Net Vertical Magnetic Flux Research Articles

Dynamics near the inner dead-zone edges in a proprotoplanetary disk

Abstract We perform three-dimensional global non-ideal magnetohydrodynamic simulations of a protoplanetary disk containing the inner dead-zone edge. We take into account realistic diffusion coefficients of the Ohmic resistivity and ambipolar diffusion based on detailed chemical reactions with single-size dust grains. We found that the conventional dead zone identified by the Elsässer numbers of the Ohmic resistivity and ambipolar diffusion is divided into two regions: “the transition zone” and “the coherent zone.” The coherent zone has the same properties as the conventional dead zone, and extends outside of the transition zone in the radial direction. Between the active and coherent zones, we discover the transition zone, the inner edge of which is identical to that of the conventional dead zone. The transition zone extends out over the regions where thermal ionization determines diffusion coefficients. The transition zone has completely different physical properties than the conventional dead zone, the so-called undead zone, and the zombie zone. The combination of amplification of the radial magnetic field owing to the ambipolar diffusion and a steep radial gradient of the Ohmic diffusivity causes the efficient evacuation of the net vertical magnetic flux from the transition zone within several rotations. Surface gas accretion occurs in the coherent zone but not in the transition zone. The presence of the transition zone prohibits mass and magnetic flux transport from the coherent zone to the active zone. Mass accumulation occurs at both edges of the transition zone as a result of mass supply from the active and coherent zones.

Local models of two-temperature accretion disc coronae – II. Ion thermal conduction and the absence of disc evaporation

ABSTRACT We use local stratified shearing-box simulations with magnetic field-aligned thermal conduction to study an idealized model of the coupling between a cold, radiatively efficient accretion disc, and an overlying, hot, two-temperature corona. Evaporation of a cold disc by conduction from the hot corona has been proposed as a means of mediating the soft-to-hard state transitions observed in X-ray binary systems. We model the coronal plasma in our local disc patch as an MHD fluid subject to both free-streaming ion conduction and a parametrized cooling function that captures the collisional transfer of energy from hot ions to colder, rapidly cooling leptons. In all of our models, independent of the initial net vertical magnetic flux (NF) threading the disc, we find no evidence of disc evaporation. The ion heat flux into the disc is radiated away before conduction can heat the disc’s surface layers. When an initial NF is present, steady-state temperature, density, and outflow velocities in our model coronae are unaffected by conduction. Instead of facilitating disc evaporation, thermal conduction is more likely to feed the disc with plasma condensing out of the corona, particularly in flows without NF. Our work indicates that uncertainties in the amount of NF threading the disc hold far greater influence over whether or not the disc will evaporate into a radiatively inefficient accretion flow compared to thermal conduction. We speculate that a change in net flux mediates disc truncation/evaporation.

Particle diffusion and acceleration in magnetorotational instability turbulence

ABSTRACT Hot accretion flows contain collisionless plasmas that are believed to be capable of accelerating particles to very high energies, as a result of turbulence generated by the magnetorotational instability (MRI). We conduct unstratified shearing-box simulations of the MRI turbulence in ideal magnetohydrodynamic (MHD), and inject energetic relativistic test particles in simulation snapshots to conduct a detailed investigation on particle diffusion and stochastic acceleration. We consider different amount of net vertical magnetic flux, with sufficiently high resolution to resolve the gyro-radii (Rg) of most particles. Particles with large Rg (≳ 0.03 disc scale height H) show spatial diffusion coefficients of ∼30 and ∼5 times Bohm values in the azimuthal and poloidal directions, respectively. We further measure particle momentum diffusion coefficient D(p) by applying the Fokker–Planck equation, finding that contribution from turbulent fluctuations scales as D(p) ∝ p, and shear acceleration takes over when Rg ≳ 0.1H, characterized by D(p) ∝ p3. For particles with smaller Rg (≲ 0.03H), their spatial diffusion coefficients roughly scale as ∼p−1, and show evidence of D(p) ∝ p2 scaling in momentum diffusion but with large uncertainties. We find that multiple effects contribute to stochastic acceleration/deceleration, and the process is likely affected by intermittency in the MRI turbulence. We also discuss the potential of accelerating PeV cosmic rays in hot accretion flows around supermassive black holes.

Magnetically modified spherical accretion in GRMHD: reconnection-driven convection and jet propagation

ABSTRACT We present 3D general relativistic magnetohydrodynamic simulations of zero angular momentum accretion around a rapidly rotating black hole, modified by the presence of initially uniform magnetic fields. We consider several angles between the magnetic field direction and the black hole spin. In the resulting flows, the mid-plane dynamics are governed by magnetic reconnection-driven turbulence in a magnetically arrested (or a nearly arrested) state. Electromagnetic jets with outflow efficiencies ∼10–200 per cent occupy the polar regions, reaching several hundred gravitational radii before they dissipate due to the kink instability. The jet directions fluctuate in time and can be tilted by as much as ∼30○ with respect to black hole spin, but this tilt does not depend strongly on the tilt of the initial magnetic field. A jet forms even when there is no initial net vertical magnetic flux since turbulent, horizon-scale fluctuations can generate a net vertical field locally. Peak jet power is obtained for an initial magnetic field tilted by 40○–80○ with respect to the black hole spin because this maximizes the amount of magnetic flux that can reach the black hole. These simulations may be a reasonable model for low luminosity black hole accretion flows such as Sgr A* or M87.

Energy transfers in magnetohydrodynamic shear turbulence

Astrophysical flows span a broad range of scales and thus require sub-grid modeling. We compute the energy fluxes in the Fourier and physical space for the turbulent magnetized shearing box simulations with a weak net vertical magnetic flux. The energy fluxes are dominated by the injection term from the mid-to-large scale range due to the Reynolds and Maxwell stresses in both cases while the small scales are dominated by dissipation. Since the nature of turbulent cascades requires a clear separation of scales, our work is unable to address these questions conclusively. But because our work is the first of its nature in trying to connect the Fourier and physical space energy flux behavior, we are able to make connections between the two profiles.

Magnetohydrodynamics in a cylindrical shearing box

ABSTRACT We develop a framework for magnetohydrodynamical (MHD) simulations in a local cylindrical shearing box by extending the formulation of the Cartesian shearing box. We construct shearing-periodic conditions at the radial boundaries of a simulation box from the conservation relations of the basic MHD equations, taking into account the explicit radial dependence of physical quantities. We demonstrate quasi-steady mass accretion, which cannot be handled by the standard Cartesian shearing box model, with an ideal MHD simulation in a vertically unstratified cylindrical shearing box for up to 200 rotations. In this demonstrative run we set up (i) net vertical magnetic flux, (ii) a locally isothermal equation of state, and (iii) a sub-Keplerian equilibrium rotation, whereas the sound velocity and the initial Alfvén velocity have the same radial dependence as that of the Keplerian velocity. Inward mass accretion is induced to balance the outward angular momentum flux of the MHD turbulence triggered by the magnetorotational instability in a self-consistent manner. We discuss detailed physical properties of the saturated magnetic field, in comparison to the results of a Cartesian shearing box simulation.

Super-Eddington Accretion Disks around Supermassive Black Holes

Abstract We use global three-dimensional radiation magnetohydrodynamical simulations to study accretion disks onto a black hole with accretion rates varying from to . We initialize the disks with a weakly magnetized torus centered at either 50 or 80 gravitational radii, leading to self-consistent turbulence generated by the magnetorotational instability (MRI). The inner regions of all disks have radiation pressure ∼104–106 times the gas pressure. Nonaxisymmetric density waves that steepen into spiral shocks form as gas flows toward the black hole. Maxwell stress from MRI turbulence can be larger than the Reynolds stress only when the net vertical magnetic flux is sufficiently large. Outflows are formed with a speed of ∼0.1–0.4c. When the accretion rate is smaller than , outflows are launched from ∼10 gravitational radii, and the radiative efficiency is ∼5%–7%. For an accretion rate reaching , most of the funnel region near the rotation axis becomes optically thick, and the outflow is launched from beyond 50 gravitational radii. The radiative efficiency is reduced to 1%. We always find that the kinetic energy luminosity associated with the outflow is at most ∼15%–30% of the radiative luminosity. The mass flux in the outflow is ∼15%–50% of the net mass accretion rates. We discuss the implications of our simulation results on the observational properties of these disks.

Turbulent and wind-driven accretion in dwarf novae threaded by a large-scale magnetic field

Dwarf novae (DNe) are accreting white dwarfs that show eruptions caused by a thermal-viscous instability in the accretion disk. The outburst timescales constrain α, the ratio of the viscous stress to the thermal pressure, which phenomenologically connects to the mechanism of angular momentum transport. The eruptive state has α ≈ 0.1 while the quiescent state has α ≈ 0.03. Turbulent transport that is due to the magneto-rotational instability (MRI) is generally considered to be the source of angular momentum transport in DNe. The presence of a large-scale poloidal field threading the disk is known to enhance MRI-driven transport. Here, we perform 3D local magnetohydrodynamic (MHD) shearing-box simulations including vertical stratification, radiative transfer, and a net constant vertical magnetic flux to investigate how transport changes between the outburst and quiescent states of DNe. We find that a net vertical constant magnetic field, as could be provided by the white dwarf or by its stellar companion, provides a higher α in quiescence than in outburst, in opposition to what is expected. Including resistivity quenches MRI turbulence in quiescence, suppressing transport, unless the magnetic field is high enough, which again leads to α ≈ 0.1. A major difference between simulations with a net poloidal flux and simulations without a net flux is that angular momentum transport in the former is shared between turbulent radial transport and wind-driven vertical transport. We find that wind-driven transport dominates in quiescence even for moderately low magnetic fields ∼1 G. This can have a great impact on observational signatures since wind-driven transport does not heat the disk. Furthermore, wind transport cannot be reduced to an α prescription. We provide fits to the dependence of α with β, the ratio of thermal to magnetic pressure, and Teff, the effective temperature of the disk, as well as a prescription for the wind torque as a function of β that is in agreement with both local and global simulations. We conclude that the evolution of the thermal-viscous instability, and its consequences on the outburst cycles of CVs, needs to be thoroughly revised to take into account that most of the accretion energy may be carried away by a wind instead of being locally dissipated.

Convection Enhances Magnetic Turbulence in AM CVn Accretion Disks

Abstract We present the results of local, vertically stratified, radiation magnetohydrodynamic shearing-box simulations of magnetorotational instability (MRI) turbulence for a (hydrogen poor) composition applicable to accretion disks in AM CVn type systems. Many of these accreting white dwarf systems are helium analogs of dwarf novae (DNe). We utilize frequency-integrated opacity and equation-of-state tables appropriate for this regime to accurately portray the relevant thermodynamics. We find bistability of thermal equilibria in the effective-temperature, surface-mass-density plane typically associated with disk instabilities. Along this equilibrium curve (i.e., the S-curve), we find that the stress to thermal pressure ratio α varied with peak values of ∼0.15 near the tip of the upper branch. Similar to DNe, we found enhancement of α near the tip of the upper branch caused by convection; this increase in α occurred despite our choice of zero net vertical magnetic flux. Two notable differences we find between DN and AM CVn accretion disk simulations are that AM CVn disks are capable of exhibiting persistent convection in outburst, and ideal MHD is valid throughout quiescence for AM CVns. In contrast, DNe simulations only show intermittent convection, and nonideal MHD effects are likely important in quiescence. By combining our previous work with these new results, we also find that convective enhancement of the MRI is anticorrelated with mean molecular weight.

Strongly magnetized accretion discs require poloidal flux

Motivated by indirect observational evidence for strongly magnetized accretion discs around black holes, and the novel theoretical properties of such solutions, we investigate how a strong magnetization state can develop and persist. To this end, we perform local simulations of accretion discs with an initially purely toroidal magnetic field of equipartition strength. We demonstrate that discs with zero net vertical magnetic flux and realistic boundary conditions cannot sustain a strong toroidal field. However, a magnetic pressure-dominated disc can form from an initial configuration with a sufficient amount of net vertical flux and realistic boundary conditions. Our results suggest that poloidal flux is a necessary prerequisite for the sustainability of strongly magnetized accretion discs.

Accretion disc dynamo activity in local simulations spanning weak-to-strong net vertical magnetic flux regimes

Strongly magnetized accretion discs around black holes have attractive features that may explain enigmatic aspects of X-ray binary behaviour. The structure and evolution of these discs are governed by a dynamo-like mechanism, which channels part of the accretion power liberated by the magnetorotational instability (MRI) into an ordered toroidal magnetic field. To study dynamo activity, we performed three-dimensional, stratified, isothermal, ideal magnetohydrodynamic shearing box simulations. The strength of the self-sustained toroidal magnetic field depends on the net vertical magnetic flux, which we vary across almost the entire range over which the MRI is linearly unstable. We quantify disc structure and dynamo properties as a function of the initial ratio of mid-plane gas pressure to vertical magnetic field pressure, $\beta_0^{\rm mid} = p_{\rm gas} / p_B$. For $10^5 \geq \beta_0^{\rm mid} \geq 10$ the effective $\alpha$-viscosity parameter scales as a power-law. Dynamo activity persists up to and including $\beta_0^{\rm mid} = 10^2$, at which point the entire vertical column of the disc is magnetic pressure-dominated. Still stronger fields result in a highly inhomogeneous disc structure, with large density fluctuations. We show that the turbulent steady state $\beta^{\rm mid}$ in our simulations is well-matched by the analytic model of Begelman et al. (2015) describing the creation and buoyant escape of toroidal field, while the vertical structure of the disc can be broadly reproduced using this model. Finally, we discuss the implications of our results for observed properties of X-ray binaries.

CONVECTION CAUSES ENHANCED MAGNETIC TURBULENCE IN ACCRETION DISKS IN OUTBURST

We present the results of local, vertically stratified, radiation MHD shearing box simulations of MRI turbulence appropriate for the hydrogen ionizing regime of dwarf nova and soft X-ray transient outbursts. We incorporate the frequency-integrated opacities and equation of state for this regime, but neglect non-ideal MHD effects and surface irradiation, and do not impose net vertical magnetic flux. We find two stable thermal equilibrium tracks in the effective temperature versus surface mass density plane, in qualitative agreement with the S-curve picture of the standard disk instability model. We find that the large opacity at temperatures near $10^4$K, a corollary of the hydrogen ionization transition, triggers strong, intermittent thermal convection on the upper stable branch. This convection strengthens the magnetic turbulent dynamo and greatly enhances the time-averaged value of the stress to thermal pressure ratio $\alpha$, possibly by generating vertical magnetic field that may seed the axisymmetric magnetorotational instability, and by increasing cooling so that the pressure does not rise in proportion to the turbulent dissipation. These enhanced stress to pressure ratios may alleviate the order of magnitude discrepancy between the $\alpha$-values observationally inferred in the outburst state and those that have been measured from previous local numerical simulations of magnetorotational turbulence that lack net vertical magnetic flux.

WIND-DRIVEN ACCRETION IN PROTOPLANETARY DISKS. II. RADIAL DEPENDENCE AND GLOBAL PICTURE

Non-ideal magnetohydrodynamical effects play a crucial role in determining the mechanism and efficiency of angular momentum transport as well as the level of turbulence in protoplanetary disks (PPDs), which are key to understanding PPD evolution and planet formation. It was shown in our previous work that at 1 AU, the magnetorotational instability (MRI) is completely suppressed when both Ohmic resistivity and ambipolar diffusion (AD) are taken into account, resulting in a laminar flow with accretion driven by magnetocentrifugal wind. In this work, we study the radial dependence of the laminar wind solution using local shearing-box simulations. Scaling relation on the angular momentum transport for the laminar wind is obtained, and we find that the wind-driven accretion rate can be approximated as M_dot~0.91x10^(-8)R_AU^(1.21)(B_z/10mG)^(0.93)M_Sun/yr, where B_z is the strength of the large-scale vertical magnetic field threading the disk. The result is independent of disk surface density. Four criteria are outlined for the existence of the laminar wind solution: 1). Ohmic resistivity dominated midplane region; 2). AD dominated disk upper layer; 3). Presence of (not too weak) net vertical magnetic flux. 4). Sufficiently well ionized gas beyond disk surface. All these criteria are likely to be met in the inner region of the disk from ~0.3 AU to about 5-10 AU for typical PPD accretion rates. Beyond this radius, angular momentum transport is likely to proceed due to a combination of the MRI and disk wind, and eventually dominated by the MRI (in the presence of strong AD) in the outer disk. Our simulation results provide key ingredients for a new paradigm on the accretion processes in PPDs.

THE FATE OF PLANETESIMALS IN TURBULENT DISKS WITH DEAD ZONES. I. THE TURBULENT STIRRING RECIPE

Turbulence in protoplanetary disks affects planet formation in many ways. While small dust particles are mainly affected by the aerodynamical coupling with turbulent gas velocity fields, planetesimals and larger bodies are more affected by gravitational interaction with gas density fluctuations. For the latter process, a number of numerical simulations have been performed in recent years, but a fully parameter-independent understanding has not been yet established. In this study, we present simple scaling relations for the planetesimal stirring rate in turbulence driven by magnetorotational instability (MRI), taking into account the stabilization of MRI due to Ohmic resistivity. We begin with order-of-magnitude estimates of the turbulence-induced gravitational force acting on solid bodies and associated diffusion coefficients for their orbital elements. We then test the predicted scaling relations using the results of recent Ohmic-resistive MHD simulations by Gressel et al. We find that these relations successfully explain the simulation results if we properly fix order-of-unity uncertainties within the estimates. We also update the saturation predictor for the density fluctuation amplitude in MRI-driven turbulence originally proposed by Okuzumi & Hirose. Combination of the scaling relations and saturation predictor allows to know how the turbulent stirring rate of planetesimals depends on disk parameters such as the gas column density, distance from the central star, vertical resistivity distribution, and net vertical magnetic flux. In Paper II, we apply our recipe to planetesimal accretion to discuss its viability in turbulent disks.

WIND-DRIVEN ACCRETION IN PROTOPLANETARY DISKS. I. SUPPRESSION OF THE MAGNETOROTATIONAL INSTABILITY AND LAUNCHING OF THE MAGNETOCENTRIFUGAL WIND

We perform local, vertically stratified shearing-box MHD simulations of protoplanetary disks (PPDs) at a fiducial radius of 1 AU that take into account the effects of both Ohmic resistivity and ambipolar diffusion (AD). The magnetic diffusion coefficients are evaluated self-consistently from a look-up table based on equilibrium chemistry. We first show that the inclusion of AD dramatically changes the conventional picture of layered accretion. Without net vertical magnetic field, the system evolves into a toroidal field dominated configuration with extremely weak turbulence in the far-UV ionization layer that is far too inefficient to drive rapid accretion. In the presence of a weak net vertical field (plasma beta~10^5 at midplane), we find that the MRI is completely suppressed, resulting in a fully laminar flow throughout the vertical extent of the disk. A strong magnetocentrifugal wind is launched that efficiently carries away disk angular momentum and easily accounts for the observed accretion rate in PPDs. Moreover, under a physical disk wind geometry, all the accretion flow proceeds through a strong current layer with thickness of ~0.3H that is offset from disk midplane with radial velocity of up to 0.4 times the sound speed. Both Ohmic resistivity and AD are essential for the suppression of the MRI and wind launching. The efficiency of wind transport increases with increasing net vertical magnetic flux and the penetration depth of the FUV ionization. Our laminar wind solution has important implications on planet formation and global evolution of PPDs.

LOCAL STUDY OF ACCRETION DISKS WITH A STRONG VERTICAL MAGNETIC FIELD: MAGNETOROTATIONAL INSTABILITY AND DISK OUTFLOW

We perform 3D vertically-stratified local shearing-box ideal MHD simulations of the magnetorotational instability (MRI) that include a net vertical magnetic flux, which is characterized by beta_0 (ratio of gas pressure to magnetic pressure of the net vertical field at midplane). We have considered beta_0=10^2, 10^3 and 10^4 and in the first two cases the most unstable linear MRI modes are well resolved in the simulations. We find that the behavior of the MRI turbulence strongly depends on beta_0: The radial transport of angular momentum increases with net vertical flux, achieving alpha=0.08 for beta_0=10^4 and alpha>1.0 for beta_0=100, where alpha is the Shakura-Sunyaev parameter. A critical value lies at beta_0=10^3: For beta_0>10^3, the disk consists of a gas pressure dominated midplane and a magnetically dominated corona. The turbulent strength increases with net flux, and angular momentum transport is dominated by turbulent fluctuations. The magnetic dynamo that leads to cyclic flips of large-scale fields still exists, but becomes more sporadic as net flux increases. For beta_0<10^3, the entire disk becomes magnetic dominated. The turbulent strength saturates, and the magnetic dynamo is quenched. Stronger large-scale fields are generated with increasing net flux, which dominates angular momentum transport. A strong outflow is launched from the disk by the magnetocentrifugal mechanism, and the mass flux increases linearly with net vertical flux and shows sign of saturation at beta_0=10^2. However, the outflow is unlikely to be directly connected to a global wind: for beta_0>10^3, the large-scale field has no permanent bending direction due to dynamo activities, while for beta_0<10^3, the outflows from the top and bottom sides of the disk bend towards opposite directions, inconsistent with a physical disk wind geometry. Global simulations are needed to address the fate of the outflow.

TURBULENCE IN THE OUTER REGIONS OF PROTOPLANETARY DISKS. I. WEAK ACCRETION WITH NO VERTICAL MAGNETIC FLUX

We use local numerical simulations to investigate the strength and nature of magnetohydrodynamic (MHD) turbulence in the outer regions of protoplanetary disks, where ambipolar diffusion is the dominant non-ideal MHD effect. The simulations include vertical stratification and assume zero net vertical magnetic flux. We employ a super time-stepping technique to ameliorate the Courant restriction on the diffusive time step. We find that in idealized stratified simulations, with a spatially constant ambipolar Elsasser number Am, turbulence driven by the magnetorotational instability (MRI) behaves in a similar manner as in prior unstratified calculations. Turbulence dies away for Am < 1, and becomes progressively more vigorous as ambipolar diffusion is decreased. Near-ideal MHD behavior is recovered for Am > 1000. In the intermediate regime (10 < Am < 1000) ambipolar diffusion leads to substantial increases in both the period of the MRI dynamo cycle and the characteristic scales of magnetic field structures. To quantify the impact of ambipolar physics on disk accretion, we run simulations at 30 AU and 100 AU that include a vertical Am profile based upon far ultraviolet (FUV) ionized disk models. These models develop a vertically layered structure analogous to the Ohmic dead zone that is present at smaller radii. We find that, although the levels of surface turbulence can be strong (and consistent with constraints on turbulent line widths at these radii), the inferred accretion rates are at least an order of magnitude smaller than those observed in T Tauri stars. This discrepancy is very likely due to the assumption of zero vertical magnetic field in our simulations and suggests that vertical magnetic fields are essential for MRI-driven accretion in the outer regions of protoplanetary disks.

LOCAL TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE COLLISIONLESS MAGNETOROTATIONAL INSTABILITY

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the rate of Coulomb collisions between particles is very small, making the disk evolve essentially as a collisionless plasma. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell (PIC) plasma simulations. In this initial study we focus on local two-dimensional (axisymmetric) simulations, deferring more realistic three-dimensional simulations to future work. For simulations with net vertical magnetic flux, the MRI continuously amplifies the magnetic field until the Alfv\'en velocity, v_A, is comparable to the speed of light, c (independent of the initial value of v_A/c). This is consistent with the lack of saturation of MRI channel modes in analogous axisymmetric MHD simulations. The amplification of the magnetic field by the MRI generates a significant pressure anisotropy in the plasma (with the perpendicular pressure being larger than the parallel pressure). We find that this pressure anisotropy in turn excites mirror modes and that the volume averaged pressure anisotropy remains near the threshold for mirror mode excitation. Particle energization is due to both reconnection and viscous heating associated with the pressure anisotropy. Reconnection produces a distinctive power-law component in the energy distribution function of the particles, indicating the likelihood of non-thermal ion and electron acceleration in collisionless accretion disks. This has important implications for interpreting the observed emission -- from the radio to the gamma-rays -- of systems such as Sgr A*.

PLANETESIMAL FORMATION IN MAGNETOROTATIONALLY DEAD ZONES: CRITICAL DEPENDENCE ON THE NET VERTICAL MAGNETIC FLUX

Turbulence driven by magnetorotational instability (MRI) affects planetesimal formation by inducing diffusion and collisional fragmentation of dust particles. We examine conditions preferred for planetesimal formation in MRI-inactive "dead zones" using an analytic dead-zone model based on our recent resistive MHD simulations. We argue that successful planetesimal formation requires not only a sufficiently large dead zone (which can be produced by tiny dust grains) but also a sufficiently small net vertical magnetic flux (NVF). Although often ignored, the latter condition is indeed important since the NVF strength determines the saturation level of turbulence in MRI-active layers. We show that direct collisional formation of icy planetesimal across the fragmentation barrier is possible when the NVF strength is lower than 10 mG (for the minimum-mass solar nebula model). Formation of rocky planetesimals via the secular gravitational instability is also possible within a similar range of the NVF strength. Our results indicate that the fate of planet formation largely depends on how the NVF is radially transported in the initial disk formation and subsequent disk accretion processes.

Dead zones as safe havens for planetesimals: influence of disc mass and external magnetic field

(Abridged) Planetesimals embedded in a protoplanetary disc are stirred by gravitational torques exerted by density fluctuations in the surrounding turbulence. In particular, planetesimals in a disc supporting fully developed magneto-rotational turbulence are readily excited to velocity dispersions above the threshold for catastrophic disruption, halting planet formation. We aim to examine the stirring of planetesimals lying instead in a magnetically-decoupled midplane dead zone, stirred only by spiral density waves propagating out of the disc's magnetically-coupled turbulent surface layers. We extend previous studies to include a wider range of disc models, and explore the effects of varying the disc column density and external magnetic field strength. [...] The strength of the stirring is found to be independent of the gas surface density, which is contrary to the increase with disc mass expected from a simple linear wave picture. The discrepancy arises from the shearing out of density waves as they propagate into the dead zone, resulting in density structures near the midplane that exert weaker stochastic torques on average. We provide a simple analytic fit to our numerically obtained torque amplitudes that accounts for this effect. The stirring on the other hand depends sensitively on the net vertical magnetic flux, up to a saturation level above which magnetic forces dominate in the turbulent layers. For the majority of our models, the equilibrium planetesimal velocity dispersions lie between the thresholds for disrupting strong and weak aggregates, suggesting that collision outcomes will depend on material properties. However, discs with relatively weak magnetic fields yield reduced stirring, and their dead zones provide safe-havens even for the weakest planetesimals against collisional destruction.