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Eduard I. Vorobyov

Publications and source records attributed to Eduard I. Vorobyov.

At least 37 records · Page 2Linked to original sources

Protostellar-disc fragmentation across all metallicities

Cosmic metallicity evolution possibly creates the diversity of star formation modes at different epochs. Gravitational fragmentation of circumstellar discs provides an important formation channel of multiple star systems, including close binaries. We here study the nature of disc fragmentation, systematically performing a suite of two-dimensional radiation-hydrodynamic simulations, in a broad range of metallicities, from the primordial to the solar values. In particular, we follow relatively long-term disc evolution over 15 kyr after the disc formation, incorporating the effect of heating by the protostellar irradiation. Our results show that the disc fragmentation occurs at all metallicities $1$--$0$ $Z_{\odot}$, yielding self-gravitating clumps. Physical properties of the clumps, such as their number and mass distributions, change with the metallicity due to different gas thermal evolution. For instance, the number of clumps is the largest for the intermediate metallicity range of $10^{-2}$--$10^{-5}$ $Z_{\odot}$, where the dust cooling is effective exclusively in a dense part of the disc and causes the fragmentation of spiral arms. The disc fragmentation is more modest for $1$--$0.1$ $Z_{\odot}$ thanks to the disc stabilization by the stellar irradiation. Such metallicity dependence agrees with the observed trend that the close binary fraction increases with decreasing metallicity in the range of $1$--$10^{-3}$ $Z_{\odot}$.

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Millimeter-sized Dust Grains Appear Surviving the Water-sublimating Temperature in the Inner 10 au of the FU Ori Disk

Previous observations have shown that the $\lesssim$10 au, $\gtrsim$400 K hot inner disk of the archetypal accretion outburst young stellar object, FU Ori, is dominated by viscous heating. To constrain dust properties in this region, we have performed radio observations toward this disk using the Karl G. Jansky Very Large Array (JVLA) in 2020 June-July, September, and November. We also performed complementary optical photometric monitoring observations. We found that the dust thermal emission from the hot inner disk mid-plane of FU Ori has been approximately stationary and the maximum dust grain size is $\gtrsim$1.6 mm in this region. If the hot inner disk of FU Ori which is inward of the 150-170 K water snowline is turbulent (e.g., corresponding to a Sunyaev & Shakura viscous $α_{t}\gtrsim$0.1), or if the actual maximum grain size is still larger than the lower limit we presently constrain, then as suggested by the recent analytical calculations and the laboratory measurements, water-ice free dust grains may be stickier than water-ice coated dust grains in protoplanetary disks. Additionally, we find that the free-free emission and the Johnson B and V bands magnitudes of these binary stars are brightening in 2016-2020. The optical and radio variability might be related to the dynamically evolving protostellar or disk accretion activities. Our results highlight that hot inner disks of outbursting objects are important laboratories for testing models of dust grain growth. Given the active nature of such systems, to robustly diagnose the maximum dust grain sizes, it is important to carry out coordinated multi-wavelength radio observations.

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Accretion bursts in high-mass protostars: a new testbed for models of episodic accretion

It is well known that low mass young stellar objects (LMYSOs) gain a significant portion of their final mass through episodes of very rapid accretion, with mass accretion rates up to $\dot M_* \sim 10^{-4} M_{\odot}$~yr$^{-1}$. Recent observations of high mass young stellar objects (HMYSO) with masses $M_* \gtrsim 10 M_{\odot}$ uncovered outbursts with accretion rates exceeding $\dot M_*\sim 10^{-3}M_{\odot}$~yr$^{-1}$. Here we examine which scenarios proposed in the literature so far to explain accretion bursts of LMYSOs can apply to the episodic accretion in HMYSOs. We utilise a 1D time dependent models of protoplanetary discs around HMYSOs to study burst properties. We find that discs around HMYSOs are much hotter than those around their low mass cousins. As a result, much more extended regions of the disc are prone to the thermal hydrogen ionisation and MRI activation instabilities. The former in particular is found to be ubiquitous in a very wide range of accretion rates and disc viscosity parameters. The outbursts triggered by these instabilities, however, always have too low $\dot M_*$, and are one to several orders of magnitude too long compared to those observed from HMYSOs so far. On the other hand, bursts generated by tidal disruptions of gaseous giant planets formed by the gravitational instability of the protoplanetary discs yield properties commensurate with observations, provided that the clumps are in the post-collapse configuration with planet radius $R_{\rm p} \gtrsim 10 $ Jupiter radii. Furthermore, if observed bursts are caused by disc ionisation instabilities then they should be periodic phenomena with the duration of the quiescent phase comparable to that of the bursts. This may yield potentially observable burst periodicity signatures in the jets, the outer disc, or the surrounding diffuse material of massive HMYSOs. (abridged)

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Gravitoviscous protoplanetary disks with a dust component. V. The dynamic model for freeze-out and sublimation of volatiles

The snowlines of various volatile species in protoplanetary disks are associated with abrupt changes in gas composition and dust physical properties. Volatiles may affect dust growth, as they cover grains with icy mantles that can change the fragmentation velocity of the grains. In turn, dust coagulation, fragmentation, and drift through the gas disk can contribute to the redistribution of volatiles between the ice and gas phases. Here we present the hydrodynamic model FEOSAD for protoplanetary disks with two dust populations and volatile dynamics. We compute the spatial distributions of major volatile molecules (H$_2$O, CO$_2$, CH$_4$, and CO) in the gas, on small and grown dust, and analyze the composition of icy mantles over the initial 0.5 Myr of disk evolution. We show that most of ice arrives to the grown dust through coagulation with small grains. Spiral structures and dust rings forming in the disk, as well as photodissociation in the outer regions, lead to the formation of complex snowline shapes and multiple snowlines for each volatile species. During the considered disk evolution, the snowlines shift closer to the star, with their final position being a factor $4-5$ smaller than that at the disk formation epoch. We demonstrate that volatiles tend to collect in the vicinity of their snowlines, both in the ice and gas phases, leading to the formation of thick icy mantles potentially important for dust dynamics. The dust size is affected by a lower fragmentation velocity of bare grains in the model with a higher turbulent viscosity.

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Simulations of Dynamical Gas-Dust Circumstellar Disks: Going Beyond the Epstein Regime

In circumstellar disks, the size of dust particles varies from submicron to several centimeters, while planetesimals have sizes of hundreds of kilometers. Therefore, various regimes for the aerodynamic drag between solid bodies and gas can be realized in these disks, depending on the grain sizes and velocities: Epstein, Stokes, and Newton, as well as transitional regimes between them. For small bodies moving in the Epstein regime, the time required to establish the constant relative velocity between the gas and bodies can be much less than the dynamical time scale for the problem - the time for the rotation of the disk about the central body. In addition, the dust may be concentrated in individual regions of the disk, making it necessary to take into account the transfer of momentum between the dust and gas. It is shown that, for a system of equations for gas and monodisperse dust, a semi-implicit first-order approximation scheme in time in which the interphase interaction is calculated implicitly, while other forces, such as the pressure gradient and gravity are calculated explicitly, is suitable for stiff problems with intense interphase interactions and for computations of the drag in non-linear regimes. The piece-wise drag coefficient widely used in astrophysical simulations has a discontinuity at some values of the Mach and Knudsen numbers that are realized in a circumstellar disk. A continuous drag coefficient is presented, which corresponds to experimental dependences obtained for various drag regimes.

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Distinguishing between different mechanisms of FU-Orionis-type luminosity outbursts

Aims. Accretion and luminosity bursts triggered by three distinct mechanisms: the magnetorotational instability in the inner disk regions, clump infall in gravitationally fragmented disks and close encounters with an intruder star, were studied to determine the disk kinematic characteristics that can help to distinguish between these burst mechanisms. Methods. Numerical hydrodynamics simulations in the thin-disk limit were employed to model the bursts in disk environments that are expected for each burst mechanism. Results. We found that the circumstellar disks featuring accretion bursts can bear kinematic features that are distinct for different burst mechanisms, which can be useful when identifying the burst origin. The disks in the stellar encounter and clump-infall models are characterized by tens of percent deviations from the Keplerian rotation, whie the disks in the MRI models are characterized only a few percent deviation, which is mostly caused by the gravitational instability that fuels the MRI bursts. Velocity channel maps also show distinct kinks and wiggles, which are caused by gas disk flows that are peculiar to each considered burst mechanism. The deviations of velocity channels in the burst-hosting disks from a symmetric pattern typical of Keplerian disks are strongest for the clump-infall and collision models, and carry individual features that may be useful for the identification of the corresponding burst mechanism. The considered burst mechanisms produce a variety of light curves with the burst amplitudes varying in the Δm=2.5-3.7 limits, except for the clump-infall model where Δm can reach 5.4, although the derived numbers may be affected by a small sample and boundary conditions. Conclusions. Burst triggering mechanisms are associated with distinct kinematic features in the burst-hosting disks that may be used for their identification. Abridged.

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Disk fragmentation and intermittent accretion onto supermassive stars

Supermassive stars (SMSs) with $\sim10^{4-5}~\mathrm{M}_{\odot}$ are candidate objects for the origin of supermassive black holes observed at redshift $z$>6. They are supposed to form in primordial-gas clouds that provide the central stars with gas at a high accretion rate, but their growth may be terminated in the middle due to the stellar ionizing radiation if the accretion is intermittent and its quiescent periods are longer than the Kelvin-Helmholtz (KH) timescales at the stellar surfaces. In this paper, we examine the role of the ionizing radiation feedback based on the accretion history in two possible SMS-forming clouds extracted from cosmological simulations, following their evolution with vertically-integrated two-dimensional hydrodynamic simulations with detailed thermal and chemical models. The consistent treatment of the gas thermal evolution is crucial for obtaining the realistic accretion history, as we demonstrate by performing an additional run with a barotropic equation of state, in which the fluctuation of the accretion rate is artificially suppressed. We find that although the accretion becomes intermittent due to the formation of spiral arms and clumps in gravitationally unstable disks, the quiescent periods are always shorter than the KH timescales, implying that SMSs can form without affected by the ionizing radiation.

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Thermal evolution of protoplanetary disks: from $β$-cooling to decoupled gas and dust temperatures

Aims: We explore the long-term evolution of young protoplanetary disks with different approaches to computing the thermal structure determined by various cooling and heating processes in the disk and its surroundings. Methods: Numerical hydrodynamics simulations in the thin-disk limit were complemented with three thermal evolution schemes: a simplified $β$-cooling approach with and without irradiation, in which the rate of disk cooling is proportional to the local dynamical time, a fiducial model with equal dust and gas temperatures calculated taking viscous heating, irradiation, and radiative cooling into account, and also a more sophisticated approach allowing decoupled dust and gas temperatures. Results: We found that the gas temperature may significantly exceed that of dust in the outer regions of young disks thanks to additional compressional heating caused by the infalling envelope material in the early stages of disk evolution and slow collisional exchange of energy between gas and dust in low-density disk regions. The outer envelope however shows an inverse trend with the gas temperatures dropping below that of dust. The global disk evolution is only weakly sensitive to temperature decoupling. Nevertheless, separate dust and gas temperatures may affect the chemical composition, dust evolution, and disk mass estimates. Constant-$β$ models without stellar and background irradiation fail to reproduce the disk evolution with more sophisticated thermal schemes because of intrinsically variable nature of the $β$-parameter. Constant-$β$ models with irradiation can better match the dynamical and thermal evolution, but the agreement is still incomplete. Conclusions: Models allowing separate dust and gas temperatures are needed when emphasis is placed on the chemical or dust evolution in protoplanetary disks, particularly in sub-solar metallicity environments.

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Gravitoviscous protoplanetary disks with a dust component. III. Evolution of gas, dust, and pebbles

We study the dynamics and growth of dust particles in circumstellar disks of different masses that are prone to gravitational instability during the critical first Myr of their evolution. The dust component is made up of two different components: micron-sized dust and grown dust of evolving size. For the dust component, we considered the dust coagulation, fragmentation, momentum exchange with the gas, and dust self-gravity. We found that the micron-sized dust particles grow rapidly in the circumstellar disk, reaching a few cm in size in the inner 100 au of the disk during less than 100 kyr after the disk formation, provided that fragmentation velocity is $30\rm~ms^{-1}$. Due to the accretion of micron dust particles from the surrounding envelope, which serves as a micron dust reservoir, the approximately cm-sized dust particles continue to be present in the disk for more than 900 kyr after the disk formation and maintain a dust-to-gas ratio close to 0.01. We show that a strong correlation exists between the gas and pebble fluxes in the disk. We find that radial surface density distribution of pebbles in the disk shows power-law distribution with an index similar to that of the Minimum-mass solar nebula (MMSN) regardless the disk mass. We also show that the gas surface density in our models agrees well with measurements of dust in protoplanetary disks of AS 209, HD 163296, and DoAr 25 systems. Pebbles are formed during the very early stages of protoplanetary disk evolution. They play a crucial role in the planet formation process. Our disc simulations reveal the early onset ($<10^5$ yr) of an inwards-drifting flux of pebble-sized particles that makes up approximately between one hundredth and one tenth of the gas mass flux, which appears consistent with mm-observations of discs. (Abridged)

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Mass Assembly of Stellar Systems and their Evolution with the SMA (MASSES) -- Full Data Release

We present and release the full dataset for the Mass Assembly of Stellar Systems and their Evolution with the SMA (MASSES) survey. This survey used the Submillimeter Array (SMA) to image the 74 known protostars within the Perseus molecular cloud. The SMA was used in two array configurations to capture outflows for scales $>$30$^{\prime\prime}$ ($>$9000 au) and to probe scales down to $\sim$1$^{\prime\prime}$ ($\sim$300 au). The protostars were observed with the 1.3 mm and 850 $μ$m receivers simultaneously to detect continuum at both wavelengths and molecular line emission from CO(2-1), $^{13}$CO(2-1), C$^{18}$O(2-1), N$_2$D$^+$(3-2), CO(3-2), HCO$^+$(4-3), and H$^{13}$CO$^+$(4-3). Some of the observations also used the SMA's recently upgraded correlator, SWARM, whose broader bandwidth allowed for several more spectral lines to be observed (e.g., SO, H$_2$CO, DCO$^+$, DCN, CS, CN). Of the main continuum and spectral tracers observed, 84% of the images and cubes had emission detected. The median C$^{18}$O(2-1) linewidth is $\sim$1.0 km s$^{-1}$, which is slightly higher than those measured with single-dish telescopes at scales of 3000-20000 au. Of the 74 targets, six are suggested to be first hydrostatic core candidates, and we suggest that L1451-mm is the best candidate. We question a previous continuum detection toward L1448 IRS2E. In the SVS13 system, SVS13A certainly appears to be the most evolved source, while SVS13C appears to be hotter and more evolved than SVS13B. The MASSES survey is the largest publicly available interferometric continuum and spectral line protostellar survey to date, and is largely unbiased as it only targets protostars in Perseus. All visibility ($uv$) data and imaged data are publicly available at https://dataverse.harvard.edu/dataverse/full_MASSES/.

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An ALMA Study of the FU-Ori Type Object V900 Mon: Implications for the Progenitor

We present ALMA observations of 12CO, 13CO, and C18O J=2--1 lines and the 230 GHz continuum for the FU Ori-type object (FUor) V900 Mon (d~1.5 kpc), for which the accretion burst was triggered between 1953 and 2009. We identified CO emission associated with a molecular bipolar outflow extending up to a ~10^4 au scale and a rotating molecular envelope extending over >10^4 au. The interaction with the hot energetic FUor wind, which was observed using optical spectroscopy, appears limited to a region within ~400 au of the star. The envelope mass and the collimation of the extended CO outflow suggest that the progenitor of this FUor is a low-mass Class I young stellar object (YSO). These parameters for V900 Mon, another FUor, and a few FUor-like stars are consistent with the idea that FUor outbursts are associated with normal YSOs. The continuum emission is marginally resolved in our observations with a 0."2x0."15 (~300x225 au) beam, and a Gaussian model provides a deconvolved FWHM of ~90 au. The emission is presumably associated with a dusty circumstellar disk, plus a possible contribution from a wind or a wind cavity close to the star. The warm compact nature of the disk continuum emission could be explained with viscous heating of the disk, while gravitational fragmentation in the outer disk and/or a combination of grain growth and their inward drift may also contribute to its compact nature.

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Gravitoviscous protoplanetary disks with a dust component. II. Spatial distribution and growth of dust in a clumpy disk

Spatial distribution and growth of dust in a clumpy protoplanetary disk subject to vigorous gravitational instability and fragmentation is studied numerically with sub-au resolution using the FEOSAD code. Hydrodynamics equations describing the evolution of self-gravitating and viscous protoplanetary disks in the thin-disk limit were modified to include a dust component consisting of two parts: sub-micron-sized dust and grown dust with a variable maximum radius. The conversion of small to grown dust, dust growth, friction of dust with gas, and dust self-gravity were also considered. We found that the disk appearance is notably time-variable with spiral arms, dusty rings, and clumps, constantly forming, evolving, and decaying. As a consequence, the total dust-to-gas mass ratio is highly non-homogeneous throughout the disk extent, showing order-of-magnitude local deviations from the canonical 1:100 value. Gravitationally bound clumps formed through gravitational fragmentation have a velocity pattern that deviates notably from the Keplerian rotation. Small dust is efficiently converted into grown dust in the clump interiors, reaching a maximum radius of several decimeters. Concurrently, grown dust drifts towards the clump center forming a massive compact central condensation (70-100 $M_\oplus$). We argue that protoplanets may form in the interiors of inward migrating clumps before they disperse through the action of tidal torques. We foresee the formation of protoplanets at orbital distances of several tens of au with initial masses of gas and dust in the protoplanetary seed in the (0.25-1.6) $M_{\rm Jup}$ and (1.0-5.5) $M_\oplus$ limits, respectively. The final masses of gas and dust in the protoplanets may however be much higher due to accretion from surrounding massive metal-rich disks/envelopes.

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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).

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Diagnosing 0.1-10 au scale morphology of the FU\,Ori disk using ALMA and VLTI/GRAVITY

We report new Atacama Large Millimeter/submillimeter Array Band 3 (86-100 GHz; $\sim$80 mas angular resolution) and Band 4 (146-160 GHz; $\sim$50 mas angular resolution) observations of the dust continuum emission towards the archetypal and ongoing accretion burst young stellar object FU Ori, which simultaneously covered its companion, FU Ori S. In addition, we present near-infrared (2-2.45 $μ$m) observations of FU Ori taken with the General Relativity Analysis via VLT InTerferometrY (GRAVITY; $\sim$1 mas angular resolution) instrument on the Very Large Telescope Interferometer (VLTI). We find that the emission in both FU Ori and FU Ori S at (sub)millimeter and near infrared bands is dominated by structures inward of $\sim$10 au radii. We detected closure phases close to zero from FU Ori with VLTI/GRAVITY, which indicate the source is approximately centrally symmetric and therefore is likely viewed nearly face-on. Our simple model to fit the GRAVITY data shows that the inner 0.4 au radii of the FU Ori disk has a triangular spectral shape at 2-2.45 $μ$m, which is consistent with the H$_{2}$O and CO absorption features in a $\dot{M}\sim$10$^{-4}$ $M_{\odot}\,yr^{-1}$, viscously heated accretion disk. At larger ($\sim$0.4-10 au) radii, our analysis shows that viscous heating may also explain the observed (sub)millimeter and centimeter spectral energy distribution when we assume a constant, $\sim$10$^{-4}$ $M_{\odot}\,yr^{-1}$ mass inflow rate in this region. This explains how the inner 0.4 au disk is replenished with mass at a modest rate, such that it neither depletes nor accumulates significant masses over its short dynamic timescale. Finally, we tentatively detect evidence of vertical dust settling in the inner 10 au of the FU Ori disk, but confirmation requires more complete spectral sampling in the centimeter bands.

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A Tail Structure Associated with Protoplanetary Disk around SU Aurigae

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of the CO ($J$=2--1) line emission from the protoplanetary disk around T-Tauri star SU Aurigae (hereafter SU Aur). Previous observations in optical and near infrared wavelengths find a unique structure in SU Aur. One of the highlights of the observational results is that an extended tail-like structure is associated with the disk, indicating mass transfer from or into the disk. Here we report the discovery of the counterpart of the tail-like structure in CO gas extending more than 1000 au long. Based on geometric and kinematic perspectives, both of the disk and the tail-like structure components physically connect to each other. Several theoretical studies predicted the observed tail-like structure via the following possible scenarios, 1) a gaseous stream from the molecular cloud remnant, 2) collision with a (sub)stellar intruder or a gaseous blob from the ambient cloud, and 3) ejection of a planetary or brown dwarf mass object due to gravitational instability via multi-body gravitational interaction. Since the tail-like structures associated with the SU Aur disk is a new example following RW Aurigae, some disks may experience the internal or external interaction and drastically lose mass during disk evolution.

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Luminosity outburst chemistry in protoplanetary discs: going beyond standard tracers

The chemical influence of luminosity outbursts on the environments of young solar-type stars is explored. Species are categorised into several types according to their response to the outburst. The first and second types imply chemical changes only during the outburst (with slightly different behaviours). These response types are mostly observed close to the star and are caused by icy mantle evaporation. However, mantles recover after the outburst almost immediately. A notable exception is benzene ice, which is accumulated on dust surfaces during and after the outburst, so that its abundance exceeds the pre-outburst level by orders of magnitude. The third type of response is mostly seen at the disc periphery and implies alteration of abundances during the outburst and preservation of these `abnormal' abundances for centuries. This behaviour is typical of organic compounds, like HCOOCH$_3$, CH$_3$CN, CH$_2$CO. Their presence in the dark disc regions can be a manifestation of the past outburst. CO and CO$_2$ only trace past outbursts at the remote disc regions. The outburst changes the C/O ratio, but it quickly returns to the pre-outburst value almost everywhere in the disc. An important factor determining the sensitivity of molecular composition to the outburst is the dust size distribution. The duration of the pre-outburst stage and of the outburst itself influence the chemical effects, if the burst duration is shorter than 50 yr and the duration of the quiescent phase between the bursts is shorter than 100 kyr.

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Episodic excursions of low-mass protostars on the Hertzsprung-Russell diagram

Following our recent work devoted to the effect of accretion on the pre-main-sequence evolution of low-mass stars, we perform a detailed analysis of episodic excursions of low-mass protostars in the Hertzsprung-Russell (H-R) diagram triggered by strong mass accretion bursts typical of FU Orionis-type objects (FUors). These excursions reveal themselves as sharp increases in the stellar total luminosity and/or effective temperature of the protostar and can last from hundreds to a few thousands of years, depending on the burst strength and characteristics of the protostar. During the excursions, low-mass protostars occupy the same part of the H-R diagram as young intermediate-mass protostars in the quiescent phase of accretion. Moreover, the time spent by low-mass protostars in these regions is on average a factor of several longer than that spent by the intermediate-mass stars in quiescence. During the excursions, low-mass protostars pass close to the position of most known FUors in the H-R diagram, but owing to intrinsic ambiguity the model stellar evolutionary tracks are unreliable in determining the FUor properties. We find that the photospheric luminosity in the outburst state may dominate the accretion luminosity already after a few years after the onset of the outburst, meaning that the mass accretion rates of known FUors inferred from the bolometric luminosity may be systematically overestimated, especially in the fading phase.

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Development and application of fast methods for computing momentum transfer between gas and dust in supercomputer simulation of planet formation

Circumstellar discs, from which planetary systems are formed, consist of gas, dust and solids. Simulations of self-consistent dynamics of gas, dust and solids in circumstellar discs is a challenging problem. In the paper we present fast algorithms for computing the drag force (momentum transfer) between solid phase and gas. These algorithms (a) are universal and applicable to dust and solids with any sizes smaller than the mean free path of gas molecules, (b) can be used to calculate the momentum transfer between dust and gas instead of one-way effect, as it is done in many models, (c) can perform simulations, without a loss in accuracy, with the time step determined by gas-dynamic parameters rather than by drag force, and (d) are compatible with the widely used parallel algorithms for solving 3D equations of gas dynamics, hydrodynamic equations for dust, and the collisionless Boltzmann equation for large bodies. Preliminary results of supercomputer simulation of the gas-dust disc dynamics within the developed approach are reported.

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