Internal shocks in relativistic jets with time-dependent sources

Abstract

We explore the possibility of formation of steady internal shocks in jets around black holes. We consider a fluid described by a relativistic equation of state, flowing about the axis of symmetry (θ = 0) in a Schwarzschild metric. We use two models for the jet geometry, (i) a conical geometry and (ii) a geometry with non-conical cross-section. Jet with conical geometry is smooth flow. While the jet with non-conical cross section undergoes multiple sonic point and even standing shock. The jet shock becomes stronger, as the shock location is situated further from the central black hole. Jets with very high energy and very low energy do not harbour shocks, but jets with intermediate energies do harbour shocks. One advantage of these shocks, as opposed to shocks mediated by external medium is that, these shocks have no effect on the jet terminal speed, but may act as possible sites for particle acceleration. Typically , a jet with energy 1.8 c 2 , will achieve a terminal speed of v ∞ = 0.813c for jet with any geometry. But for a jet of non-conical cross-section for which the length scale of the inner torus of the accretion disc is 40r g , then in addition, a steady shock will form at r sh ∼ 7.5r g and compression ratio of R ∼ 2.7. Moreover , electron-proton jet seems to harbour the strongest shock. We discuss possible consequences of such a scenario.

Gamma-Ray Burst Prompt Correlations

“…These results imply that both models can provide a physical interpretation of the iso ∝ 2 peak relation as well as the parameter . To explain the origin of this correlation, Mendoza et al [242] considered simple laws of mass and linear momentum conservation on the emission surface to give a full description of the working surface flow parameterized by the initial velocity and mass injection rate. They assumed a source-ejecting matter in a preferred direction with 20 Advances in Astronomy a velocity V( ) and a mass ejection ratė( ), both dependent on time as measured from the jet's source; that is, they studied the case of a uniform release of mass and the luminosity was measured considering simple periodic oscillations of the particle velocity, a common assumption in the internal shock model scenario.…”

Understanding the light curves of the HST-1 knot in M87 with internal relativistic shock waves along its jet

“…Long time observations of the HST-1 knot inside the jet of the galaxy M87 have produced detailed multi-wavelength light curves. In this article, we model these light curves using the semi-analytical approach developed by Mendoza et al (2009). This model was developed to account for the light curves of working surfaces moving along relativistic jets.…”

“…(b) bending of jets above a critical value (Mendoza 2000;Mendoza & Longair 2002), and (c) Periodic variations of the injected velocity and mass at the base of the jet (e.g. Rees & Meszaros 1994;Jamil et al 2008;Mendoza et al 2009, and references therein).…”

“…The semianalytical model by Mendoza et al (2009) (denoted as M09 in what follows) has been quite useful in modelling not only outbursts associated to long gamma-ray bursts but also to the many outbursts detected on the light curve of the blazar PKS 1510-089 (Cabrera et al 2013). We show in this article, that such a model is also good for modelling and understand-ing the multi-frequency features observed in the HST-1 knot of the M87 galaxy.…”

“…In section 2 we present the multi-wavelength observation campaigns of the HST-1 knot and its light curves features. In section 3 we present a brief description of the hydrodynamical model developed by Mendoza et al (2009) and the system of dimensionless units in which it is useful to make comparisons with observations. The fits to the light curves using the hydrodynamical model of Mendoza et al (2009) are developed in the section 4.…”