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

Gas mass tracers in protoplanetary disks: CO is still the best

Protoplanetary disk mass is a key parameter controlling the process of planetary system formation. CO molecular emission is often used as a tracer of gas mass in the disk. In this study we consider the ability of CO to trace the gas mass over a wide range of disk structural parameters and search for chemical species that could possibly be used as alternative mass tracers to CO. Specifically, we apply detailed astrochemical modeling to a large set of models of protoplanetary disks around low-mass stars, to select molecules with abundances correlated with the disk mass and being relatively insensitive to other disk properties. We do not consider sophisticated dust evolution models, restricting ourselves with the standard astrochemical assumption of $0.1~\mu$m dust. We find that CO is indeed the best molecular tracer for total gas mass, despite the fact that it is not the main carbon carrier, provided reasonable assumptions about CO abundance in the disk are used. Typically, chemical reprocessing lowers the abundance of CO by a factor of 3, compared to the case of photo-dissociation and freeze-out as the only ways of CO depletion. On average only 13% C-atoms reside in gas-phase CO, albeit with variations from 2 to 30%. CO$_2$, H$_2$O and H$_2$CO can potentially serve as alternative mass tracers, the latter two being only applicable if disk structural parameters are known.Comment: Accepted for publication in Ap

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

Coagulation-Fragmentation Equilibrium for Charged Dust: Abundance of Submicron Grains Increases Dramatically in Protoplanetary Disks

Dust coagulation in protoplanetary disks is not straightforward and is subject to several slow-down mechanisms, such as bouncing, fragmentation and radial drift to the star. Furthermore, dust grains in UV-shielded disk regions are negatively charged due to collisions with the surrounding electrons and ions, which leads to their electrostatic repulsion. For typical disk conditions, the relative velocities between micron-size grains are small and their collisions are strongly affected by the repulsion. On the other hand, collisions between pebble-size grains can be too energetic, leading to grain fragmentation. The aim of the present paper is to study a combined effect of the electrostatic and fragmentation barriers on dust evolution. We numerically solve the Smoluchowski coagulation-fragmentation equation for grains whose charging occurs under conditions typical for the inner disk regions, where thermal ionization operates. We find that dust fragmentation efficiently resupplies the population of small grains under the electrostatic barrier. As a result, the equilibrium abundance of sub-micron grains is enhanced by several orders of magnitude compared to the case of neutral dust. For some conditions with fragmentation velocities $\sim 1$ m s$^{-1}$, macroscopic grains are completely destroyed.Comment: accepted for publication in Ap

Using HCO+^+ isotopologues as tracers of gas depletion in protoplanetary disk gaps

The widespread rings and gaps seen in the dust continuum in protoplanetary disks are sometimes accompanied by similar substructures seen in molecular line emission. One example is the outer gap at 100 au in AS 209, which shows that the H$_{13}$CO$^+$ and C$_{18}$O emission intensities decrease along with the continuum in the gap, while the DCO$^+$ emission increases inside the gap. We aim to study the behavior of DCO$^+$/H$_{13}$CO$^+$ and DCO$^+$/HCO$^+$ ratios in protoplanetary disk gaps assuming the two scenarios: the gas depletion follows the dust depletion and only the dust is depleted. We first modeled the physical disk structure using the thermo-chemical model ANDES. This 1+1D steady-state disk model calculates the thermal balance of gas and dust and includes the FUV, X-rays, cosmic rays, and other ionization sources together with the reduced chemical network for molecular coolants. Afterward, this physical structure was adopted for calculations of molecular abundances with the extended gas-grain chemical network with deuterium fractionation. Ideal synthetic spectra and 0th-moment maps were produced with LIME. We are able to qualitatively reproduce the increase in the DCO$^+$ intensity and the decrease in the H$_{13}$CO$^+$ and C$_{18}$O intensities inside the disk gap, which is qualitatively similar to what is observed in the outer AS 209 gap. The corresponding disk model assumes that both the gas and dust are depleted in the gap. The model with the gas-rich gap, where only the dust is depleted, produces emission that is too bright in all HCO$^+$ isotopologues and C$_{18}$O. The DCO$^+$/H$_{13}$CO$^+$ line ratio can be used to probe gas depletion in dust continuum gaps outside of the CO snow line. The DCO$^+$/C$_{18}$O line ratio shows a similar, albeit weaker, effect; however, these species can be observed simultaneously with a single ALMA or NOEMA setup.Comment: 12 pages, 7 figures, Accepted for publication in Astronomy and Astrophysic

Dust grains cannot grow to millimeter sizes in protostellar envelopes

A big question in the field of star and planet formation is the time at which substantial dust grain growth occurs. The observed properties of dust emission across different wavelength ranges have been used as an indication that millimeter-sized grains are already present in the envelopes of young protostars. However, this interpretation is in tension with results from coagulation simulations, which are not able to produce such large grains in these conditions. In this work, we show analytically that the production of millimeter-sized grains in protostellar envelopes is impossible under the standard assumptions about the coagulation process. We discuss several possibilities that may serve to explain the observed dust emission in the absence of in-situ grain growth to millimeter sizes.Comment: Accepted to Ap