Dust Properties of Protoplanetary Disks in the Taurus-Auriga Star Forming Region from Millimeter Wavelengths

Abstract

We present the most sensitive 3 mm-survey to date of protoplanetary disks carried in the Taurus-Auriga star forming region (average rms of about 0.3 mJy), using the IRAM PdBI. With our high detection rate of 17/19, we provide the first detections at wavelengths longer than about 1 mm for 12 sources. This enables us to study statistically the mm SED slopes and dust properties of faint disks and compare them to brighter disks using a uniform analysis method. With these new data and literature measurements at sub-millimeter and millimeter wavelengths, we analyze the dust properties of a sample of 21 isolated disks around T Tauri stars in the Taurus-Auriga star forming region. Together with the information about the disks spatial extension from sub/mm-mm interferometric studies, we derive from the observed sub-mm/mm spectral energy distribution constraints on the dust opacity law at these wavelengths, using two-layer flared disk models and a self-consistent dust model that takes properly into account the variation of the dust opacity with grain growth. We find evidence for the presence in the disk midplane of dust particles that have grown to sizes as large as at least 1 millimeter in all the disks of our sample, confirming what was previously observed on smaller brighter objects. This indicates that the dust coagulation from ISM dust to mm-sized grains is a very fast process in protoplanetary disks, that appears to occur before a young stellar object enters the Class II evolutionary stage. Also, the amount of these large grains in the disk outer regions is stationary throughout all the Class II evolutionary stage, indicating that mechanisms slowing down the dust inward migration are playing an important role in the Taurus-Auriga protoplanetary disks. Comment: 17 pages, 10 figures, accepted for publication in A&A

Full text

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arXiv:0912.3356v1 [astro-ph.EP] 17 Dec 2009
Astronomy & Astrophysics manuscript no. 6439
December 17, 2009
c ? ESO 2009
Dust Properties of Protoplanetary Disks in the Taurus-Auriga
Star Forming Region from Millimeter Wavelengths
L. Ricci1, L. Testi1,2, A. Natta2, R. Neri3, S. Cabrit4, and G. J. Herczeg5
1European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany
2INAF - Osservatorio Astrofisico di Arcetri, Largo Fermi 5, I-50125 Firenze, Italy
3Institut de Radioastronomie Millim´ etrique, 300 Rue de la Piscine, F-38406 Saint Martin d’H` eres, France
4LERMA, UMR 8112 du CNRS, Observatoire de Paris, 61 Av. de l’Observatoire, F-75014 Paris, France
5Max Planck Institut fur Extraterrestrische Physik, Postfach 1312, D-85741 Garching, Germany
Received 2009 October 5/ Accepted 2009 December 15
ABSTRACT
We present the most sensitive 3 mm-survey to date of protoplanetary disks carried in the Taurus-Auriga star forming
region (average rms of about 0.3 mJy), using the IRAM PdBI. With our high detection rate of 17/19, we provide the
first detections at wavelengths longer than about 1 mm for 12 sources. This enables us to study statistically the mm
SED slopes and dust properties of faint disks and compare them to brighter disks using a uniform analysis method.
With these new data and literature measurements at sub-millimeter and millimeter wavelengths, we analyze the dust
properties of a sample of 21 isolated disks around T Tauri stars in the Taurus-Auriga star forming region. Together
with the information about the disks spatial extension from sub/mm-mm interferometric studies, we derive from the
observed sub-mm/mm spectral energy distribution constraints on the dust opacity law at these wavelengths, using
two-layer flared disk models and a self-consistent dust model that takes properly into account the variation of the dust
opacity with grain growth. We find evidence for the presence in the disk midplane of dust particles that have grown to
sizes as large as at least 1 millimeter in all the disks of our sample, confirming what was previously observed on smaller
brighter objects. This indicates that the dust coagulation from ISM dust to mm-sized grains is a very fast process in
protoplanetary disks, that appears to occur before a young stellar object enters the Class II evolutionary stage. Also,
the amount of these large grains in the disk outer regions is stationary throughout all the Class II evolutionary stage,
indicating that mechanisms slowing down the dust inward migration are playing an important role in the Taurus-Auriga
protoplanetary disks. Another result is that the spectral index between 1 and 3 mm for the 6 faintest disks in our sample
is on average smaller than for the brighter disks, indicating either that these fainter, yet unmapped, disks are spatially
much less extended than the brighter spatially resolved disks, or that fainter disks have typically larger dust grains in
their outer regions. Considering that these fainter disks are more representative of the bulk of the disk population than
the brighter ones, this may have important consequences for the theories of planetesimal formation and disk formation
and evolution. Finally, we investigate the relations between the derived dust properties, namely dust mass and grain
growth, and the properties of the central star, like its mass, age and mass accretion rate.
Key words. stars: planetary systems: protoplanetary disks — stars: planetary systems: formation — stars: formation
1. Introduction
Circumstellar disks play a fundamental role in the physical
processes involved in star and planet formation. In these
systems part of the material (gas and dust) loses angu-
lar momentum and accretes onto the central forming star,
while another part of it may give birth to a planetary sys-
tem. Although the content of dust is only a small fraction
of the overall material in a circumstellar disk, dust grains
are crucial elements in the early stages of planet forma-
tion. According to the core-accretion scenario (Safronov &
Zvjagina 1969, Pollack et al. 1996), growth from an ini-
tial ISM population of submicrometer-sized dust grains to
planetesimals of 1 − 100 km sizes is believed to be the key
mechanism of early planet formation. These planetesimals
“embryos” then continue to grow leading to the formation
of at least terrestrial planets and possibly the cores of giant
planets.
Observational evidence of grain growth from the ISM
dust has been obtained from a variety of techniques at dif-
ferent wavelengths. Throop et al. (2001) observed in optical
and near-infrared the translucent edge of the 114-426 pro-
toplanetary disk in the Orion Nebula Cluster, and derived
from the extinction curve of the background nebular emis-
sion a lower limit of a few microns for the dust grains in the
very outer regions of the disk, about 500 AU away from the
central star. Another method to probe the presence of large
grains in the disk is through the shape and intensity of the
10- and 20-µm silicate features. The data indicate a large
variety of silicate profiles, ranging from strongly peaked
silicate bands and steeply rising spectral energy distribu-
tions (SEDs) to “boxy” silicate profiles and flatter SEDs
(ISO, Malfait et al. 1998; Spitzer Space Telescope, Kessler-
Silacci et al. 2006). The boxy features with low feature-to-
continuum ratios are interpreted as grain growth to micron
size (Bouwman et al. 2001).
However, the techniques outlined so far can only probe
dust grains as large as some µm in the disk surface layers.
They are not sensitive to larger grains in the disk mid-

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2 Ricci et al.: Protoplanetary Disks in Taurus-Auriga
plane, the region in which planet formation is supposed to
occur. In order to probe larger grains in the midplane, ob-
servations at millimeter wavelengths are needed. Beckwith
& Sargent (1991) showed that T Tauri stars have shallow
SEDs at sub-millimeter wavelengths. Under the assumption
of optically thin emission at these frequencies, this implies a
dust opacity dependence on wavelength (κmm∝ λ−β) much
flatter than in the ISM (βISM= 1.7), which is naturally in-
terpreted in terms of grain growth (see e.g. Draine 2006).
However, this interpretation of the disk SEDs is not unique,
since the same data can be explained by very small opti-
cally thick disks. To break this degeneracy and sort out
the effect of potentially large optical depth it is neces-
sary to spatially resolve the disks to determine their actual
sizes. Furthermore, in this context observations at millime-
ter wavelengths are very useful, since at these lower fre-
quencies the impact of optically thick disk inner regions
to the total emission is expected to be lower. Therefore,
to actually probe the dust properties in protoplanetary
disks, one needs to combine the determination of the sub-
millimeter/millimeter SED with information on the disk
extension from high-angular resolution interferometric ob-
servations (see e.g. Testi et al. 2001).
In the last years, several sub-mm/mm interferometric
observations have been carried out to investigate dust grain
growth in protoplanetary disks. Wilner et al. (2000) re-
solved the disk around the TW Hya pre-main-sequence
(PMS) star at 7 mm using the Very Large Array (VLA).
Extensive modelling of the SED of this source has shown
that the dust grains in the outer parts of the TW Hya
disk have grown to at least ∼ 1 cm (Calvet et al. 2002).
An analogous result has been obtained for the disk around
CQ Tau (Testi et al. 2003). More recently, Rodmann et
al. (2006) resolved 10 disks in the Taurus-Auriga star form-
ing region and found clear evidence of grain growth in 4 of
them. Lommen et al. (2007) resolved 1 disk in Chamaeleon
and 4 in Lupus with the Submillimeter Array (SMA) at
1.4 mm and with the Australia Telescope Compact Array
(ATCA) at 3.3 mm, and found clear evidence of dust grain
growth to sizes of a few millimeter for 4 of them. Finally
Schaefer et al. (2009) observed a sample of 23 low mass
PMS stars (with spectral types of K7 and later) in Taurus-
Auriga at 1.3 mm and 2.6 mm with the Plateau de Bure
Interferometer (PdBI); they detected only 8 sources at 1.3
mm and 6 at 2.6 mm, and found evidence of grain growth
for the 3 disks that they could spatially resolve.
In this paper we present our analysis on 21 protoplane-
tary disks around T Tauri stars in the Taurus-Auriga star
forming region without stellar companions in the range
0.05′′−3.5′′. For 11 of these objects, mainly faint disks with
F1.3mm< 100 mJy, we have obtained new data at ∼ 3 mm
with the Plateau de Bure Interferometer1(hereafter PdBI)
with an average rms of about 0.3 mJy. Together with the
data already present in the literature at sub/mm- and mm-
wavelengths, and with the information obtained in the last
years on the disks spatial extension from high-angular reso-
lution interferometric observations at mm wavelengths, we
investigate the dust properties in the disks, namely grain
growth and dust mass, and their relation with the proper-
ties of the central star.
1The Plateau de Bure Interferometer at IRAM is supported
by INSU/CNRS (France), MPG (Germany) and IGN (Spain).
In Section 2 we present our new PdBI data, the proper-
ties of our sample, the method we used to estimate the main
stellar physical quantities, and the data we used for our
analysis. In Section 3 we describe the disk models adopted
for the analysis of the disks sub-mm/mm SED. In Section
4 we show and discuss the results of our study in terms of
dust grain growth and dust mass, whereas in Section 5 we
summarize our main findings.
2. New 3mm observations and sample properties
2.1. New PdBI observations
We observed a total list of 19 targets; 16 of them were se-
lected to be relatively faint, with 15 mJy< F1.3mm< 100
mJy and with no known detections beyond about 1mm;
the other 3 (HL, DO and DR Tau) are brighter sources
that were observed for references purposes. The observa-
tions were carried out with PdBI between July and August,
2007. Owing to antenna maintenance work, all observations
were carried out in a subarray of the six-element interfer-
ometer. The antennas were arranged in very compact con-
figurations that provided sensitive baselines from 15m to
80m. The dual-polarization receivers, which were observ-
ing in the 3mm band, had typical receiver temperatures of
about 35K and were providing image sideband rejection
values better than 10dB. To achieve maximum sensitivity
in the continuum, the spectral correlator was adjusted to
cover a total effective bandwidth of about 2GHz.
The observing procedures were set up to fill in gaps
in the scheduling without any specific tuning wavelength
within the 3mm band. Visibilities were obtained using on-
source integration times of 22min interspersed with 2min
calibrations on a nearby calibrator. Each star was observed
on one or more occasions for a minimum of 40min and a
maximum of 2hr on-source. The atmospheric phase stabil-
ity on the baselines was always better than 40◦, consistent
with seeing conditions of 1′′-3′′, typical for summer. The ab-
solute flux density scale was calibrated on 3C84, 0528+134,
MWC349 and Mars, and was found to be accurate to 10%.
The receiver passband shape was determined with excellent
precision on a strong calibrator like 3C84.
We used the GILDAS package for the data reduction
and analysis. The data were calibrated in the antenna based
manner. The continuum visibilities were gridded with nat-
ural weighting and no taper to maximize the sensitivity.
Since none of the target stars was found to be resolved in
synthesized beams of 2′′-4′′, a point source model was fit-
ted to the calibrated visibilities of each star to estimate the
flux density of the continuum in the 3mm band. The results
are summarized in Table 1. Among the 19 targets, 17 were
detected, including 14 of the 16 faint sources, thanks to our
good sensitivity; 12 of these are first detections longward of
about 1mm, strongly expanding the available database of
3mm data towards fainter disks. The 2.6mm detections of
LkHa 358 and GO Tau were recently published by Schaefer
et al. (2009).
In Sections 2.2, 2.3 and 2.4 we describe the final sample
used for our analysis of dust properties, the adopted method
to estimate the stellar properties and mass accretion rates
summarized in Table 2, whereas in 2.5 we report the sub-
mm/mm data that we collected from the literature for our
analysis.

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Ricci et al.: Protoplanetary Disks in Taurus-Auriga3
Table 1. Summary of the new PdBI observations.
Objectα (J2000)δ (J2000)νλFν
rmsComments1
(GHz)(mm) (mJy)(mJy)
CW Tau
CX Tau
DE Tau
DK Tau
DO Tau
DP Tau
DR Tau
DS Tau
FM Tau
FP Tau
FY Tau
FZ Tau
GK Tau
GO Tau
Haro 6-28
HL Tau
HO Tau
LkHa 358
SU Aur
04:14:17.0
04:14:47.8
04:21:55.6
04:30:44.3
04:38:28.6
04:42:37.7
04:47:06.2
04:47:48.6
04:14:13.5
04:14:47.4
04:32:30.5
04:32:31.8
04:33:34.6
04:43:03.1
04:35:56.9
04:31:38.4
04:35:20.2
04:31:36.2
04:55:59.4
28:10:56.51
26:48:11.16
27:55:05.55
26:01:23.96
26:10:49.76
25:15:37.56
16:58:43.05
29:25:10.96
28:12:48.84
26:46:26.65
24:19:56.69
24:20:02.53
24:21:06.07
25:20:17.38
22:54:36.63
18:13:57.37
22:32:13.98
18:13:43.20
30:34:10.39
84.2
86.2
92.6
84.2
84.2
84.2
100.8
100.8
100.8
100.8
100.8
100.8
100.8
86.2
87.0
84.5
87.0
84.5
84.5
3.57
3.49
3.23
3.57
3.57
3.57
2.97
2.97
2.97
2.97
2.97
2.97
2.97
3.49
3.45
3.53
3.45
3.53
3.53
3.44
1.01
3.32
4.70
13.80
< 0.78
13.90
2.96
2.65
11.80
1.90
2.89
< 0.96
4.05
0.92
43.40
2.03
2.46
2.88
0.31
0.13
0.25
0.20
0.29
0.26
0.47
0.21
0.24
0.26
0.28
0.24
0.32
0.34
0.18
0.68
0.53
0.22
0.19
2.5′′binary
no sub-mm info
no sub-mm info
no sub-mm info
2.5′′binary
0.7′′binary
flat spectrum
no sub-mm info
1) Reason why the source has not been considered in the analysis (see text for more details).
2.2. Sample
Our final sample of 21 sources consists of all young stellar
objects (YSO) in Taurus-Auriga catalogued in Andrews &
Williams (2005) that fulfill the following criteria: (1) a Class
II infrared SED, in order to avoid contamination of sub-mm
fluxes by a residual envelope; (2) information on the central
star through optical-NIR spectroscopic/photometric data,
necessary to calculate self-consistent disk SED models; (3)
one detection at ∼ 3mm (either from our new PdBI obser-
vations or from the literature) and at least one detection in
the 0.45 mm < λ < 0.85 mm spectral region. This selection
criterion was chosen in order to probe a broad enough spec-
tral window to efficiently constrain the optically thin part
of the sub-mm/mm spectral energy distribution (SED); (4)
no evidence of stellar companions in the 0.05−3.5′′range in
angular separation. This range corresponds to about 5−500
AU in projected physical separation at the Taurus-Auriga
star forming region distance, here assumed to be 140 pc for
all the sources of our sample (Bertout et al. 1999). The limit
of 3.5 arcsec ensures that mm interferometric flux measure-
ments, of typical resolution 1 arcsec, are not contaminated
by the companion’s disk, while binaries closer than 5 AU
should have outer disk properties similar to those of single
stars on the scales probed by (sub-)mm data.
Only21sourcescataloguedbyAndrews&
Williams (2005) fulfill the above 4 criteria. They are
listed in Table 2, and include 11 sources from our PdBI
sample2.
Figure 1 reports histograms that describe the com-
pleteness level of our final sample with respect to all
Taurus-Auriga Class II YSOs catalogued in Andrews &
Williams (2005), and fulfilling the “isolation” criterion (4).
Our sample contains 63% of these “isolated” class II show-
ing a flux at ∼ 0.85mm greater than 100 mJy, and 31% of
the sources with lower 0.85mm fluxes. Therefore, our sam-
ple is not complete even for the brightest YSOs at 0.85mm.
This is due to a lack of observations at ∼ 3mm for these
sources. However, thanks to the high sensitivity of our new
PdBI observations (see Section 2.1) our sample enables us
to study statistically for the first time the dust properties
2The 8 sources dropped from the PdBI sample are HL Tau
(a flat spectrum source that retains an envelope; Padgett et
al. 1999); DP Tau, FP Tau, FY Tau and LkHa 358 that have
no available submm detections for SED fitting; and DK Tau,
GK Tau and Haro 6-28 which are binary systems with an-
gular separations of 2.5′′(Simon et al. 1992), 2.5′′(Reipurth
& Zinnecker 1993) and 0.7′′(Leinert et al. 1993) respectively.
We keep in our sample the wide binaries DS Tau and HO Tau
(angular separations of 7.1′′and 6.9′′respectively, Mathieu et
al. 1994); they do not show any emission from the compan-
ions from our new 3 mm interferometric observations. The other
dropped multiple systems from the AW05 catalog are DH Tau
(2.3′′binary, Itoh et al. 2005) , GG Tau (quadruple system with
a circumbinary ring of inner and outer radii of 180 and 260 AU
respectively, Pinte et al. 2007), and UY Aur (0.9′′binary, Leinert
et al. 1993)

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4Ricci et al.: Protoplanetary Disks in Taurus-Auriga
of faint disks (i.e. with F1.3mm< 100 mJy, F0.85mm< 100
mJy) and compare them to the brighter ones using a uni-
form analysis method. In terms of the stellar properties, it is
important to note that the Andrews & Williams (2005) cat-
alogue includes only a few very low mass PMS stars: only
stars with an estimated mass higher than about 0.2 M⊙
have been detected because of the sensitivity limits of the
current facilities at sub-mm and mm wavelengths that make
the detection of disks around very low mass YSOs very diffi-
cult. The sensitivity limitation is even more severe at 3mm,
therefore our final sample includes 58% of all the class II
isolated sample of Andrews & Williams (2005) with an esti-
mated mass greater than 0.4 M⊙, but only two sources with
M⋆< 0.4 M⊙(out of 10 in Andrews & Williams 2005).
2.3. Stellar properties
Spectral types for all the sources in our sample are taken
from the literature (Kenyon & Hartmann 1995, Brice˜ no et
al. 1998) and cover a range from G2 (SU Aur) to M2.5
(CX Tau). Spectral types of M0 and earlier have been con-
verted to effective temperatures with the dwarf tempera-
ture scale of Schmidt-Kaler (1982), whereas for types later
than M0 we adopted the temperature scale developed by
Luhman 1999. Typical uncertainties for these sources are
∼ 1 − 1.5 in spectral sub-types or ∼ 100 − 150 K in tem-
perature.
The stellar luminosities of all the pre-main-sequence
(PMS) stars were computed from their J-band flux (2MASS
All Sky Catalog of point sources, Cutri et al. 2003) to min-
imize contamination from UV and IR excess emission. For
the bolometric corrections we adopted the dwarf values
from Kenyon & Hartmann (1995) that are considered to
be satisfactory approximations for these young sources in
the J-band (Luhman 1999).
In order to estimate the amount of extinction toward
these young sources, we calculated the color excesses using
intrinsic colors provided by Kenyon & Hartmann (1995) for
G2−K7 spectral types and by Leggett (1992) for M0−M2.5
types. To ensure that the color excess reflects only the ef-
fect of reddening, minimizing the emission due to accretion,
the typical selected colors are between the R and H bands.
Since for some of the objects at later spectral types in our
sample R − I measurements are not available, we dered-
dened the J − H and H − Kscolors from the 2MASS All
Sky Catalog of point sources3to the locus observed for clas-
sical T Tauri stars (CTTS) by Meyer et al. (1997), following
the method described in Brice˜ no et al. (2002). Extinctions
are finally calculated adopting the extinction law of Rieke
& Lebofsky (1985).
The computed photospheric luminosities cover a range
from 0.16 L⊙(HO Tau) to 10.6 L⊙(SU Aur). Considering
the uncertainties in the photometry, reddenings, bolometric
corrections and distance, the typical errors in the bolomet-
ric luminosities are ±0.08 − 0.13 in logL⋆. Slight differ-
ences from the values obtained by other authors are typi-
cally within the uncertainties and are not significant for the
purposes of this paper.
3For
transformed from the 2MASS photometric system to the
Johnson-Glass one using the color transformations reported in
Carpenter (2001) and Bessell & Brett (1988).
this analysisthe JHKs
magnitudes havebeen
Fig.2. H-R diagram for the sources of our sample. The
dashed lines correspond to the isochrones for ages in Myr
as labeled at the right end of the lines from the 1999 PMS
evolutionary models, while the solid ones represent the evo-
lutionary tracks from the same models for PMS stars with
masses as labeled at the top of the evolutionary track lines.
In this diagram the evolutionary tracks start from an age
of 0.1 Myr. The errorbars for the (Teff, L⋆) values of our
objects are not shown, the uncertainties in the photomet-
ric parameters are typically ∼ 0.08 − 0.13 in logL⋆ and
∼ 100 − 150 K in temperature.
Given the effective temperatures and photospheric lu-
minosities, we placed the PMS stars on the H-R diagram
and derived stellar masses and ages adopting the theoretical
tracks and isocrones of Palla & Stahler (1999) (see Figure
2). One important source of uncertainty for stellar masses
and ages is given by the spread of values obtainable by
using different PMS evolutionary models. For example, if
compared to the ones obtained with the Baraffe et al. (1998)
models, our adopted values of stellar masses and ages are
typically lower by a factor of ∼ 1.5 and ∼ 2 respectively.
Our choice of using the Palla & Stahler (1999) models is
uniquely due to the more complete coverage of the HR di-
agram plane, that allows us to use the same evolutionary
models for all the sources of our sample. One should al-
ways bear in mind the high uncertainty associated to these
quantities, expecially to the stellar age (see Section 4.1 for a
more deailed discussion about the estimates of YSO ages).
According to the Palla & Stahler (1999) models the ranges
spanned by our sample go from about 0.3 M⊙ (CX Tau)
to 2.2 M⊙(RY Tau) in stellar masses and from about 0.1
Myr (UZ Tau E) to 17 Myr (DS Tau) in stellar ages.
The main stellar quantities described here are summa-
rized in Table 2.
2.4. Mass accretion rates
Given the stellar luminosities and effective temperatures
we calculated the stellar radii using the Stefan-Boltmann
law. Once the stellar mass M⋆and radius R⋆are set, the
mass accretion rate ˙Macccan be directly obtained from an
estimate of the accretion luminosity Laccby
˙Macc= 1.25R⋆Lacc
GM⋆
, (1)

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Ricci et al.: Protoplanetary Disks in Taurus-Auriga5
Fig.1. Histograms higlighting some properties of our selected sample. In all the histograms our sample is represented
by black+grey columns, the black columns represent the disks in our sample for which we obtained new PdBI data at ∼
3 mm, while the total columns (black+grey+white) include all the class II YSOs from the Andrews & Williams (2005)
catalogue with no evidence of stellar companions in the 0.05−3.5′′interval in angular separation, from which our sample
has been selected (see text). Upper left histogram represents the distribution of the ∼0.85 mm fluxes, including upper
limits, for all the sources but two, 04113+2758 and GM Aur, that have not been observed at ∼0.85 mm. Upper right and
bottom histograms show the distribution of stellar spectral type and estimated stellar mass (see Section 2.3) respectively.
Four class II YSOs are not included in these histograms because for them an estimate of the stellar spectral type is not
available. These are 04301+2608, FT Tau, Haro 6-39 and IC 2087.
where G is the gravitational constant and the factor of ∼
1.25 is calculated assuming a disk truncation radius of ∼
5 R⋆(Gullbring et al. 1998).
The estimates of Laccwere obtained from spectroscopic
detections of excess Balmer continuum emission in the lit-
erature (see references in Table 2). These estimates are
obtained primarily from measuring the excess flux in the
Balmer continuum shortward of 3646 ˚ A. The luminos-
ity is then obtained by applying a bolometric correction
calculated from shock models (Calvet & Gullbring 1998,
Gullbring et al. 2000) or simplistic plane-parallel slabs
(Valenti et al. 1993, Gullbring et al. 1998).
Two sources in our sample, FZ Tau and GO Tau,
do not have literature estimates of accretion luminosity
from the excess Balmer continuum emission. We obtained
the accretion luminosity for these two sources from low-
resolution spectra from 3200–8700˚ A obtained with the
Double Spectrograph at the 5m Hale Telescope at Palomar.
The accretion luminosity was then calculated from the ex-
cess Balmer continuum emission, following the method de-
scribed in Herczeg & Hillenbrand (2008).
2.5. Disks sub-mm and mm data from the literature
In order to probe the sub-millimetre and millimeter SED
we collected data of the dust continuum emission between
∼ 0.450 to ∼ 7 mm from several works in the literature,
listed in Table 3. These data, except for 7 mm measure-
ments, have been used together with the new PdBI ob-
servations at ∼ 3 mm to constrain the disk properties by
fitting the sub-mm/mm SED with the models described
in Section 3. The 7-mm data is excluded because free-free
emission from ionized gas contaminates disk emission, with
free-free emission typically contributing ∼ 20% of the 7mm
flux (Rodmann et al. 2006). Simultaneous cm observations
are required to constrain the free-free emission at 7mm,
which is variable on short timescales (<
Lommen et al. 2009). Only 2 disks in our sample (RY
Tau and UZ Tau E) have been observed nearly simultane-
ously at centimeter and millimeter wavelengths (Rodmann
et al. 2006), without which the 7mm fluxes should be con-
sidered only as upper limits for the dust emission. We there-
fore did not include the 7mm data in our analysis, although
we included the available 7mm data from the literature in
Figure 4 and verified a posteriori that the fluxes of our disk
∼a few days, see