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Register a new userViscous boundary layers of radiation-dominated, relativistic jets. I. The two-stream model
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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.
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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.
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.
Relativistic jets launched by rotating black holes are powerful emitters of non-thermal radiation. Extraction of the rotational energy via electromagnetic stresses produces magnetically-dominated jets, which may become turbulent. Studies of magnetically-dominated plasma turbulence from first principles show that most of the accelerated particles have small pitch angles, i.e. the particle velocity is nearly aligned with the local magnetic field. We examine synchrotron-self-Compton radiation from anisotropic particles in the fast cooling regime. The small pitch angles reduce the synchrotron cooling rate and promote the role of inverse Compton (IC) cooling, which can occur in two different regimes. In the Thomson regime, both synchrotron and IC components have soft spectra, $ u F_ upropto u^{1/2}$. In the Klein-Nishina regime, synchrotron radiation has a hard spectrum, typically $ u F_ upropto u$, over a broad range of frequencies. Our results have implications for the modelling of BL Lacs and Gamma-Ray Bursts (GRBs). BL Lacs produce soft synchrotron and IC spectra, as expected when Klein-Nishina effects are minor. The observed synchrotron and IC luminosities are typically comparable, which indicates a moderate anisotropy with pitch angles $thetagtrsim0.1$. Rare orphan gamma-ray flares may be produced when $thetall0.1$. The hard spectra of GRBs may be consistent with synchrotron radiation when the emitting particles are IC cooling in the Klein-Nishina regime, as expected for pitch angles $thetasim0.1$. Blazar and GRB spectra can be explained by turbulent jets with a similar electron plasma magnetisation parameter, $sigma_{rm e}sim10^4$, which for electron-proton plasmas corresponds to an overall magnetisation $sigma=(m_{rm e}/m_{rm p})sigma_{rm e}sim10$.
We present results from two-dimensional, general relativistic, viscous, radiation hydrodynamic numerical simulations of Shakura-Sunyaev thin disks accreting onto stellar mass Schwarzschild black holes. We consider cases on both the gas- and radiation-pressure-dominated branches of the thermal equilibrium curve, with mass accretion rates spanning the range from $dot{M} = 0.01 L_mathrm{Edd}/c^2$ to $10 L_mathrm{Edd}/c^2$. The simulations directly test the stability of this standard disk model on the different branches. We find clear evidence of thermal instability for all radiation-pressure-dominated disks, resulting universally in the vertical collapse of the disks, which in some cases then settle onto the stable, gas-pressure-dominated branch. Although these results are consistent with decades-old theoretical predictions, they appear to be in conflict with available observational data from black hole X-ray binaries. We also find evidence for a radiation-pressure-driven instability that breaks the unstable disks up into alternating rings of high and low surface density on a timescale comparable to the thermal collapse. Since radiation is included self-consistently in the simulations, we are able to calculate lightcurves and power density spectra (PDS). For the most part, we measure radiative efficiencies (ratio of luminosity to mass accretion rate) close to 6%, as expected for a non-rotating black hole. The PDS appear as broken power laws, with a break typically around 100 Hz. There is no evidence of significant excess power at any frequencies, i.e. no quasi-periodic oscillations are observed.
Relativistic jets, or highly collimated and fast-moving outflows, are endemic to many astrophysical phenomena. The jets produced by gamma-ray bursts and tidal disruption events are accompanied by the accretion of material onto a black hole or neutron star, with the accretion rate exceeding the Eddington limit of the compact object by orders of magnitude. In such systems, radiation dominates the energy-momentum budget of the outflow, and the dynamical evolution of the jet is governed by the equations of radiation hydrodynamics. Here we show that there are analytic solutions to the equations of radiation hydrodynamics in the viscous (i.e., diffusive) regime that describe structured, relativistic jets, which consist of a fast-moving, highly relativistic core surrounded by a slower-moving, less relativistic sheath. In these solutions, the slower-moving, outer sheath contains most of the mass, and the jet structure is mediated by local anisotropies in the radiation field. We show that, depending on the pressure and density profile of the ambient medium, the angular profile of the jet Lorentz factor is Gaussian or falls off even more steeply with angle. These solutions have implications for the nature of jet production and evolution in hyperaccreting systems, and demonstrate that such jets -- and the corresponding jet structure -- can be sustained entirely by radiative processes. We discuss the implications of these findings in the context of jetted tidal disruption events and short and long gamma-ray bursts.
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