Numerically calibrated model for propagation of a relativistic unmagnetized jet in dense media

Abstract

Relativistic jets reside in high-energy astrophysical systems of all scales. Their interaction with the surrounding media is critical as it determines the jet evolution, observable signature, and feedback on the environment. During its motion the interaction of the jet with the ambient media inflates a highly pressurized cocoon, which under certain conditions collimates the jet and strongly affects its propagation. Recently, Bromberg et al. (2011b) derived a general simplified (semi)analytic solution for the evolution of the jet and the cocoon in case of an unmagnetized jet that propagates in a medium with a range of density profiles. In this work we use a large suite of 2D and 3D relativistic hydrodynamic simulations in order to test the validity and accuracy of this model. We discuss the similarities and differences between the analytic model and numerical simulations and also, to some extent, between 2D and 3D simulations. Our main finding is that although the analytic model is highly simplified, it properly predicts the evolution of the main ingredients of the jet-cocoon system, including its temporal evolution and the transition between various regimes (e.g., collimated to uncollimated). The analytic solution predicts a jet head velocity that is faster by a factor of about 3 compared to the simulations, as long as the head velocity is Newtonian. We use the results of the simulations to calibrate the analytic model which significantly increases its accuracy. We provide an applet that calculates semi-analytically the propagation of a jet in an arbitrary density profile defined by the user at

Jet Propagation in Neutron Star Mergers and GW170817

“…Through comparison with numerical simulations, we find that the analyticL 1/2 is overestimated in the same way as previously found for the static medium case (Mizuta & Ioka 2013;Harrison et al 2018). Hence, correctingL 1/2 gives the corrected form of A as:…”

“…2.1.1.8 A calibration coefficient for the analytical L Comparison of numerical simulations (of collapsar jets) shows that, in reality, the analytical modeling does not capture all the physics of fluid dynamics and the jet head propagation (e.g., oblique motion). As a result, as firstly found in Mizuta & Ioka (2013) and examined in detail in Harrison et al (2018), the analytical modeling overestimates the jet head radius (effectivelyL) in comparison with simulations. In Harrison et al (2018), the intensive comparison with simulations shows that, in the non-relativistic domain, the analytical equations give ∼ 2.5 − 3 times faster jet head velocity (see figure 12 in Harrison et al 2018).…”

“…As a result, as firstly found in Mizuta & Ioka (2013) and examined in detail in Harrison et al (2018), the analytical modeling overestimates the jet head radius (effectivelyL) in comparison with simulations. In Harrison et al (2018), the intensive comparison with simulations shows that, in the non-relativistic domain, the analytical equations give ∼ 2.5 − 3 times faster jet head velocity (see figure 12 in Harrison et al 2018). That is, for more accurate results,L 1/2 has to be corrected by a calibration coefficient Ns ∼ 1 2.5 to 1 3 .…”

“…η accounts for ignored effects such as the adiabatic expansion. rc is defined as rc ≈ c β ⊥ (t−t0) in the collapsar case, where the medium is static (Bromberg et al 2011;Harrison et al 2018). However, rc is more complex in the expanding medium case, therefore χ is an additional parameter (> 1 in the expanding medium case) which accounts for enhancement of rc due to the comoving expansion of the medium.…”

“…In both AGNs and collapsars, the medium is static. Jet propagation in a static medium is well-understood thanks to several analytic and numerical studies (Matzner 2003;Bromberg et al 2011;Mizuta & Ioka 2013;Harrison et al 2018).…”