Yoshitsugu Nakagawa

Molecular Hydrogen Emission from Protoplanetary Disks. II. Effects of X-Ray Irradiation and Dust Evolution

Detailed models for the density and temperature profiles of gas and dust in protoplanetary disks are constructed by taking into account X-ray and 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 are numerically computed by solving the coagulation equation for settling dust particles, with the result that the mass and total surface area of dust grains per unit volume of the gas in the disks are very small, except at the midplane. The H2 level populations and line emission are calculatedusingthederivedphysicalstructureofthedisks.X-rayirradiationisthedominantheatingsource ofthegas in the inner disk and in the surface layer, while the UV heating dominates otherwise. If the central star has strong X-ray and weak UV radiation, the H2 level populations are controlled by X-ray pumping, and the X-rayYinduced transition lines could be observable. If the UVirradiation is strong, the level populations are controlled by thermal collisions or UVpumping,depending onthe dustproperties. Asthedustparticlesevolveinthe disks,the gastemperatureatthe disk surface drops because the grain photoelectric heating becomes less efficient. This makes the level populations change fromLTEtonon-LTEdistributions,whichresultsinchangestothelineratios.Our resultssuggest thatdustevolutionin protoplanetary disks could be observable through the H2 line ratios. The emission lines are strong from disks irradiated by strong UV and X-rays and possessing small dust grains; such disks will be good targets in which to observe H2 emission. Subject headingg line: formation — molecular processes — planetary systems: protoplanetary disks — radiative transfer

A PLANETESIMAL ACCRETION ZONE IN A CIRCUMBINARY DISK

We investigate the conditions for planetesimal accretion in a circumbinary disk. Until recently, it had been believed that only single solar-type stars might harbor planetary systems. On the other hand, circumbinary disks have been detected by infrared or radio observation. Planets may be formed in such disks. Binary systems give stronger gravitational perturbation against planetesimals orbiting nearer to the binary. Therefore, the relative velocities between planetesimals will be larger and when they exceed the escape velocity it is impossible for the planetesimals to accumulate into planets. We performed long-term numerical integrations of binary and planetesimal orbital motions in the framework of the coplanar elliptic restricted three-body problem and have found the upper limit of the orbital radius inside of which the relative velocity between the planetesimals exceeds the escape velocity. One of our results is that planetesimal accretion cannot occur in a zone within 13 AU from the barycenter of the binary system when the binary semimajor axis is 1 AU, the binary eccentricity 0.1, the total mass m1 + m2 = 1 M☉, and the mass ratio m2/(m1 + m2) = 0.2. In regions farther out than 13 AU, planetesimals can accrete. We also derive analytic expressions of the eccentricity of a planetesimal pumped up by the gravitational perturbation of the binary and the inner boundary radius of the planetesimal accretion zone according to the secular perturbation theory.

DUST SIZE GROWTH AND SETTLING IN A PROTOPLANETARY DISK

We have studied dust evolution in a quiescent or turbulent protoplanetary disk by numerically solving a coagulation equation for settling dust particles, using the minimum mass solar nebula model. As a result, if we assume an ideally quiescent disk, the dust particles settle toward the disk midplane to form a gravitationally unstable layer within 2 × 103 to 4 × 104 yr at 1-30 AU, which is in good agreement with an analytic calculation by Nakagawa et al., although they did not take the particle size distribution into account explicitly. In an opposite extreme case of a globally turbulent disk, on the other hand, the dust particles fluctuate owing to turbulent motion of the gas and most particles become large enough to move inward very rapidly within 70 to 3 × 104 yr at 1-30 AU, depending on the strength of the turbulence. Our result suggests that global turbulent motion should cease for planetesimal formation to be possible in protoplanetary disks.

Effects of accretion flow on the chemical structure in the inner regions of protoplanetary disks

Aims. We study the dependence of the profiles of molecular abundances and line emission on the accretion flow in the hot (>100 K) inner region of protoplanetary disks. Methods. The gas-phase reactions initiated by evaporation of the ice mantle on dust grains are calculated along the accretion flow. We focus on methanol, a molecule that is formed predominantly by the evaporation of warm ice mantles, to demonstrate how its abundance profile and line emission depend on the accretion flow. Results. Our results indicate that some evaporated molecules retain high abundances only when the accretion velocity is sufficiently high, and that methanol could be useful as a diagnostic of the accretion flow by means of ALMA observations at the disk radius of <10 AU.

Cooling and Quasi-Static Contraction of the Primitive Solar Nebula After Gas Accretion

The evolution of the primitive solar nebula in the quasi-static contraction phase where the nebula cools down toward the thermal steady state is studied. The solar irradiation onto the nebula keeps the surface temperature constant, so that the convective ozone retreats from the surface as the nebula cools. Thus if thermal convection is the only source of turbulence, convection will quiet down in an early time of the cooling. Afterward, the nebula evolves toward an isothermal structure in a time scale of 1000 yr. The cooling rates in the vicinity of the midplate at 1 AU are 0.003 K/hr at T(c) = 1000 K and 3 x 10 to the -5th K/hr at T(c) = 300 K for the standard model. If some turbulence exists irrespective of convection, convection may continue for sufficiently strong turbulent heating. 39 refs.

Stability of a Planet in a Binary System: MACHO 97-BLG-41

An extrasolar planet was detected in a binary system by gravitational microlensing. This is considered to be the first one detected orbiting both components of a binary star system. The event is now known as MACHO 97-BLG-41. Whether such a planetary system can last on a large timescale is a major concern to celestial mechanics. We investigate the stability of the planetary orbits with the observed mass ratios of the three bodies by taking the binary and planetary eccentricities as parameters. The eccentricities could hardly be determined by gravitational microlensing but may be estimated by long-term numerical integrations of the binary and planetary orbital motions. We performed such long-term numerical integrations of the coplanar elliptic restricted three-body problem with various initial conditions in order to see what initial conditions produce stable planetary orbits during the integration for 106 binary periods (2.8 × 106 yr). The results of our numerical integrations permit us to estimate the upper limit of binary eccentricity, which ensures stable planetary orbital motion to be about 0.5 in the cases of circular initial orbits of the planet. In the cases of elliptic initial orbits of the planet, the planetary orbital motion is found to be less stable; hence, the upper limit of the binary eccentricity is estimated to be smaller than that in the cases of circular initial orbits of the planet. The upper limit of the initial planetary eccentricity is estimated to be about 0.4 for stable planetary orbital motion. The results of similar integrations for retrograde orbits indicate that the planetary retrograde orbits are more stable than the prograde ones.

Dust evolution in photoevaporating protoplanetary disks

We construct a model of the physical structure of photoevaporating protoplanetary disks, and numerically calculate the coagulation and settling/evaporating process of dust particles in the disks. Our result show that (sub)micron-sized-dust-particles could evaporate with the gas, which leads to dispersal of infrared excess radiation from the disks. Photoevaporation of protoplanetary disks induced by ultraviolet photons and/or X-rays from the central stars is known as one of possible mechanisms of gaseous disk dispersal. In addition, photoevaporating flow is expected to affect dust evolution that will lead to the planet formation in the disks, and observational properties of the disks. In this work we have made a detailed model of gas density, temperature, and velocity structure of one-dimensional, steady photoevaporating flow in protoplanetary disks. By using the obtained disk structure, we compare the gravitational and the gas friction forces which affect on a dust particle in the disks to estimate a critical dust radius. The result shows that (sub)micronsized-dust-particles could evaporate with the gas, instead of settling toward the disk midplane (Figure 1, left; Nomura & Inutsuka 2004). In addition, we calculate the dust evolution in the disks by numerically solving a coagulation equation for the dust particles (Nomura & Nakagawa 2006), taking into account the upward motion of the dust grains, which shows that (sub)micronsized-dust-particles disappear from the disks because they can move only upward with the flow as well as coagulate very quickly near the dense disk midplane. Finally, making use of the resulting spatial and size distributions of the dust particles, we calculate spectral energy distributions (SEDs) of dust continuum emission from the disks, which suggests that the photoevaporation process could help to reduce infrared excess radiation from the disks (Figure 1, right).

Molecular Hydrogen emission from protoplanetary disks: effects of X-ray irradiation and dust evolution

Detailed models for the density and temperature profiles of gas and dust in protoplanetary disks are constructed by taking into account X-ray and 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 are numerically computed by solving the coagulation equation for settling dust particles, with the result that the mass and total surface area of dust grains per unit volume of the gas in the disks are very small, except at the midplane. The H2 level populations and line emission are calculated using the derived physical structure of the disks. X-ray irradiation is the dominant heating source of the gas in the inner disk and in the surface layer, while the UV heating dominates otherwise. If the central star has strong X-ray and weak UV radiation, the H2 level populations are controlled by X-ray pumping, and the X-rayYinduced transition lines could be observable. If the UV irradiation is strong, the level populations are controlled by thermal collisions or UV pumping, depending on the dust properties. As the dust particles evolve in the disks, the gas temperature at the disk surface drops because the grain photoelectric heating becomes less efficient. This makes the level populations change from LTE to non-LTE distributions, which results in changes to the line ratios. Our results suggest that dust evolution in protoplanetary disks could be observable through the H2 line ratios. The emission lines are strong from disks irradiated by strong UV and X-rays and possessing small dust grains; such disks will be good targets in which to observe H2 emission. Subject headinggs: line: formation — molecular processes — planetary systems: protoplanetary disks — radiative transfer