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.

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.

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.

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.

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.

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.

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.