Massive Protoplanetary Disks Research Articles

Revising Properties of Planet–Host Binary Systems. IV. The Radius Distribution of Small Planets in Binary Star Systems Is Dependent on Stellar Separation* *Based on observations obtained with the Hobby–Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen.

Small planets (R p ≤ 4 R ⊕) are divided into rocky super-Earths and gaseous sub-Neptunes separated by a radius gap, but the mechanisms that produce these distinct planet populations remain unclear. Binary stars are the only main-sequence systems with an observable record of the protoplanetary disk lifetime and mass reservoir, and the demographics of planets in binaries may provide insights into planet formation and evolution. To investigate the radius distribution of planets in binary star systems, we observed 207 binary systems hosting 283 confirmed and candidate transiting planets detected by the Kepler mission, then recharacterized the planets while accounting for the observational biases introduced by the secondary star. We found that the population of planets in close binaries (ρ ≤ 100 au) is significantly different from the planet population in wider binaries (ρ > 300 au) or single stars. In contrast to planets around single stars, planets in close binaries appear to have a unimodal radius distribution with a peak near the expected super-Earth peak of R p ∼ 1.3 R ⊕ and a suppressed population of sub-Neptunes. We conclude that we are observing the direct impact of a reduced disk lifetime, smaller mass reservoir, and possible altered distribution of solids reducing the sub-Neptune formation efficiency. Our results demonstrate the power of binary stars as a laboratory for exploring planet formation and as a controlled experiment of the impact of varied initial conditions on mature planet populations.

Retrievals of Protoplanetary Disk Parameters Using Thermochemical Models. I. Disk Gas Mass from Hydrogen Deuteride Spectroscopy

We discuss statistical relationships between the mass of protoplanetary disks, the hydrogen deuteride (HD) line flux, and the dust spectral energy distribution (SED) determined using 3000 ProDiMo disk models. The models have 15 free parameters describing the disk physical properties, the central star, and the local radiation field. The sampling of physical parameters is done using a Monte Carlo approach to evaluate the probability density functions of observables as a function of physical parameters. We find that the mass-averaged HD fractional abundance is almost constant even though the ultraviolet flux varies by several orders of magnitude. Probing the statistical relation between the physical quantities and the HD flux, we find that low-mass (optically thin) disks display a tight correlation between the average disk gas temperature and HD line flux, while massive disks show no such correlation. We demonstrate that the central star luminosity, disk size, dust size distribution, and HD flux may be used to determine the disk gas mass within a factor of 3. We also find that the far-infrared and submillimeter/millimeter SEDs and the HD flux may serve as strong constraints for determining the disk gas mass to within a factor of 2. If the HD lines are fully spectrally resolved (R ≳ 1.5 × 106, Δv = 0.2 km s−1), the 56 and 112 μm HD line profiles alone may constrain the disk gas mass to within a factor of 2.

Evolution of the relation between the mass accretion rate and the stellar and disk mass from brown dwarfs to stars

The time evolution of the dependence of the mass accretion rate with the stellar mass and the disk mass represents a fundamental way to understand the evolution of protoplanetary disks and the formation of planets. In this work, we present observations with X-shooter of 26 Class II very low-mass stars (< 0.2 M⊙) and brown dwarfs in the Ophiuchus, Chamaeleon-I, and Upper Scorpius star-forming regions. These new observations extend the measurement of the mass accretion rate down to spectral type (SpT) M9 (∼0.02 M⊙) in Ophiuchus and Chamaeleon-I and add 11 very-low-mass stars to the sample of objects previously studied with broadband spectroscopy in Upper Scorpius. We obtained the spectral type and extinction, as well as the physical parameters of the sources. We used the intensity of various emission lines in the spectra of these sources to derive the accretion luminosity and mass accretion rates for the entire sample. Combining these new observations with data from the literature, we compare relations between accretion and stellar and disk properties of four different star-forming regions with different ages: Ophiuchus (∼1 Myr), Lupus (∼2 Myr), Chamaeleon-I (∼3 Myr), and Upper Scorpius (5−12 Myr). We find the slopes of the accretion relationships (L* − Lacc, M∗ − Ṁacc) to steepen in the 1−3 Myr age range (i.e., between Ophiuchus, Lupus, and Chamaeleon-I) and that both relationships may be better described with a single power law. We find that previous claims for a double power-law behavior of the M∗ − Ṁacc relationship may have been triggered by the use of a different SpT–Teff scale. We also find the relationship between the protoplanetary disk mass and the mass accretion rate of the stellar population to steepen with time down to the age of Upper Scorpius. Overall, we observe hints of a faster evolution into low accretion rates of low-mass stars and brown dwarfs. At the same time, we also find that brown dwarfs present higher Mdisk/Ṁacc ratios (i.e., longer accretion depletion timescales) than stars in Ophiuchus, Lupus, and Cha-I. This apparently contradictory result may imply that the evolution of protoplanetary disks around brown dwarfs may be different than what is seen in the stellar regime.

Formation of a wide-orbit giant planet in a gravitationally unstable subsolar-metallicity protoplanetary disc

ABSTRACT Direct imaging observations of planets revealed that wide-orbit (>10 au) giant planets exist even around subsolar-metallicity host stars and do not require metal-rich environments for their formation. A possible formation mechanism of wide-orbit giant planets in subsolar-metallicity environments is the gravitational fragmentation of massive protoplanetary discs. Here, we follow the long-term evolution of the disc for 1 Myr after its formation, which is comparable to disc lifetime, by way of a two-dimensional thin-disc hydrodynamic simulation with the metallicity of 0.1 $\rm {Z}_{\odot }$. We find a giant protoplanet that survives until the end of the simulation. The protoplanet is formed by the merger of two gaseous clumps at ∼0.5 Myr after disc formation, and then it orbits ∼200 au from the host star for ∼0.5 Myr. The protoplanet’s mass is ∼10 MJ at birth and gradually decreases to 1 MJ due to the tidal effect from the host star. The result provides the minimum mass of 1 MJ for the protoplanet in our simulation. We anticipate that the mass of a protoplanet experiencing reduced mass loss thanks to the protoplanetary contraction in higher resolution simulations can increase to ∼10 MJ. We argue that the disc gravitational fragmentation would be a promising pathway to form wide-orbit giant planets with masses of ≥1 MJ in subsolar-metallicity environments.

Forming Gas Giants around a Range of Protostellar M-dwarfs by Gas Disk Gravitational Instability

Recent discoveries of gas giant exoplanets around M-dwarfs from transiting and radial velocity surveys are difficult to explain with core-accretion models. We present here a homogeneous suite of 162 models of gravitationally unstable gaseous disks. These models represent an existence proof for gas giants more massive than 0.1 Jupiter masses to form by the gas disk gravitational instability (GDGI) mechanism around M-dwarfs for comparison with observed exoplanet demographics and protoplanetary disk mass estimates for M-dwarf stars. We use the Enzo 2.6 adaptive mesh refinement (AMR) 3D hydrodynamics code to follow the formation and initial orbital evolution of gas giant protoplanets in gravitationally unstable gaseous disks in orbit around M-dwarfs with stellar masses ranging from 0.1 M ⊙ to 0.5 M ⊙. The gas disk masses are varied over a range from disks that are too low in mass to form gas giants rapidly to those where numerous gas giants are formed, therefore revealing the critical disk mass necessary for gas giants to form by the GDGI mechanism around M-dwarfs. The disk masses vary from 0.01 M ⊙ to 0.05 M ⊙ while the disk to star mass ratios explored the range from 0.04 to 0.3. The models have varied initial outer disk temperatures (10–60 K) and varied levels of AMR grid spatial resolution, producing a sample of expected gas giant protoplanets for each star mass. Broadly speaking, disk masses of at least 0.02 M ⊙ are needed for the GDGI mechanism to form gas giant protoplanets around M-dwarfs.

Forming rocky exoplanets around K-dwarf stars

Context. New space telescopes, such as the upcoming PLATO mission, aim to detect and study thousands of exoplanets, especially terrestrial planets around main-sequence stars. This motivates us to study how these planets formed. How multiple close-in super-Earths form around stars with masses lower than that of the Sun is still an open issue. Several recent modeling studies have focused on planet formation around M-dwarf stars, but so far no studies have focused specifically on K dwarfs, which are of particular interest in the search for extraterrestrial life. Aims. We aim to reproduce the currently known population of close-in super-Earths observed around K-dwarf stars and their system characteristics. Additionally, we investigate whether the planetary systems that we form allow us to decide which initial conditions are the most favorable. Methods. We performed 48 high-resolution N-body simulations of planet formation via planetesimal accretion using the existing GENGA software running on GPUs. In the simulations we varied the initial protoplanetary disk mass and the solid and gas surface density profiles. Each simulation began with 12 000 bodies with radii of between 200 and 2000 km around two different stars, with masses of 0.6 and 0.8 M⊙. Most simulations ran for 20 Myr, with several simulations extended to 40 or 100 Myr. Results. The mass distributions for the planets with masses between 2 and 12 M⊕ show a strong preference for planets with masses Mp < 6 M⊕ and a lesser preference for planets with larger masses, whereas the mass distribution for the observed sample increases almost linearly. However, we managed to reproduce the main characteristics and architectures of the known planetary systems and produce mostly long-term angular-momentum-deficit-stable, nonresonant systems, but we require an initial disk mass of 15 M⊕ or higher and a gas surface density value at 1 AU of 1500 g cm−2 or higher. Our simulations also produce many low-mass planets with M < 2 M⊕, which are not yet found in the observed population, probably due to the observational biases. Earth-mass planets form quickly (usually within a few million years), mostly before the gas disk dispersal. The final systems contain only a small number of planets with masses Mp > 10 M⊕, which could possibly accrete substantial amounts of gas, and these formed after the gas had mostly dissipated. Conclusions. We mostly manage to reproduce observed K-dwarf exoplanetary systems from our GPU simulations.

Protostellar and Protoplanetary Disk Masses in the Serpens Region

We present the results from an Atacama Large Millimeter/submillimeter Array (ALMA) 1.3 mm continuum and 12CO (J = 2 − 1) line survey spread over 10 deg2 in the Serpens star-forming region of 320 young stellar objects, 302 of which are likely members of Serpens (16 Class I, 35 flat-spectrum, 235 Class II, and 16 Class III). From the continuum data, we derive disk dust masses and show that they systematically decline from Class I to flat-spectrum to Class II sources. Grouped by stellar evolutionary state, the disk mass distributions are similar to other young (<3 Myr) regions, indicating that the large-scale environment of a star-forming region does not strongly affect its overall disk dust mass properties. These comparisons between populations reinforce previous conclusions that disks in the Ophiuchus star-forming region have anomalously low masses at all evolutionary stages. Additionally, we find a single deeply embedded protostar that has not been documented elsewhere in the literature and, from the CO line data, 15 protostellar outflows, which we catalog here.

The Effects of Disk-induced Apsidal Precession on Planets Captured into Mean Motion Resonance

The process of migration into resonance capture has been well studied for planetary systems where the gravitational potential is generated exclusively by the star and planets. However, massive protoplanetary disks add a significant perturbation to these models. In this paper we consider two limiting cases of disk-induced precession on migrating planets and find that small amounts of precession significantly affect the equilibrium reached by migrating planets. We investigate these effects with a combination of semianalytic models of the resonance and numerical integrations. We also consider the case of the disk’s dispersal, which can excite significant libration amplitude and can cause ejection from resonance for large enough precession rates. Both of these effects have implications for interpreting the known exoplanet population and may prove to be important considerations as the population of well-characterized exoplanet systems continues to grow.

A Novel Way of Measuring the Gas Disk Mass of Protoplanetary Disks Using N2H+ and C18O

Abstract Measuring the gas mass of protoplanetary disks, the reservoir available for giant planet formation, has proven to be difficult. We currently lack a far-infrared observatory capable of observing HD, and the most common gas mass tracer, CO, suffers from a poorly constrained CO-to-H2 ratio. Expanding on previous work, we investigate if N2H+, a chemical tracer of CO-poor gas, can be used to observationally measure the CO-to-H2 ratio and correct CO-based gas masses. Using disk structures obtained from the literature, we set up thermochemical models for three disks, TW Hya, DM Tau and GM Aur, to examine how well the CO-to-H2 ratio and gas mass can be measured from N2H+ and C18O line fluxes. Furthermore, we compare these gas masses to gas masses independently measured from archival HD observations. The N2H+(3 − 2)/C18O(2 − 1) line ratio scales with the disk CO-to-H2 ratio. Using these two lines, we measure 4.6 × 10−3 M ⊙ ≤ M disk ≤ 1.1 × 10−1 M ⊙ for TW Hya, 1.5 × 10−2 M ⊙ ≤ M disk ≤ 9.6 × 10−2 M ⊙ for GM Aur and 3.1 × 10−2 M ⊙ ≤ M disk ≤ 9.6 × 10−2 M ⊙ for DM Tau. These gas masses agree with values obtained from HD within their respective uncertainties. The uncertainty on the N2H+ + C18O gas mass can be reduced by observationally constraining the cosmic-ray ionization rate in disks. These results demonstrate the potential of using the combination of N2H+ and C18O to measure gas masses of protoplanetary disks.

Mass determination of protoplanetary disks from dust evolution

Context. The mass of protoplanetary disks is arguably one of their most important quantities shaping their evolution toward planetary systems, but it remains a challenge to determine this quantity. Using the high spatial resolution now available on telescopes such as the Atacama Large Millimeter/submillimeter Array (ALMA), recent studies derived a relation between the disk surface density and the location of the “dust lines”. This is a new concept in the field, linking the disk size at different continuum wavelengths with the radial distribution of grain populations of different sizes. Aims. We aim to use a dust evolution model to test the dependence of the dust line location on disk gas mass. In particular, we are interested in the reliability of the method for disks showing radial substructures, as recent high-resolution observations revealed. Methods. We performed dust evolution calculations, which included perturbations to the gas surface density with different amplitudes at different radii, to investigate their effect on the global drift timescale of dust grains. These models were then used to calibrate the relation between the dust grain drift timescale and the disk gas mass. We investigated under which condition the dust line location is a good mass estimator and tested how different stellar and disk properties (disk mass, stellar mass, disk age, and dust-to-gas ratio) affect the dust line properties. Finally, we show the applicability of this method to disks such as TW Hya and AS 209 that have been observed at high angular resolution with ALMA and show pronounced disk structures. Results. Our models without pressure bumps confirm a strong dependence of the dust line location on the disk gas mass and its applicability as a reliable mass estimator. The other disk properties do not significantly affect the dust line location, except for the age of the system, which is the major source of uncertainty for this mass estimator. A population of synthetic disks was used to calibrate an analytic relation between the dust line location and the disk mass for smooth disks, finding that previous mass estimates based on dust lines overestimate disk masses by about one order of magnitude. Radial pressure bumps can alter the location of the dust line by up to ~10 au, while its location is mainly determined by the disk mass. Therefore, an accurate mass estimation requires a proper evaluation of the effect of bumps. However, when radial substructures act as traps for dust grains, the relation between the dust line location and disk mass becomes weaker, and other mass estimators need to be adopted. Conclusions. Our models show that the determination of the dust line location is a promising approach to the mass estimate of protoplanetay disks, but the exact relation between the dust line location and disk mass depends on the structure of the particular disk. We calibrated the relation for disks without evidence of radial structures, while for more complex structures we ran a simple dust evolution model. However, this method fails when there is evidence of strong dust traps. It is possible to reveal when dust evolution is dominated by traps, providing the necessary information for when the method should be applied with caution.

Rapid Formation of Gas-giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores

Abstract Gas-giant planets, such as Jupiter, Saturn, and massive exoplanets, were formed via the gas accretion onto the solid cores, each with a mass of roughly 10 Earth masses. However, rapid radial migration due to disk–planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with a lot of effort, the full evolution path from dust to planets is still uncertain. Here we report the result of full simulations for collisional evolution from dust to planets in a whole disk. Dust growth with realistic porosity allows the formation of icy planetesimals in the inner disk (≲10 au), while pebbles formed in the outer disk drift to the inner disk and there grow to planetesimals. The growth of those pebbles to planetesimals suppresses their radial drift and supplies small planetesimals sustainably in the vicinity of cores. This enables rapid formation of sufficiently massive planetary cores within 0.2–0.4 million years, prior to the planetary migration. Our models shows the first gas giants form at 2–7 au in rather common protoplanetary disks, in agreement with the exoplanet and solar systems.

The fate of planetesimals formed at planetary gap edges

The presence of rings and gaps in protoplanetary disks are often ascribed to planet–disk interactions, where dust and pebbles are trapped at the edges of planetary-induced gas gaps. Recent works have shown that these are likely sites for planetesimal formation via the streaming instability. Given the large amount of planetesimals that potentially form at gap edges, we address the question of their fate and their ability to radially transport solids in protoplanetary disks. We performed a series ofN-body simulations of planetesimal orbits, taking into account the effect of gas drag and mass loss via ablation. We considered two planetary systems: one that is akin to the young Solar System and another inspired by the structures observed in the protoplanetary disk around HL Tau. In both systems, the proximity to the gap-opening planets results in large orbital excitations, causing the planetesimals to leave their birth locations and spread out across the disk soon after formation. We find that collisions between pairs of planetesimals are rare and should not affect the outcome of our simulations. Collisions with planets occur for ~1% of the planetesimals in the Solar System and for ~20% of the planetesimals in the HL Tau system. Planetesimals that end up on eccentric orbits interior of ~10 au experience efficient ablation and lose all mass before they reach the innermost disk region. In our nominal Solar System simulation, with a stellar gas accretion rate ofṀ0= 10−7M⊙yr−1andα= 10−2, we find that 70% of the initial planetesimal mass has been ablated after 500 kyr. Since the protoplanets are located further away from the star in the HL Tau system, the ablation rate is lower and only 11% of the initial planetesimal mass has been ablated after 1 Myr using the same disk parameters. The ablated material consist of a mixture of solid grains and vaporized ices, where a large fraction of the vaporized ices re-condense to form solid ice. Assuming that the solid grains and ices grow to pebbles in the disk midplane, this results in a pebble flux of ~10−100M⊕Myr−1through the inner disk. This occurred in the Solar System at a time so early in its evolution that there is not likely to be any record of it. Our results demonstrate that scattered planetesimals can carry a significant flux of solids past planetary-induced gaps in young and massive protoplanetary disks.

The TW Hya Rosetta Stone Project. III. Resolving the Gaseous Thermal Profile of the Disk

Abstract The thermal structure of protoplanetary disks is a fundamental characteristic of the system that has wide-reaching effects on disk evolution and planet formation. In this study, we constrain the 2D thermal structure of the protoplanetary disk TW Hya structure utilizing images of seven CO lines. This includes new ALMA observations of 12CO J = 2–1 and C18O J = 2–1 as well as archival ALMA observations of 12CO J = 3–2, 13CO J = 3–2 and 6–5, and C18O J = 3–2 and 6–5. Additionally, we reproduce a Herschel observation of the HD J = 1–0 line flux and the spectral energy distribution and utilize a recent quantification of CO radial depletion in TW Hya. These observations were modeled using the thermochemical code RAC2D, and our best-fit model reproduces all spatially resolved CO surface brightness profiles. The resulting thermal profile finds a disk mass of 0.025 M ⊙ and a thin upper layer of gas depleted of small dust with a thickness of ∼1.2% of the corresponding radius. Using our final thermal structure, we find that CO alone is not a viable mass tracer, as its abundance is degenerate with the total H2 surface density. Different mass models can readily match the spatially resolved CO line profiles with disparate abundance assumptions. Mass determination requires additional knowledge, and, in this work, HD provides the additional constraint to derive the gas mass and support the inference of CO depletion in the TW Hya disk. Our final thermal structure confirms the use of HD as a powerful probe of protoplanetary disk mass. Additionally, the method laid out in this paper is an employable strategy for extraction of disk temperatures and masses in the future.

The Ophiuchus DIsc Survey Employing ALMA (ODISEA) – III. The evolution of substructures in massive discs at 3–5 au resolution

ABSTRACT We present 1.3 mm continuum ALMA long-baseline observations at 3–5 au resolution of 10 of the brightest discs from the Ophiuchus DIsc Survey Employing ALMA (ODISEA) project. We identify a total of 26 narrow rings and gaps distributed in 8 sources and 3 discs with small dust cavities (r &amp;lt;10 au). We find that two discs around embedded protostars lack the clear gaps and rings that are ubiquitous in more evolved sources with Class II SEDs. Our sample includes five objects with previously known large dust cavities (r &amp;gt;20 au). We find that the 1.3 mm radial profiles of these objects are in good agreement with those produced by numerical simulations of dust evolution and planet–disc interactions, which predict the accumulation of mm-sized grains at the edges of planet-induced cavities. Our long-baseline observations resulted in the largest sample of discs observed at ∼3–5 au resolution in any given star-forming region (15 objects when combined with Ophiuchus objects in the DSHARP Large Program) and allow for a demographic study of the brightest $\sim\! 5{{\ \rm per\ cent}}$ of the discs in Ophiuchus (i.e. the most likely formation sites of giant planets in the cloud). We use this unique sample to propose an evolutionary sequence and discuss a scenario in which the substructures observed in massive protoplanetary discs are mainly the result of planet formation and dust evolution. If this scenario is correct, the detailed study of disc substructures might provide a window to investigate a population of planets that remains mostly undetectable by other techniques.

Protoplanetary disk masses in NGC 2024: Evidence for two populations

Context. Protoplanetary disks in dense, massive star-forming regions are strongly affected by their environment. How this environmental impact changes over time is an important constraint on disk evolution and external photoevaporation models. Aims. We characterize the dust emission from 179 disks in the core of the young (0.5 Myr) NGC 2024 cluster. By studying how the disk mass varies within the cluster, and comparing these disks to those in other regions, we aim to determine how external photoevaporation influences disk properties over time. Methods. Using the Atacama Large Millimeter/submillimeter Array, a 2.9′× 2.9′ mosaic centered on NGC 2024 FIR 3 was observed at 225 GHz with a resolution of 0.25″, or ~100 AU. The imaged region contains 179 disks identified at IR wavelengths, seven new disk candidates, and several protostars. Results. The overall detection rate of disks is 32 ± 4%. Few of the disks are resolved, with the exception of a giant (R = 300 AU) transition disk. Serendipitously, we observe a millimeter flare from an X-ray bright young stellar object (YSO), and resolve continuum emission from a Class 0 YSO in the FIR 3 core. Two distinct disk populations are present: a more massive one in the east, along the dense molecular ridge hosting the FIR 1-5 YSOs, with a detection rate of 45 ± 7%. In the western population, towards IRS 1, only 15 ± 4% of disks are detected. Conclusions. NGC 2024 hosts two distinct disk populations. Disks along the dense molecular ridge are young (0.2–0.5 Myr) and partly shielded from the far ultraviolet radiation of IRS 2b; their masses are similar to isolated 1–3 Myr old SFRs. The western population is older and at lower extinctions, and may be affected by external photoevaporation from both IRS 1 and IRS 2b. However, it is possible these disks had lower masses to begin with.

Dust dynamics and vertical settling in gravitoturbulent protoplanetary discs

Abstract Gravitational instability (GI) controls the dynamics of young massive protoplanetary discs. Apart from facilitating gas accretion on to the central protostar, it must also impact on the process of planet formation: directly through fragmentation, and indirectly through the turbulent concentration of small solids. To understand the latter process, it is essential to determine the dust dynamics in gravitoturbulent flow. For that purpose, we conduct a series of 3D shearing box simulations of coupled gas and dust, including the gas’s self-gravity and scanning a range of Stokes numbers, from 10 −3 to ∼0.2. First, we show that the vertical settling of dust in the mid-plane is significantly impeded by gravitoturbulence, with the dust scale height roughly 0.6 times the gas scale height for centimetre grains. This is a result of the strong vertical diffusion issuing from (i) small-scale inertial-wave turbulence feeding off the GI spiral waves and (ii) the larger scale vertical circulations that naturally accompany the spirals. Second, we show that at R = 50 au concentration events involving submetre particles and yielding order 1 dust-to-gas ratios are rare and last for less than an orbit. Moreover, dust concentration is less efficient in 3D than in 2D simulations. We thus conclude that GI is not especially prone to the turbulent accumulation of dust grains. Finally, the large dust scale height measured in simulations could be, in the future, compared with that of edge-on discs seen by ALMA, thus aiding detection and characterization of GI in real systems.

Gravitoviscous protoplanetary disks with a dust component

Aims. 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. Methods. 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. Results. 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⊕). 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) MJup and (1.0–5.5) M⊕ 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. Conclusions. Dusty rings formed through tidal dispersal of inward-migrating clumps may have a connection to ring-like structures found in youngest and massive protoplanetary disks. Numerical disk models with a dust component that can follow the evolution of gravitationally bound clumps through their collapse phase to the formation of protoplanets are needed to make firm conclusions on the characteristics of planets forming through gravitational fragmentation.

The Effect of the Approach to Gas Disk Gravitational Instability on the Rapid Formation of Gas Giant Planets

Abstract Observational evidence suggests that gas disk instability may be responsible for the formation of at least some gas giant exoplanets, particularly massive or distant gas giants. With regard to close-in gas giants, Boss used the β cooling approximation to calculate hydrodynamical models of inner gas disk instability, finding that provided disks with low values of the initial minimum Toomre stability parameter (i.e., Q i &lt; 2 inside 20 au) form, fragmentation into self-gravitating clumps could occur even for β as high as 100 (i.e., extremely slow cooling). Those results implied that the evolution of disks toward low Q i must be taken into account. This paper presents such models: initial disk masses of 0.091 M ⊙ extending from 4 to 20 au around a 1 M ⊙ protostar, with a range (1–100) of β cooling parameters, the same as in Boss, but with all the disks starting with Q i = 2.7, i.e., gravitationally stable, and allowed to cool from their initial outer disk temperature of 180 K to as low as 40 K. All the disks eventually fragment into at least one dense clump. The clumps were again replaced by virtual protoplanets (VPs) and the masses and orbits of the resulting ensemble of VPs compare favorably with those of Boss, supporting the claim that disk instability can form gas giants rapidly inside 20 au, provided that sufficiently massive protoplanetary disks exist.

A Tight Relation between Spiral Arm Pitch Angle and Protoplanetary Disk Mass

Abstract We use two-dimensional Fourier transformation to measure the pitch angle (φ) of the dominant spiral Fourier mode of well-defined spiral arms in 13 protoplanetary disks, making use of near-infrared scattered-light images of AB Aur, SAO 206462, MWC 758, V1247 Ori, HD 142527, DZ Cha, LkHα 330, and HD 100453, and ALMA millimeter continuum images of Elias 2-27, IM Lup, AS 205, and HT Lup. We find that the measured pitch angle correlates strongly with disk mass (M D ), such that more massive protoplanetary disks have smaller pitch angles, following . Interestingly, four disks with a known companion (HD 142527, HD 100453, AS 205, and HT Lup) share the same trend. Such a strong dependence of spiral arm pitch angle on disk mass suggests that the disk mass, independent of the formation mechanism, plays a fundamental role in determining the arm tightness of the observed spiral structure. The physical origin of the relation is still not clear. The pitch angle of spiral arms in protoplanetary disks provides an independent constraint on the disk mass.

Protoplanetary Disk Masses from Radiative Transfer Modeling: A Case Study in Taurus

Abstract Measuring the masses of protoplanetary disks is crucial for understanding their planet-forming potential. Typically, dust masses are derived from (sub-)millimeter flux density measurements plus assumptions for the opacity, temperature, and optical depth of the dust. Here we use radiative transfer models to quantify the validity of these assumptions with the aim of improving the accuracy of disk dust mass measurements. We first carry out a controlled exploration of disk parameter space. We find that the disk temperature is a strong function of disk size, while the optical depth depends on both disk size and dust mass. The millimeter-wavelength spectral index can be significantly shallower than the naive expectation due to a combination of optical depth and deviations from the Rayleigh–Jeans regime. We fit radiative transfer models to the spectral energy distributions (SEDs) of 132 disks in the Taurus-Auriga region using a Markov chain Monte Carlo approach. We used all available data to produce the most complete SEDs used in any extant modeling study. We perform the fitting twice: first with unconstrained disk sizes and again imposing the disk size–brightness relation inferred for sources in Taurus. This constraint generally forces the disks to be smaller, warmer, and more optically thick. From both sets of fits, we find disks to be ∼1–5 times more massive than when derived using (sub-)millimeter measurements and common assumptions. With the uncertainties derived from our model fitting, the previously measured dust mass–stellar mass correlation is present in our study but only significant at the 2σ level.