Xue-Ning Bai

Dynamics of Solids in the Midplane of Protoplanetary Disks: Implications for Planetesimal Formation

We present local two-dimensional and three-dimensional hybrid numerical simulations of particles and gas in the midplane of protoplanetary disks (PPDs) using the Athena code. The particles are coupled to gas aerodynamically, with particle-to-gas feedback included. Magnetorotational turbulence is ignored as an approximation for the dead zone of PPDs, and we ignore particle self-gravity to study the precursor of planetesimal formation. Our simulations include a wide size distribution of particles, ranging from strongly coupled particles with dimensionless stopping time τ s ≡ Ωt stop = 10–4 (where Ω is the orbital frequency, t stop is the particle friction time) to marginally coupled ones with τ s = 1, and a wide range of solid abundances. Our main results are as follows. (1) Particles with τ s 10–2 actively participate in the streaming instability (SI), generate turbulence, and maintain the height of the particle layer before Kelvin-Helmholtz instability is triggered. (2) Strong particle clumping as a consequence of the SI occurs when a substantial fraction of the solids are large (τ s 10–2) and when height-integrated solid-to-gas mass ratio Z is super-solar. We construct a toy model to offer an explanation. (3) The radial drift velocity is reduced relative to the conventional Nakagawa-Sekiya-Hayashi (NSH) model, especially at high Z. Small particles may drift outward. We derive a generalized NSH equilibrium solution for multiple particle species which fits our results very well. (4) Collision velocity between particles with τ s 10–2 is dominated by differential radial drift, and is strongly reduced at larger Z. This is also captured by the multi-species NSH solution. Various implications for planetesimal formation are discussed. In particular, we show that there exist two positive feedback loops with respect to the enrichment of local disk solid abundance and grain growth. All these effects promote planetesimal formation.

RINGED SUBSTRUCTURE AND A GAP AT 1 au IN THE NEAREST PROTOPLANETARY DISK

We present long-baseline Atacama Large Millimeter/submillimeter Array (ALMA) observations of the 870 micron continuum emission from the nearest gas-rich protoplanetary disk, around TW Hya, that trace millimeter-sized particles down to spatial scales as small as 1 AU (20 mas). These data reveal a series of concentric ring-shaped substructures in the form of bright zones and narrow dark annuli (1-6 AU) with modest contrasts (5-30%). We associate these features with concentrations of solids that have had their inward radial drift slowed or stopped, presumably at local gas pressure maxima. No significant non-axisymmetric structures are detected. Some of the observed features occur near temperatures that may be associated with the condensation fronts of major volatile species, but the relatively small brightness contrasts may also be a consequence of magnetized disk evolution (the so-called zonal flows). Other features, particularly a narrow dark annulus located only 1 AU from the star, could indicate interactions between the disk and young planets. These data signal that ordered substructures on ~AU scales can be common, fundamental factors in disk evolution, and that high resolution microwave imaging can help characterize them during the epoch of planet formation.

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

We perform three-dimensional, vertically-stratified, local shearing-box ideal MHD simulations of the magnetorotational instability (MRI) that include a net vertical magnetic flux, which is characterized by midplane plasma β0 (ratio of gas to magnetic pressure). We have considered β0 = 102, 103, and 104, 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 β0: the radial transport of angular momentum increases with net vertical flux, achieving α ~ 0.08 for β = 104 and α 1.0 for β0 = 100, where α is the height-integrated and mass-weighted Shakura-Sunyaev parameter. A critical value lies at β0 ~ 103: for β0 103, 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 β0 103, the entire disk becomes magnetically dominated. The turbulent strength saturates, and the magnetic dynamo is fully 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 β0 102. However, the outflow is unlikely to be directly connected to a global wind: for β0 103, the large-scale field has no permanent bending direction due to dynamo activities, while for β0 103, 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.

EFFECT OF AMBIPOLAR DIFFUSION ON THE NONLINEAR EVOLUTION OF MAGNETOROTATIONAL INSTABILITY IN WEAKLY IONIZED DISKS

We study the role of ambipolar diffusion (AD) on the nonlinear evolution of the magnetorotational instability (MRI) in protoplanetary disks using the strong coupling limit, which applies in very weakly ionized gas with electron recombination time much shorter than the orbital time so that a single-fluid treatment is sufficient. The effect of AD in this limit is characterized by the dimensionless number Am, the frequency at which neutral particles collides with ions normalized to the orbital frequency. We perform three-dimensional unstratified shearing-box simulations of the MRI over a wide range of Am as well as different magnetic field strengths and geometries. The saturation level of the MRI turbulence depends on the magnetic geometry and increases with the net magnetic flux. There is an upper limit to the net flux for sustained turbulence, corresponding to the requirement that the most unstable vertical wavelength be less than the disk scale height. Correspondingly, at a given Am, there exists a maximum value of the turbulent stress αmax. For Am 1, the largest stress is associated with a field geometry that has both net vertical and toroidal flux. In this case, we confirm the results of linear analyses that show the fastest growing mode has a non-zero radial wavenumber with a growth rate exceeding that of the pure vertical field case. We find there is a very tight correlation between the turbulent stress α and the plasma β ≡ P gas/P mag ≈ 1/2α at the saturated state of the MRI turbulence regardless of field geometry, and αmax rapidly decreases with decreasing Am. In particular, we find αmax ≈ 7 × 10–3 for Am = 1 and αmax ≈ 6 × 10–4 for Am = 0.1.

HEAT AND DUST IN ACTIVE LAYERS OF PROTOSTELLAR DISKS

Requirements for magnetic coupling and accretion in the active layer of a protostellar disk are re-examined, and some implications for thermal emission from the layer are discussed. The ionization and electrical conductivity are calculated following the general scheme of Ilgner and Nelson but with an updated UMIST database of chemical reactions and some improvements in the grain physics, and for the minimum-mass solar nebula rather than an alpha disk. The new limits on grain abundance are slightly more severe than theirs. Even for optimally sized grains, the layer should be at least marginally optically thin to its own thermal radiation, so that narrow, highly saturated emission lines of water and other molecular species would be expected if accretion is driven by turbulence and standard rates of ionization prevail. If the grain size distribution extends broadly from well below a micron to a millimeter or more, as suggested by observations, then the layer may be so optically thin that its cooling is dominated by molecular emission. Even under such conditions, it is difficult to have active layers of more than 10 g cm-2 near 1 AU unless dust is entirely eliminated or greatly enhanced ionization rates are assumed. Equipartition-strength magnetic fields are then required in these regions of the disk if observed accretion rates are driven by magnetorotational turbulence. Wind-driven accretion might allow weaker fields and less massive active layers but would not heat the layer as much as turbulence and therefore might not produce emission lines.

HALL-EFFECT-CONTROLLED GAS DYNAMICS IN PROTOPLANETARY DISKS. I. WIND SOLUTIONS AT THE INNER DISK

The gas dynamics of protoplanetary disks (PPDs) is largely controlled by non-ideal magnetohydrodynamic (MHD) effects including Ohmic resistivity, the Hall effect, and ambipolar diffusion. Among these the role of the Hall effect is the least explored and most poorly understood. In this series, we have included, for the first time, all three non-ideal MHD effects in a self-consistent manner to investigate the role of the Hall effect on PPD gas dynamics using local shearing-box simulations. In this first paper, we focus on the inner region of PPDs, where previous studies (Bai & Stone 2013; Bai 2013) excluding the Hall effect have revealed that the inner disk up to ~10 AU is largely laminar, with accretion driven by a magnetocentrifugal wind. We confirm this basic picture and show that the Hall effect modifies the wind solutions depending on the polarity of the large-scale poloidal magnetic field threading the disk. When , the horizontal magnetic field is strongly amplified toward the disk interior, leading to a stronger disk wind (by ~50% or less in terms of the wind-driven accretion rate). The enhanced horizontal field also leads to much stronger large-scale Maxwell stress (magnetic braking) that contributes to a considerable fraction of the wind-driven accretion rate. When , the horizontal magnetic field is reduced, leading to a weaker disk wind (by 20%) and negligible magnetic braking. Under fiducial parameters, we find that when , the laminar region extends farther to ~10-15 AU before the magnetorotational instability sets in, while for , the laminar region extends only to ~3-5 AU for a typical accretion rate of ~10?8 to10?7 M ? yr?1. Scaling relations for the wind properties, especially the wind-driven accretion rate, are provided for aligned and anti-aligned field geometries.

HALL EFFECT CONTROLLED GAS DYNAMICS IN PROTOPLANETARY DISKS. II. FULL 3D SIMULATIONS TOWARD THE OUTER DISK

We perform 3D stratified shearing-box MHD simulations on the gas dynamics of protoplanetary disks threaded by net vertical magnetic field Bz. All three non-ideal MHD effects, Ohmic resistivity, the Hall effect and ambipolar diffusion are included in a self-consistent manner based on equilibrium chemistry. We focus on regions toward outer disk radii, from 5-60AU, where Ohmic resistivity tends to become negligible, ambipolar diffusion dominates over an extended region across disk height, and the Hall effect largely controls the dynamics near the disk midplane. We find that around R=5AU, the system launches a laminar/weakly turbulent magnetocentrifugal wind when the net vertical field Bz is not too weak, as expected. Moreover, the wind is able to achieve and maintain a configuration with reflection symmetry at disk midplane. The case with anti-aligned field polarity (Omega. Bz<0) is more susceptible to the MRI when Bz drops, leading to an outflow oscillating in radial directions and very inefficient angular momentum transport. At the outer disk around and beyond R=30AU, the system shows vigorous MRI turbulence in the surface layer due to far-UV ionization, which efficiently drives disk accretion. The Hall effect affects the stability of the midplane region to the MRI, leading to strong/weak Maxwell stress for aligned/anti-aligned field polarities. Nevertheless, the midplane region is only very weakly turbulent. Overall, the basic picture is analogous to the conventional layered accretion scenario applied to the outer disk. In addition, we find that the vertical magnetic flux is strongly concentrated into thin, azimuthally extended shells in most of our simulations beyond 15AU. This is a generic phenomenon unrelated to the Hall effect, and leads to enhanced zonal flow. Observational and theoretical implications, as well as future prospects are briefly discussed.

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 ? 103. In the intermediate regime (10 ? Am ? 103) 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.

Numerical Simulation of Hot Accretion Flows. III. Revisiting Wind Properties Using the Trajectory Approach

United States. National Aeronautics and Space Administration. Einstein Postdoctoral Fellowship Award (PF4-150126)

ALMA OBSERVATIONS OF A GAP AND A RING IN THE PROTOPLANETARY DISK AROUND TW HYA

We report the first detection of a gap and a ring in 336 GHz dust continuum emission from the protoplanetary disk around TW Hya, using the Atacama Large Millimeter/Submillimeter Array (ALMA). The gap and ring are located at around 25 and 41 au from the central star, respectively, and are associated with the CO snow line at ~30 au. The gap has a radial width of less than 15 au and a mass deficit of more than 23%, taking into account that the observations are limited to an angular resolution of ~15 au. In addition, the 13CO and C18O J = 3 - 2 lines show a decrement in CO line emission throughout the disk, down to ~10 au, indicating a freeze-out of gas-phase CO onto grain surfaces and possible subsequent surface reactions to form larger molecules. The observed gap could be caused by gravitational interaction between the disk gas and a planet with a mass less than super-Neptune (2M_{Neptune}), or could be the result of the destruction of large dust aggregates due to the sintering of CO ice.