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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. We also extend the existing solution of jets in a static medium to power-law density media with index $alpha<5$. 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 $ t_d $ 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 $ eta $. Strong jets start their propagation in the ejecta on a timescale shorter than $t_d$ with $eta gg 1$, and within several ejecta dynamical times $eta$ drops below unity. Weak jets are unable to penetrate the ejecta at first (start with $eta ll 1$), and breach the ejecta only after the ejecta expands over a timescale longer than $ t_d $, thus their evolution is independent of $ t_d $. After enough time, both strong and weak jets approach an asymptotic phase where $eta$ is constant. Applying our model to short GRBs, we find that there is most likely a large diversity of ejecta mass, where mass $ lesssim 10^{-3}~{rm M}_{odot} $ (at least along the poles) is common.
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The binary neutron star (BNS) merger event GW170817 clearly shows that a BNS merger launches a short Gamma-Ray Burst (sGRB) jet. Unlike collapsars, where the ambient medium is static, in BNS mergers the jet propagates through the merger ejecta that is expanding outward at substantial velocities ($sim 0.2c$). Here, we present semi-analytic and analytic models to solve the propagation of GRB jets through their surrounding media. These models improve our previous model by including the jet collimation by the cocoon self-consistently. We also perform a series of 2D numerical simulations of jet propagation in BNS mergers and in collapsars to test our models. Our models are consistent with numerical simulations in every aspect (the jet head radius, the cocoons lateral width, the jet opening angle including collimation, the cocoon pressure, and the jet-cocoon morphology). The energy composition of the cocoon is found to be different depending on whether the ambient medium is expanding or not; in the case of BNS merger jets, the cocoon energy is dominated by kinetic energy, while it is dominated by internal energy in collapsars. Our model will be useful for estimating electromagnetic counterparts to gravitational waves.
Observations from the radio to the gamma-ray wavelengths indicate that supernova remnant (SNR) shocks are sites of effective particle acceleration. It has been proposed that the presence of dense clumps in the environment where supernovae explode might have a strong impact in shaping the hadronic gamma-ray spectrum. Here we present a detailed numerical study about the penetration of relativistic protons into clumps which are engulfed by a SNR shock, taking into account the magneto-hydrodynamical properties of the background plasma. We show that the spectrum of protons inside clumps is much harder than that in the diffuse inter-clump medium and we discuss the implications for the formation of the spectrum of hadronic gamma rays, which does not reflect anymore the acceleration spectrum of protons, resulting substantially modified inside the clumps due to propagation effects. For the Galactic SNR RX J1713.7-3946, we show that a hadronic scenario including dense clumps inside the remnant shell is able to reproduce the broadband gamma-ray spectrum from GeV to TeV energies. Moreover, we argue that small clumps crossed by the shock could provide a natural explanation to the non-thermal X-ray variability observed in some hot spots of RX J1713.7-3946. Finally we discuss the detectability of gamma-ray emission from clumps with the upcoming Cherenkov Telescope Array and the possible detection of the clumps themselves through molecular lines.
We present 3D general relativistic magnetohydrodynamic(GRMHD) simulations of zero angular momentum accretion around a rapidly rotating black hole, modified by the presence of initially uniform magnetic fields. We consider serveral angles between the magnetic field direction and the black hole spin. In the resulting flows, the midplane dynamics are governed by magnetic reconnection-driven turbulence in a magnetically arrested (or a nearly arrested) state. Electromagnetic jets with outflow efficiencies ~10-200% occupy the polar regions, reaching several hundred gravitational radii before they dissipate due to the kink instability. The jet directions fluctuate in time and can be tilted by as much as ~30 degrees with respect to black hole spin, but this tilt does not depend strongly on the tilt of the initial magnetic field. A jet forms even when there is no initial net vertical magnetic flux since turbulent, horizon-scale fluctuations can generate a net vertical field locally. Peak jet power is obtained for an initial magnetic field tilted by 40-80 degrees with respect to the black hole spin because this maximizes the amount of magnetic flux that can reach the black hole. These simulations may be a reasonable model for low luminosity black hole accretion flows such as Sgr A* or M87.
Current observations have shown that astrophysical jets reveal strong signs of radial structure. They suggest that the inner region of the jet, the jet spine, consists of a low-density, fast-moving gas, while the outer region of the jet consists of a more dense and slower moving gas, called the jet sheath. Moreover, if jets carry angular momentum, the resultant centrifugal forces lead to a radial stratification. Current observations are not able to fully resolve the radial structure, so little is known about its actual profile. We present three AGN jet models in $2.5D$ of which two have been given a radial structure. The first model is a homogeneous jet, the only model that doesnt carry angular momentum; the second model is a spine-sheath jet with an isothermal equation of state; and the third jet model is a (piecewise) isochoric spine-sheath jet, with constant but different densities for jet spine and jet sheath. In this paper, we look at the effects of radial stratification on jet integrity, mixing between the different jet components and global morphology of the jet-head and surrounding cocoon.
We numerically find that transmission coefficients have a rich structure as a function of wavelength in Cantor media. Complete transmission and complete reflection are observed. We also find that light propagation has scalings with respect to number of layers.
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