Christian Fendt

The Axisymmetric Pulsar Magnetosphere

We present, for the first time, the structure of the axisymmetric force-free magnetosphere of an aligned rotating magnetic dipole, in the case in which there exists a sufficiently large charge density (whose origin we do not question) to satisfy the ideal MHD condition, E B=0, everywhere. The unique distribution of electric current along the open magnetic field lines that is required for the solution to be continuous and smooth is obtained numerically. With the geometry of the field lines thus determined, we compute the dynamics of the associated MHD wind. The main result is that the relativistic outflow contained in the magnetosphere is not accelerated to the extremely relativistic energies required for the flow to generate gamma rays. We expect that our solution will be useful as the starting point for detailed studies of pulsar magnetospheres under more general conditions, namely, when the force-free and/or the ideal MHD condition, E B=0, are not valid in the entire magnetosphere. Based on our solution, we consider that the most likely positions of such an occurrence are the polar cap, the crossings of the zero space charge surface by open field lines, and the return current boundary, but not the light cylinder.

Can Protostellar Jets Drive Supersonic Turbulence in Molecular Clouds

Jets and outflows from young stellar objects have been proposed as candidates to drive supersonic turbulence in molecular clouds. Here we present the results from multidimensional jet simulations where we investigate in detail the energy and momentum deposition from jets into their surrounding environment and quantify the character of the excited turbulence with velocity probability density functions. Our study includes jet-clump interaction, transient jets, and magnetized jets. We find that collimated supersonic jets do not excite supersonic motions far from the vicinity of the jet. Supersonic fluctuations are damped quickly and do not spread into the parent cloud. Instead, subsonic, noncompressional modes occupy most of the excited volume. This is a generic feature that cannot be fully circumvented with overdense jets or magnetic fields. Nevertheless, jets are able to leave strong imprints in the cloud structure and can disrupt dense clumps. Our results question the ability of collimated jets to sustain supersonic turbulence in molecular clouds.

FORMATION OF PROTOSTELLAR JETS AS TWO-COMPONENT OUTFLOWS FROM STAR-DISK MAGNETOSPHERES

Axisymmetric magnetohydrodynamic simulations have been applied to investigate (1) the interrelation between a central stellar magnetosphere and stellar wind with a surrounding magnetized disk outflow, and (2) how the overall formation of a large scale jet is affected by that. The initial magnetic field distribution applied is a superposition of two components?the stellar dipole and the surrounding disk magnetic field?in either parallel or antiparallel alignment. Correspondingly, the mass outflow is launched as stellar wind plus disk wind. Our simulations evolve from an initial state in hydrostatic equilibrium with an initially force-free magnetic field configuration. Due to differential rotation between star and disk, a strong toroidal magnetic field component is induced. The stellar dipole inflates and opens up on large scale. Stellar wind and disk wind may evolve in a pair of collimated outflows. However, the existence of a reasonably strong disk wind component is essential for collimation. The classical disk jet, as known from previous numerical studies, becomes less collimated due to the pressure of the central stellar wind. In some simulations we observe the generation of strong flares triggering a sudden change in the outflow mass loss rate (or velocity) by a factor of two, accompanied by a redistribution in the radial profile of momentum flux and jet velocity across the jet. We discuss the hypothesis that these flares may trigger internal shocks in the asymptotic jets which are observed as knots.

Formation of protostellar jets - effects of magnetic diffusion

Protostellar jets most probably originate in turbulent accretion disks surrounding young stellar objects. We investigate the evolution of a disk wind into a collimated jet under the influence of magnetic diusivity, assuming that the turbulent pattern in the disk will also enter the disk corona and the jet. Using the ZEUS-3D code in the axisymmetry option we solve the time- dependent resistive MHD equations for a model setup of a central star surrounded by an accretion disk. The disk is taken as a time-independent boundary condition for the mass flow rate and the magnetic flux distribution. We derive analytical estimates for the magnitude of magnetic diusion in a protostellar jet connecting our results to earlier work in the limit of ideal MHD. We find that the diusive jets propagate slower into the ambient medium, most probably due to the lower mass flow rate in the axial direction. Close to the star we find that a quasi stationary state evolves after several hundred (weak diusion) or thousand (strong diusion) disk rotations. Magnetic diusivity aects the protostellar jet structure as follows. The jet poloidal magnetic field becomes de-collimated. The jet velocity increases with increasing diusivity, while the degree of collimation for the hydrodynamic flow remains more or less the same. We suggest that the mass flux is a proper tracer for the degree of jet collimation and find indications of a critical value for the magnetic diusivity above which the jet collimation is only weak. We finally develop a self-consistent picture in which all these eects can be explained in the framework of the Lorentz force.

ACCELERATION AND COLLIMATION OF RELATIVISTIC MAGNETOHYDRODYNAMIC DISK WINDS

We perform axisymmetric relativistic magnetohydrodynamic simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. Newtonian gravity is added to the relativistic treatment in order to establish the physical boundary condition of an underlying accretion disk in centrifugal and pressure equilibrium. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Substantial effort has been made to implement a current-free, numerical outflow boundary condition in order to avoid artificial collimation present in the standard outflow conditions. Our simulations using the PLUTO code run for 500 inner disk rotations and on a physical grid size of 100 × 200 inner disk radii. The simulations evolve from an initial state in hydrostatic equilibrium and an initially force-free magnetic field configuration. Two options for the initial field geometries are applied—an hourglass-shaped potential magnetic field and a split monopole field. Most of our parameter runs evolve into a steady state solution which can be further analyzed concerning the physical mechanism at work. In general, we obtain collimated beams of mildly relativistic speed with Lorentz factors up to 6 and mass-weighted half-opening angles of 3-7 deg. The split-monopole initial setup usually results in less collimated outflows. The light surface of the outflow magnetosphere tends to align vertically—implying three relativistically distinct regimes in the flow—an inner subrelativistic domain close to the jet axis, a (rather narrow) relativistic jet and a surrounding subrelativistic outflow launched from the outer disk surface—similar to the spine-sheath structure currently discussed for asymptotic jet propagation and stability. The outer subrelativistic disk-wind is a promising candidate for the X-ray absorption winds that are observed in many radio-quiet active galactic nuclei. The hot winds under investigation acquire only low Lorentz factors due to the rather high plasma-β we have applied in order to provide an initial force-balance in the disk corona. When we increase the outflow Poynting flux by injecting an additional disk toroidal field into the outflow, the jet velocities achieved are higher. These flows gain super-magnetosonic speed and remain Poynting flux dominated.

Bipolar Jets Launched from Accretion Disks. II. The Formation of Asymmetric Jets and Counter Jets

We investigate the jet launching process from accretion disks extending our recent study (paper I) to a truly bipolar setup. We perform axisymmetric MHD simulations of the disk-jet interaction on a computational domain covering both hemispheres, in particular addressing the question of an intrinsically asymmetric origin of jet / counter jet systems. Treating both hemispheres simultaneously, we overcome the equatorial plane symmetry boundary condition used in most previous studies which naturally fosters a symmetric evolution. For the magnetic diffusivity prescription we apply an alpha-parametrisation, considering both, globally models of diffusivity, and local models. We first approve the quality of our numerical setup by generating perfectly symmetric jets, lasting over a 1000s of dynamical time scales. We then disturb the hemispheric symmetry in the disk, and investigate the subsequent evolution of the outflow. The evolution first leads to a substantial disk warping with electric currents intersecting the equatorial plane. We investigate two models, i) a disk with (initially) different thermal scale height in both hemispheres, and ii) a symmetric disk into which a local disturbance is injected in one hemisphere. In both cases the disk asymmetry results in asymmetric outflows with mass fluxes differing by 10-20%. We find up to 30% difference in mass flux between jet and counter jet for this setup, lasting over 1000s of dynamical time scales (i.e. lasting for the whole simulation). In summary, our results suggest that the jet asymmetries in protostellar and extragalactic jets can indeed be generated intrinsically and maintained over long time by disk asymmetries and the standard jet launching mechanism.

Bipolar Jets Launched from Magnetically Diffusive Accretion Disks. I. Ejection Efficiency versus Field Strength and Diffusivity

We investigate the launching of jets and outflows from magnetically diffusive accretion disks. Using the PLUTO code, we solve the time-dependent resistive magnetohydrodynamic equations taking into account the disk and jet evolution simultaneously. The main question we address is which kind of disks launch jets and which kind of disks do not? In particular, we study how the magnitude and distribution of the (turbulent) magnetic diffusivity affect mass loading and jet acceleration. We apply a turbulent magnetic diffusivity based on α-prescription, but also investigate examples where the scale height of diffusivity is larger than that of the disk gas pressure. We further investigate how the ejection efficiency is governed by the magnetic field strength. Our simulations last for up to 5000 dynamical timescales corresponding to 900 orbital periods of the inner disk. As a general result, we observe a continuous and robust outflow launched from the inner part of the disk, expanding into a collimated jet of superfast-magnetosonic speed. For long timescales, the disks internal dynamics change, as due to outflow ejection and disk accretion the disk mass decreases. For magnetocentrifugally driven jets, we find that for (1) less diffusive disks, (2) a stronger magnetic field, (3) a low poloidal diffusivity, or (4) a lower numerical diffusivity (resolution), the mass loading of the outflow is increased—resulting in more powerful jets with high-mass flux. For weak magnetization, the (weak) outflow is driven by the magnetic pressure gradient. We consider in detail the advection and diffusion of magnetic flux within the disk and we find that the disk and outflow magnetization may substantially change in time. This may have severe impact on the launching and formation process—an initially highly magnetized disk may evolve into a disk of weak magnetization which cannot drive strong outflows. We further investigate the jet asymptotic velocity and the jet rotational velocity in respect of the different launching scenarios. We find a lower degree of jet collimation than previous studies, most probably due to our revised outflow boundary condition.

Accretion Disks Around Massive Stars: Hydrodynamic Structure, Stability, and Dust Sublimation

We investigate the structure of accretion disks around massive protostar applying steady state models of thin disks. The thin disk equations are solved with proper opacities for dust and gas taking into account the huge temperature variation along the disk. We explore a wide parameter range concerning stellar mass, accretion rate, and viscosity parameter α. The most essential finding is a very high temperature of the inner disk. For e.g., a 10 M ☉ protostar with an accretion rate of ~10–4 M ☉ yr–1, the disk midplane temperature may reach almost 105 K. The disk luminosity in this case is about 104 L ☉ and, thus, potentially higher than that of a massive protostar. We motivate our disk model with similar hot disks around compact stars. We calculate a dust sublimation radius by turbulent disk self-heating of more than 10 AU, a radius, which is 3 times larger than that caused by stellar irradiation. We discuss implications of this result on the flashlight effect and the consequences for the radiation pressure of the central star. In deference to disks around low-mass protostars, our models suggest rather high values for the disk turbulence parameter α ≤ 1. However, disk stability to fragmentation due to thermal effects and gravitational instability would require a lower α value. For α = 0.1, we find stable disks out to 80 AU. Essentially, our model allows us to compare the outer disk to some of the observed massive protostellar disk sources, and from that, extrapolate the disk structure close to the star which is yet impossible to observe.

Full characterization of binary-lens event OGLE-2002-BLG-069 from PLANET observations

We analyze the photometric data obtained by PLANET and OGLE on the caustic-crossing binary-lens microlensing event OGLE-2002-BLG-069. Thanks to the excellent photometric and spectroscopic coverage of the event, we are able to constrain the lens model up to the known ambiguity between close and wide binary lenses. The detection of annual parallax in combination with measurements of extended-source effects allows us to determine the mass, distance and velocity of the lens components for the competing models. While the model involving a close binary lens leads to a Bulge-Disc lens scenario with a lens mass of M=(0.51 +- 0.15) M_sol and distance of D_L=(2.9 +- 0.4) kpc, the wide binary lens solution requires a rather implausible binary black-hole lens (M >=126 M_sol). Furthermore we compare current state-of-the-art numerical and empirical models for the surface brightness profile of the source, a G5III Bulge giant. We find that a linear limb-darkening model for the atmosphere of the source star is consistent with the data whereas a PHOENIX atmosphere model assuming LTE and with no free parameter does not match our observations.

Magnetically driven superluminal motion from rotating black holes - Solution of the magnetic wind equation in Kerr metric

We have investigated magnetically driven superluminal jets originating from rotating black holes. The stationary, general relativistic, magnetohydrodynamic wind equation along collimating magnetic flux surfaces has been solved numerically. Our jet solutions are calculated on a global scale of a spatial range from several to several 1000 gravitational radii. Dierent magnetic eld geometries were investigated, parameterized by the shape of the magnetic flux surface and the magnetic flux distribution. For a given magnetic flux surface we obtain the complete set of physical parameters for the jet flow. In particular, we apply our results to the Galactic superluminal sources GRS 1915+105 and GRO 1655 40. Motivated by the huge size indicated for the Galactic superluminal knots of about 10 9 Schwarzschild radii, we point out the possibility that the jet collimation process in these sources may be less ecient and therefore intrinsically dierent to the AGN. Our results show that the observed speed of more than 0.9c can be achieved in general by magnetohydrodynamic acceleration. The velocity distribution along the magnetic eld has a saturating prole. The asymptotic jet velocity depends either on the plasma magnetization (for a xed eld structure) or on the magnetic flux distribution (for xed magnetization). The distance where the asymptotic velocity is reached, is below the observational resolution for GRS 1915+105 by several orders of magnitude. Further, we nd that highly relativistic speeds can be reached also for jets not emerging from a region close to the black hole, if the flow magnetization is suciently large. The plasma temperature rapidly decreases from about 10 10 K at the foot point of the jet to about 10 6 K at a distance of 5000 gravitational radii from the source. Temperature and the mass density follow a power law distribution with the radius. The jet magnetic eld is dominated by the toroidal component, whereas the velocity eld is dominated by the poloidal component.