Investigation of the physical properties of protoplanetary disks around T Tauri stars by a one

52 Pages·2002·1.12 MB·English

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
usingtheNobeyamaMillimeterArray(NMA).Diskimageshavebeensuccessfully
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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
canbeinterpretedasradialexpansionofaccretiondisksduetooutwardtransport
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
density distribution (Σ(r) = Σ (r/r )−p) is 0 - 1 in most cases, which is smaller
0 0
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
extrapolatedvalueintheHayashimodel. Thesefactsmayimplythatinthedisks
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)arecommonlyaccompaniedbycircumstellardisks. Theirphysicalpropertieshavebeen
derived mainly from analysis of spectral energy distributions (SEDs) under the assumptions
thatthediskisaxisymmetricanditstemperatureandsurfacedensitydistributions(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
(cid:2)
within several hundredsAU in radius andthe power-law index of T(r), q, is 0.5−0.75. Since
such characteristics of the disks are reminiscent of the “primordial solar nebula” assumed in
standardtheoriesoftheformationofthesolarsystem(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 centralstars 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 ∼ 5×10−6M yr−1 (e.g., Hayashi, Ohashi, & Miyama
(cid:2)
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 andgas 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
thedisks in theearlyT Tauristage is still limited. Althoughthe total mass andtemperature
distributionof thedisksarederivedfromtheanalysis oftheirSEDs, theouterradiusandthe
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 beamswhich provideno informationaboutthe 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 andnear-infraredwavelengths, becomeslower 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)becausethese two categoriesare based on the equivalent width of the Hα emission line
that mustbe tightly connectedto 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
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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(cid:3)(cid:3) −2(cid:3)(cid:3)), 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. (1994), Simon et al. (1992), Reipurth & Zinnecker (1993), and Mathieu (1994). 2) The
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expectedfluxdensityof2mmdustcontinuumemissionislargerthan20mJy. The2mmflux
densityofeachobjectisestimatedfromthesurveysof1.3mmcontinuumemission(Beckwith
et al. 1990; 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 ∼ 20 mJy, simple calculations show that imaging
of the disk with a radius of ∼ 100 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
10 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, becausethese objects have equivalent widths of the
Hα emission line as narrow as ∼ 10 ˚A (see Table 2).
3. Observations
Observations were carried out with the NMA, which consists of six 10 m antennas,
over the three winter seasons of 1998 December to 1999 February, 1999 December to 2000
February, and 2000 November to 2001 February. We used all the array configurations, D, C,
and AB, and their projected baseline lengths ranged from (5 - 40), (10 - 80), 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
observationsweretypically200KinDSBatthezenith. Forthebackend,thedigitalspectral
Ultra Wide Band Correlator, UWBC (Okumura et al. 2000) was employed. Visibility data
of the continuumemission in both the lower (135±0.512 GHz) andupper (147±0.512 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(cid:3)(cid:3) FWHM. In the lowest-resolution D configuration,
we used the source positions previously reported (e.g., Strom et al. 1989). In the higher-
resolution AB and C configurations, the peak positions in the D configuration were used as
– 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
sourceswiththecompactDconfigurationtodetectthediskemissionaspoint-likesources. In
the D configuration,the size of the synthesized beam was ∼ 5(cid:3)(cid:3) and the array was insensitive
to structures extending more than 20(cid:3)(cid:3) (∼ 2800 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(cid:3)(cid:3) and the array was insensitive to
structuresextendingmorethan4(cid:3)(cid:3) (∼560AU)FWHM.Thebeamshapewasnearlycircular,
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(cid:3)(cid:3) and structures extending
more than 10(cid:3)(cid:3) (∼ 1400 AU) FWHM were probably resolved out.
The response across the observed passband for each sideband was determined from 30-
40 minute observations of 3C454.3 or 3C273. A gain calibrator, 0446+112, 0507+179, or
0528+134 was observed every 30 minutes in the D configuration. In the AB and C config-
urations, the gain calibrators were observed as frequently as possible (every 8-10 minutes)
to minimize phase error in resultant images. The flux densities at 2 mm of 0446+112,
0507+179, and 0528+134 were derived to be (1.9 - 2.1) Jy, (1.7 - 2.2) Jy, and (1.5 - 2.5) Jy,
respectively, by comparison with Uranus or Neptune (Griffin & Orton 1993). The overall
uncertainty in the flux calibration was about 10%.
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(cid:3)(cid:3) beam in the D configuration, about 2 mJy beam−1 with ∼ 1(cid:3)(cid:3)
beam in the AB configuration, and about 2 mJy beam−1 with ∼ 2(cid:3)(cid:3) beam in the AB+C
configurations. Positional accuracy was dominated by S/N and absolute positional errors
were less than 0.3(cid:3)(cid:3). Since source sizes were much smaller than the field of view, the primary
beam attenuation was negligible.
– 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(cid:3)(cid:3)), indicating
that most emission originates from the region of r < 350 AU from the central star and that
thecontributionofextendedcomponentssuch as an envelopeis negligible. Detailed analyses
of the SEDs of some T Tauri stars have revealed that continuumflux densities at frequencies
higherthan100GHzareattributedsolelytodustthermalradiation,thoughthecontribution
of free-free emission from ionized gas should be taken into accountat 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.
Thespatialextentoftheemission inthemapsconstructedfromthedatawiththesparse
configurations(ABandC)ismoreextendedthanthebeamsize(1(cid:3)(cid:3)−2(cid:3)(cid:3)): detaileddescriptions
ofthespatialdistributionsarepresentedin§4.2. Figure1showsacomparisonofthedetected
total flux densities in the compact (D) and sparse (AB and AB+C) configurations. In the
case of 10 sources, the total flux density detected by the D configuration,F (D), agrees with
ν
that by the AB configuration,F (AB), within uncertainties, suggesting all the disk emission
ν
is successfully detected and mapped with ∼ 1(cid:3)(cid:3) beam. In the case of the other three sources
(AA Tau, IQ Tau, and LkCa 15), F (AB) is only (40 − 60) % of F (D). This is due to
ν ν
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 (D) = F (AB), suggesting that
ν ν
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 (D) as much as
ν
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 (AB+C),
ν
becomes greater than 70 % of F (D) (see Table 1 and Figure 1). Although the sensitivity of
ν
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 –
4.2. 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 (AB) agrees with F (D), and those
ν ν
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-deconvolvedGaussian 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).
Wecompareourimagingresultswithpreviousonesfortheninesourcesdescribedbelow,
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-deconvolvedGaussian 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
positionangles. Thisis becausetheradiusofadisktracedbylineemission tendstobelarger
than that of the disk traced by continuum emission owing to large optical depths (τ > 1) of
theline emission. Furthermore,thedisk massfrom the lineobservationsdoesnotnecessarily
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 becausethe line and continuum
emission often traces different regions.
4.2.1. 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-infraredwavelengths, and an envelopeand
a disk were revealed as a reflection nebula and a dark lane, respectively (Krist et al. 1998;
– 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. (2001). The non-axisymmetric component extended
to the south-west seen in Figure 2 would be a part of the envelope around the star.
4.2.2. 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 70 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(cid:3)(cid:3).0 ± 0(cid:3)(cid:3).2) × (0(cid:3)(cid:3).5 ± 0(cid:3)(cid:3).2) at PA = 125◦ ± 10◦. 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(cid:3)(cid:3).04 ± 0(cid:3)(cid:3).03) × (0(cid:3)(cid:3).60 ± 0(cid:3)(cid:3).04) 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.
4.2.3. CY Tau
Thissource is a CTTS inthe HBCandarotatingdisk was imagedin CO J = 2−1 with
the IRAM interferometer (Simon, Dutrey, & Guilloteau 2001). The radius of the gas disk
was derived to be (270 ± 10) 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 –
4.2.4. 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 110 AU, 25◦, and 48◦ ± 5◦,
respectively, by Gaussian fitting. They also derived the disk mass of 1 × 10−5 M from the
(cid:2)
linedataandnotedthemassismuchsmallerthanthatderivedfromcontinuumobservations.
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◦, and 27◦ ± 7◦, respectively. Furthermore, we
estimatethedisk massto be6×10−3 M fromourmodelfitting(see§5). Thepeakposition
(cid:2)
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.
4.2.5. DL Tau
A rotatingdisk was imagedin COJ = 2−1 with millimeter interferometers. Koerner&
Sargent (1995) found the disk with a radius of 250 AU with the OVRO array, and recently,
Simon et al. (2001) revealed the more detailed velocity structure of the disk with the IRAM
array. The radius of the gas disk was estimated to be (250 - 520) AU, and the inclination
and position angles from the line and continuum observations were 12◦ - 49◦ and 44◦ - 84◦,
respectively. Thedisk masswasderivedtobe1× 10−6 M fromthelineobservations, which
(cid:2)
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 (80 ± 4) AU, 47◦ ± 4◦, 52◦ ± 6◦, and 5 × 10−2 M , respectively.
(cid:2)
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.
4.2.6. DM Tau
Double-peaked profiles of 12CO and 13CO emission were first detected with the NRO 45
mandIRAM30mtelescopesandthedetectionstronglysuggestedthepresenceofa 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