Improving the thin-disk models of circumstellar disk evolution. The 2+1-dimensional model

Circumstellar disks of gas and dust are naturally formed from contracting pre-stellar molecular cores during the star formation process. To study various dynamical and chemical processes that take place in circumstellar disks prior to their dissipation and transition to debris disks, the appropriate numerical models capable of studying the long-term disk chemodynamical evolution are required. We present a new 2+1-dimensional numerical hydrodynamics model of circumstellar disk evolution, in which the thin-disk model is complemented with the procedure for calculating the vertical distributions of gas volume density and temperature in the disk. The reconstruction of the disk vertical structure is performed at every time step via the solution of the time-dependent radiative transfer equations coupled to the equation of the vertical hydrostatic equilibrium. We perform a detailed comparison between circumstellar disks produced with our previous 2D model and with the improved 2+1D approach. The structure and evolution of resulting disks, including the differences in temperatures, densities, disk masses and protostellar accretion rates, are discussed in detail. The new 2+1D model yields systematically colder disks, while the in-falling parental clouds are warmer. Both effects act to increase the strength of disk gravitational instability and, as a result, the number of gravitationally bound fragments that form in the disk via gravitational fragmentation as compared to the purely 2D thin-disk simulations with a simplified thermal balance calculation.Comment: Accepted for publication in Astronomy & Astrophysic

Structure and evolution of protoplanetary disks

We present here a few thoughts on how high-angular resolution observations can give clues to some properties of protoplanetary disks that are fundamental to theories of planet formation. High-angular resolution infrared spectroscopy, either with a large single mirror telescope, or by using infrared interferometry, allows us to probe the abundance of thermally processed dust in the disk as a function of distance to the star. We show that this radial abundance profile can give information about the early evolution of the protoplanetary disk as well as about the nature of the turbulence. Since turbulence is one of the main ingredients in theories of planet formation, this latter result is particularly important. We also show that Nature itself provides an interesting way to perform high-angular resolution observations with intermediate-angular resolution telescopes: if a disk has a (nearly) edge-on orientation and is located in a low-density ambient dusty medium, the disk casts a shadow into this medium, as it blocks the starlight in equatorial direction. We argue how these shadows can be used to characterize the dust in the disk

The early evolution of viscous and self-gravitating circumstellar disks with a dust component

The long-term evolution of a circumstellar disk starting from its formation and ending in the T Tauri phase was simulated numerically with the purpose of studying the evolution of dust in the disk with distinct values of viscous \alpha-parameter and dust fragmentation velocity v_frag. We solved numerical hydrodynamics equations in the thin-disk limit, which are modified to include a dust component consisting of two parts: sub-micron-sized dust and grown dust with a maximum radius a_r. The former is strictly coupled to the gas, while the latter interacts with the gas via friction. The conversion of small to grown dust, dust growth, and dust self-gravity are also considered. We found that the process of dust growth known for the older protoplanetary phase also holds for the embedded phase of disk evolution. The dust growth efficiency depends on the radial distance from the star - a_r is largest in the inner disk and gradually declines with radial distance. In the inner disk, a_r is limited by the dust fragmentation barrier. The process of small-to-grown dust conversion is very fast once the disk is formed. The total mass of grown dust in the disk (beyond 1 AU) reaches tens or even hundreds of Earth masses already in the embedded phase of star formation and even a greater amount of grown dust drifts in the inner, unresolved 1 AU of the disk. Dust does not usually grow to radii greater than a few cm. A notable exception are models with \alpha <= 10^{-3}, in which case a zone with reduced mass transport develops in the inner disk and dust can grow to meter-sized boulders in the inner 10 AU. Grown dust drifts inward and accumulates in the inner disk regions. This effect is most pronounced in the \alpha <= 10^{-3} models where several hundreds of Earth masses can be accumulated in a narrow region of several AU from the star by the end of embedded phase. (abridged).Comment: accepted by Astronomy & Astrophysic

Gravitoviscous protoplanetary disks with a dust component. I. The importance of the inner sub-au region

The central region of a circumstellar disk is difficult to resolve in global numerical simulations of collapsing cloud cores, but its effect on the evolution of the entire disk can be significant. We use numerical hydrodynamics simulations to model the long-term evolution of self-gravitating and viscous circumstellar disks in the thin-disk limit. Simulations start from the gravitational collapse of prestellar cores of 0.5--1.0~$M_\odot$ and both gaseous and dusty subsystems were considered, including a model for dust growth. The inner unresolved 1.0 au of the disk is replaced with a central "smart" cell (CSC) -- a simplified model that simulates physical processes that may occur in this region. We found that the mass transport rate through the CSC has an appreciable effect on the evolution of the entire disk. Models with slow mass transport form more massive and warmer disks and they are more susceptible to gravitational instability and fragmentation, including a newly identified episodic mode of disk fragmentation in the T Tauri phase of disk evolution. Models with slow mass transport through the CSC feature episodic accretion and luminosity bursts in the early evolution, while models with fast transport are characterized by a steadily declining accretion rate with low-amplitude flickering. Dust grows to a larger, decimeter size in the slow transport models and efficiently drifts in the CSC, where it accumulates reaching the limit when streaming instability becomes operational. We argue that gravitational instability, together with streaming instability likely operating in the inner disk regions, constitute two concurrent planet-forming mechanisms, which may explain the observed diversity of exoplanetary orbits (Abridged).Comment: Accepted for publication in Astronomy \& Astrophysic

Evolution of dust in protoplanetary disks of eruptive stars

Aims. Luminosity bursts in young FU Orionis-type stars warm up the surrounding disks of gas and dust, thus inflicting changes on their morphological and chemical composition. In this work, we aim at studying the effects that such bursts may have on the spatial distribution of dust grain sizes and the corresponding spectral index in protoplanetary disks. Methods. We use the numerical hydrodynamics code FEOSAD, which simulates the co-evolution of gas, dust, and volatiles in a protoplanetary disk, taking dust growth and back reaction on gas into account. The dependence of the maximum dust size on the water ice mantles is explicitly considered. The burst is initialized by increasing the luminosity of the central star to 100-300 L-circle dot for a time period of 100 yr. Results. The water snowline shifts during the burst to a larger distance, resulting in the drop of the maximum dust size interior to the snowline position because of more efficient fragmentation of bare grains. After the burst, the water snowline shifts quickly back to its preburst location followed by renewed dust growth. The timescale of dust regrowth after the burst depends on the radial distance so that the dust grains at smaller distances reach the preburst values faster than the dust grains at larger distances. As a result, a broad peak in the radial distribution of the spectral index in the millimeter dust emission develops at approximate to 10 au, which shifts further out as the disk evolves and dust grains regrow to preburst values at progressively larger distances. This feature is most pronounced in evolved axisymmetric disks rather than in young gravitationally unstable counterparts, although young disks may still be good candidates if gravitational instability is suppressed. We confirmed our earlier conclusion that spiral arms do not act as strong dust accumulators because of the Stokes number dropping below 0.01 within the arms, but this trend may change in low-turbulence disks. Conclusions. We argue that, depending on the burst strength and disk conditions, a broad peak in the radial distribution of the spectral index can last for up to several thousand years after the burst has ended and can be used to infer past bursts in otherwise quiescent protostars. The detection of a similar peak in the disk around V883 Ori, an FU Orionis-type star with an unknown eruption date, suggests that such features may be common in the post-outburst objects