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Astronomy & Astrophysics manuscript no.
(will be inserted by hand later)
A search for evolved dust in Herbig Ae stars
A. Natta 1 , L. Testi 1 , R. Neri 2 , D. S. Shepherd 3 , D.J. Wilner 4
1 Osservatorio Astrosico di Arcetri, INAF, Largo E.Fermi 5, I-50125 Firenze, Italy
2 IRAM, 300 rue de la Piscine, F-38406 St Martin d'Heres, France
3 National Radio Astronomy Observatory,P.O. Box O, Socorro, NM 87801
4 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138
Received ...; accepted ...
Abstract. We present observations of six isolated, pre-main-sequence, intermediate mass stars selected for shallow
spectra at submillimeter wavelengths at 1.3, 2.6, 7.0, and 36 millimeters from the IRAM PdBI and the VLA. We
analyze the new observations of these stars (HD34282, HD35187, HD142666, HD143006, HD150193, HD163296)
together with similar observations of three additional stars from the literature (CQ Tau, UX Ori, TW Hya), in
the context of self-consistent irradiated disk models. Our aim is to constrain the wavelength dependence of the
dust opacity and the total dust mass in the disks. The shallow wavelength dependence of the opacity is conrmed
and for a few stars extended to signicantly longer wavelengths. For any plausible dust properties, this requires
grain growth from interstellar sizes to maximum sizes of at least a few millimeters, and very likely to several
centimeters or more. For four of the stars (HD34282, HD163296, CQ Tau, TW Hya), the millimeter emission
has been spatially resolved, and the large disk radii (> 100 AU) rule out that high optical depths play a role.
The mass of dust that has been processed into large grains is substantial, and in some cases implies a disk mass
comparable to the mass of the central star.
Key words. stars:planetary systems: protoplanetary disks - stars: planetary systems: formation - stars: formation
1. Introduction
In the dense environment of circumstellar disks, grains
are subject to coalescence and fragmentation, which will,
in time, alter their properties and very likely cause sig-
nicant growth from the sub-micron size typical of dust
in the diuse interstellar medium (ISM). This is a neces-
sary step for all theories of planet formation. However, the
interplay of a multiplicity of poorly known physical pro-
cesses and their dependence on details of the grain struc-
ture make it diфcult to reach consensus on the extent and
timescale of dust processing (see Beckwith et al. 2000 and
references therein). It is therefore important to derive con-
straints from the observations, determining the properties
of dust in disks surrounding pre-main{sequence stars of
well known ages.
The spectral energy distribution (SED) of T Tauri
stars at millimeter and submillimeter wavelengths has a
shallow dependence on wavelength, consistent with opti-
cally thin emission from millimeter-size grains (Beckwith
& Sargent 1991). However, this interpretation of the SEDs
has remained controversial, since it was soon realized that
it is not possible to infer the dust opacity law from the
SED alone, and that the eect of potentially large optical
Send oprint requests to: lt@arcetri.astro.it
depth needs to be sorted out. To do that, one needs to
combine the determination of the long-wavelength SED
with spatially resolved images of the disk at one (or possi-
bly more) wavelengths (see e.g. the discussion in Testi et
al. 2001). Recently, this has been done for two pre-main{
sequence stars, TW Hya (Calvet et al. 2002) and CQ Tau
(Testi et al. 2003), using the VLA array at 7 mm to re-
solve the disk emission. In both cases, it was found that
the dust opacity depends on wavelength roughly as  0:6 ,
and this was interpreted as evidence for grain growth to
centimeter sizes.
Following our work on CQ Tau, we have started a
search for pre-main{sequence stars of intermediate mass
with shallow SEDs extending to 7 mm. The choice of this
rather long wavelength was motivated by the advantages
of using the largest wavelength range for the determina-
tion of the spectral index and by the fact that the VLA
oers the best resolution available today, provided that
the source is strong enough. In addition, the longer the
wavelength the more severe the constraints on dust prop-
erties one can set.
We report in this paper the results for a sample of six
stars. The sample and the observations obtained with the
PdB and VLA interferometers are described in x2. The

2 Natta et al.: VLA survey
results are presented in x3 and their implications for grain
properties and evolution are discussed in x4.
2. Observations
2.1. Sample Stars
Our sample is composed by nine pre-main{sequence stars,
whose properties are summarized in Table 1 (Column 1{
7). The rst six stars listed are new observations, while the
last three are from the literature (Testi et al. 2001,2003,
Calvet et al. 2002). The six new stars were selected be-
cause they were known to have shallow spectra at sub-
millimeter or millimeter wavelengths from previous ob-
servations (Sylvester et al. 1996, Mannings & Sargent
1997,2000). We adopted distances and spectral types from
Hipparcos and computed the stellar parameters (eective
temperature and luminosity) as in Natta et al. (2000).
Slight dierences from the values obtained by other au-
thors are within the uncertainties; they are not signicant
for the purposes of this paper. For HD 34282, we have
adopted the recent estimate of the distance and luminos-
ity of Pietu et al. (2003). HD 35187 is a binary with sepa-
ration of 1.38 00 ; following Dunkin & Crawford (1998), we
have attributed the disk emission to the primary compo-
nent HD 35187B. HD 143006 has no measured Hipparcos
distance; we have adopted the distance of 82 pc estimated
by Sylvester et al. (1996), as well as their spectral type.
Stellar masses and ages are estimated from the location
of the stars on the HR diagram, using Palla & Stahler
(1993) evolutionary tracks. The stars in the sample are
all relatively old objects (>few million years), as expected
given their \isolated" nature. They cover a range of masses
from about 1 to 2.3 solar masses, and luminosities from
0.23 to 42 L .
2.2. VLA observations
New NRAO 1 VLA 7 mm and 3.6 cm observations of
HD 34282, HD 35187, HD 142666, HD 143006, HD 150193,
and HD 163296 (for the latter only 7 mm data was
obtained) were performed on several occasions from
November 2001 to May 2003. The array was mainly
used in the most compact D conguration, oering base-
lines from the shadowing limit to 350 m; the corre-
sponding angular resolution at 7 mm is  2 arcsec.
HD 142666, HD 143006, HD 150193, and HD 163296 were
also observed in the C conguration, with baselines up to
3.4 km and resolution  0:5 arcsec. In both cases the
largest angular scale that can be accurately imaged is
 40 00 . Calibration and editing of the (u; v) data were
performed using standard techniques within the AIPS
package. Images were produced using the AIPS IMAGR
task with natural weighting of the visibilities. The mea-
sured uxes or upper limits are reported in Table 2. For
1 The National Radio Astronomy Observatory is a facility of
the National Science Foundation operated under cooperative
agreement by Associated Universities, Inc.
Table 2. VLA Observation Summary
Star  (J2000) ф (J2000)  F
(mm) (mJy)
HD 34282 05:16:00 09:48:35.4 36 <0.2 a
7 < 1 a
HD 35187 05:24:01 24:57:37.6 36 1.0 0.03
7 1.00.2
HD 142666 15:56:40 22:01:40.0 36 <0.2 a
7 1.70.2
HD 143006 15:58:37 22:57:15.0 36 <0.15 a
7 <0.7 a
HD 150193 16:40:18 23:53:45.2 36 0.20.02
7 0.70.2
HD 163296 17:56:21 21:57:21.9 61 b 0.250.04
36 b 0.420.025
13 b 0.90.25
7 60.5
a ) Upper limits are 3; b ) Data obtained from VLA Archive,
originally observed by Bouwman et al. (2000)
Table 3. PdB Observation Summary
Star  (J2000) ф (J2000)  F
(mm) (mJy)
HD 34282 05:16:00 09:48:35.4 3.2 5.51
1.3 10023
HD 35187 05:24:01 24:57:37.6 3.6 2.50.4
1.3 202
HD 142666 15:56:40 22:01:40.0 3.3 111
3.1 131
1.2 794
HD 143006 15:58:37 22:57:15.0 3.1 4.60.7
1.2 433
HD 163296, there were previous data at centimeter wave-
lengths in the VLA archive (see also Bouwman et al. 2000);
we have re-reduced them with the same procedure used
for our new observations and added the resulting uxes to
Table 2. Flux calibration was performed using standard
techniques at 3.6 and 0.7 cm observing 3C286 and/or 3C48
and deriving the ux density at the time of observations
for the phase calibrators. This procedure is expected to be
accurate within 1% at 3.6 cm and within 15% at 0.7 cm.
2.3. Plateau de Bure observations
Observations of four of our target stars were made simulta-
neously at  3 mm and 1.2 mm using the Plateau de Bure
interferometer 2 on May 18 and 29, 2001 and August 18
and 19, 2001. Visibilities were obtained in the most com-
2 The Plateau de Bure interferometer at IRAM is supported
by INSU/CNRS (France), MPG (Germany) and IGN (Spain).

Natta et al.: VLA survey 3
Table 1. Star and Disk Properties
Star a ST Te L? D M? Age max mm  M 
d
b SD
(K) (L) (pc) (M) (Myr) (mm) (M )
HD 34282 A0 9800 36 400 2.3 3 3.2 3.0 1.3 0.09 1.3
HD 150193 A1 9500 21 160 2.3 6 7.0 4.0 1.6 0.02 1.0
HD 163296 A1 9500 36 122 2.3 5 7.0 2.6 0.8 0.05 1.0
HD 35187 A2 9100 34 150 2.2 5 3.6 2.6 0.7 0.003 1.5
UX Ori A3 8600 42 450 2.2 3 7.0 2.0 0.0 0.03 0.1
HD 142666 A8 7600 8 116 1.6 >10 7.0 2.2 0.4 0.01 0.7
CQ Tau F2 6900 4 100 1.5 > 10 7.0 2.4 0.5 0.02 0.7
HD 143006 G6 5770 0.8 82 1 >10 3.1 2.5 0.8 0.005 1.2
TW Hya K8 4000 0.23 55 0.6 10 7.0 2.3 0.7 0.03 0.7
a Disks resolved at millimeter wavelengths are underlined.
b M 
d =Md  (1mm=0:01).
pact conguration of the 5 antenna array, yielding pro-
jected baselines which range from about 64 m down to the
antenna diameter of 15 m. The largest angular scales that
can be imaged range from 20 00 at 3.5 mm to less than 8 00
at 1.2 mm. The 46 00 (20 00 at 1.2 mm) primary beam eld
of the interferometer was centered at the nominal position
of the each star (see Table 3).
At 1.2 mm, data were taken in double sideband mode,
while at  3 mm observations were made in upper side-
band only (see Table 3 for the tuning frequencies).
Data calibration was performed in the antenna-based
manner. Flux densities were obtained from the visibilities
using standard IRAM tting procedures. The calibration
is expected to have an uncertainty of 15% at 3 mm and
20% at 1.2 mm. All the sources turned out to be unre-
solved; the derived uxes are given in Table 3.
3. Results
Fig. 1 shows the observed uxes as function of wavelength
for each star. PdB and VLA detections are shown as lled
dots; the errors are smaller than the symbol size. Arrows
are 3 upper limits.
We show in Fig. 1 also interferometric data from the
literature, obtained with PdB (Pietu et al. 2003) and
OVRO (Manning & Sargent 1997; 2000), as well as single-
dish uxes measured with the JCMT by Sylvester et
al. (1996) and Mannings (1994). At about 1 mm, where
the two sets of data overlap, the single-dish uxes tend to
be larger than the interferometric ones by factors of or-
der 1.3{1.6, somewhat larger than the calibration errors
(which are of the order of 20%). Note however that this
is not always the case, e.g. HD 34282 where the single-
dish and interferometric uxes agree within the errors. It
is likely that this dierence is caused by calibration uncer-
tainties and by the dierent width of the interferometer
and single-dish bolometer bandpass , but it is also possible
that the interferometers are missing some diuse emission.
We will go back to this point in x3.3.
3.1. Radio uxes and gas emission
The main purpose of our 3.6cm observations was to check
for contamination of the millimeter dust emission by free-
free or non-thermal emission. Three objects in our sample
were not detected at 3.6cm: HD 34282, HD 142666 and
HD 143006; two of these (HD 34282 and HD 143006) were
not detected at 7 mm either. The upper limits shown in
Fig.1 indicate that at millimeter wavelengths there should
be very little contribution from gas emission.
Three objects were detected. HD 35187 is a very strong
radio source; the spectral index between 7 mm and 3.5 cm
is  0. It is possible that we have detected a radio are;
in any case, we have made the conservative assumption
that only a negligible fraction of the observed 7 mm ux
is due to dust, and evaluated the ionized gas contribution
to shorter wavelength as a power-law of slope -0.1 (dashed
line in Fig. 1).
HD 150193 has a rather steep slope between 7 mm and
3.5 cm. We have assumed that the 3.5cm ux is free-free
emission from a wind, for which we expect a spectral slope
of  0:6 (Felli & Panagia 1981). The dashed line in Fig. 1
shows the estimated gas emission; it accounts for  70%
of the observed 7 mm ux.
In the case of HD 163296 there are additional radio ob-
servations at 1.3cm and 6cm (Bouwman et al. 2000). The
three centimeter-wavelength uxes are consistent with
wind emission with slope  0:6 (dashed line in Fig. 1);
the corresponding contribution at 7 mm is negligible.
3.2. Dust emission
Table 1, Column 9 shows the spectral index of the dust
emission mm (F  /  mm ), after subtraction of the free-
free component, measured between 1.3 mm and a maxi-
mum wavelength (either 2.6 or 7.0 mm) given in Column
8. The error on mm is about 0:2 and is dominated by
the systematic uncertainties on the ux scale at dierent
wavelengths and telescopes. In all objects but one mm <  3.
The exception is HD 150193, which has no interferometric

4 Natta et al.: VLA survey
Fig. 1. Observed uxes for the six stars in our sample. Filled dots and arrows show detections and 3 upper limits from
this paper (PdB and VLA); lled squares are interferometric data from Pietu et al.(2003; HD 34282, nearly coincident with
our points) and Mannings and Sargent (1997; HD 150193 and HD 163296), respectively. Open dots are single dish JCM data
(Sylvester et al. 1996 and Mannings 1994). Dashed lines show the adopted t to the centimeter uxes; The solid lines show the
results of disk models, to which we have added the estimated free-free contribution (see text). Dotted lines show disk models
that t the single-dish uxes (rather than the interferometric ones) at   1:3 mm. The corresponding values of , the opacity
power-law exponent, are shown on each panel; the rst value has been derived tting our interferometric data at all wavelengths
( in the text and in Table 2), the second using single-dish data for   1:3 mm (SD in the text and in Table 2). Note that for
HD 163296 the models overpredict the 1.3 cm ux; this happens because we have assumed that the dust opacity is an unbroken
power-law to  = 3 cm, which is likely not the case.

Natta et al.: VLA survey 5
measurement at 1.3 mm; mm is computed between 2.6
and 7 mm, and is therefore much more uncertain than in
the other objects.
3.3. Disk models
Relatively at spectral indices at millimeter wavelengths
can be the signature of optically thin emission from grains
whose opacity has a very shallow dependence on wave-
length, but also of optically thick emission from grains of
any kind. Once all other parameters are xed, it is possible
to obtain shallower and shallower values of mm down to
the limit mm=2 by increasing the disk mass (and there-
fore making the dust emission optically thick). However,
at any given wavelength the corresponding ux will in-
crease to very large values, unless the disk is very small
and highly tilted to the line of sight (see the discussion in
Testi et al. 2001).
A good illustration is the case of UX Ori, which has
the attest spectral index so far (mm=2.030.26; Testi et
al. 2001). The observations could be reproduced by disks
with ISM grains if R d =30 AU, =66 o , M d 2 M . Larger
disks need to be more tilted ( =86 o for R d =100 AU,
for example), obscuring the central star, and even more
massive, well above the limit where disks become unstable
to self-gravity. If the disk is large (say, >100 AU), then
it must be optically thin at millimeter wavelengths; the
observed mm can only be reproduced if the dust opacity
is practically independent of wavelengths.
We have analyzed the stars in this sample following the
same procedure already used for UX Ori and CQ Tau by
Testi et al. (2001). We derive the dust opacity law by com-
paring for each star the observed uxes, corrected for free-
free contamination, to the predictions of self-consistent
disk models. We use the two-layer models of ared disks
(i.e., in hydrostatic equilibrium) heated by stellar irradi-
ation as developed by Dullemond et al. (2001), following
the schematization of Chiang & Goldreich (1997). These
models have been used in the analysis of CQ Tau by Testi
et al. (2003) and we refer to that paper for a more detailed
description.
To characterize completely such a disk model, once the
stellar properties are known, one needs to specify a num-
ber of parameters, namely the inclination  with respect
to the observer ( = 0 for face-on disks), the disk inner
and outer radii (R in and R d ), the disk mass (M d ), the de-
pendence of the surface density on radius ( / R p ), the
properties of dust on the disk surface and in the midplane.
However, millimeter uxes are practically independent of
some of these parameters, for example the disk inner ra-
dius and the surface dust properties. Also, they are in-
sensitive to most details of the adopted radiation transfer
scheme (see Dullemond & Natta 2003).
For each star we have computed a large grid of mod-
els, varying R d , M d , p,  and the dust opacity in the mid-
plane, described by a power-law  = 1mm (=1mm) 
with 1mm=0.01 cm 2 g 1 as a ducial value (which in-
cludes the gas contribution to the total mass for a gas-to-
dust mass ratio 100). R in is xed at the dust sublimation
radius; for the properties of the dust on the disk surface
we have adopted the same model as Testi et al. (2003);
neither of these model parameters is constrained by our
data, nor do these choices aect the interpretation of the
millimeter spectra.
For two of the stars in the sample, the millimeter obser-
vations resolve the disk emission and provide lower limits
on R d . HD 34282 has been resolved at 1.3 mm by Pietu
et al. (2003), who measure a deconvolved FWHM size
of 1:74  0:07 00  0:89  0:06 00 and derive an inclination
of 56  3deg. Note that the uxes measured by Pietu et
al. (2003) agree with our measurements to within the er-
rors. Since the deconvolved FWHM size is a lower limit
to the physical size (Dutrey et al. 1996; Pietu et al. 2003;
Testi et al. 2003), at a distance of 400 pc, the outer disk
radius must be R d > 350 AU. With this lower limit to
R d and the observed , our models t the observed uxes
only if the disk is optically thin at millimeter wavelengths.
Thus, the only quantities that one can derive from the
data are  and the disk mass for the ducial value of 1mm ,
that we will call M 
d =M d  ( 1mm =0:01). The results are
  0:7 and M 
d  0:1 M , respectively. The uncertainties
are typically about 0:1 for beta and a factor of 2 for M 
d
(for p = 1 2), as discussed in Testi et al. (2003). They
are due to the fact that the surface density prole is not
well constrained by the data, and it is possible to repro-
duce the same intensity map with dierent values of p by
changing R d (the larger R d , the steeper the density prole
one needs). Note that for HD 34282 the value of  would
be the same if the distance were D=160 pc, as measured
by Hipparcos, but the disk mass would be reduced by a
factor 6.
HD 163296 is partially resolved in 1.3 mm continuum
emission by Mannings & Sargent (1997), who measure a
deconvolved FWHM size of 11095 AU; in the CO (2-1)
line the disk size is 310160 AU. Our 7 mm observations
with the VLA in C conguration indicate that the emis-
sion is resolved with deconvolved size about 300180 AU
and inclination 55 ф (Testi et al. 2004). As soon as R d >  100
AU, the millimeter emission is optically thin with   0:8
and M 
d 0.05 M .
To the best of our knowledge, none of the other disks
have been resolved at any wavelength, and we have no in-
dication of the disk outer radius. However, we consider it
unlikely that they are all very small, massive disks, seen
almost edge-on, as one would require to reproduce the ob-
servations if the grains are as in the ISM. We have there-
fore proceeded assuming R d >100 AU and allowing the
other disk parameters to vary, including the dust opacity.
The resulting values of  and M 
d are shown in Table 1,
Column 9 and 10, respectively. Note that a small, trun-
cated disk may be more likely in HD 35187, which is a
binary with separation of 200 AU. Still, a disk with R d 
70 AU (i.e., 1/3 the separation) reproduces the observed
uxes only if it is optically thin.

6 Natta et al.: VLA survey
The unresolved uxes analyzed here do not constrain
the value of p, since it is generally possible to t the SED
data with either very at (p = 0:5) or very steep (p = 2)
surface density proles. Increasing p increases the contri-
bution to the millimeter uxes of the inner, optically thick
disk, whose emission does not depend on , and we may
wonder how much mass can be "hidden" in this region.
However, we nd that M 
d is a rather good estimate of the
total mass of the grains that contribute to the millimeter-
wavelength opacity. It should be noted however, that all
available high angular resolution observations suggest that
p  1:5 (Dutrey et al. 1996; Wilner et al. 2000; Kitamura
et al. 2002; Testi et al. 2003). Typically, in disks with at
surface density prole (p <  1:5), the inner, optically thick
(at 1.2 mm) part of the disk contains only about 10% of
the total mass.
One nal potential source of uncertainties on our es-
timates of  stems from the characteristics of the in-
terferometers themselves, which lter out any emission
more extended than the largest angular scale mentioned in
Sect. 2.2; in particular, at 1.2 mm, this eect could be im-
portant. To estimate the eect of this potential problem,
we have computed values of  ( SD ) tting the single-dish
uxes at   1:3 mm and the longer wavelength inter-
ferometric points (Column 11). This combination gives a
steeper spectral slope, and a correspondingly higher value
of . This value is likely to be largely overestimated. In
fact, if there is a diuse overlying emission component,
this should also be present at longer wavelengths, and by
combining in this way single-dish and interferometer data
we are biasing our results toward steeper spectral slopes.
Additionally, if diuse emission is indeed present, it is un-
likely to come from the disk itself, so that we should in
any case exclude it when tting disk models to the data.
In spite of these considerations, one shoud keep in mind
the possibility that the interferometric uxes are some-
what underestimated, and the values of SD provide a
rough estimate of the observational uncertainties in the
derivation of .
4. Discussion
The results of our analysis are summarized in Table 1. To
the six stars in our sample, we have added UX Ori and
CQ Tau (data from Testi et al. 2001, 2003 and references
therein) and TW Hya (data from Weintraub et al. 1989,
Wilner et al. 2000,2003 and references therein), and we
have reanalyzed them again in the same manner for ho-
mogeneity. The objects that have been spatially resolved
are underlined. In all the objects the values of  are well
below 2, which is the typical wavelength dependence of the
opacity of small ISM grains. This is true also if we con-
sider the upper limits SD . For the four resolved systems,
the disk sizes are such that optically thick emission is not
a viable possibility (see x3.2 and Testi et al. 2001, 2003,
Calvet et al. 2002). There is no doubt that in these objects
the grains have been hugely processed. The remaining ve
systems have not been resolved; however, as discussed in
x3.2, although the values of  we derive for these objects
are more uncertain (because the observations do not ex-
clude an optically thick contribution to the emission), it
is very unlikely that all of these stars have very compact
disks with unprocessed ISM grains.
Once we have established that the grains originally
present in the disk have undergone a large degree of pro-
cessing, can we make the next step and derive the prop-
erties that characterize the actual grain population, for
example the maximum grain size? This is not straightfor-
ward when considering the complexity added by a wide
distribution of grain sizes and composition, as we will now
illustrate.
Let us consider a population of grains with a power-
law size distribution n(a) / a q between a minimum
and a maximum size, amin and amax , respectively. In the
ISM, amin is few tens of  A, amax is  0:1 0:2 m,
and q = 3:5. These values will change if grains are pro-
cessed in disks, and one can expect much larger values of
amin , amax , and a variety of values of q. Small values of q
are expected when coagulation processes dominate, while
large values of q characterize fragmentation (see, for ex-
ample, Weidenschilling 1997). For a given dust model, i.e.,
once the chemical structure, composition, porosity etc. are
specied, one can compute the opacity for dierent values
of amin , amax and q. We choose for our discussion porous
composite grains with 50% vacuum and state-of-the-art
cross sections, as detailed in the caption of Fig. 2. The top
panel shows the average dust opacity at 1 mm as function
of amax for various values of q; the bottom panel the cor-
responding values of . The results do not depend on amin
as long as it is  .
The value of  that characterizes the average opac-
ity of a grain distribution decreases as amax increases,
as expected since grains with size   have wavelength-
independent opacity. However, only for q < 3,  goes to
zero for large amax ; for q > 3, the small grains always
contribute to the opacity, so that, as amax increases, 
reaches an asymptotic values that depends on q and on
the  of the small grains. For q=4, the asymptotic value
is practically that of the small grains.
Three objects in our sample (CQ Tau, TW Hya, HD
142666) have   0:5 0:7. This is consistent with q  2:5
and amax  80 cm; a distribution with q = 3:3 has an
asymptotic value =0.5, and it is consistent with the ob-
servations as soon as amax> 300 cm. In both cases the
1 mm opacity is much lower than our ducial value, and
the estimates of the disk mass needs to be raised by a
factor > 40 for q = 3:3 and about 15 for q = 2:5. The
corresponding disk masses are high (>0.3, 0.9, 0.3 M ,
respectively); however, only in the case of TW Hya they
violate the requirement that the disks must be gravita-
tionally stable, i.e., M d /M ? <  30%. Objects like HD 163296
have 0.8{1; they are consistent with q = 2:5, amax
10 cm, that would results in a disk mass 0.3 M , or with
any steeper size distribution with larger amax . A distribu-
tion with q = 3:6 has an asymptotic value   1 for amax
>  150 cm, the corresponding disk mass would be >0.5 M .

Natta et al.: VLA survey 7
Fig. 2. Top Panel: dust opacity at 1 mm as function of amax
for a size distribution n(a) / a q between amin=0.01m and
amax . Dierent curves are for dierent values of q, as la-
belled. The grains are porous conglomerates of 5% (in vol-
ume) olivine ([Fe0:3 Mg0:7 ] 2 SiO4 ), 15% organic materials, 35%
water ice and 50% vacuum; see http : ==www:astro:uni
jena:de=Users=dima=Opacities=RI=new ri:html for the cross
sections of the individual components. Cross sections of the
porous conglomerates have been computed as in Krugel and
Siebenmorgen 1994. Bottom Panel:  between 1 mm and 7 mm
as function of amax for the same grain distributions.
Very steep size distributions, such as q = 4, never t the
observations.
The most extreme case in our sample, UX Ori (for
which, however, there is no spatially-resolved disk image)
has   0. If the disk is optically thin, this would require
at grain size distributions and very large amax ; for ex-
ample,  = 0:2 corresponds to q = 2:5, amax 10 3 cm.
For such grain size distribution, however, the disk mass
becomes  4 M , i.e., M ?
These results depend on the dust model one adopts.
For example, if the fraction of vacuum in the same grain
model of Fig. 2 is reduced from 50% to 10%, the value of
amax which reproduces the observations is reduced by a
factor  3 8 and M d by a factor 2 3 (q  3:3). Grains of
the same size and composition, but dierent structure and
topology (homogeneous, composite aggregates, porous ho-
mogeneous or composite spherical particles, onion-shells
particles, etc.) can have dierent values of  and  1mm
(see, for example, Miyake and Nakagawa 1993, Krugel and
Siebenmorgen 1994, Semenov et al. 2003 and the Jena web
page), leading to rather dierent estimates of amax and of
the disk mass. Just to mention two examples of how all this
aects the interpretation of the data, Testi et al. (2001),
tted the same UX Ori spectrum discussed above with
ice-coated silicates of about 10 cm radius and a disk mass
in the range 0.3{1 M , depending on the grain density.
Calvet et al. (2002) obtained a good t to the millimeter
properties of TW Hya for q = 3:5, amax  1 cm and M d
0.1 M , using the dust model of Pollack et al. (1994)
of compact segregate spheres where the relative fraction
of water ice to organic materials was somewhat decreased
(P. D'Alessio, private communication).
All this shows that it is not possible to disentangle from
the value of , which is just an average quantity, all the
details that specify a given dust model. However, there are
some basic grain properties that are constrained, since no
realistic grain model results in < 1 for amax< 1 mm. In
fact, for most known grain mixtures, our observations are
consistent with power-law grain size distributions where
amax is few ten to few hundred centimeters.
To account for the observed uxes, the amount of mass
in these grains has to be very large, implying that, at least
when gas was present in the standard ISM ratio, the disk
was close or above the limit for gravitational instability.
Note that we have converted the solid mass into gas+dust
mass assuming a gas-to-dust ratio of 100. This conversion
factor may not be appropriate for the present-time disk,
if a signicant fraction of the gas has evaporated from the
system. Still, it provides a correct estimate of the original
disk mass, when the disk composition re ected that of the
parent cloud. It is interesting that the value of M 
d of our
sample stars is similar to what is found for all the other
pre-main{sequence stars studied so far (see Fig. 3). One
wonders in how many cases the disk masses are underes-
timated by using  1mm = 0:01 cm 2 g 1 .
Our data do not rule out the possibility that a non-
negligible fraction of the original solid mass is in even
larger bodies (km-size), from which planets can be formed.
However, it seems unlikely that these could contain most
of the solid mass, and that the millimeter-emitting grains
were just the tail of the size distribution. If, for example,
99% of the solid mass is in kilometer-size bodies, whose
contribution to the millimeter opacity is negligible, their
mass should be added to the values we have derived, mak-
ing the disk mass 100 times larger.
An implicit assumption we have made so far is
that the grain size distribution is continuous be-
tween amin and amax . Models of planetesimal formation
(Weidenschilling 1997) show the developement of a gap in
the size distribution between a 1  few centimeters and
a 2  few meters, which tends to ll-in with time. In this
case, one should compare amax with a 1 , and our results
are consistent with these model predictions. Still, as we
have seen, it is unlikely that most of the dust mass is on
sizes  a 2 , i.e., in bona-de planetesimals , since the solid
mass with sizes < a 1 is already very large (see Testi et
al. 2003 for a more detailed discussion of this point). This
is an interesting point, especially because all the stars in
the sample are relatively old, >  few million years, and in
some case >  10 million years. Most models of grain evo-
lution have a very short timescale for the formation of

8 Natta et al.: VLA survey
Fig. 3. Ratio of the disk to the stellar mass as function of
M?for a large sample of pre-main{sequence stars (adapted from
Natta et al. 2000). Crosses are detections, upper limits are
indicated with arrows The objects studied in this paper are
marked as circles; the four resolved ones are indicated with
lled circles. All the disk masses have been computed for an
opacity 1mm = 0:01 cm 2 g 1 . The dotted line corresponds to
Md  (1mm=0:01)/M?=0.3.
planetesimals (e.g., Weidenschilling 2000 and references
therein). One possibility is that the growth of kilometer-
size bodies is in fact very ineфcient, either because it is
much slower than predicted or because it involves only a
small fraction of the dust. Another intriguing possibility is
that the formation of planetesimals takes place in a very
early stage of the star formation, in very massive disks
which are gravitationally unstable. However, a discussion
of these points is well behond the scope of this paper.
5. Conclusions
This paper presents the results of a study of six pre-main{
sequence, isolated, intermediate mass stars, performed
with the PdB (at 1.3 and 2.6 mm) and VLA (at 7 mm
and 3.6 cm) interferometers. All the stars were selected to
have indications of at spectral indexes from previous mil-
limeter and submillimeter data. Our measurements con-
rm this indication, and extend our knowledge of the dust
emission continuum down to 7 mm. In all the objects mm
<  3 for wavelengths between  1 mm and 2.6 mm, and in
3 cases between  1 mm and 7 mm.
We have added to these six stars two others (UX Ori
and CQ Tau), previously studied in the same way by our
group (Testi et al. 2001,2003) and TW Hya, for which
similar data exist in the literature (Calvet et al. 2002 and
references therein).
The observations have been compared to the predic-
tions of self-consistent irradiated disk models to derive the
properties of the millimeter-emitting dust. As discussed
by various authors, this cannot be done unambiguously
if only the SED is known. To solve the ambiguity intro-
duced by optical depth eects, one needs to spatially re-
solve the emission at some millimeter wavelength, or, at
least, to have an estimate of the FWHM size. This addi-
tional information is available for two stars in our sample
(HD34282 and HD 163296), and for CQ Tau and TW Hya.
For these objects, there is no doubt that grains in disks
are heavily processed, causing a net growth, to maximum
sizes that are certainly larger than few millimeters and,
for the majority of grain models available in the litera-
ture, of at least few centimeters. The mass of the grains
that have been thus processed is very large, in some cases
comparable to the mass of the central star. Many grain
size distributions are consistent with the data, but not
very steep ones, (q >  4), unless micron-size grains have 
<  0.5{1.
The uncertainty on amax and q re ects our ignorance
on the details of the grain chemistry, structure and topol-
ogy. However, in spite of these uncertainties, we are de-
veloping a view of the outer disks of pre-main-sequence
stars as made of a huge mass of sand and pebbles, rather
than of micron-size grains. Grain growth models can and
should be tested against these observations.
Acknowledgements. We thank Endrik Krugel for having pro-
vided to us his codes to compute the dust opacity and for
very useful discussions on dust properties. Nuria Calvet and
Lee Hartmann for interesting comments and discussions. This
work was partly supported by ASI grant ARS 1/R/27/00 and
ARS-1/R/073/01 to the Osservatorio di Arcetri.
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