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Register a new userEntropy Production in Relativistic Jet Boundary Layers
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Hot relativistic jets, passing through a background medium with a pressure gradient p propto r^{-eta} where 2 < eta <= 8/3, develop a shocked boundary layer containing a significant fraction of the jet power. In previous work, we developed a self-similar description of the boundary layer assuming isentropic flow, but we found that such models respect global energy conservation only for the special case eta = 8/3. Here we demonstrate that models with eta < 8/3 can be made self-consistent if we relax the assumption of constant specific entropy. Instead, the entropy must increase with increasing r along the boundary layer, presumably due to multiple shocks driven into the flow as it gradually collimates. The increase in specific entropy slows the acceleration rate of the flow and provides a source of internal energy that could be channeled into radiation. We suggest that this process may be important for determining the radiative characteristics of tidal disruption events and gamma-ray bursts from collapsars.
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We study the collimation of relativistic hydrodynamic jets by the pressure of an ambient medium in the limit where the jet interior has lost causal contact with its surroundings. For a jet with an ultrarelativistic equation of state and external pressure that decreases as a power of spherical radius, p propto r^(-eta), the jet interior will lose causal contact when eta > 2. However, the outer layers of the jet gradually collimate toward the jet axis as long as eta < 4, leading to the formation of a shocked boundary layer. Assuming that pressure-matching across the shock front determines the shape of the shock, we study the resulting structure of the jet in two ways: first by assuming that the pressure remains constant across the shocked boundary layer and looking for solutions to the shock jump equations, and then by constructing self-similar boundary-layer solutions that allow for a pressure gradient across the shocked layer. We demonstrate that the constant-pressure solutions can be characterized by four initial parameters that determine the jet shape and whether the shock closes to the axis. We show that self-similar solutions for the boundary layer can be constructed that exhibit a monotonic decrease in pressure across the boundary layer from the contact discontinuity to the shock front, and that the addition of this pressure gradient in our initial model generally causes the shock front to move outwards, creating a thinner boundary layer and decreasing the tendency of the shock to close. We discuss trends based on the value of the pressure power-law index eta.
We analyze the interaction of a radiation-dominated jet and its surroundings using the equations of radiation hydrodynamics in the viscous limit. In a previous paper we considered the two-stream scenario, which treats the jet and its surroundings as distinct media interacting through radiation viscous forces. Here we present an alternative boundary layer model, known as the free-streaming jet model -- where a narrow stream of fluid is injected into a static medium -- and present solutions where the flow is ultrarelativistic and the boundary layer is dominated by radiation. It is shown that these jets entrain material from their surroundings and that their cores have a lower density of scatterers and a harder spectrum of photons, leading to observational consequences for lines of sight that look down the barrel of the jet. These jetted outflow models may be applicable to the jets produced during long gamma-ray bursts and super-Eddington phases of tidal disruption events.
Using the relativistic equations of radiation hydrodynamics in the viscous limit, we analyze the boundary layers that develop between radiation-dominated jets and their environments. In this paper we present the solution for the self-similar, 2-D, plane-parallel two-stream problem, wherein the jet and the ambient medium are considered to be separate, interacting fluids, and we compare our results to those of previous authors. (In a companion paper we investigate an alternative scenario, known as the free-streaming jet model.) Consistent with past findings, we show that the boundary layer that develops between the jet and its surroundings creates a region of low-density material. These models may be applicable to sources such as super-Eddington tidal disruption events and long gamma-ray bursts.
We discuss stationary and axisymmetric trans-magnetosonic outflows in the magnetosphere of a rotating black hole (BH). Ejected plasma from the plasma source located near the BH is accelerated far away to form a relativistic jet. In this study, the plasma acceleration efficiency and conversion of fluid energy from electromagnetic energy are considered by employing the trans-fast magnetosonic flow solution derived by Takahashi & Tomimatsu (2008). Considering the parameter dependence of magnetohydrodynamical flows, we search for the parameters of the trans-magnetosonic outflow solution to the recent M87 jet observations and obtain the angular velocity values of the magnetic field line and angular momentum of the outflow in the magnetized jet flow. Therefore, we estimate the locations of the outer light surface, Alfven surface, and separation surface of the flow. We also discuss the electromagnetic energy flux from the rotating BH (i.e., the Blandford-Znajek process), which suggests that the energy extraction mechanism is effective for the M87 relativistic jet.
High energy gamma-rays have been detected from Cygnus X-3, a system composed of a Wolf-Rayet star and a black hole or neutron star. The gamma-ray emission is linked to the radio emission from the jet launched in the system. The flux is modulated with the 4.8 hr orbital period, as expected if high energy electrons are upscattering photons emitted by the Wolf-Rayet star to gamma-ray energies. This modulation is computed assuming that high energy electrons are located at some distance along a relativistic jet of arbitrary orientation. Modeling shows that the jet must be inclined and that the gamma ray emitting electrons cannot be located within the system. This is consistent with the idea that the electrons gain energy where the jet is recollimated by the stellar wind pressure and forms a shock. Jet precession should strongly affect the gamma-ray modulation shape at different epochs. The power in non-thermal electrons represents a small fraction of the Eddington luminosity only if the inclination is low i.e. if the compact object is a black hole.
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