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

Abstract

Aims. 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 α-parameter and dust fragmentation velocity v frag . Methods. 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 ar. 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. Results. 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 -ar is largest in the inner disk and gradually declines with radial distance. In the inner disk, ar 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 α ≤ 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 α ≤ 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. The efficiency of grown dust accumulation in spiral arms is stronger near corotation where the azimuthal velocity of dust grains is closest to the local velocity of the spiral pattern. In the framework of the adopted dust growth model, the efficiency of small-to-grown dust conversion was found to increase for lower values of α and v frag .

Dynamical Gaseous Rings in Global Simulations of Protoplanetary Disk Formation

“…However, building a comprehensive model is challenging due to the complexity of the physics involved and running such simulations is generally computationally expensive (e.g., see Haworth et al 2016). In the future we plan to conduct simulations of magnetically layered protoplanetary disks using a hydrodynamic model similar to Vorobyov et al (2018), which includes evolution of a two-part dusty component.…”

“…A solution to this problem is to allow matter to flow freely from the disk to the central sink cell and vice versa. This inflow-outflow boundary condition was presented in Vorobyov et al (2018) and is schematically illustrated in Figure 1. The mass of material that passes to the sink cell through the sink-disk interface is further redistributed between the central protostar and the sink cell as ∆M flow = ∆M * + ∆M s.c. according to the following algorithm (note that ∆M flow is always positive definite):…”

“…The exact partition between ∆M * and ∆M s.c. is usually set to 95%:5%. The influence of the ∆M * : ∆M s.c. partition on the disk evolution is studied in Vorobyov et al (2019). The calculated surface densities in the sink cell Σ n+1 s.c.…”

“…where the assumed values of fragmentation velocity is v frag = 10 m s −1 , and the internal density of the dust aggregate is ρ s = 1.6 g cm −3 . The a frag is a measure of the maximum size that the dust particles can achieve before they are destroyed through the process of fragmentation, which tends to limit the dust size in the inner disk (Birnstiel et al 2012;Vorobyov et al 2018). The Stokes number for a particle of size a, under typical assumptions, is calculated as…”

Revealing dust segregation in protoplanetary discs with the help of multifrequency spectral index maps

“…The initial temperature of the prestellar core is set equal to 20 K. The initial pre-stellar core is similar to the Bonnor-Ebert sphere with a central plateau and gas surface density declining at the core periphery. For more details on the initial configuration we refer to Vorobyov et al (2018). Using the distributions of dust density, maximum dust radius and dust temperature obtained by the FEOSAD code, we calculated the radiation intensity distributions for the wavelengths that were selected to produce spectral index maps.…”