Dust growth in protoplanetary disks-a comprehensive experimental / theoretical approach

More than a decade of dedicated experimental work on the collisional physics of protoplanetary dust has brought us to a point at which the growth of dust aggregates can - for the first time - be self-consistently and reliably modeled. In this article, the emergent collision model for protoplanetery dust aggregates, as well as the numerical model for the evolution of dust aggregates in protoplanetary disks, is reviewed. It turns out that, after a brief period of rapid collisional growth of fluffy dust aggregates to sizes of a few centimeters, the protoplanetary dust particles are subject to bouncing collisions, in which their porosity is considerably decreased. The model results also show that low-velocity fragmentation can reduce the final mass of the dust aggregates but that it does not trigger a new growth mode as discussed previously. According to the current stage of our model, the direct formation of kilometer-sized planetesimals by collisional sticking seems unlikely, implying that collective effects, such as the streaming instability and the gravitational instability in dust-enhanced regions of the protoplanetary disk, are the best candidates for the processes leading to planetesimals.

Ice lines as the origin for the gap/ring structure in protoplanetary disks: the issue of the assumed temperature profile

Gaps and rings are commonly seen in recent high-resolution ALMA observations of protoplanetary disks. Ice lines of volatiles are one of the mechanisms proposed to explain the origin for these substructures. To examine the ice line hypothesis, literature studies usually parameterize the midplane temperature with the analytic formula of a passively heated, flared disk. The temperature in this simplified expression is basically dependent on the stellar luminosity. I have built a grid of self-consistent radiative transfer models that feature the same stellar properties, but different disk parameters. The midplane temperature of these models shows a large dispersion over a wide range of radii, indicating that besides the stellar luminosity, the disk parameters also play an important role in determining the thermal structure.Comparing the mid-plane temperature from radiative transfer simulation with the analytic solution shows a large difference between both approaches. This result suggests that special care on the assumed temperature profile has to be taken in the analysis of gap/ring origins, and conclusions drawn in previous works on the basis of the analytic temperature should be revisited. I further took the AS 209 disk as an example, and conducted a detailed radiative transfer modeling of the spectral energy distribution and the ALMA Band 6 image. The D137, D24 and D9 gaps are associated with the ice lines of major volatiles in the disk according to such a thorough analysis. However, if the temperature profile simply follows the analytic formula, none of these gaps matches the ice lines of the species considered here.

An SPH simulation for cooling and self-gravitating protoplanetary disks

We investigate the effects of the cooling function in the formation of clumps of protoplanetary disks using two-dimensional smoothed particle hydrody- namic simulations. We use a simple prescription for the cooling rate of the flow, du/dt = -u/τcool, where u and %ool are the internal energy and cooling timeseale, respectively. We assume the ratio of local＇cooling to dynamical timescale, Ωτcool =β, to be a constant and also a function of the local temperature. We found that for the constantβ and γ = 5/3, fragmentation occurs only forβ ≤ 7. However, in the case ofβ having temperature dependence and γ = 5/3, fragmentation can also occur for larger values ofβ. By increasing the temperature dependence of the cooling timescale, the mass accretion rate decreases, the population of clumps/fragments increases, and the clumps/fragments can also form in the smaller radii. Moreover, we found that the clumps can form even in a low mass accretion rate, ≤10-7M⊙yr-1, in the case of temperature-dependentβ. However, clumps form with a larger mass accretion rate, 〉 10-7M⊙ yr-1, in the case of constantβ.

A numerical study of self-gravitating protoplanetary disks

The effect of self-gravity on protoplanetary disks is investigated.The mechanisms of angular momentum transport and energy dissipation are assumed to be the viscosity due to turbulence in the accretion disk.The energy equation is considered in a situation where the released energy by viscosity dissipation is balanced with cooling processes.The viscosity is obtained by equality of dissipation and cooling functions,and is used to derive the angular momentum equation.The cooling rate of the flow is calculated by a prescription,du/dt = u/τ cool,where u and τ cool are the internal energy and cooling timescale,respectively.The ratio of local cooling to dynamical timescales Ωτ cool is assumed to be a constant and also a function of the local temperature.The solutions for protoplanetary disks show that in the case of Ωτ cool = constant,the disk does not exhibit any gravitational instability over small radii for a typical mass accretion rate,˙ M = 10 6 M yr 1,but when choosing Ωτ cool to be a function of temperature,gravitational instability can occur for this value of mass accretion rate or even less in small radii.Also,by studying the viscosity parameter α,we find that the strength of turbulence in the inner part of self-gravitating protoplanetary disks is very low.These results are qualitatively consistent with direct numerical simulations of protoplanetary disks.Also,in the case of cooling with temperature dependence,the effect of physical parameters on the structure of the disk is investigated.These solutions demonstrate that disk thickness and the Toomre parameter decrease by adding the ratio of disk mass to central object mass.However,the disk thickness and the Toomre parameter increase by adding mass accretion rate.Furthermore,for typical input parameters such as mass accretion rate 10 6 M yr 1,the ratio of the specific heat γ = 5/3 and the ratio of disk mass to central object mass q = 0.1,gravitational instability can occur over the whole radius of the disk excluding the region very near the central object.

Ionization of protoplanetary disks by galactic cosmic rays,solar protons,and supernova remnants

Galactic cosmic rays and solar protons ionize the present terrestrial atmosphere,and the air showers are simulated by well-tested Monte-Carlo simulations,such as PHITS code.We use the latest version of PHITS to evaluate the possible ionization of protoplanetary disks by galactic cosmic rays（GCRs）,solar protons,and by supernova remnants.The attenuation length of GCR ionization is updated as 118 g cm^-2,which is approximately 20% larger than the popular value.Hard and soft possible spectra of solar protons give comparable and 20% smaller attenuation lengths compared with those from standard GCR spectra,respectively,while the attenuation length is approximately 10% larger for supernova remnants.Further,all of the attenuation lengths become 10% larger in the compound gas of cosmic abundance,e.g.128 g cm^-2 for GCRs,which can affect the minimum estimate of the size of dead zones in protoplanetary disks when the incident flux is unusually high.

Millimeter gap contrast as a probe for turbulence level in protoplanetary disks

Turbulent motions are believed to regulate angular momentum transport and influence dust evolution in protoplanetary disks.Measuring the strength of turbulence is challenging through gas line observations because of the requirement for high spatial and spectral resolution data,and an exquisite determination of the temperature.In this work,taking the well-known HD 163296 disk as an example,we investigated the contrast of gaps identified in high angular resolution continuum images as a probe for the level of turbulence.With self-consistent radiative transfer models,we simultaneously analyzed the radial brightness profiles along the disk major and minor axes,and the azimuthal brightness profiles of the B67 and B100 rings.By fitting all the gap contrasts measured from these profiles,we constrained the gas-to-dust scale height ratioΛto be 3.0^(+0.3)_(−0.8),1.2^(+0.1)_(−0.1),and≥6.5 for the D48,B67,and B100 regions,respectively.The varying gas-to-dust scale height ratios indicate that the degree of dust settling changes with radius.The inferred values forΛtranslate into a turbulence level of α_(turb)<3×10^(−3) in the D48 and B100 regions,which is consistent with previous upper limits set by gas line observations.However,turbulent motions in the B67 ring are strong with α_(turb)∼1.2×10^(−2).Due to the degeneracy betweenΛand the depth of dust surface density drops,the turbulence strength in the D86 gap region is not constrained.

Probing the Kinematic Signatures of Planet Formation in the Gas Disk of MWC 480

The disk around MWC 480 has shown multiple substructures in both dust and gas observations,possibly suggesting ongoing planet formation in situ.In this paper,we explore the gas kinematics of the MWC 480 disk by analyzing the archival Atacama Large Millimeter/submillimeter Array observations of^(12)CO(J=2-1),^(13)CO(J=2-1),and C^(18)O(J=2-1).By modeling the line-of-sight velocities,inferred from the Doppler shifts of the emission lines,we are able to decompose the three-dimensional(3D)velocity field of the disk into rotational,radial,and vertical components.Further analysis reveals the presence of large-scale gas flows in the(r,z)plane.Notably,we identify potential meridional flows across various heights as traced by all three CO isotopologues in the 80–120 au region,possibly associated with ongoing planet formation activities in this region.Moreover,we find upward flows near 200 au for all three CO isotopologues,which may point to the presence of disk winds.

The snowline in the protoplanetary disk and extrasolar planets

We investigate the behavior of the snowline in a protoplanetary disk and the relationship between the radius of the snowline and properties of molecular cloud cores.In our disk model,we consider mass influx from the gravitational collapse of a molecular cloud core,irradiation from the central star,and thermal radiation from the ambient molecular cloud gas.As the protoplanetary disk evolves,the radius of the snowline increases first to a maximum value Rmax,and then decreases in the late stage of evolution of the protoplanetary disk.The value of Rmaxis dependent on the properties of molecular cloud cores(mass M;,angular velocity ω and temperature T;).Many previous works found that solid material tends to accumulate at the location of the snowline,which suggests that the snowline is the preferred location for giant planet formation.With these conclusions,we compare the values of R;with semimajor axes of giant planets in extrasolar systems,and find that Rmaxmay provide an upper limit for the locations of the formation of giant planets which are formed by the core accretion model.

A WISE view of IRAS debris disks: revising the dust properties

Debris disks around stars are considered as components of planetary systems.Constraining the dust properties of these disks can give crucial information to formation and evolution of planetary systems.As an all-sky survey,InfRared Astronomical Satellite(IRAS)gave great contribution to the debris disk searching which discovered the first debris disk host star(Vega).The IRAS-detected debris disk sample published by Rhee(Rhee et al.2007)contains 146 stars with detailed information of dust properties.While the dust properties of 45 of them still cannot be determined due to the limitations with the IRAS database(have IRAS detection at 60μm only).Therefore,using more sensitivity data of Wide-.field Infrared Survey Explorer(WISE),we can better characterize the sample stars:for the stars with IRAS detection at 60μm only,we refit the excessive flux densities and obtain the dust temperatures and fractional luminosities;while for the remaining stars with multi-bands IRAS detections,the dust properties are revised which show that the dust temperatures were overestimated in the high temperature band before.Moreover,we identify 17 stars with excesses at the WISE 22μm which have smaller distribution of distance from Earth and higher fractional luminosities than the other stars without mid-infrared excess emission.Among them,15 stars can be found in previous works.

The density and temperature dependence of the cooling timescale for fragmentation of self-gravitating disks

The purpose of this paper is to explore the influences of cooling timescale on fragmentation of self-gravitating protoplanetary disks. We assume the cooling timescale, expressed in terms of the dynamical timescale Ω tcool, has a power-law dependence on temperature and density, Ω toool ∝∑-aT-b, where a and b are con- stants. We use this cooling timescale in a simple prescription for the cooling rate, du/dt = -u/tcoll, where u is the internal energy. We perform our simulations using the smoothed particle hydrodynamics method. The simulations demonstrate that the disk is very sensitive to the cooling timescale, which depends on density and tem- perature. Under such a cooling timescale, the disk becomes gravitationally unstable and clumps form in the disk. This property even occurs for cooling timescales which are much longer than the critical cooling timescale, Ω toool≥ 7. We show that by adding the dependence of a cooling timescale on temperature and density, the number of clumps increases and the clumps can also form at smaller radii. The simulations im- ply that the sensitivity of a cooling timescale to density is more than to temperature, because even for a small dependence of the cooling timescale on density, clumps can still form in the disk. However, when the cooling timescale has a large dependence on temperature, clumps form in the disk. We also consider the effects of artificial viscos- ity parameters on fragmentation conditions. This consideration is performed in two cases, where Ω tcool is a constant and Ω tcool is a function of density and temperature. The simulations consider both cases, and results show the artificial viscosity param- eters have rather similar effects. For example, using too small of values for linear and quadratic terms in artificial viscosity can suppress the gravitational instability and consequently the efficiency of the clump formation process decreases. This property is consistent with recent simulations of self-gravitating disks. We perform simulations with and without the Balsara form of artificial viscosity. We find that in the cooling and self-gravitating disks without the Balsara switch, the clumps can form more easily than those with the Balsara switch. Moreover, in both cases where the Balsara switch is present or absent, the simulations show that the cooling timescale strongly depends on density and temperature.

A tale of planet formation: from dust to planets

The characterization of exoplanets and their birth protoplanetary disks has enormously advanced in the last decade.Benefitting from that,our global understanding of the planet formation processes has been substantially improved.In this review,we first summarize the cutting-edge states of the exoplanet and disk observations.We further present a comprehensive panoptic view of modern core accretion planet formation scenarios,including dust growth and radial drift,planetesimal formation by the streaming instability,core growth by planetesimal accretion and pebble accretion.We discuss the key concepts and physical processes in each growth stage and elaborate on the connections between theoretical studies and observational revelations.Finally,we point out the critical questions and future directions of planet formation studies.

FGK 22 μm excess stars in LAMOST DR2 stellar catalog

Since the release of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope（LAMOST）catalog, we have had the opportunity to use the LAMOST DR2 stellar catalog and the WISE All-Sky Data Release catalog to search for 22 μm excess candidates. In this paper, we present 10 FGK candidates which show an excess in the infrared at 22 μm. All the 10 sources are newly identified 22 μm excess candidates.Of these 10 stars, five stars are F type and five stars are G type. The criterion for selecting candidates is Ks[22].387. In addition, we present the spectral energy distributions covering wavelengths from the optic-≥0al to mid-infrared band. Most of them show an obvious excess from the 12 μm band and three candidates even show excess from 3.4 μm. To characterize the amount of dust, we also estimate the fractional luminosity of10 22 μm excess candidates.

The debris disk candidates:eleven 24μm excess stars in the Spitzer SWIRE fields

We present the optical to mid-infrared SEDs of 11 debris disk candidates from Spitzer SWIRE fields. All the candidates are selected from SWIRE 24 μm sources matched with both the SDSS star catalog and the 2MASS point source catalog. They show an excess in the mid-infrared at 24 μm （Ks-[24]vega 〉 0.44）, indicating the presence of a circumstellar dust disk. The observed optical spectra show that they are all late-type main-sequence stars covering the spectral types of FGKM. Their fractional luminosities are well above 5× 10-5, even up to the high fractional luminosity of 1×10-3. The high galactic latitudes of SWIRE fields indicate that most of these candidates could belong to the oldest stars in the thick disk. Our results indicate that high fractional luminosity debris disks could exist in old solar-like star systems, though they are still quite rare. Their discovery at high galactic latitudes also provides an exellent opportunity for further study of the properties and evolution of debris disks in regions of the Galaxy with low densities of ISM, called ISM poor environments.

A physical interpretation of the Titius-Bode rule and its connection to the closed orbits of Bertrand's theorem

We consider the geometric Titius-Bode rule for the semimajor axes of planetary orbits. We derive an equivalent rule for the midpoints of the segments between consecutive orbits along the radial direction and we interpret it physically in terms of the work done in the gravitational field of the Sun by particles whose orbits are perturbed around each planetary orbit. On such energetic grounds, it is not surprising that some exoplanets in multiple-planet extrasolar systems obey the same relation. However,it is surprising that this simple interpretation of the Titius-Bode rule also reveals new properties of the bound closed orbits predicted by Bertrand’s theorem, which has been known since 1873.

Morphology of the ^(13)CO(3–2) millimetre emission across the gas disc surrounding the triple protostar GG Tau A using ALMA observations

Observations by the Atacama Large Millimetre/sub-millimetre Array of the dust continuum and ^13 CO（3–2） millimetre emissions of the triple stellar system GG Tau A are analysed,giving evidence for a rotating gas disc and a concentric and coplanar dust ring. The present work complements an earlier analysis（Tang et al.） by exploring detailed properties of the gas disc. A 95% confidence level upper limit of 0.24＂（34 au） is placed on the disc scale height at a distance of 1＂（140 au） from the central stars. Evidence for Keplerian rotation of the gas disc is presented,with the rotation velocity reaching-3.1 km s^-1 at 1＂ from the central stars,and a 99% confidence level upper limit of 9% is placed on relative contribution from a possible in-fall velocity. Variations of the intensity across the disc area are studied in detail and confirm the presence of a hot spot in the south-eastern quadrant. However several other significant intensity variations,in particular a depression in the northern direction,are also revealed. Variations of the intensity are found to be positively correlated to variations of the line width. Possible contributions to the measured line width are reviewed,suggesting an increase of the disc temperature and opacity with decreasing distance from the stars.

A comparison of approaches in fitting continuum SEDs

We present a detailed comparison of two approaches, the use of a precalculated database and simulated annealing （SA）, for fitting the continuum spectral energy distribution （SED） of astrophysical objects whose appearance is dominated by surrounding dust. While pre-calculated databases are commonly used to model SED data, only a few studies to date employed SA due to its unclear accuracy and convergence time for this specific problem. From a methodological point of view, different approaches lead to different fitting quality, demand on computational resources and calculation time. We compare the fitting quality and computational costs of these two approaches for the task of SED fitting to provide a guide to the practitioner to find a compromise between desired accuracy and available resources. To reduce uncertainties inherent to real datasets, we introduce a reference model resembling a typical circumstellar system with 10 free parameters. We derive the SED of the reference model with our code MC3 D at 78 logarithmically distributed wavelengths in the range [0.3 μm, 1.3 mini and use this setup to simulate SEDs for the database and SA. Our result directly demonstrates the applicability of SA in the field of SED modeling, since the algorithm regularly finds better solutions to the optimization problem than a precalculated database. As both methods have advantages and shortcomings, a hybrid approach is preferable. While the database provides an approximate fit and overall probability distributions for all parameters deduced using Bayesian analysis, SA can be used to improve upon the results returned by the model grid.

Radiative transfer modeling of three T Tauri stars: selecting candidates for studying circumstellar disk evolution

We present modeling work on three young stellar objects that are promis-ing targets for future high-resolution observations to investigate circumstellar disk evolution. The currently available data comprise the spectral energy distribution from optical to millimeter wavelengths which allow constraining the structure of the cir-cumstellar disk using self-consistent radiative transfer models. The results suggest that the assumption of well-mixed dust and gas leads to overestimation of flux in the far-infrared. Observational and theoretical arguments suggest that an overall decrease in far-infrared excess can be explained by dust settling towards the midplane. A new disk model is hence employed to take the effect of dust sedimentation into account. The extended model satisfactorily reproduces all existing observations. The three tar-gets studied here therefore deserve follow-up observations to reveal the evolutionary state of their protoplanetary disks.

Gap formation in a self-gravitating disk and the associated migration of the embedded giant planet

We present the results of our recent study on the interactions between a giant planet and a self-gravitating gas disk. We investigate how the disk＇s self-gravity affects the gap formation process and the migration of the giant planet. Two series of 1-D and 2-D hydrodynamic simulations are performed. We select several surface densities and focus on the gravitationally stable region. To obtain more reliable gravity torques exerted on the planet, a refined treatment of the disk＇s gravity is adopted in the vicinity of the planet. Our results indicate that the net effect of the disk＇s self- gravity on the gap formation process depends on the surface density of the disk. We notice that there are two critical values, ∑I and ∑n. When the surface density of the disk is lower than the first one,∑0 〈 ∑I, the effect of self-gravity suppresses the formation of a gap. When ∑0 〉 ∑I, the self-gravity of the gas tends to benefit the gap formation process and enlarges the width/depth of the gap. According to our 1-D and 2-D simulations, we estimate the first critical surface density to be ∑I ≈ 0.8 MMSN. This effect increases until the surface density reaches the second critical value ∑n- When ∑0 〉 ∑n, the gravitational turbulence in the disk becomes dominant and the gap formation process is suppressed again. Our 2-D simulations show that this critical surface density is around 3.5 MMSN. We also study the associated orbital evolution of a giant planet. Under the effect of the disk＇s self-gravity, the migration rate of the giant planet increases when the disk is dominated by gravitational turbulence. We show that the migration timescale correlates with the effective viscosity and can be up to 104 yr.

Delay of planet formation at large radius and the outward decrease in mass and gas content of Jovian planets

A prominent observation of the solar system is that the mass and gas content of Jovian planets decrease outward with orbital radius, except that, in terms of these properties, Neptune is almost the same as Uranus. In previous studies, the solar nebula was assumed to preexist and the formation process of the solar nebula was not considered. It was therefore assumed that planet formation at different radii started at the same time in the solar nebula. We show that planet formation at different radii does not start at the same time and is delayed at large radii. We suggest that this delay might be one of the factors that causes the outward decrease in the masses of Jovian planets. The nebula starts to form from its inner part because of the inside-out collapse of its progenitorial molecular cloud core. The nebula then expands outward due to viscosity. Material first reaches a small radius and then reaches a larger radius, so planet formation is delayed at the large radius. The later the material reaches a planet＇s location, the less time it has to gain mass and gas content. Hence, the delay tends to cause the outward decrease in mass and gas content of Jovian planets. Our nebula model shows that the material reaches Jupiter, Saturn, Uranus and Neptune at t = 0.40, 0.57, 1.50 and 6.29 × 10^6 yr, respectively. We discuss the effects of time delay on the masses of Jovian planets in the framework of the core accretion model of planet formation. Saturn＇s formation is not delayed by much time relative to Jupiter so that they both reach the rapid gas accretion phase and become gas giants. However, the delay in formation of Uranus and Neptune is long and might be one of the factors that cause them not to reach the rapid gas accretion phase before the gas nebula is dispersed. Saturn has less time to go through the rapid gas accretion, so Saturn＇s mass and gas content are significantly less than those of Jupiter.

Exact Axisymmetric Solutions of the 2-D Lane-Emden Equations with Rotation

We have derived exact axisymmetric solutions of the two-dimensional Lane-Emden equations with rotation. These solutions are intrinsically favored by the differential equations regardless of any adopted boundary conditions and the physical solutions of the Cauchy problem are bound to oscillate about and remain close to these intrinsic solutions. The isothermal solutions are described by power-law density profiles in the radial direction, whereas the polytropic solutions are described by radial density profiles that are powers of the zeroth-order Bessel function of the first kind. Both families of solutions decay exponentially in the vertical direction and both result in increasing or nearly flat radial rotation curves. The results are applicable to gaseous spiral-galaxy disks that exhibit flat rotation curves and to the early stages of protoplanetary disk formation before the central star is formed.