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Investigation of the Physical Properties of Protoplanetary Disks Around T

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Investigation of the Physical Properties of Protoplanetary Disks Around T accepted for publication in Astrophysical Journal Investigation of the physical properties of protoplanetary disks around T Tauri stars by a one-arcsecond imaging survey: Evolution and diversity of the disks in their accretion stage1 Yoshimi Kitamura Institute of Space and Astronautical Science, Yoshinodai, Sagamihara, Kanagawa, 229-8510, Japan. [email protected] Munetake Momose Institute of Astrophysics and Planetary Sciences, Ibaraki University, Bunkyo 2-1-1, Mito, 310-8512, Japan. [email protected] Sozo Yokogawa, Ryohei Kawabe, and Motohide Tamura National Astronomical Observatory, Mitaka, Tokyo, 181-8588, Japan. [email protected], [email protected], [email protected] and Shigeru Ida Department of Earth and Planetary Science, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, 152-8551, Japan. [email protected] ABSTRACT We present the results of an imaging survey of protoplanetary disks around single T Tauri stars in Taurus. Thermal emission at 2 mm from dust in the disks has been imaged with a maximum spatial resolution of one arcsecond by using the Nobeyama Millimeter Array (NMA). Disk images have been successfully –2– obtained under almost uniform conditions for 13 T Tauri stars, two of which are thought to be embedded. We have derived the disk properties of outer radius, surface density distribution, mass, temperature distribution, and dust opacity coefficient, by analyzing both our images and the spectral energy distributions (SEDs) on the basis of two disk models: the usual power-law model and the standard model for viscous accretion disks. By examining correlations between the disk properties and disk clocks, we have found radial expansion of the disks with decreasing Hα line luminosity, a measure of disk evolution. This expansion can be interpreted as radial expansion of accretion disks due to outward transport of angular momentum with evolution. The increasing rate of the disk radius suggests that the viscosity has weak dependence on radius r and α ∼ 0.01 for the α parameterization of the viscosity. The power-law index p of the surface −p density distribution (Σ(r)=Σ0(r/r0) ) is 0 - 1 in most cases, which is smaller than 1.5 adopted in the Hayashi model for the origin of our solar system, while the surface density at 100 AU is 0.1 - 10 g cm−2, which is consistent with the extrapolated value in the Hayashi model. These facts may imply that in the disks of our sample it is very difficult to make planets like ours without redistribution of solids, if such low values for p hold even in the innermost regions. Subject headings: circumstellar matter—stars: pre-main-sequence 1. Introduction It has been revealed in last 15 years that low-mass pre-main-sequence stars (T Tauri stars) are commonly accompanied by circumstellar disks. Their physical properties have been derived mainly from analysis of spectral energy distributions (SEDs) under the assumptions that the disk is axisymmetric and its temperature and surface density distributions (T (r)and Σ(r)) have power-law dependence on radius r with inner and outer cutoffs (e.g., Beckwith et al. 1990). The analysis has shown that the disks contain gas and dust of (0.1 − 0.001)M within several hundreds AU in radius and the power-law index of T (r), q,is0.5−0.75. Since such characteristics of the disks are reminiscent of the “primordial solar nebula” assumed in standard theories of the formation of the solar system (e.g., Hayashi, Nakazawa, & Nakagawa 1Based on the long-term open use observations made at the Nobeyama Radio Observatory, which is a branch of the National Astronomical Observatory, an interuniversity research institute operated by the Ministry of Education, Science, Sports, Culture, and Technology. –3– 1985; Safronov & Ruzmaikina 1985), the disks are believed to be precursors of planetary systems, or “protoplanetary” disks (e.g., Beckwith & Sargent 1996). Dust particles in the disks emit optically thin thermal radiation, which traces the disk mass well at millimeter and submillimeter wavelengths. Gas molecules in the disks also emit thermal radiation, which provides us information about the disk kinematics. Therefore high-resolution imaging with interferometers at these wavelengths have played a crucial role in revealing various aspects of disk evolution in the course of star formation. Survey obser- vations of low-mass young stellar objects (YSOs) showed that the dust continuum emission around protostar candidates is more extended than that around T Tauri stars (Ohashi et al. 1991, 1996; Looney, Mundy, & Welch 2000), suggesting disks as well as central stars grow by accretion of matter caused by dynamical collapse of circumstellar envelopes in the protostar stage. Detailed velocity fields in several protostellar envelopes were obtained by aperture synthesis observations with molecular lines, showing that the typical mass accretion rate −6 −1 onto the central star/disk system is ∼ 5 × 10 M yr (e.g., Hayashi, Ohashi, & Miyama 1993; Ohashi et al. 1997; Momose et al. 1998). The timescale for disk persistence in later stages of star formation, on the other hand, has been investigated by systematic searches for dust and gas emission toward evolved T Tauri stars. For example, Duvert et al. (2000) made survey observations of T Tauri stars with a wide range of ages and found that all objects with no infrared excess do not have disks detectable in the dust continuum or molecular line emission at millimeter wavelengths. These results may imply that the entire disks disappear on almost the same timescale as that for disappearing of the innermost regions emitting infrared radiation (see Strom et al. 1989; Skrutskie et al. 1990). In spite of the above progress, understanding of the internal structure and evolution of the disks in the early T Tauri stage is still limited. Although the total mass and temperature distribution of the disks are derived from the analysis of their SEDs, the outer radius and the surface density distribution cannot be evaluated by this method (see Beckwith et al. 1990). This is easily understood because the SED data were obtained by flux measurements with large beams which provide no information about the spatial distribution of the emission. On the other hand, it has been revealed that, in the T Tauri stage, the mass accretion rate from the disk to the central star, which can be estimated from the amount of excess emission at ultraviolet and near-infrared wavelengths, becomes lower as the stellar age increases (Calvet, Hartmann, & Strom 2000). This trend is consistent with a possible evolutionary sequence from classical T Tauri stars (CTTSs) to weak-line T Tauri stars (WTTSs) (e.g., Strom et al. 1989) because these two categories are based on the equivalent width of the Hα emission line that must be tightly connected to the outflow activity, which is originally driven by the mass accretion activity (e.g., Edwards, Ray, & Mundt 1993). Owing to the lack of systematic studies of disk internal structures, however, it is still unclear how this evolutionary trend is –4– related to the internal structure of the disks themselves. Imaging at higher angular resolutions is crucial for studying the internal structure of the disks. One of the most important disk properties is the surface density distribution that dominates planet formation processes. High resolution images of several disks have been obtained in “silhouette” or in scattered light at optical and near infrared wavelengths, pro- viding us fairly firm information about the spatial extent of disk matter (e.g., McCaughrean & O’Dell 1996; McCaughrean et al. 1998; Padgett et al. 1999). In order to evaluate their surface density distributions as well as their outer radii, however, observations of thermal radiation at millimeter and submillimeter wavelengths are required. Detailed observations of some circumstellar or circumbinary disks were made at these wavelengths (e.g., Kawabe et al. 1993; Saito et al. 1995; Mundy et al. 1996; Guilloteau, Dutrey, & Simon 1999). Mundy et al. (1996) estimated, for the first time, the surface density distribution in the disk around HL Tau. Despite these case studies, a survey of a well-coordinated sample is required to reveal the evolutionary trend or diversity of the disk characteristics. We have carried out an imaging survey of protoplanetary disks associated with single T Tauri stars in the Taurus molecular cloud in dust continuum emission at 2 mm with the Nobeyama Millimeter Array (NMA). Physical properties of the disks, including the outer radius and the surface density distribution, have systematically been derived from the combination of SED analysis and image-based model fitting. Our survey is the first systematic study of the surface density distribution with the outer radius based on high- resolution images taken under almost uniform conditions. The images obtained by small synthesized beams (1 − 2), which can resolve the spatial extent of the disks, enable us to successfully estimate their internal structure. A sample of more than 10 sources allows us to extract some possible evolutionary trend and diversity of the disks, which would contribute to the understanding of diverse planetary systems. The outline of this paper is as follows. The sample selection is described in §2 and the details of the observations are in §3. Our observational results are presented in §4. In §5, our analysis to derive the disk physical parameters is described and their evolutionary trend or diversity is discussed. 2. Sample We selected about 20 T Tauri stars by the following two criteria: 1) The star is known to be single and is located in the Taurus molecular cloud (d = 140 pc). We examined the multiplicity of the star on the basis of the catalogues of multiple T Tauri stars by Leinert et al. (1993), Ghez, Neugebauer, & Matthews (1993), Kohler & Leinert (1998), Richichi et al.
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