Nektarios Vlahakis

Magnetic acceleration of ultrarelativistic jets in gamma-ray burst sources

We present numerical simulations of axi symmetric, 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 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 ≥ 10 2 on scales ∼ 10 10 -10 12 cm, consistent with the possibility that long/soft GRB jets are accelerated within envelopes of collapsing massive stars, and r ≥ 30 on scales ∼9 x 10 8 -3 x 10 10 cm, 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 Γθ v ∼ 1 for outflows that undergo an efficient magnetic-to-kinetic energy conversion, where θ v 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 θ v ≤ 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.

Relativistic Magnetohydrodynamics with Application to Gamma-Ray Burst Outflows. I. Theory and Semianalytic Trans-Alfvénic Solutions

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-Alfv?nic solutions and consider outflows that are super-Alfv?nic 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.

Magnetic Driving of Relativistic Outflows in Active Galactic Nuclei. I. Interpretation of Parsec-Scale Accelerations

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.

Systematic construction of exact magnetohydrodynamic models for astrophysical winds and 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.

A disc-wind model with correct crossing of all magnetohydrodynamic critical surfaces

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, Alfven 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.

RELATIVISTIC MAGNETOHYDRODYNAMICS WITH APPLICATION TO GAMMA-RAY BURST OUTFLOWS. II. SEMIANALYTIC SUPER-ALFVENIC SOLUTIONS

We present exact radially self-similar solutions of special relativistic magnetohydrodynamics representing hot super-Alfv?nic 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-Alfv?nic 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-Alfv?nic 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-Alfv?nic flows.

Rarefaction acceleration of ultrarelativistic magnetized jets in gamma-ray burst sources

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.

Ideal Magnetohydrodynamic Solution to the σ Problem in Crab-like Pulsar Winds and General Asymptotic Analysis of Magnetized Outflows

Using relativistic, steady, axisymmetric, ideal magnetohydrodynamics (MHD), we analyze the super-Alfvenic 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.

Relativistic Parker winds with variable effective polytropic index

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.

SYNTHETIC SYNCHROTRON EMISSION MAPS FROM MHD MODELS FOR THE JET OF M87

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.