arXiv subjects
Publications and source records attributed to Christian Fendt.
Magnetic fields are fundamental to the dynamics of both accretion disks and the jets that they often drive. We review the basic physics of these phenomena, the past and current efforts to model them numerically with an emphasis on the jet-disk connection, and the observational constraints on the role of magnetic fields in the jets of active galaxies on all scales.
We present MHD simulations exploring the launching, acceleration and collimation of jets and disk winds. The evolution of the disk structure is consistently taken into account. Extending our earlier studies, we now consider the self-generation of the magnetic field by an $α^2Ω$ mean-field dynamo. The disk magnetization remains on a rather low level, that helps to evolve the simulations for $T > 10,000$ dynamical time steps on a domain extending 1500 inner disk radii. We find a magnetic field of the inner disk similar to the commonly found open field structure, favoring magneto-centrifugal launching. The outer disk field is highly inclined and predominantly radial. Here, differential rotation induces a strong toroidal component that plays a key role in outflow launching. These outflows from the outer disk are slower, denser, and less collimated. If the dynamo action is not quenched, magnetic flux is continuously generated, diffuses outward the disk, and fills the entire disk. We have invented a toy model triggering a time-dependent mean-field dynamo. The duty cycles of this dynamo lead to episodic ejections on similar timescales. When the dynamo is suppressed as the magnetization falls below a critical value, the generation of the outflows and also accretion is inhibited. The general result is that we can steer episodic ejection and {\em large-scale jet knots} by a {\em disk-intrinsic dynamo} that is time-dependent and regenerates the jet-launching magnetic field.
We present results of axisymmetric magnetohydrodynamic (MHD) simulations investigating the launching of jets and outflows from a magnetically diffusive accretion disk. The time evolution of the disk structure is self-consistently taken into account. In contrast to previous works we have applied {\em spherical} coordinates for the numerical grid, implying substantial benefits concerning the numerical resolution and the stability of the simulation. Thanks to the new setup we were able to run simulations for more than 150,000 dynamical times on a domain extending 1500 inner disk radii with a resolution of up to 24 cells per disk height in the inner disk. Depending on the disk magnetization, jet launching occurs in two different but complementary regimes - jets driven predominantly by centrifugal or magnetic forces. These regimes differ in the ejection efficiency concerning mass, energy and angular momentum. We show that it is the {\em actual} disk magnetization and not so much the initial magnetization which describes the disk-jet evolution best. Considering the actual disk magnetization we also find that simulations starting with different initial magnetization evolve in a similar - typical - way as due to advection and diffusion the magnetic flux in the disk evolves in time. Exploring a new, modified diffusivity model we confirm the self-similar structure of the global jet-launching disk, obtaining power laws for the radial profiles of the disk physical variables such as density, magnetic field strength, or accretion velocity.
We present results of magnetohydrodynamic (MHD) simulations of jet formation and propagation, discussing a variety of astrophysical setups. In the first approach we consider simulations of relativistic MHD jet formation, considering jets launched from the surface of a Keplerian disk, demonstrating numerically - for the first time - the self-collimating ability of relativistic MHD jets. We obtain Lorentz factors up to about 10 while acquiring a high degree of collimation of about 1 degree. We then present synchrotron maps calculated from the intrinsic jet structure derived from the MHD jet formation simulation. We finally present (non-relativistic) MHD simulations of jet lauching, treating the transition between accretion and ejection. These setups include a physical magnetic diffusivity which is essential for loading the accretion material onto the outflow. We find relatively high mass fluxes in the outflow, of the order of 20-40 % of the accretion rate.
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.
We investigate the launching of jets and outflows from magnetically diffusive accretion disks. Using the PLUTO code we solve the time-dependent resistive MHD equations taking into account the disk and jet evolution simultaneously. The main question we address is which kind of disks do 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 have applied a turbulent magnetic diffusivity based on α-prescription, but have 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 time scales 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 super fast magneto-sonic speed. For long time scales the disk internal dynamics changes, as due to outflow ejection and disk accretion the disk mass decreases. For magneto-centrifugally driven jets we find that for i) less diffusive disks, ii) a stronger magnetic field, iii) a low poloidal diffusivity, or a iv) 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 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.
Observations indicate that outflows from massive young stars are more collimated during their early evolution compared to later stages. Our paper investigates various physical processes that impacts the outflow dynamics, i.e. its acceleration and collimation. We perform axisymmetric MHD simulations particularly considering the radiation pressure exerted by the star and the disk. We have modified the PLUTO code to include radiative forces in the line-driving approximation. We launch the outflow from the innermost disk region (r < 50 AU) by magneto-centrifugal acceleration. In order to disentangle MHD effects from radiative forces, we start the simulation in pure MHD, and later switch on the radiation force. We perform a parameter study considering different stellar masses (thus luminosity), magnetic flux, and line-force strength. For our reference simulation - assuming a 30 Msun star, we find substantial de-collimation of 35 % due to radiation forces. The opening angle increases from 20 deg to 32 deg for stellar masses from 20 Msun to 60 Msun. A small change in the line-force parameter 'alpha' from 0.60 to 0.55 changes the opening angle by ~ 8 deg. We find that it is mainly the stellar radiation which affects the jet dynamics. Unless the disk extends very close to the star, its pressure is too small to have much impact. Essentially, our parameter runs with different stellar mass can be understood as a proxy for the time evolution of the star-outflow system. Thus, we have shown that when the stellar mass (thus luminosity) increases (with age), the outflows become less collimated.
In this paper we present a detailed numerical investigation of the hypothesis that a rotation of astrophysical jets can be caused by magnetohydrodynamic shocks in a helical magnetic field. Shock compression of the helical magnetic field results in a toroidal Lorentz force component which will accelerate the jet material in toroidal direction. This process transforms magnetic angular momentum (magnetic stress) carried along the jet into kinetic angular momentum (rotation). The mechanism proposed here only works in a helical magnetic field configuration. We demonstrate the feasibility of this mechanism by axisymmetric MHD simulations in 1.5D and 2.5D using the PLUTO code. In our setup the jet is injected into the ambient gas with zero kinetic angular momentum (no rotation). Different dynamical parameters for jet propagation are applied such as the jet internal Alfven Mach number and fast magnetosonic Mach number, the density contrast of jet to ambient medium, or the external sonic Mach number of the jet. The mechanism we suggest should work for a variety of jet applications, e.g. protostellar or extragalactic jets, and internal jet shocks (jet knots) or external shocks between the jet and ambient gas (entrainment). For typical parameter values for protostellar jets, the numerically derived rotation feature looks consistent with the observations, i.e. rotational velocities of 0.1-1 percent of the jet bulk velocity.
The goal of this paper is to derive signatures of synchrotron radiation from state-of-the-art simulation models of collimating relativistic magnetohydrodynamic (MHD) jets featuring a large-scale helical magnetic field. We perform axisymmetric special relativistic MHD simulations of the jet acceleration region using the PLUTO code. The computational domain extends from the slow magnetosonic launching surface of the disk up to 6000^2 Schwarzschild radii allowing to reach highly relativistic Lorentz factors. The Poynting dominated disk wind develops into a jet with Lorentz factors of 8 and is collimated to 1 degree. In addition to the disk jet, we evolve a thermally driven spine jet, emanating from a hypothetical black hole corona. Solving the linearly polarized synchrotron radiation transport within the jet, we derive VLBI radio and (sub-) mm diagnostics such as core shift, polarization structure, intensity maps, spectra and Faraday rotation measure (RM), directly from the Stokes parameters. We also investigate depolarization and the detectability of a lambda^2-law RM depending on beam resolution and observing frequency. We find non-monotonic intrinsic RM profiles which could be detected at a resolution of 100 Schwarzschild radii. In our collimating jet geometry, the strict bi-modality in polarization direction (as predicted by Pariev et al.) can be circumvented. Due to relativistic aberration, asymmetries in the polarization vectors across the jet can hint to the spin direction of the central engine.
Using axisymmetric MHD simulations we investigate how the overall jet formation is affected by a variation in the disk magnetic flux profile and/or the existence of a central stellar magnetosphere. Our simulations evolve from an initial, hydrostatic equilibrium state in a force-free magnetic field configuration. We find a unique relation between the collimation degree and the disk wind magnetization power law exponent. The collimation degree decreases for steeper disk magnetic field profiles. Highly collimated outflows resulting from a flat profile tend to be unsteady. We further consider a magnetic field superposed of a stellar dipole and a disk field in parallel or anti-parallel alignment. Both stellar and disk wind may evolve in a pair of outflows, however, a reasonably strong disk wind component is essential for jet collimation. Strong flares may lead to a sudden change in mass flux by a factor two. We hypothesize that such flares may eventually trigger jet knots.
We discuss numerical results of relativistic magnetohydrodynamic (MHD) jet formation models. We first review some examples of stationary state solutions treating the collimation and acceleration process of relativistic MHD jets. We provide an a posteriori check for the MHD condition in highly magnetized flows, namely the comparison of particle density to Goldreich-Julian density. Using the jet dynamical parameters calculated from the MHD model we show the rest-frame thermal X-ray spectra of the jet, from which we derive the overall spectrum taking into account a variation of Doppler boosting and Doppler shift of emission lines along the outflow. Finally, we present preliminary results of relativistic MHD simulations of jet formation demonstrating the acceleration of a low velocity (0.01c) disk wind to a collimated high velocity (0.8c).
Axisymmetric magnetohydrodynamic (MHD) simulations have been applied to investigate the interrelation of a central stellar magnetosphere and stellar wind with a surrounding magnetized disk outflow and how the overall formation of a large scale jet is affected. The initial magnetic field distribution applied is a superposition of two components - a stellar dipole and a surrounding disk magnetic field, in both either parallel or anti-parallel alignment. Correspondingly, the mass outflow is launched as stellar wind plus a disk wind. Our simulations evolve from an initial state in hydrostatic equilibrium and an initially force-free magnetic field configuration. Due to initial differential rotation and induction of a strong toroidal magnetic field the stellar dipolar field inflates and is disrupted on large scale. Stellar and disk wind may evolve in a pair of collimated outflows. The existence of a reasonably strong disk wind component is essential for collimation. A disk jet as known from previous numerical studies will become de-collimated by the stellar wind. In some simulations we observe the generation of strong flares triggering a sudden change in the outflow mass loss rate by a factor of two and also a re-distribution 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.
Jets and outflows from young stellar objects are proposed candidates to drive supersonic turbulence in molecular clouds. Here, we present the results from multi-dimensional 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 include jet--clump interaction, transient jets, and magnetised 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, non-compressional modes occupy most of the excited volume. This is a generic feature which can not be fully circumvented by overdense jets or magnetic fields. Nevertheless, jets are able to leave strong imprints in their cloud structure and can disrupt dense clumps. Our results question the ability of collimated jets to sustain supersonic turbulence in molecular clouds.
NGC 4258 is a well known spiral galaxy with a peculiar large scale jet flow detected in the radio and in H-alpha. Due to the special geometry of the galaxy, the jets emerge from the nuclear region through the galactic disk. Also the distribution of molecular gas looks different from that in other spiral galaxies: [12]CO(1-0)emission has only been detected in the center and along the jets and only up to distances of about 50 arcsec (1.8 kpc) from the nucleus. The reason for the CO concentration along the inner jets in NGC 4258 was not understood and is the motivation for the observations presented here. Using the IRAM interferometer, we mapped the [12]CO(1-0) emission of the central part of NGC 4258 along the nuclear jet direction in the inner 3 kpc. We detected two parallel CO ridges along a position angle of -25 degr with a total length of about 80 arcsec (2.8 kpc), separated by a CO-depleted funnel with a width of about 5 arcsec (175 pc). The H-alpha emission is more extended and broader than the CO emission with its maximum just in between the two CO ridges. In CO we see a peculiar velocity distribution in the iso-velocity map and p-v diagrams. We discuss different scenarios for an interpretation and present a model which can explain the observational results consistently. We propose here that the concentration of CO along the ridges is due to interaction of the rotating gas clouds with the jet's magnetic field by ambipolar diffusion. This magnetic interaction is thought to increase the time the molecular clouds reside near the jet thus leading to the quasi-static CO ridge.
We have applied axisymmetric MHD simulations to investigate the impact of the accretion disk magnetic flux profile on the jet collimation. Using the ZEUS-3D code modified for magnetic diffusivity, our simulations evolve from an initial hydrostatic equilibrium state in a force-free magnetic field. Considering a power law for the disk poloidal magnetic field profile Bp ~ r^{-mu} and for the disk wind density profile rho ~ r^{-mu_rho} we performed a systematic study over a wide parameter range mu and mu_rho. We find a degree of collimation (ratio of mass flow rates in axial and lateral direction) decreasing for steeper disk magnetic field profiles (increasing mu). Varying the total magnetic flux doesn't change the degree of jet collimation substantially, it only affects the time scale of outflow evolution and the terminal jet speed. As our major result we find a general relation between the collimation degree with the disk wind magnetization power law exponent. Outflows with high collimation degree resulting from a flat disk magnetic field profile tend to be unsteady, producing axially propagating knots as discussed earlier. Depending slightly on the inflow density profile this unsteady behavior sets in for mu < 0.4. We also performed simulations of jet formation with artificially enhanced decay of the toroidal magnetic field in order to investigate the idea of a purely "poloidal collimation" discussed in the literature. These outflows remain weakly collimated and propagate with lower velocity. Thanks to our large numerical grid size (7x14 AU for protostars), we may apply our results to recently observed hints of jet rotation (DG Tau) indicating a relatively flat disk magnetic field profile, mu ~ 0.5. In general, our results are applicable to both stellar and extragalactic sources of MHD jets.
We review advances in the theoretical and computational studies of disk winds, jets and outflows including: the connection between accretion and jets, the launch of jets from magnetized disks, the coupled evolution of jets and disks, the interaction of magnetized young stellar objects with their surrounding disks and the relevance to outflows, and finally, the link between jet formation and gravitational collapse. We also address the predictions that the theory makes about jet kinematics, collimation, and rotation, that have recently been confirmed by high spatial and spectral resolution observations. Disk winds have a universal character that may account for jets and outflows during the formation of massive stars as well as brown dwarfs.
We investigate possible formation sites of the cannonballs (in the gamma ray bursts context) by calculating their physical parameters, such as density, magnetic field and temperature close to the origin. Our results favor scenarios where the cannonballs form as instabilities (knots) within magnetized jets from hyperaccreting disks. These instabilities would most likely set in beyond the light cylinder where flow velocity with Lorentz factors as high as 2000 can be achieved. Our findings challenge the cannonball model of gamma ray bursts if these indeed form inside core-collapse supernovae (SNe) as suggested in the literature; unless hyperaccreting disks and the corresponding jets are common occurrences in core-collapse SNe.
We present a detailed numerical study of the dynamics and evolution of ultrarelativistic magnetohydrodynamic jets in the black hole-disk system under extreme magnetization conditions. We find that Lorentz factors of up to 3000 are achieved and derived a modifiedMichel scaling (Gamma ~ sigma) which allows for a wide variation in the flow Lorentz factor. Pending contamination induced by mass-entrainment, the linear Michel scaling links modulations in the ultrarelativistic wind to variations in mass accretion in the disk for a given magnetization. The jet is asymptotically dominated by the toroidal magnetic field allowing for efficient collimation. We discuss our solutions (jets) in the context of Gamma ray bursts and describe the relevant features such as the high variability in the Lorentz factor and how high collimation angles (~ 0-5 degrees), or cylindrical jets, can be achieved. We isolate a jet instability mechanism we refer to as the "bottle-neck" instability which essentially relies on a high magnetization and a recollimation of the magnetic flux surfaces. The instability occurs at large radii where any dissipation of the magnetic energy into radiation would in principle result in an optically thin emission.