Taku Takeuchi

Three-Dimensional Interaction between a Planet and an Isothermal Gaseous Disk. I. Corotation and Lindblad Torques and Planet Migration

Gravitational interaction between a planet and a three-dimensional isothermal gaseous disk is studied. In the present paper we mainly examine the torque on a planet and the resultant radial migration of the planet. A planet excites density waves at Lindblad and corotation resonances and experiences a negative torque by the density waves, which causes a rapid inward migration of the planet during its formation in a protoplanetary disk. We formulate the linear wave excitation in three-dimensional isothermal disks and calculate the torques of Lindblad resonances and corotation resonances. For corotation resonances, a general torque formula is newly derived, which is also applicable to two-dimensional disks. The new formula succeeds in reproducing numerical results on the corotation torques, which do not agree with the previously well-known formula. The net torque of the inner and the outer Lindblad resonances (i.e., the differential Lindblad torque) is caused by asymmetry such as the radial pressure gradient and the scale height variation. In three-dimensional disks, the differential Lindblad torques are generally smaller than those in two-dimensional disks. Especially, the effect of a pressure gradient becomes weak. The scale height variation, which is a purely three-dimensional effect, makes the differential Lindblad torque decrease. As a result, the migration time of a planet is obtained as of the order of 106 yr for an Earth-size planet at 5 AU for a typical disk model, which is longer than the result of two-dimensional calculation by the factor of 2 or 3. The reflected waves from disk edges, which are neglected in the torque calculation, can further weaken the disk-planet interaction.

DUST MIGRATION AND MORPHOLOGY IN OPTICALLY THIN CIRCUMSTELLAR GAS DISKS

We analyze the dynamics of gas-dust coupling in the presence of stellar radiation pressure in circumstellar disks, which are in a transitional stage between the gas-dominated, optically thick, primordial nebulae, and the dust-dominated, optically thin Vega-type disks. Dust grains undergo radial migration, either leaving the disk owing to a strong radiation pressure or seeking a stable equilibrium orbit in corotation with gas. In our models of A-type stars surrounded by a total gas mass from a fraction to dozens of Earth masses, the outward migration speed of dust is comparable with the gas sound speed. Equilibrium orbits are circular, with exception of those significantly affected by radiation pressure, which can be strongly elliptic with apocenters extending beyond the bulk of the gas disk. The migration of dust gives rise to radial fractionation of dust and creates a variety of possible observed disk morphologies, which we compute by considering the equilibrium between the dust production and the dust-dust collisions removing particles from their equilibrium orbits. Large grains (typically 200 μm) are distributed throughout most of the gas disk. Smaller grains (in the range of 10-200 μm) concentrate in a prominent ring structure in the outer region of the gas disk (presumably at radius ~100 AU), where gas density is rapidly declining with radius. The width and density, as well as density contrast of the dust ring with respect to the inner dust disk, depend on the distribution of gas and the mechanical strength of the particles. Our results open the prospect for deducing the distribution of gas in circumstellar disks by observing their dust. We have qualitatively compared our models with two observed transitional disks around HR 4796A and HD 141569A. Dust migration can result in observation of a ring or a bimodal radial dust distribution, possibly very similar to the ones produced by gap-opening planets embedded in the disk, or shepherding it from inside or outside. We conclude that a convincing planet detection via dust imaging should include specific nonaxisymmetric structure (spiral waves, streamers, resonant arcs) following from the dynamical simulations of perturbed disks.

Spiral Structure in the Circumstellar Disk around AB Aurigae

We present a near-infrared image of the Herbig Ae star AB Aur obtained with the Coronagraphic Imager with Adaptive Optics mounted on the Subaru Telescope. The image shows a circumstellar emission extending out to a radius of r = 580 AU, with a double spiral structure detected at r = 200-450 AU. The surface brightness decreases as r-3.0±0.1, steeper than the radial profile of the optical emission possibly affected by the scattered light from the envelope surrounding AB Aur. This result, together with the size of the infrared emission similar to that of the 13CO (J = 1-0) disk, suggests that the spiral structure is indeed associated with the circumstellar disk but is not part of the extended envelope. We identified four major spiral arms, which are trailing if the brighter southeastern part of the disk is the near side. The weak gravitational instability, maintained for millions of years by continuous mass supply from the envelope, might explain the presence of the spiral structure at the relatively late phase of the pre-main-sequence period.

Local Enhancement of the Surface Density in the Protoplanetary Ring Surrounding HD 142527

We report ALMA observations of dust continuum, 13CO J=3--2, and C18O J=3--2 line emission toward a gapped protoplanetary disk around HD 142527. The outer horseshoe-shaped disk shows the strong azimuthal asymmetry in dust continuum with the contrast of about 30 at 336 GHz between the northern peak and the southwestern minimum. In addition, the maximum brightness temperature of 24 K at its northern area is exceptionally high at 160 AU from a star. To evaluate the surface density in this region, the grain temperature needs to be constrained and was estimated from the optically thick 13CO J=3--2 emission. The lower limit of the peak surface density was then calculated to be 28 g cm-2 by assuming a canonical gas-to-dust mass ratio of 100. This finding implies that the region is locally too massive to withstand self-gravity since Toomres Q <~1--2, and thus, it may collapse into a gaseous protoplanet. Another possibility is that the gas mass is low enough to be gravitationally stable and only dust grains are accumulated. In this case, lower gas-to-dust ratio by at least 1 order of magnitude is required, implying possible formation of a rocky planetary core.

Gravitational Interaction between a Protoplanet and a Protoplanetary Disk. I. Local Three-Dimensional Simulations

The gravitational interaction between a protoplanet and an isothermal gaseous disk is investigated through three-dimensional hydrodynamical simulations with the shearing sheet model. The torque exerted on the disk is evaluated and compared with previous estimates by the linear theory. It is found that a protoplanet mainly excites waves without vertical motion. Thus, the motion of the gas in a disk with thickness is similar to that in an infinitesimally thin disk. The angular momentum transfer is also dominated by waves without vertical motion, and the torque has a similar value to that in an infinitesimally thin disk, except for the correction factor 0.43 owing to the vertical averaging of the gravitational potential of the protoplanet. If the mass of the protoplanet is small enough, the torque increases proportionally with the square of the mass, as is predicted by the linear theory. However, for a large protoplanet whose Hill radius is larger than about the disk scale height, a nonlinear effect reduces the torque from the value proportional to the square of the mass. The torque reduction due to the nonlinearity is less significant for a disk with thickness than for an infinitesimally thin disk and is not effective for a small protoplanet with mass less than 10 times the Earth mass at 1 AU. This result suggests that during the formation of terrestrial planets and the cores of giant planets, the torque continues to increase as the protoplanets grow. The reduction in the torque due to the thickness of the disk and the nonlinearity is not large enough to solve the problem that the migration of protoplanets is too fast. Before protoplanets acquire the masses needed to suppress torque by the nonlinearity, they would experience large migration and some protoplanets would fall onto the central star in the lifetime of the gas in the protoplanetary disks.

Attenuation of Millimeter Emission from Circumstellar Disks Induced by the Rapid Dust Accretion

From millimeter observations of classical T Tauri stars, it is suggested that dust grains in circumstellar disks have grown to millimeter sizes or larger. However, gas drag on such large grains induces rapid accretion of the dust. We examine the evolution of dust disks composed of millimeter-sized grains and show that rapid accretion of the dust disk causes attenuation of millimeter continuum emission. If a dust disk is composed mainly of grains of 1 cm to 1 m, its millimeter emission goes off within 106 yr. Hence, grains in this size range cannot be the main population of the dust. Considering our results together with grain growth suggested by the millimeter continuum observations, we expect that the millimeter continuum emission of disks comes mainly from grains in a narrow size range of 1 mm to 1 cm. This suggests either that growth of millimeter-sized grains to centimeter size takes more than 106 yr or that millimeter-sized grains are continuously replenished. In the former case, planet formation is probably difficult, especially in the outer disks. In the latter case, reservoirs of millimeter grains are possibly large (10 m) bodies, which can reside in the disk more than 106 yr. Constraints on the grain growth timescale are discussed for the above two cases.

ELECTROSTATIC BARRIER AGAINST DUST GROWTH IN PROTOPLANETARY DISKS. I. CLASSIFYING THE EVOLUTION OF SIZE DISTRIBUTION

Collisional growth of submicron-sized dust grains into macroscopic aggregates is the first step of planet formation in protoplanetary disks. These grains are expected to carry nonzero negative charges in the weakly ionized disks, but its effect on their collisional growth has not been fully understood so far. In this paper, we investigate how the charging affects the evolution of the dust size distribution properly taking into account the charging mechanism in a weakly ionized gas as well as porosity evolution through low-energy collisions. To clarify the role of the size distribution, we divide our analysis into two steps. First, we analyze the collisional growth of charged aggregates assuming a monodisperse (i.e., narrow) size distribution. We show that the monodisperse growth stalls due to the electrostatic repulsion when a certain condition is met, as was already expected in our previous work. Second, we numerically simulate dust coagulation using Smoluchowskis method to see how the outcome changes when the size distribution is allowed to freely evolve. We find that, under certain conditions, the dust undergoes bimodal growth where only a limited number of aggregates continue to grow, carrying a major part of the dust mass in the system. This occurs because remaining small aggregates efficiently sweep up free electrons to prevent the larger aggregates from being strongly charged. We obtain a set of simple criteria that allows us to predict how the size distribution evolves for a given condition. In Paper II, we apply these criteria to dust growth in protoplanetary disks.

Radial transport of large-scale magnetic fields in accretion disks. I. Steady solutions and an upper limit on the vertical field strength

Large-scale magnetic fields are key ingredients of magnetically driven disk accretion. We study how large-scale poloidal fields evolve in accretion disks, with the primary aim of quantifying the viability of magnetic accretion mechanisms in protoplanetary disks. We employ a kinematic mean-field model for poloidal field transport and focus on steady states where inward advection of a field balances with outward diffusion due to effective resistivities. We analytically derive the steady-state radial distribution of poloidal fields in highly conducting accretion disks. The analytic solution reveals an upper limit on the strength of large-scale vertical fields attainable in steady states. Any excess poloidal field will diffuse away within a finite time, and we demonstrate this with time-dependent numerical calculations of the mean-field equations. We apply this upper limit to large-scale vertical fields threading protoplanetary disks. We find that the maximum attainable strength is about 0.1 G at 1 AU, and about 1 mG at 10 AU from the central star. When combined with recent magnetic accretion models, the maximum field strength translates into the maximum steady-state accretion rate of ~10–7 M ☉ yr–1, in agreement with observations. We also find that the maximum field strength is ~1 kG at the surface of the central star provided that the disk extends down to the stellar surface. This implies that any excess stellar poloidal field of strength kG can be transported to the surrounding disk. This might in part resolve the magnetic flux problem in star formation.

MASS ESTIMATES OF A GIANT PLANET IN A PROTOPLANETARY DISK FROM THE GAP STRUCTURES

A giant planet embedded in a protoplanetary disk forms a gap. An analytic relationship among the gap depth, planet mass

ON THE INTERACTION BETWEEN A PROTOPLANETARY DISK AND A PLANET IN AN ECCENTRIC ORBIT: APPLICATION OF DYNAMICAL FRICTION

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