Protostellar Accretion Disks Research Articles

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

We continue our study of weakly ionized protostellar accretion discs that are threaded by a large-scale magnetic field and power a centrifugally driven wind. It has been argued that there is already evidence in several protostellar systems that such a wind transports a significant fraction of the angular momentum from at least some part of the disc. We model this situation by considering a radially localized disc model in which the matter is everywhere well coupled to the field and the wind is the main repository of excess angular momentum. We consider stationary configurations in which magnetic diffusivity counters the shearing and advection of the magnetic field lines. In Wardle & Königl we analysed the disc structure in the hydrostatic approximation (vertical motions neglected inside the disc) and presented exact disc/wind solutions for the ambipolar diffusivity regime. In Königl, Salmeron & Wardle (Paper I) we generalized the hydrostatic analysis to the Hall and Ohm diffusivity domains and used it to identify the disc parameter sub-regimes in which viable solutions with distinct physical properties can be expected to occur. In this paper we test the results of Paper I by deriving full numerical solutions (integrated through the sonic critical surface) of the disc equations in the Hall domain. We confirm all the predictions of the hydrostatic analysis and demonstrate its usefulness for clarifying the behaviour of the derived solutions. We further show that the outflow solutions can be extended to larger scales (so that, in particular, they also cross the Alfvén critical surface) by matching the localized disc solutions to global ‘cold’ wind solutions of the type introduced by Blandford & Payne. To facilitate this matching, we construct a library of wind solutions for a wide range of wind model parameters; this library is made available to the community. The results presented in Wardle & Königl, Paper I and this work combine to form a comprehensive framework for the study of wind-driving accretion discs in protostellar and other astrophysical environments. This theoretical tool could be useful for interpreting observations and for guiding numerical simulations of such systems.

The near-infrared reflected spectrum of source I in Orion-KL

Source I in the Orion-KL nebula is believed to be the nearest example of a massive star still in the main accretion phase. It is thus one of the best cases for studying the properties of massive protostars to constrain high-mass star formation theories. Near-infrared radiation from source I escapes through the cavity opened by the OMC1 outflow and is scattered by dust towards our line of sight. The reflected spectrum offers a unique possibility of observing the emission from the innermost regions of the system and probing the nature of source I and its immediate surroundings. We obtained moderately high spectral-resolution (R~9000) observations of the near-infrared diffuse emission in several locations around source I/Orion-KL. We observed a widespread rich absorption line spectrum that we compare with cool stellar photospheres and protostellar accretion disk models. The spectrum is broadly similar to strongly veiled, cool, low-gravity stellar photospheres in the range Teff~3500-4500 K, luminosity class I-III. An exact match explaining all features has not been found, and a plausible explanation is that a range of different temperatures contribute to the observed absorption spectrum. The 1D velocity dispersions implied by the absorption spectra, sigma~30 km/s, can be explained by the emission from a disk around a massive, mstar~10 Msun, protostar that is accreting at a high rate, mdot~3x10^{-3} Msun/yr. Our observations suggest that the near-infrared reflection spectrum observed in the Orion-KL region is produced close to source I and scattered to our line of sight in the OMC1 outflow cavity. The spectrum allows us to exclude source I being a very large, massive protostar rotating at breakup speed. We suggest that the absorption spectrum is produced in a disk surrounding a ~10 Msun protostar, accreting from its disk at a high rate of a few 10^{-3} Msun/yr.

Wind-driving protostellar accretion discs – I. Formulation and parameter constraints

We study a model of weakly ionized, protostellar accretion discs that are threaded by a large-scale, ordered magnetic field and power a centrifugally driven wind. We consider the limiting case where the wind is the main repository of the excess disc angular momentum and generalize the radially localized disc model of Wardle & K\"onigl (1993), which focussed on the ambipolar diffusion regime, to other field diffusivity regimes, notably Hall and Ohm. We present a general formulation of the problem for nearly Keplerian, vertically isothermal discs using both the conductivity-tensor and the multi-fluid approaches and simplify it to a normalized system of ordinary differential equations in the vertical space coordinate. We determine the relevant parameters of the problem and investigate, using the vertical-hydrostatic-equilibrium approximation and other simplifications, the parameter constraints on physically viable solutions for discs in which the neutral particles are dynamically well coupled to the field already at the midplane. When the charged particles constitute a two-component ion--electron plasma one can identify four distinct sub-regimes in the parameter domain where the Hall diffusivity dominates and three sub-regimes in the Ohm-dominated domain. Two of the Hall sub-regimes can be characterized as being ambipolar diffusion-like and two as being Ohm-like. When the two-component plasma consists instead of positively and negatively charged grains of equal mass, the entire Hall domain and one of the Ohm sub-regimes disappear. In all viable solutions the midplane neutral--ion momentum exchange time is shorter than the local orbital time. Vertical magnetic squeezing always dominates over gravitational tidal compression in this model. (Abridged)

COMPRESSIBLE STREAMING INSTABILITIES IN ROTATING THERMAL VISCOUS OBJECTS

We study electromagnetic streaming instabilities in thermal viscous regions of rotating astrophysical objects, such as protostellar and protoplanetary magnetized accretion disks, molecular clouds, their cores, and elephant trunks. The obtained results can also be applied to any regions of interstellar medium, where different equilibrium velocities between charged species can arise. We consider a weakly and highly ionized three-component plasma consisting of neutrals and magnetized electrons and ions. The vertical perturbations along the background magnetic field are investigated. The effect of perturbation of collisional frequencies due to density perturbations of species is taken into account. The growth rates of perturbations are found in a wide region of wave number spectrum for media, where the thermal pressure is larger than the magnetic pressure. It is shown that in cases of strong collisional coupling of neutrals with ions the contribution of the viscosity is negligible.

Magnetic Fields of Nondegenerate Stars

Magnetic fields are present in a wide variety of stars throughout the HR diagram and play a role at basically all evolutionary stages, from very-low-mass dwarfs to very massive stars, and from young star-forming molecular clouds and protostellar accretion discs to evolved giants/supergiants and magnetic white dwarfs/neutron stars. These fields range from a few μG (e.g., in molecular clouds) to TG and more (e.g., in magnetic neutron stars); in nondegenerate stars in particular, they feature large-scale topologies varying from simple nearly axisymmetric dipoles to complex nonaxsymmetric structures, and from mainly poloidal to mainly toroidal topologies. After recalling the main techniques of detecting and modeling stellar magnetic fields, we review the existing properties of magnetic fields reported in cool, hot, and young nondegenerate stars and protostars, and discuss our understanding of the origin of these fields and their impact on the birth and life of stars.

Protostellar discs formed from turbulent cores

We investigate the collapse and fragmentation of low-mass, trans-sonically turbulent prestellar cores, using SPH simulations. The initial conditions are slightly supercritical Bonnor-Ebert spheres, all with the same density profile, the same mass (M_O=6.1 Msun) and the same radius (R_O=17,000 AU), but having different initial turbulent velocity fields. Four hundred turbulent velocity fields have been generated, all scaled so that the mean Mach number is M=1. Then a subset of these, having a range of net angular momenta, j, has been evolved. The evolution of these turbulent cores is not strongly correlated with j. Instead it is moderated by the formation of filamentary structures due to converging turbulent flows. A high fraction (~ 82%) of the protostars forming from turbulent cores are attended by protostellar accretion discs, but only a very small fraction (~16%) of these discs is sufficiently cool and extended to develop non-linear gravitational instabilities and fragment.

The formation of brown dwarfs

AbstractWe argue that brown dwarfs (BDs) and planemos form by the same mechanisms as low-mass hydrogen-burning stars, but that as one moves to lower and lower masses, an increasing fraction of these objects is formed by fragmentation of the outer parts (R ≳ 100 AU) of protostellar accretion discs around more massive primary protostars, which in turn formed in their own very-low-mass prestellar cores. Numerical simulations of disc fragmentation with realistic thermodynamics show that low-mass objects are readily formed by fragmentation of short-lived massive, extended protostellar accretion discs. Such objects tend subsequently to be liberated into the field at low speed, due to mutual interactions with the primary protostar. Many (~20%) are in low-mass (M1 + M2 < 0.2M⊙) binary systems with semi-major axes a ~ 1 to 2 AU or ~200 AU and mass ratios q ≡ M2/M1 ≳ 0.7. Most of the brown dwarfs have sufficiently large attendant discs to sustain accretion and outflows. Most of the BDs that remain bound to the primary protostar have wide orbits (i.e., there is a BD desert), and these BDs also have a significantly higher probability of being in a BD/BD binary system than do the brown dwarfs that are liberated into the field (just as observed). In this picture, the multiplicity statistics and velocity dispersion of brown dwarfs are largely determined by the eigen evolution of a small-N system, born from a single prestellar core, rather than the larger-scale dynamics of the parent cluster. Consequently, many of the statistical properties of brown dwarfs should not differ very much from one star-formation region to another.

Dust settling in magnetorotationally driven turbulent discs - I. Numerical methods and evidence for a vigorous streaming instability

In this paper, we have used the riemann code for computational astrophysics to study the interaction of a realistic distribution of dust grains with gas at specific radial locations in a vertically stratified protostellar accretion disc. The disc was modelled to have the density and temperature of a minimum mass solar nebula, and shearing box simulations at radii of 0.3 and 10 au are reported here. The disc was driven to a fully developed turbulence via the magnetorotational instability (MRI). The simulations span three gas scaleheights about the disc's midplane. We find that the inclusion of standard dust-to-gas ratios does not have any significant effect on the MRI even when the dust sediments to the midplane of the accretion disc. The density distribution of the dust of all sizes reached a Gaussian profile within two scaleheights of the disc's midplane. The vertical scaleheights of these Gaussian profiles are shown to be proportional to the reciprocal of the square root of the dust radius when large spherical dust grains are considered. This result is consistent with theoretical expectation. The largest two families of dust in one of our simulations show a strong tendency to settle to the midplane of the accretion disc. The large dust tends to organize itself into elongated clumps of high density. The dynamics of these clumps is shown to be consistent with a streaming instability. The streaming instability is seen to be very vigorous and persistent once it forms. Each stream of high-density dust displays a reduced rms velocity dispersion. The velocity directions within the streams are also aligned relative to the mean shear, providing further evidence that we are witnessing a streaming instability. The densest clumpings of large dust are shown to form where the streams intersect. We have also shown that the mean free path and collision time for dust that participates in the streaming instability are reduced by almost two orders of magnitude relative to the average mean free paths and collision times. The rms velocities between the grains also need to fall below a minimum threshold in order for the grains to stick and we show that a small amount of the large dust in our 10 au simulation should have a propensity for grain coalescence. The results of our simulations are likely to be useful for those who model spectral energy distributions of protostellar discs and also for those who model dust coagulation and growth.

Turbulent protostellar discs

Aspects of turbulence in protostellar accretion discs are being reviewed. The emergence of dead zones due to poor ionization and alternatives to the magneto-rotational instability are discussed. The coupling between dust and gas in protostellar accretion discs is explained and the turbulent drag is compared with laminar drag in the Stokes and Epstein regimes. Finally, the significance of magnetic-field generation in turbulent discs is emphasized in connection with driving outflows and with star–disc coupling.

Global Models for the Evolution of Embedded, Accreting Protostellar Disks

Most analytic work to date on protostellar disks has focused on those in isolation from their environments. However, observations are now beginning to probe the earliest, most embedded phases of star formation, during which disks are rapidly accreting from their parent cores and cannot be modeled in isolation. We present a simple, one-zone model of protostellar accretion disks with high mass infall rates. Our model combines a self-consistent calculation of disk temperatures with an approximate treatment of angular momentum transport via two mechanisms. We use this model to survey the properties of protostellar disks across a wide range of stellar masses and evolutionary times, and make predictions for disks' masses, sizes, spiral structure, and fragmentation that will be directly testable by future large-scale surveys of deeply embedded disks. We define a dimensionless accretion-rotation parameter which, in conjunction with the disk's temperature, controls the disk evolution. We track the dominant mode of angular momentum transport, and demonstrate that for stars with final masses greater than roughly one solar mass, gravitational instabilities are the most important mechanism as most of the mass accumulates. We predict that binary formation through disk fission, fragmentation of the disk into small objects, and spiral arm strength all increase in importance to higher stellar masses.

Turbulent transport and its effect on the dead zone in protoplanetary discs

Protostellar accretion discs have cool, dense midplanes where externally originating ionisation sources such as X-rays or cosmic rays are unable to penetrate. This suggests that for a wide range of radii, MHD turbulence can only be sustained in the surface layers where the ionisation fraction is sufficiently high. A dead zone is expected to exist near the midplane, such that active accretion only occurs near the upper and lower disc surfaces. Recent work, however, suggests that under suitable conditions the dead zone may be enlivened by turbulent transport of ions from the surface layers into the dense interior. In this paper we present a suite of simulations that examine where, and under which conditions, a dead zone can be enlivened by turbulent mixing. We use three-dimensional, multifluid shearing box MHD simulations, which include vertical stratification, ionisation chemistry, ohmic resistivity, and ionisation due to X-rays from the central protostar. We compare the results of the MHD simulations with a simple reaction-diffusion model. The simulations show that in the absence of gas-phase heavy metals, such as magnesium, turbulent mixing has essentially no effect on the dead zone. The addition of a relatively low abundance of magnesium, however, increases the recombination time and allows turbulent mixing of ions to enliven the dead zone completely beyond a distance of 5 AU from the central star, for our particular disc model. During the late stages of protoplanetary disc evolution, when small grains have been depleted and the disc surface density has decreased below its high initial value, the structure of the dead zone may be significantly altered by the action of turbulent transport.

The radial structure of protostellar accretion disks: influence of jets

The radial structure of accretion disks is a fundamental issue regarding star and planet formation. Many theoretical studies, focussing on different aspects such as e.g. disk emissivity or ionization, have been conducted in the context of the Standard Accretion Disk (SAD) model, where no jet is present. We wish to calculate the structure of YSO accretion disks in an approach that takes into account the presence of the protostellar jets. The radial structure of these Jet Emitting Disks (JED) should then be compared to that of standard accretion disks. The analytical treatment used in this work is very similar to that of standard accretion disks but is using the parameter space of Magnetised Accretion-Ejection Structures that include the jet torque on the underlying disk. In this framework, the analytical expressions of key quantities, such as mid-plane temperatures, surface densities or disk aspect ratio are derived. It is found that JEDs present a structure very different from the SADs and that can be observationally tested. The implications on planet formation in the inner regions of accretion disks are briefly discussed. We also supply sets of analytical formulae, valid in different opacity regimes, for the disk quantities. These expressions can be readily used for any work where the disk structure is needed as an input for the model.

Ammonia Imaging of the Disks in the NGC 1333 IRAS 4A Protobinary System

The NGC 1333 IRAS 4A protobinary was observed in the ammonia (2, 2) and (3, 3) lines and in the 1.3 cm continuum with a high resolution (about 1.0''). The ammonia maps show two compact sources, one for each protostar, and they are probably protostellar accretion disks. The disk associated with IRAS 4A2 is seen nearly edge-on and shows an indication of rotation. The A2 disk is brighter in the ammonia lines but dimmer in the dust continuum than its sibling disk, with the ammonia-to-dust flux ratios different by about an order of magnitude. This difference suggests that the twin disks have surprisingly dissimilar characters, one gas-rich and the other dusty. The A2 disk may be unusually active or hot, as indicated by its association with water vapor masers. The existence of two very dissimilar disks in a binary system suggests that the formation process of multiple systems has a controlling agent lacking in the isolated star formation process and that stars belonging to a multiple system do not necessarily evolve in phase with each other.

A three-dimensional numerical method for modelling weakly ionized plasmas

Astrophysical fluids under the influence of magnetic fields are often subjected to single-fluid or two-fluid approximations. In the case of weakly ionized plasmas however, this can be inappropriate due to distinct responses from the multiple constituent species to both collisional and non-collisional forces. As a result, in dense molecular clouds and proto-stellar accretion discs for instance, the conductivity of the plasma may be highly anisotropic leading to phenomena such as Hall and ambipolar diffusion strongly influencing the dynamics. Diffusive processes are known to restrict the stability of conventional numerical schemes which are not implicit in nature. Furthermore, recent work establishes that a large Hall term can impose an additional severe stability limit on standard explicit schemes. Following a previous paper which presented the one-dimensional case, we describe a fully three-dimensional method which relaxes the normal restrictions on explicit schemes for multifluid processes. This is achieved by applying the little known Super TimeStepping technique to the symmetric (ambipolar) component of the evolution operator for the magnetic field in the local plasma rest-frame, and the new Hall Diffusion Scheme to the skew-symmetric (Hall) component.

Local stability of self-gravitating fluid disks made of two components in relative motion

Context. We consider a simple self-gravitating disk, made of two fluid components characterized by different effective thermal speeds and interacting with one another only through gravity; two-component models of this type have often been considered in order to estimate the impact of the cold interstellar medium on gravitational instabilities in star-dominated galaxy disks. Aims. This simple model allows us to produce a unified description of instabilities in non-viscous self-gravitating disks, some originating from Jeans collapse, and others from the relative motion between the two components. In particular, the model suggests that the small streaming velocity between the two components associated with the so-called asymmetric drift may be the origin of instability for suitable non-axisymmetric perturbations. Methods. The result is obtained by examining the properties of a local, linear dispersion relation for tightly wound density waves in such two-component model. The parameters characterizing the equilibrium model and the related dispersion relation allow us to recover as natural limits the cases, known in the literature, in which the relative drift between the two components is ignored. Results. Dynamically, the instability is similar to (although gentler than) that known to affect counter-rotating disks. However, in contrast to the instability induced by counter-rotation, which is a relatively rare phenomenon, the mechanism discussed in this paper is likely to be rather common in nature. Conclusions. We briefly indicate some consequences of the instability on the evolution of galaxy disks and possible applications to other astrophysical systems, in particular to protostellar disks and accretion disks.

IRAS 16293−2422: Evidence for Infall onto a Counterrotating Protostellar Accretion Disk

We report high spatial resolution VLA observations of the low-mass star-forming region IRAS 16293-2422 using four molecular probes: ethyl cyanide (CH3CH2CN), methyl formate (CH3OCHO), formic acid (HCOOH), and the ground vibrational state of silicon monoxide (SiO). Ethyl cyanide emission has a spatial scale of ~20'' and encompasses binary cores A and B as determined by continuum emission peaks. Surrounded by formic acid emission, methyl formate emission has a spatial scale of ~6'' and is confined to core B. SiO emission shows two velocity components with spatial scales less than 2'' that map ~2'' northeast of the A and B symmetry axis. The redshifted SiO is ~2'' northwest of blueshifted SiO along a position angle of ~135° which is approximately parallel to the A and B symmetry axis. We interpret the spatial position offset in red- and blueshifted SiO emission as due to rotation of a protostellar accretion disk, and we derive ~1.4 M☉ interior to the SiO emission. In the same vicinity, Mundy et al. also concluded rotation of a nearly edge-on disk from OVRO observations of much stronger and ubiquitous 13CO emission, but the direction of rotation is opposite to the SiO emission findings. Taken together, SiO and 13CO data suggest evidence for a counterrotating disk. Moreover, archival BIMA array 12CO data show an inverse P Cygni profile with the strongest absorption in close proximity to the SiO emission, indicating unambiguous material infall toward the counterrotating protostellar disk at a new source location within the IRAS 16293-2422 complex. The details of these observations and our interpretations are discussed.

Direct detection of a magnetic field in the innermost regions of an accretion disk

Models predict that magnetic fields play a crucial role in the physics of astrophysical accretion disks and their associated winds and jets. For example, the rotation of the disk twists around the rotation axis the initially vertical magnetic field, which responds by slowing down the plasma in the disk and by causing it to fall towards the central star. The magnetic energy flux produced in this process points away from the disk, pushing the surface plasma outwards, leading to a wind from the disk and sometimes a collimated jet. But these predictions have hitherto not been supported by observations. Here we report the direct detection of the magnetic field in the core of the protostellar accretion disk FU Orionis. The surface field reaches strengths of about 1 kG close to the centre of the disk, and it includes a significant azimuthal component, in good agreement with recent models. But we find that the field is very filamentary and slows down the disk plasma much more than models predict, which may explain why FU Ori fails to collimate its wind into a jet.

Protostellar Disks: Formation, Fragmentation, and the Brown Dwarf Desert

We argue that gravitational instability of typical protostellar disks is not a viable mechanism for the fragmentation into multiple systems -- binary stars, brown dwarf companions, or gas giant planets -- except at periods above roughly 20,000 years. Our conclusion is based on a comparison between prior numerical work on disk self-gravity by Gammie (2001) with our own analytical models for the dynamical and thermal state of protostellar disks. For this purpose we first develop a simple theory for the initial conditions of low-mass star formation, accounting for the effect of turbulence on the characteristic mass, accretion rate, and angular momentum of collaping cores. Second, we examine the criterion for fragmentation to occur during star formation, concentrating on the self-gravitational instabilities of protostellar accretion disks in their main accretion phase. Self-gravitational instabilities are strongly dependent on the thermal state of the disk, and we find that the combination of viscous heating and stellar irradiation quenches fragmentation due to Toomre's local instability. Global instability of the disk may be required to process mass supply, but is unlikely to produce fragments. Our findings help to explain the dearth of substellar companions to stellar type stars: the brown dwarf desert.

High‐Resolution Near‐Infrared Observations of the Circumstellar Disk System in the Bok Globule CB 26

We report on results of near-infrared and optical observations of the millimeter disk embedded in the Bok globule CB 26. The near-infrared images show a bipolar reflection nebula with a central extinction lane that coincides with the millimeter disk. Imaging polarimetry of this object yielded a polarization pattern that is typical of a young stellar object (YSO) surrounded by a large circumstellar disk and an envelope, seen almost edge-on. The strong linear polarization in the bipolar lobes is caused by single scattering at dust grains and reveals the location of the illuminating source that coincides with the center of the millimeter disk. The spectral energy distribution of the YSO embedded in CB 26 resembles that of a Class I source with a luminosity of 0.5 L☉. Using the pre-main-sequence evolutionary tracks and the stellar mass inferred from the rotation curve of the disk, we derive an age of the system of ≤106 yr. Hα and [S II] narrowband imaging as well as optical spectroscopy revealed a Herbig-Haro object 615 northwest of CB 26 YSO 1, perfectly aligned with the symmetry axis of the bipolar nebula. This Herbig-Haro object (HH 494) indicates ongoing accretion and outflow activity in CB 26 YSO 1. Its excitation characteristics show that the Herbig-Haro flow is propagating into a low-density environment. We suggest that CB 26 YSO 1 represents the transition stage between embedded protostellar accretion disks and more evolved protoplanetary disks around T Tauri stars in an undisturbed environment.

A note on the snow line in protostellar accretion disks

Abstract— The temperature of ice grains in a protostellar disk is computed for a series of disk models. The region of stability against sublimation is calculated for small ice grains composed of either pure ice or “dirty” ice. We show that in the optically thin photosphere of the disk the gas temperature must be around 145 K for ice grains to be stable. This is much lower than the temperature of 170 K that is usually assumed.