The temperature in the optically thick interior of protoplanetary discs is essential for the interpretation of millimeter observations of the discs, for the vertical structure of the discs, for models of the disc evolution and the planet formation, and for the chemistry in the discs. Since large icy grains have a large albedo even in the infrared, the effect of scattering of the diffuse radiation in the discs on the interior temperature should be examined. We have performed a series of numerical radiation transfer simulations including isotropic scattering by grains with various typical sizes for the diffuse radiation as well as for the incident stellar radiation. We also have developed an analytic model including isotropic scattering to understand the physics concealed in the numerical results. With the analytic model, we have shown that the standard two-layer approach is valid only for grey opacity (i.e. grain size $\ga10$ \micron) even without scattering. A three-layer interpretation is required for grain size $\la10$ \micron. When the grain size is 0.1--10 \micron, the numerical simulations show that isotropic scattering reduces the temperature of the disc interior. This reduction is nicely explained by the analytic three-layer model as a result of the energy loss by scatterings of the incident stellar radiation and of the warm diffuse radiation in the disc atmosphere. For grain size $\ga10$ \micron (i.e. grey scattering), the numerical simulations show that isotropic scattering does not affect the interior temperature. This is nicely explained by the analytic two-layer model; the energy loss by scattering in the disc atmosphere is exactly offset by the "green-house effect" due to scattering of the cold diffuse radiation in the interior.
We critically examine the best lines of evidence for grain growth in protoplanetary disks, based on modelling of observed spectral energy distributions and images of T Tauri and Herbig Ae stars. The data are consistent with millimeter-sized grains near disk midplanes, and micron-sized grains near disk surfaces. We review three channels by which grains can grow, including direct condensation from the vapor phase, grain-grain collisional sticking, and gravitational instability. The utility of dust in identifying as yet unseen extrasolar planets is highlighted.
We examine the ability of stellar X-rays to desorb molecules from grains in outer protoplanetary disks. In particular, we consider the possibility of spot heating by X-rays and examine its effectiveness, compared to whole grain heating by X-rays, in sustaining a gas phase abundance of CO. As found in previous studies, whole grain heating is effective only for small grains (< 500 A). As a result, large grains are a permanent sink of CO and whole grain heating cannot sustain an equilibrium gas phase abundance of CO. Spot heating, in which the incident X-ray deposits energy in only a restricted r…
We show that grains have grown to ~mm size (sand sized) or larger in the terrestrial zone (within ~3 AU) of the protoplanetary disk surrounding the 3 Myr old binary star KH 15D. We also argue that the reflected light in the system reaches us by back scattering off the far side of the same ring whose near side causes the obscuration.
We present the first results of the treatment of grain growth in our 3D, two-fluid (gas+dust) SPH code describing protoplanetary disks. We implement a scheme able to reproduce the variation of grain sizes caused by a variety of physical processes and test it with the analytical expression of grain growth given by Stepinski & Valageas (1997) in simulations of a typical T Tauri disk around a one solar mass star. The results are in agreement with a turbulent growing process and validate the method. We are now able to simulate the grain growth process in a protoplanetary disk given by a more reali…
We present the first results of the treatment of grain growth in our 3D, two-fluid (gas+dust) SPH code describing protoplanetary disks. We implement a scheme able to reproduce the variation of grain sizes caused by a variety of physical processes and test it with the analytical expression of grain growth given by Stepinski & Valageas (1997) in simulations of a typical T Tauri disk around a one solar mass star. The results are in agreement with a turbulent growing process and validate the method. We are now able to simulate the grain growth process in a protoplanetary disk given by a more reali…
Aims: We wish to investigate what the effect of dust sedimentation is on the observed 10 mum feature of protoplanetary disks and how this may affect the interpretation of the observations. Methods: Using a combination of modeling tools, we simulated the sedimentation of a dust grain size distribution in an axisymmetric 2-D model of a turbulent protoplanetary disk, and we used a radiative transfer program to compute the resulting spectra. Results: We find that the sedimentation can turn a flat feature into a pointy one, but only to a limited degree and for a very limited set of particle size di…
Aims: In order to understand the first stages of planet formation, when tiny grains aggregate to form planetesimals, one needs to simultaneously model grain growth, vertical settling and radial migration of dust in protoplanetary disks. In this study, we implement an analytical prescription for grain growth into a 3D two-phase hydrodynamics code to understand its effects on the dust distribution in disks. Methods: Following the analytic derivation of Stepinski & Valageas (1997), which assumes that grains stick perfectly upon collision, we implement a convenient and fast method of following gra…
We have computed the size distribution of silicate grains in the outer radiative region of the envelope of a protoplanet evolving according to the scenario of Pollack et al. (1996). Our computation includes grain growth due to Brownian motion and overtake of smaller grains by larger ones. We also include the input of new grains due to the breakup of planetesimals in the atmosphere. We follow the procedure of Podolak (2003), but have speeded it up significantly. This allows us to test the sensitivity of the code to various parameters. We have also made a more careful estimate of the resulting g…
We model the process of dust coagulation in protoplanetary disks and calculate how it affects their observational appearance. Our model involves the detailed solution of the coagulation equation at every location in the disk. At regular time intervals we feed the resulting 3-D dust distribution functions into a continuum radiative transfer code to obtain spectral energy distributions. We find that, even if only the very basic -- and well understood -- coagulation mechanisms are included, the process of grain growth is much too quick to be consistent with infrared observations of T Tauri disks.…
We report spatially resolved 11.8 micron images, obtained at the W. M. Keck 10 m telescope, of the protoplanetary disk around the pre--main-sequence star HK Tau B. The mid-infrared morphology and astrometry of HK Tau B with respect to HK Tau A indicate that the flux observed in the mid-infrared from HK Tau B has been scattered off the upper surface of its nearly edge-on disk. This is the first example of a protoplanetary disk observed in scattered light at mid-infrared wavelengths. Monte Carlo simulations of this disk show that the extent (FWHM =0."5, or 70 AU) of the scattered light nebula in…
Observational studies show that the probability of finding gas giant planets around a star increases with the star's metallicity. Our latest simulations of disks undergoing gravitational instabilities (GIs) with realistic radiative cooling indicate that protoplanetary disks with lower metallicity generally cool faster and thus show stronger overall GI-activity. More importantly, the global cooling times in our simulations are too long for disk fragmentation to occur, and the disks do not fragment into dense protoplanetary clumps. Our results suggest that direct gas giant planet formation via d…
We analyze the ionization state of the magnetohydrodynamically turbulent protoplanetary disks and propose a new mechanism of sustaining ionization. First, we show that in the quasi-steady state of turbulence driven by magnetorotational instability in a typical protoplanetary disk with dust grains, the amount of energy dissipation should be sufficient for providing the ionization energy that is required for activating magnetorotational instability. Second, we show that in the disk with dust grains the energetic electrons that compose electric currents in weakly ionized gas can provide collision…
We investigate the linear growth and vertical structure of the MRI in protoplanetary discs when dust grains are well mixed with the gas over the entire disc thickness. All the grains have the same radius (a = 0.1, 1 or 3 micron) and constitute 1 % of the total mass of the gas. Solutions are obtained at R = 5 and 10 AU for a minimum-mass solar nebula model and different choices of the initially vertical magnetic field strength (B), configuration of the diffusivity tensor and grain sizes. We find that when no grains are present, or they are > 1 micron, the midplane remains magnetically coupled f…
Recent research on the buildup of rocks from small dust grains has reaffirmed that grain growth in protoplanetary disks should occur quickly. Calculation of growth rates have been made for a variety of growth processes and generally predict high probabilities of sticking in low-velocity collisions that may be brought about in a number of ways in protoplanetary disks. Laboratory experiments have measured sticking coefficients for some materials largely confirming the calculations. Although the detailed velocity fields of disks are not well understood, many of the important processes leading to …
We present the results of a three dimensional, locally isothermal, non-self-gravitating SPH code which models protoplanetary disks with two fluids: gas and dust. We ran simulations of a 1 Msun star surrounded by a 0.01 Msun disk comprising 99% gas and 1% dust in mass and extending from 0.5 to ~300 AU. The grain size ranges from 0.001 mm to 10 m for the low resolution (~25 000 SPH particles) simulations and from 0.1 mm to 10 cm for the high resolution (~160 000 SPH particles) simulations. Dust grains are slowed down by the sub-Keplerian gas and lose angular momentum, forcing them to migrate tow…
Millimeter interferometry provides evidence for the presence of mm to cm size "pebbles" in the outer parts of disks around pre-main-sequence stars. The observations suggest that large grains are produced relatively early in disk evolution (< 1 Myr) and remain at large radii for longer periods of time (5 to 10 Myr). Simple theoretical estimates of the radial drift time of solid particles, however, imply that they would drift inward over a time scale of less than 0.1 Myr. In this paper, we address this conflict between theory and observation, using more detailed theoretical models, including the…
The first challenge in the formation of both terrestrial planets and the cores of gas giants is the retention of grains in protoplanetary disks. In most regions of these disks, gas attains sub-Keplerian speeds as a consequence of a negative pressure gradient. Hydrodynamic drag leads to orbital decay and depletion of the solid material in the disk, with characteristic timescales as short as only a few hundred years for meter-sized objects at 1 AU. In this paper, we suggest a particle retention mechanism which promotes the accumulation of grains and the formation of planetesimals near the water …
We present the results of three-dimensional numerical simulations that include the effects of hydrodynamical forces and gas drag upon an evolving dusty gas disk. We briefly describe a new parallel, two phase numerical code based upon the smoothed particle hydrodynamics (SPH) technique in which the gas and dust phases are represented by two distinct types of particles. We use the code to follow the dynamical evolution of a population of grains in a gaseous protoplanetary disk in order to understand the distribution of grains of different sizes within the disk. Our ``grains'' range from metre to…
We consider the dynamics of dust and gas during the clearing of protoplanetary discs. We work within the context of a photoevaporation/viscous model for the evolution of the gas disc, and use a two-fluid model to study the dynamics of dust grains as the gas disc is cleared. Small (<~10um) grains remain well-coupled to the gas, but larger (~1mm) grains are subject to inward migration from large radii (~50AU), suggesting that the time-scale for grain growth in the outer disc is ~10^4-10^5yr. We describe in detail the observable appearance of discs during clearing, and find that pressure gradient…
We study the effect of an imposed magnetic field on the motion of charged dust particles in magnetically active regions of a protoplanetary disc. Assuming a power law structure for the vertical and the toroidal components of the magnetic field for the regions beyond magnetically dead region of the disc, the radial and the vertical velocities of the charged particles, in the asymptotic case of small particles, are calculated analytically. While grains with radii smaller than a critical radius significantly are affected by the magnetic force, motion of the particles with larger radii is independ…
We investigate where in protoplanetary disks magnetorotational instability operates, which can cause angular momentum transport in the disks. We investigate the spatial distribution of various charged particles and the unstable regions for a variety of models for protoplanetary disks taking into account the recombination of ions and electrons at grain surfaces, which is an important process in most parts of the disks. We find that for all the models there is an inner region which is magnetorotationally stable due to ohmic dissipation. This must make the accretion onto the central star non-stea…
Dust growth and settling considerably affect the spectral energy distributions (SEDs) of protoplanetary disks. We investigated dust growth and settling in protoplanetary disks through numerical simulations to examine time-evolution of the disk optical thickness and SEDs. In the present paper, we considered laminar disks as a first step of a series of papers. As a result of dust growth and settling, a dust layer forms around the mid-plane of a gaseous disk. After the formation of the dust layer, small dust grains remain floating above the layer. Although the surface density of the floating smal…
Mid-infrared spectra of 65 T Tauri stars (TTS) taken with the Infrared Spectrograph (IRS) on board the Spitzer Space Telescope are modeled using dust at two temperatures to probe the radial variation in dust composition in the uppermost layers of protoplanetary disks. Most spectra indicating crystalline silicates require Mg-rich minerals and silica, but a few suggest otherwise. Spectra indicating abundant enstatite at higher temperatures also require crystalline silicates at temperatures lower than those required for spectra showing high abundance of other crystalline silicates. A few spectra …
Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary discs. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface, and magnetically-driven mixing has implications for disk chemistry and evolution of the grain population. However, the weak ionisation of protoplanetary discs means that magnetic fields may not be able to effectively couple to the matter. I present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height fro…
Solid particles with the composition of interstellar dust and power-law size distribution dn/da propto a^{-p} for a < a_max with a_{max} > 3 lambda and 3 < p < 4 will have submm opacity spectral index beta(lambda) = dln(kappa)/dln(nu) approx (p-3) beta_{ism}, where beta_{ism} approx 1.7 is the opacity spectral index of interstellar dust material in the Rayleigh limit. For the power-law index p approx 3.5 that characterizes interstellar dust, and that appears likely for particles growing by agglomeration in protoplanetary disks, grain growth to sizes a > 3 mm will result in beta(1 mm) < ~1. Gra…
We calculate the physical structure of protoplanetary disks by evaluating the gas density and temperature self-consistently and solving separately for the dust temperature. The effect of grain growth is taken into account by assuming a power-law size distribution and varying the maximum radius of grains a_max. In our fiducial model with a_max=10um, the gas is warmer than the dust in the surface layer of the disk, while the gas and dust have the same temperature in deeper layers. In the models with larger a_max, the gas temperature in the surface layer is lower than in the fiducial model becaus…
We analyze the stability of dust layer in protoplanetary disk to understand the effect of the relative motion between gas and dust. The previous analyses not including the effect of relative motion between gas and dust show that the shear-induced turbulence may prevent the dust grains from settling sufficiently to be gravitationally unstable. We determine the growth rate of Kelvin-Helmholtz instability in wide range of parameter space, and propose a possible path toward the planetesimal formation through the gravitational instability. We expect the density of dust layer becomes $ρ_\mathrm{d}/ρ…
We calculate the ionisation fraction in protostellar disk models using a number of different chemical reaction networks, including gas-phase and gas-grain reaction schemes. The disk models we consider are conventional alpha-disks, which include viscous heating and radiative cooling. The primary source of ionisation is assumed to be X-ray irradiation from the central star. We consider a number of gas-phase chemical networks. In general we find that the simple models predict higher fractional ionisation levels and more extensive active zones than the more complex models. When heavy metal atoms a…
Detailed models for the density and temperature profiles of gas and dust in protoplanetary disks are constructed by taking into account X-ray and ultraviolet (UV) irradiation from a central T Tauri star, as well as dust size growth and settling toward the disk midplane. The spatial and size distributions of dust grains in the disks are numerically computed by solving the coagulation equation for settling dust particles. The level populations and line emission of molecular hydrogen are calculated using the derived physical structure of the disks. X-ray irradiation is the dominant heating source…
We study magnetic field steepening due to ambipolar diffusion (Brandenburg & Zweibel 1994) in protoplanetary disk environments and draw the following conclusions. Current sheets are generated in magnetically active regions of the disk where the ionization fraction is high enough for the magnetorotational instability to operate. In late stages of solar nebula evolution, the surface density is expected to have lowered and dust grains to have gravitationally settled to the midplane. If the local dust-to-gas mass ratio near the midplane is increased above cosmic abundances by factors > 10^3, curre…
Turbulent coagulation in protoplanetary disks is known to operate on timescale far shorter than the lifetime of the disk. In the absence of mechanisms that replenish the small dust grain population, protoplanetary disks would rapidly lose their continuum opacity-bearing dust. This is inconsistent with infrared observations of disks around T Tauri stars and Herbig Ae/Be stars, which are usually optically thick at visual wavelengths and show signatures of small (a<~ 3um) grains. A plausible replenishing mechanism of small grains is collisional fragmentation or erosion of large dust aggregates, w…
Context: Sticking of colliding dust particles through van der Waals forces is the first stage in the grain growth process in protoplanetary disks, eventually leading to the formation of comets, asteroids and planets. A key aspect of the collisional evolution is the coupling between dust and gas motions, which depends on the internal structure (porosity) of aggregates. Aims: To quantify the importance of the internal structure on the collisional evolution of particles, and to create a new coagulation model to investigate the difference between porous and compact coagulation in the context of a …
In a disk around DM Tau, previous observation of 13CO (J=2-1 and 1-0 transitions) derived the 13CO gas temperature of \sim 13-20K, which is lower than the sublimation temperature of CO (20 K). We argue that the existence of such cold CO can be explained by a vertical mixing of disk material. As the gas is transported from a warm layer to a cold layer, CO is depleted onto dust grains with a timescale of \sim 10^3 yr. Because of the steep temperature gradient in the vertical direction, an observable amount of CO is still in the gas phase when the fluid parcel reaches the layer of \sim 13 K. Appa…
Aims: We investigate the behaviour of dust in protoplanetary disks under the action of gas drag in the presence of a planet. Our goal is twofold: to determine the spatial distribution of dust depending on grain size and planet mass, and therefore to provide a framework for interpretation of coming observations and future studies of planetesimal growth. Method: We numerically model the evolution of dust in a protoplanetary disk using a two-fluid (gas + dust) Smoothed Particle Hydrodynamics (SPH) code, which is non-self-gravitating and locally isothermal. The code follows the three dimensional d…
