The paradigm in which magnetic fields play a crucial role in launching/collimating outflows in many astrophysical objects continues to gain support. However, semi-analytical 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 non-linear 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 magnetohydrodynamic (MHD) equations describing collimated, relativistic outflows crossing smoothly all the singular points (Alfven point and modified slow/fast points). For the first time, we are able to integrate from the disc mid-plane to downstream of the modified fast point. We discuss an ensemble of jet solutions, emphasizing 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) and 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.

Accretion discs and black holes (BHs) have angular momenta that are generally misaligned, which can lead to warped discs and bends in any jets produced. We examine whether a disc that is misaligned at large radii can be aligned more efficiently by the torque of a Blandford-Znajek (BZ) jet than by Lense-Thirring (LT) precession. To obtain a strong result, we will assume that these torques maximally align the disc, rather than cause precession, or disc tearing. We consider several disc states that include radiatively inefficient thick discs, radiatively efficient thin discs, and super-Eddington accretion discs. The magnetic field strength of the BZ jet is chosen as either from standard equipartition arguments or from magnetically arrested disc (MAD) simulations. We show that standard thin accretion discs can reach spin-disc alignment out to large radii long before LT would play a role, due to the slow infall time that gives even a weak BZ jet time to align the disc. We show that geometrically thick radiatively inefficient discs and super-Eddington discs in the MAD state reach spin-disc alignment near the BH when density profiles are shallow as in magnetohydrodynamical simulations, while the BZ jet aligns discs with steep density profiles (as in advection-dominated accretion flows) out to larger radii. Our results imply that the BZ jet torque should affect the cosmological evolution of BH spin magnitude and direction, spin measurements in active galactic nuclei and X-ray binaries, and the interpretations for Event Horizon Telescope observations of discs or jets in strong-field gravity regimes.

We present a new, semi-analytic formalism to model the acceleration and collimation of relativistic jets in a gravitational potential. The gravitational energy density includes the kinetic, thermal and electromagnetic mass contributions. The solutions are close to self-similar throughout the integration, from very close to the black hole to the region where gravity is unimportant. The field lines are tied to the conditions very close to the central object and eventually overcollimate, possibly leading to a collimation shock. This collimation shock could provide the conditions for diffusive shock acceleration, leading to the observed electron populations with a power-law energy distribution in jets. We provide the derivation, a detailed analysis of a solution and describe the effects the parameters have on the properties of the solutions, such as the Lorentz factor and location of the collimation shock. We also discuss the deviations from self-similarity. By comparing the new gravity term with the gravity term obtained from a non-relativistic formalism in a previous work, we show they are equivalent in the non-relativistic limit. This equivalence shows the approach taken in that work is valid and allows us to comment on its limitations.

We present a new, approximate method for modelling the acceleration and collimation of relativistic jets in the presence of gravity. This method is self-similar throughout the computational domain where gravitational effects are negligible and, where significant, self-similar within a flux tube. These solutions are applicable to jets launched from a small region (e.g. near the inner edge of an accretion disc). As implied by earlier work, the flow can converge on to the rotation axis, potentially creating a collimation shock.In this first version of the method, we derive the gravitational contribution to the relativistic equations by analogy with non-relativistic flow.This approach captures the relativistic kinetic gravitational mass of the flowing plasma, but not that due to internal thermal and magnetic energies. A more sophisticated treatment, derived from the basic general relativistic magnetohydrodynamical equations, is currently being developed.Here we present an initial exploration of parameter space, describing the effects the model parameters have on flow solutions and the location of the collimation shock. These results provide the groundwork for new, semi-analytic models of relativistic jets which can constrain conditions near the black hole by fitting the jet break seen increasingly in X-ray binaries.

Jets can contribute to the spectra of X-ray binaries (XRBs) and active galactic nuclei (AGN) from the radio through the gamma-ray bands; thus understanding their physics is key for interpreting the data. Recent VLBI observations suggest that jets begin to accelerate particles into power-law distributions at a point offset from the black hole by similar to 10(4) r(g), possibly via a collimation shock. Spectral fitting of simultaneous, broadband data from both XRBs and AGN in jet-dominated states corroborates this picture. From a magnetohydrodynamical (MHD) point of view, it is natural to associate the onset of particle acceleration with the final MHD critical point in the flow, the modified fast point (MFP), where causal contact with the upstream flow is broken. In this way a standing disruption like a shock can form, and this location might vary with the physical parameters of the jet. In order to study this issue, we have used the self-similar formalism of Vlahakis & Konigl (2003, hereafter VK03) to simplify the MHD equations and to derive solutions that cross the critical points. We have found a new parameter space of solutions that cross the MFP at a finite height above the disc and are relativistic, spanning a range of Lorentz factors Gamma <= 10 (Polko et al. 2010). We present; these results, as well as preliminary work connecting the relativistic formalism to the non-relativistic conditions with gravity near the base of the jets.

Observations of relativistic jets from black holes systems suggest that particle acceleration often occurs at fixed locations within the flow. These sites could be associated with critical points that allow the formation of standing shock regions, such as the magnetosonic modified fast point. Using the self-similar formulation of special relativistic magnetohydrodynamics by Vlahakis & K\"onigl, we derive a new class of flow solutions that are both relativistic and cross the modified fast point at a finite height. Our solutions span a range of Lorentz factors up to at least 10, appropriate for most jets in X-ray binaries and active galactic nuclei, and a range in injected particle internal energy. A broad range of solutions exists, which will allow the eventual matching of these scale-free models to physical boundary conditions in the analysis of observed sources.