Observational Signatures of Recollimation Shocks in Relativistic Jets: The Case of a Disordered Upstream Magnetic Field

Abstract

Astrophysical jets launched from active galactic nuclei can remain highly collimated over large distances due, in part, to recollimation shocks; the aim of this work was to determine what signatures of a recollimation shock are imparted into a hydrodynamic flow after crossing these shocks, for plasma with an initially completely disordered flux-frozen magnetic field. This work uses a statistical treatment of the magnetic field (c.f. Matthews & Scheuer, 1990), in which initially orthogonal vector triads (each vector monitoring one side of a parallelepipedic volume) are advected with the flow; these vectors are then used to determine the volume's emissivity. A modified version of the Hughes et al. (2002) code was employed to determine the parallelepiped advection using the same Godunov-type solver it employs to solve the Euler equations; it was found that the jets developed strong cylindrical asymmetries, however, and some parallelepiped components experienced huge growth, inexplicable in terms of the jet's velocity gradients. It was then decided to determine the parallelepipeds for time-independent, axisymmetric jets from the code of Fuentes et al. (2018). The parallelepiped evolution in steady flows may be determined by advecting marker particles with the flow, as the pathlines and streamlines are identical. We present the equations to describe the polarization for the cases of initial magnetic field that are (i) completely disordered, and (ii) partially ordered, consisting of a disordered component with a uniform or helical component. We present the data from three jet models with the same initial Lorentz factor and over-pressure ratio, characterized by their levels of internal energy as either “hot”, “intermediate”, or “cold”. For each model, we determine the total and fractional polarizations for lines of sight through the centre of widest and narrowest parts of the jets, for a range of viewing angles; similar variations of these parameters are found to occur in each model, but at higher viewing angles in the hotter models. Simulated images of the total and polarized flux densities, and fractional polarization are discussed for a range of viewing angles; importantly, we find that the recollimation shock structures in a jet may be clearly seen in its fractional polarization distribution. This work may be further developed by the inclusion of opacity and spectral ageing, and through the exploration of parameter space of the jet and initial magnetic field properties.