Viscous Boundary Layers of Radiation-Dominated, Relativistic Jets. Ii. The Free-Streaming Jet Model

Abstract

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.

Structured, relativistic jets driven by radiation

“…When there is no pressure gradient and the ambient medium is characterized by a constant density, so that q = n = 0, the outflow decelerates according to Γ ∝ r −1 and represents a "freely expanding" jet within a homogeneous medium. An analogous situation was considered in the relativistic, compressible limit by Coughlin & Begelman (2015b), who adopted a Cartesian geometry 6 and found that the flow decelerates according to Γv ∝ z −1/4 , in agreement with the result for incompressible, non-relativistic flow (e.g., Kundu & Cohen 2008). This rate of deceleration is clearly much less rapid than the one derived here in spherical coordinates, and this difference arises from the fact that in spherical coordinates the increase in the cross-sectional area of the jet grows as the square of the boundary layer thickness.…”

“…In contrast, the plane-parallel approximation implies that the area of the outflow grows only as a single power of the boundary layer thickness, as the flow is infinite (and unchanging) in the x-direction. Thus, and as argued heuristically in Section 5 of Coughlin & Begelman (2015b), the fact that the area of the jet increases more rapidly along the axis in spherical coordinates, and the corresponding larger rate of increase of the inertia contained in the flow, results in the more rapid deceleration of the jet.…”

Tidal disruption of a white dwarf by a black hole: the diversity of nucleosynthesis, explosion energy, and the fate of debris streams

“…In the cases of Type III TDEs where the early selfintersection occurs, extremely super-Eddington accretion rates would be realized. In such situations, there would be relativistic winds and/or jets driven by radiation pressure, and these events could be so-called jetted TDEs (Strubbe & Quataert 2009;Coughlin & Begelman 2014;Shen & Matzner 2014;Coughlin & Begelman 2015;Lu et al 2017). An observer along with the jet axis would see beamed emission resembling ultra-long γ-ray bursts that would be observable even if the events are very distant.…”

Tidal disruption by extreme mass ratio binaries and application to ASASSN-15lh

“…While these hyper-Eddington periods are predicted analytically (Rees 1988;Evans & Kochanek 1989), the peak accretion rates in Figure 1 can actually exceed the analytical one (shown by the dashed curve in the top-left panel in this figure), which is a consequence of self-gravity (Coughlin & Nixon 2015) and the non-zero energy of the stellar center of mass. In these highly supercritical regimes, one might expect winds (Strubbe & Quataert 2009; or, in the more extreme cases, jets (Giannios & Metzger 2011;Coughlin & Begelman 2014;Tchekhovskoy et al 2014;Coughlin & Begelman 2015) to be launched from the vicinity of the accreting SMBH. From these outflows one would expect an additional source of radiation, with properties distinct from the disc.…”