The Effects of Large-Scale Magnetic Fields on Disk Formation and Evolution

This is a draft chapter for a book, entitled Physical Processes in Circumstellar Disks around Young Stars, which is scheduled for publication by the University of Chicago Press as one of its Theoretical Astrophysics Series volumes. Sect. 1 presents the motivation for considering the effects of a large-scale, ordered magnetic field on the formation and evolution of protostellar disks. Sect. 2 outlines the physical principles that underlie the magnetohydrodynamics of disks that are threaded by such a field. Sect. 3 discusses the formation and early evolution of disks that result from the collapse of a rotating molecular cloud core that is coupled to the insterstellar magnetic field. Sect. 4 reviews the observational evidence for the disk--wind connection and describes the structure of magnetically accelerated disk outflows, focusing on centrifugally driven winds; it then goes on to discuss the equilibrium and stability properties of weakly ionized protostellar accretion disks in which the transport of angular momentum is dominated by a wind of this type. Sect. 5 considers the coupling between the central protostar and the surrounding disk through the protostellar magnetic field, covering, in turn, the phenomenology, basic concepts, and results of numerical simulations. The chapter is summarized in Sect. 6, which also contains a discussion of future research directions.Comment: 68 pages, 8 figures, to appear in Physical Processes in Circumstellar Disks around Young Stars, ed. P. J. V. Garcia (Chicago: University of Chicago Press), uses svmult.cl

Magnetorotational Instability in Protostellar Discs

We investigate the linear growth and vertical structure of the magnetorotational instability (MRI) in weakly ionised, stratified accretion discs. The magnetic field is initially vertical and perturbations have vertical wavevectors only. Solutions are obtained at representative radial locations from the central protostar for different choices of the initial magnetic field strength, sources of ionisation, disc structure and configuration of the conductivity tensor. The MRI is active over a wide range of magnetic field strengths and fluid conditions in low conductivity discs. For the minimum-mass solar nebula model, incorporating cosmic ray and x-ray ionisation and assuming that charges are carried by ions and electrons only, perturbations grow at 1 AU for B 200 mG), ambipolar diffusion alters the envelope shapes of the unstable modes, which peak at an intermediate height, instead of being mostly flat as modes in the Hall limit are in this region of parameter space. Similarly, when cosmic rays are assumed to be excluded from the disc by the winds emitted by the magnetically active protostar, unstable modes grow at this radius for B 100 mG (B ~ 1 mG), but for weaker fields, a small dead region exists. When a population of 0.1 um grains is assumed to be present, perturbations grow at 10 AU for B < 10 mG. We estimate that the figure for R = 1 AU would be of order 400 mG. We conclude that, despite the low magnetic coupling, the magnetic field is dynamically important for a large range of fluid conditions and field strengths in protostellar discs. An example of such magnetic activity is the generation of MRI unstable modes, which are supported at 1 AU for field strengths up to a few gauss. Hall diffusion largely determines the structure and growth rate of these perturbations for all studied radii. At radii of order 1 AU, in particular, it is crucial to incorporate the full conductivity tensor in the analysis of this instability, and more generally, in studies of the dynamics of astrophysical discs

Enhanced MHD transport in astrophysical accretion flows: turbulence, winds and jets

Astrophysical accretion is arguably the most prevalent physical process in the Universe; it occurs during the birth and death of individual stars and plays a pivotal role in the evolution of entire galaxies. Accretion onto a black hole, in particular, is also the most efficient mechanism known in nature, converting up to 40% of accreting rest mass energy into spectacular forms such as high-energy (X-ray and gamma-ray) emission and relativistic jets. Whilst magnetic fields are thought to be ultimately responsible for these phenomena, our understanding of the microphysics of MHD turbulence in accretion flows as well as large-scale MHD outflows remains far from complete. We present a new theoretical model for astrophysical disk accretion which considers enhanced vertical transport of momentum and energy by MHD winds and jets, as well as transport resulting from MHD turbulence. We also describe new global, 3D simulations that we are currently developing to investigate the extent to which non-ideal MHD effects may explain how small-scale, turbulent fields (generated by the magnetorotational instability -- MRI) might evolve into large-scale, ordered fields that produce a magnetized corona and/or jets where the highest energy phenomena necessarily originate.Comment: 8 pages, 2 figures. Minor revision, published version: Proc 14th International Congress on Plasma Physics, Fukuoka, Japan, Sep 200

Multi-epoch Sub-arcsecond [Fe II] Spectroimaging of the DG Tau Outflows with NIFS. II. On the Nature of the Bipolar Outflow Asymmetry

The origin of bipolar outflow asymmetry in young stellar objects (YSOs) remains poorly understood. It may be due to an intrinsically asymmetric outflow launch mechanism, or it may be caused by the effects of the ambient medium surrounding the YSO. Answering this question is an important step in understanding outflow launching. We have investigated the bipolar outflows driven by the T Tauri star DG Tauri on scales of hundreds of AU, using the Near-infrared Integral Field Spectrograph (NIFS) on Gemini North. The approaching outflow consists of a well-collimated jet, nested within a lower-velocity disc wind. The receding outflow is composed of a single-component bubble-like structure. We analyse the kinemat- ics of the receding outflow using kinetic models, and determine that it is a quasi-stationary bubble with an expanding internal velocity field. We propose that this bubble forms because the receding counterjet from DG Tau is obstructed by a clumpy ambient medium above the circumstellar disc surface, based on similarities between this structure and those found in the modeling of active galactic nuclei outflows. We find evidence of interaction between the obscured counterjet and clumpy ambient material, which we attribute to the large molecular envelope around the DG Tau system. An analytical model of a momentum-driven bubble is shown to be consistent with our interpretation. We conclude that the bipolar outflow from DG Tau is intrinsically symmetric, and the observed asymmetries are due to environmental effects. This mechanism can potentially be used to explain the observed bipolar asymmetries in other YSO outflows.Comment: 16 pages, 10 figures, accepted for publication in MNRA

Wind-driving protostellar accretion discs. II. Numerical method and illustrative solutions

(abridged) We continue our study of weakly ionized protostellar discs that are threaded by a large-scale magnetic field and power a centrifugally driven wind. It has been argued that in several protostellar systems such a wind transports a significant fraction of the angular momentum from at least some part of the disc. We model this case by considering a radially localized disc model in which the matter is well coupled to the field and the wind is the main repository of excess angular momentum. We consider stationary solutions in which magnetic diffusion counters the shearing and advection of the field lines. In Wardle & K\"onigl we analysed the disc structure in the hydrostatic approximation and presented disc/wind solutions for the ambipolar diffusivity regime. In K\"onigl, Salmeron & Wardle (Paper I) we generalized the hydrostatic analysis to the Hall and Ohm diffusivity domains and identified the parameter sub-regimes in which viable solutions occur. In this paper we test these results by deriving numerical solutions (integrated through the sonic critical surface) of the disc equations in the Hall domain. We confirm the predictions of the hydrostatic analysis and demonstrate its usefulness for clarifying the behaviour of the derived solutions. We show that the solutions can be extended to larger scales (so that they also cross the Alfv\'en critical surface) by matching the localized disc solutions to global wind solutions of the type introduced by Blandford & Payne. To facilitate this matching, we construct a library of wind solutions, which is made available to the community. The results presented in Wardle & K\"onigl, Paper I and this work form a comprehensive framework for the study of wind-driving accretion discs in protostellar and other astrophysical environments. This tool could be useful for interpreting observations and for guiding numerical simulations of such systems.Comment: 20 pages, 13 figures, 3 tables; submitted for publication in MNRA

New Global 3D MHD Simulations of Black Hole Disk Accretion and Outflows

It is widely accepted that quasars and other active galactic nuclei (AGN) are powered by accretion of matter onto a central supermassive black hole. While numerical simulations have demonstrated the importance of magnetic fields in generating the turbulence believed necessary for accretion, so far they have not produced the high mass accretion rates required to explain the most powerful sources. We describe new global 3D simulations we are developing to assess the importance of radiation and non-ideal MHD in generating magnetized outflows that can enhance the overall rates of angular momentum transport and mass accretion.Comment: 2 pages, including 1 colour figure. To appear in proceedings of IAU Symposium 259: "Cosmic Magnetic Fields: From Planets, To Stars and Galaxies", Tenerife, Nov 200

Turbulent mixing layers in supersonic protostellar outflows, with application to DG Tauri

Turbulent entrainment processes may play an important role in the outflows from young stellar objects at all stages of their evolution. In particular, lateral entrainment of ambient material by high-velocity, well-collimated protostellar jets may be the cause of the multiple emission-line velocity components observed in the microjet-scale outflows driven by classical T Tauri stars. Intermediate-velocity outflow components may be emitted by a turbulent, shock- excited mixing layer along the boundaries of the jet. We present a formalism for describing such a mixing layer based on Reynolds decomposition of quantities measuring fundamental properties of the gas. In this model, the molecular wind from large disc radii provides a continual supply of material for entrainment. We calculate the total stress profile in the mixing layer, which allows us to estimate the dissipation of turbulent energy, and hence the luminosity of the layer. We utilize MAPPINGS IV shock models to determine the fraction of total emission that occurs in [Fe II] 1.644 {\mu}m line emission in order to facilitate comparison to previous observations of the young stellar object DG Tauri. Our model accurately estimates the luminosity and changes in mass outflow rate of the intermediate-velocity component of the DG Tau approaching outflow. Therefore, we propose that this component represents a turbulent mixing layer surrounding the well-collimated jet in this object. Finally, we compare and contrast our model to previous work in the field.Comment: 18 pages, 13 figures, accepted for publication in MNRA

Tables of phase functions, opacities, albedos, equilibrium temperatures, and radiative accelerations of dust grains in exoplanets

There has been growing observational evidence for the presence of condensates in the atmospheres and/or comet-like tails of extrasolar planets. As a result, systematic and homogeneous tables of dust properties are useful in order to facilitate further observational and theoretical studies. In this paper we present calculations and analysis of non-isotropic phase functions, asymmetry parameter (mean cosine of the scattering angle), absorption and scattering opacities, single scattering albedos, equilibrium temperatures, and radiative accelerations of dust grains relevant for extrasolar planets. Our assumptions include spherical grain shape, Deirmendjian particle size distribution, and Mie theory. We consider several species: corundum/alumina, perovskite, olivines with 0 and 50 per cent iron content, pyroxenes with 0, 20, and 60 per cent iron content, pure iron, carbon at two different temperatures, water ice, liquid water, and ammonia. The presented tables cover the wavelength range of 0.2–500 μm and modal particle radii from 0.01 to 100 μm. Equilibrium temperatures and radiative accelerations assume irradiation by a non-blackbody source of light with temperatures from 7000 to 700 K seen at solid angles from 2π to 10−6 sr. The tables are provided to the community together with a simple code which allows for an optional, finite, angular dimension of the source of light (star) in the phase function

Magnetorotational instability in stratified, weakly ionized accretion discs

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionized accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and is assumed to be constant with height. We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field and coupling between ionized and neutral components of the fluid. The envelopes of short-wavelength perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation. Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic 'dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly ionized discs

Hall diffusion and the magnetorotational instability in protoplanetary discs

The destabilizing effect of Hall diffusion in a weakly ionized Keplerian disc allows the magnetorotational instability (MRI) to occur for much lower ionization levels than would otherwise be possible. However, simulations incorporating Hall and Ohm diffusion give the impression that the consequences of this for the non-linear saturated state are not as significant as suggested by the linear instability. Close inspection reveals that this is not actually the case as the simulations have not yet probed the Hall-dominated regime. Here we revisit the effect of Hall diffusion on the MRI and the implications for the extent of magnetohydrodynamic (MHD) turbulence in protoplanetary discs, where Hall diffusion dominates over a large range of radii. We conduct a local, linear analysis of the instability for a vertical, weak magnetic field subject to axisymmetric perturbations with a purely vertical wave vector. In contrast to previous analyses, we express the departure from ideal MHD in terms of Hall and Pedersen diffusivities η H and η P, which provide transparent notation that is directly connected to the induction equation. This allows us to present a crisp overview of the dependence of the instability on magnetic diffusivity. We present analytic expressions and contours in the η H-η P plane for the maximum growth rate and corresponding wavenumber, the upper cut-off for unstable wavenumbers and the loci that divide the plane into regions of different characteristic behaviour. We find that for where v A is the Alfvén speeds and Ω is the Keplerian frequency, Hall diffusion suppresses the MRI irrespective of the value of η P. In the highly diffusive limit, the magnetic field decouples from the fluid perturbations and simply diffuses in the background Keplerian shear flow. The diffusive MRI reduces to a diffusive plane-parallel shear instability with effective shear rate (3/2)Ω. We give simple analytic expressions for the growth rate and wavenumber of the most unstable mode. We review the varied and confusing parametrizations of magnetic diffusion in discs that have appeared in the literature, and confirm that simulations examining the saturation of the instability under Hall-Ohm diffusion are consistent with the linear analysis and have yet to probe the 'deep' Hall regime characteristic of protoplanetary discs where Hall diffusion is expected to overcome resistive damping. Finally, we illustrate the critical effect of Hall diffusion on the extent of dead zones in protoplanetary discs by applying a local stability criterion to a simple model of the minimum-mass solar nebula at 1au, including X-ray and cosmic ray ionization and a population of 1-m grains. Hall diffusion increases or decreases the MRI-active column density by an order of magnitude or more, depending on whether B is parallel or antiparallel to the rotation axis, respectively. We conclude that existing estimates of the depth of magnetically active layers in protoplanetary discs based on damping by Ohm diffusion are likely to be wildly inaccurate