A minimalist approach to the linear stability problem in fluid dynamics is developed that ensures efficiency by utilizing only the essential elements required to find the eigenvalues for given boundary conditions. It is shown that the problem is equivalent to a single first-order ordinary differential equation, and that studying the argument of the unknown complex function in the eigenvalue space is sufficient to find the dispersion relation. The method is applied to a model for relativistic magnetized astrophysical jets.

Theoretical arguments as well as observations of young stellar objects (YSO) support the presence of a diversified circumstellar environment. A stellar jet is thought to account for most of the stellar spin down and disk wind outflow for the observed high mass loss rate, thus playing a major role in the launching of powerful jets. RY Tau, for instance, is an extensively studied intermediate mass pre-main sequence star. Observational data reveal a small scale jet called microjet. Nevertheless, it is not clear how the microjet shapes the jet observed at a large scale. The goal is to investigate the spatial stability and structure of the central jet at a large scale by mixing the stellar and disk components. We mix two existing analytical self-similar models for the disk and the stellar winds to build the initial set-ups. Instead of using a polytropic equation of state, we map from the analytical solutions, the heating and cooling sources. The heating exchange rate is controlled by two parameters, its spatial extent and its intensity. The central jet and the surrounding disk are strongly affected by these two parameters. We separate the results in three categories, which show different emissivity, temperature, and velocity maps. We reached this categorization by looking at the opening angle of the stellar solution. For cylindrically, well collimated jets, we have opening angles as low as 10 degrees between 8 and 10 au, and for the wider jets, we can reach 30 degrees with a morphology closer to radial solar winds. Our parametric study shows that the less heated the outflow is, the more collimated it appears. We also show that recollimation shocks appear consistently with UV observations in terms of temperature but not density.

Context. Relativistic shocks are present in all high-energy astrophysical processes involving relativistic plasma outflows interacting with their ambient medium. While they are well understood in the context of relativistic hydrodynamics and ideal magnetohydrodynamics (MHD), there is a limited understanding of the properties related to their propagation in media characterized by finite electrical conductivity. Aims: This work presents a systematic method for the derivation and solution of the jump conditions for relativistic shocks propagating in MHD media with finite electrical conductivity. This method is applied to the numerical solution of the Riemann problem and the determination of the conditions inside the blastwave that is formed when ultrarelativistic magnetized ejecta interact with the circumburst medium during a gamma-ray burst. Methods: We derived the covariant relations expressing the jump conditions in a frame-independent manner. The resulting algebraic equations expressing the Rankine-Hugoniot conditions in the propagation medium's frame were then solved numerically. A variable adiabatic index equation of state was used in order to obtain a realistic description of the post-shock fluid's thermodynamics. This method was then employed for the solution of the Riemann problem for the case of a forward and a reverse shock, both of which form during the interaction of a gamma-ray burst ejecta with the circumburst medium. This allowed us to determine the kinematics of the resulting blastwave and the dynamical conditions in its interior. Results: Our solutions clearly depict the impact of the plasma's electrical conductivity in the properties of the post-shock medium. Two characteristic regimes are identified with respect to the value of a dimensionless parameter that has a linear dependence on the conductivity. For small values of this parameter, the shock affects only the hydrodynamic properties of the propagation medium and leaves its electromagnetic field unaffected. No current layer forms in the shock front; thus, we refer to this as the current-free regime. For large values of this parameter, the ideal MHD regime has been retrieved. We also show that the assumption of a finite electrical conductivity can lead to higher efficiencies in the conversion of the ejecta energy into thermal energy of the blastwave through the reverse shock. The theory developed in this work can be applied to the construction of Riemann solvers for resistive relativistic MHD (RR4MHD).

Aims: We study the stability properties of relativistic magnetized astrophysical jets in the linear regime. We consider cylindrical cold jet configurations with constant Lorentz factor and constant density profiles across the jet. We are interested in probing the properties of the instabilities and identifying the physical quantities that affect the stability profile of the outflows. Methods: We conducted a linear stability analysis on the unperturbed outflow configurations we are interested in. We focus on the unstable branches, which can disrupt the initial outflow. We proceeded with a parametric study regarding the Lorentz factor, the ratio of the rest mass density of the jet to that of the environment, the magnetization, and the ratio of the poloidal component of the magnetic field to its toroidal counterpart measured on the boundary of the jet. We also consider two choices for the pressure of the environment, either thermal or magnetic, and check if this choice affects the results. Additionally, we applied a WKBJ method at the radius of the jet in order to study the local stability properties. Finally, we adapted the jet configuration in Cartesian geometry and compared the planar flow results with the results of the cylindrical counterpart. Results: While investigating the stability properties of the configurations, we observed the existence of a specific solution branch, which showcases the growth timescale of the instability comparable to the light crossing time of the jet radius. Our analysis focuses on this solution. All of the quantities considered for the parametric study affect the behavior of the mode while the magnetized environments seem to hinder its development compared to the hydrodynamic equivalent. Also, our analysis of the eigenfunctions of the system alongside the WKBJ results show that the mode develops in a very narrow layer near the boundary of the jet, establishing the notion of locality for the specific solution. The results indicate that the mode is a relativistic generalization of the Kelvin-Helmholtz instability. We compare this mode with the corresponding solution in Cartesian geometry and define the prerequisites for the Cartesian Kelvin-Helmholtz to successfully approximate the cylindrical counterpart. Conclusions: We identify the Kelvin-Helmholtz instability for a cold nonrotating relativistic jet carrying a helical magnetic field. Our parametric study reveals the important physical quantities that affect the stability profile of the outflow and their respective value ranges for which the instability is active. The Kelvin-Helmholtz mode and its stability properties are characterized by the locality of the solutions, the value of the angle between the magnetic field and the wavevector, the linear dependence between the mode's growth rate and the wavevector, and finally the stabilization of the mode for flows that are ultrafast magnetosonic. The cylindrical mode can be approximated successfully by the Cartesian Kelvin-Helmholtz instability whenever certain length scales are much larger than the jet radius.

Physics-informed neural networks (PINNs) are machine learning models that integrate data-based learning with partial differential equations (PDEs). In this work, for the first time we extend PINNs to model the numerically challenging case of astrophysical shock waves in the presence of a stellar gravitational field. Notably, PINNs suffer from competing losses during gradient descent that can lead to poor performance especially in physical setups involving multiple scales, which is the case for shocks in the gravitationally stratified solar atmosphere. We applied PINNs in three different setups ranging from modeling astrophysical shocks in cases with no or little data to data-intensive cases. Namely, we used PINNs (a) to determine the effective polytropic index controlling the heating mechanism of the space plasma within 1% error, (b) to quantitatively show that data assimilation is seamless in PINNs and small amounts of data can significantly increase the model's accuracy, and (c) to solve the forward time-dependent problem for different temporal horizons. We addressed the poor performance of PINNs through an effective normalization approach by reformulating the fluid dynamics PDE system to absorb the gravity-caused variability. This led to a huge improvement in the overall model performance with the density accuracy improving between 2 and 16 times. Finally, we present a detailed critique on the strengths and drawbacks of PINNs in tackling realistic physical problems in astrophysics and conclude that PINNs can be a powerful complimentary modeling approach to classical fluid dynamics solvers.

The stability of astrophysical jets in the linear regime is investigated by presenting a methodology to find the growth rates of the various instabilities. We perturb a cylindrical axisymmetric steady jet, linearize the relativistic ideal magnetohydrodynamic (MHD) equations, and analyze the evolution of the eigenmodes of the perturbation by deriving the differential equations that need to be integrated, subject to the appropriate boundary conditions, in order to find the dispersion relation. We also apply the WKBJ approximation and, additionally, give analytical solutions in some subcases corresponding to unperturbed jets with constant bulk velocity along the symmetry axis.

A number of observations of astrophysical jets, at different scales, have shown that jets are often non-uniform outflows in their cross-section. Their structure is believed to play an important role in their overall stability. In this work, we combine analytical methods and numerical simulations to investigate the stability of non-uniform jets originating from active galactic nuclei. We adopt a standard 'spine and sheath' model, using a fast, light inner spine and a heavier, slower outer sheath. In the first part of this work, we conduct a linear stability analysis, finding the time-scales for the growth of the instabilities and the corresponding eigenfunctions. We focus on the nature of the physical processes that dominate and drive the destabilization of configurations. In the second part, we examine the evolution of the perturbed jets through relativistic 3D numerical simulations using the PLUTO code. Starting with the eigenfunctions found in the first part as initial conditions, we derive instability growth times and evolution which are in good agreement with the linear analysis.

Recent observations of supermassive black holes have brought us new information on their magnetospheres. In this study, we attempt a theoretical modelling of the coupling of black holes with their jets and discs, via three innovations. First, we propose a semi-analytical MHD description of a steady relativistic inflow-outflow structure characteristic to the extraction of the hole rotational energy. The mass-loading is ensured in a thin layer, the stagnation surface, by a two-photon pair production originating to a gamma-ray emission from the surrounding disc. The double flow is described near the polar axis by an axisymmetric meridionally self-similar MHD model. Secondly, the inflow and outflow solutions are crossing the MHD critical points and are matched at the stagnation surface. Knowledge of the MHD field on the horizon gives us the angular momentum and energy extracted from the black hole. Finally, we illustrate the model with three specific examples of double-flow solutions by varying the energetic interaction between the MHD field and the rotating black hole. When the isorotation frequency is half of the black hole one, the extracted Poynting flux is comparable to the one obtained using the force-free assumption. In two of the presented solutions, the Penrose process dominates at large colatitudes, while the third is Poynting flux dominated at mid-colatitudes. Mass injection rate estimations, from disc luminosity and inner radius, give an upper limit just above the values obtained for two solutions. This model is pertinent to describe the flows near the polar axis, where pair production is more efficient.

The dynamics of plasmas produced by low current X-pinch devices are explored. This comprehensive computational study is the first step in the preparation of an experimental campaign aiming to understand the formation of plasma jets in table-top pulsed power X-pinch devices. Two state-of-the-art magneto-hydro-dynamic codes, GORGON and PLUTO, are used to simulate the evolution of the plasma and describe its key dynamic features. GORGON and PLUTO are built on different approximation schemes and the simulation results obtained are discussed and analyzed in relation to the physics adopted by each code. Both codes manage to accurately handle the numerical demands of the X-pinch plasma evolution and provide precise details on the mechanisms of the plasma expansion, the jet-formation, and the pinch generation. Furthermore, the influence of electrical resistivity, radiation transport and optically thin losses on the dynamic behaviour of the simulated X-pinch produced plasma is studied in PLUTO. Our findings highlight the capabilities of the GORGON and PLUTO codes in simulating the wide range of plasma conditions found in X-pinch experiments, enabling a direct comparison to the scheduled experiments.

Cepheids are pulsating variable stars with a periodic chromospheric response at UV wavelengths close to their minimum radius phase. Recently, an X-ray variable signature was captured in observations during the maximum radius phase. This X-ray emission came as a surprise and is not understood. In this work, we use the modern astrophysical code PLUTO to investigate the effects of pulsations on Cepheid X-ray emission. We run a number of hydrodynamic numerical simulations with a variety of initial and boundary conditions in order to explore the capability of shocks to produce the observed phase-dependent X-ray behavior. Finally, we use the Simulated Observations of X-ray Sources (SOXS) package to create synthetic spectra for each simulation case and link our simulations to observables. We show that, for certain conditions, we can reproduce observed X-ray fluxes at phases 0.4-0.8 when the Cepheid is at maximum radius. Our results span a wide range of mass-loss rates, 2 × 10-13 M⊙ yr-1 to 3 × 10-8 M⊙ yr-1, and peak X-ray luminosities, 5 × 10-17 erg cm-2 s-1 to 1.4 × 10-12 erg cm-2 s-1. We conclude that Cepheids exhibit two-component emission with (a) shock waves being responsible for the phase-dependent variable emission (phases 0.2-0.6) and (b) a separate quiescent mechanism being the dominant emission mechanism for the remaining phases.

The computational study of x-pinch plasmas driven by pulsed power generators demands the development of advanced numerical models and simulation schemes, able to enlighten the experiments. The capabilities of PLUTO code are here extended to enable the investigation of low current produced x-pinch plasmas. The numerical modules of the code used and modified are presented and discussed. The simulations results are compared to experiments, carried out on a table-top pulsed power plasma generator implemented in a mode of producing a peak current of ∼45 kA with a rise time (10%-90%) of 50 ns, loaded with Tungsten wires. The structural evolution of plasma density is studied and its influence on the magnetic field is analyzed with the help of the new simulation data. The simulated areal mass density is compared with the experimentally measured dense opaque region to enlighten the dense plasma evolution. In addition, the measured areal electron density is compared to the simulation results. Moreover, the new simulation data offer valuable insights to the main jet formation mechanisms, which are further analyzed and discussed in relation to the influence of the J× B force and the momentum.

The computational study of x-pinch plasmas driven by pulsed power generators demands the development of advanced numerical models and simulation schemes, able to enlighten the experiments. The capabilities of PLUTO code are here extended to enable the investigation of low current produced x-pinch plasmas. The numerical modules of the code used and modified are presented and discussed. The simulations results are compared to experiments, carried out on a table-top pulsed power plasma generator implemented in a mode of producing a peak current of ∼45 kA with a rise time (10%-90%) of 50 ns, loaded with Tungsten wires. The structural evolution of plasma density is studied and its influence on the magnetic field is analyzed with the help of the new simulation data. The simulated areal mass density is compared with the experimentally measured dense opaque region to enlighten the dense plasma evolution. In addition, the measured areal electron density is compared to the simulation results. Moreover, the new simulation data offer valuable insights to the main jet formation mechanisms, which are further analyzed and discussed in relation to the influence of the J× B force and the momentum.

Cepheids are pulsating variable stars with a periodic chromospheric response at UV wavelengths close to their minimum radius phase. Recently, an X-ray variable signature was captured in observations during the maximum radius phase. This X-ray emission came as a surprise and is not understood. In this work, we use the modern astrophysical code PLUTO to investigate the effects of pulsations on Cepheid X-ray emission. We run a number of hydrodynamic numerical simulations with a variety of initial and boundary conditions in order to explore the capability of shocks to produce the observed phase-dependent X-ray behavior. Finally, we use the Simulated Observations of X-ray Sources (SOXS) package to create synthetic spectra for each simulation case and link our simulations to observables. We show that, for certain conditions, we can reproduce observed X-ray fluxes at phases 0.4-0.8 when the Cepheid is at maximum radius. Our results span a wide range of mass-loss rates, 2 × 10-13 M☉ yr-1 to 3 × 10-8 M☉ yr-1, and peak X-ray luminosities, 5 × 10-17 erg cm-2 s-1 to 1.4 × 10-12 erg cm-2 s-1. We conclude that Cepheids exhibit two-component emission with (a) shock waves being responsible for the phase-dependent variable emission (phases 0.2-0.6) and (b) a separate quiescent mechanism being the dominant emission mechanism for the remaining phases.

Context. High-resolution radio imaging of active galactic nuclei (AGN) has revealed that the jets of some sources present superluminal knots and transverse stratification. Recent observational projects, such as ALMA and γ-ray telescopes, such as HESS and HESS2 have provided new observational constraints on the central regions of rotating black holes in AGN, suggesting that there is an inner- or spine-jet surrounded by a disk wind. This relativistic spine-jet is likely to be composed of electron-positron pairs extracting energy from the black hole and will be explored by the future γ-ray telescope CTA. Aims: In this article we present an extension to and generalization of relativistic jets in Kerr metric of the Newtonian meridional self-similar mechanism. We aim at modeling the inner spine-jet of AGN as a relativistic light outflow emerging from a spherical corona surrounding a Kerr black hole and its inner accretion disk. Methods: The model is built by expanding the metric and the forces with colatitude to first order in the magnetic flux function. As a result of the expansion, all colatitudinal variations of the physical quantities are quantified by a unique parameter. Unlike previous models, effects of the light cylinder are not neglected. Results: Solutions with high Lorentz factors are obtained and provide spine-jet models up to the polar axis. As in previous publications, we calculate the magnetic collimation efficiency parameter, which measures the variation of the available energy across the field lines. This collimation efficiency is an integral part of the model, generalizing the classical magnetic rotator efficiency criterion to Kerr metric. We study the variation of the magnetic efficiency and acceleration with the spin of the black hole and show their high sensitivity to this integral. Conclusions: These new solutions model collimated or radial, relativistic or ultra-relativistic outflows in AGN or γ-ray bursts. In particular, we discuss the relevance of our solutions to modeling the M 87 spine-jet. We study the efficiency of the central black hole spin to collimate a spine-jet and show that the jet power is of the same order as that determined by numerical simulations.

We present a detailed study of the properties of the molecular gas in the fast outflow driven by the active galactic nucleus (AGN) in the nearby radio-loud Seyfert galaxy IC 5063. By using ALMA observations of a number of tracers of the molecular gas (12CO(1-0), 12CO(2-1), 12CO(3-2), 13CO(2-1) and HCO+(4-3)), we map the differences in excitation, density and temperature of the gas as function of position and kinematics. The results show that in the immediate vicinity of the radio jet, a fast outflow, with velocities up to 800 km s-1, is occurring of which the gas has high excitation with excitation temperatures in the range 30-55 K, demonstrating the direct impact of the jet on the ISM. The relative brightness of the 12CO lines, as well as that of 13CO(2-1) vs. 12CO(2-1), show that the outflow is optically thin. We estimate the mass of the molecular outflow to be at least 1.2 × 106 M⊙ and likely to be a factor between two and three larger than this value. This is similar to that of the outflow of atomic gas, but much larger than that of the ionised outflow, showing that the outflow in IC 5063 is dominated by cold gas. The total mass outflow rate we estimated to be 12 M⊙ yr-1. The mass of the outflow is much smaller than the total gas mass of the ISM of IC 5063. Therefore, although the influence of the AGN and its radio jet is very significant in the inner regions of IC 5063, globally speaking the impact will be very modest. We used RADEX non-LTE modelling to explore the physical conditions of the molecular gas in the outflow. Models with the outflowing gas being quite clumpy give the most consistent results and our preferred solutions have kinetic temperatures in the range 20-100 K and densities between 105 and 106 cm-3. The resulting pressures are 106-107.5 K cm-3, about two orders of magnitude higher than in the outer quiescent disk. The highest densities and temperatures are found in the regions with the fastest outflow. The results strongly suggest that the outflow in IC 5063 is driven by the radio plasma jet expanding into a clumpy gaseous medium and creating a cocoon of (shocked) gas which is pushed away from the jet axis resulting in a lateral outflow, very similar to what is predicted by numerical simulations.

We present a detailed study of the properties of the molecular gas in the fast outflow driven by the active galactic nucleus (AGN) in the nearby radio-loud Seyfert galaxy IC 5063. By using ALMA observations of a number of tracers of the molecular gas (12CO(1-0), 12CO(2-1), 12CO(3-2), 13CO(2-1) and HCO+(4-3)), we map the differences in excitation, density and temperature of the gas as function of position and kinematics. The results show that in the immediate vicinity of the radio jet, a fast outflow, with velocities up to 800 km s-1, is occurring of which the gas has high excitation with excitation temperatures in the range 30-55 K, demonstrating the direct impact of the jet on the ISM. The relative brightness of the 12CO lines, as well as that of 13CO(2-1) vs. 12CO(2-1), show that the outflow is optically thin. We estimate the mass of the molecular outflow to be at least 1.2 × 106 M☉ and likely to be a factor between two and three larger than this value. This is similar to that of the outflow of atomic gas, but much larger than that of the ionised outflow, showing that the outflow in IC 5063 is dominated by cold gas. The total mass outflow rate we estimated to be 12 M☉ yr-1. The mass of the outflow is much smaller than the total gas mass of the ISM of IC 5063. Therefore, although the influence of the AGN and its radio jet is very significant in the inner regions of IC 5063, globally speaking the impact will be very modest. We used RADEX non-LTE modelling to explore the physical conditions of the molecular gas in the outflow. Models with the outflowing gas being quite clumpy give the most consistent results and our preferred solutions have kinetic temperatures in the range 20-100 K and densities between 105 and 106 cm-3. The resulting pressures are 106-107.5 K cm-3, about two orders of magnitude higher than in the outer quiescent disk. The highest densities and temperatures are found in the regions with the fastest outflow. The results strongly suggest that the outflow in IC 5063 is driven by the radio plasma jet expanding into a clumpy gaseous medium and creating a cocoon of (shocked) gas which is pushed away from the jet axis resulting in a lateral outflow, very similar to what is predicted by numerical simulations.

Using CO (4-3) and (2-1) Atacama Large Millimeter Array (ALMA) data, we prove that the molecular gas in the jet-driven winds of the galaxy IC 5063 is more highly excited than the rest of the molecular gas in the disk of the same galaxy. On average, the CO(4 - 3) /CO(2 - 1) flux ratio is 1 for the disk and 5 for the jet accelerated or impacted gas. Spatially-resolved maps reveal that in regions associated with winds, the CO(4 - 3) /CO(2 - 1) flux ratio significantly exceeds the upper limit of 4 for optically thick gas. It frequently takes values between 5 and 11, and it occasionally further approaches the upper limit of 16 for optically thin gas. Excitation temperatures of 30-100 K are common for the molecules in these regions. If all of the outflowing molecular gas is optically thin, at 30-50 K, then its mass is 2 × 106 M⊙. This lower mass limit is an order of magnitude below the mass derived from the CO(2 - 1) flux in the case of optically thick gas. Molecular winds can thus be less massive, but more easily detectable at high z than they were previously thought to be.

Using CO (4-3) and (2-1) Atacama Large Millimeter Array (ALMA) data, we prove that the molecular gas in the jet-driven winds of the galaxy IC 5063 is more highly excited than the rest of the molecular gas in the disk of the same galaxy. On average, the CO(4 - 3) /CO(2 - 1) flux ratio is 1 for the disk and 5 for the jet accelerated or impacted gas. Spatially-resolved maps reveal that in regions associated with winds, the CO(4 - 3) /CO(2 - 1) flux ratio significantly exceeds the upper limit of 4 for optically thick gas. It frequently takes values between 5 and 11, and it occasionally further approaches the upper limit of 16 for optically thin gas. Excitation temperatures of 30-100 K are common for the molecules in these regions. If all of the outflowing molecular gas is optically thin, at 30-50 K, then its mass is 2 × 106 M☉. This lower mass limit is an order of magnitude below the mass derived from the CO(2 - 1) flux in the case of optically thick gas. Molecular winds can thus be less massive, but more easily detectable at high z than they were previously thought to be.

List of contributions from the Cherenkov Telescope Array (CTA) Consortium presented at the 6th International Symposium on High-Energy Gamma-Ray Astronomy (Gamma 2016), July 11-15, 2016, in Heidelberg, Germany.

We analyzed near-infrared data of the nearby galaxy IC5063 taken with the Very Large Telescope SINFONI instrument. IC5063 is an elliptical galaxy that has a radio jet nearly aligned with the major axis of a gas disk in its center. The data reveal multiple signatures of molecular and atomic gas that has been kinematically distorted by the passage of the jet plasma or cocoon within an area of ∼1 kpc2. Concrete evidence that the interaction of the jet with the gas causes the gas to accelerate comes from the detection of outflows in four different regions along the jet trail: near the two radio lobes, between the radio emission tip and the optical narrow-line-region cone, and at a region with diffuse 17.8 GHz emission midway between the nucleus and the north radio lobe. The outflow in the latter region is biconical, centered 240 pc away from the nucleus, and oriented perpendicularly to the jet trail. The diffuse emission that is observed as a result of the gas entrainment or scattering unfolds around the trail and away from the nucleus with increasing velocity. It overall extends for ≳700 pc parallel and perpendicular to the trail. Near the outflow starting points, the gas has a velocity excess of 600-1200 km s-1 with respect to ordered motions, as seen in [Fe ii], {Pa}α , or {{{H}}}2 lines. High {{{H}}}2 (1-0) S(3)/S(1) flux ratios indicate non-thermal excitation of gas in the diffuse outflow.

Relativistic jets in active galactic nuclei (AGN) are among the most powerful astrophysical objects discovered to date. Indeed, jetted AGN studies have been considered a prominent science case for SKA, and were included in several different chapters of the previous SKA Science Book (Carilli & Rawlings 2004). Most of the fundamental questions about the physics of relativistic jets still remain unanswered, and await high-sensitivity radio instruments such as SKA to solve them. These questions will be addressed specially through analysis of the massive data sets arising from the deep, all-sky surveys (both total and polarimetric flux) from SKA1. Wide-field very-long-baseline-interferometric survey observations involving SKA1 will serve as a unique tool for distinguishing between extragalactic relativistic jets and star forming galaxies via brightness temperature measurements. Subsequent SKA1 studies of relativistic jets at different resolutions will allow for unprecedented cosmological studies of AGN jets up to the epoch of re-ionization, enabling detailed characterization of the jet composition, magnetic field, particle populations, and plasma properties on all scales. SKA will enable us to study the dependence of jet power and star formation on other properties of the AGN system. SKA1 will enable such studies for large samples of jets, while VLBI observations involving SKA1 will provide the sensitivity for pc-scale imaging, and SKA2 (with its extraordinary sensitivity and dynamic range) will allow us for the first time to resolve and model the weakest radio structures in the most powerful radio-loud AGN.

Relativistic jets can be modeled as magnetohydrodynamic flows. We analyze the related equations and discuss the involved acceleration mechanisms, their relation to the collimation, to the jet confinement by its environment, and to possible rarefaction waves triggered by pressure imbalances.

Relativistic jets in active galactic nuclei (AGN) are among the most powerful astrophysical objects discovered to date. Indeed, jetted AGN studies have been considered a prominent science case for SKA, and were included in several different chapters of the previous SKA Science Book (Carilli & Rawlings 2004). Most of the fundamental questions about the physics of relativistic jets still remain unanswered, and await high-sensitivity radio instruments such as SKA to solve them. These questions will be addressed specially through analysis of the massive data sets arising from the deep, all-sky surveys (both total and polarimetric flux) from SKA1. Wide-field very-long-baseline-interferometric survey observations involving SKA1 will serve as a unique tool for distinguishing between extragalactic relativistic jets and star forming galaxies via brightness temperature measurements. Subsequent SKA1 studies of relativistic jets at different resolutions will allow for unprecedented cosmological studies of AGN jets up to the epoch of re-ionization, enabling detailed characterization of the jet composition, magnetic field, particle populations, and plasma properties on all scales. SKA will enable us to study the dependence of jet power and star formation on other properties of the AGN system. SKA1 will enable such studies for large samples of jets, while VLBI observations involving SKA1 will provide the sensitivity for pc-scale imaging, and SKA2 (with its extraordinary sensitivity and dynamic range) will allow us for the first time to resolve and model the weakest radio structures in the most powerful radio-loud AGN.

Relativistic jets can be modeled as magnetohydrodynamic flows. We analyze the related equations and discuss the involved acceleration mechanisms, their relation to the collimation, to the jet confinement by its environment, and to possible rarefaction waves triggered by pressure imbalances.

We analyzed near-infrared data of the nearby galaxy IC5063 taken with the Very Large Telescope SINFONI instrument. IC5063 is an elliptical galaxy that has a radio jet nearly aligned with the major axis of a gas disk in its center. The data reveal multiple signatures of molecular and atomic gas that has been kinematically distorted by the passage of the jet plasma or cocoon within an area of ∼1 kpc2. Concrete evidence that the interaction of the jet with the gas causes the gas to accelerate comes from the detection of outflows in four different regions along the jet trail: near the two radio lobes, between the radio emission tip and the optical narrow-line-region cone, and at a region with diffuse 17.8 GHz emission midway between the nucleus and the north radio lobe. The outflow in the latter region is biconical, centered 240 pc away from the nucleus, and oriented perpendicularly to the jet trail. The diffuse emission that is observed as a result of the gas entrainment or scattering unfolds around the trail and away from the nucleus with increasing velocity. It overall extends for ≳700 pc parallel and perpendicular to the trail. Near the outflow starting points, the gas has a velocity excess of 600-1200 km s-1 with respect to ordered motions, as seen in [Fe ii], {Pa}α , or {{{H}}}2 lines. High {{{H}}}2 (1-0) S(3)/S(1) flux ratios indicate non-thermal excitation of gas in the diffuse outflow.

List of contributions from the CTA Consortium presented at the 34th International Cosmic Ray Conference, 30 July - 6 August 2015, The Hague, The Netherlands.

Disc winds originating from the inner parts of accretion discs are considered as the basic component of magnetically collimated outflows. The only available analytical magnetohydrodynamic (MHD) solutions to describe disc-driven jets are those characterized by the symmetry of radial self-similarity. However, radially self-similar MHD jet models, in general, have three geometrical shortcomings: (i) a singularity at the jet axis, (ii) the necessary assumption of axisymmetry and (iii) the non-existence of an intrinsic radial scale, i.e. the jets formally extend to radial infinity. Hence, numerical simulations are necessary to extend the analytical solutions towards the axis, by solving the full three-dimensional equations of MHD and impose a termination radius at finite radial distance. We focus here on studying the effects of relaxing the (ii) assumption of axisymmetry, i.e. of performing full 3D numerical simulations of a disc wind crossing all MHD critical surfaces. We compare the results of these runs with previous axisymmetric 2.5D simulations. The structure of the flow in all simulations shows strong similarities. The 3D runs reach a steady state and stay close to axisymmetry for most of the physical quantities, except for the poloidal magnetic field and the toroidal velocity which slightly deviate from axisymmetry. The latter quantities show signs of instabilities, which, however, are confined to the region inside the fast magnetosonic separatrix surface. The forces present in the flow, both of collimating and accelerating nature, are in good agreement in both the 2.5D and the 3D runs. We conclude that the analytical solution behaves well also after relaxing the basic assumption of axisymmetry.

Context. Astronomical observations, analytical solutions, and numerical simulations have provided the building blocks to formulate the current theory of young stellar object jets. Although each approach has made great progress independently, it is only during the past decade that significant efforts have been made to bring the separate pieces together. Aims: Building on previous work that combined analytical solutions and numerical simulations, we apply a sophisticated cooling function to incorporate optically thin energy losses in the dynamics. On one hand, this allows a self-consistent treatment of the jet evolution, and on the other hand, it provides the necessary data to generate synthetic emission maps. Methods: Firstly, analytical disk and stellar outflow solutions are properly combined to initialize numerical two-component jet models inside the computational box. Secondly, magneto-hydrodynamical simulations are performed in 2.5D, correctly following the ionization and recombination of a maximum of 29 ions. Finally, the outputs are post-processed to produce artificial observational data. Results: The values for the density, temperature, and velocity that the simulations provide along the axis are within the typical range of protostellar outflows. Moreover, the synthetic emission maps of the doublets [O i], [N ii], and [S ii] outline a well-collimated and knot-structured jet, which is surrounded by a less dense and slower wind that is not observable in these lines. The jet is found to have a small opening angle and a radius that is also comparable to observations. Conclusions: The first two-component jet simulations, based on analytical models, that include ionization and optically thin radiation losses demonstrate promising results for modeling specific young stellar object outflows. The generation of synthetic emission maps provides the link to observations, as well as the necessary feedback for further improvement of the available models.

We investigate the differences between an outflow in a highly resistive accretion disc corona, and the results with smaller or vanishing resistivity. For the first time, we determine conditions at the base of a two-dimensional radially self-similar outflow in the regime of very large resistivity. We performed simulations using the PLUTO magnetohydrodynamics (MHD) code, and found three modes of solutions. The first mode, with small resistivity, is similar to the ideal-MHD solutions. In the second mode, with larger resistivity, the geometry of the magnetic field changes, with a `bulge' above the superfast critical surface. At even larger resistivities, the third mode of solutions sets in, in which the magnetic field is no longer collimated, but is pressed towards the disc. This third mode is also the final one: it does not change with further increase of resistivity. These modes describe topological change in a magnetic field above the accretion disc because of the uniform, constant Ohmic resistivity.

We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.

Young stellar object observations suggest that some jets rotate in the opposite direction with respect to their disk. In a recent study, Sauty et al. showed that this does not contradict the magnetocentrifugal mechanism that is believed to launch such outflows. Motion signatures that are transverse to the jet axis, in two opposite directions, have recently been measured in M87. One possible interpretation of this motion is that of counter-rotating knots. Here, we extend our previous analytical derivation of counter-rotation to relativistic jets, demonstrating that counter-rotation can indeed take place under rather general conditions. We show that both the magnetic field and a non-negligible enthalpy are necessary at the origin of counter-rotating outflows, and that the effect is associated with a transfer of energy flux from the matter to the electromagnetic field. This can be realized in three cases: if a decreasing enthalpy causes an increase of the Poynting flux, if the flow decelerates, or if strong gradients of the magnetic field are present. An illustration of the involved mechanism is given by an example of a relativistic magnetohydrodynamic jet simulation.

We investigate the differences between an outflow in a highly resistive accretion disc corona, and the results with smaller or vanishing resistivity. For the first time, we determine conditions at the base of a two-dimensional radially self-similar outflow in the regime of very large resistivity. We performed simulations using the PLUTO magnetohydrodynamics (MHD) code, and found three modes of solutions. The first mode, with small resistivity, is similar to the ideal-MHD solutions. In the second mode, with larger resistivity, the geometry of the magnetic field changes, with a `bulge' above the superfast critical surface. At even larger resistivities, the third mode of solutions sets in, in which the magnetic field is no longer collimated, but is pressed towards the disc. This third mode is also the final one: it does not change with further increase of resistivity. These modes describe topological change in a magnetic field above the accretion disc because of the uniform, constant Ohmic resistivity.

We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.

Young stellar object observations suggest that some jets rotate in the opposite direction with respect to their disk. In a recent study, Sauty et al. showed that this does not contradict the magnetocentrifugal mechanism that is believed to launch such outflows. Motion signatures that are transverse to the jet axis, in two opposite directions, have recently been measured in M87. One possible interpretation of this motion is that of counter-rotating knots. Here, we extend our previous analytical derivation of counter-rotation to relativistic jets, demonstrating that counter-rotation can indeed take place under rather general conditions. We show that both the magnetic field and a non-negligible enthalpy are necessary at the origin of counter-rotating outflows, and that the effect is associated with a transfer of energy flux from the matter to the electromagnetic field. This can be realized in three cases: if a decreasing enthalpy causes an increase of the Poynting flux, if the flow decelerates, or if strong gradients of the magnetic field are present. An illustration of the involved mechanism is given by an example of a relativistic magnetohydrodynamic jet simulation.

Disc winds originating from the inner parts of accretion discs are considered as the basic component of magnetically collimated outflows. The only available analytical magnetohydrodynamic (MHD) solutions to describe disc-driven jets are those characterized by the symmetry of radial self-similarity. However, radially self-similar MHD jet models, in general, have three geometrical shortcomings: (i) a singularity at the jet axis, (ii) the necessary assumption of axisymmetry and (iii) the non-existence of an intrinsic radial scale, i.e. the jets formally extend to radial infinity. Hence, numerical simulations are necessary to extend the analytical solutions towards the axis, by solving the full three-dimensional equations of MHD and impose a termination radius at finite radial distance. We focus here on studying the effects of relaxing the (ii) assumption of axisymmetry, i.e. of performing full 3D numerical simulations of a disc wind crossing all MHD critical surfaces. We compare the results of these runs with previous axisymmetric 2.5D simulations. The structure of the flow in all simulations shows strong similarities. The 3D runs reach a steady state and stay close to axisymmetry for most of the physical quantities, except for the poloidal magnetic field and the toroidal velocity which slightly deviate from axisymmetry. The latter quantities show signs of instabilities, which, however, are confined to the region inside the fast magnetosonic separatrix surface. The forces present in the flow, both of collimating and accelerating nature, are in good agreement in both the 2.5D and the 3D runs. We conclude that the analytical solution behaves well also after relaxing the basic assumption of axisymmetry.

We study the bulk acceleration in relativistic axisymmetric magnetized outflows, by solving the momentum equation along the flow, the so-called wind equation. The solutions for the bulk Lorentz factor depend on the geometry of the field/streamlines through the "bunching function" S. We investigate the general characteristics of the S function and how its choice affects the acceleration. In our study, various fast rise and slow decay examples are selected for S, with a global maximum near the fast magnetosonic critical point, as required from the regularity condition. For each case we determine the terminal Lorentz factor γ∞ and the acceleration efficiency γ∞/μ, where μ is the total energy-to-mass flux ratio (which equals the maximum possible Lorentz factor of the outflow). With proper choices of S we can achieve efficiencies greater than 50%. Last, we examine the shape of the field/streamlines with respect to the choice of the S function. The results of this work, depending on the choices of μ, can be applied to relativistic GRB or AGN jets.

Context. Astronomical observations, analytical solutions, and numerical simulations have provided the building blocks to formulate the current theory of young stellar object jets. Although each approach has made great progress independently, it is only during the past decade that significant efforts have been made to bring the separate pieces together. Aims: Building on previous work that combined analytical solutions and numerical simulations, we apply a sophisticated cooling function to incorporate optically thin energy losses in the dynamics. On one hand, this allows a self-consistent treatment of the jet evolution, and on the other hand, it provides the necessary data to generate synthetic emission maps. Methods: Firstly, analytical disk and stellar outflow solutions are properly combined to initialize numerical two-component jet models inside the computational box. Secondly, magneto-hydrodynamical simulations are performed in 2.5D, correctly following the ionization and recombination of a maximum of 29 ions. Finally, the outputs are post-processed to produce artificial observational data. Results: The values for the density, temperature, and velocity that the simulations provide along the axis are within the typical range of protostellar outflows. Moreover, the synthetic emission maps of the doublets [O i], [N ii], and [S ii] outline a well-collimated and knot-structured jet, which is surrounded by a less dense and slower wind that is not observable in these lines. The jet is found to have a small opening angle and a radius that is also comparable to observations. Conclusions: The first two-component jet simulations, based on analytical models, that include ionization and optically thin radiation losses demonstrate promising results for modeling specific young stellar object outflows. The generation of synthetic emission maps provides the link to observations, as well as the necessary feedback for further improvement of the available models.

Relativistic jets associated with long/soft gamma-ray bursts are formed and initially propagate in the interior of the progenitor star. Because of the subsequent loss of their external pressure support after they cross the stellar surface, these flows can be modelled as moving around a corner. A strong steady-state rarefaction wave is formed, and the sideways expansion is accompanied by a rarefaction acceleration. We investigate the efficiency and the general characteristics of this mechanism by integrating the steady-state, special relativistic, magnetohydrodynamic equations, using a special set of partial exact solutions in planar geometry (r self-similar with respect to the `corner'). We also derive analytical approximate scalings in the ultrarelativistic cold/magnetized, and hydrodynamic limits. The mechanism is more effective in magnetized than in purely hydrodynamic flows. It substantially increases the Lorentz factor without much affecting the opening of the jet; the resulting values of their product can be much greater than unity, allowing for possible breaks in the afterglow light curves. These findings are similar to the ones from numerical simulations of axisymmetric jets by Komissarov et al. and Tchekhovskoy et al., although in our approach we describe the rarefaction as a steady-state simple wave and self-consistently calculate the opening of the jet that corresponds to zero external pressure.

Young stellar object observations suggest that some jets rotate in the opposite direction with respect to their disk. In a recent study, we have shown that this can be well in agreement with the magnetocentrifugal mechanism that is believed to launch such outflows. Here, we extend this analytical derivation to relativistic jets demonstrating that under rather general conditions counterrotation can indeed take place. We also illustrate the involved mechanism by performing relativistic magnetohydrodynamic jet simulations.

We approach the problem of bulk acceleration in relativistic, cold, magnetized outflows, by solving the momentum equation along the flow, a.k.a. the wind equation, under the assumptions of steady-state and axisymmetry. The bulk Lorentz factor of the flow depends on the geometry of the field/streamlines and by extension, on the form of the "bunching function" S=r^2 B_p/ A, where r is the cylindrical distance, B_p the poloidal magnetic field, and A the magnetic flux function. We investigate the general characteristics of the S function and how its choice affects the terminal Lorentz factor gamma_f and the acceleration efficiency gamma_f/mu, where mu is the total energy to mass flux ratio (which equals the maximum possible Lorentz factor of the outflow). Various fast-rise, slow-decay examples are selected for S, each one with a corresponding field/streamlines geometry, with a global maximum near the fast magnetosonic critical point, as required from the regularity condition. As it is proved, proper choices of S can lead to efficiencies greater than 50%. Last, we apply our results to the momentum equation across the flow, in an effort to estimate their validity, as well as identifying the factors that lead to an accurate full-problem solution. The results of this work, depending on the choices of the flow integral mu, can be applied to relativistic GRB or AGN jets.

In the collapsar model of long GRBs the jet is formed at the center of the progenitor star, propagates in its interior, and produces the observed gamma rays much after its breakout from the star. The loss of pressure support during breakout induces a strong rarefaction wave that propagates inside the jet and causes its bulk acceleration. This mechanism has been already studied using axisymmetric magnetohydrodynamic (MHD) simulations assuming a prescribed shape for the surface between the jet and its environment, as well as using simple rarefaction waves in planar geometry. Trying to improve over these works, we solve the steady-state, axisymmetric, relativistic MHD equations using the method of characteristics. In this way the jet boundary is found self-consistently and the rarefaction wave is studied in the axisymmetric geometry. In this poster we present our first results and a comparison with previous works.

Compilation of CTA contributions to the proceedings of the 33rd International Cosmic Ray Conference (ICRC2013), which took place in 2-9 July, 2013, in Rio de Janeiro, Brazil

Analytical radially self-similar models are the best available solutions describing disk-winds, but they need several improvements. We introduce models of jets from truncated disks, i.e. numerical simulations based on a radially self-similar MHD solution but including the effects of a finite radius of the jet-emitting disk, hence the outflow. We compare these models with available observational data, by varying the jet density and velocity, the mass of the protostar, the radius of this truncation and the inclination. In order to our models with observed jet widths inferred from recent optical images taken with HST and ground-based AO observations, we create emission maps in different forbidden lines, and from such emission maps, determine the jet width as the full-width half-maximum of the emission. We can reproduce the jet widths of several examples and its variations very well. We conclude that truncation - i.e. taking the finite radius of the jet launching region into account - is needed to reproduce the observed jet widths, and our simulations limit the possible range of truncation radii. The effects of inclination are important for modeling the intrinsic variations seen in observed jet widths. Our models can be used to infer the inclinations in the observed sample independently.

The Cherenkov Telescope Array (CTA) is a new observatory for very high-energy (VHE) gamma rays. CTA has ambitions science goals, for which it is necessary to achieve full-sky coverage, to improve the sensitivity by about an order of magnitude, to span about four decades of energy, from a few tens of GeV to above 100 TeV with enhanced angular and energy resolutions over existing VHE gamma-ray observatories. An international collaboration has formed with more than 1000 members from 27 countries in Europe, Asia, Africa and North and South America. In 2010 the CTA Consortium completed a Design Study and started a three-year Preparatory Phase which leads to production readiness of CTA in 2014. In this paper we introduce the science goals and the concept of CTA, and provide an overview of the project.

Relativistic jets associated with long/soft gamma-ray bursts are formed and initially propagate in the interior of the progenitor star. Because of the subsequent loss of their external pressure support after they cross the stellar surface, these flows can be modelled as moving around a corner. A strong steady-state rarefaction wave is formed, and the sideways expansion is accompanied by a rarefaction acceleration. We investigate the efficiency and the general characteristics of this mechanism by integrating the steady-state, special relativistic, magnetohydrodynamic equations, using a special set of partial exact solutions in planar geometry (r self-similar with respect to the `corner'). We also derive analytical approximate scalings in the ultrarelativistic cold/magnetized, and hydrodynamic limits. The mechanism is more effective in magnetized than in purely hydrodynamic flows. It substantially increases the Lorentz factor without much affecting the opening of the jet; the resulting values of their product can be much greater than unity, allowing for possible breaks in the afterglow light curves. These findings are similar to the ones from numerical simulations of axisymmetric jets by Komissarov et al. and Tchekhovskoy et al., although in our approach we describe the rarefaction as a steady-state simple wave and self-consistently calculate the opening of the jet that corresponds to zero external pressure.

A plethora of analytical studies have addressed the physical mechanisms of jet launching and propagation in young stellar objects. However, their link to observations is still missing due to the complexity of the emission processes involved. In this work we address this issue, by presenting MHD simulations of two-component YSO jet models that are based on analytical disk and stellar outflow solutions. We include ionization and optically thin radiation losses during the temporal evolution of the flow and we post process the output files to generate synthetic emission maps. Our results are confronted to observational data and we find that our models predict the correct range of values for the density, temperature and velocity of YSO jets. Moreover, the synthetic emission maps of the - 39 - doublets [OI], [N II] and [S II] outline a well collimated and knot-structured jet, which is surrounded by a less dense and slower wind, not observable in these lines. The jet is found to have a small opening angle and a radius that is also comparable to observations.

Context. It is well established that some YSO jets (e.g. RW Aur) display different propagation speeds between their blue and red shifted parts, a feature possibly associated with the central engine or the environment in which the jet propagates. Aims: To understand the origin of asymmetric YSO jet velocities, we investigate the efficiency of two candidate mechanisms, one based on the intrinsic properties of the system and the other on the role of the external medium. In particular, a parallel or anti-parallel configuration between the protostellar magnetosphere and the disk magnetic field is considered, and the resulting dynamics examined both in an ideal and in a resistive magneto-hydrodynamical (MHD) regime. Moreover, we explore the effects of a potential difference in the pressure of the environment, as a consequence of the nonuniform density distribution of molecular clouds. Methods: Ideal and resistive axisymmetric numerical simulations were carried out for a variety of models, all of which are based on a combination of two analytical solutions, a disk wind and a stellar outflow. The initial two-component jet is modified by either inverting the orientation of its inner magnetic field or imposing a constant surrounding pressure. The velocity profiles are studied by assuming steady flows as well as after strong time variable ejection is incorporated. Results: Discrepancies between the speeds of the two outflows in opposite directions can indeed occur both due to unaligned magnetic fields and different outer pressures. In the former case, the asymmetry appears only on the dependence of the velocity on the cylindrical distance, but the implied observed value is significantly altered when the density distribution is also taken into account. On the other hand, a nonuniform medium collimates the two jets unevenly, directly affecting their propagation speed. A further interesting feature of the pressure-confined outflow simulations is the formation of static knots whose spacing seems to be associated with the ambient pressure. Conclusions: Jet velocity asymmetries are anticipated both when multipolar magnetic moments are present in the star-disk system and when nonuniform environments are considered. The latter is an external mechanism that can easily explain the large timescale of the phenomenon, whereas the former naturally relates it to the YSO intrinsic properties.

We investigate the characteristics of a relativistic magnetized fluid flowing around a corner. If the flow is faster than the fast-magnetosonic speed the non-smooth boundary induces a rarefaction wave propagating in the body of the flow. The subsequent expansion is accompanied with a very efficient increase of the flow speed and bulk Lorentz factor. We apply this "rarefaction acceleration mechanism" to the collapsar model of gamma-ray bursts, in which a relativistic jet initially propagates in the interior of the progenitor star, before crossing the stellar surface with a simultaneous drop in the external pressure support. We integrate the steady-state equations using a special set of partial (r-self similar) solutions. The use of these solutions degrades the system of the complex, non-linear, 2nd order partial differential equations into a system of two 1st order ordinary differential equations whose integration is straightforward. For the conditions expected in a gamma-ray burst, a fully analytical solution can be obtained. The aim of this work is to better understand the results of recent time-depended numerical simulations and show that rarefaction acceleration is a plausible mechanism in gamma-ray burst outflows.

Ground-based gamma-ray astronomy has had a major breakthrough with the impressive results obtained using systems of imaging atmospheric Cherenkov telescopes. Ground-based gamma-ray astronomy has a huge potential in astrophysics, particle physics and cosmology. CTA is an international initiative to build the next generation instrument, with a factor of 5-10 improvement in sensitivity in the 100 GeV-10 TeV range and the extension to energies well below 100 GeV and above 100 TeV. CTA will consist of two arrays (one in the north, one in the south) for full sky coverage and will be operated as open observatory. The design of CTA is based on currently available technology. This document reports on the status and presents the major design concepts of CTA.

Ground-based gamma-ray astronomy has had a major breakthrough with the impressive results obtained using systems of imaging atmospheric Cherenkov telescopes. Ground-based gamma-ray astronomy has a huge potential in astrophysics, particle physics and cosmology. CTA is an international initiative to build the next generation instrument, with a factor of 5-10 improvement in sensitivity in the 100 GeV-10 TeV range and the extension to energies well below 100 GeV and above 100 TeV. CTA will consist of two arrays (one in the north, one in the south) for full sky coverage and will be operated as open observatory. The design of CTA is based on currently available technology. This document reports on the status and presents the major design concepts of CTA.

We investigate conditions in a radially self-similar outflow in the regime of large resistivity. Using the PLUTO code, we performed simulations with proper choice of boundary conditions, relaxed at the footpoints of critical surfaces in the flow. We investigate outflow propagation in a high-resistive disk corona, and compare it to the results with small or vanishing resistivity.

When a magnetically dominated superfast-magnetosonic long/soft gamma-ray burst (GRB) jet leaves the progenitor star, the external pressure support will drop and the jet may enter the regime of ballistic expansion, during which additional magnetic acceleration becomes ineffective. However, recent numerical simulations by Tchekhovskoy et al. have suggested that the transition to this regime is accompanied by a spurt of acceleration. We confirm this finding numerically and attribute the acceleration to a sideways expansion of the jet, associated with a strong magnetosonic rarefaction wave that is driven into the jet when it loses pressure support, which induces a conversion of magnetic energy into kinetic energy of bulk motion. This mechanism, which we dub rarefaction acceleration, can only operate in a relativistic outflow because in this case the total energy can still be dominated by the magnetic component even in the superfast-magnetosonic regime. We analyse this process using the equations of relativistic magnetohydrodynamics and demonstrate that it is more efficient at converting internal energy into kinetic energy when the flow is magnetized than in a purely hydrodynamic outflow, as was found numerically by Mizuno et al. We show that, just as in the case of the magnetic acceleration of a collimating jet that is confined by an external pressure distribution - the collimation-acceleration mechanism - the rarefaction-acceleration process in a magnetized jet is a consequence of the fact that the separation between neighbouring magnetic flux surfaces increases faster than their cylindrical radius. However, whereas in the case of effective collimation-acceleration the product of the jet opening angle and its Lorentz factor does not exceed ~1, the addition of the rarefaction-acceleration mechanism makes it possible for this product to become >>1, in agreement with the inference from late-time panchromatic breaks in the afterglow light curves of long/soft GRBs.

We study semi-analytical time-dependent solutions of the relativistic MHD equations for the fields and the fluid emerging from a spherical source. We assume uniform expansion of the field and the fluid and a polytropic relation between the density and the pressure of the fluid. The expansion velocity is small near the base but approaches the speed of light at the light sphere where the flux terminates. We find self-consistent solutions for the density and the magnetic flux. The details of the solution depend on the ratio of the toroidal and the poloidal magnetic field, the ratio of the energy carried by the fluid and the electromagnetic field and the maximum velocity it reaches.

When a magnetically dominated superfast-magnetosonic long/soft gamma-ray burst (GRB) jet leaves the progenitor star, the external pressure support will drop and the jet may enter the regime of ballistic expansion, during which additional magnetic acceleration becomes ineffective. However, recent numerical simulations by Tchekhovskoy et al. have suggested that the transition to this regime is accompanied by a spurt of acceleration. We confirm this finding numerically and attribute the acceleration to a sideways expansion of the jet, associated with a strong magnetosonic rarefaction wave that is driven into the jet when it loses pressure support, which induces a conversion of magnetic energy into kinetic energy of bulk motion. This mechanism, which we dub rarefaction acceleration, can only operate in a relativistic outflow because in this case the total energy can still be dominated by the magnetic component even in the superfast-magnetosonic regime. We analyse this process using the equations of relativistic magnetohydrodynamics and demonstrate that it is more efficient at converting internal energy into kinetic energy when the flow is magnetized than in a purely hydrodynamic outflow, as was found numerically by Mizuno et al. We show that, just as in the case of the magnetic acceleration of a collimating jet that is confined by an external pressure distribution - the collimation-acceleration mechanism - the rarefaction-acceleration process in a magnetized jet is a consequence of the fact that the separation between neighbouring magnetic flux surfaces increases faster than their cylindrical radius. However, whereas in the case of effective collimation-acceleration the product of the jet opening angle and its Lorentz factor does not exceed ~1, the addition of the rarefaction-acceleration mechanism makes it possible for this product to become >>1, in agreement with the inference from late-time panchromatic breaks in the afterglow light curves of long/soft GRBs.

We study semi-analytical time-dependent solutions of the relativistic magnetohydrodynamic (MHD) equations for the fields and the fluid emerging from a spherical source. We assume uniform expansion of the field and the fluid and a polytropic relation between the density and the pressure of the fluid. The expansion velocity is small near the base but approaches the speed of light at the light sphere where the flux terminates. We find self-consistent solutions for the density and the magnetic flux. The details of the solution depend on the ratio of the toroidal and the poloidal magnetic field, the ratio of the energy carried by the fluid and the electromagnetic field and the maximum velocity it reaches.

Young stellar object jets are supersonic and highly collimated plasma outflows that propagate for large distances. Although their association to star formation is a well established fact, there are still open questions such as whether the outflow is of disk or stellar origin, how the jet’s time variable structure is produced and why there is an asymmetry between the opposite bipolar flows. The increasing angular resolution of modern telescopes gradually provides the clues to clarify and understand such issues. An emerging picture is that of a two-component protostellar jet, where a high mass loss rate disk wind surrounds a hot stellar outflow. In this context, our group has carried out numerical simulations of several two-component magnetohydrodynamic jet models, setting as initial conditions a combination of two well studied analytical solutions. We investigated the dynamics and the steady state features of many interesting cases as a function of the mixing parameters and the enforced time variability. A highly significant result was the morphological reproduction of the large scale knot-like structure of many young stellar objects jets. Moreover, with the assumption of a quadrupolar disk field we found asymmetric velocities between the bipolar outflows suggesting a possible explanation for this observational fact. In this article we summarize the results on the dynamics and the velocity profiles of a few interesting two-component jet scenarios.

Context. Significant progress has been made in the last years in the understanding of the jet formation mechanism through a combination of numerical simulations and analytical MHD models for outflows characterized by the symmetry of self-similarity. Analytical radially self-similar models successfully describe disk-winds, but need several improvements. In a previous article we introduced models of truncated jets from disks, i.e. evolved in time numerical simulations based on a radially self-similar MHD solution, but including the effects of a finite radius of the jet-emitting disk and thus the outflow. Aims: These models need now to be compared with available observational data. A direct comparison of the results of combined analytical theoretical models and numerical simulations with observations has not been performed as yet. This is our main goal. Methods: In order to compare our models with observed jet widths inferred from recent optical images taken with the Hubble Space Telescope (HST) and ground-based adaptive optics (AO) observations, we use a new set of tools to create emission maps in different forbidden lines, from which we determine the jet width as the full-width half-maximum of the emission. Results: It is shown that the untruncated analytical disk outflow solution considered here cannot fit the small jet widths inferred by observations of several jets. Furthermore, various truncated disk-wind models are examined, whose extracted jet widths range from higher to lower values compared to the observations. Thus, we can fit the observed range of jet widths by tuning our models. Conclusions: We conclude that truncation is necessary to reproduce the observed jet widths and our simulations limit the possible range of truncation radii. We infer that the truncation radius, which is the radius on the disk mid-plane where the jet-emitting disk switches to a standard disk, must be between around 0.1 up to about 1 AU in the observed sample for the considered disk-wind solution. One disk-wind simulation with an inner truncation radius at about 0.11 AU also shows potential for reproducing the observations, but a parameter study is needed.

Outflows emanating from the environment of stellar or galactic objects are a widespread phenomenon in astrophysics. Their morphology ranges from nearly spherically symmetric winds to highly collimated jets. In some cases, e.g., in jets associated with young stellar objects, the bulk outflow speeds are nonrelativistic, while in others, e.g., in jets associated with active galactic nuclei or gamma-ray bursts, it can even be highly relativistic. The main driving mechanism of collimated outflows is likely related to magnetic fields. These fields are able to tap the rotational energy of the compact object or disk, accelerate, and collimate matter ejecta. To zeroth order these outflows can be described by the highly intractable theory of magnetohydrodynamics (MHD). Even in systems where the assumptions of zero resistivity (ideal MHD), steady state, axisymmetry, one fluid description, and polytropic equation of state are applicable, the problem remains difficult. In this case the problem reduces to only two equations, corresponding to the two components of the momentum equation along the flow and in the direction perpendicular to the magnetic field (transfield direction). The latter equation is the most difficult to solve, but also the most important. It answers the question on the degree of the collimation, but also crucially affects the solution of the first, the acceleration efficiency and the bulk velocity of the flow. The first and second parts of this chapter refer to nonrelativistic and relativistic flows, respectively. These Parts can be read independently. In each one, the governing equations are presented and discussed, focusing on the case of flows that are magnetically dominated near the central source. The general characteristics of the solutions in relation to the acceleration and collimation mechanisms are analyzed. As specific examples of exact solutions of the full system of the MHD equations that satisfy all the analyzed general characteristics, self-similar models are presented.

Stellar winds seem to be very efficient at removing angular momentum from stars. By means of analytical axisymmetric solutions of the ideal MHD equations for steady outflows, we show via a specific example how collimated stellar winds can brake Weak T Tauri stars in a reasonable time. This result can be generalized to Classical T Tauri stars provided that part of the accreted angular momentum is removed by the inner disk wind. We also extend briefly to Kerr metrics the self similar MHD solutions for relativistic flows and conjecture that relativistic outflows may efficiently slow down spinning black holes at the center of Active Galactic Nuclei or microquasars.

The available analytical MHD models for jets, characterized by the symmetries of radial self-similarity (ADO, Analytical Disk Outflow solutions) in general have two geometrical shortcomings, a singularity at the jet axis and the non-existence of an intrinsic scale, i.e., the jets formally extend to radial infinity. The present study focuses on imposing an outer ejecting radius of the underlying accreting disk and thus providing a finite width disk-wind. The simulations are carried out using the PLUTO code. We study the time evolution of these modified analytical models and we investigate the rich parameter space and compare the results directly with observations.

Axisymmetric resistive MHD simulations for radially self-similar initial conditions are performed, using the NIRVANA code. The magnetic diffusivity could occur in outflows above an accretion disk, being transferred from the underlying disk into the disk corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We introduce, in addition to the classical magnetic Reynolds number Rm, which measures the importance of resistive effects in the induction equation, a new number Rb, which measures the importance of the resistive effects in the energy equation. We find two distinct regimes of solutions in our simulations. One is the low-resistivity regime, in which results do not differ much from ideal-MHD solutions. In the high-resistivity regime, results seem to show some periodicity in time-evolution, and depart significantly from the ideal-MHD case. Whether this departure is caused by numerical or physical reasons is of considerable interest for numerical simulations and theory of astrophysical outflows and is currently investigated.

We present numerical simulations of axisymmetric, magnetically driven outflows that reproduce the inferred properties of ultrarelativistic gamma-ray burst (GRB) jets. These results extend our previous simulations of outflows accelerated to moderately relativistic speeds, which are applicable to jets of active galactic nuclei. In contrast to several recent investigations, which have employed the magnetodynamics approximation, our numerical scheme solves the full set of equations of special relativistic, ideal magnetohydrodynamics, which enables us to explicitly calculate the jet velocity and magnetic-to-kinetic energy conversion efficiency - key parameters of interest for astrophysical applications. We confirm that the magnetic acceleration scheme remains robust into the ultrarelativistic regime, as previously indicated by semi-analytic self-similar solutions. We find that all current-carrying outflows exhibit self-collimation and consequent acceleration near the rotation axis, but that unconfined outflows lose causal connectivity across the jet and therefore do not collimate or accelerate efficiently in their outer regions. We show that magnetically accelerated jets confined by an external pressure that varies as z-α (0 < α <= 2) assume a paraboloidal shape z ~ ra (where r,z are cylindrical coordinates and a > 1), and we obtain analytic expressions for the one-to-one correspondence between the pressure distribution and the asymptotic jet shape. We demonstrate that the acceleration efficiency of jets with paraboloidal streamlines is >~50 per cent, with the numerical value being higher the lower the initial magnetization. We derive asymptotic analytic expressions for the acceleration of initially cold outflows along paraboloidal streamlines and verify that they provide good descriptions of the simulated flows. Our modelled jets (corresponding to 3/2 < a < 3) attain Lorentz factors Γ >~ 102 on scales ~ 1010-1012cm, consistent with the possibility that long/soft GRB jets are accelerated within envelopes of collapsing massive stars, and Γ >~ 30 on scales ~9 × 108-3 × 1010cm, consistent with the possibility that short/hard GRB jets are accelerated on scales where they can be confined by moderately relativistic winds from accretion discs. We also find that Γθv ~ 1 for outflows that undergo an efficient magnetic-to-kinetic energy conversion, where θv is the opening half-angle of the poloidal streamlines. This relation implies that the γ-ray emitting components of GRB outflows accelerated in this way are very narrow, with θv <~ 1° in regions where Γ >~ 100, and that the afterglow light curves of these components would either exhibit a very early jet break or show no jet break at all.

We present self-consistent global steady state MHD models and synthetic optically thin synchrotron emission maps for the jet of M87. The model consists of two distinct zones: an inner relativistic outflow, which we identify with the observed jet, and an outer cold disk wind. While the former does not self-collimate efficiently due to its high effective inertia, the latter fulfills all the conditions for efficient collimation by the magnetocentrifugal mechanism. Given the right balance between the effective inertia of the inner flow and the collimation efficiency of the outer disk wind, the relativistic flow is magnetically confined into a well-collimated beam and matches the measurements of the opening angle of M87 over several orders of magnitudes in spatial extent. The synthetic synchrotron maps reproduce the morphological structure of the jet of M87, i.e., center bright profiles near the core and limb bright profiles away from the core. At the same time, they also show a local increase of brightness at some distance along the axis associated with a recollimation shock in the MHD model. Its location coincides with the position of the optical knot HST-1. In addition, our best fitting model is consistent with a number of observational constraints such as the magnetic field in the knot HST-1 and the jet-to-counterjet brightness ratio.

Outflows in the form of jets is a widespread phenomenon in astrophysics. Their main driving mechanism is likely related to magnetic fields. These fields are able to tap the rotational energy of the central object and its surrounding disk, and accelerate and collimate matter ejecta. To zeroth order these outflows can be described within the theory of steady, axisymmetric, ideal magnetohydrodynamics (MHD). The analytical insight into the equations of the theory (mostly on the transfield component of the momentum equation) gives simple analytical scalings for the flow speed, density, and magnetic field. The analysis is focused on nonrelativistic YSO jets; similar works [1, 2] exist for relativistic AGN, and highly relativistic GRB jets.

Recent observations as well as theoretical studies of YSO jets suggest the presence of two steady components: a disk wind type outflow needed to explain the observed high mass loss rates and a stellar wind type outflow probably accounting for the observed stellar spin down. In this framework, we construct numerical two-component jet models by properly mixing an analytical disk wind solution with a complementary analytically derived stellar outflow. Their combination is controlled by both spatial and temporal parameters, in order to address different physical conditions and time variable features. We study the temporal evolution and the interaction of the two jet components on both small and large scales. The simulations reach steady state configurations close to the initial solutions. Although time variability is not found to considerably affect the dynamics, flow fluctuations generate shocks, whose large scale structures have a strong resemblance to observed YSO jet knots.

Stellar winds seem to be very efficient at removing angular momentum from stars. By means of analytical axisymmetric solutions of the ideal MHD equations for steady outflows, we show via a specific example how collimated stellar winds can brake Weak T Tauri stars in a reasonable time. This result can be generalized to Classical T Tauri stars provided that part of the accreted angular momentum is removed by the inner disk wind. We also extend briefly to Kerr metrics the self similar MHD solutions for relativistic flows and conjecture that relativistic outflows may efficiently slow down spinning black holes at the center of Active Galactic Nuclei or microquasars.

The available analytical MHD models for jets, characterized by the symmetries of radial self-similarity (ADO, Analytical Disk Outflow solutions) in general have two geometrical shortcomings, a singularity at the jet axis and the non-existence of an intrinsic scale, i.e., the jets formally extend to radial infinity. The present study focuses on imposing an outer ejecting radius of the underlying accreting disk and thus providing a finite width disk-wind. The simulations are carried out using the PLUTO code. We study the time evolution of these modified analytical models and we investigate the rich parameter space and compare the results directly with observations.

Outflows in the form of jets is a widespread phenomenon in astrophysics. Their main driving mechanism is likely related to magnetic fields. These fields are able to tap the rotational energy of the central object and its surrounding disk, and accelerate and collimate matter ejecta. To zeroth order these outflows can be described within the theory of steady, axisymmetric, ideal magnetohydrodynamics (MHD). The analytical insight into the equations of the theory (mostly on the transfield component of the momentum equation) gives simple analytical scalings for the flow speed, density, and magnetic field. The analysis is focused on nonrelativistic YSO jets; similar works [1, 2] exist for relativistic AGN, and highly relativistic GRB jets.

Axisymmetric resistive MHD simulations for radially self-similar initial conditions are performed, using the NIRVANA code. The magnetic diffusivity could occur in outflows above an accretion disk, being transferred from the underlying disk into the disk corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We introduce, in addition to the classical magnetic Reynolds number Rm, which measures the importance of resistive effects in the induction equation, a new number Rb, which measures the importance of the resistive effects in the energy equation. We find two distinct regimes of solutions in our simulations. One is the low-resistivity regime, in which results do not differ much from ideal-MHD solutions. In the high-resistivity regime, results seem to show some periodicity in time-evolution, and depart significantly from the ideal-MHD case. Whether this departure is caused by numerical or physical reasons is of considerable interest for numerical simulations and theory of astrophysical outflows and is currently investigated.

Context: Theoretical arguments along with observational data of YSO jets suggest the presence of two steady components: a disk wind type outflow needed to explain the observed high mass loss rates and a stellar wind type outflow probably accounting for the observed stellar spin down. Each component's contribution depends on the intrinsic physical properties of the YSO-disk system and its evolutionary stage. Aims: The main goal of this paper is to understand some of the basic features of the evolution, interaction and co-existence of the two jet components over a parameter space and when time variability is enforced. Methods: Having studied separately the numerical evolution of each type of the complementary disk and stellar analytical wind solutions in Paper I of this series, we proceed here to mix together the two models inside the computational box. The evolution in time is performed with the PLUTO code, investigating the dynamics of the two-component jets, the modifications each solution undergoes and the potential steady state reached. Results: The co-evolution of the two components, indeed, results in final steady state configurations with the disk wind effectively collimating the inner stellar component. The final outcome stays close to the initial solutions, supporting the validity of the analytical studies. Moreover, a weak shock forms, disconnecting the launching region of both outflows with the propagation domain of the two-component jet. On the other hand, several cases are being investigated to identify the role of each two-component jet parameter. Time variability is not found to considerably affect the dynamics, thus making all the conclusions robust. However, the flow fluctuations generate shocks, whose large scale structures have a strong resemblance to observed YSO jet knots. Conclusions: Analytical disk and stellar solutions, even sub modified fast ones, provide a solid foundation to construct two-component jet models. Tuning their physical properties along with the two-component jet parameters allows a broad class of realistic scenarios to be addressed. The applied flow variability provides very promising perspectives for the comparison of the models with observations.

We present numerical simulations of axisymmetric, magnetically driven outflows that reproduce the inferred properties of ultrarelativistic gamma-ray burst (GRB) jets. These results extend our previous simulations of outflows accelerated to moderately relativistic speeds, which are applicable to jets of active galactic nuclei. In contrast to several recent investigations, which have employed the magnetodynamics approximation, our numerical scheme solves the full set of equations of special relativistic, ideal magnetohydrodynamics, which enables us to explicitly calculate the jet velocity and magnetic-to-kinetic energy conversion efficiency - key parameters of interest for astrophysical applications. We confirm that the magnetic acceleration scheme remains robust into the ultrarelativistic regime, as previously indicated by semi-analytic self-similar solutions. We find that all current-carrying outflows exhibit self-collimation and consequent acceleration near the rotation axis, but that unconfined outflows lose causal connectivity across the jet and therefore do not collimate or accelerate efficiently in their outer regions. We show that magnetically accelerated jets confined by an external pressure that varies as z-α (0 < α <= 2) assume a paraboloidal shape z ~ ra (where r,z are cylindrical coordinates and a > 1), and we obtain analytic expressions for the one-to-one correspondence between the pressure distribution and the asymptotic jet shape. We demonstrate that the acceleration efficiency of jets with paraboloidal streamlines is >~50 per cent, with the numerical value being higher the lower the initial magnetization. We derive asymptotic analytic expressions for the acceleration of initially cold outflows along paraboloidal streamlines and verify that they provide good descriptions of the simulated flows. Our modelled jets (corresponding to 3/2 < a < 3) attain Lorentz factors Γ >~ 102 on scales ~ 1010-1012cm, consistent with the possibility that long/soft GRB jets are accelerated within envelopes of collapsing massive stars, and Γ >~ 30 on scales ~9 × 108-3 × 1010cm, consistent with the possibility that short/hard GRB jets are accelerated on scales where they can be confined by moderately relativistic winds from accretion discs. We also find that Γθv ~ 1 for outflows that undergo an efficient magnetic-to-kinetic energy conversion, where θv is the opening half-angle of the poloidal streamlines. This relation implies that the γ-ray emitting components of GRB outflows accelerated in this way are very narrow, with θv <~ 1° in regions where Γ >~ 100, and that the afterglow light curves of these components would either exhibit a very early jet break or show no jet break at all.

We present self-consistent global steady state MHD models and synthetic optically thin synchrotron emission maps for the jet of M87. The model consists of two distinct zones: an inner relativistic outflow, which we identify with the observed jet, and an outer cold disk wind. While the former does not self-collimate efficiently due to its high effective inertia, the latter fulfills all the conditions for efficient collimation by the magnetocentrifugal mechanism. Given the right balance between the effective inertia of the inner flow and the collimation efficiency of the outer disk wind, the relativistic flow is magnetically confined into a well-collimated beam and matches the measurements of the opening angle of M87 over several orders of magnitudes in spatial extent. The synthetic synchrotron maps reproduce the morphological structure of the jet of M87, i.e., center bright profiles near the core and limb bright profiles away from the core. At the same time, they also show a local increase of brightness at some distance along the axis associated with a recollimation shock in the MHD model. Its location coincides with the position of the optical knot HST-1. In addition, our best fitting model is consistent with a number of observational constraints such as the magnetic field in the knot HST-1 and the jet-to-counterjet brightness ratio.

Recent observations as well as theoretical studies of YSO jets suggest the presence of two steady components: a disk wind type outflow needed to explain the observed high mass loss rates and a stellar wind type outflow probably accounting for the observed stellar spin down. In this framework, we construct numerical two-component jet models by properly mixing an analytical disk wind solution with a complementary analytically derived stellar outflow. Their combination is controlled by both spatial and temporal parameters, in order to address different physical conditions and time variable features. We study the temporal evolution and the interaction of the two jet components on both small and large scales. The simulations reach steady state configurations close to the initial solutions. Although time variability is not found to considerably affect the dynamics, flow fluctuations generate shocks, whose large scale structures have a strong resemblance to observed YSO jet knots.

Numerical simulations with self-similar initial and boundary conditions provide a link between theoretical and numerical investigations of jet dynamics. We perform axisymmetric resistive magnetohydrodynamic (MHD) simulations for a generalized solution of the Blandford & Payne type, and compare them with the corresponding analytical and numerical ideal MHD solutions. We disentangle the effects of the numerical and physical diffusivity. The latter could occur in outflows above an accretion disc, being transferred from the underlying disc into the disc corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We conclude that while the classical magnetic Reynolds number Rm measures the importance of resistive effects in the induction equation, a new introduced number, Rβ = (β/2)Rm with β the plasma beta, measures the importance of the resistive effects in the energy equation. Thus, in magnetized jets with β < 2, when Rβ <~ 1 resistive effects are non-negligible and affect mostly the energy equation. The presented simulations indeed show that for a range of magnetic diffusivities corresponding to Rβ >~ 1, the flow remains close to the ideal MHD self-similar solution.

Context: Finite radius accretion disks are a strong candidate for launching astrophysical jets from their inner parts and disk-winds are considered as the basic component of such magnetically collimated outflows. Numerical simulations are usually employed to answer several open questions regarding the origin, stability and propagation of jets. The inherent uncertainties, however, of the various numerical codes, applied boundary conditions, grid resolution, etc., call for a parallel use of analytical methods as well, whenever they are available, as a tool to interpret and understand the outcome of the simulations. The only available analytical MHD solutions to describe disk-driven jets are those characterized by the symmetry of radial self-similarity. Those exact MHD solutions are used to guide the present numerical study of disk-winds. Aims: Radially self-similar MHD models, in general, have two geometrical shortcomings, a singularity at the jet axis and the non-existence of an intrinsic radial scale, i.e. the jets formally extend to radial infinity. Hence, numerical simulations are necessary to extend the analytical solutions towards the axis and impose a physical boundary at finite radial distance. Methods: We focus here on studying the effects of imposing an outer radius of the underlying accreting disk (and thus also of the outflow) on the topology, structure and variability of a radially self-similar analytical MHD solution. The initial condition consists of a hybrid of an unchanged and a scaled-down analytical solution, one for the jet and the other for its environment. Results: In all studied cases, we find at the end steady two-component solutions. The boundary between both solutions is always shifted towards the solution with reduced quantities. Especially, the reduced thermal and magnetic pressures change the perpendicular force balance at the “surface” of the flow. In the models where the scaled-down analytical solution is outside the unchanged one, the inside solution converges to a solution with different parameters. In the models where the scaled-down analytical solution is inside the unchanged one, the whole two-component solution changes dramatically to stop the flow from collapsing totally to the symmetry axis. Conclusions: It is thus concluded that truncated exact MHD disk-wind solutions that may describe observed jets associated with finite radius accretion disks, are topologically stable.

Numerical simulations with self-similar initial and boundary conditions provide a link between theoretical and numerical investigations of jet dynamics. We perform axisymmetric resistive magnetohydrodynamic (MHD) simulations for a generalized solution of the Blandford & Payne type, and compare them with the corresponding analytical and numerical ideal MHD solutions. We disentangle the effects of the numerical and physical diffusivity. The latter could occur in outflows above an accretion disc, being transferred from the underlying disc into the disc corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We conclude that while the classical magnetic Reynolds number Rm measures the importance of resistive effects in the induction equation, a new introduced number, Rβ = (β/2)Rm with β the plasma beta, measures the importance of the resistive effects in the energy equation. Thus, in magnetized jets with β < 2, when Rβ <~ 1 resistive effects are non-negligible and affect mostly the energy equation. The presented simulations indeed show that for a range of magnetic diffusivities corresponding to Rβ >~ 1, the flow remains close to the ideal MHD self-similar solution.

The main characteristics of relativistic, steady, ideal magnetohydrodynamic (MHD) outflows are discussed, focusing on their bulk acceleration and collimation. It is shown that the Bernoulli equation relates the bulk Lorentz factor with the shape of the flow, permitting an analytic estimation of the acceleration efficiency, while the transfield force-balance equation gives a simple relation of the bulk Lorentz factor to the distance.

We consider the internal shock formation in magnetized outflows and we examine the plastic collision between such relativistic blobs taking into account a possible dissipation of magnetic flux. We find that after the collision a large amount of energy is released in thermal form and consequently we assume that this is transferred into protons which obtain a relativistic Maxwellian distribution. The relativistic thermal proton plasma is dense enough to suffer substantial energy losses through proton-proton interactions and thus to transfer its initial energy into photons, electron-positron pairs and neutrinos. We estimate the radiated spectrum by following the evolution of protons, electrons and photons as they interact with each other and with the magnetic field as well.

The main driving mechanism of relativistic jets is likely related to magnetic fields. These fields are able to tap the rotational energy of the central compact object or disk, accelerate and collimate matter ejecta. To zeroth order these outflows can be described by the theory of steady, axisymmetric, ideal magnetohydrodynamics. Results from recent numerical simulations of magnetized jets, as well as analytical studies, show that the efficiency of the bulk acceleration could be more than ∼ 50 %. They also shed light to the degree of the collimation and how it is related to the pressure distribution of the environment, the apparent kinematics of jet components, and the observed polarization properties.

Context: Observations of collimated outflows in young stellar objects indicate that several features of the jets can be understood by adopting the picture of a two-component outflow, wherein a central stellar component around the jet axis is surrounded by an extended disk wind. The precise contribution of each component may depend on the intrinsic physical properties of the YSO-disk system as well as its evolutionary stage. Aims: This article reports a systematic separate investigation of these jet components via time-dependent simulations of two prototypical and complementary analytical solutions, each closely related to the properties of stellar outflows and disk winds. These models describe a meridionally and a radially self-similar exact solution of the steady-state, ideal hydromagnetic equations, respectively. Methods: Using the PLUTO code to carry out the simulations, the study focuses on the topological stability of each of the two analytical solutions, which are successfully extended to all space by removing their singularities. In addition, their behavior and robustness over several physical and numerical modifications is extensively examined. Therefore, this work serves as the starting point for the analysis of the two-component jet simulations. Results: It is found that radially self-similar solutions (disk winds) always reach a final steady-state while maintaining all their well-defined properties. The different ways to replace the singular part of the solution around the symmetry axis, being a first approximation towards a two-component outflow, lead to the appearance of a shock at the super-fast domain corresponding to the fast magnetosonic separatrix surface. These conclusions hold true independently of the numerical modifications and/or evolutionary constraints that the models have undergone, such as starting with a sub-modified-fast initial solution or different types of heating/cooling assumptions. Furthermore, the final outcome of the simulations remains close enough to the initial analytical configurations, thus showing their topological stability. Conversely, the asymptotic configuration and the stability of meridionally self-similar models (stellar winds) is related to the heating processes at the base of the wind. If the heating is modified by assuming a polytropic relation between density and pressure, a turbulent evolution is found. On the other hand, adiabatic conditions lead to the replacement of the outflow by an almost static atmosphere.

We present numerical simulations of axisymmetric, magnetically driven relativistic jets. Our special-relativistic, ideal-magnetohydrodynamics numerical scheme is specifically designed to optimize accuracy and resolution and to minimize numerical dissipation. In addition, we implement a grid-extension method that reduces the computation time by up to three orders of magnitude and makes it possible to follow the flow up to six decades in spatial scale. To eliminate the dissipative effects induced by a free boundary with an ambient medium we assume that the flow is confined by a rigid wall of a prescribed shape, which we take to be z ~ ra (in cylindrical coordinates, with a ranging from 1 to 3). We also prescribe, through the rotation profile at the inlet boundary, the injected poloidal current distribution: we explore cases where the return current flows either within the volume of the jet or on the outer boundary. The outflows are initially cold, sub-Alfvénic and Poynting flux-dominated, with a total-to-rest-mass energy flux ratio μ ~ 15. We find that in all cases they converge to a steady state characterized by a spatially extended acceleration region. The acceleration process is very efficient: on the outermost scale of the simulation as much as ~ 77 per cent of the Poynting flux has been converted into kinetic energy flux, and the terminal Lorentz factor approaches its maximum possible value (Γ∞ ~= μ). We also find a high collimation efficiency: all our simulated jets (including the limiting case of an unconfined flow) develop a cylindrical core. We argue that this could be the rule for current-carrying outflows that start with a low initial Lorentz factor (Γ0 ~ 1). Our conclusions on the high acceleration and collimation efficiencies are not sensitive to the particular shape of the confining boundary or to the details of the injected current distribution, and they are qualitatively consistent with the semi-analytic self-similar solutions derived by Vlahakis and Königl. We apply our results to the interpretation of relativistic jets in active galactic nuclei: we argue that they naturally account for the spatially extended accelerations inferred in these sources (Γ∞ >~ 10 attained on radial scales R >~ 1017cm) and are consistent with the transition to the matter-dominated regime occurring already at R >~ 1016cm.

In parallel to the development of numerical simulations, analytical solutions for modelling the acceleration and the collimation of winds and jets have been proposed. We present here how meridionally self-similar solutions can be used to model the solar wind using Ulysses data at solar minimum. Such solutions may also be adapted to explain the formation core or spine jets in classical and weak TTauri stars (class II and III young stellar jets) as well as relativistic jet cores from AGN. The criterion for collimation explains how the jet evolves towards a wind as the star approaches the main sequence. A similar scenario could explain the winds from Seyfert galaxies by opposition to the powerful jets from Fanaroff Riley sources.

We present numerical simulations of axisymmetric, magnetically driven relativistic jets. Our special-relativistic, ideal-magnetohydrodynamics numerical scheme is specifically designed to optimize accuracy and resolution and to minimize numerical dissipation. In addition, we implement a grid-extension method that reduces the computation time by up to three orders of magnitude and makes it possible to follow the flow up to six decades in spatial scale. To eliminate the dissipative effects induced by a free boundary with an ambient medium we assume that the flow is confined by a rigid wall of a prescribed shape, which we take to be z ~ ra (in cylindrical coordinates, with a ranging from 1 to 3). We also prescribe, through the rotation profile at the inlet boundary, the injected poloidal current distribution: we explore cases where the return current flows either within the volume of the jet or on the outer boundary. The outflows are initially cold, sub-Alfvénic and Poynting flux-dominated, with a total-to-rest-mass energy flux ratio μ ~ 15. We find that in all cases they converge to a steady state characterized by a spatially extended acceleration region. The acceleration process is very efficient: on the outermost scale of the simulation as much as ~ 77 per cent of the Poynting flux has been converted into kinetic energy flux, and the terminal Lorentz factor approaches its maximum possible value (Γ∞ ~= μ). We also find a high collimation efficiency: all our simulated jets (including the limiting case of an unconfined flow) develop a cylindrical core. We argue that this could be the rule for current-carrying outflows that start with a low initial Lorentz factor (Γ0 ~ 1). Our conclusions on the high acceleration and collimation efficiencies are not sensitive to the particular shape of the confining boundary or to the details of the injected current distribution, and they are qualitatively consistent with the semi-analytic self-similar solutions derived by Vlahakis and Königl. We apply our results to the interpretation of relativistic jets in active galactic nuclei: we argue that they naturally account for the spatially extended accelerations inferred in these sources (Γ∞ >~ 10 attained on radial scales R >~ 1017cm) and are consistent with the transition to the matter-dominated regime occurring already at R >~ 1016cm.

Observations of collimated outflows in young stellar objects indicate that several features of the jets can be understood by adopting the picture of a two-component outflow wherein a central stellar component around the jet axis is surrounded by an extended disk-wind. The precise contribution of each component may depend on the intrinsic physical properties of the YSO and also its evolutionary stage. In this context, we study a numerical model based on such a two-component outflow by using as an initial condition a combination of two prototypical models, each describing a meridionally self-similar and a radially self-similar exact solution of the steady-state, ideal hydromagnetic equations. These two classes of radially and meridionally self-similar solutions, have already been well studied and have been found to be related to the properties of disk- and stellar-wind, respectively. By properly mixing the two solutions, a variety of models is constructed with different contribution weights for each component in the initial set-up. The models are evolved in time by using the PLUTO code and the interaction and co-existence of the two components in the jet is investigated. It is found that a steady-state is always reached, independently of the mixing parameters of the two model ingredients. Moreover, the final outcome of the time evolution stays rather close to the initial analytical solutions. The results are compared and discussed along the lines of recent observational data.

Recent observations of jets in young stellar objects suggest that although both disk- and stellar-outflows seem to be present, each one of these two components may dominate at the various stages of the YSO. Over the past several years the only analytical solutions of the steady-state MHD equations which have been studied, correspond to the radially (magneto-centrifugally driven disk winds) and meridionally (thermally accelerated stellar outflows) self-similar models. In this context, we study through time dependent numerical simulations, using the PLUTO code, one prototypical case of each of these two classes examining many of their physical and numerical properties. We find that the solutions are structurally stable and robust, maintaining all their well defined features, despite several modifications they have been subject to. Therefore, their proper matching could explain a two-component jet.

In parallel to the development of numerical simulations, analytical solutions for modelling the acceleration and the collimation of winds and jets have been proposed. We present here how meridionally self-similar solutions can be used to model the solar wind using Ulysses data at solar minimum. Such solutions may also be adapted to explain the formation core or spine jets in classical and weak TTauri stars (class II and III young stellar jets) as well as relativistic jet cores from AGN. The criterion for collimation explains how the jet evolves towards a wind as the star approaches the main sequence. A similar scenario could explain the winds from Seyfert galaxies by opposition to the powerful jets from Fanaroff Riley sources.

We perform a numerical simulation of magnetohydrodynamics (MHD) radially self-similar jets, whose prototype is the Blandford & Payne analytical example. The final steady state that is reached is valid close to the rotation axis and also at large distances above the disc where the classical analytical model fails to provide physically acceptable solutions. The outflow starts with a subslow magnetosonic speed, which subsequently crosses all relevant MHD critical points and corresponding magnetosonic separatrix surfaces. The characteristics are plotted together with the Mach cones and the superfast magnetosonic outflow satisfies MHD causality. The final solution remains close enough to the analytical one, which is thus shown to be topologically stable and robust for various boundary conditions.

AGN are associated with relativistic winds and jets. We discuss the application of meridionally self-similar models to winds and jets from hot relativistic coronae, in particular in the central region of accretion disks. We try to understand the respective role of the disk and the central super massive black hole in the source of the jet as well as the classification of those jets. If the orientation of the jet respectively to the observer is one of the key to understand the standard classification, another parameter is the energy distribution of the magnetic rotator which efficiency should increase between jets from Seyferts and jets from Fanaroff Riley (FR) objects. Moreover the thermal confinement in FRI jets may turn out to be more important than in the magnetically confined FRII jets whose environment is clearly poorer. This scenario deduced from analytical modeling needs further investigation trough numerical simulations.

We present self-similar semi-analytical solutions obtained in the framework of general relativistic magnetohydrodynamics (GRMHD) which describe steady and axisymmetric outflows from the system of a hot coronal magnetosphere of a Schwarzschild black hole and its surrounding accretion disk. The model allows to extend previous non relativistic MHD studies for coronal winds from young stars to spine jets from Active Galactic Nuclei surrounded by disk-driven outflows, The collimation depends critically on an energetic integral measuring the efficiency of the magnetic rotator, similarly to the non relativistic case. The outflows are thermally driven and magnetically (thermally) collimated if the magnetic rotator is efficient (inefficient). It is also shown that relativistic effects affect quantitatively the depth of the gravitational well and the coronal temperature distribution in the launching region of the outflow. Similarly to previous analytical and numerical studies, relativistic effects tend to increase the efficiency of the thermal driving but reduce the effect of magnetic self-collimation.

Jets in active galactic nuclei are collimated, relativistic flows that emanate from accretion disks around supermassive black holes. Electromagnetic stresses are the most plausible candidate for extracting energy at the source and converting it into outflow kinetic energy. Questions that need to be answered in order for these processes to be well understood are: Can we explain parsec-scale accelerations that the observations infer? How the conditions near the disk are related to the terminal Lorentz factor of the jet and what is the asymptotic value of the Poynting-to-matter energy flux ratio? Can we model the apparent kinematics of the observed jet components? I present solutions of the ideal magnetohydrodynamic equations that help to shed light on these questions.

We perform a numerical simulation of magnetohydrodynamics (MHD) radially self-similar jets, whose prototype is the Blandford & Payne analytical example. The final steady state that is reached is valid close to the rotation axis and also at large distances above the disc where the classical analytical model fails to provide physically acceptable solutions. The outflow starts with a subslow magnetosonic speed, which subsequently crosses all relevant MHD critical points and corresponding magnetosonic separatrix surfaces. The characteristics are plotted together with the Mach cones and the superfast magnetosonic outflow satisfies MHD causality. The final solution remains close enough to the analytical one, which is thus shown to be topologically stable and robust for various boundary conditions.

Steady axisymmetric outflows originating at the hot coronal magnetosphere of a Schwarzschild black hole and surrounding accretion disk are studied in the framework of general relativistic magnetohydrodynamics (GRMHD). The assumption of meridional self-similarity is adopted for the construction of semi-analytical solutions of the GRMHD equations describing outflows close to the polar axis. In addition, it is assumed that relativistic effects related to the rotation of the black hole and the plasma are negligible compared to the gravitational and other energetic terms. The constructed model allows us to extend previous MHD studies for coronal winds from young stars to spine jets from Active Galactic Nuclei surrounded by disk-driven outflows. The outflows are thermally driven and magnetically or thermally collimated. The collimation depends critically on an energetic integral measuring the efficiency of the magnetic rotator, similarly to the non relativistic case. It is also shown that relativistic effects quantitatively affect the depth of the gravitational well and the coronal temperature distribution in the launching region of the outflow. Similarly to previous analytical and numerical studies, relativistic effects tend to increase the efficiency of the thermal driving but reduce the effect of magnetic self-collimation.

Jets in active galactic nuclei are collimated, relativistic flows that emanate from accretion disks around supermassive black holes. Electromagnetic stress- es are the most plausible candidate for extracting energy from the source and converting it into outflow kinetic energy. Questions that need to be answered in order for these processes to be well understood are: Can we explain parsec-scale accelerations that the observations infer? How the conditions near the disk are related to the terminal Lorentz factor of the jet and what is the asymptotic value of the Poynting-to-matter energy flux ratio? Can we model the apparent kinematics of the observed jet components? I present solutions of the ideal magnetohydrodynamic equations that help to shed light on these questions.

AGN are associated with relativistic winds and jets. We discuss the application of meridionally self-similar models to winds and jets from hot relativistic coronae, in particular in the central region of accretion disks. We try to understand the respective role of the disk and the central super massive black hole in the source of the jet as well as the classification of those jets. If the orientation of the jet respectively to the observer is one of the key to understand the standard classification, another parameter is the energy distribution of the magnetic rotator which efficiency should increase between jets from Seyferts and jets from Fanaroff Riley (FR) objects. Moreover the thermal confinement in FRI jets may turn out to be more important than in the magnetically confined FRII jets whose environment is clearly poorer. This scenario deduced from analytical modeling needs further investigation trough numerical simulations.

We present self-similar semi-analytical solutions obtained in the framework of general relativistic magnetohydrodynamics (GRMHD) which describe steady and axisymmetric outflows from the system of a hot coronal magnetosphere of a Schwarzschild black hole and its surrounding accretion disk. The model allows to extend previous non relativistic MHD studies for coronal winds from young stars to spine jets from Active Galactic Nuclei surrounded by disk-driven outflows, The collimation depends critically on an energetic integral measuring the efficiency of the magnetic rotator, similarly to the non relativistic case. The outflows are thermally driven and magnetically (thermally) collimated if the magnetic rotator is efficient (inefficient). It is also shown that relativistic effects affect quantitatively the depth of the gravitational well and the coronal temperature distribution in the launching region of the outflow. Similarly to previous analytical and numerical studies, relativistic effects tend to increase the efficiency of the thermal driving but reduce the effect of magnetic self-collimation.

Jets in active galactic nuclei are collimated, relativistic flows that emanate from accretion disks around supermassive black holes. Electromagnetic stresses are the most plausible candidate for extracting energy at the source and converting it into outflow kinetic energy. Questions that need to be answered in order for these processes to be well understood are: Can we explain parsec-scale accelerations that the observations infer? How the conditions near the disk are related to the terminal Lorentz factor of the jet and what is the asymptotic value of the Poynting-to-matter energy flux ratio? Can we model the apparent kinematics of the observed jet components? I present solutions of the ideal magnetohydrodynamic equations that help to shed light on these questions.

AGN jets are collimated, relativistic flows that emanate from accretion disks around supermassive black holes. Electromagnetic stresses are the most plausible candidate for extracting energy at the source and converting it into outflow kinetic energy. Among the questions that need to be answered in order for these processes to be well understood are: How the conditions near the disk are related to the terminal Lorentz factor of the jet? What is the asymptotic value of the Poynting-to-matter energy flux ratio? Can we explain the apparent kinematics of the observed jet components? I present exact solutions as well as a general analysis of the ideal magnetohydrodynamic equations that help to shed light on these questions.

Gamma-ray bursts (GRBs) have been inferred to arise in highly collimated, ultrarelativistic jets that emanate from the vicinity of a solar-mass compact object. Electromagnetic stresses are the most plausible candidate for extracting rotational energy at the source and converting it into outflow kinetic energy. Two questions that need to be answered in order for this process to be well understood are: what determines the terminal Lorentz factor of the flow? What is the asymptotic value of the Poynting-to-matter energy flux ratio? We discuss the general characteristics of the relativistic magnetohydrodynamic (MHD) solutions that, together with previously obtained exact results, help to shed light on these questions.

Using steady, axisymmetric, ideal magnetohydrodynamics (MHD) we analyze relativistic outflows by means of examining the momentum equation along the flow and in the transfield direction. We argue that the asymptotic Lorentz factor is γ∞∼μ-σ M , and the asymptotic value of the Poynting-to-matter energy flux ratio—the so-called σ function—is given by σ∞/(1 +σ∞) ∼σ M /μ, where σ M is the Michel’s magnetization parameter and μc 2 the total energy-to-mass flux ratio. We discuss how these values depend on the conditions near the origin of the flow. By employing self-similar solutions we verify the above result, and show that a Poynting-dominated flow near the source reaches equipartition between Poynting and matter energy fluxes, or even becomes matter-dominated, depending on the value of σ M /μ.

Using ideal magnetohydrodynamics we examine an outflow from a disk surrounding a stellar-mass compact object. We demonstrate that the magnetic acceleration is efficient (>~ 50% of the magnetic energy can be transformed into kinetic energy of γ > 102 baryons) and also that the jet becomes collimated to very small opening angles. Observational implications, focusing on the case of an initially neutron-rich outflow, are discussed in Königl's contribution.

A brief review is given of some results of our work on the construction of (I) steady and (II) time-dependent MHD models for nonrelativistic and relativistic astrophysical outflows and jets, analytically and numerically. The only available exact solutions for MHD outflows are those in separable coordinates, i.e., with the symmetry of radial or meridional self-similarity. Physically accepted solutions pass from the fast magnetosonic separatrix surface in order to satisfy MHD causality. An energetic criterion is outlined for selecting radially expanding winds from cylindrically expanding jets. Numerical simulations of magnetic self-collimation verify the conclusions of analytical steady solutions. We also propose a two-component model consisting of a wind outflow from a central object and a faster rotating outflow launched from a surrounding accretion disk which plays the role of the flow collimator. We also discuss the problem of shock formation during the magnetic collimation of wind-type outflows into jets.

There are observational indications that relativistic outflows in AGNs are accelerated over distances that far exceed the scale of the central engine. Examples include the radio galaxy NGC 6251, where knots in the radio jets were inferred to accelerate from ∼0.13 c at a distance of ∼0.53 pc from the galactic nucleus to ∼0.42 c at r=1.0 pc, and the quasar 3C 345, where the Lorentz factor of the radio knot C7 was deduced to increase from ∼ 5 to >10 as it moved from r=3 pc to r=20 pc}. It is argued, using exact semianalytic solutions of the relativistic MHD equations, that this behavior is a signature of magnetic acceleration. The same basic driving mechanism may apply to the relativistic jets in AGNs, gamma-ray burst sources, and microquasars.

There is growing evidence that relativistic jets in active galactic nuclei undergo extended (parsec-scale) acceleration. We argue that, contrary to some suggestions in the literature, this acceleration cannot be purely hydrodynamic. Using exact semianalytic solutions of the relativistic MHD equations, we demonstrate that the parsec-scale acceleration to relativistic speeds inferred in sources such as the radio galaxy NGC 6251 and the quasar 3C 345 can be attributed to magnetic driving. Additional observational implications of this model will be explored in future papers in this series.

Using relativistic, steady, axisymmetric, ideal magnetohydrodynamics (MHD), we analyze the super-Alfvénic regime of a pulsar wind by solving the momentum equation along the flow, as well as in the transfield direction. Employing a self-similar model, we demonstrate that ideal MHD can account for the full acceleration from high (>>1) to low (<<1) values of σ, the Poynting-to-matter energy flux ratio. The solutions also show a transition from a current-carrying to a return-current regime, partly satisfying the current-closure condition. We discuss the kind of boundary conditions near the base of the ideal MHD regime that are necessary in order to have the required transition from high to low σ in realistic distances and argue that this is a likely case for an equatorial wind. Examining the MHD asymptotics in general, we extend the analysis of Heyvaerts & Norman and Chiueh, Li, & Begelman by including two new elements: classes of quasi-conical and parabolic field line shapes that do not preclude an efficient and much faster than logarithmic acceleration, and the transition σ=σc after which the centrifugal forces (poloidal and azimuthal) are the dominant terms in the transfield force-balance equation.

There are observational indications that relativistic outflows in AGNs are accelerated over distances that far exceed the scale of the central engine. Examples include the radio galaxy NGC 6251, where knots in the radio jets were inferred to accelerate from ∼0.13 c at a distance of ∼0.53 pc from the galactic nucleus to ∼0.42 c at r=1.0 pc, and the quasar 3C 345, where the Lorentz factor of the radio knot C7 was deduced to increase from ∼ 5 to >10 as it moved from r=3 pc to r=20 pc}. It is argued, using exact semianalytic solutions of the relativistic MHD equations, that this behavior is a signature of magnetic acceleration. The same basic driving mechanism may apply to the relativistic jets in AGNs, gamma-ray burst sources, and microquasars.

There is growing evidence that relativistic jets in active galactic nuclei undergo extended (parsec-scale) acceleration. We argue that, contrary to some suggestions in the literature, this acceleration cannot be purely hydrodynamic. Using exact semianalytic solutions of the relativistic MHD equations, we demonstrate that the parsec-scale acceleration to relativistic speeds inferred in sources such as the radio galaxy NGC 6251 and the quasar 3C 345 can be attributed to magnetic driving. Additional observational implications of this model will be explored in future papers in this series.

Using relativistic, steady, axisymmetric, ideal magnetohydrodynamics (MHD), we analyze the super-Alfvénic regime of a pulsar wind by solving the momentum equation along the flow, as well as in the transfield direction. Employing a self-similar model, we demonstrate that ideal MHD can account for the full acceleration from high (>>1) to low (<<1) values of σ, the Poynting-to-matter energy flux ratio. The solutions also show a transition from a current-carrying to a return-current regime, partly satisfying the current-closure condition. We discuss the kind of boundary conditions near the base of the ideal MHD regime that are necessary in order to have the required transition from high to low σ in realistic distances and argue that this is a likely case for an equatorial wind. Examining the MHD asymptotics in general, we extend the analysis of Heyvaerts & Norman and Chiueh, Li, & Begelman by including two new elements: classes of quasi-conical and parabolic field line shapes that do not preclude an efficient and much faster than logarithmic acceleration, and the transition σ=σc after which the centrifugal forces (poloidal and azimuthal) are the dominant terms in the transfield force-balance equation.

Spherically symmetric hydrodynamical outflows accelerated thermally in the vicinity of a compact object are studied by generalizing an equation of state with a variable effective polytropic index, appropriate to describe relativistic temperatures close to the central object and nonrelativistic ones further away. Relativistic effects introduced by the Schwarzschild metric and the presence of relativistic temperatures in the corona are compared with previous results for a constant effective polytropic index and also with results of the classical wind theory. By a parametric study of the polytropic index and the location of the sonic transition it is found that space time curvature and relativistic temperatures tend to increase the efficiency of thermal driving in accelerating the outflow. Thus conversely to the classical Parker wind, the outflow is accelerated even for polytropic indices higher than 3/2. The results of this simple but fully relativistic extension of the polytropic equation of state may be useful in simulations of outflows from hot coronae in black hole magnetospheres.

Using steady, axisymmetric, ideal magnetohydrodynamics (MHD) we analyze relativistic outflows by means of examining the momentum equation along the flow and in the transfield direction. We argue that the asymptotic Lorentz factor is γ∞∼μ-σ M , and the asymptotic value of the Poynting-to-matter energy flux ratio—the so-called σ function—is given by σ∞/(1 +σ∞) ∼σ M /μ, where σ M is the Michel’s magnetization parameter and μc 2 the total energy-to-mass flux ratio. We discuss how these values depend on the conditions near the origin of the flow. By employing self-similar solutions we verify the above result, and show that a Poynting-dominated flow near the source reaches equipartition between Poynting and matter energy fluxes, or even becomes matter-dominated, depending on the value of σ M /μ.

Using ideal magnetohydrodynamics we examine an outflow from a disk surrounding a stellar-mass compact object. We demonstrate that the magnetic acceleration is efficient (>~ 50% of the magnetic energy can be transformed into kinetic energy of γ > 102 baryons) and also that the jet becomes collimated to very small opening angles. Observational implications, focusing on the case of an initially neutron-rich outflow, are discussed in Königl's contribution.

A brief review is given of some results of our work on the construction of (I) steady and (II) time-dependent MHD models for nonrelativistic and relativistic astrophysical outflows and jets, analytically and numerically. The only available exact solutions for MHD outflows are those in separable coordinates, i.e., with the symmetry of radial or meridional self-similarity. Physically accepted solutions pass from the fast magnetosonic separatrix surface in order to satisfy MHD causality. An energetic criterion is outlined for selecting radially expanding winds from cylindrically expanding jets. Numerical simulations of magnetic self-collimation verify the conclusions of analytical steady solutions. We also propose a two-component model consisting of a wind outflow from a central object and a faster rotating outflow launched from a surrounding accretion disk which plays the role of the flow collimator. We also discuss the problem of shock formation during the magnetic collimation of wind-type outflows into jets.

We demonstrate that hydromagnetic acceleration can be the driving mechanism of outflows in GRB sources. Using semianalytical solutions of the full set of the steady, axisymmetric, ideal hydromagnetic equations in flat spacetime -- i.e., solving the momentum equation along the flow as well as in the transfield direction -- we model the acceleration of the baryon/e±/photon fluid that emanates from a stellar-mass compact object/debris-disk system. We prove that for highly relativistic, multiple-shell outflows one can study the motion of each shell using steady-state equations. Employing a radially self-similar model, we find that the flow is initially thermally and subsequently magnetically accelerated. The Lorentz force is capable of transferring close to a half of the total energy of an initially Poynting-dominated flow to baryonic kinetic energy.

We explain in simple terms why a rotating and magnetized outflow forms a core with a jet and show numerical simulations which substantiate this argument. The outflow from a solar-type inefficient magnetic rotator is found to be very weakly collimated while the outflow from a ten times faster rotating YSO is shown to produce a tightly collimated jet. This gives rise to an evolutionary scenario for stellar outflows. We also propose a two-component model consisting of a wind outflow from a central object and a faster rotating outflow launched from a surrounding accretion disk which plays the role of the flow collimator.

We demonstrate that ``hot'' MHD outflows from neutron-rich black hole debris disks can significantly alleviate the baryon-loading problem in gamma-ray burst sources. We argue that the neutron-to-proton ratio in disk-fed outflows might be as high as ~30 and show, with the help of an exact semianalytic relativistic-MHD solution, that the neutrons can decouple at a Lorentz factor γd~15 even as the protons continue to accelerate to γ∞~200 and end up acquiring ~30% of the injected energy. We clarify the crucial role that the magnetic field plays in this process and prove that purely hydrodynamic outflows must have γd>~few×102. The motion of the decoupled neutrons is not collinear with that of the decoupled protons, so, in contrast to previous suggestions based on purely hydrodynamic models, the two particle groups most likely do not collide after decoupling. The decoupled neutron flow might nevertheless contribute to the observed afterglow emission.

Using relativistic, axisymmetric, ideal MHD, we examine the outflow from a debris disk around a newly formed stellar-mass black hole, taking into account the baryonic matter, the electron-positron/photon fluid, and the large-scale electromagnetic field. We clarify the relationship between the thermal (fireball) and magnetic (Poynting flux) acceleration mechanisms, identify the parameter regimes where qualitatively different behaviors are expected, and demonstrate that the observationally inferred properties of the GRB outflows can be attributed to magnetic driving. We show that the Lorentz force can convert up to 50% of the initial total energy into kinetic energy of a collimated flow of baryons. This energy, in turn, may be converted into radiation by internal shocks. We examine how baryon loading and magnetic collimation affect the structure of the flow.

By using relativistic, axisymmetric, ideal MHD, we examine the motion of the baryon/e±/ photon fluid that emanates from a stellar-mass compact object/debris-disk system (a common outcome of many progenitor models). We prove that the motion can be described as a frozen pulse, which permits the study of each shell of the pancake-shaped outflow using steady-state equations. The ejected energy flux is dominated by the electromagnetic (Poynting) contribution, but it can also have a non negligible e±/radiation (thermal fireball)component. We demonstrate, through exact self-similar solutions, that the flow is first thermally and subsequently magnetically accelerated up to equipartition between kinetic and Poynting fluxes, i.e., ∼ 50% of the total energy is converted into baryonic kinetic energy. The electromagnetic forces also collimate the flow, reaching a cylindrical structure asymptotically.

We present a general formulation of special relativistic magnetohydrodynamics and derive exact radially self-similar solutions for axisymmetric outflows from strongly magnetized, rotating compact objects. We generalize previous work by including thermal effects and analyze in detail the various forces that guide, accelerate, and collimate the flow. We demonstrate that, under the assumptions of a quasi-steady poloidal magnetic field and of a highly relativistic poloidal velocity, the equations become effectively time independent and the motion can be described as a frozen pulse. We concentrate on trans-Alfvénic solutions and consider outflows that are super-Alfvénic throughout in the companion paper. Our results are applicable to relativistic jets in gamma-ray burst (GRB) sources, active galactic nuclei, and microquasars, but our discussion focuses on GRBs. We envision the outflows in this case to initially consist of a hot and optically thick mixture of baryons, electron-positron pairs, and photons. We show that the flow is at first accelerated thermally but that the bulk of the acceleration is magnetic, with the asymptotic Lorentz factor corresponding to a rough equipartition between the Poynting and kinetic energy fluxes (i.e., ~50% of the injected total energy is converted into baryonic kinetic energy). The electromagnetic forces also strongly collimate the flow, giving rise to an asymptotically cylindrical structure.

We present exact radially self-similar solutions of special relativistic magnetohydrodynamics representing ``hot'' super-Alfvénic outflows from strongly magnetized, rotating compact objects. We argue that such outflows can plausibly arise in gamma-ray burst (GRB) sources and demonstrate that, just as in the case of the trans-Alfvénic flows considered in the companion paper, they can attain Lorentz factors that correspond to a rough equipartition between the Poynting and kinetic energy fluxes and become cylindrically collimated on scales compatible with GRB observations. As in the trans-Alfvénic case, the initial acceleration is thermal, but, in contrast to the solutions presented in the companion paper, part of the enthalpy flux is transformed into Poynting flux during this phase. The subsequent, magnetically dominated acceleration can be significantly less rapid than in trans-Alfvénic flows.

Using relativistic, axisymmetric, ideal MHD, we examine the outflow from a debris disk around a newly formed stellar-mass black hole, taking into account the baryonic matter, the electron-positron/photon fluid, and the large-scale electromagnetic field. We clarify the relationship between the thermal (fireball) and magnetic (Poynting flux) acceleration mechanisms, identify the parameter regimes where qualitatively different behaviors are expected, and demonstrate that the observationally inferred properties of the GRB outflows can be attributed to magnetic driving. We show that the Lorentz force can convert up to 50% of the initial total energy into kinetic energy of a collimated flow of baryons. This energy, in turn, may be converted into radiation by internal shocks. We examine how baryon loading and magnetic collimation affect the structure of the flow.

We use exact self-similar solutions of the steady, axisymmetric, relativistic, hydromagnetic equations to study the formation of AGN jets. Our formalism allows us to examine the effects of the thermal, centrifugal, and electromagnetic forces on the flow acceleration and collimation. We apply our analysis to the jet in NGC 6251 and show that the puzzling sub-pc scale acceleration to mildly relativistic speeds recently inferred in this source from VLBI measurements can be attributed to magnetic driving.

We explain in simple terms why a rotating and magnetized outflow forms a core with a jet and show numerical simulations which substantiate this argument. The outflow from a solar-type inefficient magnetic rotator is found to be very weakly collimated while the outflow from a ten times faster rotating YSO is shown to produce a tightly collimated jet. This gives rise to an evolutionary scenario for stellar outflows. We also propose a two-component model consisting of a wind outflow from a central object and a faster rotating outflow launched from a surrounding accretion disk which plays the role of the flow collimator.

By using relativistic, axisymmetric, ideal MHD, we examine the motion of the baryon/e+/-/ photon fluid that emanates from a stellar-mass compact object/debris-disk system (a common outcome of many progenitor models). We prove that the motion can be described as a frozen pulse, which permits the study of each shell of the pancake-shaped outflow using steady-state equations. The ejected energy flux is dominated by the electromagnetic (Poynting) contribution, but it can also have a nonnegligible e+/-/radiation (thermal fireball) component. We demonstrate, through exact self-similar solutions, that the flow is first thermally and subsequently magnetically accelerated up to equipartition between kinetic and Poynting fluxes, i.e., ~ 50% of the total energy is converted into baryonic kinetic energy. The electromagnetic forces also collimate the flow, reaching a cylindrical structure asymptotically.

There are observational indications that relativistic outflows in AGNs are accelerated over distances that far exceed the scale of the central engine. Examples include the radio galaxy NGC 6251, where knots in the radio jets were inferred to accelerate from ~0.13c at a distance of ~0.53 pc from the galactic nucleus to ~0.42c at r=1.0 pc, and the quasar 3C 345, where the Lorentz factor of the radio knot C7 was deduced to increase from ~5 to >10 as it moved from r=3 pc to r=20 pc. It is argued, using exact semianalytic solutions of the relativistic MHD equations, that this behavior is a signature of magnetic acceleration. The same basic driving mechanism may apply to the relativistic jets in AGNs, gamma-ray burst sources, and microquasars.

We demonstrate that hydromagnetic acceleration can be the driving mechanism of relativistic outflows in AGNs as well as in Gamma-ray burst sources and Crab-like pulsars. Using semianalytical solutions of the full set of the steady, axisymmetric, ideal hydromagnetic equations in flat spacetime—i.e., solving the momentum equation along the flow as well as in the transfield direction—we model the acceleration of relativistic outflows. We find that a Poynting-flux dominated flow near the source reaches equipartition between matter and magnetic energy-fluxes, or even becomes completely matter-dominated (as in the case of Crab-like pulsar winds).

We present a general formulation of special relativistic magnetohydrodynamics and derive exact radially self-similar solutions for axisymmetric outflows from strongly magnetized, rotating compact objects. We generalize previous work by including thermal effects and analyze in detail the various forces that guide, accelerate, and collimate the flow. We demonstrate that, under the assumptions of a quasi-steady poloidal magnetic field and of a highly relativistic poloidal velocity, the equations become effectively time independent and the motion can be described as a frozen pulse. We concentrate on trans-Alfvénic solutions and consider outflows that are super-Alfvénic throughout in the companion paper. Our results are applicable to relativistic jets in gamma-ray burst (GRB) sources, active galactic nuclei, and microquasars, but our discussion focuses on GRBs. We envision the outflows in this case to initially consist of a hot and optically thick mixture of baryons, electron-positron pairs, and photons. We show that the flow is at first accelerated thermally but that the bulk of the acceleration is magnetic, with the asymptotic Lorentz factor corresponding to a rough equipartition between the Poynting and kinetic energy fluxes (i.e., ~50% of the injected total energy is converted into baryonic kinetic energy). The electromagnetic forces also strongly collimate the flow, giving rise to an asymptotically cylindrical structure.

We present exact radially self-similar solutions of special relativistic magnetohydrodynamics representing ``hot'' super-Alfvénic outflows from strongly magnetized, rotating compact objects. We argue that such outflows can plausibly arise in gamma-ray burst (GRB) sources and demonstrate that, just as in the case of the trans-Alfvénic flows considered in the companion paper, they can attain Lorentz factors that correspond to a rough equipartition between the Poynting and kinetic energy fluxes and become cylindrically collimated on scales compatible with GRB observations. As in the trans-Alfvénic case, the initial acceleration is thermal, but, in contrast to the solutions presented in the companion paper, part of the enthalpy flux is transformed into Poynting flux during this phase. The subsequent, magnetically dominated acceleration can be significantly less rapid than in trans-Alfvénic flows.

We demonstrate that ``hot'' MHD outflows from neutron-rich black hole debris disks can significantly alleviate the baryon-loading problem in gamma-ray burst sources. We argue that the neutron-to-proton ratio in disk-fed outflows might be as high as ~30 and show, with the help of an exact semianalytic relativistic-MHD solution, that the neutrons can decouple at a Lorentz factor γd~15 even as the protons continue to accelerate to γ∞~200 and end up acquiring ~30% of the injected energy. We clarify the crucial role that the magnetic field plays in this process and prove that purely hydrodynamic outflows must have γd>~few×102. The motion of the decoupled neutrons is not collinear with that of the decoupled protons, so, in contrast to previous suggestions based on purely hydrodynamic models, the two particle groups most likely do not collide after decoupling. The decoupled neutron flow might nevertheless contribute to the observed afterglow emission.

We present a systematic method for constructing two-dimensional magnetohydrodynamic equilibria with compressible flow in Cartesian geometry. This systematic method has already been developed in spherical geometry and applied in modelling solar and stellar winds and outflows (Vlahakis & Tsinganos \cite{Vlahakis98}) but is derived here in Cartesian geometry in the context of the solar atmosphere for the first time. Using the method we find several new classes of solutions, some of which generalise known solutions, including the Kippenhahn & Schlüter (\cite{Kippenhahn57}) and Hood & Anzer (\cite{Hood90}) solar prominence models and the Tsinganos et al. (\cite{Tsinganos93}) coronal loop model with flow, and some of which are completely new. Having developed the method in full and summarised the several classes of solutions, we explore in a some detail one of the classes to illustrate the general construction method. From one of the new classes of solutions we calculate two loop-like solutions, one of which is the first exact two-dimensional magnetohydrodynamic equilibrium with trans-Alfvénic flow.

We present a systematic method for constructing two-dimensional magnetohydrodynamic equilibria with compressible flow in Cartesian geometry. This systematic method has already been developed in spherical geometry and applied in modelling solar and stellar winds and outflows (Vlahakis & Tsinganos \cite{Vlahakis98}) but is derived here in Cartesian geometry in the context of the solar atmosphere for the first time. Using the method we find several new classes of solutions, some of which generalise known solutions, including the Kippenhahn & Schlüter (\cite{Kippenhahn57}) and Hood & Anzer (\cite{Hood90}) solar prominence models and the Tsinganos et al. (\cite{Tsinganos93}) coronal loop model with flow, and some of which are completely new. Having developed the method in full and summarised the several classes of solutions, we explore in a some detail one of the classes to illustrate the general construction method. From one of the new classes of solutions we calculate two loop-like solutions, one of which is the first exact two-dimensional magnetohydrodynamic equilibrium with trans-Alfvénic flow.

Using relativistic, axisymmetric, ideal MHD, we examine the outflow from a disk around a compact object, taking into account the baryonic matter, the electron-positron/photon fluid, and the large-scale electromagnetic field. Focusing on the parameter regime appropriate to γ-ray burst outflows, we demonstrate, through exact self-similar solutions, that the thermal force (which dominates the initial acceleration) and the Lorentz force (which dominates farther out and contributes most of the acceleration) can convert up to ~50% of the initial total energy into asymptotic baryon kinetic energy. We examine how baryon loading and magnetic collimation affect the structure of the flow, including the regime where emission due to internal shocks could take place.

Using relativistic, axisymmetric, ideal MHD, we examine the outflow from a disk around a compact object, taking into account the baryonic matter, the electron-positron/photon fluid, and the large-scale electromagnetic field. Focusing on the parameter regime appropriate to γ-ray burst outflows, we demonstrate, through exact self-similar solutions, that the thermal force (which dominates the initial acceleration) and the Lorentz force (which dominates farther out and contributes most of the acceleration) can convert up to ~50% of the initial total energy into asymptotic baryon kinetic energy. We examine how baryon loading and magnetic collimation affect the structure of the flow, including the regime where emission due to internal shocks could take place.

The modelling of plasma outflows from central gravitating objects such as AGN is briefly discussed via analytic examples in the context of ideal MHD. The exact solutions are produced via a nonlinear separation of the variables in the full set of the MHD equations. Attention is given to the questions of initial acceleration and collimation of the outflow. A quantitative criterion is provided for the transition of the morphologies from highly collimated jets to non collimated winds.

The classical Blandford & Payne model for the magneto-centrifugal acceleration and collimation of a disc-wind is revisited and refined. In the original model, the gas is cold and the solution is everywhere subfast magnetosonic. In the present model the plasma has a finite temperature and the self-consistent solution of the MHD equations starts with a subslow magnetosonic speed which subsequently crosses all critical points, at the slow magnetosonic, Alfvén and fast magnetosonic separatrix surfaces. The superfast magnetosonic solution thus satisfies MHD causality. Downstream of the fast magnetosonic critical point the poloidal streamlines overfocus towards the axis and the solution is terminated. The validity of the model to disc winds associated with young stellar objects is briefly discussed.

The classical Blandford & Payne model for the magneto-centrifugal acceleration and collimation of a disc-wind is revisited and refined. In the original model, the gas is cold and the solution is everywhere subfast magnetosonic. In the present model the plasma has a finite temperature and the self-consistent solution of the MHD equations starts with a subslow magnetosonic speed which subsequently crosses all critical points, at the slow magnetosonic, Alfvén and fast magnetosonic separatrix surfaces. The superfast magnetosonic solution thus satisfies MHD causality. Downstream of the fast magnetosonic critical point the poloidal streamlines overfocus towards the axis and the solution is terminated. The validity of the model to disc winds associated with young stellar objects is briefly discussed.

This paper examines a new class of exact and self-consistent MHD solutions which describe steady and axisymmetric hydromagnetic outflows from the atmosphere of a magnetized and rotating central object with possibly an orbiting accretion disk. The plasma is driven against gravity by a thermal pressure gradient, as well as by magnetic rotator and radiative forces. At the Alfvenic and fast critical points the appropriate criticality conditions are applied. The outflow starts almost radially but after the Alfven transition and before the fast critical surface is encountered the magnetic pinching force bends the poloidal streamlines into a cylindrical jet-type shape. The terminal speed, Alfven number, cross-sectional area of the jet, as well as its final pressure and density obtain uniform values at large distances from the source. The goal of the study is to give an analytical discussion of the two-dimensional interplay of the thermal pressure gradient, gravitational, Lorentz and inertial forces in accelerating and collimating an MHD flow. A parametric study of the model is also given, as well as a brief sketch of its applicability to a self-consistent modelling of collimated outflows from various astrophysical objects. {The analysed model succeeds to give for the first time an exact and self-consistent MHD solution for jet-type outflows extending from the stellar surface to infinity where it can be superfast, in agreement with the MHD causality principle.

A convenient approach to model MHD steady axisymmetric outflows is the so-called self-similar technique wherein the physical variables are factorized and a scaling law is assumed along one of the coordinates. This scaling depends on the astrophysical process under investigation. In this note we summarize all possible self-similar MHD outflow solutions; furthermore, we briefly discuss the main properties of a class of solutions which are self-similar in the meridional direction and allow to analyse in simple terms the dynamical properties of an outflow close to its rotational axis. Special attention is focused on the asymptotic structure of collimated winds. It will be shown that different regimes are possible for jets, in particular they can be either thermally or magnetically confined, depending on the physical conditions of the flow. This analysis is complementary with the well known radial self-similar models which are invoked to study winds from accretion disks.

This paper examines a new class of exact and self-consistent MHD solutions which describe steady and axisymmetric hydromagnetic outflows from the atmosphere of a magnetized and rotating central object with possibly an orbiting accretion disk. The plasma is driven against gravity by a thermal pressure gradient, as well as by magnetic rotator and radiative forces. At the Alfvenic and fast critical points the appropriate criticality conditions are applied. The outflow starts almost radially but after the Alfven transition and before the fast critical surface is encountered the magnetic pinching force bends the poloidal streamlines into a cylindrical jet-type shape. The terminal speed, Alfven number, cross-sectional area of the jet, as well as its final pressure and density obtain uniform values at large distances from the source. The goal of the study is to give an analytical discussion of the two-dimensional interplay of the thermal pressure gradient, gravitational, Lorentz and inertial forces in accelerating and collimating an MHD flow. A parametric study of the model is also given, as well as a brief sketch of its applicability to a self-consistent modelling of collimated outflows from various astrophysical objects. {The analysed model succeeds to give for the first time an exact and self-consistent MHD solution for jet-type outflows extending from the stellar surface to infinity where it can be superfast, in agreement with the MHD causality principle.

A convenient approach to model MHD steady axisymmetric outflows is the so-called self-similar technique wherein the physical variables are factorized and a scaling law is assumed along one of the coordinates. This scaling depends on the astrophysical process under investigation. In this note we summarize all possible self-similar MHD outflow solutions; furthermore, we briefly discuss the main properties of a class of solutions which are self-similar in the meridional direction and allow to analyse in simple terms the dynamical properties of an outflow close to its rotational axis. Special attention is focused on the asymptotic structure of collimated winds. It will be shown that different regimes are possible for jets, in particular they can be either thermally or magnetically confined, depending on the physical conditions of the flow. This analysis is complementary with the well known radial self-similar models which are invoked to study winds from accretion disks.

By a systematic method we construct general classes of exact and self-consistent axisymmetric magnetohydrodynamic (MHD) solutions describing flows that originate in the near environment of a central gravitating astrophysical object. The unifying scheme contains two large groups of exact MHD outflow models: (I) meridionally self-similar models with spherical critical surfaces; and (II) radially self-similar models with conical critical surfaces. This classification includes known polytropic models, such as the classical Parker description of a stellar wind and the Blandford &38 Payne model of a disc wind; it also contains non-polytropic models, such as those of winds/jets in Sauty &38 Tsinganos, Lima, Tsinganos &38 Priest, and Trussoni, Tsinganos &38 Sauty. Besides the unification of all known cases under a common scheme, several new classes emerge and some are briefly analysed; they could be explored for a further understanding of the physical properties of MHD outflows from various magnetized and rotating astrophysical objects in stellar or galactic systems.

A widespread phenomenon in astrophysics is the outflow of plasma from the environment of stellar or galactic objects. This plasma outflows range from nonuniform winds to highly collimated jets which are common to many stages of stellar evolution. For example, collimated outflows are found around young stars (e.g., as in HH 30), older mass losing stars (as in eta-Carinae), symbiotic stars (e.g. in R Aqr), planetary nebulae nuclei (as in the hourglass nebula), black hole X-ray transients (as in GRS 1915+105 and GRO J1655-40), low- and high-mass X-ray binaries and recently also in cataclysmic variables (e.g. T Pyxidis). Similarly, they are also found emerging from the nuclei of many radio galaxies and quasars. Nevertheless, despite their abundance the questions of the formation, acceleration and propagation of nonuniform winds and jets have not been fully resolved. One of the main difficulties in dealing with the theoretical problem posed by cosmical outflows is that their dynamics needs to be described - even to lowest order - by the highly intractable set of the MHD equations. As is well known, this is a nonlinear system of partial differential equations with several critical points, and only very few classes of solutions are available for axisymmetric systems obtained by assuming a separation of variables in several key functions. This hypothesis allows an analysis in a 2-D geometry of the full MHD equations which reduce then to a system of ordinary differential equations. By a systematic method we construct general classes of exact and self-consistent axisymmetric MHD solutions. The unifying scheme contains three large groups of exact MHD outflow models, (I) meridionally self-similar ones with spherical critical surfaces, (II) radially self-similar models with conical critical surfaces and (III) generalized self-similar models with arbitrary shape critical surfaces. This classification includes known polytropic models, such as the classical Parker description of a stellar wind and the Blandford and Payne (1982) model of a disk-wind; it also contains nonpolytropic models, such as those of winds/jets in Sauty and Tsinganos (1994), Lima et al (1996) and Trussoni et al (1997). Besides the unification of all known cases under a common scheme, several new classes emerge and some are briefly analyzed; they could be explored for a further understanding of the physical properties of MHD outflows from various magnetized astrophysical rotators. We also propose a new class of exact and self-consistent MHD solutions which describe steady and axisymmetric hydromagnetic outflows from the magnetized atmosphere of a rotating gravitating central object with possibly an orbiting accretion disk. The plasma is driven by a thermal pressure gradient, as well as by magnetic rotator and radiative forces. At the Alfvenic and fast critical points the appropriate criticality conditions are applied. The outflows start almost radially but after the Alfven transition and before the fast critical surface is encountered the magnetic pinching force bends the poloidal streamlines into a cylindrical jet-type shape. The terminal speed, Alfven number, cross-sectional area of the jet, as well as its final pressure and density obtain uniform values at large distances from the source. The goal of the study is to give an analytical discussion of the two-dimensional interplay of the thermal pressure gradient, gravitational, Lorentz and inertial forces in accelerating and collimating an MHD flow. A parametric study of the model is given, as well as a brief sketch of its applicability to a self-consistent modeling of collimated outflows from various astrophysical objects. For example, the obtained characteristics of the collimated outflow in agreement with those in jets associated with YSO's. General theoretical arguments and various analytic self-similar solutions have recently shown that magnetized and rotating astrophysical outflows may become asymptotically cylindrical, in agreement with observations of cosmical jets. A notable common feature in all such self-consistent, self-similar MHD solutions is that before final cylindrical collimation is achieved, the jet passes from a stage of oscillations in its radius, Mach number and other physical parameters. It is shown that under rather general assumptions this oscillatory behaviour of collimated outflows is not restricted to the few specific models examined so far, but instead it seems to be a rather general physical property of an MHD outflow which starts noncylindrically before it reaches collimation. It is concluded thence that astrophysical jets are topologically stable to small amplitude, time-independent perturbations in their asymptotically cylindrical shape. Also, similarly to the familiar fluid instabilities these oscillations may give rise to brightness enhancements along jets.

By a systematic method we construct general classes of exact and self-consistent axisymmetric magnetohydrodynamic (MHD) solutions describing flows that originate in the near environment of a central gravitating astrophysical object. The unifying scheme contains two large groups of exact MHD outflow models: (I) meridionally self-similar models with spherical critical surfaces; and (II) radially self-similar models with conical critical surfaces. This classification includes known polytropic models, such as the classical Parker description of a stellar wind and the Blandford &38 Payne model of a disc wind; it also contains non-polytropic models, such as those of winds/jets in Sauty &38 Tsinganos, Lima, Tsinganos &38 Priest, and Trussoni, Tsinganos &38 Sauty. Besides the unification of all known cases under a common scheme, several new classes emerge and some are briefly analysed; they could be explored for a further understanding of the physical properties of MHD outflows from various magnetized and rotating astrophysical objects in stellar or galactic systems.

General theoretical arguments and various analytic self-similar solutions have recently shown that magnetized and rotating astrophysical outflows may become asymptotically cylindrical, in agreement with observations of cosmical jets. A notable common feature in all such self-consistent, self-similar MHD solutions is that before final cylindrical collimation is achieved, the jet passes from a stage of oscillations in its radius, Mach number and other physical parameters. It is shown that under rather general assumptions this oscillatory behaviour of collimated outflows is not restricted to the few specific models examined so far, but instead seems to be a rather general physical property of an MHD outflow that starts non-cylindrically before it reaches collimation. It is concluded thence that astrophysical jets are topologically stable to small-amplitude, time-independent perturbations in their asymptotically cylindrical shape. Also, similarly to the familiar fluid instabilities, these oscillations may give rise to brightness enhancements along jets.

General theoretical arguments and various analytic self-similar solutions have recently shown that magnetized and rotating astrophysical outflows may become asymptotically cylindrical, in agreement with observations of cosmical jets. A notable common feature in all such self-consistent, self-similar MHD solutions is that before final cylindrical collimation is achieved, the jet passes from a stage of oscillations in its radius, Mach number and other physical parameters. It is shown that under rather general assumptions this oscillatory behaviour of collimated outflows is not restricted to the few specific models examined so far, but instead seems to be a rather general physical property of an MHD outflow that starts non-cylindrically before it reaches collimation. It is concluded thence that astrophysical jets are topologically stable to small-amplitude, time-independent perturbations in their asymptotically cylindrical shape. Also, similarly to the familiar fluid instabilities, these oscillations may give rise to brightness enhancements along jets.

General theorems and various analytical self-similar solutions have recently shown that magnetized and rotating astrophysical outflows may become asymptotically cylindrical, in agreement with observations of cosmical jets. A notable common feature in all such self-consistent, self-similar MHD solutions is that before final cylindrical collimation is achieved, the jet passes from a stage of oscillations in its radius, Mach number and other physical parameters. It is shown that under rather general assumptions this oscillatory behavior of collimated outflows is not restricted to the few specific models examined so far, but instead it seems to be a rather general physical property of an MHD outflow which starts noncylindrically before it reaches collimation. It is concluded thence that astrophysical jets are structurally stable to small amplitude, time-independent perturbations in their asymptotically cylindrical shape.