface (MacFadyen et al 2001).…”

“…A distinction is being made here between simple "jet spreading," which all jets do eventually, and this rapid lateral expansion characterized by a choked jet, as described in Irwin et al (2019). In this study we choose to define a "choked jet" to mean one which spreads rapidly according to Irwin et al (2019) as soon as the jet head receives the information that the engine has been shut off. A jet that evolves in this fashion would redistribute its energy into a roughly spherical blastwave by the time it emerges from the dense CSM surrounding the star.…”

Conditions for jet breakout in neutron stars’ mergers

“…The approach of Lyutikov (2011) follows the original Kompaneets pressure-equilibrating prescription (Kompaneets 1960). Irwin et al (2019) followed this procedure in details.…”