On the Transitional Disk Class: Linking Observations of T Tauri Stars & Physical Disk Models

Abstract

Two decades ago "transitional disks" described spectral energy distributions
(SEDs) of T Tauri stars with small near-IR excesses, but significant mid- and
far-IR excesses. Many inferred this indicated dust-free holes in disks,
possibly cleared by planets. Recently, this term has been applied disparately
to objects whose Spitzer SEDs diverge from the expectations for a typical full
disk. Here we use irradiated accretion disk models to fit the SEDs of 15 such
disks in NGC 2068 and IC 348. One group has a "dip" in infrared emission while
the others' continuum emission decreases steadily at all wavelengths. We find
that the former have an inner disk hole or gap at intermediate radii in the
disk and we call these objects "transitional" and pre-transitional" disks,
respectively. For the latter group, we can fit these SEDs with full disk models
and find that millimeter data are necessary to break the degeneracy between
dust settling and disk mass. We suggest the term "transitional" only be applied
to objects that display evidence for a radical change in the disk's radial
structure. Using this definition, we find that transitional and
pre-transitional disks tend to have lower mass accretion rates than full disks
and that transitional disks have lower accretion rates than pre-transitional
disks. These reduced accretion rates onto the star could be linked to forming
planets. Future observations of transitional and pre-transitional disks will
allow us to better quantify the signatures of planet formation in young disks.

Full text

Page 1

arXiv:1201.1518v1 [astro-ph.SR] 6 Jan 2012
Draft version January 10, 2012
Preprint typeset using LATEX style emulateapj v. 5/2/11
ON THE TRANSITIONAL DISK CLASS: LINKING OBSERVATIONS OF T TAURI STARS & PHYSICAL DISK
MODELS
C. Espaillat1,2, L. Ingleby3, J. Hern´ andez4, E. Furlan5,6, P. D’Alessio7, N. Calvet3, S. Andrews1, J. Muzerolle8,
C. Qi1, & D. Wilner1
Draft version January 10, 2012
ABSTRACT
Two decades ago “transitional disks” described spectral energy distributions (SEDs) of T Tauri stars
with small near-IR excesses, but significant mid- and far-IR excesses. Many inferred this indicated
dust-free holes in disks, possibly cleared by planets. Recently, this term has been applied disparately
to objects whose Spitzer SEDs diverge from the expectations for a typical full disk. Here we use
irradiated accretion disk models to fit the SEDs of 15 such disks in NGC 2068 and IC 348. One
group has a “dip” in infrared emission while the others’ continuum emission decreases steadily at all
wavelengths. We find that the former have an inner disk hole or gap at intermediate radii in the
disk and we call these objects “transitional” and “pre-transitional” disks, respectively. For the latter
group, we can fit these SEDs with full disk models and find that millimeter data are necessary to
break the degeneracy between dust settling and disk mass. We suggest the term “transitional” only
be applied to objects that display evidence for a radical change in the disk’s radial structure. Using
this definition, we find that transitional and pre-transitional disks tend to have lower mass accretion
rates than full disks and that transitional disks have lower accretion rates than pre-transitional disks.
These reduced accretion rates onto the star could be linked to forming planets. Future observations
of transitional and pre-transitional disks will allow us to better quantify the signatures of planet
formation in young disks.
Subject headings: accretion disks, stars: circumstellar matter, planetary systems: protoplanetary disks,
stars: formation, stars: pre-main sequence
1. INTRODUCTION
Disks around T Tauri stars (TTS) are thought to be
the sites of planet formation. However, many questions
exist concerning how the gas and dust in the disk evolve
into a planetary system and observations of TTS may
provide clues. There are some objects in particular that
have gained increasing attention in this regard. Over
two decades ago, Strom et al. (1989) detected “possible
evidence of changes in disk structure with time” as evi-
denced by “small near-IR excesses, but significant mid-
and far-IR excesses” indicating “inner holes” in disks.
Those authors proposed that these objects were “in tran-
sition from massive, optically thick structures that ex-
tend inward to the stellar surface, to low-mass, tenuous,
perhaps post-planet-building structures.”
1NSF Astronomy & Astrophysics Postdoctoral Fellow
2Harvard-SmithsonianCenter
GardenStreet, MS-78,
cespaillat@cfa.harvard.edu,
cqi@cfa.harvard.edu, dwilner@cfa.harvard.edu
3Department of Astronomy, University of Michigan, 830
Dennison Building, 500 Church Street, Ann Arbor, MI 48109,
USA; lingleby@umich.edu, ncalvet@umich.edu
4Centro de Investigaciones de Astronom´ ıa (CIDA), Merida,
5101-A, Venezuela; jesush@cida.ve
5Visitor at the Infrared Processing and Analysis Center, Cal-
ifornia Institute of Technology, 770 S. Wilson Ave., Pasadena,
CA 91125, USA
6National Optical Astronomy Observatory, 950 N. Cherry
Ave., Tucson, AZ 85719, USA; Elise.Furlan@jpl.nasa.gov
7Centro de Radioastronom´ ıa y Astrof´ ısica,
Nacional Aut´ onoma de M´ exico, 58089 Morelia, Michoac´ an,
M´ exico; p.dalessio@crya.unam.mx
8Space Telescope Institute, 3700 San Martin Drive, Balti-
more, MD 21218, USA; muzerol@stsci.edu
forAstrophysics,
MA,02138,
sandrews@cfa.harvard.edu,
60
Cambridge,USA;
Universidad
Usage of the term “transitional disk” gained sub-
stantial momentum in the literature after it was used
by Calvet et al. (2005b) to describe disks with in-
ner holes using data from the Spitzer Space Tele-
scope’s (Werner et al. 2004) Infrared Spectrograph (IRS;
Houck et al. 2004). Before Spitzer, the spectral en-
ergy distributions (SEDs) used to identify disks with
inner holes were based solely on near-infrared (NIR)
ground-based photometry and IRAS mid-IR (MIR)
photometry (Strom et al. 1989; Skrutskie et al. 1990).
Spitzer allowed the opportunity to study these objects
in greater detail. The unprecedented resolution and
simultaneous wavelength coverage (∼5 and 38 µm) of
Spitzer IRS uncovered new details regarding these disks
(D’Alessio et al. 2005; Calvet et al. 2005b; Furlan et al.
2006).Some SEDs had nearly photospheric NIR (1–
5 µm) and MIR (5–20 µm) emission, coupled with sub-
stantial emission above the stellar photosphere at wave-
lengths beyond ∼20 µm.Others had significant NIR
excesses relative to their stellar photospheres, but still
exhibited MIR dips and substantial excesses beyond
∼20 µm.
Detailed modeling of many of the above-mentioned
SEDs has been performed. SEDs of disks with little or
no NIR and MIR emission have been fit with models
of inwardly truncated optically thick disks (Calvet et al.
2002, 2005b; Espaillat et al. 2007b, 2008b). The inner
edge or “wall” of the outer disk is frontally illuminated
by the star, dominating most of the emission seen in the
IRS spectrum. In this paper, we refer to these objects
with holes in their dust distribution as transitional disks
(TD). Some of the holes in TD are relatively dust-free
(e.g. DM Tau; Calvet et al. 2005b; Espaillat et al. 2010)

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2Espaillat et al.
while SED model fitting indicates that others with strong
10µm silicate emission have a small amount of optically
thin dust in their disk holes to explain this feature (e.g.
GM Aur; Calvet et al. 2005b; Espaillat et al. 2010). For
SEDs with substantial NIR emission accompanied by a
MIR dip, we can fit the observed SED with an optically
thick inner disk separated by an optically thin gap from
an optically thick outer disk (Espaillat et al. 2007a).
Here we call these pre-transitional disks (PTD). Like the
TD, we see evidence for relatively dust-free gaps (e.g. UX
Tau A; Espaillat et al. 2007a, 2010) as well as gaps with
some small, optically thin dust to explain strong 10µm
silicate emission features (e.g. LkCa 15; Espaillat et al.
2007a, 2010). For many TDs and PTDs, the trunca-
tion of the outer disk has been confirmed with sub-
millimeter and millimeter interferometric imaging (e.g.
DM Tau, GM Aur, UX Tau A, LkCa 15; Hughes et al.
2007, 2009; Andrews et al. 2009, 2010, 2011) as well as
NIR imaging (i.e. LkCa 15; Thalmann et al. 2010). In
a few cases, the optically thick inner disk of PTD has
been confirmed using the “veiling9” of near-infrared spec-
tra (Espaillat et al. 2008a, 2010) and near-infrared in-
terferometry has confirmed that the inner disk is small
(Pott et al. 2010; Olofsson et al. 2011).
The distinct SEDs of TD and PTD most likely signify
that these objects are being caught in an important phase
in disk evolution. Many researchers have posited that
these disks are forming planets on the basis that cleared
dust regions are predicted by planet formation mod-
els (e.g. Paardekooper & Mellema 2004; Zhu et al. 2011;
Dodson-Robinson & Salyk 2011). Recently, a potential
protoplanet has been reported in the pre-transitionaldisk
around LkCa 15 (Kraus et al. 2011) as well as around
T Cha (Hu´ elamo et al. 2011). Stellar companions can
also clear the inner disk (Artymowicz & Lubow 1994)
but many stars harboring transitional disks are single
stars (Kraus et al. 2011). Even in cases where stellar-
mass companions have not been ruled out, the large holes
and gaps observed are most likely evidence of dynamical
clearing. Photoevaporation cannot explain disks with
large cavities and high mass accretion rates (Owen et al.
2011) and dust evolution alone can not explain the sharp
decreases in surface density seen in the SED and inter-
ferometric visibilities.
Given the potential link between disks with gaps and
holes and planet formation, interest in transitional disks
has grown. Some studies have focused on further un-
derstanding the behavior of the currently known mem-
bers in this class of objects and have discovered IR vari-
ability (Muzerolle et al. 2010; Espaillat et al. 2011, E11).
Other studies have taken a broader approach, working
towards expanding the known number of disks undergo-
ing clearing (e.g. Lada et al. 2006; Hern´ andez et al. 2007;
Cieza et al. 2010; Muzerolle et al. 2010; Luhman et al.
2010; Mer´ ın et al. 2010; Currie & Sicilia-Aguilar 2011).
As the literature on Spitzer observations of TTS ex-
pands, so does the terminology applied to disks around
9
“Veiling” occurs when an excess continuum (Hartigan et al.
1989) “fills in” absorption lines, causing them to appear signifi-
cantly weaker than the spectrum of a standard star of the same
spectral type (Hartigan et al. 1989). The veiling observed in pre-
transitional disks is similar to that observed in full disks where the
veiling has been explained by emission from the inner disk edge or
“wall” of an optically thick disk (Muzerolle et al. 2003).
TTS. These disks are referred to as primordial, full,
transitional, pre-transitional, kink, cold, anemic, ho-
mologously depleted, classical transitional, weak ex-
cess, warm excess, and evolved.
terms are not applied consistently. The issue is high-
lighted with the discrepancies in the reported frac-
tions of transitional disks and disk clearing timescales
(Mer´ ın et al. 2010; Luhman et al. 2010; Muzerolle et al.
2010; Currie & Sicilia-Aguilar 2011; Hern´ andez et al.
2010). In many cases, the data is the same; the dif-
ferences arise from nomenclature.
If the goal is to better understand disk evolution, it
is important to look past the nomenclature and deci-
pher the underlying disk structure we can infer from the
observations, while paying special attention to the lim-
itations of both the observations and the tools we use
to interpret them, namely disk models.
we chose a sample for our study which incorporated ob-
jects whose SEDs are similar to those that have been
referred to as “transitional” in the literature. We fo-
cus on 15 disks in NGC 2068 and IC 348 with Spitzer
IRS spectra. NGC 2068 and IC 348 are older (∼2 Myr
and ∼3 Myr, respectively; Flaherty & Muzerolle 2008;
Luhman et al. 2003) and more clustered star-forming re-
gions with higher extinction than Taurus, where most
detailed studies of transitional disks have focused. Ac-
cording to our definitions stated above, our sample con-
tains five TD, five PTD, and five objects with decreas-
ing emission at all IR wavelengths (i.e. negative MIR
slopes) which we classify as full disks. Out of the ob-
jects reported by Muzerolle et al. (2010), this includes 5
of the 15 transitional and pre-transitional disks in IC 348
and 4 of the 6 transitional and pre-transitional disks in
NGC 2068. One of the objects classified as a full disk in
that work is classified as a PTD here.
In Section 2, we present optical photometry and spec-
troscopy, infrared spectra, and millimeter flux densities
that we used to compile SEDs for our objects, derive
stellar properties, and measure mass accretion rates. In
Section 3, we fit the SEDs of our objects with irradiated
accretion disk models and in Section 4 we discuss the
limitations of the models and the observations, disk se-
mantics, and the mass accretion rates of transitional and
pre-transitional disks.
However, these
To this end,
2. OBSERVATIONS & DATA REDUCTION
Before conducting modeling, we first compiled SEDs
and mass accretion rates for the targets in our sample
(Table 1). To supplement the existing information in the
literature, we collected optical photometry for all of our
IC 348 objects, optical spectra for three of the IC 348
targets and all of our NGC 2068 targets, and millimeter
flux densities for two of our IC 348 targets. We also
present infrared spectra for all the targets in this paper.
Below we discuss the details of the observations and data
reduction.
2.1. Optical Photometry
During November 19–23, 2011 we used the 4K CCD
imager on the 1.3-m McGraw-Hill telescope10of the
MDM Observatory to obtain UVRI photometry of the
IC348 stellar cluster.The FOV of the instrument is
10http://www.astronomy.ohio-state.edu/∼ jdeast/4k/

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The Transitional Disk Class3
21′×21′(0.315′′per unbinned pixel). For these obser-
vations, we used 2×2 binning (0.62′′per pixel).
flat-field, overscan, and astrometric calibration were per-
formed using an IDL program written by Jason East-
man11specifically designed for the 4K CCD imager.
Since large electronic structures are not stable enough
to be reliably subtracted, we did not apply corrections
using two dimensional biases. The photometric calibra-
tion of all images was carried out using the standard pro-
cedure and the daophot and photcal packages in IRAF,
with standard stars selected from Landolt (1992). Pho-
tometry is presented in Table 2.
The
2.2. Optical Spectroscopy
In order to obtain mass accretion rate estimates (Sec-
tion 3.1.1 and Figure 1), we collected MIKE double-
echelle spectrograph (Bernstein et al. 2003) data on the
6.5m Magellan Clay telescope for all of our targets in
NGC 2068 (FM 177, FM 281, FM 515, FM 581, and
FM 618) and some of our objects in IC 348 (LRLL 21,
LRLL 67, and LRLL 72).
NGC 2068 and IC 348 objects were taken on February
10-11, 2007 and January 19, 2009, respectively. We used
a slit size of 0.7′′×5.0′′and 2×2 pixel on-chip binning
with exposure times of 800-1200s. Data were reduced
using the MIKE data reduction pipeline.12
The observations for the
2.3. Infrared Spectroscopy
Here we present Spitzer IRS spectra for each of our tar-
gets. Spectra for NGC 2068 and IC 348 were obtained
in Program 58 (PI: Rieke) and Program 2 (PI: Houck),
respectively.All of the observations were performed
in staring mode using the IRS low-resolution modules,
Short-Low (SL) and Long-Low (LL), which span wave-
lengths from 5–14 µm and 14-38 µm, respectively, with
a resolution λ/δλ ∼90.
Details on the observational techniques and general
data reduction steps can be found in Furlan et al. (2006)
and Watson et al. (2009). We provide a brief summary.
Each object was observed twice along the slit, at a third
of the slit length from the top and bottom edges of the
slit. Basic calibrated data (BCD) with pipeline version
S18.7 were obtained from the Spitzer Science Center.
With the BCDs, we extracted and calibrated the spectra
using the SMART package (Higdon et al. 2004).
and rogue pixels were corrected by interpolating from
neighboring pixels.
Most of the data were sky subtracted using optimal ex-
traction (Lebouteiller et al. 2010). The exceptions were
LRLL 37, LRLL 55, and LRLL 68. In LRLL 37, there
was an artificial structure in the 5–8 µm region which
was removed by performing off-nod sky subtraction. A
similar structure was seen in LRLL 55 and LRLL 68, but
due to the high background in the area, optimal extrac-
tion was necessary for the LL order. Therefore, the final
spectra for LRLL 55 and LRLL 68 are a combination of
the off-nod sky-subtracted SL spectra and the optimally
extracted LL spectra.
To flux calibrate the observations we used a spectrum
of α Lac (A1 V). We performed a nod-by-nod division of
Bad
11
http://www.astronomy.ohio-state.edu/∼jdeast/4k
/proc4k.pro
12http://web.mit.edu/∼burles/www/MIKE/
the target spectra and the α Lac spectrum and then mul-
tiplied the result by a template spectrum (Cohen et al.
2003). The final spectrum was produced by averagingthe
calibrated spectra from the two nods. Our spectropho-
tometric accuracy is 2–5% estimated from half the dif-
ference between the nodded observations, which is con-
firmed by comparison with IRAC and MIPS photometry.
We note that there are artifacts in the spectra of LRLL 68
and LRLL 133 beyond ∼30 µm. For clarity, we manually
trim the spectra to exclude these regions. The final spec-
tra used in this study are shown in Figures 2, 3, and 4.
2.4. Millimeter Flux Densities
We observed LRLL 21, LRLL 31, LRLL 67, LRLL 68,
and LRLL 72 in IC 348 with the Submillimeter Array
(SMA) on November 12, 2008. We used the Compact
Configuration with six of the 6 meter diameter anten-
nas at 345 GHz (860 µm) with a full correlator band-
width of 2 GHz. Calibration of the visibility phases
and amplitudes was achieved with observations of the
quasars 3C 111 and 3C 84, typically at intervals of 20
minutes. Observations of Uranus provided the absolute
scale for the flux density calibration.
calibrated using the MIR software package.13
tected LRLL 31 and LRLL 67 with flux densities of
0.062±0.006Jy and 0.025±0.011Jy, respectively. We did
not detect LRLL 21, LRLL 68, or LRLL 72 and measure
a 3σ upper limit of 0.015 Jy for these objects.
The data were
We de-
3. ANALYSIS
Here we model the SEDs of the targets in our sample.
First we collect the stellar properties of our objects, ei-
ther by adopting literature values or deriving our own in
Section 3.1. These stellar properties are important input
parameters for our physically motivated models which
we discuss in Section 3.2. In Section 3.3 we discuss the
results of our SED model fitting, as well as the degenera-
cies that exist given that we lack millimeter observations
for many of our targets.
3.1. Stellar Properties
Stellar parameters are listed in Table 3. M∗ was de-
rived from the HR diagram and the Siess et al. (2000)
evolutionary tracks using T∗ and L∗.
peratures are from Kenyon & Hartmann (1995), based
upon the spectral types adopted for the targets in
NGC 2068 and IC 348 (Flaherty & Muzerolle 2008;
Luhman et al. 2003, respectively).
calculated with dereddened J-band photometry follow-
ing Kenyon & Hartmann (1995) assuming a distance of
400 pc for NGC 2068 (Flaherty & Muzerolle 2008) and
315 pc for IC 348 (Luhman et al. 2003). R∗is calculated
using the derived luminosity and adopted temperature.
The derivation of the mass accretion rates and accretion
luminosities are discussed in Section 3.1.1.
All photometry for our NGC 2068 objects is taken
from Flaherty & Muzerolle (2008). This includes BVRI,
2MASS JHK, IRAC, and MIPS data.
Flaherty & Muzerolle (2008) present photometry from
the SDSS survey, which we convert to Johnson-Cousins
BVRI following Jordi et al. (2006).
Stellar tem-
Luminosities are
We note that
IRAC and MIPS
13http://www.cfa.harvard.edu/∼cqi/mircook.html

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4Espaillat et al.
photometry for IC 348 comes from Lada et al. (2006)
and 2MASS JHK data is from Skrutskie et al. (2006).
UBVRI photometry for our IC 348 targets comes mainly
from this work, but is supplemented by values in the lit-
erature. All UBVRI photometry for LRLL 31, LRLL 55,
LRLL 67, LRLL 68, LRLL 72, and LRLL 133 are solely
from this work. UVR data for LRLL 21 and LRLL 37
are from this work, but we use I-band magnitudes from
Luhman et al. (2003) for both and a B-band magnitude
for LRLL 21 from Herbig (1998). We use R and I data
from Herbig (1998) for LRLL 2. BVRI data for LRLL 6
is also from Herbig (1998). All L-band magnitudes are
from Haisch et al. (2001).
Extinctions were measured by comparing V-R, V-
I, R-I, and I-J colors to photospheric colors from
Kenyon & Hartmann (1995). We used the Mathis (1990)
extinction law for objects with AV< 3. For AV≥ 3, we
use the McClure (2009) extinction law. We adopt RV=5
which is more appropriate for the denser regions stud-
ied here (Mathis 1990). In most cases, extinctions based
on I-J colors gave the best fit. Since we have no I-band
data for FM 581 we adopt an extinction based on V-R;
LRLL 2 and LRLL 6 have no VRI photometry in the
literature and so we adopt the extinction measured by
Luhman et al. (2003). All extinctions used in this work
are listed in Table 3. We note that most of our extinc-
tions are similar to those in the literature (Luhman et al.
2003; Flaherty & Muzerolle 2008).
found differences, we chose to rely on our measurements
since they are based on I-J colors which have recently
been shown to be the least affected by excess emission
at shorter wavelengths (Fischer et al. 2011, McClure et
al., in preparation). For early-type stars, the peak of the
stellar emission would be at shorter wavelengths. How-
ever, the early-type star in our sample (LRLL 2) has bad
photometry so we do not explore this point further.
In cases where we
3.1.1. Accretion Rates
During the classical TTS phase of stellar evolution,
young objects accrete material from the disk onto the
star via magnetospheric accretion (Uchida & Shibata
1984). The infalling gas impacts the stellar surface at ap-
proximately the free fall velocity creating a shock which
heats the gas to ∼ 1 MK (Calvet & Gullbring 1998).
The shock emission is reprocessed in the accretion col-
umn and the observed spectrum peaks in the ultraviolet
(Calvet & Gullbring 1998). The best estimate of the ac-
cretion rate is found by measuring the total luminosity
emitted in the accretion shock, i.e. the accretion lumi-
nosity. While ultraviolet emission is difficult to observe
from ground-based observatories, there are many tracers
of the accretion luminosity at longer wavelengths (see
Rigliaco et al. (2011) for a comprehensive list). A few of
those tracers include excess emission observed in U-band
photometry, emission in the NIR Ca II triplet lines, and
the Hα line profile.
Second to the ultraviolet excess, U-band excesses are
the best measure of the flux produced in the shock and
have been shown to correlate with the total shock ex-
cess (Calvet & Gullbring 1998).
emission at U may be dominated by chromospheric
emission (Houdebine et al. 1996; Franchini et al. 1998);
this chromospheric excess can confuse determinations of
the accretion rate (Ingleby et al. 2011).
However, at low
˙ M
While possi-
ble from the ground, U-band observations are still dif-
ficult to obtain, especially when extinction towards the
source is relatively high as in the case of our sample,
all with AV
> 1. Observations of the Ca II near-
infrared triplet are easily obtained from the ground,
even for high AV sources, and the flux in the 8542
˚ A line also correlates with the accretion luminosity
(Muzerolle et al. 1998). Ca II is observed in emission in
accreting sources but is unreliable at low accretion rates,
when the chromospheric emission rivals that from accre-
tion in strength (Yang et al. 2007; Batalha & Basri 1993;
Ingleby & et al. 2011). Hα is commonly used as a tracer
of accretion, both by measuring the equivalent width and
the velocity width of the line in the wings (White & Basri
2003; Barrado y Navascu´ es & Mart´ ın 2003; Natta et al.
2004). Models of magnetospheric accretion have repro-
duced the observed velocities in Hα, tracing material
traveling at several hundred km s−1near the accretion
shock (Lima et al. 2010; Muzerolle et al. 2003).
The mass accretion rates adopted for our sample are
listed in Table 3. We used U-band photometry from this
work and the relation in Gullbring et al. (1998) to mea-
sure mass accretion rates for LRLL 37 and LRLL 68 and
an upper limit for LRLL 133.14For FM 177, FM 281,
FM 515, FM 581, FM 618, LRLL 21, LRLL 67, and
LRLL 72, we used high resolution echelle spectra ob-
tained with MIKE to measure the width of the Hα line in
the wings (at 10% of the maximum flux; Figure 1). We
then compared this to the relation between line width
and
˙M in Natta et al. (2004) to obtain mass accretion
rate estimates for these eight sources. While our MIKE
spectra covered both Hα and the Ca II triplet, Hα pro-
vided a more accurate estimate of
with chromospheric Ca II emission at the levels of accre-
tion found in these sources. Given the chromospheric ap-
pearance of the Hα profile of LRLL 72, its mass accretion
rate should be taken as an upper limit. For LRLL 31 we
adopted a mass accretion rate from the literature. We do
not have mass accretion rate measurements for LRLL 2
or LRLL 6.
For NGC 2068, we compared our derived accretion
rates to those in Flaherty & Muzerolle (2008) who cal-
culated the amount of excess continuum emission nec-
essary to produce the observed veiling of the photo-
spheric lines.Within a factor of 2–3, the normal er-
ror in ˙M estimations, both calculations of the accretion
rate agree, with a few exceptions. When comparing the
Hα line widths at 10% we find that our MIKE line pro-
file of FM 281 is ∼ 180 km s−1narrower than when
observed by Flaherty & Muzerolle (2008). In addition,
our observation of FM 177 is consistent with an accret-
ing source, while when observed by Flaherty & Muzerolle
(2008) its Hα profile was consistent with that of chromo-
spheric emission. Variability is known to occur in T Tauri
stars so the decrease in Hα and
(Cody & Hillenbrand 2010). For these objects we chose
to adopt the accretion rate obtained from our MIKE ob-
servations. The biggest uncertainty in calculating accre-
˙ M due to confusion
˙ M are not unexpected
14We measured an upper limit for LRLL 55 of 4×10−6M⊙
yr−1using U-band photometry.
limit does not provide useful constraints for the purposes of this
paper and so we do not comment on it further.
However, this very high upper

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The Transitional Disk Class5
tion rates using veiling is the choice of bolometric cor-
rection, which can vary in value by a factor of 10 de-
pending on which analysis is used (White & Hillenbrand
2004) and the spectrum of the excess emission which veils
the photospheric lines can be complicated (Fischer et al.
2011).
3.2. Disk Model
We try to reproduce the SEDs presented in Fig-
ures 2, 3, & 4 using the irradiated accretion disk models
of D’Alessio et al. (1998, 1999, 2001, 2005, 2006). We
point the reader to those papers for details of the model
and to Espaillat et al. (2010) for a summary of how we
apply the model to the SEDs of transitional and pre-
transitional disks. Here we provide a brief review of the
salient points of the above works.
When we refer to a “full disk model” we mean a disk
model composed of an irradiated accretion disk and a
frontally illuminated wall at the inner edge of the disk
which is located at the dust sublimation radius. The
inner wall dominates the emission in the NIR, the wall
and disk both contribute to the MIR emission, and the
disk dominates the emission at longer wavelengths. Com-
pared to a full disk model, a pre-transitional disk model
has a gap within the disk. In this case, we include a
frontally illuminated wall at the dust sublimation ra-
dius and another wall at the gap’s outer edge. For this
outer wall we include the shadow cast by the inner wall
(Espaillat et al. 2010). We do not include an inner irra-
diated accretion disk behind the inner wall since previous
work has shown that the inner wall dominates the emis-
sion at these shorter wavelengths (Espaillat et al. 2010).
Behind the outer wall we include an irradiated accretion
disk in cases where we have millimeter data, which is
necessary to constrain the outer disk. The inner wall
dominates the NIR emission while the outer wall dom-
inates the emission from ∼20–30 µm. The outer disk
dominates the emission beyond ∼40 µm. A transitional
disk model is very similar to that of a pre-transitional
disk model except that we do not include an inner wall
at the dust sublimation radius. In some instances, we in-
clude a small amount of optically thin dust in the inner
hole or gap in transitional and pre-transitional disks to
reproduce the 10 µm silicate emission feature. We cal-
culate the emission from this optically thin dust region
following Calvet et al. (2002).
3.2.1. Disk Properties
Table 4 lists the model-derived properties of our sam-
ple. The heights of the inner and outer walls (zwall) and
the maximum grain sizes (amax) are adjusted to fit the
SED. Twallis the temperature at the surface of the opti-
cally thin wall atmosphere. The temperature of the in-
ner wall of full disks and pre-transitional disks (Ti
held fixed at 1400 K (except for FM 515, see Section 3.3)
which is the typical temperature of dust at the sublima-
tion radius (Muzerolle et al. 2003). The temperature of
the outer wall (To
wall) in transitional and pre-transitional
disks is varied to fit the SED, particularly the IRS spec-
trum. The radius of the wall (Rwall) is derived using the
best fitting Twallfollowing Equation 2 in Espaillat et al.
(2010).
Previously, we have seen that in transitional and pre-
transitional disks, the IRS spectrum is dominated by the
wall) is
outer wall while the outer disk dominates the millimeter
emission (E11). Since the majority of the emission seen
by IRS is from the outer wall, the IRS spectrum is a good
constraint of the hole/gap size and in most cases SED-
derived hole/gap sizes are in reasonable agreement with
those obtained with millimeter imaging (Andrews et al.
2011). For objects in this work with no millimeter data,
we do not include an outer disk given that its contribu-
tion to the IRS SED is expected to be small. We did
include an outer disk for the two objects in the sample
for which we have millimeter data: the transitional disk
LRLL 67 and the pre-transitional disk LRLL 31. We also
included an outer disk when modeling each of our full
disk targets since additional emission from an outer disk
is necessary to reproduce the observed MIR emission.
The parameters of the outer disk which are varied to fit
the SED are the viscosity parameter (α) and the settling
parameter (ǫ; see Section 3.2.2). One can interpret vary-
ing α as fitting for the disk mass since Mdisk∝˙M/α (see
Equation 38 in D’Alessio et al. 1998). We note that the
mass accretion rate onto the star does not necessarily re-
flect the mass transport across the outer disk, especially
in the case of TD and PTD where the mass accretion
rate onto the star is likely an underestimate of the mass
transport across the outer disk (see Section 4.4). We
also do not expect that the mass accretion rate is con-
stant throughout the disk. However, for simplicity, here
we assume that the mass accretion rate measured onto
the star is representative of the disk’s accretion rate.
We will discuss how the lack of millimeter constraints
leads to degeneracies in our outer disk model fitting in
Section 3.3. There we also discuss the effect the adopted
disk inclination and outer radius have on the simulated
SED. We assume that the inclination of the disk is 60◦
for all of our objects and that they have an outer disk
radius of 300 AU (except FM 581, see Section 3.3).
3.2.2. Dust Properties
The opacity of the disk, and hence the temperature
structure and resulting emission, is controlled by dust.
The dust opacity depends on the composition of the dust
assumed. It also depends on changes in the dust due to
grain growth and settling. Grains grow through colli-
sional coagulation and settle to the disk midplane due to
gravity. Since in this work we include models of several
full disks, here we review the effect that the dust prop-
erties have on the disk structure in more detail following
D’Alessio et al. (2006).
Dust Settling.
The settling of dust has important,
and often overlooked, effects on the disk’s density–
temperature distribution and emission. When there is
some degree of settling, the dust-to-gas mass ratio of
grains in the disk atmosphere decreases with respect to
the standard value (i.e. the diffuse interstellar medium).
This has several effects: (1) it decreases the opacity of
the upper layers; this allows the impinging external ra-
diation to penetrate deeper into the disk, decreasing the
height of the irradiation surface15and making it geo-
metrically flatter (see Figure 3 in D’Alessio et al. 2006),
which in turn decreases the fraction of the irradiation
15The height of the disk irradiation surface, zs, is defined by the
region where τs, the radial optical depth to the stellar radiation, is
∼ 1.

Page 6

6Espaillat et al.
flux intercepted by this surface,16decreasing the contin-
uum flux emerging from the disk, (2) since most of the
external radiation is deposited at the irradiation surface,
lowering it changes the temperature-density structure of
the atmospheric layers, where the temperature inversion
occurs (also called the super-heated layers), modifying
their contribution to the SED, and finally, (3) it changes
the emissivity of the disk interior; in this region the dust-
to-gas mass ratio of the grains increases given that the
grains removed by depletion from the upper layers are
now located deeper in the disk.
Some of the above-mentioned effects can be ac-
counted for by arbitrarily changing the disk surface
height as a function of radius (e.g. Miyake & Nakagawa
1995; Currie & Sicilia-Aguilar 2011; Sicilia-Aguilar et al.
2011), and this will probably give a reasonable estimate
of the continuum SED of the disk. However, the con-
tribution of the upper layers to the SED or the role of
the deeper layers in millimeter images and emergent flux,
would not be consistent for this simple approach to set-
tling. On the other hand, taking into account the de-
tailed physics of settling (e.g. Weidenschilling et al. 1997;
Dullemond & Dominik 2004) is complex and simulations
show that disks should be completely settled within ∼106
years, in contradiction with observations, reflecting that
we are missing some processes that can keep some small
grains in the upper layers for longer timescales (e.g.
turbulence; Dullemond & Dominik 2005; Birnstiel et al.
2011).
In our SED modeling we have adopted a different ap-
proach following D’Alessio et al. (2006) by parameteriz-
ing settling as a depletion of dust in the upper layers,
with a corresponding increment of the dust-to-gas mass
ratio near the midplane. The maximum grain sizes in the
disk atmosphere and interior are allowed to change, re-
flecting the possibility of grain growth. We can also vary
the height in the disk that separates the atmosphere from
the interior as well as the degree of settling. The amount
of settling is parameterized by ǫ = ζatm/ζstd, (i.e., the
dust-to-gas mass ratio of the disk atmosphere divided by
the standard value). The main point of this approach is
that the same grains that determine the height and shape
of the irradiation surface and the amount of intercepted
external flux, are the ones that are emitting in the mid-
IR silicate bands, and their emissivity and temperature
distribution are consistent with their properties. Also,
the grains near the midplane which are responsible for
the mm emergent intensity have a dust-to-gas mass ra-
tio related to the properties of the atmospheric grains.
The advantage of such an approach is that, in principle,
observations can be used to constrain the grains’ com-
position, size and spatial distribution, and this can be
related to models of the detailed dust evolution in disks.
However, to really fulfill this goal, we need observations
that cover a wide range of wavelengths with high reso-
lution. Given our present observations, we have chosen
to adopt a radially constant ǫ and to assume that the
16As stellar radiation enters the disk, it does so at an angle
to the normal of the disk surface (θ0 = cos−1µ0). A fraction of
the stellar radiation is scattered and the stellar radiation captured
by the disk is ∼ (σT4
∗/π)(R∗/R)2µ0 (see Calvet et al. (1991) for
further discussion).Therefore, if the disk is more flared, µ0 is
larger and more stellar irradiation will be intercepted by the disk
and it will be hotter and emit more radiation.
interior grains are concentrated very close to the mid-
plane (at z ? 0.1 H). These assumptions will not affect
the mid-IR SED (D’Alessio et al. 2006, Qi et al. 2011)
and we avoid introducing new sets of free parameters to
the problem, retaining the important physical properties
of settling.
Dust Grain Growth. In this work we also change the
maximum grain size in the disk. The models assume
spherical grains with a distribution of a−pwhere a is
the grain radius between amin and amax and p is 3.5
(Mathis et al. 1977). A mixture with a smaller amaxhas
a larger opacity at shorter wavelengths than a mixture
with a larger amax. Since the height of the disk surface,
zs, is defined by the region where τs∼ 1 small grains will
reach this limit higher in the disk relative to big grains.
Therefore, disks with a small amaxare more flared than
disks with a large amax for the same dust-to-gas mass
ratio. One difference between increasing the settling and
increasing the grain size is that with settling, small grains
remain in the upper disk layers and so we still see silicate
emission while with grain growth in the disk atmosphere,
the silicate emission disappears since larger grains do not
have this feature in their opacity. In the walls and the
outer disk, aminis held fixed at 0.005 µm while amaxis
varied between 0.25 µm and 10 µm to achieve the best
fit to the silicate emission features. In the outer disk,
there are two dust grain size distributions as mentioned
above. In the disk interior the maximum grain size is
1 mm (D’Alessio et al. 2006). The maximum grain size
of the disk atmosphere is adjusted as noted earlier.
Dust Composition. The composition of dust used in
the disk model impacts the resulting SED and derived
disk properties (see Espaillat et al. (2010) for a discus-
sion). We follow E11 and perform a detailed dust compo-
sition fit for the silicates seen in the IRS spectra including
olivines, pyroxenes, forsterite, enstatite, and silica. We
list the derived silicate mass fractions in Tables 6 and 7 of
the Appendix. In addition to silicates, we also included
organics, troilite, and water ice following Espaillat et al.
(2010) and E11. We note that only silicates exist at
the high temperatures at which the inner wall is located.
In transitional and pre-transitional objects where we in-
clude optically thin dust within the hole, the silicate dust
composition and abundances are listed in Tables 8 and 9
of the Appendix, respectively.
3.3. SED Modeling
In this work we present the first detailed modeling of
disks with IRS spectra in NGC 2068 and IC 348. We find
that all the objects are reasonably reproduced with tran-
sitional, pre-transitional, or full disk models. It is not the
goal of this paper to find a unique fit to the SED. To ar-
rive at a unique fit, one would ideally have a finely sam-
pled, multi-wavelength SED as well as spatially resolved
data at multiple wavelengths. Finely sampled data on
the time domain would also be necessary since the emis-
sion of TTS is known to be variable (e.g. Espaillat et al.
2011). Given that this situation is not currently achiev-
able, here we focus on finding a fit that is consistent
with the observations presented in this work. Our as-
sumptions of the disk structure are an oversimplification.
Recent hydrodynamical simulations show that the inner
regions of transitional and pre-transitional disks should
be complex (Zhu et al. 2011; Dodson-Robinson & Salyk

Page 7

The Transitional Disk Class7
2011). However, in the absence of data capable of con-
firming these simulations, we proceed with our simple
model. We discuss additional assumptions and how they
play into the degeneracies of our modeling in Section 4.2.
We present details of the derived dust composition in the
Appendix.
3.3.1. Results
We find a large range of hole and gap sizes for our
transitional and pre-transitional disks.
holes spanning 4 to 49 AU (Figure 5, Table 4).
pre-transitional disk targets have gaps ranging from 5–
45 AU (Table 4 and Figures 5, 6, and 7).
objects easily identified by dips in the SED (FM 515,
FM 618, LRLL 31) have gap sizes of 11-45 AU. We note
that here we classify LRLL 21 as a PTD even though
its NIR emission is weaker than the other PTD in our
sample and it resembles the emission expected from a
TD. Flaherty et al. (2012) find that LRLL 21 has sig-
nificant NIR emission in more recent IRS observations,
pointing to strong intrinsic variability in the inner disk
linked to changes in the inner wall (Espaillat et al. 2011).
Therefore, here we classify LRLL 21 as a PTD. Another
PTD in our sample that is not obvious based on its SED
alone is LRLL 37 which has the smallest gap size in our
sample (5 AU; Figure 6). It is not possible to fit the
IRS data of LRLL 37 with a full disk model, even within
the uncertainties of the observations. In particular, we
could not fit the strong 10 µm silicate emission with our
full disk model. This could be a sign that LRLL 37 is
a pre-transitional disk with a small gap that contains
some small optically thin dust, reminiscent of RY Tau
(E11) and we will return to this point in Section 4.1. We
only have millimeter fluxes for two objects in our sample,
LRLL 31 and LRLL 67. For these disks we derive a disk
mass of 0.06 M⊙for each (Figure 7). The best fitting ǫ
and α for LRLL 31 are 0.001 and 0.005, respectively. For
LRLL 67, ǫ=0.001 and α=4×10−5.
Most of the transitional and pre-transitional disks have
small optically thin dust within the inner 1 AU of the
hole or gap. The exceptions are the transitional disk
LRLL 72, where we find the 10 µm silicate emission can
be produced by the optically thin atmosphere of the outer
wall, and the pre-transitional disk LRLL 31, where the
10 µm silicate emission comes from the inner wall’s at-
mosphere and optically thin dust within the gap is not
necessary to fit the observations. The mass of dust and
sizes of the grains in this region are given in the Ap-
pendix.
For FM 581, LRLL 2, LRLL 6, LRLL 55, and LRLL 68
we can fit the SED reasonably well using full disk mod-
els (Figure 8). Unlike LRLL 31 and LRLL 67 above, we
do not have millimeter detections for FM 581, LRLL 2,
LRLL 6, LRLL 55, and LRLL 68 and so we cannot con-
strain the mass of the disk. Therefore, the models pre-
sented here are more uncertain, but we show them to
illustrate that a disk model with dust settling and no
holes or gaps in the disk can reproduce the observed
Our TD have
Our
17The three
17As mentioned in Section 3.2, we do not include an inner disk
behind the inner wall. Espaillat et al. (2010) find that the inner
wall dominates the NIR emission of PTD. Pott et al. (2010) con-
firm that the inner disk in PTD is small. High resolution imaging
is needed to further constrain the gap sizes of the objects presented
in this work.
SEDs. We do have an upper limit for the millimeter
flux of LRLL 68 and we use this object as an example
to discuss the degeneracies inherent in the modeling pre-
sented, mainly due to lack of millimeter detections, in
Section 3.3.2. To briefly summarize, disk models with
the same ǫ-to-α ratio will produce very similar emission
in the IR but substantially different emission in the mil-
limeter. Therefore, millimeter data is crucial to disen-
tangle this degeneracy and the disk parameters in this
work should only be taken as indicative of a model that
can reproduce the observed SEDs.
With the above degeneracies in mind, we limited our
parameter search and set ǫ=0.001, changing only α until
we achieved a good fit to the SED. We could have also
set α to a certain value and fit for ǫ instead, however, as
mentioned above and as discussed in Section 3.3.2, ǫ/α
is the most relevant result. For LRLL 2, LRLL 55, and
LRLL 68 we find α=0.06, 0.004, 0.006, respectively. For
LRLL 6 using an ǫ of 0.001 required α>0.1 which would
lead to a viscous timescale shorter than the lifetime of
the disk (Hartmann et al. 1998), so instead we set ǫ=
0.0001; the best-fitting α in this case was 0.1. To fit
the very steep downward slope of FM 581, we needed
to significantly truncate the outer disk radius, down to
0.6 AU.18We fit FM 581 with ǫ=0.001 and α=0.00006.
3.3.2. Model Degeneracies and Millimeter Constraints
Here we explore the degeneracies introduced into the
modeling presented in this paper due to the lack of mil-
limeter data. Rather than do this for each object, we
selected LRLL 68 for this test since it has an upper limit
to its millimeter flux at 860 µm from the SMA observa-
tions reported in this paper.
First, disk models (around the same star) with the
same ǫ-to-α ratio will have SEDs with similar emission in
the IR. This is because disks with equal ǫ/α have similar
disk surfaces. The disk surface is defined as the point
in the upper disk layers where the radial optical depth
(which depends on the product of the opacity and col-
umn density) to the stellar radiation reaches one. ǫ de-
termines the abundance of small dust (i.e. the opacity of
the upper disk layers) while α affects the surface density.
Therefore, in disks with equal ǫ/α the same fraction of
stellar flux will be intercepted by the disk. Since the IR
is dominated by the upper layers of the inner disk, their
emergent intensity in the IR will be similar.
While the IR emission is similar, the emission seen
in the millimeter will be different.
α−viscosity has a mass surface density given by Σ ≈
˙MΩk/α < cs>, where Ωk is the Keplerian angular ve-
locity and < cs> is the sound speed. This implies that
the disk mass, for a given disk radius and similar outer
disk temperature distribution, would be proportional to
α−1. Therefore, a disk with a smaller α will have a larger
disk mass. In the millimeter, we are more sensitive to the
A disk with an
18The SED of FM 581 resembles that of the 5–10 AU binary
SR 20 (McClure et al. 2008). SR 20’s disk is outwardly truncated
at 0.4 AU, too far to be attributable to the known companion, and
so this truncation would have to be due to an unseen companion
at ∼1–2 AU (McClure et al. 2008). Likewise, it seems that the
most viable mechanism to truncate the disk of FM 581 to such
small radii would also be a companion. However, FM 581 still has
a substantial accretion rate. Millimeter observations are necessary
to constrain the mass and size of this disk.

Page 8

8Espaillat et al.
big grains in the midplane of the disk, where most of the
disk’s mass is stored, and so disks with small α and a
higher column density will have more millimeter emis-
sion. This means that models with similar ǫcos(i)˙M/α
would have similar IR SEDs, but different millimeter
SEDs. Millimeter data is necessary to disentangle this
degeneracy.
Because of the above, we can find a best-fit ǫ/α to the
IR emission if we hold i and ˙M constant. However, each
model will have different emission in the millimeter and
since we have no millimeter data, we cannot claim that
a particular combination of ǫ and α is better than an-
other. For the models shown in Figure 9 (Models 1, 2,
& 3 in Table 5) we hold the mass accretion rate, stel-
lar parameters, inclination (i), and outer disk radius Rd
fixed and change only ǫ and α. We set ǫ to 0.0001, 0.001,
0.01, and 0.1, the values given in D’Alessio et al. (2006),
and fit the SED by changing α. We do not discuss cases
where α≥0.1 since these disks would have short viscous
timescales (Hartmann et al. 1998). For LRLL 68, we find
that the best-fitting ǫ/α is 0.2.
We also look at how varying the outer disk radius and
inclination affect the simulated SED. Changing the ra-
dius changes the mass of the disk but the millimeter
emission does not change significantly (Figure 10). This
is because the mass depends on the disk radius (Md =
?Rd
nuli contributing to the mm flux remains the same. This
highlights that disk sizes cannot be firmly constrained
without resolved imaging. We find that changing the
inclination angle while holding other parameters fixed
changes the IR emission, but does not significantly alter
the millimeter emission (Figure 11). The disk is mostly
optically thin at millimeter wavelengths so we can see
through the disk at any inclination. Therefore, the mil-
limeter emission does not change with inclination. On
the other hand, the IR emission does change; as the in-
clination decreases, we see more of the inner disk, which
mainly dominates the IR emission. We note that the
near-IR emission also depends on the shape of the wall.
We assume the wall is vertical, therefore it will not con-
tribute to the SED at 0◦or 90◦and will produce the
most emission at 60◦(Dullemond et al. 2001). If the wall
is curved, we would expect to see more emission at lower
inclinations (Isella & Natta 2005).
RiΣ2πRdR). However, the column density of the an-
4. DISCUSSION
4.1. Limitations of Observations
As discussed by Espaillat et al. (2010), the sizes of gaps
and holes we can detect in the disk are limited by broad-
band SEDs. Given that the majority of the emission at
∼10 µm in a typical disk traces the dust within the inner
1 AU of the disk (D’Alessio et al. 2006; Espaillat 2009),
the Spitzer IRS instrument will be most sensitive to clear-
ings in which much of the dust located at radii <1 AU
has been removed. Because of this, IRS is more effective
in picking out disk holes where dust at small radii has
been removed. However, IRS cannot easily detect gaps
whose inner boundary is outside of ∼1 AU. For exam-
ple, a disk with a gap ranging from 5 – 10 AU will be
difficult to distinguish from a full disk (Espaillat et al.
2010). The gaps currently inferred solely from SEDs,
which have been modeled and imaged in the millimeter,
are typically quite large. This reflects an observational
bias towards picking out pre-transitional disks with large
gaps since their mid-infrared deficits will be more obvious
in Spitzer spectra. Smaller gaps will not have as obvious
of a deficit and will be difficult to detect. Broad-band
colors from IRAC and MIPS have their limitations as
well. They are useful for picking out TD, but it is diffi-
cult to distinguish the NIR colors of a PTD from a full
disk.
LRLL 37 may be a case of a disk with a small 5 AU
gap. The dip in the SED is not obvious, but the strong
silicate emission seen in this object is reminiscent of RY
Tau. RY Tau has a large cavity in its disk based on
millimeter imaging (Isella et al. 2010) and its SED was
modeled with a gap of ∼20 AU (E11). There are many
other disks that exhibit strong 10 µm silicate emission
(Furlan et al. 2009) and perhaps this is a hint pointing
to small gaps in disks. That said, we cannot exclude
the presence of small gaps in what we have labeled full
disks in this paper, or for that matter any full disks in
general. High-resolution imaging is crucial to investigate
this further and current TD fractions should be taken as
lower limits.
4.2. Limitations of Models
The underlying physical structure inferred from the
SED is dependent on the model one uses.
ample, there are five disks in Taurus with decreas-
ing emission at IR wavelengths, much like the disks
studied in this work, that have seemingly contrast-
ing interpretations presented by Luhman et al. (2010)
and Currie & Sicilia-Aguilar (2011).
ence between the two papers are the models adopted.
Currie & Sicilia-Aguilar (2011) use the model grid pre-
sented in Robitaille et al. (2007). The authors account
for the observed SEDs by decreasing the mass of models
with well-mixed gas and dust in the disk (i.e. a disk with
no settling) to the point where it becomes entirely opti-
cally thin. The Luhman et al. (2010) results are based on
synthetic colors from the model grid of Espaillat (2009).
Those models are the same in this work, where dust set-
tling is incorporated. Luhman et al. (2010) can repro-
duce the observed colors with disks that have dust set-
tling. To illustrate that a settled disk can reproduce the
broad-band SED as well, in the Appendix we model ZZ
Tau, one of the five disks in question. Therefore, it be-
comes clear that the different interpretation between the
two groups is biased by the models adopted. The most
one can say is that both a well-mixed low-mass disk and
a settled disk can reproduce the observations. In the for-
mer case the disk is optically thin to its own radiation
at all radii; for the latter case the innermost disk is still
optically thick to its own radiation.
Sicilia-Aguilar et al. (2011) also independently find
that they need to incorporate settling to reproduce the
SED of objects with decreasing IR emission. We note
that the implementation of settling in that work and
our work are very different. Sicilia-Aguilar et al. (2011)
simulate settling in their modeling by lowering the disk
surface, but its shape remains the same. In addition,
the dust-to-gas mass ratio is held fixed throughout the
disk (i.e. there is no dust depletion in the upper disk
layers). Since the surface is still flared and the opacity
remains the same, the disk is hotter than it would be if
For ex-
The main differ-

Page 9

The Transitional Disk Class9
the disk was geometrically flatter and the opacity was
lower. Therefore, such a disk will produce more emission
and there will be an inherent bias towards decreasing the
disk mass in order to reproduce lower observed fluxes. In
the models used in this work we deplete the small grains
in the upper atmosphere of the disk and self-consistently
calculate the disk height and shape. This is an iterative
process given that the height of the disk irradiation sur-
face dictates how much energy is captured by the disk
and this depends on the opacity set by the dust proper-
ties and the density of the disk, which in turn depends on
the temperature through the scale height. We note that
it is still possible to have a disk which is both settled
and low-mass. Our point is that in order to constrain
the disk mass and avoid the degeneracies discussed in
Section 3.3.2, millimeter data is necessary and the full
effects of dust settling need to be taken into account.
This leads to another issue that is quite model de-
pendent: the disk mass. Not only does the disk mass
depend on the opacity one assumes, it also depends on
the surface density and temperature radial profiles. For
example, our mass determinations (i.e. E11) are con-
sistently higher than Andrews & Williams (2005) since
our opacities are ∼3 times lower, we assume the outer
disk radius is larger, and we use a self-consistent surface
density and temperature instead of power-law approxi-
mations. Therefore, masses obtained by different models
cannot be meaningfully compared.
4.3. Disk Structure & Semantics
There are many terms in the literature aiming to cat-
egorize SEDs of TTS surrounded by disks. At times this
leads to confusion. For example, what some researchers
call a transitional disk others would call an anemic disk or
an evolved disk or a homologously depleted disk. The ef-
fect of not consistently applying the term “transitional”
in the literature is seen when looking at TD fractions
in the literature. Some call “transitional” any objects
whose SED does not resemble the median SED of Tau-
rus. Others use the more restrictive definition of disks
that have holes. If we only consider objects with IR dips
in their SEDs as transitional, the TD fraction is lower;
including objects with decreasing emission at all wave-
lengths increases the reported “transitional disk” fraction
from 20% to 70% at ∼10 Myr (Muzerolle et al. 2010).
This difference is not trivial and presents an unclear pic-
ture when attempting to compare theoretical simulations
of planet formation that predict disk holes with a “transi-
tional disk” fraction that encompasses objects which do
not have apparent evidence for cleared regions in their
disks.
Another related issue is encountered when trying to
discern the disk clearing timescale. These timescales usu-
ally include transitional and pre-transitional disks and
evolved disks (which are optically thin), and are mea-
sured with respect to full disks. Defining the boundaries
between transitional, pre-transitional, evolved, and full
disks is crucial in order to obtain an accurate estimate
of the disk clearing timescale. TD are relatively easier to
identify, whether looking at broad-band SEDs or colors.
PTD are harder to tell apart from full disks based on col-
ors alone. Evolved disks are also difficult to separate from
full disks and this is the main driving force behind the dif-
ferent disk clearing timescales reported in the literature.
Currie & Sicilia-Aguilar (2011) find a ∼1 Myr timescale
for inner disk clearing, which is longer than the ∼0.5 Myr
timescale obtained by Luhman et al. (2010).
most part, both groups are using the same data. The
main difference is what one considers a full disk versus
evolved (also called homologously depleted). As pointed
out by Hern´ andez et al. (2010), the reported fraction of
optically thin disks (i.e. evolved disks or homologously
depleted disks) is highly dependent on the cutoff. Obser-
vationally, Currie & Sicilia-Aguilar (2011) use the lower
quartile of Taurus. Therefore, by construction, 25% of
disks in Taurus are evolved disks. Luhman et al. (2010)
use a gap in the IR color-color diagrams which leads to
fewer objects in this phase.
Here we focus on the physical structure that could be
underlying the observed SEDs by using physical models
to motivate our interpretation. We find that it is possible
to group objects based on their observed SEDs and find a
general model-based interpretation to fit objects within
a group. In our work we have cases of disks with holes
and gaps and full disks (see Section 3.3). We emphasize,
as noted previously in Section 4.1, that possibly all disks
have gaps that cannot be detected in SEDs. However,
our goal here is to discern when one can identify a hole
or gap in a disk based on its SED.
In essence, all disks around TTS are “in transition” as
they are all evolving in one way or another. The expec-
tation is that all TTS with disks will eventually become
diskless stars. However, they are not all necessarily going
down the same evolutionary path. Here we suggest that
the term “transitional” be used for a disk which appears
to be undergoing a radical disturbance in the radial struc-
ture of its inner disk (i.e., a hole or gap). While above we
point out the inherent deficiencies in using the evolution-
ary term “transitional” to define a disk, introducing new
classification schemes to the literature is not warranted
given the limitations of currently available data.
One motivation for separating disks with holes and
gaps from full disks is that it is not obvious these
disks are undergoing the same type of disk clear-
ing. Many researchers have suggested that the
holes and gaps in disks observed to date are due
to planets (see discussion in Espaillat et al. 2010).
Simulations have shown that newly forming plan-
ets will clear regions of the disk through accretion
and tidal disturbances (Goldreich & Tremaine 1980;
Ward 1988; Rice et al. 2003; Paardekooper & Mellema
2004; Quillen et al. 2004; Varni` ere et al. 2006; Zhu et al.
2011). It is less clear how a disk with weak emission at
all wavelengths could be related to disk clearing caused
by a planet. As pointed out by Cieza et al. (2010) and
Currie & Sicilia-Aguilar (2011), disks with weak MIR
emission could instead be the result of another mech-
anism that may have a different rate of evolution (e.g.
photoevaporation). Alternatively, full disks with SEDs
such as those in this paper could simply be the tail end
of continuous distribution of full disks. This could be
related to a large spread in disk properties (˙ M, Md, dust
composition) in a given population as well as a distribu-
tion in the initial conditions. Another possibility, that we
cannot fully test in this paper due to a lack of millimeter
detections, is that the full disks in our sample have expe-
rienced a greater degree of dust settling than other full
disks. In this case, we would see more of these disks in
For the

Page 10

10 Espaillat et al.
older regions since settling is expected to increase with
age.
4.4. Mass Accretion Rates of Transitional and
Pre-transitional Disks
Najita et al. (2007) showed that the mass accretion
rates of transitional disks in Taurus tend to be lower
than those of full disks in the same region. If planets are
the clearing agent in transitional disks, then lower mass
accretion rates are expected onto the star since a giant
planet that opens a gap in the disk will intercept and ac-
crete material from the outer disk (Lubow & D’Angelo
2006). To explore this further we compared the distribu-
tion of mass accretion rates of full disks and transitional
and pre-transitional disks in Taurus, Chamaeleon, and
NGC 2068 (Figure 12; see the Appendix for details). We
note that Najita et al. (2007) used a broader definition
of “transitional disk” which included all objects with less
emission than the median SED of Taurus. As discussed
in Section 4.3, the link between these disks and planet
formation is less clear. Therefore, here we use our more
restrictive definition of transitional and pre-transitional
disks which includes only objects with holes and gaps.
We find that the mass accretion rates of transitional and
pre-transitional disks tend to be about 5 times lower than
the full disks in these three regions. The median mass ac-
cretion rate for the full disks is 1.3×10−8M⊙yr−1and for
the transitional and pre-transitional disks it is 3.1×10−9
M⊙ yr−1. A Kolmogorov-Smirnov (KS) test indicates
that the full disk and transitional and pre-transitional
disk mass accretion rate samples are not drawn from the
same distribution (the KS-probability is 0.02).
While the mass accretion rates of transitional and pre-
transitional disks are overall lower than those of full
disks, they are still too high to be compatible with cur-
rent models of disk clearing by planets. This is espe-
cially seen in the cases of transitional and pre-transitional
disks with higher mass accretion rates and large gaps and
holes. Zhu et al. (2011) find that multiple planets are
needed to open these large clearings in the dust distri-
bution. However, more planets in the disk should lead
to lower mass accretion rates onto the star than those
observed. Our results suggest that possible planets in
transitional and pre-transitional disks could be lowering
the mass accretion rate onto the star somewhat, but that
there is another mechanism taking effect that we have
not accounted for, possibly dust evolution as proposed
by Zhu et al. (2011). More simulations of disk clearing
by planets are needed to reconcile the large gap sizes and
mass accretion rates currently observed.
We also see that the transitional disks tend to have
have lower mass accretion rates than the pre-transitional
disks in our sample, by a factor of ∼10. The median mass
accretion rate for our five transitional disks is 9.7×10−10
M⊙ yr−1while the median for the ten pre-transitional
disks in the sample is 8.8×10−9M⊙yr−1. (More obser-
vations of PTD and TD are needed to expand the sample
size and confirm this result given that the KS-probability
that the samples are drawn from the same distribution is
0.27.) Given that the evolution and relationship between
TD and PTD is not currently completely understood,
the underlying reason for this apparent discrepancy in
mass accretion rates is not obvious. One can speculate
that the difference is due to the same mechanism clear-
ing the holes and gaps in these disks. In the case of
planet formation, Zhu et al. (2011) find that the mass
accretion rate onto the star will decrease with time as
planets grow in the disk. The difference in mass accre-
tion rate between PTD and TD could then possibly indi-
cate that pre-transitional disks are in the early stages of
planet formation while transitional disks are in the later
stages. However, refinement of planet forming simula-
tions is needed to study this further given the complex
structure expected in the inner disk region.
5. SUMMARY
Here we modeled the broad-band SEDs of 15 disks in
NGC 2068 and IC 348. We presented IRS spectra for
all our targets as well as mass accretion rates estimated
with U-band photometry obtained at the MDM Observa-
tory and Hαprofiles from the MIKE spectrograph on the
Magellan telescope. We also presented SMA millimeter
data for some of our sources in IC 348.
The observed SEDs of the objects in our sample are
diverse, yet can be separated into three groups. Some of
our targets have dips in both their NIR and MIR emis-
sion, some have dips in only their MIR emission, and
some have decreasing emission at all IRS wavelengths.
We modeled the first group as transitional disks (i.e. ob-
jects with holes in their disk’s dust distribution), the sec-
ond group as pre-transitional disks (i.e. objects with gaps
in their disk’s dust distribution), and the last group as
full disks (i.e. objects with no cleared regions in their
disks). We found that millimeter data are crucial in
breaking model degeneracies between the amount of dust
settling in the disk and the disk’s mass.
We discussed the limitations of the observations,
namely that we currently do not have high enough reso-
lution to discern very small gaps in disks, and the limita-
tions of disk models, especially with respect to simulating
the effects of dust settling and determining masses. We
pointed out that much of the disagreement in the lit-
erature over reported transitional disk frequencies and
disk clearing timescales is mainly due to inconsistent
application of the term “transitional” in the literature.
We suggested that only objects showing evidence of an
abrupt change in their radial disk structure be referred
to as “transitional.” Specifically, here we use “transi-
tional disk” when referring to disks with holes and “pre-
transitional disk” for disks with gaps. Finally, we com-
pared the mass accretion rates of transitional and pre-
transitional disks to full disks in Taurus, Chamaeleon,
and NGC 2068 and find that PTD and TD have lower
accretion rates overall. We also find that the TD have
lower mass accretion rates than PTD, but due to our
small sample more objects are needed to confirm this.
Significant progress will be made in the near future on
the issues raised in this paper. Herschel SPIRE will pro-
vide us with a large, consistent sample of sub-millimeter
fluxes to help break model degeneracies. With the high
resolution of ALMA we can soon test if the above clas-
sifications used in this paper hold and modify them if
necessary.
We thank Lee Hartmann for helpful discussions and the
referee for a careful review of the manuscript. C. E. was
supported by the National Science Foundation under

Page 11

The Transitional Disk Class11
Award No. 0901947. P. D. acknowledges a grant from
PAPIIT-DGAPA UNAM. N. C. acknowledges support
from NASA Origins Grant NNX08AFM 5154G.
REFERENCES
Andrews, S. M., & Williams, J. P. 2005, ApJ, 631, 1134
Andrews, S. M., Wilner, D. J., Espaillat, C., Hughes, A. M.,
Dullemond, C. P., McClure, M. K., Qi, C., & Brown, J. M.
2011, ApJ, 732, 42
Andrews, S. M., Wilner, D. J., Hughes, A. M., Qi, C., &
Dullemond, C. P. 2009, ApJ, 700, 1502
—. 2010, ApJ, 723, 1241
Artymowicz, P., & Lubow, S. H. 1994, ApJ, 421, 651
Barrado y Navascu´ es, D., & Mart´ ın, E. L. 2003, AJ, 126, 2997
Batalha, C. C., & Basri, G. 1993, ApJ, 412, 363
Bernstein, R., Shectman, S. A., Gunnels, S. M., Mochnacki, S., &
Athey, A. E. 2003, in Society of Photo-Optical Instrumentation
Engineers (SPIE) Conference Series, Vol. 4841, Society of
Photo-Optical Instrumentation Engineers (SPIE) Conference
Series, ed. M. Iye & A. F. M. Moorwood, 1694–1704
Birnstiel, T., Ormel, C. W., & Dullemond, C. P. 2011, A&A, 525,
A11+
Calvet, N., Brice˜ no, C., Hern´ andez, J., Hoyer, S., Hartmann, L.,
Sicilia-Aguilar, A., Megeath, S. T., & D’Alessio, P. 2005a, AJ,
129, 935
Calvet, N., D’Alessio, P., Hartmann, L., Wilner, D., Walsh, A., &
Sitko, M. 2002, ApJ, 568, 1008
Calvet, N., & Gullbring, E. 1998, ApJ, 509, 802
Calvet, N., Patino, A., Magris, G. C., & D’Alessio, P. 1991, ApJ,
380, 617
Calvet, N., et al. 2005b, ApJ, 630, L185
Cieza, L. A., et al. 2010, ApJ, 712, 925
Cody, A. M., & Hillenbrand, L. A. 2010, ApJS, 191, 389
Cohen, M., Megeath, S. T., Hammersley, P. L., Mart´ ın-Luis, F.,
& Stauffer, J. 2003, AJ, 125, 2645
Currie, T., & Sicilia-Aguilar, A. 2011, ApJ, 732, 24
D’Alessio, P., Calvet, N., & Hartmann, L. 2001, ApJ, 553, 321
D’Alessio, P., Calvet, N., Hartmann, L., Franco-Hern´ andez, R., &
Serv´ ın, H. 2006, ApJ, 638, 314
D’Alessio, P., Calvet, N., Hartmann, L., Lizano, S., & Cant´ o, J.
1999, ApJ, 527, 893
D’Alessio, P., Canto, J., Calvet, N., & Lizano, S. 1998, ApJ, 500,
411
D’Alessio, P., et al. 2005, ApJ, 621, 461
Dodson-Robinson, S. E., & Salyk, C. 2011, ApJ, 738, 131
Dullemond, C. P., & Dominik, C. 2004, A&A, 417, 159
—. 2005, A&A, 434, 971
Dullemond, C. P., Dominik, C., & Natta, A. 2001, ApJ, 560, 957
Espaillat, C. 2009, PhD thesis, University of Michigan
Espaillat, C., Calvet, N., D’Alessio, P., Hern´ andez, J., Qi, C.,
Hartmann, L., Furlan, E., & Watson, D. M. 2007a, ApJ, 670,
L135
Espaillat, C., Calvet, N., Luhman, K. L., Muzerolle, J., &
D’Alessio, P. 2008a, ApJ, 682, L125
Espaillat, C., Furlan, E., D’Alessio, P., Sargent, B., Nagel, E.,
Calvet, N., Watson, D. M., & Muzerolle, J. 2011, ApJ, 728, 49
Espaillat, C., et al. 2007b, ApJ, 664, L111
—. 2008b, ApJ, 689, L145
—. 2010, ApJ, 717, 441
Fischer, W., Edwards, S., Hillenbrand, L., & Kwan, J. 2011, ApJ,
730, 73
Flaherty, K. M., & Muzerolle, J. 2008, AJ, 135, 966
Flaherty, K. M., Muzerolle, J., Rieke, G., Gutermuth, R., Balog,
Z., Herbst, W., Megeath, S. T., & Kun, M. 2011, ApJ, 732, 83
Flaherty, K. M., Muzerolle, J., Rieke, G., Gutermuth, R., Balog,
Z., Herbst, W., Megeath, S. T., & Kun, M. 2012, ApJ,
submitted
Franchini, M., Morossi, C., & Malagnini, M. L. 1998, ApJ, 508,
370
Furlan, E., et al. 2006, ApJS, 165, 568
—. 2009, ApJ, 703, 1964
—. 2011, ApJS, 195, 3
Goldreich, P., & Tremaine, S. 1980, ApJ, 241, 425
Gullbring, E., Hartmann, L., Briceno, C., & Calvet, N. 1998,
ApJ, 492, 323
Haisch, Jr., K. E., Lada, E. A., & Lada, C. J. 2001, AJ, 121, 2065
Hartigan, P., Hartmann, L., Kenyon, S., Hewett, R., & Stauffer,
J. 1989, ApJS, 70, 899
Hartmann, L., Calvet, N., Gullbring, E., & D’Alessio, P. 1998,
ApJ, 495, 385
Herbig, G. H. 1998, ApJ, 497, 736
Hern´ andez, J., Morales-Calderon, M., Calvet, N., Hartmann, L.,
Muzerolle, J., Gutermuth, R., Luhman, K. L., & Stauffer, J.
2010, ApJ, 722, 1226
Hern´ andez, J., et al. 2007, ApJ, 671, 1784
Higdon, S. J. U., et al. 2004, PASP, 116, 975
Houck, J. R., et al. 2004, ApJS, 154, 18
Houdebine, E. R., Mathioudakis, M., Doyle, J. G., & Foing, B. H.
1996, A&A, 305, 209
Hu´ elamo, N., Lacour, S., Tuthill, P., et al. 2011, A&A, 528, L7
Hughes, A. M., Wilner, D. J., Calvet, N., D’Alessio, P., Claussen,
M. J., & Hogerheijde, M. R. 2007, ApJ, 664, 536
Hughes, A. M., et al. 2009, ApJ, 698, 131
Ingleby, L., Calvet, N., Hern´ andez, J., Brice˜ no, C., Espaillat, C.,
Miller, J., Bergin, E., & Hartmann, L. 2011, AJ, 141, 127
Ingleby, L., & et al. 2011, submitted to ApJ
Isella, A., Carpenter, J. M., & Sargent, A. I. 2010, ApJ, 714, 1746
Isella, A., & Natta, A. 2005, A&A, 438, 899
Jensen, E. L. N., Mathieu, R. D., & Fuller, G. A. 1994, ApJ, 429,
L29
Jordi, K., Grebel, E. K., & Ammon, K. 2006, A&A, 460, 339
Kenyon, S. J., & Hartmann, L. 1995, ApJS, 101, 117
Kraus, A. L., Ireland, M. J., Martinache, F., & Hillenbrand, L. A.
2011, ApJ, 731, 8
Kraus, A. L., & Ireland, M. J., ApJ, in press
Lada, C. J., et al. 2006, AJ, 131, 1574
Landolt, A. U. 1992, AJ, 104, 340
Lebouteiller, V., Bernard-Salas, J., Sloan, G. C., & Barry, D. J.
2010, PASP, 122, 231
Lima, G. H. R. A., Alencar, S. H. P., Calvet, N., Hartmann, L., &
Muzerolle, J. 2010, A&A, 522, A104+
Lubow, S. H., & D’Angelo, G. 2006, ApJ, 641, 526
Luhman, K. L., Allen, P. R., Espaillat, C., Hartmann, L., &
Calvet, N. 2010, ApJS, 186, 111
Luhman, K. L., Stauffer, J. R., Muench, A. A., Rieke, G. H.,
Lada, E. A., Bouvier, J., & Lada, C. J. 2003, ApJ, 593, 1093
Mathis, J. S. 1990, ARA&A, 28, 37
Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425
McClure, M. 2009, ApJ, 693, L81
McClure, M. K., et al. 2008, ApJ, 683, L187
Mer´ ın, B., et al. 2010, ApJ, 718, 1200
Miyake, K., & Nakagawa, Y. 1995, ApJ, 441, 361
Muzerolle, J., Allen, L. E., Megeath, S. T., Hern´ andez, J., &
Gutermuth, R. A. 2010, ApJ, 708, 1107
Muzerolle, J., Calvet, N., & Hartmann, L. 1998, ApJ, 492, 743
Muzerolle, J., Calvet, N., Hartmann, L., & D’Alessio, P. 2003,
ApJ, 597, L149
Najita, J. R., Strom, S. E., & Muzerolle, J. 2007, MNRAS, 378,
369
Natta, A., Testi, L., Muzerolle, J., Randich, S., Comer´ on, F., &
Persi, P. 2004, A&A, 424, 603
Olofsson, J., Benisty, M., Augereau, J.-C., et al. 2011, A&A, 528,
L6
Owen, J. E., Ercolano, B., & Clarke, C. J. 2011, MNRAS, 412, 13
Paardekooper, S.-J., & Mellema, G. 2004, A&A, 425, L9
Pott, J.-U., Perrin, M. D., Furlan, E., et al. 2010, ApJ, 710, 265
Quillen, A. C., Blackman, E. G., Frank, A., & Varni` ere, P. 2004,
ApJ, 612, L137
Rice, W. K. M., Wood, K., Armitage, P. J., Whitney, B. A., &
Bjorkman, J. E. 2003, MNRAS, 342, 79
Rigliaco, E., Natta, A., Randich, S., Testi, L., Covino, E.,
Herczeg, G., & Alcal´ a, J. M. 2011, A&A, 526, L6+
Robitaille, T. P., Whitney, B. A., Indebetouw, R., & Wood, K.
2007, ApJS, 169, 328
Sargent, B. A., Forrest, W. J., Tayrien, C., et al. 2009, ApJ, 690,
1193
Schaefer, G. H., Simon, M., Beck, T. L., Nelan, E., & Prato, L.
2006, AJ, 132, 2618
Sicilia-Aguilar, A., Henning, T., Dullemond, C. P., Patel, N.,
Juhasz, A., Bouwman, J., & Sturm, B. 2011, submitted to ApJ
Siess, L., Dufour, E., & Forestini, M. 2000, A&A, 358, 593

Page 12

12 Espaillat et al.
Skrutskie, M. F., Dutkevitch, D., Strom, S. E., Edwards, S.,
Strom, K. M., & Shure, M. A. 1990, AJ, 99, 1187
Skrutskie, M. F., et al. 2006, AJ, 131, 1163
Strom, K. M., Strom, S. E., Edwards, S., Cabrit, S., & Skrutskie,
M. F. 1989, AJ, 97, 1451
Thalmann, C., et al. 2010, ApJ, 718, L87
Uchida, Y., & Shibata, K. 1984, PASJ, 36, 105
Varni` ere, P., Blackman, E. G., Frank, A., & Quillen, A. C. 2006,
ApJ, 640, 1110
Ward, W. R. 1988, Icarus, 73, 330
Watson, D. M., et al. 2009, ApJS, 180, 84
Weidenschilling, S. J., Spaute, D., Davis, D. R., Marzari, F., &
Ohtsuki, K. 1997, Icarus, 128, 429
Werner, M. W., et al. 2004, ApJS, 154, 1
White, R. J., & Basri, G. 2003, ApJ, 582, 1109
White, R. J., & Ghez, A. M. 2001, ApJ, 556, 265
White, R. J., & Hillenbrand, L. A. 2004, ApJ, 616, 998
Yang, H., Johns-Krull, C. M., & Valenti, J. A. 2007, AJ, 133, 73
Zhu, Z., Nelson, R. P., Hartmann, L., Espaillat, C., & Calvet, N.
2011, ApJ, 729, 47
APPENDIX
DUST COMPOSITION OF SAMPLE
We performed fitting of the silicate emission features visible in the IRS spectra and derived the mass fraction of
amorphous and crystalline silicates in the disk (Tables 6, 7 and 8). See E11 for a discussion of the degeneracies inherent
in deriving the dust composition. The results here should be taken as representative of a dust composition that can
reasonably explain the observed silicate features in the SED. We leave it to future work to further constrain the mass
fractions of silicates in these disks.
For the inner wall of our pre-transitional objects, we adopted a silicate composition consisting solely of amorphous
olivines. This is because the inner wall does not produce significant 10 µm silicate emission in most of the objects in
this study and so we have no way to distinguish between pyroxene and olivine silicates in the inner wall. The exception
is LRLL 31 where we need 60% amorphous olivine and 40% forsterite in the inner wall in order to fit the 10 µm silicate
emission feature. For transitional and pre-transitional disks we changed the silicate composition in the optically thin
dust region and outer wall to fit the SED (Tables 7). For the full disks, we changed the silicate composition in the
inner wall and disk (Table 6 and 8). The silicate composition was not allowed to vary between the inner wall and disk
in the full disk models.
COMMENTS ON FITTING ZZ TAU WITH A SETTLED, IRRADIATED ACCRETION DISK MODEL
Here we present modeling of the SED of ZZ Tau using the disk model of D’Alessio et al. (2006) discussed in Sec-
tion 3.2. Stellar parameters used in the disk model (T∗=3470 K; L∗=0.75 L⊙; M∗=0.35 M⊙; R∗=2.4 R⊙) were
derived in the same manner as other objects in this work (see Section 3.1) using a spectral type of M3 adopted from
Kenyon & Hartmann (1995) and a visual extinction (AV) of 0.98 taken from Furlan et al. (2006). We adopt a mass
accretion rate of 1.3×10−9M⊙yr−1from White & Ghez (2001). We note that this is slightly higher than the mass
accretion rate measured from U-band photometry (9×10−10M⊙yr−1).
In Figure 13 we present two models with different outer radii. In one model we use an outer disk radius of 100 AU for
comparison with previous modeling performed by Currie & Sicilia-Aguilar (2011). The best-fit parameters are ǫ=0.001
and α=0.02 and this disk has a mass of 5×10−4M⊙. We also explored disks with other ǫ values. A disk with a higher
ǫ of 0.01 needs an α of 0.2 to the fit the SED, but this α results in a viscous timescale shorter than the lifetime of the
disk (Hartmann et al. 1998). A disk with ǫ=0.0001 and α=0.002 with a higher mass of 0.005 M⊙is excluded by the
millimeter upper limits. Here we use amorphous silicates to fit the disk with amax=10 µm. Crystalline silicate features
are evident in the IRS spectrum (Sargent et al. 2009), but we leave a detailed fit to McClure et al. (in preparation).
In Figure 14, we show that ZZ Tau is optically thick to its own radiation (τRoss>1) out to about ∼1 AU in the disk.
Over 80% of the emission seen at 40 µm is from within these radii (see Figure 2.16 in Espaillat 2009). Therefore, the
optically thick part of the disk of ZZ Tau dominates the emission seen in the IRS spectrum.
We also present a model with an outer radius of 3 AU in Figure 13. This is because ZZ Tau is a close binary with a
separation of 0.06′′(Schaefer et al. 2006), which corresponds to 8 AU at the distance of Taurus (140 pc). Therefore,
the IRS spectrum presented here includes both objects. (ZZ Tau IRS, which is 36′′away, did not enter the IRS slit and
could be a wide companion (Furlan et al. 2011).) If a circumbinary disk is present, its inner edge would be located
at ∼16 AU according to expectations of dynamical clearing by companions (Artymowicz & Lubow 1994). However,
we detect NIR blackbody emission which indicates that instead we are seeing a circumprimary disk. In this case, the
outer edge of the disk would be truncated to ∼3 AU (Artymowicz & Lubow 1994) and have a mass of 2×10−5M⊙.
As discussed in Section 3.3.2 and shown in Figure 14, since the IRS emission is dominated by the inner AU of the disk,
changing the outer radius of the disk does not significantly alter the IR emission.
COMMENTS ON THE DISTRIBUTION OF MASS ACCRETION RATES
When plotting the distribution of mass accretion rates of full disks and transitional and pre-transitional disks in
Taurus, Chamaeleon, and NGC 2068 (Figure 12) we restricted ourselves to transitional and pre-transitional disks
whose SEDs have been modeled. Mass accretion rates for transitional and pre-transitional disks are taken from
Espaillat et al. (2011) for Taurus and Chamaeleon and from this work for NGC 2068. The mass accretion rates for full
disks in Taurus were taken from Najita et al. (2007). Since here we use a different definition of “transitional disk” than
used in that work, we use the mass accretion rates for objects that do not overlap with what we label a pre-transitional
or transitional disk. For Chamaeleon, mass accretion rates for full disks are from Hartmann et al. (1998) and for
NGC 2068 mass accretion rates for full disks are from Flaherty & Muzerolle (2008). We do not include objects which

Page 13

The Transitional Disk Class13
have upper limits for their mass accretion rates or those that are known to be binaries. We also excluded IC 348 in
this analysis since, to the best of our knowledge, there are no mass accretion rates in the literature for the full disks
in this region. In addition, IC 348 is older than Taurus, Chamaeleon, and NGC 2068 which may bias the results given
that mass accretion rates are known to decrease with age (e.g. Calvet et al. 2005a). In total we have 45 full disks and
15 transitional and pre-transitional disks.
We note that the majority of these mass accretion rates are derived using U-band photometry and the relation
in Gullbring et al. (1998). The exceptions are objects in NGC 2068. The mass accretion rates for transitional and
pre-transitional disks in NGC 2068 are taken from this work and the mass accretion rates for the full disks are adopted
from (Flaherty & Muzerolle 2008). In Section 3.1.1, we discuss the derivation methods used in both works. In short,
the typical error (a factor of 2–3) inherent to mass accretion rate estimation methods should not lead to systematic
differences between different samples.

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14 Espaillat et al.
Table 1
Target Sample
Name
FM 177
FM 281
FM 515
FM 581
FM 618
LRLL 2
LRLL 6
LRLL 21
LRLL 31
LRLL 37
LRLL 55
LRLL 67
LRLL 68
LRLL 72
LRLL 133
Region
NGC 2068
NGC 2068
NGC 2068
NGC 2068
NGC 2068
IC 348
IC 348
IC 348
IC 348
IC 348
IC 348
IC 348
IC 348
IC 348
IC 348
RA
05h45m42s
05h45m53s
05h46m12s
05h46m19s
05h46m23s
03h44m35s
03h44m37s
03h44m56s
03h44m18s
03h44m38s
03h44m31s
03h43m45s
03h44m29s
03h44m23s
03h44m42s
DEC
–00d12m05s
–00d13m25s
+00d32m26s
–00d05m38s
–00d08m53s
+32d10m04s
+32d06m45s
+32d09m15s
+32d04m57s
+32d03m29s
+32d00m14s
+32d08m17s
+31d59m54s
+32d01m53s
+32d12m02s
Note.
Flaherty & Muzerolle (2008) and Luhman et al. (2003)
for targets in NGC 2068 and IC 348, respectively.
— TargetID’s are takenfrom
Table 2
IC 348 Optical Photometry
Target
LRLL 2
LRLL 6
LRLL 21
LRLL 31
LRLL 37
LRLL 55
LRLL 67
LRLL 68
LRLL 72
LRLL 133
V U–V
sat.
sat.
V–R
sat.
sat.
V–I
sat.
sat.
sat.
sat.
sat.
15.68±0.03
19.30±0.08
15.85±0.04
21.68±0.33
16.23±0.02
17.49±0.03
17.55±0.03
20.00±0.30
3.51±0.06
<0.8
2.68±0.25
<–1.58
2.04±0.11
2.53±0.31
2.38±0.20
<0.1
1.35±0.08
2.00±0.09
1.24±0.05
2.03±0.22
1.16±0.04
1.64±0.03
1.62±0.03
1.50±0.50
3.89±0.09
1.19±0.06
4.19±0.38
2.50±0.04
3.46±0.03
3.32±0.03
3.70±0.30
Note. — We use “sat.” to refer to observations that were sat-
urated and note upper limits for bands in which sources were not
detected.
Table 3
Source Properties
TargetAV
Spectral
Type
K4
M1
K2
K4
K1
A2
G3
K0
G6
K6
M0.5
M0.75
M3.5
M2.5
M5
T∗
(K)
4590
3720
4900
4590
5080
8970
5830
5250
5700
4205
3850
3720
3470
3580
3240
L∗
(M⊙)
1.0
0.4
2.5
4.1
2.2
57.1
16.6
3.8
5.0
1.3
1.0
0.5
0.5
0.7
0.2
M∗
(M⊙)
1.2
0.5
1.5
1.6
1.5
2.8
2.4
1.6
1.6
0.9
0.6
0.5
0.3
0.4
0.2
R∗
(R⊙)
1.5
1.6
2.2
3.1
1.9
3.1
4.0
2.4
2.3
2.2
2.2
1.8
2.0
2.1
1.5
˙ M
( 10−8M⊙yr−1)
0.004
0.002
3.10
2.57
1.21
–
–
0.20
1.4
0.13
–
0.01
0.04
<0.0003
<0.8
Lacc
(L⊙)
0.0009
0.0002
0.68
0.40
0.29
–
–
0.04
0.3
0.02
–
0.001
0.002
<0.00001
<0.78
˙ M
Source
Hα
Hα
Hα
Hα
Hα
–
–
Hα
F11
U-band
–
Hα
U-band
Hα
U-band
FM 177
FM 281
FM 515
FM 581
FM 618
LRLL 2
LRLL 6
LRLL 21
LRLL 31
LRLL 37
LRLL 55
LRLL 67
LRLL 68
LRLL 72
LRLL 133
1.6
2.0
1.6
4.1
2.9
3.8
3.9
4.7
8.6
2.8
8.5
2.0
2.1
3.0
3.6
Note. — Spectral types for objects in NGC
(2008) and Luhman et al. (2003), respectively, except in the case of LRLL 31 where we adopt the spectral
type of Flaherty et al. (2011). T∗ is taken from Kenyon & Hartmann (1995), based on the adopted spectral
type. L∗, M∗ and R∗ are calculated in this work. AV measurements for most of the objects are from this
work except for LRLL 2 and LRLL 6 where this value is adopted from Luhman et al. (2003). The last column
lists the method with which our mass accretion rates were calculated: Hα and U-band are from this work;
F11 is from Flaherty et al. (2011). For sources where mass accretion rate estimates are not listed here, we
adopt 1×10−8M⊙ yr−1.
2068 and IC 348 are adopted from Flaherty & Muzerolle

Page 15

The Transitional Disk Class 15
Table 4
Wall Properties of Sample
Target Disk
Type
Inner Wall
Ti
wall
(K)
(4)
–
–
–
–
–
1700a
1400
1800b
1400
1400
1400
1400
1400
1400
1400
Outer Wall
zo
wall
(K)
(8)
90
90
130
190
180
150
180
220
180
240
–
–
–
–
–
amax
(µm)
(3)
–
–
–
–
–
10
1.0
2
1.0
0.25
0.25
0.25
1.0
0.25
10.0
zi
(AU)
(5)
–
–
–
–
–
0.0071
0.0055
0.0017
0.01
0.0098
0.016
0.013
0.005
0.02
0.0023
wall
Ri
(AU)
(6)
–
–
–
–
–
0.12
0.22
0.13
0.32
0.17
0.3
1.68
0.54
0.14
0.07
wall
amax
(µm)
(7)
0.25
0.25
5.0
1.0
0.25
0.25
5.0
2.0
5.0
0.25
–
–
–
–
–
To
wall
Ro
(AU)
(10)
49
31
10
5
4
45
11
9
14
5
–
–
–
–
–
wall
(AU)
(9)
3.1
3.6
1.5
0.6
0.6
5
0.7
0.9
1.5
0.6
–
–
–
–
–
(1) (2)
TD
TD
TD
TD
TD
PTD
PTD
PTD
PTD
PTD
FD
FD
FD
FD
FD
FM 177
FM 281
LRLL 67
LRLL 72
LRLL 133
FM 515
FM 618
LRLL 21
LRLL 31
LRLL 37
FM 581
LRLL 2
LRLL 6
LRLL 55
LRLL 68
Note. — Col (1): Name of target. Col (2): Assigned classification for our targets. We label objects as
transitional disks (TD), pre-transitional disks (PTD), and full disks (FD). Col (3): Maximum grain size
of dust used for the inner wall of the disk. The superscript i denotes “inner wall.” Col (4): Temperature
of the inner wall. Col (5): Height of the inner wall. Col (6): Radius of the inner wall. Col (7): Maximum
grain size of dust used for the outer wall of the disk. The superscript o denotes “outer wall.” Col (8):
Temperature of the outer wall. Col (9): Height of the outer wall. Col (10): Radius of the outer wall.
aFor FM 515, the inner wall model required a temperature of 1700 K in order to fit the slope of the
NIR emission. In some cases, temperatures >1400 K for the inner wall have also been needed to fit the
SED previously (e.g. T35, UX Tau A; Espaillat et al. 2010, E11).
bWe adopt a temperature of 1800 K for the inner wall based upon NIR SpeX spectral fitting
Flaherty et al. (2012).
Table 5
Model Runs for LRLL 68
ModeliRd
(AU)
100
100
100
300
20
100
100
100
ǫαMdisk
(M⊙)
0.005
0.0005
0.00004
0.001
0.0001
0.001
0.001
0.001
1
2
3
4
5
6
7
8
60
60
60
60
60
20
40
80
0.0001
0.001
0.01
0.001
0.001
0.001
0.001
0.001
0.0006
0.006
0.06
0.006
0.006
0.006
0.006
0.006
Table 6
Mass Fraction (in %) of Silicates in Outer Wall in Transitional and
Pre-transitional Objects
TargetAmorphous
Olivine
80
90
100
100
80
80
70
100
60
90
Amorphous
Pyroxene
–
–
–
–
–
–
–
–
30
–
Crystalline
Forsterite
10
–
–
–
20
–
20
–
5
10
Crystalline
Enstatite
–
–
–
–
–
20
10
–
5
–
Crystalline
Silica
10
10
–
–
–
–
–
–
–
–
FM 177
FM 281
FM 515
FM 618
LRLL 21
LRLL 31
LRLL 37
LRLL 67
LRLL 72
LRLL 133