A new method for extending solutions to the self-similar relativistic magnetohydrodynamic equations for black hole outflows

Abstract

The paradigm in which magnetic fields play a crucial role in launching/collimating outflows in many astrophysical objects continues to gain support. However, semianalytical models including the effect of magnetic fields on the dynamics and morphology of jets are still missing due to the intrinsic difficulties in integrating the equations describing a collimated, relativistic flow in the presence of gravity. Only few solutions have been found so far, due to the highly nonlinear character of the equations together with the need to blindly search for singularities. These numerical problems prevented a full exploration of the parameter space. We present a new integration scheme to solve r-self-similar, stationary, axisymmetric magnetohydrodynamics equations describing collimated, relativistic outflows crossing smoothly all the singular points (Alfvén point and modified slow/fast points). For the first time, we are able to integrate from the disk mid-plane to downstream of the modified fast point. We discuss an ensemble of jet solutions, emphasising trends and features that can be compared to observables. We present, for the first time with a semi-analytical MHD model, solutions showing counter-rotation of the jet for a substantial fraction of its extent. We find diverse jet configurations with bulk Lorentz factors up to 10 and potential sites for recollimation between 10 3 − 10 7 gravitational radii. Such extended coverage of the intervals of quantities, such as magnetic-to-thermal energy ratios at the base or the heights/widths of the recollimation region, makes our solutions suitable for application to many different systems where jets are launched.

Accelerating AGN jets to parsec scales using general relativistic MHD simulations

“…14. There is significant time variation in shape of the B10 and B50 field lines beyond the FMS due to the presence of toroidal pinch instabilities, which continue throughout the entire jet. The fast surface moves outward as the jet magnetisation increases (similar to Ceccobello et al 2018). (Panel b) The relative deviation with respect to the time-averaged jet opening angle along the B10 field line shows that there is > 10% deviation in the pinched region.…”

“…The location where this causal breakdown occurs is the fast magnetosonic separatrix surface (FMSS; for a review, see Meier 2012). Self-similar models (such as e.g., Vlahakis 2004;Polko et al 2010;Ceccobello et al 2018) predict that a jet collapses on its axis once the jet reaches the FMSS and may form a highly radiating hot-spot. Could then bright features in the jets, such as HST-1, be powered by such over-collimation seen in selfsimilar models?…”

Combining timing characteristics with physical broad-band spectral modelling of black hole X-ray binary GX 339–4

“…An improved treatment would involve reducing the number of free parameters by physically linking the radiative calculations with the jet dynamics. Self-similar MHD solutions of a relativistic jet presented by Ceccobello et al (2018) (building on work by Polko et al 2010Polko et al , 2013Polko et al , 2014 provide the groundwork for such a treatment. By combining the plethora of dynamical jet solutions presented by Ceccobello et al (2018) with radiative calculations such as those presented in this work, we shall in future be able to find more physically-realistic solutions for a given system (BHB or AGN) and perform model-fitting to retrieve more meaningful results with less degeneracies.…”

The appearance of a compact jet in the soft–intermediate state of 4U 1543−47

“…In the compact jet scenario, the IR emission -if optically thin -is produced by the accelerated particles in the collimated outflow that are closest to the jet base, at distances ∼10 2 -10 4 gravitational radii (r g = GM/c 2 ) from the BH (e.g. Markoff, Falcke & Fender 2001;Markoff et al 2003;Ceccobello et al 2018). This size scale has been confirmed from rapid variability time-scales and IR-X-ray cross-correlations, and corresponds to ∼0.1 lightseconds (e.g.…”