The growth of solid particles towards meter sizes in protoplanetary disks has to circumvent at least two hurdles, namely the rapid loss of material due to radial drift and particle fragmentation due ...to destructive collisions. In this paper, we present the results of numerical simulations with more and more realistic physics involved. Step by step, we include various effects, such as particle growth, radial/vertical particle motion and dust particle fragmentation in our simulations. We demonstrate that the initial dust-to-gas ratio is essential for the particles to overcome the radial drift barrier. If this value is increased by a factor of 2 compared with the canonical value for the interstellar medium, km-sized bodies can form in the inner disk (<2 AU) within 104 yrs. However, we find that solid particles get destroyed through collisional fragmentation. Only with the unrealistically high-threshold velocities needed for fragmentation to occur (>30 m/s), particles are able to grow to larger sizes in disks with low α values. We also find that less than 5% of the small dust grains remain in the disk after 1 Myr due to radial drift, no matter whether fragmentation is included in the simulations or not. In this paper, we also present considerable improvements to existing algorithms for dust-particle coagulation, which speed up the coagulation scheme by a factor of ~ 104.
We model the process of dust coagulation in protoplanetary disks and calculate how it affects their observational appearance. Our model involves the detailed solution of the coagulation equation at ...every location in the disk. At regular time intervals we feed the resulting 3D dust distribution functions into a continuum radiative transfer code to obtain spectral energy distributions. We find that, even if only the very basic – and well understood – coagulation mechanisms are included, the process of grain growth is much too quick to be consistent with infrared observations of T Tauri disks. Small grains are removed so efficiently that, long before the disk reaches an age of 106 years typical of T Tauri stars, the SED shows only very weak infrared excess. This is inconsistent with observed SEDs of most classical T Tauri stars. Small grains must be replenished, for instance by aggregate fragmentation through high-speed collisions. A very simplified calculation shows that when aggregate fragmentation is included, a quasi-stationary grain size distribution is obtained in which growth and fragmentation are in equilibrium. This quasi-stationary state may last 106 years or even longer, depending on the circumstances in the disk, and may bring the time scales into the right regime. If this is indeed the case, or if other processes are responsible for the replenishment of small grains, then the typical grain sizes inferred from infrared spectral features of T Tauri disks do not necessarily reflect the age of the system (small grains $\rightarrow$ young, larger grains $\rightarrow$ older), as is often proposed. Indeed, there is evidence reported in the literature that the typical inferred grain sizes do not correlate with the age of the star. Instead, it is more likely that the typical grain sizes found in T Tauri star (and Herbig Ae/Be star and Brown Dwarf) disks reflect the state of the disk in some more complicated way, e.g. the strength of the turbulence, the amount of dust mass transformed into planetesimals, the amount of gas lost via evaporation etc. A simple evolutionary scenario in which grains slowly grow from pristine $0.1~\mu$m grains to larger grains over a period of a few Myr is most likely incorrect.
To understand how planetary systems form in the dusty disks around pre-main-sequence stars, a detailed knowledge of the structure and evolution of these disks is required. Although this is reasonably ...well understood for the regions of the disk beyond about 1 AU, the structure of these disks inward of 1 AU remains a puzzle. This is partly because it is very difficult to spatially resolve these regions with current telescopes. But it is also because the physics of this region, where the disk becomes so hot that the dust starts to evaporate, is poorly understood. With infrared interferometry it has become possible in recent years to directly spatially resolve the inner 1 AU of protoplanetary disks, albeit in a somewhat limited way. These observations have partly confirmed current models of these regions, but also posed new questions and puzzles. Moreover, it has turned out that the numerical modeling of these regions is extremely challenging. In this review, we give a rough overview of the history and recent developments in this exciting field of astrophysics. PUBLICATION ABSTRACT
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.
We analyze how the process of dust settling affects the spectral energy distribution and optical appearance of protoplanetary disks. Using simple analytic estimates on the one hand, and detailed ...1+1-D models on the other hand, we show that, while the time scale for settling down to the equator may exceed the life time of the disk, it takes much less time for even small grains of 0.1 μm to settle down to a few pressure scale heights. This is often well below the original location of the disk's photosphere, and the disk therefore becomes effectively “flatter”. If turbulent stirring is included, a steady state solution can be found, which is typically reached after a few $\times$105 years. In this state, the downward settling motion of the dust is balanced by vertical stirring. Dependent on the strength of the turbulence, the shape of the disk in such a steady state can be either fully flaring, or flaring only up to a certain radius and self-shadowed beyond that radius. These geometries are similar to the geometries that were found for disks around Herbig Ae/Be stars in our previous papers (Dullemond CITE A&A, 395, 853; Dullemond & Dominik 2004, A&A, 417, 159, henceforth DD04). In those papers, however, the reason for a disk to turn self-shadowed was by loss of optical depth through dust grain growth. Here we show that dust settling can achieve a similar effect without loss of vertical optical depth, although the self-shadowing in this case only affects the outer regions of the disk, while in DD04 the entire disk outside of the puffed-up inner rim was shadowed. In reality it is likely that both grain growth and grain settling act simultaneously. The spectral energy distributions of such self-shadowed – or partly self-shadowed – disks have a relatively weak far-infrared excess (in comparison to flaring disks). We show here that, when dust settling is the cause of self-shadowing, these self-shadowed regions of the disk are also very weak in resolved images of scattered light. A reduction in the brightness was already predicted in DD04, but we find that dust settling is far more efficient than grain growth at dimming the scattered light image of the disk. Settling is also efficient in steepening the spectral energy distribution at mid- to far-infrared wavelengths. From the calculations with compact grains it follows that, after about 106 years, most disks should be self-shadowed. The fact that some older disks are still observed with the characteristics of flaring disks therefore seems somewhat inconsistent with the time scales predicted by the settling model based on compact grains. This suggests that perhaps even the small grains ($\la$$0.1~\mu$m) have a porous or fractal structure, slowing down the settling. Alternatively, it could mean that the different geometries of observed disks is merely a reflection of the turbulent state of these disks.
Context. Streaming instability can be a very efficient way of overcoming growth and drift barriers to planetesimal formation. However, it was shown that strong clumping, which leads to planetesimal ...formation, requires a considerable number of large grains. State-of-the-art streaming instability models do not take into account realistic size distributions resulting from the collisional evolution of dust. Aims. We investigate whether a sufficient quantity of large aggregates can be produced by sticking and what the interplay of dust coagulation and planetesimal formation is. Methods. We develop a semi-analytical prescription of planetesimal formation by streaming instability and implement it in our dust coagulation code based on the Monte Carlo algorithm with the representative particles approach. Results. We find that planetesimal formation by streaming instability may preferentially work outside the snow line, where sticky icy aggregates are present. The efficiency of the process depends strongly on local dust abundance and radial pressure gradient, and requires a super-solar metallicity. If planetesimal formation is possible, the dust coagulation and settling typically need ~100 orbits to produce sufficiently large and settled grains and planetesimal formation lasts another ~1000 orbits. We present a simple analytical model that computes the amount of dust that can be turned into planetesimals given the parameters of the disk model.
Context.
Planetary migration is a key link between planet formation models and observed exoplanet statistics. So far, the theory of planetary migration has focused on the interaction of one or more ...planets with an inviscid or viscously evolving gaseous disk. Turbulent viscosity is thought to be the main driver of the secular evolution of the disk, and it is known to affect the migration process for intermediate- to high-mass planets. Recently, however, the topic of wind-driven accretion has experienced a renaissance because evidence is mounting that protoplanetary disks may be less turbulent than previously thought, and 3D non-ideal magnetohydrodynamic modeling of the wind-launching process is maturing.
Aims.
We investigate how wind-driven accretion may affect planetary migration. We aim for a qualitative exploration of the main effects and not for a quantitative prediction.
Methods.
We performed 2D hydrodynamic planet-disk interaction simulations with the FARGO3D code in the (
r
,
ϕ
) plane. The vertical coordinate in the disk and the launching of the wind are not treated explicitly. Instead, the torque caused by the wind onto the disk is treated using a simple two-parameter formula. The parameters are the wind mass-loss rate and the lever arm.
Results.
We find that the wind-driven accretion process replenishes the co-orbital region in a different way than the viscous accretion process. The former always injects mass from the outer edge of the co-orbital region, and always removes mass from the inner edge, while the latter injects or removes mass from the co-orbital region depending on the radial density gradients in the disk. As a consequence, the migration behavior can differ strongly, and can under certain conditions drive rapid type-III-like outward migration. We derive an analytic expression for the parameters under which this outward migration occurs.
Conclusions.
If wind-driven accretion plays a role in the secular evolution of protoplanetary disks, planetary migration studies have to include this process as well because it can strongly affect the resulting migration rate and migration direction.
A leading paradigm in planet formation is currently the streaming instability and pebble accretion scenario. Notably, dust must grow into sizes in a specific regime of Stokes numbers in order to make ...the processes in the scenario viable and sufficiently effective. The dust growth models currently in use do not implement some of the growth barriers suggested to be relevant in the literature. We investigate if the bouncing barrier, when effective, has an impact on the timescales and efficiencies of processes such as the streaming instability and pebble accretion as well as on the observational appearance of planet-forming disks. We implemented a formalism for the bouncing barrier into the publicly available dust growth model DustPy and ran a series of models to understand the impact. We found that the bouncing barrier has a significant effect on the dust evolution in planet-forming disks. In many cases, it reduces the size of the typical or largest particles available in the disk; it produces a very narrow, almost monodisperse, size distribution; and it removes most grains in the process, with an impact on scattered light images. It modifies the settling and therefore the effectiveness of and timescales for the streaming instability and for pebble accretion. An active bouncing barrier may well have observational consequences: It may reduce the strength of the signatures of small particles (e.g., the 10 silicate feature), and it may create additional shadowed regions visible in scattered light images. Modeling of planet formation that leans heavily on the streaming instability and on pebble accretion should take the bouncing barrier into account. The complete removal of small grains in our model is not consistent with observations. However, this could be resolved by incomplete vertical mixing or some level of erosion in collisions.
Context.
Meteorites preserve an imprint of conditions in the early Solar System. By studying the distribution of calcium-aluminium-rich inclusions (CAIs) that are embedded within meteorites, we can ...learn about the dynamical history of the protoplanetary disk from which our Solar System formed. A long-standing problem concerning CAIs is the CAI storage problem. CAIs are thought to have formed at high temperatures near the Sun, but they are primarily found in carbonaceous chondrites, which formed much further out, beyond the orbit of Jupiter. Additionally, radial drift of CAI particles should have removed them from the solar protoplanetary disk several million years before the parent bodies of meteorites in which they are encountered would have accreted.
Aims.
We revisit a previously suggested solution to the CAI storage problem by Desch, Kalyaan, and Alexander which proposed that CAIs were mixed radially outward through the disk and subsequently got trapped in a pressure maximum created by Jupiter’s growing core opening a planet gap. Our aim is to investigate whether their solution still works when we take into account the infall phase during which the disk builds up from the collapse of a molecular cloud core.
Methods.
We build a 1D numerical code in Python using the DISKLAB package to simulate the evolution of the solar protoplanetary disk, starting with a collapsing molecular cloud. CAIs are created in the model by thermal processing of solar nebula composition dust, and subsequently transported through the disk by turbulent diffusion, radial drift and advection by the gas.
Results.
We find that outward transport of CAIs during the infall phase is very efficient, possibly mixing them all the way into the far outer disk. Subsequent inward radial drift collects CAIs in the pressure maximum beyond Jupiter’s orbit while draining the inner disk, roughly reproducing parts of the result by Desch et al. By introducing CAI formation so early, abundances out to 100 AU remain significant, possibly not consistent with some meteoritic data. It is possible to create a disk that does not expand as far out and also does not push CAIs as far out by using a very slowly rotating cloud.
Protoplanetary disks often appear as multiple concentric rings in dust continuum emission maps and scattered light images. These features are often associated with possible young planets in these ...disks. Many non-planetary explanations have also been suggested, including snow lines, dead zones and secular gravitational instabilities in the dust. In this paper we suggest another potential origin. The presence of copious amounts of dust tends to strongly reduce the conductivity of the gas, thereby inhibiting the magneto-rotational instability, and thus reducing the turbulence in the disk. From viscous disk theory it is known that a disk tends to increase its surface density in regions where the viscosity (i.e. turbulence) is low. Local maxima in the gas pressure tend to attract dust through radial drift, increasing the dust content even more. We have investigated mathematically if this could potentially lead to a feedback loop in which a perturbation in the dust surface density could perturb the gas surface density, leading to increased dust drift and thus amplification of the dust perturbation and, as a consequence, the gas perturbation. We find that this is indeed possible, even for moderately small dust grain sizes, which drift less efficiently, but which are more likely to affect the gas ionization degree. We speculate that this instability could be triggered by the small dust population initially, and when the local pressure maxima are strong enough, the larger dust grains get trapped and lead to the familiar ring-like shapes. We also discuss the many uncertainties and limitations of this model.
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