Dust Grains In Protoplanetary Disks Research Articles

An implicit algorithm for simulating the dynamics of small dust grains with smoothed particle hydrodynamics

ABSTRACT We present an implicit method for solving the diffusion equation for the evolution of the dust fraction in the terminal velocity approximation using dust-as-mixture smoothed particle hydrodynamics. The numerical scheme involves casting the dust diffusion equation into implicit form, rearranging into its resolvent cubic equation and solving analytically. This method is relevant for small grains that are tightly coupled to the gas, such as sub-micron dust grains in the interstellar medium or millimetre-sized dust grains in protoplanetary discs. The method avoids problems with the variable used to evolve the dust fraction becoming negative when evolved explicitly and is fast and accurate, avoiding the need for dust stopping time limiters and significantly reducing computational expense. Whilst this method is an improvement over using the explicit terminal velocity approximation method, as with any dust-as-mixture method it still fails to give accurate solutions in the limit of large (weakly coupled) grains.

The radial profile of dust grain size in the protoplanetary disc of DS Tau

ABSTRACT How do dust grains in protoplanetary discs overcome rapid radial drift and grow from micron size particles to planets is not well understood. The key is to search for evidence of dust accumulation and growth as a function of radius in the disc. We investigate the radial profile of grain size in the DS Tau disc by fitting multiband ALMA observations with self-consistent radiative transfer models. The best-fit grain sizes range from centimeters in the inner disc down to ${\sim }\, 30\, \mu {\rm m}$ in the outer regions. Such an inside-out decreasing tendency is consistent with theories of dust evolution. Based on the best-fit model, we find that dust of ${\sim }\, 2$ Jupiter masses has been depleted within the gap. By taking the gas-to-dust mass ratio into account, the lost mass is enough to form the 3.5 Jupiter mass planet inferred by literature hydrodynamic simulations. Moreover, our modelling also indicates that at the interface region between the gap and the ring, the grain size profile shows a discontinuity, with its amplitude dependent on the dust model adopted in the radiative transfer analysis. Future multiwavelength observations at higher angular resolutions are required to better constrain the grain size and its variation in the vicinity of disc substructures.

Underestimation of the dust mass in protoplanetary disks: Effects of disk structure and dust properties

The total number of dust grains in protoplanetary disks is one of the key properties that characterizes the potential for planet formation. With (sub-)millimeter flux measurements, literature studies usually derive the dust mass using an analytic formula under the assumption of optically thin emission, which may lead to a substantial underestimation. In this work, we conduct a parameter study with the goal of investigating the effects of disk structure and dust properties on the underestimation through self-consistent radiative transfer models. Different dust models, scattering modes, and approaches for dust settling are considered and compared. The influences of disk substructures, such as rings and crescents, on the mass derivation are investigated as well. The results indicate that the traditional analytic method can underestimate the mass by a factor of a few to several hundreds, depending on the optical depth along the line of sight set mainly by the true dust mass, disk size, and inclination. As an application, we performed a detailed radiative transfer modeling of the spectral energy distribution of DoAr 33, one of the disks observed by the Disk Substructures at High Angular Resolution Project (DSHARP). When the DSHARP dust opacities are adopted, the most probable dust mass returned from the Bayesian analysis is roughly seven times higher than the value given by the analytic calculation. Our study demonstrates that estimating disk dust masses from radiative transfer modeling is one solution to alleviate the problem of insufficient mass for planet formation that was raised in the era of the Atacama Large Millimeter/submillimeter Array.

Scattering properties of protoplanetary dust analogs with microwave analogy: Aggregates of fractal dimensions from 1.5 to 2.8

Context. The growth of dust grains in protoplanetary disks is not understood in detail. Several studies have proposed the presence of aggregates and irregular grains to overcome the physical barriers in grain growth models. In order to understand the scattering properties of these aggregates, laboratory measurements of light scattering and microwave scattering have been developed over the last 50 years. Aims. We aim to measure the scattering properties of different protoplanetary analog aggregates with fractal dimensions of 1.5, 1.7, 2.0, 2.5, and 2.8. Methods. We used the microwave scattering technique (microwave analogy) for the measurements. The analog particles were virtually generated and fabricated by 3D printing with a controlled size (scaling factor), geometry, and refractive index. The seven analogs were measured at wavelengths ranging from 16.7 mm to 100 mm, leading to aggregate size parameters ranging from Xagg = 1 to Xagg = 20. The results were compared to finite element method calculations of the same analogs for cross-validation. Results. The phase function and the degree of linear polarization were deduced from the scattered field measurements of the different aggregates. These scattering properties are compared and discussed as a function of the fractal dimension. Conclusions. The scattering properties of aggregates with different fractal dimensions are different. Three different realizations of aggregates with the same fractal dimension but different monomer configurations yield the same phase functions. We verified that the maximum degree of linear polarization is higher for porous aggregates than for compact aggregates. Furthermore, the maximum polarization occurs at larger scattering angles for high fractal dimensions, while the half width at half maximum of the phase functions present larger values for small fractal dimensions.

A Laboratory-driven Multiscale Investigation of X-Ray Induced Mass Loss and Photochemical Evolution in Cosmic Carbon and Silicate Dust

Abstract We present the results of an integrated laboratory and modeling investigation into the impact of stellar X-rays on cosmic dust. Carbonaceous grains were prepared in a cooled (<200 K) supersonic expansion from aromatic molecular precursors, and were later irradiated with 970 eV X-rays. Silicate (enstatite) grains were prepared via laser ablation, thermally annealed, and later irradiated with 500 eV X-rays. Infrared spectra of the 3.4 μm band of the carbon sample prepared with benzene revealed 84% ± 5% band area loss for an X-ray dose of 5.2 ×1023 eV.cm−2. Infrared spectra of the 8–12 μm Si–O band of the silicate sample revealed band area loss up to 63% ± 5% for doses of 2.3 × 1023 eV.cm−2. A hybrid Monte Carlo particle trajectory approach was used to model the impact of X-rays and ensuing photoelectrons, Auger and collisionally ionized electrons through the bulk. As a result of X-ray ionization and ensuing Coulomb explosions on surface molecules, the calculated mass loss is 60% for the carbonaceous sample and 46% for the silicate sample, within a factor of 2 of the IR band loss, supporting an X-ray induced mass-loss mechanism. We apply the laboratory X-ray destruction rates to estimate the lifetimes of dust grains in protoplanetary disks surrounding 1 M ⊙ and 0.1 M ⊙ G and M stars. In both cases, X-ray destruction timescales are short (a few million years) at the disk surface, but are found to be much longer than typical disk lifetimes (≳10 Myr) over the disk bulk.

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

Abstract Previous observations have shown that the ≲10 au, ≳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 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 ≳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 ≳ 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-band magnitudes of these binary stars were 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 the 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 multiwavelength radio observations.

New mid-infrared imaging constraints on companions and protoplanetary disks around six young stars

Context. Mid-infrared (mid-IR) imaging traces the sub-micron and micron-sized dust grains in protoplanetary disks and it offers constraints on the geometrical properties of the disks and potential companions, particularly if those companions have circumplanetary disks. Aims. We use the VISIR instrument and its upgrade NEAR on the VLT to take new mid-IR images of five (pre-)transition disks and one circumstellar disk with proposed planets and obtain the deepest resolved mid-IR observations to date in order to put new constraints on the sizes of the emitting regions of the disks and the presence of possible companions. Methods. We derotated and stacked the data to find the disk properties. Where available, we compare the data to PRODIMO (Protoplanetary Disk Model) radiation thermo-chemical models to achieve a deeper understanding of the underlying physical processes within the disks. We applied the circularised point spread function subtraction method to find upper limits on the fluxes of possible companions and model companions with circumplanetary disks. Results. We resolved three of the six disks and calculated position angles, inclinations, and (upper limits to) sizes of emission regions in the disks, improving upper limits on two of the unresolved disks. In all cases the majority of the mid-IR emission comes from small inner disks or the hot inner rims of outer disks. We refined the existing PRODIMO HD 100546 model spectral energy distribution (SED) fit in the mid-IR by increasing the PAH abundance relative to the ISM, adopting coronene as the representative PAH, and increasing the outer cavity radius to 22.3 AU. We produced flux estimates for putative planetary-mass companions and circumplanetary disks, ruling out the presence of planetary-mass companions with L > 0.0028 L⊙ for a > 180 AU in the HD 100546 system. Upper limits of 0.5–30 mJy are obtained at 8–12 μm for potential companions in the different disks. We rule out companions with L > 10−2 L⊙ for a > 60 AU in TW Hydra, a > 110 AU in HD 169142, a > 150 AU in HD 163296, and a > 160 AU in HD 36112. Conclusions. The mid-IR emission comes from the central regions and traces the inner areas of the disks, including inner disks and inner rims of outer disks. Planets with mid-IR luminosities corresponding to a runaway accretion phase can be excluded from the HD 100546, HD 169142, TW Hydra, and HD 36112 systems at separations >1′′. We calculated an upper limit to the occurrence rate of wide-orbit massive planets with circumplanetary disks of 6.2% (68% confidence). Future observations with METIS on the ELT will be able to achieve a factor of 10 better sensitivity with a factor of five better spatial resolution. MIRI on JWST will be able to achieve 250 times better sensitivity. Both will possibly detect the known companions to all six targets.

New Growth Mechanism of Dust Grains in Protoplanetary Disks with Magnetically Driven Disk Winds

Abstract We discovered a new growth mode of dust grains to kilometer-size bodies in protoplanetary disks that evolve via viscous accretion and magnetically driven disk winds (MDWs). We solved an approximate coagulation equation of dust grains with time-evolving disks that consist of both gas and solid components using a one-dimensional model. With grain growth, all solid particles initially drift inward toward the central star due to the gas drag force. However, the radial profile of gas pressure, P, is modified by the MDW that disperses the gas in an inside-out manner. Consequently, a local concentration of solid particles is created by the converging radial flux of drifting dust grains at the location with a convex-upward profile of P. When the dimensionless stopping time, St, exceeds unity there, the solid particles spontaneously reach the growth-dominated state because of the positive feedback between the suppressed radial drift and the enhanced accumulation of dust particles that drift from the outer part. Once the solid particles are in the drift-limited state, the above-mentioned condition of St for dust growth is equivalent to Σd/Σg ≳ η, where Σd/Σg is the dust-to-gas surface-density ratio and η is the dimensionless radial pressure-gradient force. As a consequence of the successful growth of dust grains, a ring-like structure containing planetesimal-size bodies is formed at the inner part of the protoplanetary disks. Such a ring-shaped concentration of planetesimals is expected to play a vital role in the subsequent planet formation.

ALMA Observations of the Inner Cavity in the Protoplanetary Disk around Sz 84

Abstract We present Atacama Large Millimeter/submillimeter Array observations of a protoplanetary disk around the T Tauri star Sz 84 and analyses of the structures of the inner cavity in the central region of the dust disk. Sz 84's spectral energy distribution (SED) has been known to exhibit negligible infrared excess at λ ≲ 10 μm due to the disk’s cavity structure. Analyses of the observed visibilities of dust continuum at 1.3 mm and the SED indicate that the size of the cavity in the disk of large (millimeter size) dust grains is 8 au in radius and that in the disk of small (submicron size) dust grains is 60 au in radius. Furthermore, from the SED analyses, we estimate that the upper limit mass of small dust grains at r < 60 au is less than ∼10−3 M ⊕, which is ≲0.01% of the total (small + large) dust mass at r < 60 au. These results suggest that large dust grains are dominant at r < 60 au, implying that dust grains efficiently grow with less efficient fragmentation in this region, potentially due to weak turbulence and/or stickier dust grains. The balance of grain growth and dust fragmentation is an important factor for determining the size of large dust grains in protoplanetary disks, and thus Sz 84 could serve as a good testbed for investigations of grain growth in such disks.

Particle-Gas Hybrid Schemes in the PLUTO Code

Hybrid codes treating composite systems made up of fluid and particle components are becoming increasing more popular in order to address multiple scale in complex astrophysical environments. Here we review some recent additions to the PLUTO code consisting of three flexible particle physics implementations targeting i) cosmic ray particles, ii) sub-grid electron acceleration and emission from high-energy astrophysical environments and iii) dust grains in protoplanetary disks. While the fluid equations are generally solved using standard finite-volume techniques, integration of particles as well as their feedback onto the gas is treated using standard techniques borrowed from Particle-In-Cell (PIC) frameworks. Some novel numerical benchmarks, not discussed in the original method papers, are also presented.

Evolution of porous dust grains in protoplanetary discs – I. Growing grains

ABSTRACT One of the main problems in planet formation, hampering the growth of small dust to planetesimals, is the so-called radial-drift barrier. Pebbles of cm to dm sizes are thought to drift radially across protoplanetary discs faster than they can grow to larger sizes, and thus to be lost to the star. To overcome this barrier, drift has to be slowed down or stopped, or growth needs to be sped up. In this paper, we investigate the role of porosity on both drift and growth. We have developed a model for porosity evolution during grain growth and applied it to numerical simulations of protoplanetary discs. We find that growth is faster for porous grains, enabling them to transition to the Stokes drag regime, decouple from the gas, and survive the radial-drift barrier. Direct formation of small planetesimals from porous dust is possible over large areas of the disc.

Evidence for the start of planet formation in a young circumstellar disk

The growth of dust grains in protoplanetary disks is a necessary first step towards planet formation. This growth has been inferred via observations of thermal dust emission towards mature protoplanetary systems (age >2 million years) with masses that are, on average, similar to Neptune3. In contrast, the majority of confirmed exoplanets are heavier than Neptune. Given that young protoplanetary disks are more massive than their mature counterparts, this suggests that planet formation starts early, but evidence for grain growth that is spatially and temporally coincident with a massive reservoir in young disks remains scarce. Here, we report observations on a lack of emission of carbon monoxide isotopologues within the inner ~15 au of a very young (age ~100,000 years) disk around the Solar-type protostar TMC1A. By using the absence of spatially resolved molecular line emission to infer the gas and dust content of the disk, we conclude that shielding by millimeter-size grains is responsible for the lack of emission. This suggests that grain growth and millimeter-size dust grains can be spatially and temporally coincident with a mass reservoir sufficient for giant planet formation. Hence, planet formation starts during the earliest, embedded phases in the life of young stars.

Resonant drag instabilities in protoplanetary discs: the streaming instability and new, faster growing instabilities

We identify and study a number of new, rapidly growing instabilities of dust grains in protoplanetary disks, which may be important for planetesimal formation. The study is based on the recognition that dust-gas mixtures are generically unstable to a Resonant Drag Instability (RDI), whenever the gas, absent dust, supports undamped linear modes. We show that the "streaming instability" is an RDI associated with epicyclic oscillations; this provides simple interpretations for its mechanisms and accurate analytic expressions for its growth rates and fastest-growing wavelengths. We extend this analysis to more general dust streaming motions and other waves, including buoyancy and magnetohydrodynamic oscillations, finding various new instabilities. Most importantly, we identify the disk "settling instability," which occurs as dust settles vertically into the midplane of a rotating disk. For small grains, this instability grows many orders of magnitude faster than the standard streaming instability, with a growth rate that is independent of grain size. Growth timescales for realistic dust-to-gas ratios are comparable to the disk orbital period, and the characteristic wavelengths are more than an order of magnitude larger than the streaming instability (allowing the instability to concentrate larger masses). This suggests that in the process of settling, dust will band into rings then filaments or clumps, potentially seeding dust traps, high-metallicity regions that in turn seed the streaming instability, or even overdensities that coagulate or directly collapse to planetesimals.

Characterizing the Variable Dust Permeability of Planet-induced Gaps

Abstract Aerodynamic theory predicts that dust grains in protoplanetary disks will drift radially inward on comparatively short timescales. In this context, it has long been known that the presence of a gap opened by a planet can significantly alter the dust dynamics. In this paper, we carry out a systematic study employing long-term numerical simulations aimed at characterizing the critical particle size for retention outside a gap as a function of particle size, as well as various key parameters defining the protoplanetary disk model. To this end, we perform multifluid hydrodynamical simulations in two dimensions, including different dust species, which we treat as pressureless fluids. We initialize the dust outside of the planet’s orbit and study under which conditions dust grains are able to cross the gap carved by the planet. In agreement with previous work, we find that the permeability of the gap depends both on dust dynamical properties and the gas disk structure: while small dust follows the viscously accreting gas through the gap, dust grains approaching a critical size are progressively filtered out. Moreover, we introduce and compute a depletion factor that enables us to quantify the way in which higher viscosity, smaller planet mass, or a more massive disk can shift this critical size to larger values. Our results indicate that gap-opening planets may act to deplete the inner reaches of protoplanetary disks of large dust grains—potentially limiting the accretion of solids onto forming terrestrial planets.

Protoplanetary dust porosity and FU Orionis outbursts: Solving the mystery of Earth’s missing volatiles

The Earth is known to be depleted in volatile lithophile elements in a fashion that defies easy explanation. We resolve this anomaly with a model that combines the porosity of collisionally grown dust grains in protoplanetary disks with heating from FU Orionis events that dramatically raise protoplanetary disk temperatures. The heating from an FU Orionis event alters the aerodynamical properties of the dust while evaporating the volatiles. This causes the dust to settle, abandoning those volatiles. The success of this model in explaining the elemental composition of the Earth is a strong argument in favor of highly porous collisionally grown dust grains in protoplanetary disks outside our Solar System. Further, it demonstrates how thermal (or condensation based) alterations of dust porosity, and hence aerodynamics, can be a strong factor in planet formation, leading to the onset of rapid gravitational instabilities in the dust disk and the subsequent collapse that forms planetesimals.

Growing dust grains in protoplanetary discs – III. Vertical settling

We aim to derive a simple analytic model to understand the essential properties of vertically settling growing dust grains in laminar protoplanetary discs. Separating the vertical dynamics from the motion in the disc mid-plane, we integrate the equations of motion for both a linear and an exponential grain growth rate. Numerical integrations are performed for more complex growth models. We find that the settling efficiency depends on the value of the dimensionless parameter γ, which characterizes the relative efficiency of grain growth with respect to the gas drag. Since γ is expected to be of the same order as the initial dust-to-gas ratio in the disc (≃10−2), grain growth enhances the energy dissipation of the dust particles and improves the settling efficiency in protoplanetary discs. This behaviour is mostly independent of the growth model considered as well as of the radial drift of the particles.

Growing dust grains in protoplanetary discs – II. The radial-drift barrier problem

We aim to study the migration of growing dust grains in protoplanetary discs, where growth and migration are tightly coupled. This includes the crucial issue of the radial-drift barrier for growing dust grains. We therefore extend the study performed in Paper I, considering models for grain growth and grain dynamics where both the migration and growth rate depend on the grain size and the location in the disc. The parameter space of disc profiles and growth models is exhaustively explored. In doing so, interpretations for the grain motion found in numerical simulations are also provided. We find that a large number of cases is required to characterise entirely the grains radial motion, providing a large number of possible outcomes. Some of them lead dust particles to be accreted onto the central star and some of them don't. We find then that q<1 is required for discs to retain their growing particles, where q is the exponent of the radial temperature profile T(R) proportional to R^-q. Additionally, the initial dust-to gas ratio has to exceed a critical value for grains to pile up efficiently, thus avoiding being accreted onto the central star. Discs are also found to retain efficiently small dust grains regenerated by fragmentation. We show how those results are sensitive to the turbulent model considered. Even though some physical processes have been neglected, this study allows to sketch a scenario in which grains can survive the radial-drift barrier in protoplanetary discs as they grow.

Growing dust grains in protoplanetary discs – I. Radial drift with toy growth models

In a series of papers, we present a comprehensive analytic study of the global motion of growing dust grains in protoplanetary discs, addressing both the radial drift and the vertical settling of the particles. Here we study how the radial drift of dust particles is affected by grain growth. In a first step, toy models in which grain growth can either be constant, accelerate or decelerate are introduced. The equations of motion are analytically integrable and therefore the grains dynamics is easy to understand. The radial motion of growing grains is governed by the relative efficiency of the growth and migration processes which is expressed by the dimensionless parameter Lambda, as well as the exponents for the gas surface density and temperature profiles, denoted p and q respectively. When Lambda is of order unity, growth and migration are strongly coupled, providing the most efficient radial drift. For the toy models considered, grains pile up when -p+q+1/2<0. Importantly, we show the existence of a second process which can help discs to retain their solid materials. For accelerating growth, grains end up their migration at a finite radius, thus avoiding being accreted onto the central star.

Probing dust settling in proto-planetary discs with ALMA

Investigating the dynamical evolution of dust grains in proto-planetary discs is a key issue to understand how planets should form. We identify under which conditions dust settling can be constrained by high angular resolution observations at mm wavelengths, and which observational strategies are suited for such studies. Exploring a large range of models, we generate synthetic images of discs with different degrees of dust settling, and simulate high angular resolution (∼0.05–0.3 arcsec) Atacama Large Millimeter/submillimeter Array (ALMA) observations of these synthetic discs. The resulting data sets are then analysed blindly with homogeneous disc models (where dust and gas are totally mixed) and the derived disc parameters are used as tracers of the settling factor. Our dust discs are partially resolved by ALMA and present some specific behaviours on radial and mainly vertical directions, which can be used to quantify the level of settling. We find out that an angular resolution better than or equal to ∼0.1 arcsec (using 2.3 km baselines at 0.8mm) allows us to constrain the dust scale height and flaring index with sufficient precision to unambiguously distinguish between settled and non-settled discs, provided the inclination is close enough to edge-on (i ≥ 75°). Ignoring dust settling and assuming hydrostatic equilibrium when analysing such discs affect the derived dust temperature and the radial dependency of the dust emissivity index. The surface density distribution can also be severely biased at the highest inclinations. However, the derived dust properties remain largely unaffected if the disc scale height is fitted separately. ALMA has the potential to test some of the dust settling mechanisms, but for real discs, deviations from ideal geometry (warps, spiral waves) may provide an ultimate limit on the dust settling detection.

Probing Dust Settling in Proto-planetary Disks with ALMA

Investigating the dynamical evolution of dust grains in proto-planetary disks is a key issue to understand how planets should form. We identify under which conditions dust settling can be constrained by high angular resolution ALMA observations at mm wavelengths, and which observational strategies are suited for such studies. We find out that an angular resolution better than or equal to » 0.1” (using 2.3 km baselines at 0.8mm) allows us to constrain the dust scale height and flaring index with sufficient precision to unambiguously distinguish between settled and non-settled disks, provided the inclination is close enough to edge-on (i > 75°). Ignoring dust settling and assuming hydrostatic equilibrium when analyzing such disks biase the derived dust temperature, the radial dependency of the dust emissivity index and the surface density distribution.