Gaseous Inner Disks
Gaseous Inner Disks
Joan R. Najita
National Optical Astronomy Observatory
John S. Carr
Naval Research Laboratory
Alfred E. Glassgold
University of California, Berkeley
Jeff A. Valenti
Space Telescope Science Institute
As the likely birthplaces of planets and an essential conduit for the buildup of stellar
masses, inner disks are of fundamental interest in star and planet formation. Studies of the
gaseous component of inner disks are of interest because of their ability to probe the dynamics,
physical and chemical structure, and gas content of this region. We review the observational
and theoretical developments in this field, highlighting the potential of such studies to, e.g.,
measure inner disk truncation radii, probe the nature of the disk accretion process, and chart the
evolution in the gas content of disks. Measurements of this kind have the potential to provide
unique insights on the physical processes governing star and planet formation.
1. INTRODUCTION
Circumstellar disks play a fundamental role in the for-
mation of stars and planets. A significant fraction of the
mass of a star is thought to be built up by accretion through
the disk. The gas and dust in the inner disk (r <10 AU)
also constitute the likely material from which planets form.
As a result, observations of the gaseous component of in-
ner disks have the potential to provide critical clues to the
physical processes governing star and planet formation.
From the planet formation perspective, probing the
structure, gas content, and dynamics of inner disks is of
interest, since they all play important roles in establish-
ing the architectures of planetary systems (i.e., planetary
masses, orbital radii, and eccentricities). For example, the
lifetime of gas in the inner disk (limited by accretion onto
the star, photoevaporation, and other processes) places an
upper limit on the timescale for giant planet formation (e.g.,
Zuckerman et al., 1995).
The evolution of gaseous inner disks may also bear on
the efficiency of orbital migration and the eccentricity evo-
lution of giant and terrestrial planets. Significant inward
orbital migration, induced by the interaction of planets with
a gaseous disk, is implied by the small orbital radii of extra-
solar giant planets compared to their likely formation dis-
tances (e.g., Ida and Lin, 2004). The spread in the orbital
radii of the planets (0.05–5 AU) has been further taken to in-
dicate that the timing of the dissipation of the inner disk sets
the final orbital radius of the planet (Trilling et al., 2002).
Thus, understanding how inner disks dissipate may impact
our understanding of the origin of planetary orbital radii.
Similarly, residual gas in the terrestrial planet region may
play a role in defining the final masses and eccentricities of
terrestrial planets. Such issues have a strong connection to
the question of the likelihood of solar systems like our own.
An important issue from the perspective of both star and
planet formation is the nature of the physical mechanism
that is responsible for disk accretion. Among the proposed
mechanisms, perhaps the foremost is the magnetorotational
instability (Balbus and Hawley, 1991) although other pos-
sibilities exist. Despite the significant theoretical progress
that has been made in identifying plausible accretion mech-
anisms (e.g., Stone et al., 2000), there is little observational
evidence that any of these processes are active in disks.
Studies of the gas in inner disks offer opportunities to probe
the nature of the accretion process.
For these reasons, it is of interest to probe the dynami-
cal state, physical and chemical structure, and the evolution
of the gas content of inner disks. We begin this Chapter
with a brief review of the development of this field and an
overview of how high resolution spectroscopy can be used
to study the properties of inner disks (Section 1). Previ-
ous reviews provide additional background on these top-
ics (e.g., Najita et al., 2000). In Sections 2 and 3, we re-
view recent observational and theoretical developments in
this field, first describing observational work to date on the
gas in inner disks, and then describing theoretical models
for the surface and interior regions of disks. In Section 4,
we look to the future, highlighting several topics that can be
explored using the tools discussed in Sections 2 and 3.
http://arxiv.org/abs/0704.1841v1
1.1 Historical Perspective
One of the earliest studies of gaseous inner disks was
the work by Kenyon and Hartmann on FU Orionis objects.
They showed that many of the peculiarities of these sys-
tems could be explained in terms of an accretion outburst in
a disk surrounding a low-mass young stellar object (YSO;
cf. Hartmann and Kenyon, 1996). In particular, the varying
spectral type of FU Ori objects in optical to near-infrared
spectra, evidence for double-peaked absorption line pro-
files, and the decreasing widths of absorption lines from
the optical to the near-infrared argued for an origin in an
optically thick gaseous atmosphere in the inner region of a
rotating disk. Around the same time, observations of CO
vibrational overtone emission, first in the BN object (Scov-
ille et al., 1983) and later in other high and low mass objects
(Thompson, 1985; Geballe and Persson, 1987; Carr, 1989),
revealed the existence of hot, dense molecular gas plausibly
located in a disk. One of the first models for the CO over-
tone emission (Carr, 1989) placed the emitting gas in an
optically-thin inner region of an accretion disk. However,
only the observations of the BN object had sufficient spec-
tral resolution to constrain the kinematics of the emitting
The circumstances under which a disk would produce
emission or absorption lines of this kind were explored in
early models of the atmospheres of gaseous accretion disks
under the influence of external irradiation (e.g., Calvet et
al., 1991). The models interpreted the FU Ori absorption
features as a consequence of midplane accretion rates high
enough to overwhelm external irradiation in establishing
a temperature profile that decreases with disk height. At
lower accretion rates, the external irradiation of the disk was
expected to induce a temperature inversion in the disk atmo-
sphere, producing emission rather than absorption features
from the disk atmosphere. Thus the models potentially pro-
vided an explanation for the FU Ori absorption features and
CO emission lines that had been detected.
By PPIV (Najita et al., 2000), high-resolution spec-
troscopy had demonstrated that CO overtone emission
shows the dynamical signature of a rotating disk (Carr et
al., 1993; Chandler et al., 1993), thus confirming theoreti-
cal expectations and opening the door to the detailed study
of gaseous inner disks in a larger number of YSOs. The
detection of CO fundamental emission (Section 2.3) and
emission lines of hot H2O (Section 2.2) had also added new
probes of the inner disk gas.
Seven years later, at PPV, we find both a growing number
of diagnostics available to probe gaseous inner disks as well
as increasingly detailed information that can be gleaned
from these diagnostics. Disk diagnostics familiar from
PPIV have been used to infer the intrinsic line broaden-
ing of disk gas, possibly indicating evidence for turbulence
in disks (Section 2.1). They also demonstrate the differen-
tial rotation of disks, provide evidence for non-equilibrium
molecular abundances (Section 2.2), probe the inner radii
of gaseous disks (Section 2.3), and are being used to probe
the gas dissipation timescale in the terrestrial planet region
(Section 4.1). Along with these developments, new spectral
line diagnostics have been used as probes of the gas in inner
disks. These include transitions of molecular hydrogen at
UV, near-infrared, and mid-infrared wavelengths (Sections
2.4, 2.5) and the fundamental ro-vibrational transitions of
the OH molecule (Section 2.2). Additional potential diag-
nostics are discussed in Section 2.6.
1.2 High Resolution Spectroscopy of Inner Disks
The growing suite of diagnostics can be used to probe in-
ner disks using standard high resolution spectroscopic tech-
niques. Although inner disks are typically too small to
resolve spatially at the distance of the nearest star form-
ing regions, we can utilize the likely differential rotation
of the disk along with high spectral resolution to separate
disk radii in velocity. At the warm temperatures (∼100 K–
5000 K) and high densities of inner disks, molecules are ex-
pected to be abundant in the gas phase and sufficiently ex-
cited to produce rovibrational features in the infrared. Com-
plementary atomic transitions are likely to be good probes
of the hot inner disk and the photodissociated surface lay-
ers at larger radii. By measuring multiple transitions of
different species, we should therefore be able to probe the
temperatures, column densities, and abundances of gaseous
disks as a function of radius.
With high spectral resolution we can resolve individual
lines, which facilitates the detection of weak spectral fea-
tures. We can also work around telluric absorption fea-
tures, using the radial velocity of the source to shift its spec-
tral features out of telluric absorption cores. This approach
makes it possible to study a variety of atomic and molecular
species, including those present in the Earth’s atmosphere.
Gaseous spectral features are expected in a variety of
situations. As already mentioned, significant vertical vari-
ation in the temperature of the disk atmosphere will pro-
duce emission (absorption) features if the temperature in-
creases (decreases) with height (Calvet et al., 1991; Mal-
bet and Bertout, 1991). In the general case, when the disk
is optically thick, observed spectral features measure only
the atmosphere of the disk and are unable to probe directly
the entire disk column density, a situation familiar from the
study of stellar atmospheres.
Gaseous emission features are also expected from re-
gions of the disk that are optically thin in the continuum.
Such regions might arise as a result of dust sublimation
(e.g., Carr, 1989) or as a consequence of grain growth and
planetesimal formation. In these scenarios, the disk would
have a low continuum opacity despite a potentially large gas
column density. Optically thin regions can also be produced
by a significant reduction in the total column density of the
disk. This situation might occur as a consequence of giant
planet formation, in which the orbiting giant planet carves
out a “gap” in the disk. Low column densities would also
be characteristic of a dissipating disk. Thus, we should be
able to use gaseous emission lines to probe the properties of
inner disks in a variety of interesting evolutionary phases.
2. OBSERVATIONS OF GASEOUS INNER DISKS
2.1 CO Overtone Emission
The CO molecule is expected to be abundant in the gas
phase over a wide range of temperatures, from the tem-
perature at which it condenses on grains (∼20 K) up to its
thermal dissociation temperature (∼4000 K at the densities
of inner disks). As a result, CO transitions are expected
to probe disks from their cool outer reaches (>100 AU) to
their innermost radii. Among these, the overtone transitions
of CO (∆v=2, λ=2.3µm) were the emission line diagnostics
first recognized to probe the gaseous inner disk.
CO overtone emission is detected in both low and high
mass young stellar objects, but only in a small fraction of
the objects observed. It appears more commonly among
higher luminosity objects. Among the lower luminosity
stars, it is detected from embedded protostars or sources
with energetic outflows (Geballe and Persson, 1987; Carr,
1989; Greene and Lada, 1996; Hanson et al., 1997; Luh-
man et al., 1998; Ishii et al., 2001; Figueredo et al., 2002;
Doppmann et al., 2005). The conditions required to excite
the overtone emission, warm temperatures (& 2000 K) and
high densities (>1010 cm−3), may be met in disks (Scoville
et al., 1983; Carr, 1989; Calvet et al., 1991), inner winds
(Carr, 1989), or funnel flows (Martin, 1997).
High resolution spectroscopy can be used to distinguish
among these possibilities. The observations typically find
strong evidence for the disk interpretation. The emission
line profiles of the v=2–0 bandhead in most cases show the
characteristic signature of bandhead emission from sym-
metric, double-peaked line profiles originating in a rotating
disk (e.g., Carr et al., 1993; Chandler et al., 1993; Na-
jita et al., 1996; Blum et al., 2004). The symmetry of the
observed line profiles argues against the likelihood that the
emission arises in a wind or funnel flow, since inflowing
or outflowing gas is expected to produce line profiles with
red- or blue-shifted absorption components (alternatively
line asymmetries) of the kind that are seen in the hydrogen
Balmer lines of T Tauri stars (TTS). Thus high resolution
spectra provide strong evidence for rotating inner disks.
The velocity profiles of the CO overtone emission are
normally very broad (>100km s−1). In lower mass stars
(∼1M⊙), the emission profiles show that the emission ex-
tends from very close to the star, ∼0.05 AU, out to ∼0.3 AU
(e.g., Chandler et al., 1993; Najita et al., 2000). The small
radii are consistent with the high excitation temperatures
measured for the emission (∼1500–4000K). Velocity re-
solved spectra have also been modeled in a number of high
mass stars (Blum et al., 2004; Bik and Thi, 2004), where the
CO emission is found to arise at radii ∼ 3AU.
The large near-infrared excesses of the sources in which
CO overtone emission is detected imply that the warm emit-
ting gas is located in a vertical temperature inversion re-
gion in the disk atmosphere. Possible heating sources for
the temperature inversion include: external irradiation by
the star at optical through UV wavelengths (e.g., Calvet
et al., 1991; D’Alessio et al., 1998) or by stellar X-rays
(Glassgold et al., 2004; henceforth GNI04); turbulent heat-
ing in the disk atmosphere generated by a stellar wind flow-
ing over the disk surface (Carr et al., 1993); or the dissi-
pation of turbulence generated by disk accretion (GNI04).
Detailed predictions of how these mechanisms heat the
gaseous atmosphere are needed in order to use the observed
bandhead emission strengths and profiles to investigate the
origin of the temperature inversion.
The overtone emission provides an additional clue that
suggests a role for turbulent dissipation in heating disk at-
mospheres. Since the CO overtone bandhead is made up
of closely spaced lines with varying inter-line spacing and
optical depth, the emission is sensitive to the intrinsic line
broadening of the emitting gas (as long as the gas is not op-
tically thin). It is therefore possible to distinguish intrinsic
line broadening from macroscopic motions such as rotation.
In this way, one can deduce from spectral synthesis model-
ing that the lines are suprathermally broadened, with line
widths approximately Mach 2 (Carr et al., 2004; Najita et
al., 1996). Hartmann et al. (2004) find further evidence for
turbulent motions in disks based on high resolution spec-
troscopy of CO overtone absorption in FU Ori objects.
Thus disk atmospheres appear to be turbulent. The tur-
bulence may arise as a consequence of turbulent angular
momentum transport in disks, as in the magnetorotational
instability (MRI; Balbus and Hawley, 1991) or the global
baroclinic instability (Klahr and Bodenheimer, 2003). Tur-
bulence in the upper disk atmosphere may also be generated
by a wind blowing over the disk surface.
2.2 Hot Water and OH Fundamental Emission
Water molecules are also expected to be abundant in
disks over a range of disk radii, from the temperature at
which water condenses on grains (∼150 K) up to its thermal
dissociation temperature (∼2500 K). Like the CO overtone
transitions, the rovibrational transitions of water are also ex-
pected to probe the high density conditions in disks. While
the strong telluric absorption produced by water vapor in
the Earth’s atmosphere will restrict the study of cool wa-
ter to space or airborne platforms, it is possible to observe
from the ground water that is much hotter than the Earth’s
atmosphere. Very strong emission from hot water can be
detected in the near-infrared even at low spectral resolution
(e.g., SVS-13; Carr et al., 2004). More typically, high reso-
lution spectroscopy of individual lines is required to detect
much weaker emission lines.
For example, emission from individual lines of water in
the K- and L-bands have been detected in a few stars (both
low and high mass) that also show CO overtone emission
(Carr et al., 2004; Najita et al., 2000; Thi and Bik, 2005).
Velocity resolved spectra show that the widths of the water
lines are consistently narrower than those of the CO emis-
sion lines. Spectral synthesis modeling further shows that
the excitation temperature of the water emission (typically
∼1500 K), is less than that of the CO emission. These re-
sults are consistent with both the water and CO originat-
ing in a differentially rotating disk with an outwardly de-
creasing temperature profile. That is, given the lower dis-
sociation temperature of water (∼2500 K) compared to CO
(∼4000 K), CO is expected to extend inward to smaller radii
than water, i.e., to higher velocities and temperatures.
The ∆v=1 OH fundamental transitions at 3.6µm have
also been detected in the spectra of two actively accreting
sources, SVS-13 and V1331 Cyg, that also show CO over-
tone and hot water emission (Carr et al., in preparation).
As shown in Fig. 1, these features arise in a region that
is crowded with spectral lines of water and perhaps other
species. Determining the strengths of the OH lines will,
therefore, require making corrections for spectral features
that overlap closely in wavelength.
Spectral synthesis modeling of the detected CO, H2O
and OH features reveals relative abundances that depart sig-
nificantly from chemical equilibrium (cf. Prinn, 1993), with
the relative abundances of H2O and OH a factor of 2–10
below that of CO in the region of the disk probed by both
diagnostics (Carr et al., 2004; Carr et al., in preparation;
see also Thi and Bik, 2005). These abundance ratios may
arise from strong vertical abundance gradients produced by
the external irradiation of the disk (see Section 3.4).
2.3 CO Fundamental Emission
The fundamental (∆v=1) transitions of CO at 4.6µm are
an important probe of inner disk gas in part because of their
broader applicability compared, e.g., to the CO overtone
lines. As a result of their comparatively small A-values, the
CO overtone transitions require large column densities of
warm gas (typically in a disk temperature inversion region)
in order to produce detectable emission. Such large column
densities of warm gas may be rare except in sources with
the largest accretion rates, i.e., those best able to tap a large
Fig. 1.— OH fundamental ro-vibrational emission from SVS-13
on a relative flux scale.
Fig. 2.— Gaseous inner disk radii for TTS from CO fundamental
emission (filled squares) compared with corotation radii for the
same sources. Also shown are dust inner radii from near-infrared
interferometry (filled circles; Akeson et al., 2005a,b) or spectral
energy distributions (open circles; Muzerolle et al., 2003). The
solid and dashed lines indicate an inner radius equal to, twice,
and 1/2 the corotation radius. The points for the three stars with
measured inner radii for both the gas and dust are connected by
dotted lines. Gas is observed to extend inward of the dust inner
radius and typically inward of the corotation radius.
accretion energy budget and heat a large column density
of the disk atmosphere. In contrast, the CO fundamental
transitions, with their much larger A-values, should be de-
tectable in systems with more modest column densities of
warm gas, i.e., in a broader range of sources. This is borne
out in high resolution spectroscopic surveys for CO funda-
mental emission from TTS (Najita et al., 2003) and Herbig
AeBe stars (Blake and Boogert, 2004) which detect emis-
sion from essentially all sources with accretion rates typical
of these classes of objects.
In addition, the lower temperatures required to excite
the CO v=1–0 transitions make these transitions sensitive
to cooler gas at larger disk radii, beyond the region probed
by the CO overtone lines. Indeed, the measured line profiles
for the CO fundamental emission are broad (typically 50–
100km s−1 FWHM) and centrally peaked, in contrast to
the CO overtone lines which are typically double-peaked.
These velocity profiles suggest that the CO fundamental
emission arises from a wide range of radii, from .0.1 AU
out to 1–2 AU in disks around low mass stars, i.e., the ter-
restrial planet region of the disk (Najita et al., 2003).
CO fundamental emission spectra typically show sym-
metric emission lines from multiple vibrational states (e.g.,
v=1–0, 2–1, 3–2); lines of 13CO can also be detected when
the emission is strong and optically thick. The ability to
study multiple vibrational states as well as isotopic species
within a limited spectral range makes the CO fundamental
lines an appealing choice to probe gas in the inner disk over
a range of temperatures and column densities. The relative
strengths of the lines also provide insight into the excitation
mechanism for the emission.
In one source, the Herbig AeBe star HD141569, the
excitation temperature of the rotational levels (∼200 K) is
much lower than the excitation temperature of the vibra-
tional levels (v=6 is populated), which is suggestive of UV
pumping of cold gas (Brittain et al., 2003). The emis-
sion lines from the source are narrow, indicating an origin
at &17 AU. The lack of fluorescent emission from smaller
radii strongly suggests that the region within 17 AU is de-
pleted of gaseous CO. Thus detailed models of the fluores-
cence process can be used to constrain the gas content in the
inner disk region (S. Brittain, personal communication).
Thus far HD141569 appears to be an unusual case. For
the majority of sources from which CO fundamental is de-
tected, the relative line strengths are consistent with emis-
sion from thermally excited gas. They indicate typical ex-
citation temperatures of 1000–1500K and CO column den-
sities of ∼1018 cm−2 for low mass stars. These temper-
atures are much warmer than the dust temperatures at the
same radii implied by spectral energy distributions (SEDs)
and the expectations of some disk atmosphere models (e.g.,
D’Alessio et al., 1998). The temperature difference can be
accounted for by disk atmosphere models that allow for the
thermal decoupling of the gas and dust (Section 3.2).
For CTTS systems in which the inclination is known, we
can convert a measured HWZI velocity for the emission to
an inner radius. The CO inner radii, thus derived, are typ-
ically ∼0.04 AU for TTS (Najita et al., 2003; Carr et al.,
in preparation), smaller than the inner radii that are mea-
sured for the dust component either through interferometry
(e.g., Eisner et al., 2005; Akeson et al., 2005a; Colavita et
al., 2003; see chapter by Millan-Gabet et al.) or through the
interpretation of SEDs (e.g., Muzerolle et al., 2003). This
shows that gaseous disks extend inward to smaller radii than
dust disks, a result that is not surprising given the relatively
low sublimation temperature of dust grains (∼1500–2000
K) compared to the CO dissociation temperature (∼4000
K). These results are consistent with the suggestion that the
inner radius of the dust disk is defined by dust sublimation
rather than by physical truncation (Muzerolle et al., 2003;
Eisner et al., 2005).
Perhaps more interestingly, the inner radius of the CO
emission appears to extend up to and usually within the
corotation radius (i.e., the radius at which the disk rotates
at the same angular velocity as the star; Fig. 2). In the cur-
rent paradigm for TTS, a strong stellar magnetic field trun-
cates the disk near the corotation radius. The coupling be-
tween the stellar magnetic field and the gaseous inner disk
regulates the rotation of the star, bringing the star into coro-
tation with the disk at the coupling radius. From this re-
gion emerge both energetic (X-)winds and magnetospheric
accretion flows (funnel flows; Shu et al., 1994). The ve-
locity extent of the CO fundamental emission shows that
gaseous circumstellar disks indeed extend inward beyond
Fig. 3.— The distribution of gaseous inner radii, measured with
the CO fundamental transitions, compared to the distribution of
orbital radii of short-period extrasolar planets. A minimum plane-
tary orbital radius of ∼0.04 AU is similar to the minimum gaseous
inner radius inferred from the CO emission line profiles.
the dust destruction radius to the corotation radius (and be-
yond), providing the material that feeds both X-winds and
funnel flows. Such small coupling radii are consistent with
the rotational rates of young stars.
It is also interesting to compare the distribution of inner
radii for the CO emission with the orbital radii of the “close-
in” extrasolar giant planets (Fig. 3). Extra-solar planets
discovered by radial velocity surveys are known to pile-up
near a minimum radius of 0.04 AU. The similarity between
these distributions is roughly consistent with the idea that
the truncation of the inner disk can halt the inward orbital
migration of a giant planet (Lin et al., 1996). In detail, how-
ever, the planet is expected to migrate slightly inward of
the truncation radius, to the 2:1 resonance, an effect that
is not seen in the present data. A possible caveat is that
the wings of the CO lines may not trace Keplerian motion
or that the innermost gas is not dynamically significant. It
would be interesting to explore this issue further since the
results impact our understanding of planet formation and
the origin of planetary architectures. In particular, the ex-
istence of a stopping mechanism implies a lower efficiency
for giant planet formation, e.g., compared to a scenario in
which multiple generations of planets form and only the last
generation survives (e.g., Trilling et al., 2002).
2.4 UV Transitions of Molecular Hydrogen
Among the diagnostics of inner disk gas developed since
PPIV, perhaps the most interesting are those of H2. H2 is
presumably the dominant gaseous species in disks, due to
high elemental abundance, low depletion onto grains, and
robustness against dissociation. Despite its expected ubiq-
uity, H2 is difficult to detect because permitted electronic
transitions are in the far ultraviolet (FUV) and accessible
only from space. Optical and rovibrational IR transitions
have radiative rates that are 14 orders of magnitude smaller.
1208  1212  1216  1220  
Vacuum Wavelength (Å)
TW Hya
v"=0 v"=1 v"=2 v"=3
  E/k =
20,000 K
Fig. 4.— Lyα emission from TW Hya, an accreting T Tauri star,
and a reconstruction of the Lyα profile seen by the circumstel-
lar H2. Each observed H2 progression (with a common excited
state) yields a single point in the reconstructed Lyα profile. The
wavelength of each point in the reconstructed Lyα profile corre-
sponds to the wavelength of the upward transition that pumps the
progression. The required excitation energies for the H2 before the
pumping is indicated in the inset energy level diagram. There are
no low excitation states of H2 with strong transitions that overlap
Lyα. Thus, the H2 must be very warm to be preconditioned for
pumping and subsequent fluorescence.
Considering only radiative transitions with spontaneous
rates above 107 s−1, H2 has about 9000 possible Lyman-
band (B-X) transitions from 850-1650 Å and about 5000
possible Werner-band (C-X) transitions from 850-1300 Å
(Abgrall et al., 1993a,b). However, only about 200 FUV
transitions have actually been detected in spectra of accret-
ing TTS. Detected H2 emission lines in the FUV all origi-
nate from about two dozen radiatively pumped states, each
more than 11 eV above ground. These pumped states of
H2 are the only ones connected to the ground electronic
configuration by strong radiative transitions that overlap the
broad Lyα emission that is characteristic of accreting TTS
(see Fig. 4). Evidently, absorption of broad Lyα emission
pumps the H2 fluorescence. The two dozen strong H2 tran-
sitions that happen to overlap the broad Lyα emission are
all pumped out of high v and/or high J states at least 1 eV
above ground (see inset in Fig. 4). This means some mech-
anism must excite H2 in the ground electronic configura-
tion, before Lyα pumping can be effective. If the excitation
mechanism is thermal, then the gas must be roughly 103 K
to obtain a significant H2 population in excited states.
H2 emission is a ubiquitous feature of accreting TTS.
Fluoresced H2 is detected in the spectra of 22 out of 24 ac-
creting TTS observed in the FUV by HST/STIS (Herczeg et
al., 2002; Walter et al., 2003; Calvet et al., 2004; Bergin et
al., 2004; Gizis et al., 2005; Herczeg et al., 2005; unpub-
lished archival data). Similarly, H2 is detected in all 8 ac-
creting TTS observed by HST/GHRS (Ardila et al., 2002)
and all 4 published FUSE spectra (Wilkinson et al., 2002;
Herczeg et al., 2002; 2004; 2005). Fluoresced H2 was even
detected in 13 out of 39 accreting TTS observed by IUE,
despite poor sensitivity (Brown et al., 1981; Valenti et al.,
2000). Fluoresced H2 has not been detected in FUV spec-
tra of non-accreting TTS, despite observations of 14 stars
with STIS (Calvet et al., 2004; unpublished archival data),
1 star with GHRS (Ardila et al., 2002), and 19 stars with
IUE (Valenti et al., 2000). However, the existing observa-
tions are not sensitive enough to prove that the circumstellar
H2 column decreases contemporaneously with the dust con-
tinuum of the inner disk. When accretion onto the stellar
surface stops, fluorescent pumping becomes less efficient
because the strength and breadth of Lyα decreases signifi-
cantly and the H2 excitation needed to prime the pumping
mechanism may become less efficient. COS, if installed on
HST, will have the sensitivity to set interesting limits on H2
around non-accreting TTS in the TW Hya association.
The intrinsic Lyα profile of a TTS is not observable at
Earth, except possibly in the far wings, due to absorption by
neutral hydrogen along the line of sight. However, observa-
tions of H2 line fluxes constrain the Lyα profile seen by the
fluoresced H2. The rate at which a particular H2 upward
transition absorbs Lyα photons is equal to the total rate
of observed downward transitions out of the pumped state,
corrected for missing lines, dissociation losses, and propa-
gation losses. If the total number of excited H2 molecules
before pumping is known (e.g., by assuming a temperature),
then the inferred pumping rate yields a Lyα flux point at the
wavelength of each pumping transition (Fig. 4).
Herczeg et al. (2004) applied this type of analysis to
TW Hya, treating the circumstellar H2 as an isothermal,
self-absorbing slab. Fig. 4 shows reconstructed Lyα flux
points for the upward pumping transitions, assuming the
fluoresced H2 is at 2500 K. The smoothness of the recon-
structed Lyα flux points implies that the H2 level popula-
tions are consistent with thermal excitation. Assuming an
H2 temperature warmer or cooler by a few hundred degrees
leads to unrealistic discontinuities in the reconstructed Lyα
flux points. The reconstructed Lyα profile has a narrow
absorption component that is blueshifted by −90 kms−1,
presumably due to an intervening flow.
The spatial morphology of fluoresced H2 around TTS
is diverse. Herczeg et al. (2002) used STIS to observe TW
Hya with 50 mas angular resolution, corresponding to a spa-
tial resolution of 2.8 AU at a distance of 56 pc, finding no
evidence that the fluoresced H2 is extended. At the other
extreme, Walter et al. (2003) detected fluoresced H2 up to
9 arcsec from T Tau N, but only in progressions pumped by
H2 transitions near the core of Lyα. Fluoresced H2 lines
have a main velocity component at or near the stellar radial
velocity and perhaps a weaker component that is blueshifted
by tens of km s−1 (Herczeg et al., 2006). These two compo-
nents are attributed to the disk and the outflow, respectively.
TW Hya has H2 lines with no net velocity shift, consistent
with formation in the face-on disk (Herczeg et al., 2002).
On the other hand, RU Lup has H2 lines that are blueshifted
by 12 kms−1, suggesting formation in an outflow. In both
of these stars, absorption in the blue wing of the C II 1335
Å wind feature strongly attenuates H2 lines that happen to
overlap in wavelength, so in either case H2 forms inside the
warm atomic wind (Herczeg et al., 2002; 2005).
The velocity widths of fluoresced H2 lines (after re-
moving instrumental broadening) range from 18 km s−1 to
28 km s−1 for the 7 accreting TTS observed at high spec-
tral resolution with STIS (Herczeg et al., 2006). Line width
does not correlate well with inclination. For example, TW
Hya (nearly face-on disk) and DF Tau (nearly edge-on disk)
both have line widths of 18 km s−1. Thermal broadening
is negligible, even at 2000 K. Keplerian motion, enforced
corotation, and outflow may all contribute to H2 line width
in different systems. More data are needed to understand
how velocity widths (and shifts) depend on disk inclination,
accretion rate, and other factors.
2.5 Infrared Transitions of Molecular Hydrogen
Transitions of molecular hydrogen have also been stud-
ied at longer wavelengths, in the near- and mid-infrared.
The v=1–0 S(1) transition of H2 (at 2µm) has been de-
tected in emission in a small sample of classical T Tauri
stars (CTTS) and one weak T Tauri star (WTTS; Bary et
al., 2003 and references therein). The narrow emission
lines (.10kms−1), if arising in a disk, indicate an origin at
large radii, probably beyond 10 AU. The high temperatures
required to excite these transitions thermally (1000s K), in
contrast to the low temperatures expected for the outer disk,
suggest that the emission is non-thermally excited, possibly
by X-rays (Bary et al., 2003). The measurement of other
rovibrational transitions of H2 is needed to confirm this.
The gas mass detectable by this technique depends on
the depth to which the exciting radiation can penetrate the
disk. Thus, the emission strength may be limited either by
the strength of the radiation field, if the gas column density
is high, or by the mass of gas present, if the gas column
density is low. While it is therefore difficult to measure to-
tal gas masses with this approach, clearly non-thermal pro-
cesses can light up cold gas, making it easier to detect.
Emission from a WTTS is surprising since WTTS are
thought to be largely devoid of circumstellar dust and gas,
given the lack of infrared excesses and the low accre-
tion rates for these systems. The Bary et al. results call
this assumption into question and suggest that longer lived
gaseous reservoirs may be present in systems with low ac-
cretion rates. We return to this issue in Section 4.1.
At longer wavelengths, the pure rotational transitions of
H2 are of considerable interest because molecular hydrogen
carries most of the mass of the disk, and these mid-infrared
transitions are capable of probing the ∼100 K temperatures
that are expected for the giant planet region of the disk.
These transitions present both advantages and challenges
as probes of gaseous disks. On the one hand, their small A-
values make them sensitive, in principle, to very large gas
masses (i.e., the transitions do not become optically thick
until large gas column densities NH=10
− 1024 cm−2 are
reached). On the other hand, the small A-values also im-
ply small critical densities, which allows the possibility of
contaminating emission from gas at lower densities not as-
sociated with the disk, including shocks in outflows and UV
excitation of ambient gas.
In considering the detectability of H2 emission from
gaseous disks mixed with dust, one issue is that the dust
continuum can become optically thick over column densi-
ties NH ≪ 10
− 1024 cm−2. Therefore, in a disk that is
optically thick in the continuum (i.e., in CTTS), H2 emis-
sion may probe smaller column densities. In this case, the
line-to-continuum contrast may be low unless there is a
strong temperature inversion in the disk atmosphere, and
high signal-to-noise observations may be required to detect
the emission. In comparison, in disk systems that are op-
tically thin in the continuum (e.g., WTTS), H2 could be a
powerful probe as long as there are sufficient heating mech-
anisms (e.g., beyond gas-grain coupling) to heat the H2.
A thought-provoking result from ISO was the report
of approximately Jupiter-masses of warm gas residing in
∼20 Myr old debris disk systems (Thi et al., 2001) based
on the detection of the 28 µm and 17 µm lines of H2. This
result was surprising because of the advanced age of the
sources in which the emission was detected; gaseous reser-
voirs are expected to dissipate on much shorter timescales
(Section 4.1). This intriguing result is, thus far, uncon-
firmed by either ground-based studies (Richter et al., 2002;
Sheret et al., 2003; Sako et al., 2005) or studies with Spitzer
(e.g., Chen et al., 2004).
Nevertheless, ground-based studies have detected pure
rotational H2 emission from some sources. Detections to
date include AB Aur (Richter et al., 2002). The narrow
width of the emission in AB Aur (∼10 kms−1 FWHM),
if arising in a disk, locates the emission beyond the giant
planet region. Thus, an important future direction for these
studies is to search for H2 emission in a larger number of
sources and at higher velocities, in the giant planet region
of the disk. High resolution mid-IR spectrographs on >3-
m telescopes will provide the greater sensitivity needed for
such studies.
2.6 Potential Disk Diagnostics
In a recent development, Acke et al. (2005) have reported
high resolution spectroscopy of the [OI] 6300 Å line in Her-
big AeBe stars. The majority of the sources show a narrow
(<50 km s−1 FWHM), fairly symmetric emission compo-
nent centered at the radial velocity of the star. In some
cases, double-peaked lines are detected. These features are
interpreted as arising in a surface layer of the disk that is
irradiated by the star. UV photons incident on the disk sur-
face are thought to photodissociate OH and H2O, produc-
ing a non-thermal population of excited neutral oxygen that
decays radiatively, producing the observed emission lines.
Fractional OH abundances of ∼10−7 − 10−6 are needed to
account for the observed line luminosities.
Another recent development is the report of strong ab-
sorption in the rovibrational bands of C2H2, HCN, and CO2
in the 13–15 µm spectrum of a low-mass class I source in
Ophiuchus, IRS 46 (Lahuis et al., 2006). The high excita-
tion temperature of the absorbing gas (400-900 K) suggests
an origin close to the star, an interpretation that is consis-
tent with millimeter observations of HCN which indicate a
source size ≪100 AU. Surprisingly, high dispersion obser-
vations of rovibrational CO (4.7 µm) and HCN (3.0 µm)
show that the molecular absorption is blueshifted relative
to the molecular cloud. If IRS 46 is similarly blueshifted
relative to the cloud, the absorption may arise in the at-
mosphere of a nearly edge-on disk. A disk origin for the
absorption is consistent with the observed relative abun-
dances of C2H2, HCN, and CO2 (10
−6–10−5), which are
close to those predicted by Markwick et al. (2002) for the
inner region of gaseous disks (.2 AU; see Section 3). Alter-
natively, if IRS 46 has approximately the same velocity as
the cloud, then the absorbing gas is blueshifted with respect
to the star and the absorption may arise in an outflowing
wind. Winds launched from the disk, at AU distances, may
have molecular abundances similar to those observed if the
chemical properties of the wind change slowly as the wind
is launched. Detailed calculations of the chemistry of disk
winds are needed to explore this possibility. The molecular
abundances in the inner disk midplane (Section 3.3) provide
the initial conditions for such studies.
3. THERMAL-CHEMICAL MODELING
3.1 General Discussion
The results discussed in the previous section illustrate
the growing potential for observations to probe gaseous in-
ner disks. While, as already indicated, some conclusions
can be drawn directly from the data coupled with simple
spectral synthesis modeling, harnessing the full diagnos-
tic potential of the observations will likely rely on detailed
models of the thermal-chemical structure (and dynamics)
of disks. Fortunately, the development of such models has
been an active area of recent research. Although much of
the effort has been devoted to understanding the outer re-
gions of disks (∼100 AU; e.g., Langer et al., 2000; chap-
ters by Bergin et al. and Dullemond et al.), recent work has
begun to focus on the region within 10 AU.
Because disks are intrinsically complex structures, the
models include a wide array of processes. These encom-
pass heating sources such as stellar irradiation (including
far UV and X-rays) and viscous accretion; chemical pro-
cesses such as photochemistry and grain surface reactions;
and mass transport via magnetocentrifugal winds, surface
evaporative flows, turbulent mixing, and accretion onto the
star. The basic goal of the models is to calculate the den-
sity, temperature, and chemical abundance structures that
result from these processes. Ideally, the calculation would
be fully self-consistent, although approximations are made
to simplify the problem.
A common simplification is to adopt a specified density
distribution and then solve the rate equations that define the
chemical model. This is justifiable where the thermal and
chemical timescales are short compared to the dynamical
timescale. A popular choice is the α-disk model (Shakura
and Sunyaev, 1973; Lynden-Bell and Pringle, 1974) in
which a phenomenological parameter α characterizes the
efficiency of angular momentum transport; its vertically av-
eraged value is estimated to be ∼10−2 for T Tauri disks
on the basis of measured accretion rates (Hartmann et al.,
1998). Both vertically isothermal α-disk models and the
Hayashi minimum mass solar nebula (e.g., Aikawa et al.,
1999) were adopted in early studies.
An improved method removes the assumption of vertical
isothermality and calculates the vertical thermal structure of
the disk including viscous accretion heating at the midplane
(specified by α) and stellar radiative heating under the as-
sumption that the gas and dust temperatures are the same
(Calvet et al., 1991; D’Alessio et al., 1999). Several chemi-
cal models have been built using the D’Alessio density dis-
tribution (e.g., Aikawa and Herbst, 1999; GNI04; Jonkheid
et al., 2004).
Starting about 2001, theoretical models showed that the
gas temperature can become much larger than the dust tem-
perature in the atmospheres of outer (Kamp and van Zadel-
hoff, 2001) and inner (Glassgold and Najita, 2001) disks.
This suggested the need to treat the gas and dust as two in-
dependent but coupled thermodynamic systems. As an ex-
ample of this approach, Gorti and Hollenbach (2004) have
iteratively solved a system of chemical rate equations along
with the equations of hydrostatic equilibrium and thermal
balance for both the gas and the dust.
The chemical models developed so far are character-
ized by diversity as well as uncertainty. There is diver-
sity in the adopted density distribution and external radi-
ation field (UV, X-rays, and cosmic rays; the relative im-
portance of these depends on the evolutionary stage) and
in the thermal and chemical processes considered. The rel-
evant heating processes are less well understood than line
cooling. One issue is how UV, X-ray, and cosmic rays
heat the gas. Another is the role of mechanical heating
associated with various flows in the disk, especially accre-
tion (GNI04). The chemical processes are also less cer-
tain. Our understanding of astrochemistry is based mainly
on the interstellar medium, where densities and tempera-
tures are low compared to those of inner disks, except per-
haps in shocks and photon-dominated regions. New reac-
tion pathways or processes may be important at the higher
densities (> 107 cm−3) and higher radiation fields of in-
ner disks. A basic challenge is to understand the thermal-
chemical role of dust grains and PAHs. Indeed, perhaps the
most significant difference between models is the treatment
of grain chemistry. The more sophisticated models include
adsorption of gas onto grains in cold regions and desorption
Fig. 5.— Temperature profiles from GNI04 for a protoplanetary
disk atmosphere. The lower solid line shows the dust temperature
of D’Alessio et al. (1999) at a radius of 1 AU and a mass accretion
rate of 10−8M⊙ yr
−1. The upper curves show the corresponding
gas temperature as a function of the phenomenological mechani-
cal heating parameter defined by Equation 1, αh = 1 (solid line),
0.1 (dotted line), and 0.01 (dashed line). The αh = 0.01 curve
closely follows the limiting case of pure X-ray heating. The lower
vertical lines indicate the major chemical transitions, specifically
CO forming at ∼ 1021cm−2, H2 forming at ∼ 6 × 10
and water forming at higher column densities.
in warm regions. Yet another level of complexity is intro-
duced by transport processes which can affect the chemistry
through vertical or radial mixing.
An important practical issue in thermal-chemical mod-
eling is that self-consistent calculations become increas-
ingly difficult as the density, temperature, and the number
of species increase. Almost all models employ truncated
chemistries with with somewhere from 25 to 215 species,
compared with 396 in the UMIST data base (Le Teuff et
al., 2000). The truncation process is arbitrary, determined
largely by the goals of the calculations. Wiebe et al., (2003)
have an objective method for selecting the most important
reactions from large data bases. Additional insights into
disk chemistry are offered in the chapter by Bergin et al.
3.2 The Disk Atmosphere
As noted above, Kamp and van Zadelhoff (2001) con-
cluded in their model of debris disks that the gas and dust
temperature can differ, as did Glassgold and Najita (2001)
for T Tauri disks. The former authors developed a compre-
hensive thermal-chemical model where the heating is pri-
marily from the dissipation of the drift velocity of the dust
through the gas. For T Tauri disks, stellar X-rays, known
to be a universal property of low-mass YSOs, heat the gas
to temperatures thousands of degrees hotter than the dust
temperature.
Fig. 5 shows the vertical temperature profile obtained
by Glassgold et al. (2004) with a thermal-chemical model
based on the dust model of D’Alessio et al. (1999) for a
generic T Tauri disk. Near the midplane, the densities are
high enough to strongly couple the dust and gas. At higher
altitudes, the disk becomes optically thin to the stellar opti-
cal and infrared radiation, and the temperature of the (small)
grains rises, as does the still closely-coupled gas tempera-
ture. However, at still higher altitudes, the gas responds
strongly to the less attenuated X-ray flux, and its tempera-
ture rises much above the dust temperature. The presence
of a hot X-ray heated layer above a cold midplane layer was
obtained independently by Alexander et al. (2004).
GNI04 also considered the possibility that the surface
layers of protoplanetary disks are heated by the dissipation
of mechanical energy. This might arise through the interac-
tion of a wind with the upper layers of the disk or through
disk angular momentum transport. Since the theoretical un-
derstanding of such processes is incomplete, a phenomeno-
logical treatment is required. In the case of angular momen-
tum transport, the most widely accepted mechanism is the
MRI (Balbus and Hawley, 1991; Stone et al., 2000), which
leads to the local heating formula,
Γacc =
2Ω, (1)
where ρ is the mass density, c is the isothermal sound speed,
Ω is the angular rotation speed, and αh is a phenomeno-
logical parameter that depends on how the turbulence dis-
sipates. One can argue, on the basis of simulations by
Miller and Stone (2000), that midplane turbulence gener-
ates Alfvén waves which, on reaching the diffuse surface
regions, produce shocks and heating. Wind-disk heating
can be represented by a similar expression on the basis of
dimensional arguments. Equation 1 is essentially an adap-
tation of the expression for volumetric heating in an α-disk
model, where α can in general depend on position. GNI04
used the notation αh to distinguish its value in the disk at-
mosphere from the usual midplane value.
In the top layers fully exposed to X-rays, the gas tem-
perature at 1 AU is ∼5000 K. Further down, there is a warm
transition region (500–2000 K) composed mainly of atomic
hydrogen but with carbon fully associated into CO. The
conversion from atomic H to H2 is reached at a column
density of ∼6× 1021 cm−2, with more complex molecules
such as water forming deeper in the disk. The location
and thickness of the warm molecular region depends on the
strength of the surface heating. The curves in Fig. 5 illus-
trate this dependence for a T Tauri disk at r = 1AU. With
αh = 0.01, X-ray heating dominates this region, whereas
with αh > 0.1, mechanical heating dominates.
Gas temperature inversions can also be produced by
UV radiation operating on small dust grains and PAHs, as
demonstrated by the thermal-chemical models of Jonkheid
et al. (2004) and Kamp and Dullemond (2004). Jonkheid et
al. use the D’Alessio et al. (1999) model and focus on the
disk beyond 50 AU. At this radius, the gas temperature can
rise to 800 K or 200 K, depending on whether small grains
are well mixed or settled. For a thin disk and a high stel-
lar UV flux, Kamp and Dullemond obtain temperatures that
asymptote to several 1000 K inside 50 AU. Of course these
results are subject to various assumptions that have been
made about the stellar UV, the abundance of PAHs, and the
growth and settling of dust grains.
Many of the earlier chemical models, oriented towards
outer disks (e.g., Willacy and Langer, 2000; Aikawa and
Herbst, 1999; 2001; Markwick et al., 2002), adopt a value
for the stellar UV radiation field that is 104 times larger
than Galactic at a distance of 100 AU. This choice can be
traced back to early IUE measurements of the stellar UV
beyond 1400 Å for several TTS (Herbig and Goodrich,
1986). Although the UV flux from TTS covers a range
of values and is undoubtedly time-variable, detailed stud-
ies with IUE (e.g., Valenti et al., 2000; Johns-Krull et al.,
2000) and FUSE (e.g., Wilkinson et al., 2002; Bergin et al.,
2003) indicate that it decreases into the FUV domain with a
typical value ∼10−15erg cm−2s−1 Å−1, much smaller than
earlier estimates. A flux of ∼10−15erg cm−2s−1 Å−1 at
Earth translates into a value at 100 AU of ∼100 times the
traditional Habing value for the interstellar medium. The
data in the FUV range are sparse, unfortunately, as a func-
tion of age or the evolutionary state of the system. More
measurements of this kind are needed since it is obviously
important to use realistic fluxes in the crucial FUV band be-
tween 912 and 1100 Å where atomic C can be photoionized
and H2 and CO photodissociated (Bergin et al., 2003 and
the chapter by Bergin et al.).
Whether stellar FUV or X-ray radiation dominates the
ionization, chemistry, and heating of protoplanetary disks is
important because of the vast difference in photon energy.
The most direct physical consequence is that FUV photons
cannot ionize H, and thus the abundance of carbon provides
an upper limit to the ionization level produced by the pho-
toionization of heavy atoms, xe ∼10
−4–10−3. Next, FUV
photons are absorbed much more readily than X-rays, al-
though this depends on the size and spatial distribution of
the dust grains, i.e, on grain growth and sedimentation. Us-
ing realistic numbers for the FUV and X-ray luminosities
of TTS, we estimate that LFUV ∼ LX. The rates used in
many early chemical models correspond to LX ≪ LFUV.
This suggests that future chemical modeling of protoplan-
etary disks should consider both X-rays and FUV in their
treatment of ionization, heating, and chemistry.
3.3 The Midplane Region
Unlike the warm upper atmosphere of the disk, which
is accessible to observation, the optically thick midplane is
much more difficult to study. Nonetheless, it is extremely
important for understanding the dynamics of the basic flows
in star formation such as accretion and outflow. The impor-
tant role of the ionization level for disk accretion via the
MRI was pointed out by Gammie (1996). The physical rea-
son is that collisional coupling between electrons and neu-
trals is required to transfer the turbulence in the magnetic
field to the neutral material of the disk. Gammie found
that Galactic cosmic rays cannot penetrate beyond a surface
layer of the disk. He suggested that accretion only occurs in
the surface of the inner disk (the “active region”) and not in
the much thicker midplane region (the “dead zone”) where
the ionization level is too small to mediate the MRI.
Glassgold et al. (1997) argued that the Galactic cosmic
rays never reach the inner disk because they are blown away
by the stellar wind, much as the solar wind excludes Galac-
tic cosmic rays. They showed that YSO X-rays do almost
as good a job as cosmic rays in ionizing surface regions,
thus preserving the layered accretion model of the MRI
for YSOs. Igea and Glassgold (1999) supported this con-
clusion with a Monte Carlo calculation of X-ray transport
through disks, demonstrating that scattering plays an impor-
tant role in the MRI by extending the active surface layer to
column densities greater than 1025 cm−2, approaching the
Galactic cosmic ray range used by Gammie (1996). This
early work showed that the theory of disk ionization and
chemistry is crucial for understanding the role of the MRI
for YSO disk accretion and possibly for planet formation.
Indeed, Glassgold, Najita, and Igea suggested that Gam-
mie’s dead zone might provide a good environment for the
formation of planets.
These challenges have been taken up by several groups
(e.g., Sano et al., 2000; Fromang et al., 2002; Semenov et
al., 2004; Kunz and Balbus, 2004; Desch, 2004; Matsumura
and Pudritz, 2003, 2005; and Ilgner and Nelson, 2006a,b).
Fromang et al. discussed many of the issues that affect the
size of the dead zone: differences in the disk model, such as
a Hayashi disk or a standard α-disk; temporal evolution of
the disk; the role of a small abundance of heavy atoms that
recombine mainly radiatively; and the value of the mag-
netic Reynolds number. Sano et al. (2000) explored the
role played by small dust grains in reducing the electron
fraction when it becomes as small as the abundance of dust
grains. They showed that the dead zone decreases and even-
tually vanishes as the grain size increases or as sedimenta-
tion towards the midplane proceeds. More recently, Inut-
suka and Sano (2005) have suggested that a small fraction
of the energy dissipated by the MRI leads to the produc-
tion of fast electrons with energies sufficient to ionize H2.
When coupled with vertical mixing of highly ionized sur-
face regions, Inutsuka and Sano argue that the MRI can self
generate the ionization it needs to be operative throughout
the entire disk.
Recent chemical modeling (Semenov et al., 2004; Ilgner
and Nelson, 2006a,b) confirms that the level of ionization in
the midplane is affected by many microphysical processes.
These include the abundances of radiatively-recombining
atomic ions, molecular ions, small grains, and PAHs. The
proper treatment of the ions represents a great challenge for
disk chemistry, one made particularly difficult by the lack
of observations of the dense gas at the midplane of the in-
ner disk. Thus the uncertainties in inner disk chemistry pre-
clude definitive quantitative conclusions about the midplane
ionization of protoplanetary disks. Perhaps the biggest wild
card is the issue of grain growth, emphasized anew by Se-
menov et al., (2004). If the disk grain size distribution were
close to interstellar, then the small grains would be effective
in reducing the electron fraction and producing dead zones.
But significant grain growth is expected and observed in the
disks of YSOs, limiting the extent of dead zones (e.g., Sano
et al., 2002).
The broader chemical properties of the inner midplane
region are also of great interest since most of the gas in the
disk is within one or two scale heights. The chemical com-
position of the inner midplane gas is important because it
provides the initial conditions for outflows and for the for-
mation of planets and other small bodies; it also determines
whether the MRI operates. Relatively little work has been
done on the midplane chemistry of the inner disk. For ex-
ample, GNI04 excluded N and S species and restricted the
carbon chemistry to species closely related to CO. However,
Willacy et al. (1998), Markwick et al. (2002), and Ilgner et
al. (2004) have carried out interesting calculations that shed
light on a possible rich organic chemistry in the inner disk.
Using essentially the same chemical model, these au-
thors follow mass elements in time as they travel in a steady
accretion flow towards the star. At large distances, the gas
is subject to adsorption, and at small distances to thermal
desorption. In between it reacts on the surface of the dust
grains; on being liberated from the dust, it is processed by
gas phase chemical reactions. The gas and dust are assumed
to have the same temperature, and all effects of stellar radi-
ation are ignored. The ionizing sources are cosmic rays and
26Al. Since the collisional ionization of low ionization po-
tential atoms is ignored, a very low ionization level results.
Markwick et al. improve on Willacy et al. by calculating the
vertical variation of the temperature, and Ilgner et al. con-
sider the effects of mixing. Near 1 AU, H2O and CO are
very abundant, as predicted by simpler models, but Mark-
wick et al. find that CH4 and CO have roughly equal abun-
dances. Nitrogen-bearing molecules, such as NH3, HCN,
and HNC are also predicted to be abundant, as are a vari-
ety of hydrocarbons such as CH4, C2H2, C2H3, C2H4, etc.
Markwick et al. also simulate the presence of penetrating X-
rays and find increased column densities of CN and HCO+.
Despite many uncertainties, these predictions are of interest
for our future understanding of the midplane region.
Infrared spectroscopic searches for hydrocarbons in
disks may be able to test these predictions. For example,
Gibb et al. (2004) searched for CH4 in absorption toward
HL Tau. The upper limit on the abundance of CH4 relative
to CO (<1%) in the absorbing gas may contradict the pre-
dictions of Markwick et al. (2002) if the absorption arises in
the disk atmosphere. However, some support for the Mark-
wick et al. (2002) model comes from a recent report by
Lahuis et al. (2006) of a rare detection by Spitzer of C2H2
and HCN in absorption towards a YSO, with ratios close to
those predicted for the inner disk (Section 2.6).
3.4 Modeling Implications
An interesting implication of the irradiated disk atmo-
sphere models discussed above is that the region of the at-
mosphere over which the gas and dust temperatures differ
includes the region that is accessible to observational study.
Indeed, the models have interesting implications for some
of the observations presented in Section 2. They can ac-
count roughly for the unexpectedly warm gas temperatures
that have been found for the inner disk region based on the
CO fundamental (Section 2.3) and UV fluorescent H2 tran-
sitions (Section 2.4). In essence, the warm gas temperatures
arise from the direct heating of the gaseous component and
the poor thermal coupling between the gas and dust com-
ponents at the low densities characteristic of upper disk at-
mospheres. The role of X-rays in heating disk atmospheres
has some support from the results of Bergin et al. (2004);
they suggested that some of the UV H2 emission from TTS
arises from excitation by fast electrons produced by X-rays.
In the models, CO is found to form at a column den-
sity NH≃10
21 cm−2 and temperature ∼1000 K in the ra-
dial range 0.5–2 AU (GNI04; Fig. 5), conditions similar to
those deduced for the emitting gas from the CO fundamen-
tal lines (Najita et al., 2003). Moreover, CO is abundant in
a region of the disk that is predominantly atomic hydrogen,
a situation that is favorable for exciting the rovibrational
transitions because of the large collisional excitation cross
section for H + CO inelastic scattering. Interestingly, X-
ray irradiation alone is probably insufficient to explain the
strength of the CO emission observed in actively-accreting
TTS. This suggests that other processes may be important
in heating disk atmospheres. GNI04 have explored the role
of mechanical heating. Other possible heating processes are
FUV irradiation of grains and or PAHs.
Molecular hydrogen column densities comparable to the
UV fluorescent column of ∼5 × 1018cm−2 observed from
TW Hya are reached at 1 AU at a total vertical hydrogen
column density of ∼5 × 1021cm−2, where the fractional
abundance of H2 is ∼10
−3 (GNI04; Fig. 5). Since Lyα
photons must traverse the entire ∼5×1021cm−2 in order to
excite the emission, the line-of-sight dust opacity through
this column must be relatively low. Observations of this
kind, when combined with atmosphere models, may be able
to constrain the gas-to-dust ratio in disk atmospheres, with
consequent implications for grain growth and settling.
Work in this direction has been carried out by Nomura
and Millar (2005). They have made a detailed thermal
model of a disk that includes the formation of H2 on grains,
destruction via FUV lines, and excitation by Lyα photons.
The gas at the surface is heated primarily by the photoelec-
tric effect on dust grains and PAHs, with a dust model ap-
propriate for interstellar clouds, i.e., one that reflects little
grain growth. Both interstellar and stellar UV radiation are
included, the latter based on observations of TW Hya. The
gas temperature at the surface of their flaring disk model
reaches 1500 K at 1 AU. They are partially successful in ac-
counting for the measurements of Herczeg et al. (2002), but
their model fluxes fall short by a factor of five or so. A
likely defect in their model is that the calculated tempera-
ture of the disk surface is too low, a problem that might be
remedied by reducing the UV attenuation by dust and by
including X-ray or other surface heating processes.
The relative molecular abundances that are predicted by
these non-turbulent, layered model atmospheres are also of
interest. At a distance of 1 AU, the calculations of GNI04
indicate that the relative abundance of H2O to CO is ∼10
in the disk atmosphere for column densities <1022 cm−2;
only at column densities >1023 cm−2 are H2O and CO
comparably abundant. The abundance ratio in the atmo-
sphere is significantly lower than the few relative abun-
dances measurements to date (0.1–0.5) at <0.3 AU (Carr
et al., 2004; Section 2.2). Perhaps layered model atmo-
spheres, when extended to these small radii, will be able to
account for the abundant water that is detected. If not, the
large water abundance may be evidence of strong vertical
(turbulent) mixing that carries abundant water from deeper
in the disk up to the surface. Thus, it would be of great in-
terest to develop the modeling for the sources and regions
where water is observed in the context of both layered mod-
els and those with vertical mixing. Work in this direction
has the potential to place unique constraints on the dynam-
ical state of the disk.
4. CURRENT AND FUTURE DIRECTIONS
As described in the previous sections, significant progress
has been made in developing both observational probes of
gaseous inner disks as well as the theoretical models that
are needed to interpret the observations. In this section,
we describe some areas of current interest as well as future
directions for studies of gaseous inner disks.
4.1 Gas Dissipation Timescale
The lifetime of gas in the inner disk is of interest in the
context of both giant and terrestrial planet formation. Since
significant gas must be present in the disk in order for a
gas giant to form, the gas dissipation timescale in the gi-
ant planet region of the disk can help to identify dominant
pathways for the formation of giant planets. A short dissi-
pation time scale favors processes such as gravitational in-
stabilities which can form giant planets on short time scales
(< 1000 yr; Boss, 1997; Mayer et al., 2002). A longer dissi-
pation time scale accommodates the more leisurely forma-
tion of planets in the core accretion scenario (few–10 Myr;
Bodenheimer and Lin, 2002).
Similarly, the outcome of terrestrial planet formation
(the masses and eccentricities of the planets and their con-
sequent habitability) may depend sensitively on the resid-
ual gas in the terrestrial planet region of the disk at ages
of a few Myr. For example, in the picture of terrestrial
planet formation described by Kominami and Ida (2002),
if the gas column density in this region is ≫1 g cm−2 at the
epoch when protoplanets assemble to form terrestrial plan-
ets, gravitational gas drag is strong enough to circularize
the orbits of the protoplanets, making it difficult for them
to collide and build Earth-mass planets. In contrast, if the
gas column density is ≪1 g cm−2, Earth-mass planets can
be produced, but gravitational gas drag is too weak to re-
circularize their orbits. As a result, only a narrow range of
gas column densities around ∼1 g cm−2 is expected to lead
to planets with the Earth-like masses and low eccentricities
that we associate with habitability on Earth.
From an observational perspective, relatively little is
known about the evolution of the gaseous component. Disk
lifetmes are typically inferred from infrared excesses that
probe the dust component of the disk, although processes
such as grain growth, planetesimal formation, and rapid
grain inspiraling produced by gas drag (Takeuchi and Lin,
2005) can compromise dust as a tracer of the gas. Our un-
derstanding of disk lifetimes can be improved by directly
probing the gas content of disks and using indirect probes
of disk gas content such as stellar accretion rates (see Na-
jita, 2006 for a review of this topic).
Several of the diagnostics decribed in Section 2 may be
suitable as direct probes of disk gas content. For example,
transitions of H2 and other molecules and atoms at mid-
through far-infrared wavelengths are thought to be promis-
ing probes of the giant planet region of the disk (Gorti and
Hollenbach, 2004). This is a important area of investigation
currently for the Spitzer Space Telescope and, in the future,
for Herschel and 8- to 30-m ground-based telescopes.
Studies of the lifetime of gas in the terrestrial planet
region are also in progress. The CO transitions are well
suited for this purpose because the transitions of CO and its
isotopes probe gas column densities in the range of inter-
est (10−4 − 1 g cm−2). A current study by Najita, Carr,
and Mathieu, which explores the residual gas content of
optically thin disks (Najita, 2004), illustrates some of the
challenges in probing the residual gas content of disks.
Firstly, given the well-known correlation between IR ex-
cess and accretion rate in young stars (e.g., Kenyon and
Hartmann, 1995), CO emission from sources with optically
thin inner disks may be intrinsically weak if accretion con-
tributes significantly to heating disk atmospheres. Thus,
high signal-to-noise spectra may be needed to detect this
emission. Secondly, since the line emission may be intrin-
sically weak, structure in the stellar photosphere may com-
plicate the identification of emission features. Fig. 6 shows
an example in which CO absorption in the stellar photo-
sphere of TW Hya likely veils weak emission from the disk.
Correcting for the stellar photosphere would not only am-
plify the strong v=1–0 emission that is clearly present (cf.
Rettig et al., 2004), it would also uncover weak emission
in the higher vibrational lines, confirming the presence of
the warmer gas probed by the UV fluorescent lines of H2
(Herczeg et al., 2002).
Stellar accretion rates provide a complementary probe
of the gas content of inner disks. In a steady accretion disk,
the column density Σ is related to the disk accretion rate Ṁ
by a relation of the form Σ ∝ Ṁ/αT , where T is the disk
temperature. A relation of this form allows us to infer Σ
from Ṁ given a value for the viscosity parameter α. Alter-
natively, the relation could be calibrated empirically using
measured disk column densities.
Fig. 6.— (Top) Spectrum of the transitional disk system TW
Hya at 4.6 µm (histogram). The strong emission in the v=1–0
CO fundamental lines extend above the plotted region. Although
the model stellar photospheric spectrum (light solid line) fits the
weaker features in the TW Hya spectrum, it predicts stronger ab-
sorption in the low vibrational CO transitions (indicated by the
lower vertical lines) than is observed. This suggests that the stellar
photosphere is veiled by CO emission from warm disk gas. (Bot-
tom) CO fundamental emission from the transitional disk system
V836 Tau. Vertical lines mark the approximate line centers at the
velocity of the star. The velocity widths of the lines locate the
emission within a few AU of the star, and the relative strengths of
the lines suggest optically thick emission. Thus, a large reservoir
of gas may be present in the inner disk despite the weak infrared
excess from this portion of the disk.
Accretion rates are available for many sources in the
age range 0.5–10 Myr (e.g., Gullbring et al., 1998; Hart-
mann et al., 1998; Muzerolle et al., 1998, 2000). A typical
value of 10−8M⊙ yr
−1 for TTS corresponds to a(n active)
disk column density of ∼100 g cm−2 at 1 AU for α=0.01
(D’Alessio et al., 1998). The accretion rates show an overall
decline with time with a large dispersion at any given age.
The existence of 10 Myr old sources with accretion rates as
large as 10−8M⊙ yr
−1 (Sicilia-Aguilar et al., 2005) sug-
gests that gaseous disks may be long lived in some systems.
Even the lowest measured accretion rates may be dy-
namically significant. For a system like V836 Tau (Fig. 6), a
∼3 Myr old (Siess et al., 1999) system with an optically thin
inner disk, the stellar accretion rate of 4 × 10−10M⊙ yr
(Hartigan et al., 1995; Gullbring et al., 1998) would corre-
spond to ∼4 g cm−2 at 1 AU. Although the accretion rate is
irrelevant for the buildup of the stellar mass, it corresponds
to a column density that would favorably impact terrestrial
planet formation. More interesting perhaps is St34, a TTS
with a Li depletion age of 25 Myr; its stellar accretion rate
of 2× 10−10M⊙ yr
−1 (White and Hillenbrand, 2005) sug-
gests a dynamically significant reservoir of gas in the inner
disk region. These examples suggest that dynamically sig-
nificant reservoirs of gas may persist even after inner disks
become optically thin and over the timescales needed to in-
fluence the outcome of terrestrial planet formation.
The possibility of long lived gaseous reservoirs can be
confirmed by using the diagnostics described in Section 2
to measure total disk column densities. Equally important,
a measured the disk column density, combined with the stel-
lar accretion rate, would allow us to infer a value for viscos-
ity parameter α for the system. This would be another way
of constraining the disk accretion mechanism.
4.2 Nature of Transitional Disk Systems
Measurements of the gas content and distribution in in-
ner disks can help us to identify systems in various states
of planet formation. Among the most interesting objects to
study in this context are the transitional disk systems, which
possess optically thin inner and optically thick outer disks.
Examples of this class of objects include TW Hya, GM Aur,
DM Tau, and CoKu Tau/4 (Calvet et al., 2002; Rice et al.,
2003; Bergin et al., 2004; D’Alessio et al., 2005; Calvet et
al., 2005). It was suggested early on that optically thin in-
ner disks might be produced by the dynamical sculpting of
the disk by orbiting giant planets (Skrutskie et al., 1990; see
also Marsh and Mahoney, 1992).
Indeed, optically thin disks may arise in multiple phases
of disk evolution. For example, as a first step in planet for-
mation (via core accretion), grains are expected to grow into
planetesimals and eventually rocky planetary cores, produc-
ing a region of the disk that has reduced continuum opac-
ity but is gas-rich. These regions of the disk may there-
fore show strong line emission. Determining the fraction
of sources in this phase of evolution may help to establish
the relative time scales for planetary core formation and the
accretion of gaseous envelope.
If a planetary core accretes enough gas to produce a low
mass giant planet (∼1MJ), it is expected to carve out a gap
in its vicinity (e.g., Takeuchi et al., 1996). Gap crossing
streams can replenish an inner disk and allow further accre-
tion onto both the star and planet (Lubow et al., 1999). The
small solid angle subtended by the accretion streams would
produce a deficit in the emission from both gas and dust in
the vicinity of the planet’s orbit. We would also expect to
detect the presence of an inner disk. Possible examples of
systems in this phase of evolution include GM Aur and TW
Hya in which hot gas is detected close to the star as is accre-
tion onto the star (Bergin et al., 2004; Herczeg et al., 2002;
Muzerolle et al., 2000). The absence of gas in the vicinity of
the planet’s orbit would help to confirm this interpretation.
Once the planet accretes enough mass via the accretion
streams to reach a mass ∼5–10MJ , it is expected to cut off
further accretion (e.g., Lubow et al., 1999). The inner disk
will accrete onto the star, leaving a large inner hole and no
trace of stellar accretion. CoKu Tau/4 is a possible example
of a system in this phase of evolution (cf. Quillen et al.,
2004) since it appears to have a large inner hole and a low
to negligible accretion rate (<few×10−10M⊙ yr
−1). This
interpretation predicts little gas anywhere within the orbit
of the planet.
At late times, when the disk column density around
10 AU has decreased sufficiently that the outer disk is being
photoevaporated away faster than it can resupply material
to the inner disk via accretion, the outer disk will decouple
from the inner disk, which will accrete onto the star, leav-
ing an inner hole that is devoid of gas and dust (the “UV
Switch” model; Clarke et al., 2001). Measurements of the
disk gas column density and the stellar accretion rate can
be used to test this possibility. As an example, TW Hya
is in the age range (∼10 Myr) where photoevaporation is
likely to be significant. However, the accretion rate onto
star, gas content of the inner disk (Sections 2 and 4), as well
as the column density inferred for the outer disk (32 g cm−2
at 20 AU based on the dust SED; Calvet et al., 2002) are all
much larger than is expected in the UV switch model. Al-
though this mechanism is, therefore, unlikely to explain the
SED for TW Hya, it may explain the presence of inner holes
in less massive disk systems of comparable age.
4.3 Turbulence in Disks
Future studies of gaseous inner disks may also help to
clarify the nature of the disk accretion process. As indicated
in Section 2.1, evidence for suprathermal line broadening in
disks supports the idea of a turbulent accretion process. A
turbulent inner disk may have important consequences for
the survival of terrestrial planets and the cores of giant plan-
ets. An intriguing puzzle is how these objects avoid Type-I
migration, which is expected to cause the object to lose an-
gular momentum and spiral into the star on short timescales
(e.g., Ward, 1997). A recent suggestion is that if disk accre-
tion is turbulent, terrestral planets will scatter off turbulent
fluctuations, executing a “random walk” which greatly in-
creases the migration time as well as the chances of survival
(Nelson et al., 2000; see chapter by Nelson et al.).
It would be interesting to explore this possible connec-
tion further by extending the approach used for the CO over-
tone lines to a wider range of diagnostics to probe the intrin-
sic line width as a function of radius and disk height. By
comparing the results to the detailed predictions of theoret-
ical models, it may be possible to distinguish between the
turbulent signature, produced e.g., by the MRI instability,
from the turbulence that might be produced by, e.g., a wind
blowing over the disk.
A complementary probe of turbulence may come from
exploring the relative molecular abundances in disks. As
noted in Section 3.4, if relative abundances cannot be ex-
plained by model predictions for non-turbulent, layered ac-
cretion flows, a significant role for strong vertical mixing
produced by turbulence may be implied. Although model-
dependent, this approach toward diagnosing turbulent ac-
cretion appears to be less sensitive to confusion from wind-
induced turbulence, especially if one can identify diagnos-
tics that require vertical mixing from deep down in the disk.
Another complementary approach toward probing the ac-
cretion process, discussed in Section 4.1, is to measure to-
tal gas column densities in low column density, dissipating
disks in order to infer values for the viscosity parameter α.
5. SUMMARY AND CONCLUSIONS
Recent work has lent new insights on the structure, dy-
namics, and gas content of inner disks surrounding young
stars. Gaseous atmospheres appear to be hotter than the dust
in inner disks. This is a consequence of irradiative (and pos-
sibly mechanical) heating of the gas as well as the poor ther-
mal coupling between the gas and dust at the low densities
of disk atmospheres. In accreting systems, the gaseous disk
appears to be turbulent and extends inward beyond the dust
sublimation radius to the vicinity of the corotation radius.
There is also evidence that dynamically significant reser-
voirs of gas can persist even after the inner disk becomes
optically thin in the continuum. These results bear on im-
portant star and planet formation issues such as the origin
of winds, funnel flows, and the rotation rates of young stars;
the mechanism(s) responsible for disk accretion; and the
role of gas in the determining the architectures of terres-
trial and giant planets. Although significant future work
is needed to reach any conclusions on these issues, the fu-
ture for such studies is bright. Increasingly detailed studies
of the inner disk region should be possible with the advent
of powerful spectrographs and interferometers (infrared and
submillimeter) as well as sophisticated models that describe
the coupled thermal, chemical, and dynamical state of the
disk.
Acknowledgments. We thank Stephen Strom who con-
tributed significantly to the discussion on the nature of tran-
sitional disk systems. We also thank Fred Lahuis and Matt
Richter for sharing manuscripts of their work in advance of
publication. AEG acknowledges support from the NASA
Origins and NSF Astronomy programs. JSC and JRN also
thank the NASA Origins program for its support.
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	INTRODUCTION
	OBSERVATIONS OF GASEOUS INNER DISKS
	THERMAL-CHEMICAL MODELING
	CURRENT AND FUTURE DIRECTIONS
	SUMMARY AND CONCLUSIONS
