Yoshimi Kitamura. Institute of Space and Astronautical Science, Yoshinodai, Sagamihara, Kanagawa, , Japan.

Transcription

1 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 stage 1 Yoshimi Kitamura Institute of Space and Astronautical Science, Yoshinodai, Sagamihara, Kanagawa, , Japan. kitamura@pub.isas.ac.jp Munetake Momose Institute of Astrophysics and Planetary Sciences, Ibaraki University, Bunkyo 2-1-1, Mito, , Japan. momose@mito.ipc.ibaraki.ac.jp Sozo Yokogawa, Ryohei Kawabe, and Motohide Tamura National Astronomical Observatory, Mitaka, Tokyo, , Japan. yokogawa@nro.nao.ac.jp, kawabe@nro.nao.ac.jp, tamuramt@cc.nao.ac.jp and Shigeru Ida Department of Earth and Planetary Science, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, , Japan. ida@geo.titech.ac.jp 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 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.1 for the α parameterization of the viscosity. The power-law index p of the surface density distribution (Σ(r) =Σ (r/r ) p ) is - 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 1 AU is.1-1 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. 199). The analysis has shown that the disks contain gas and dust of (.1.1)M within several hundreds AU in radius and the power-law index of T (r), q, is 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 1 Based 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 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 observations 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 2), 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 onto the central star/disk system is M yr 1 (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. (2) 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. 199). 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. 199). 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 2). 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 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, providing 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 highresolution 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 1 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 2 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 = 14 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. (1994), Simon et al. (1992), Reipurth & Zinnecker (1993), and Mathieu (1994). 2) The

5 5 expected flux density of 2 mm dust continuum emission is larger than 2 mjy. The 2 mm flux density of each object is estimated from the surveys of 1.3 mm continuum emission (Beckwith et al. 199; Osterloh & Beckwith 1995) and the measurements of the β index (Beckwith & Sargent 1991; Moriarty-Schieven et al. 1994), where we assume β = 1 for unknown cases. If the total flux density from a disk exceeds 2 mjy, simple calculations show that imaging of the disk with a radius of 1 AU becomes successful by achieving a rms noise level of 2 mjy beam 1. Since such a low noise level requires one or two day observations under good weather conditions for each source, we were able to complete the disk imaging for more than 1 objects in three winter seasons. In our survey we have succeeded in imaging the disks for 13 objects among the T Tauri stars selected prior to the survey. Table 1 lists the 13 objects. We mainly observed CTTSs and 8 objects are typical CTTSs. Haro 6-5B and HL Tau are now thought to be transient sources from protostars to CTTSs on the basis of the HST images, which show the presence of envelopes as reflection nebulae (Stapelfeldt et al. 1995; Krist et al. 1998). The remaining three sources, IQ Tau, DN Tau, and LkCa 15 are relatively older and are likely to be on the borderline between CTTSs and WTTSs, because these objects have equivalent widths of the Hα emission line as narrow as 1 Å (see Table 2). 3. Observations Observations were carried out with the NMA, which consists of six 1 m antennas, over the three winter seasons of 1998 December to 1999 February, 1999 December to 2 February, and 2 November to 21 February. We used all the array configurations, D, C, and AB, and their projected baseline lengths ranged from (5-4), (1-8), and (25-175) kλ, respectively. Dust continuum emission at 2 mm from the disks was detected with SIS receivers operated in double sideband (DSB) mode. System noise temperatures during the observations were typically 2 K in DSB at the zenith. For the back end, the digital spectral Ultra Wide Band Correlator, UWBC (Okumura et al. 2) was employed. Visibility data of the continuum emission in both the lower (135±.512 GHz) and upper (147±.512 GHz) sidebands were obtained simultaneously with the phase-switching technique. To obtain a higher signal-to-noise ratio (S/N), the data of both the sidebands were equally added in a final image with center frequency 141 GHz. The field center was set on the position of each object and the size of the primary beam (i.e., the field of view) was about 46 FWHM. In the lowest-resolution D configuration, we used the source positions previously reported (e.g., Strom et al. 1989). In the higherresolution AB and C configurations, the peak positions in the D configuration were used as

6 6 the center positions. Table 1 shows peak positions in the 2 mm continuum images obtained with the AB or AB+C configurations. The 13 objects in Table 1 were observed in the following way. First, we observed all the sources with the compact D configuration to detect the disk emission as point-like sources. In the D configuration, the size of the synthesized beam was 5 and the array was insensitive to structures extending more than 2 ( 28 AU) FWHM (see Appendix in Wilner & Welch 1994). We can accurately measure the total flux density from a disk in this compact configuration. In contrast, the estimation of the total flux density over a resolved disk in a higher-resolution image is much likely to be affected by noise, because the determination of the disk periphery highly depends on the noise. Therefore, we used the disk total flux densities measured with the D configuration to check the depth of integration for successive higher-resolution images with the AB and AB+C configurations: we tried to integrate the disk image as deeply as possible in order that the total flux density over the entire disk area may reproduce the total flux density with the D configuration. In the highest-resolution AB configuration, the size of the synthesized beam was 1 and the array was insensitive to structures extending more than 4 ( 56 AU) FWHM. The beam shape was nearly circular, and thus the distortion of the disk image due to the beam pattern was minimized. In the AB+C configurations, the size of the synthesized beam was 2 and structures extending more than 1 ( 14 AU) FWHM were probably resolved out. The response across the observed passband for each sideband was determined from 3-4 minute observations of 3C454.3 or 3C273. A gain calibrator, , , or was observed every 3 minutes in the D configuration. In the AB and C configurations, the gain calibrators were observed as frequently as possible (every 8-1 minutes) to minimize phase error in resultant images. The flux densities at 2 mm of , , and were derived to be ( ) Jy, ( ) Jy, and ( ) Jy, respectively, by comparison with Uranus or Neptune (Griffin & Orton 1993). The overall uncertainty in the flux calibration was about 1%. After the calibrations, we made final images only from data taken under good weather conditions. Using the AIPS package developed at the NRAO, we CLEANed the continuum maps by natural weighting with no taper in the UV plane. The rms noise levels were (2-7) mjy beam 1 with 5 beam in the D configuration, about 2 mjy beam 1 with 1 beam in the AB configuration, and about 2 mjy beam 1 with 2 beam in the AB+C configurations. Positional accuracy was dominated by S/N and absolute positional errors were less than.3. Since source sizes were much smaller than the field of view, the primary beam attenuation was negligible.

7 7 4. Results 4.1. Total flux densities with different array configurations Total flux densities of the continuum emission in the maps obtained with the different array configurations are shown in Table 1. The spatial extent of each continuum emission with the D configuration is almost the same as the synthesized beam size ( 5 ), indicating that most emission originates from the region of r<35 AU from the central star and that the contribution of extended components such as an envelope is negligible. Detailed analyses of the SEDs of some T Tauri stars have revealed that continuum flux densities at frequencies higher than 1 GHz are attributed solely to dust thermal radiation, though the contribution of free-free emission from ionized gas should be taken into account at lower frequencies (e.g., Mundy et al. 1996; Wilner, Ho, & Rodriguez 1996). We therefore consider all the detected emission is from dust particles in circumstellar disks in the following. The spatial extent of the emission in the maps constructed from the data with the sparse configurations (AB and C) is more extended than the beamsize (1 2 ): detailed descriptions of the spatial distributions are presented in 4.2. Figure 1 shows a comparison of the detected total flux densities in the compact (D) and sparse (AB and AB+C) configurations. In the case of 1 sources, the total flux density detected by the D configuration, F ν (D), agrees with that by the AB configuration, F ν (AB), within uncertainties, suggesting all the disk emission is successfully detected and mapped with 1 beam. In the case of the other three sources (AA Tau, IQ Tau, and LkCa 15), F ν (AB) is only (4 6) % of F ν (D). This is due to lower sensitivity to surface brightness and missing more extended components in the AB configuration. The total flux densities by the D configuration for these three sources are comparable to that for DM Tau or DN Tau, which shows F ν (D) = F ν (AB), suggesting that the disks around the three sources have larger radii, or lower surface brightness. Since our purpose is to reveal the whole disk structure, it is essential to recover F ν (D) as much as possible even when we try to obtain a higher-resolution image. We therefore add the data with the C configuration to improve the sensitivity to low-brightness and more extended components of the emission. The resultant flux density for the three sources, F ν (AB+C), becomes greater than 7 % of F ν (D) (see Table 1 and Figure 1). Although the sensitivity of the present observations is still insufficient to recover all the emission from the circumstellar disks around IQ Tau and LkCa 15, we use in our analysis the images constructed from the data with the AB+C configurations for these sources.

8 Disk imaging and comparison with previous results The high-resolution images of the disks are presented in Figure 2: the images obtained by the AB configuration for the ten objects whose F ν (AB) agrees with F ν (D), and those by the AB+C configurations for the other three sources (AA Tau, IQ Tau, and LkCa 15). The spatial extent of each continuum emission is more extended than the synthesized beam size, indicating that all the disks are spatially resolved. The continuum emission in Figure 2 clearly exhibits a source-to-source difference in the spatial extent or the contour spacing, suggesting there are varieties of disk characteristics such as the outer radius or the surface density distribution. Table 3 shows beam-deconvolved Gaussian sizes of the emission, which were derived from Gaussian fitting in regions where the intensity is stronger than half the peak intensity, giving us a rough estimate of the spatial extent of the disks. The synthesized beam sizes and estimated seeing sizes, which are described in detail in 4.3, are also listed in Table 3. The nearly circular synthesized beams and the fairly small seeing sizes in our imaging allow us to accurately derive disk physical parameters such as the outer radius and the surface density distribution (see 5). We compare our imaging results with previous ones for the nine sources described below, whose disk images were independently taken at other frequencies, to check the quality and reliability of our results. For our results we mainly use the beam-deconvolved Gaussian sizes of the disks traced by the dust continuum emission (i.e., major and minor axes and position angles), listed in Table 3. In some sources we use the radius and inclination angle of the disk calculated from the beam-deconvolved size by assuming a geometrically thin disk. If only line data are reported in the previous studies, we consider mainly the inclination and position angles. This is because the radius of a disk traced by line emission tends to be larger than that of the disk traced by continuum emission owing to large optical depths (τ >1) of the line emission. Furthermore, the disk mass from the line observations does not necessarily agree with that from the continuum observations (see Table 4 for our sources), because the disk mass from the line observations is likely to be underestimated owing to depletion of the molecular species used to trace the disk mass such as CO (Guilloteau & Dutrey 1994; Dutrey, Guilloteau, & Guelin 1997; Aikawa et al. 1996), and because the line and continuum emission often traces different regions Haro 6-5B The source, a CTTS in the Herbig-Bell Catalogue (HBC; Herbig & Bell 1988), was recently imaged with the HST at visible and near-infrared wavelengths, and an envelope and a disk were revealed as a reflection nebula and a dark lane, respectively (Krist et al. 1998;

9 9 Padgett et al. 1999). The central star is found to be obscured by the dark lane, suggesting that this source is an embedded source, i.e., a protostar candidate. The spatial extent of the dust emission in Figure 2 agrees well with that of the reflection nebula with the dark lane, as already reported by Yokogawa et al. (21). The non-axisymmetric component extended to the south-west seen in Figure 2 would be a part of the envelope around the star HL Tau This source was also classified as a CTTS in the HBC, but is now thought to be a protostar candidate. An infalling envelope around the source was found by Hayashi et al. (1993) with the NMA, and HST observations demonstrated that the source is really embedded in circumstellar matter (Stapelfeldt et al. 1995; Close et al. 1997). Furthermore, a compact dust disk with a radius of 7 AU was imaged in 2.7 mm dust continuum emission by Mundy et al. (1996) with the BIMA array. The beam-deconvolved Gaussian size of the disk was (1. ±.2) (.5 ±.2) at PA = 125 ± 1. On the other hand, our 2 mm image in Figure 2 clearly shows the centrally peaked dust disk with a weak ridge-like structure extended to the north, probably a part of the infalling envelope. The Gaussian size of the dust disk imaged at 2 mm is (1.4 ±.3) (.6 ±.4) at PA = 144 ± 2 and agrees with that at 2.7 mm within uncertainties. In addition, our peak position of the 2 mm image agrees with the position of the 3.6 cm continuum source observed by Rodriguez et al. (1994) with the VLA CY Tau This source is a CTTS in the HBC and a rotating disk was imaged in CO J = 2 1 with the IRAM interferometer (Simon, Dutrey, & Guilloteau 21). The radius of the gas disk was derived to be (27 ± 1) AU on the basis of a power-law disk model. The inclination and position angles of the disk were estimated to be 47 ± 8 and 124 ± 7, respectively, from the 1.3 mm continuum data. In our 2 mm observations, the radius, inclination angle and position angle of the dust disk are (63 ± 7) AU, 57 ± 8, and 68 ± 8, respectively. Both the inclination angles show agreement, while our position angle differs from PA at 1.3 mm by 56. In the CO channel maps, however, one can see an elongated feature along the direction at our PA.

10 RY Tau Koerner & Sargent (1995) detected the CO J =2 1 emission toward the source with the OVRO millimeter interferometer. Although their S/N was not high, the profile of the CO emission seems to have double peaks suggesting a rotating disk. The radius, inclination angle, and position angle of the gas disk were estimated to be 11 AU, 25, and 48 ± 5, respectively, by Gaussian fitting. They also derived the disk mass of M from the line data and noted the mass is much smaller than that derived from continuum observations. From our 2 mm observations, the radius, inclination angle, and position angle of the dust disk are estimated to be (51 ± 4) AU, 59 ± 7,and27 ± 7, respectively. Furthermore, we estimate the disk mass to be M from our model fitting (see 5). The peak position of the 2 mm continuum emission agrees with that of the CO emission, while the inclination and position angles at 2 mm differ from those at 1.3 mm. The disagreement might be due to a difference between the gas and dust distributions DL Tau A rotating disk was imaged in CO J = 2 1 with millimeter interferometers. Koerner & Sargent (1995) found the disk with a radius of 25 AU with the OVRO array, and recently, Simon et al. (21) revealed the more detailed velocity structure of the disk with the IRAM array. The radius of the gas disk was estimated to be (25-52) AU, and the inclination and position angles from the line and continuum observations were and 44-84, respectively. The disk mass was derived to be M from the line observations, which is much smaller than the mass from continuum observations (Koerner & Sargent 1995). We have obtained from the 2 mm imaging that the radius, inclination angle, position angle, and mass of the dust disk are (8 ± 4) AU, 47 ± 4,52 ± 6,and5 1 2 M, respectively. Our inclination and position angles agree with the CO results, and are also consistent with the inclination angle of 49 ± 3 and the position angle of 44 ± 3 derived from the IRAM continuum observations DM Tau Double-peaked profiles of 12 CO and 13 CO emission were first detected with the NRO 45 m and IRAM 3 m telescopes and the detection strongly suggested the presence of a rotating disk around the source (Handa et al. 1995; Guilloteau & Dutrey 1994). Subsequently, the disk was imaged with the NMA and the IRAM interferometer, and Keplerian rotation was

11 11 revealed (Saito et al. 1995; Guilloteau & Dutrey 1998). Furthermore, more detailed studies of disk properties were made with the IRAM interferometer (Dutrey et al. 1997; Simon et al. 21). The radius of the gas disk was estimated to be (8 ± 5) AU on the basis of a power-law disk model, and its inclination and position angles were and , respectively, from both the line and continuum data. The disk mass was also derived to be (.2 -.2) M. Our 2 mm continuum observations show that the radius, inclination angle, position angle, and mass of the dust disk are (172 ± 12) AU, 68 ± 4,134 ± 4,and (.1 -.2) M, respectively. The inclination and position angles differ from the IRAM results owing to the presence of a new component elongated in the south-east direction in Figure 2, which was not detected by the IRAM interferometer. Since the component was seen at independent observing runs, it would suggest some non-axisymmetric distribution of the disk matter DO Tau Koerner & Sargent (1995) found a disk with a radius of 35 AU around the source in CO J =2 1 with the OVRO interferometer. The velocity structure of the disk, however, can not be described simply by Keplerian rotation, and outflow and infall motions seem to be required. Although their S/N was not high, the radius, inclination angle, position angle, and mass of the gas disk were estimated to be 35 AU, 45, 16 ± 5,and1 1 4 M, respectively. Subsequently, Koerner, Chandler, & Sargent (1995) obtained a.6 resolution image of 7 mm continuum emission from the disk with the VLA, and accurately estimated the disk mass of M, which is much larger than the above mass derived from the line data and is consistent with our estimated mass described below. From our map in Figure 2, the radius, inclination angle, position angle, and mass of the dust disk are estimated to be (71 ± 3) AU, 38 ± 5,67 ± 9,and.4M, respectively. Our inclination angle is roughly consistent with the previous value. Our position angle, however, is significantly different from the previous value of 16 : this fact means that the elongation of the dust disk in Figure 2 is parallel to the optical jet. Since it is not likely that the dust continuum emission traces the jet, there seems to exist misalignment between the disk and the jet as in the DG Tau case (Kitamura, Kawabe, & Saito 1996; Tamura et al. 1999). Note that the elongation at the 1.5σ level shown in Figure 2 seems to be vertical to the jet. This extended weak component does not seem to be an outer part of the disk and might be a part of an envelope remaining around the source.

12 GM Aur A Keplerian disk was found around the source in 13 CO J =2 1 by Koerner, Sargent, & Beckwith (1993) with the OVRO interferometer. Furthermore, higher-resolution 12 CO J = 2 1 observations were made with the IRAM interferometer (Dutrey et al. 1998; Simon et al. 21) and these studies revealed the detailed properties of the disk. The beamdeconvolved Gaussian sizes of the dust disk were (1.7 ±.5) (.63 ±.5) with PA = 57 ± 5 at 1.3 mm and (1.25 ±.2) (.65 ±.17) with PA = 58 ± 11 at 2.7 mm. The disk mass was derived to be.3 M from the 1.3 mm and 2.7 mm data. On the other hand, the beam-deconvolved Gaussian size of the 2 mm continuum image in Figure 2 is (1.5 ±.1) (.8 ±.1) at PA = 57 ± 6, and the disk mass is.4 M. Our derived parameters of the disk are consistent with the previous values, and the peak position at 2 mm agrees well with that at 1.3 mm. However, the elongated feature to the south seen in the 2 mm image has no counterpart at 1.3 mm. This feature would indicate non-axisymmetry of the disk as in the case of DM Tau LkCa 15 A rotating disk with a radius of 6 AU was imaged in HCO + J =1 andco J =2 1 with the IRAM interferometer (Duvert et al. 2; Simon et al. 21). The beamdeconvolved Gaussian size of the dust disk was estimated to be (1.45 ±.8) (1.2 ±.8) with PA = 64 ± 13 at 1.3 mm. Our 2 mm image shows that the Gaussian size of the dust disk is (2.1 ±.2) (.6 ±.4) at PA = 79 ± 5. Our disk size differs from the previous one, while the peak position at 2 mm agrees with that at 1.3 mm Estimation of atmospheric seeing To estimate the size of the atmospheric seeing disk during our observations, we made CLEAN maps of the 141 GHz continuum emission from the gain calibrators , , and In the maps the continuum emission seems slightly extended compared with the synthesized beams, and non-zero beam-deconvolved Gaussian sizes of the calibrators are derived. Since the angular sizes of the calibrators are much smaller than the NMA beam sizes of 1, the spatial extent of the calibrators in the CLEAN maps is probably attributed to the phase fluctuation due to the atmospheric turbulence (i.e., the seeing sizes toward the calibrators). In this paper we define the seeing size as the geometrical mean of the lengths of the major and minor axes of the deconvolved Gaussian profile ((S major S minor ) 1/2 ),

13 13 assuming that the turbulence is isotropic and that the image distortion is described by a Gaussian profile. The estimated seeing size for each imaging is listed in Table 3. Since the seeing sizes are smaller than the source sizes, as shown in Table 3, it is not likely that the disk images in Figure 2 were seriously distorted by the atmospheric turbulence. For some sources, however, the estimation of disk inclination angles might be influenced by the seeing because the lengths of the source minor axes are comparable to the seeing sizes. We consider the seeing sizes toward the calibrators as those toward the target objects. This approximation would be valid as previously discussed in the case of Haro 6-5B by Yokogawa et al. (21), although the angular distances between the calibrators and the sources are 1 2 and the integration time of the calibrators (2-3 minutes) was shorter than that of the sources (4-5 minutes). For Haro 6-5B they analyzed the bandpass calibrator as well as the gain calibrator and concluded that the seeing size did not sensitively depend on both the sky direction and the integration time at least under good weather conditions in Nobeyama. 5. Discussion 5.1. Analysis of the disk images and the SEDs based on disk models To estimate the physical properties of the protoplanetary disks, we analyze the disk images obtained by this study together with the SEDs on the basis of two disk models. The disk parameters to be determined are as follows: inner and outer radii (R in, R out ), mass (M disk ), inclination angle (i), position angle (PA), surface density distribution (Σ(r)), temperature distribution (T (r)), and dust opacity coefficient with the β index. Here we assume the dust opacity coefficient follows the usual power-law form of κ ν =.1(ν/1 12 Hz) β [cm 2 g 1 ] (e.g., Beckwith et al. 199). We adopt the following two disk models. The first model (model 1) is a power-law model that is most frequently used in data analysis of disk observations (e.g., Beckwith et al. 199). In the model 1, the radial profiles of the surface density and temperature of a disk have the power-law forms of Σ (r) =Σ (r/r ) p and T (r) =T (r/r ) q, respectively, for R in r R out. In our paper the lower limit of the temperature is fixed at 8 K (Goldsmith & Langer 1978). It is to be noted that the model was used in the standard model for the origin of our solar system by Hayashi et al. (1985). The model, however, seems to have the unphysical nature that the mass distribution is sharply truncated at the outer radius. In contrast to the model 1, the second model (model 2) has a surface density distribution of Σ (r) =Σ (r/r ) p exp[ 3(r/R out ) 2 p ], the same form as in a similarity solution for viscous

14 14 accretion disks (Lynden-Bell & Pringle 1974; Hartmann et al. 1998). This distribution does not have any sharp outer edge. Since the radial profile is extended to the infinite, we define the disk outer radius as the radius of a region which contains 95% of the total disk mass (see Appendix). In the similarity solution, the power-law index p of the surface density distribution is equivalent to the index γ of the power-law function of the viscosity (ν(r) =ν (r/r ) γ ). The temperature distribution has the same form as in the model 1 with the free parameter of q, although the viscous accretion disks are predicted to have 3/4 for q in a steady state. We take account of the distortion of disk images due to the radio seeing in applying the disk models to the disk images. Prior to the model fitting, we convolved the synthesized beam patterns, which are approximately Gaussian, with the Gaussian profiles of the radio seeing obtained in 4.3, and we used the new effective beam patterns in calculating contour maps for the model disks. The seeing does not seem to seriously affect the estimation of the disk parameters, because the seeing sizes are smaller than both the beam and source sizes. Actually our disk images at 2 mm agree with the previous ones at other wavelengths, as shown in 4.2. It would be almost impossible that a point-like source happens to mimic the disk obtained previously owing to the radio seeing. We have determined R out, Σ(r), i, and PA of the disk by applying the two disk models to the disk image at 2 mm. These disk parameters are sensitive to the disk image. In the χ 2 fitting, we assumed a geometrically thin disk for simplicity. Thus the flux density from the model disks at frequency ν, F ν,isgivenby F ν (r) = P beam+seeing (r r )B ν (T (r ))(1 exp( τ ν (r )/ cos i)) cos idr /d 2, (1) where P beam+seeing is the effective beam pattern including the seeing, B ν is the Planck function, and τ ν = κ ν Σ. The peak positions of the 2 mm continuum emission were considered as the stellar positions, i.e., the disk centers. As the first guess about the disk parameters we adopted Σ =1gcm 2 at r = 1 AU and p = 1. The initial values of R out, i, andpa were the best-fit values in the Gaussian fitting (see Table 3). By simultaneously applying the same models to the SED we have determined R in, T (r), β, and Σ. These parameters are well estimated from the energy spectrum from millimeter to near-infrared wavelengths. Although Σ can be determined in the above image fitting, we also treated it as a free parameter in the SED fitting. This is mainly because the disk models could not be well fitted to the SED particularly over the range from millimeter to submillimeter wavelengths for the fixed value of Σ determined in the image fitting. For the central star only the stellar radius was treated as a free parameter, for simplicity, with fixing the effective temperature, which is shown in Table 2: the stellar radius was determined

15 15 so as to reproduce the flux densities from near-infrared to ultraviolet wavelengths, without considering the excess at ultraviolet. These stellar parameters affect only the inner radius of the disk, which is not discussed in this paper. Detailed analysis of the stellar properties is beyond this work. The cycle of the image fitting followed by the SED fitting was repeated until all the disk parameters were converged within uncertainties. The convergence was achieved after a few repetitions, because the two groups of the disk parameters are not strongly coupled with each other. Although two different best-fit values for Σ were determined by both the image and SED fitting, we adopt the best-fit value by the image fitting in the following. There exists a serious problem of runaway increase of the disk outer radius in the above model fitting. The main reason is as follows: the outer part of the model disk comes to have surface brightness equal to or lower than the rms noise level when the model disk becomes more extended than the observed disk, and as a result, the contribution of the outer part of the model disk to χ 2 becomes small, which makes the sensitivity of the radius to χ 2 very weak. Such problems are usually associated with analysis of data having finite S/N (e.g., Mundy et al. 1996). In order to suppress the runaway increase we impose the following constraint on the model fitting: The total flux density of a model disk should be equal to the observed one, F ν (D or AB(+C)). Since F ν (AB+C) is only 7% of F ν (D) for the two sources IQ Tau and LkCa 15, we consider the two total flux densities of F ν (D) and F ν (AB(+C)) in the constraint. With the constraint we treat the disk outer radius as a dependent variable. To estimate all the disk parameters in a consistent way, higher-resolution images with higher S/N at many frequencies will be required Fitting results The best-fit results for the images and the SEDs are shown in Figures 3 & 4, respectively. The corresponding best-fit parameters with errors are listed in Table 4 for the disks. These errors include the rms noise on the images and the uncertainties in our and previous flux measurements, but mutual coupling among the disk parameters is not considered. If the coupling is taken into account, the errors would become greater by a factor of 1.5. In the images, the disk models were fitted to pixels higher than the 1.5σ levels over the regions of 4 α, δ +4. Figure 3 shows that the model fitting seems fairly good and the residual intensities are comparable to the 1.5σ levels except for some non-axisymmetric components. Although there seem to exist non-axisymmetric components for Haro 6-5B, HL Tau, DM Tau, DO Tau, and GM Aur, as described in 4.2, we equally treated all the components higher than the 1.5σ levels, and applied the axisymmetric models in our fitting.

16 16 This is because we have no firm theoretical disk model including such non-axisymmetry. Therefore, it is likely that the estimated disk parameters are somewhat affected by the non-axisymmetry. Our flux measurements strongly suggest that R out of the disks around IQ Tau and LkCa 15 is larger than that expected from the disk images shown in Figure 2. Since F ν (AB+C) is only about 7% of F ν (D) for the two sources, as shown in Figure 1, the best-fit value of R out with the constraint using F ν (D) becomes larger than that for F ν (AB+C) (see the positive errors of R out in Table 4). Of course, calculated images for the models with R out based on F ν (AB+C) agree well with the observed images in Figure 2. Considering S/N in Figure 2, it is very likely that the outer parts of the large disks around the two sources are embedded in the noise levels because of low brightness. The model fitting to the SEDs over the frequency range from 1 11 to 1 14 Hz seems good, as shown in Figure 4, as well as the image fitting. For the two embedded sources Haro 6-5B and HL Tau, the stellar parameters of the effective temperatures and radii were fixed in such a way that the star/disk systems reproduce the flux densities at near-infrared, but the excess at ultraviolet was ignored in the fitting. For the other sources, the best-fit values of the stellar radii were reasonable values of.1 AU. The stellar luminosities determined by the SED fitting, however, do not agree with those in literature (see Table 2), probably because our analysis to derive the stellar parameters is simplified. In the best-fit curve of CY Tau a shallow dip is seen at 1 12 Hz because of the lower limit of 8 K for the disk temperature Evolution and diversity of the disks in their accretion stage Diversity in the disk properties has been reported by previous surveys. The diversity in the temperature distribution and mass of the disks was revealed by Beckwith et al. (199). Furthermore, recent HST imaging found several silhouette disks with various radii in the Orion region (McCaughrean & O Dell 1996). On the other hand, in this study we will investigate the disk diversity in more detail by comparing the disk properties on the basis of the disk images taken under almost uniform conditions. In addition to the disk diversity, previous infrared and millimeter observations have accumulated much evidence for the overall evolution of the disks during the stellar evolution from protostars to WTTSs through CTTSs (e.g., Looney et al. 2; Strom et al. 1989; Osterloh & Beckwith 1995; Duvert et al. 2). If the disks really evolve, can we find out some evidence for the disk evolution in the CTTS stage? We will try to extract the disk

17 17 evolution from the diversity in the disk properties Clock for the disk evolution First of all, we need to select good measures of the disk evolution, i.e., the clock. There are at least two good candidates for the clock: the age of the central star and the mass accretion rate (the accretion luminosity) of the disk. The two clocks become equivalent if the disk evolution completely synchronizes with the stellar evolution. The stellar age is the most fundamental clock for a star and is usually determined from the comparison between observations and theoretical calculations on HR diagrams (e.g., Kenyon & Hartmann 1995). We made new determinations of the stellar ages and masses from the effective temperatures and luminosities in literature (see Table 2). Here we did not use the stellar luminosities obtained from our SED fitting, because they depend on our adopted models. The disk activity tends to decrease with the stellar evolution from the CTTS stage of 1 6 yr to the WTTS stage of 1 7 yr (e.g., Hartmann et al. 1998; Calvet et al. 2). Since the timescale of Keplerian rotation is likely to control the dynamical evolution of the disk, the stellar age normalized by the Kepler time must be also considered. The normalized age, however, is essentially the same as the stellar age itself, because the Kepler time is weakly dependent on the stellar mass, which almost falls into a narrow range of (.5-1) M, as shown in Table 2. The clock of the disk mass accretion rate, Ṁ acc, or the disk accretion luminosity, L acc,is theoretically thought to be an important parameter, which is closely related to the evolution of viscous accretion disks. In the standard model for viscous accretion disks, the timescale of the viscosity processes characterizes the disk evolution, and both M acc and L acc decrease with the disk evolution. These two parameters, however, can not be derived directly from any observations and have been estimated from other observable quantities such as the infrared excess luminosity and the luminosities of the line and continuum emission from the boundary layer between the star and the disk (e.g., Valenti, Basri, & Johns 1993; Hartigan, Edwards, & Ghandour 1995; Gullbring et al. 1998; Hartmann et al. 1998). We will now examine the infrared excess luminosity and the Hα line luminosity as potential disk clocks. The infrared excess luminosity, L IR, comes to be equal to L acc after subtraction of the luminosity of reprocessed stellar radiation, L rep, while the Hα line luminosity, L Hα, is thought to represent the activity of T Tauri winds or the mass ejection rate. Since the mass ejection rate is very likely to be proportional to the mass accretion rate, a good correlation between L Hα and L IR is seen, as shown in Figure 5 (Cabrit et al. 199). We obtained the best-fit curve given by L Hα.2L IR.2L acc. (2)

18 18 The luminosity L IR is roughly equal to L acc for large L IR. In Figure 5 the scatter around the best-fit curve seems to increase with decreasing L IR, probably because both the contribution of L rep to L IR and that of the luminosity of the chromospheric radiation to L Hα increase. There exist uncertainties in estimating L IR and L Hα. The estimation of L IR from SEDs requires some disk models and the subtraction of L rep is highly dependent on the models (e.g., Miyake & Nakagawa 1995; Kenyon & Hartmann 1987; Gullbring et al. 1998; Basri & Batalha 199). On the other hand, the estimation of L Hα does not depend on any models, although the luminosity often shows time variability and is uncertain by a factor of 2 (Cabrit et al. 199). We prefer L Hα as the disk clock, because it can directly be observed. The luminosity is expected to decrease with the disk evolution. In the following, we use both the stellar age and L Hα as the measures of the disk evolution. For the two embedded sources Haro 6-5B and HL Tau, however, there exists no definite estimate of either measure Disk radius The disk outer radius seems to increase with decreasing L Hα, as shown in Figure 6. This increasing trend is likely to be a signature of the disk evolution, because we can not find any distinct correlation between the disk radius and the stellar parameters of mass and luminosity. In the case of the L Hα clock the trend seems clear except for the two protostars in both the models 1 & 2. Although the luminosity is thought to have uncertainty by a factor of 2, the disk radius likely increases with a scatter as the luminosity decreases, or the disk evolves. The trend, however, becomes unclear against the stellar age, and this situation is not improved even for the age normalized by the Kepler time. These results may suggest that the disk evolution does not synchronize well with the stellar evolution. Although the decrease in the disk activity has been observationally reported over a long time span of CTTS to WTTS, it is likely that the disk evolution over a short span comparable to the timescale of the disk accretion is somewhat embedded in the diversity of disk formation and evolution processes, such as different termination times of mass supply from envelopes and various timescales of the viscosity controlling the disk evolution. In fact, the distribution of WTTSs slightly overlaps with that of CTTSs on HR diagrams (e.g., Strom et al. 1989; Stahler & Walter 1993). The increase in the disk radius with the evolution can be interpreted as radial expansion of an accretion disk due to outward transport of angular momentum (Lynden-Bell & Pringle 1974; Hartmann et al. 1998). The viscosity transports angular momentum from the inner to outer parts of the disk, resulting in the accreting motion of the inner part and the expansion of the outer part. If we compare the disk expansion with the similarity solution in the standard

19 19 model for viscous accretion disks, we are able to obtain some insight into the viscosity. In the similarity solution the disk outer radius can be related to the Hα line luminosity, as shown by Equation (A11). The relation is applied to the data in Figure 6a. The best-fit curve is given by R out = 128(L Hα /.1L ) 2/5 AU for the model 2 under the condition that γ, suggesting γ. The disk expansion with γ is supported by the fact that p for the model 2, as shown in Figure 7: the index γ is equivalent to the power-law index p of the surface density distribution in the similarity solution. Figure 6 suggests that the disk expands radially from 1 AU to 5 AU at a time interval of 1 7 yr. If this is the case, then the viscosity parameter α is estimated to be.1 (see Equation (A7)), which is predicted in theoretical models for the MHD turbulence caused by the B-H mechanism (Balbus & Hawley 1998). The B-H mechanism is one of the most promising candidates to generate the viscosity. Recently, Tamura et al. (1999) have revealed from the detection of submillimeter polarization that toroidal components of the magnetic field are dominant in some disks, which would put a tight constraint on the viscosity models. The radius of 1 AU at the beginning of the expansion is roughly consistent with the centrifugal radii of four protostars (35 AU for B335, 4 AU for HL Tau, 82 AU for IRAS4169, and 113 AU for L1527), which are derived from the rotating motion of the infalling envelopes with specific angular momentum conserved (Ohashi et al. 1997). Here we exclude a protobinary system L1551 IRS 5 (Looney, Mundy, & Welch 1997), because the disk formation process in such a binary system with its separation comparable to the disk sizes can be significantly different from that in the case of single stars. On the other hand, the large radii of the expanded disks agree with the spatial extent of the silhouette disks in Orion, the dust debris disks found around Vega-like stars, and the hypothetical extended Kuiper belt as a possible source of short-period comets beyond the orbit of Neptune (e.g., McCaughrean & O Dell 1996; Holland et al. 1998; Backman & Paresce 1993; Mumma, Weissman, & Stern 1993). Note, however, that recent observations (e.g., Chiang & Brown 1999; Gladman et al. 21) suggest significant depletion of the Edgeworth-Kuiper Belt Objects beyond 5 AU, which might suggest disk truncation due to a stellar encounter (McCaughrean & O Dell 1996; Ida, Larwood, & Burkert 2; Kobayashi & Ida 21) or inward movement of solid material (Stepinski & Valageas 1997; Kornet, Stepinski, & Różyczka 21). A scatter of 1 AU remains in the disk radius even after subtracting the increasing trend in Figure 6. This scatter can be attributed to the disk formation process in an infalling envelope around a protostar (e.g., Nakamoto & Nakagawa 1994). Since the specific angular momentum of the envelope gas is shown to be conserved during infall (Momose et al. 1998; Ohashi et al. 1997), a scatter in the specific angular momentum probably generates various centrifugal radii, resulting in the scatter in the disk radius. This is supported by the fact that the centrifugal radii of the four protostars have a similar scatter of 5 AU. It is to