Layered Accretion Research Articles

Planetesimal formation during protoplanetary disk buildup (Corrigendum)

Models of dust coagulation and subsequent planetesimal formation are usually computed on the backdrop of an already fully formed protoplanetary disk model. At the same time, observational studies suggest that planetesimal formation should start early, possibly even before the protoplanetary disk is fully formed. In this paper, we investigate under which conditions planetesimals already form during the disk buildup stage, in which gas and dust fall onto the disk from its parent molecular cloud. We couple our earlier planetesimal formation model at the water snow line to a simple model of disk formation and evolution. We find that under most conditions planetesimals only form after the buildup stage when the disk becomes less massive and less hot. However, there are parameters for which planetesimals already form during the disk buildup. This occurs when the viscosity driving the disk evolution is intermediate ($\alpha_v \sim 10^{-3}-10^{-2}$) while the turbulent mixing of the dust is reduced compared to that ($\alpha_t \le 0.03 \cdot \alpha_v$), and with the assumption that water vapor is vertically well-mixed with the gas. Such $\alpha_t \ll \alpha_v$ scenario could be expected for layered accretion, where the gas flow is mostly driven by the active surface layers, while the midplane layers, where most of the dust resides, are quiescent.

Depletion of Moderately Volatile Elements by Open-system Loss in the Early Solar Nebula

Rocky bodies of the inner solar system display a systematic depletion of “moderately volatile elements” (MVEs) that correlates with the expected condensation temperature of their likely host materials under protoplanetary nebula conditions. In this paper, we present and test a new hypothesis in which open-system loss processes irreversibly remove vaporized MVEs from high nebula altitudes, leaving behind the more refractory solids residing much closer to the midplane. The MVEs irreversibly lost from the nebula through these open-system loss processes are then simply unavailable for condensation onto planetesimals forming even much later, after the nebula has cooled, overcoming a critical difficulty encountered by previous models of this type. We model open-system loss processes operating at high nebula altitudes, such as resulting from disk winds flowing out of the system entirely, or layered accretion directly onto the young Sun. We find that mass-loss rates higher than those found in typical T-Tauri disk winds, lasting short periods of time, are most satisfactory, pointing to multiple intense early outburst stages. Using our global nebula model, incorporating realistic particle growth and inward drift for solids, we constrain how much the MVE-depletion signature in the inner region is diluted by the drift of undepleted material from the outer nebula. We also find that a significant irreversible loss of the common rock-forming elements (Fe, Mg, Si) can occur, leading to a new explanation of another long-standing puzzle of the apparent “enhancement” in the relative abundance of highly refractory elements in chondrites.

Planetesimal formation during protoplanetary disk buildup

Context. Models of dust coagulation and subsequent planetesimal formation are usually computed on the backdrop of an already fully formed protoplanetary disk model. At the same time, observational studies suggest that planetesimal formation should start early, possibly even before the protoplanetary disk is fully formed. Aims. In this paper we investigate under which conditions planetesimals already form during the disk buildup stage, in which gas and dust fall onto the disk from its parent molecular cloud. Methods. We couple our earlier planetesimal formation model at the water snow line to a simple model of disk formation and evolution. Results. We find that under most conditions planetesimals only form after the buildup stage, when the disk becomes less massive and less hot. However, there are parameters for which planetesimals already form during the disk buildup. This occurs when the viscosity driving the disk evolution is intermediate (αv ~ 10−3−10−2) while the turbulent mixing of the dust is reduced compared to that (αt ≲ 10−4), and with the assumption that the water vapor is vertically well-mixed with the gas. Such a αt ≪ αv scenario could be expected for layered accretion, where the gas flow is mostly driven by the active surface layers, while the midplane layers, where most of the dust resides, are quiescent. Conclusions. In the standard picture where protoplanetary disk accretion is driven by global turbulence, we find that no planetesimals form during the disk buildup stage. Planetesimal formation during the buildup stage is only possible in scenarios in which pebbles reside in a quiescent midplane while the gas and water vapor are diffused at a higher rate.

The origin and evolution of a differentiated Mimas

In stark contrast with its neighbor moon Enceladus, Mimas is surprisingly geologically quiet, despite an eccentric orbit and distance to Saturn prone to levels of tidal dissipation 30 times higher. While Mimas’ lack of geological activity could be due to a stiff, frigid interior, libration data acquired using the Cassini spacecraft suggest that its interior is not homogeneous. Here, we present one-dimensional models of the thermal, structural, and orbital evolution of Mimas under two accretion scenarios: primordial, undifferentiated formation in the Saturnian sub-nebula, and late, layered formation from a debris ring created by the disruption of one or more previous moons. We find it difficult to reproduce a differentiated, eccentric Mimas under a primordial accretion scenario: either Mimas never differentiates, or the internal warming that leads to differentiation increases tidal dissipation, yielding runaway heating that produces a persistent ocean, thereby circularizing Mimas’ orbit. Only if Mimas accretes very early (so that the decay of short-lived radionuclides initiates differentiation) but its rheology is not highly dissipative (in order to stop runaway tidal heating even if the eccentricity is not negligible) can the simulations match the observational constraints. Alternatively, a late, layered accretion scenario yields a present-day Mimas that matches observational constraints, independently of the magnitude of tidal dissipation. Consistent with previous findings, these models do not produce an ocean on Enceladus unless its orbital eccentricity is higher than today’s value.

VISCOUS INSTABILITY TRIGGERED BY LAYERED ACCRETION IN PROTOPLANETARY DISKS

Layered accretion is one of the inevitable ingredients in protoplanetary disks when disk turbulence is excited by magnetorotational instabilities (MRIs). In the accretion, disk surfaces where MRIs fully operate have a high value of disk accretion rate ($\dot{M}$), while the disk midplane where MRIs are generally quenched ends up with a low value of $\dot{M}$. Significant progress on understanding MRIs has recently been made by a number of dedicated MHD simulations, which requires improvement of the classical treatment of $\alpha$ in 1D disk models. To this end, we obtain a new expression of $\alpha$ by utilizing an empirical formula that is derived from recent MHD simulations of stratified disks with Ohmic diffusion. It is interesting that this new formulation can be regarded as a general extension of the classical $\alpha$. Armed with the new $\alpha$, we perform a linear stability analysis of protoplanetary disks that undergo layered accretion, and find that a viscous instability can occur around the outer edge of dead zones. Disks become stable in using the classical $\alpha$. We identify that the difference arises from $\Sigma-$dependence of $\dot{M}$; whereas $\Sigma$ is uniquely determined for a given value of $\dot{M}$ in the classical approach, the new approach leads to $\dot{M}$ that is a multi-valued function of $\Sigma$. We confirm our finding both by exploring a parameter space as well as by performing the 1D, viscous evolution of disks. We finally discuss other non-ideal MHD effects that are not included in our analysis, but may affect our results.

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.

ACCRETION OUTBURSTS IN SELF-GRAVITATING PROTOPLANETARY DISKS

We improve on our previous treatments of long-term evolution of protostellar disks by explicitly solving disk self-gravity in two dimensions. The current model is an extension of the one-dimensional layered accretion disk model of Bae et al. We find that gravitational instability (GI)-induced spiral density waves heat disks via compressional heating (i.e. $P\rm{d}V$ work), and can trigger accretion outbursts by activating the magnetorotational instability (MRI) in the magnetically inert disk dead-zone. The GI-induced spiral waves propagate well inside of gravitationally unstable region before they trigger outbursts at $R \lesssim 1$ AU where GI cannot be sustained. This long-range propagation of waves cannot be reproduced with the previously used local $\alpha$ treatments for GI. In our standard model where zero dead-zone residual viscosity ($\alpha_{\rm rd}$) is assumed, the GI-induced stress measured at the onset of outbursts is locally as large as $0.01$ in terms of the generic $\alpha$ parameter. However, as suggested in our previous one-dimensional calculations, we confirm that the presence of a small but finite $\alpha_{\rm rd}$ triggers thermally-driven bursts of accretion instead of the GI + MRI-driven outbursts that are observed when $\alpha_{\rm rd}=0$. The inclusion of non-zero residual viscosity in the dead-zone decreases the importance of GI soon after mass feeding from the envelope cloud ceases. During the infall phase while the central protostar is still embedded, our models stay in a quiescent accretion phase with $\dot{M}_{acc}\sim10^{-8}-10^{-7}~M_{\odot}~{\rm yr^{-1}}$ over $60~\%$ of the time and spend less than $15~\%$ of the infall phase in accretion outbursts.

Thanatology in protoplanetary discs

Protoplanetary discs are poorly ionised due to their low temperatures and high column densities, and are therefore subject to three "non-ideal" magnetohydrodynamic effects: Ohmic dissipation, ambipolar diffusion, and the Hall effect. The existence of magnetically driven turbulence in these discs has been a central question since the discovery of the magnetorotational instability. Early models considered Ohmic diffusion only and led to a scenario of layered accretion, in which a magnetically "dead" zone in the disc midplane is embedded within magnetically "active" surface layers at distances ~1-10 au from the central protostellar object. Recent work has suggested that a combination of Ohmic dissipation and ambipolar diffusion can render both the midplane and surface layers of the disc inactive and that torques due to magnetically driven outflows are required to explain the observed accretion rates. We reassess this picture by performing three-dimensional numerical simulations that include, for the first time, all three non-ideal MHD effects. We find that the Hall effect can generically "revive" dead zones by producing a dominant azimuthal magnetic field and a large-scale Maxwell stress throughout the midplane, provided the angular velocity and magnetic field satisfy Omega.B > 0. The attendant large magnetic pressure modifies the vertical density profile and substantially increases the disc scale height beyond its hydrostatic value. Outflows are produced, but are not necessary to explain accretion rates <10^{-7} Msun/yr. The flow in the disc midplane is essentially laminar, suggesting that dust sedimentation may be efficient. These results demonstrate that, if the MRI is relevant for driving mass accretion in protoplanetary discs, one must include the Hall effect to obtain even qualitatively correct results.

Testing large-scale vortex formation against viscous layers in three-dimensional discs

Vortex formation through the Rossby wave instability (RWI) in protoplanetary discs has been invoked to play a role in planet formation theory, and suggested to explain the observation of large dust asymmetries in several transitional discs. However, whether or not vortex formation operates in layered accretion discs, i.e. models of protoplanetary discs including dead zones near the disc midplane --- regions that are magnetically inactive and the effective viscosity greatly reduced --- has not been verified. As a first step toward testing the robustness of vortex formation in layered discs, we present non-linear hydrodynamical simulations of global 3D protoplanetary discs with an imposed kinematic viscosity that increases away from the disc midplane. Two sets of numerical experiments are performed: (i) non-axisymmetric instability of artificial radial density bumps in viscous discs; (ii) vortex-formation at planetary gap edges in layered discs. Experiment (i) shows that the linear instability is largely unaffected by viscosity and remains dynamical. The disc-planet simulations also show the initial development of vortices at gap edges, but in layered discs the vortices are transient structures which disappear well into the non-linear regime. We suggest that the long term survival of columnar vortices, such as those formed via the RWI, requires low effective viscosity throughout the vertical extent of the disc, so such vortices do not persist in layered discs.

Reference configurations of growing bodies

The growing bodies are considered as bodies with induced inhomogeneity caused by junction of inconsistently deformed parts. The body is formalized as an abstract smooth manifold, and all possible affine connections on it are classified. A method is shown for introducing a special connection—material connection—for which neighborhoods of all material points of a growing body pass into a stress-free state. A method for constructing a global stress-free reference configuration of a growing body as an embedding in a space with absolute parallelism is proposed. It is shown that in the case of layered accretion, the material connection corresponding to the stress-free embedding is determined by three independent functions and is in general non-Euclidean. The property of being non-Euclidean is determined by the fact that the torsion of the material connection is nonzero. We suggest to formalize the growing body as a fibration of a three-dimensional smooth manifold over a one-dimensional base, and this formalization characterizes the structure of the material connection.

Magnetic self-organization in Hall-dominated magnetorotational turbulence

The magnetorotational instability (MRI) is the most promising mechanism by which angular momentum is efficiently transported outwards in astrophysical discs. However, its application to protoplanetary discs remains problematic. These discs are so poorly ionised that they may not support magnetorotational turbulence in regions referred to as `dead zones'. It has recently been suggested that the Hall effect, a non-ideal magnetohydrodynamic (MHD) effect, could revive these dead zones by enhancing the magnetically active column density by an order of magnitude or more. We investigate this idea by performing local, three-dimensional, resistive Hall-MHD simulations of the MRI in situations where the Hall effect dominates over Ohmic dissipation. As expected from linear stability analysis, we find an exponentially growing instability in regimes otherwise linearly stable in resistive MHD. However, instead of vigorous and sustained magnetorotational turbulence, we find that the MRI saturates by producing large-scale, long-lived, axisymmetric structures in the magnetic and velocity fields. We refer to these structures as zonal fields and zonal flows, respectively. Their emergence causes a steep reduction in turbulent transport by at least two orders of magnitude from extrapolations based upon resistive MHD, a result that calls into question contemporary models of layered accretion. We construct a rigorous mean-field theory to explain this new behaviour and to predict when it should occur. Implications for protoplanetary disc structure and evolution, as well as for theories of planet formation, are briefly discussed.

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.

Effects of Layered Accretion on the Mechanics of Masonry Structures

Masonry constructions are built up in successive layers of bricks or blocks that may have considerable effect on the deformation and equilibrium of these structures when they are statically indeterminate and when gravity loads are predominant. This problem is analyzed by referring to a thick arch that reaches its final shape by means of a continuous deposition of heavy brick layers in stress free condition. The brick/block units of the accreting layer are assumed to have a negligible size in comparison to the structural size and the resulting continuous deposition is described taking into account their possible sliding on the current extrados at the instant of deposition. The kinematics of the growing body is described by the superposition of the displacement resulting from the continuing addition of heavy layers to the initial displacement at the considered point when it is attached to the current extrados, i.e., on the accreting layer. The two corresponding strain tensor fields do not satisfy the equations of compatibility, while the total strain field results to be compatible. The stress field is the cumulative effect of the incremental stress induced by the weight of the added layers during the growing process with residual stresses, which are shown to be independent of the initial strain field. Two examples are analyzed to show the effects of the growing process on the stress field and the properties of the strain field are discussed. The first example concerns a masonry wall supported at periodic points while the second example concerns a segmental multileaf thick arch in which the growing process begins from a thin arch resting on its own weight. In both cases a remarkable increase of the stress field is observed in comparison to the solution where the gravity loads are applied on the final domain.

Weathered Ilmenite: Diverse Mechanisms of Sintering and Association with Contaminants

We briefly review the nature and provenance of extremely weathered ilmenite, then investigate its fate when it is 10 % of a blended feed in the reduction kilns of the Becher process. There it is bound, unintentionally and intermittently, in sinter, which is discarded. It takes with it discrete aluminosilicate grains as well as contaminants, adsorbed and occluded within the ilmenite. Two distinct sintering mechanisms are identified. A layered wall accretion forms purely by solid state reaction, and is thickest early in the kiln. It occasionally detaches under its own weight or is eroded, and is tolerated between scheduled shutdowns for maintenance. However, if the weathered ilmenite and accompanying silica escape earlier wall accretion, a transitory aluminosilicate melt may later promote sintering of this material within the bed, adhering catastrophically to constrictions and obstructions on the kiln wall. The mechanisms and controlling factors are discussed.

TEMPERATURE STRUCTURE OF PROTOPLANETARY DISKS UNDERGOING LAYERED ACCRETION

We calculate the temperature structures of protoplanetary disks (PPDs) around T Tauri stars heated by both incident starlight and viscous dissipation. We present a new algorithm for calculating the temperatures in disks in hydrostatic and radiative equilibrium, based on Rybicki's method for iteratively calculating the vertical temperature structure within an annulus. At each iteration, the method solves for the temperature at all locations simultaneously, and converges rapidly even at high (>>10{sup 4}) optical depth. The method retains the full frequency dependence of the radiation field. We use this algorithm to study for the first time disks evolving via the magnetorotational instability. Because PPD midplanes are weakly ionized, this instability operates preferentially in their surface layers, and disks will undergo layered accretion. We find that the midplane temperatures T{sub mid} are strongly affected by the column density {Sigma}{sub a} of the active layers, even for fixed mass accretion rate M-dot . Models assuming uniform accretion predict midplane temperatures in the terrestrial planet forming region several x 10{sup 2} K higher than our layered accretion models do. For M-dot < 10{sup -7} M{sub sun} yr{sup -1} and the column densities {Sigma}{sub a} < 10 g cm{sup -2} associated with layered accretion, diskmore » temperatures are indistinguishable from those of a passively heated disk. We find emergent spectra are insensitive to {Sigma}{sub a}, making it difficult to observationally identify disks undergoing layered versus uniform accretion.« less

The baroclinic instability in the context of layered accretion

Context. Turbulence and angular momentum transport in accretion disks remains a topic of debate. With the realization that dead zones are robust features of protoplanetary disks, the search for hydrodynamical sources of turbulence continues. A possible source is the baroclinic instability (BI), which has been shown to exist in unmagnetized non-barotropic disks.

The Evolution of Protoplanetary Disks around Millisecond Pulsars: The PSR 1257+12 System

We model the evolution of protoplanetary disks surrounding millisecond pulsars, using PSR 1257+12 as a test case. Initial conditions were chosen to correspond to initial angular momenta expected for supernova-fallback disks and disks formed from the tidal disruption of a companion star. Models were run under two models for the viscous evolution of disks: fully viscous and layered accretion disk models. Supernova-fallback disks result in a distribution of solids confined to within 1-2 AU and produce the requisite material to form the three known planets surrounding PSR 1257+12. Tidal disruption disks tend to slightly underproduce solids interior to 1 AU, required for forming the pulsar planets, while overproducing the amount of solids where no body, lunar mass or greater, exists. Disks evolving under 'layered' accretion spread somewhat less and deposit a higher column density of solids into the disk. In all cases, circumpulsar gas dissipates on $\lesssim 10^{5}$ year timescales, making formation of gas giant planets highly unlikely.

Evolution of protoplanetary discs driven by the MRI, self-gravity and hydrodynamical turbulence

We study the viscous evolution of protoplanetary discs driven by the combined action of magnetohydrodynamic turbulence, resulting from the magneto-rotational instability (MRI), self-gravity torques, parametrized in terms of an effective viscosity and an additional viscous agent of unspecified origin. The distribution of torques driving the evolution of the disc is calculated by analysing where in the disc the MRI develops and, to incorporate the effect of self-gravity, calculating the Toomre parameter. We find that, generally, discs rapidly evolve towards a configuration where the intermediate regions, from a fraction of an au to a few au, are stable against the MRI due to their low-ionization degree. As an additional source of viscosity is assumed to operate in those regions, subsequent evolution of the disc is eruptive. Brief episodes of high mass accretion ensue as the criterion for the development of the MRI is met in the low-ionization region. The radial distribution of mass and temperature in the disc differs considerably from disc models with constant α parameter or layered accretion models, with potentially important consequences on the process of planet formation.

Local Magnetohydrodynamic Models of Layered Accretion Disks

Using numerical MHD simulations, we have studied the evolution of the magnetorotational instability (MRI) 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 that 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 quiescent. The vertical Poynting flux into the central zone is small; however, velocity fluctuations in the dead zone driven by the turbulence in the active layers generate a significant Reynolds stress in the midplane. When normalized by the thermal pressure, the Reynolds stress in the midplane never drops below about 10% of the value of the Maxwell stress in the active layers, even though the Maxwell stress in the dead zone may be orders of magnitude smaller than this. Significant mass mixing occurs between the dead zone and active layers. Fluctuations in the magnetic energy in the active layers can drive vertical oscillations of the disk in models in which the ratio of the column density in the dead zone to that in the active layers is less than 10. These results have important implications for the global evolution of a layered disk; in particular, there may be residual mass inflow in the dead layer. We discuss the effects that dust in the disk may have on our results.

Note on the “Dead Zone” in Layered Accretion Models

Abstract 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 mixing together with the two active layers.