Planets form inside protostellar disks in a dead zone where the electrical resistivity of the gas is too high for magnetic forces to drive turbulence. We show that much of the dead zone nevertheless is active and flows toward the star while smooth, large-scale magnetic fields transfer the orbital angular momentum radially outward. Stellar X-ray and radionuclide ionization sustain a weak coupling of the dead zone gas to the magnetic fields, despite the rapid recombination of free charges on dust grains. Net radial magnetic fields are generated in the magneto-rotational turbulence in the electrically conducting top and bottom surface layers of the disk, and reach the midplane by Ohmic diffusion. A toroidal component to the fields is produced near the midplane by the orbital shear. The process is similar to the magnetization of the Solar tachocline. The result is a laminar, magnetically-driven accretion flow in the region where the planets form.
We investigate the conditions for the presence of a magnetically inactive dead zone in protostellar disks, using 3-D shearing-box MHD calculations including vertical stratification, Ohmic resistivity and time-dependent ionization chemistry. Activity driven by the magnetorotational instability fills the whole thickness of the disk at 5 AU, provided cosmic ray ionization is present, small grains are absent and the gas-phase metal abundance is sufficiently high. At 1 AU the larger column density of 1700 g/cm^2 means the midplane is shielded from ionizing particles and remains magnetorotationally …
The final masses of Jovian planets are attained when the tidal torques that they exert on their surrounding protostellar disks are sufficient to open gaps in the face of disk viscosity, thereby shutting off any further accretion. In sufficiently well-ionized disks, the predominant form of disk viscosity originates from the Magneto-Rotational Instability (MRI) that drives hydromagnetic disk turbulence. In the region of sufficiently low ionization rate -- the so-called dead zone -- turbulence is damped and we show that lower mass planets will be formed. We considered three ionization sources (X-…
Protoplanets accrete material from their natal protostellar disks until they are sufficiently massive to open a gap in the face of the disk's viscosity that arises from the magneto-rotational instability (MRI). By computing the ionization structure within observationally well-constrained disk models, we demonstrate that poorly ionized, low viscosity "dead zones" stretch out to 12 AU within typical disks. We find that planets of terrestrial mass robustly form within the dead zones while massive Jovian planets form beyond. Dead zones will also halt the rapid migration of planets into their centr…
Most low-mass protostellar disks evolve in clustered environments where they are affected by external radiation fields, while others evolve in more isolated star-forming regions. Assuming that the magneto-rotational instability (MRI) is the main source of viscosity, we calculate the size of a poorly ionized, MRI inactive, and hence low viscosity region - the "dead zone" - in these protostellar disks. We include disk ionization by X-rays, cosmic rays, radioactive elements and thermal collisions, recombination by molecules, metals, and grains, as well as the effect of turbulence stimulation in t…
The growth of Jovian mass planets during migration in their protoplanetary disks is one of the most important problems that needs to be solved in light of observations of the exosolar planets. Studies of the migration of planets in standard gas disk models routinely show that migration is too fast to form Jovian planets, and that such migrating planetary cores generally plunge into the central stars in less than a Myr. In previous work, we have shown that a poorly ionized, less viscous region in a protoplanetary disk called a dead zone slows down the migration of fixed-mass planets. In this pa…
Models of the accretion disks of Young Stellar Objects show that they should not be ionized at a few AU from the star, and thus not subject to the MHD turbulence believed to cause accretion. This has been suggested to create a 'Dead Zone' where accretion remains unexplained. Here we show that the existence of the Dead Zone self-consistently creates a density profile favorable to the Rossby Wave Instability of Lovelace et al. (1999). This instability will create and sustain Rossby vortices in the disk which could lead to enhanced planet formation.
Current layered accretion models neglect the properties of the ``dead zone''. However, as argued here from simple considerations, the thickness of this zone is a critical quantity when the disc is in hydrostatic equilibrium. It controls not only the structure of the superficial, active layers, but also the mid-plane density and the total disc mass, and should therefore be introduced in models of that kind, steady or not. But in the absence of intrinsic heating, the dead zone must have a tiny size which, given the non-stationary and turbulent character of the global flow, makes very likely its …
We study an accretion disk in which three different regions may coexist: MHD turbulent regions, dead zones and gravitationally unstable regions. Although the dead zones are stable, there is some transport due to the Reynolds stress associated with waves emitted from the turbulent layers. We model the transport in each of the different regions by its own $α$ parameter, this being 10 to $10^{3}$ times smaller in dead zones than in active layers. In gravitationally unstable regions, $α$ is determined by the fact that the disk self-adjusts to a state of marginal stability. We construct steady-stat…
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 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.
The tidal interaction between a disk and a planet leads to the planet's migration. A long-standing question regarding this mechanism is how to stop the migration before planets plunge into their central stars. In this paper, we propose a new, simple mechanism to significantly slow down planet migration, and test the possibility by using a hybrid numerical integrator to simulate the disk-planet interaction. The key component of the scenario is the role of low viscosity regions in protostellar disks known as dead zones, which affect planetary migration in two ways. First of all, it allows a smal…
Axisymmetric stellar wind solutions are presented, obtained by numerically solving the ideal magnetohydrodynamic (MHD) equations. Stationary solutions are critically analysed using the knowledge of the flux functions. These flux functions enter in the general variational principle governing all axisymmetric stationary ideal MHD equilibria. The magnetized wind solutions for (differentially) rotating stars contain both a `wind' and a `dead' zone. We illustrate the influence of the magnetic field topology on the wind acceleration pattern, by varying the coronal field strength and the extent of th…
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 …
Migration of protoplanets in their gaseous host disks may be largely responsible for the observed orbital distribution of extrasolar planets. Recent simulations have shown that the magnetorotational turbulence thought to drive accretion in protoplanetary disks can affect migration by turning it into an orbital random walk. However, these simulations neglected the disk's ionization structure. Low ionization fraction near the midplane of the disk can decouple the magnetic field from the gas, forming a dead zone with reduced or no turbulence. Here, to understand the effect of dead zones on protop…
We study axisymmetric models of layered protoplanetary discs taking radiative transfer effects into account, and allowing for a residual viscosity in the dead zone. We also explore the effect of different viscosity prescriptions. In addition to the ring instability reported in the first paper of the series we find an oscillatory instability of the dead zone, accompanied by variations of the accretion rate onto the central star. We provide a simplified analytical description explaining the mechanism of the oscillations. Finally, we find that the residual viscosity enables stationary accretion i…
In the borders of the dead zones of protoplanetary disks, the inflow of gas produces a local density maximum that triggers the Rossby wave instability. The vortices that form are efficient in trapping solids. We aim to assess the possibility of gravitational collapse of the solids within the Rossby vortices. We perform global simulations of the dynamics of gas and solids in a low mass non-magnetized self-gravitating thin protoplanetary disk with the Pencil code. We use multiple particle species of radius 1, 10, 30, and 100 cm. The dead zone is modeled as a region of low viscosity. The Rossby v…
We examine the linear stability of a flow threaded by a weak, vertical magnetic field in a disk with a keplerian rotation profile and a vertical stratification of the ionization degree as that predicted for vast portions of protoplanetary disks. A quasi-global analysis is carried out, where the form of the perturbations in the vertical direction is determined. Considering the ohmic magnetic diffusivity of the gas, the conditions leading to the magnetorotational instability are analyzed as a function of the diffusivity at the disk surfaces, its vertical profile and the strength of the unperturb…
The central engine of gamma-ray bursts (GRBs) is believed to be a hot and dense disk with hyperaccretion onto a few solar-mass black hole. We investigate where the magnetorotational instability (MRI) actively operates in the hyperaccretion disk, which can cause angular momentum transport in the disk. The inner region of hyperaccretion disks can be neutrino opaque, and the energy- and momentum-transport by neutrinos could affect the growth of the MRI significantly. Assuming reasonable disk models and a weak magnetic field $B \lesssim 10^{14} \rm{G}$, it is found that the MRI is strongly suppres…
In this work we use the radiation hydrodynamic code TRAMP to perform a two-dimensional axially symmetric model of the layered disc. Using this model we follow the accumulation of mass in the dead zone due to the radially varying accretion rate. We found a new type of instability which causes the dead zone to split into rings. This "ring instability" works due to the positive feedback between the thickness of the dead zone and the mass accumulation rate. We give an analytical description of this instability, taking into account non-zero thickness of the dead zone and deviations from the Kepleri…
Using numerical MHD simulations, we have studied the evolution of the magnetorotational instability in stratified accretion disks in which the ionization fraction (and therefore resistivity) varies substantially with height. This model is appropriate to dense, cold disks around protostars or dwarf nova systems which are ionized by external irradiation of cosmic rays or high-energy photons. We find the growth and saturation of the MRI occurs only in the upper layers of the disk where the magnetic Reynolds number exceeds a critical value; in the midplane the disk remains queiscent. The vertical …
We analyze the ionization state of the magnetohydrodynamically turbulent protoplanetary disks and propose a new mechanism of sustaining ionization. First, we show that in the quasi-steady state of turbulence driven by magnetorotational instability in a typical protoplanetary disk with dust grains, the amount of energy dissipation should be sufficient for providing the ionization energy that is required for activating magnetorotational instability. Second, we show that in the disk with dust grains the energetic electrons that compose electric currents in weakly ionized gas can provide collision…
Radiative transfer models of multi-transition observations are used to determine molecular abundances as functions of position in pre- and protostellar cores. The data require a "drop" abundance profile with radius, with high abundances in the outermost regions probed by low excitation 3 mm lines, and much lower abundances at intermediate zones probed by higher frequency lines. The results are illustrated by detailed analysis of CO and HCO+ lines for a subset of objects. We propose a scenario in which the molecules are frozen out in a region of the envelope where the temperature is low enough …
Context. Recent observations of the X-ray emission from T Tauri stars in the Orion nebula have shown that they undergo frequent outbursts in their X-ray luminosity. These X-ray flares are characterised by increases in luminosity by two orders of magnitude, a typical duration of less than one day, and a significant hardening of the X-ray spectrum. Aims. It is unknown what effect these X-ray flares will have on the ionisation fraction and dead-zone structure in protoplanetary disks. We present the results of calculations designed to address this question. Methods. We have performed calculations …
A chondrule formation theory is presented where the chondrule formation zone is located within 0.1 AU of the protosun. This hot, optically thick, inner zone of the solar accretion disk is coincident with the formation region of the protosolar jet. The model assumes that particles, ranging in diameter from 1 micron to 1 cm, can be ejected from the inner-accretion disk by the jet flow, and that the angular momentum of this material is sufficient to eject it from the jet flow. Given these assumptions, any material so ejected, will fly across the face of the accretion disk at speeds greater than t…
Previous models of dust growth in protoplanetary disks considered either uniformly laminar or turbulent disks. This Letter explores how dust growth occurs in a layered protoplanetary disk in which the magnetorotational instability generates turbulence only in the surface layers of a disk. Two cases are considered: a completely laminar dead zone and a dead zone in which turbulence is ``stirred up'' from the MRI acting above. It is found that dust is depleted from high altitudes in layered disks faster than in those cases of a uniformly laminar or turblent disks. This is a result of the accelera…
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 propertie…
