# High-Resolution Mid-Infrared Spectroscopy of GV Tau N: Surface Accretion and
Detection of NH3 in a Young Protoplanetary Disk

Joan R. Najita  NSF’s NOIRLab, 950 N. Cherry Avenue, Tucson, AZ 85719, USA
John S. Carr  Department of Astronomy, University of Maryland, College Park,
MD 20742, USA  Sean D. Brittain  Clemson University, 118 Kinard Laboratory,
Clemson, SC 29634, USA  John H. Lacy  Department of Astronomy, University of
Texas at Austin, Austin, TX 78712, USA  Matthew J. Richter  Physics
Department, University of California at Davis, Davis, CA 95616, USA  Greg W.
Doppmann  W. M. Keck Observatory, 65-1120 Mamalahoa Hwy., Kamuela, HI 96743,
USA

###### Abstract

Physical processes that redistribute or remove angular momentum from
protoplanetary disks can drive mass accretion onto the star and affect the
outcome of planet formation. Despite ubiquitous evidence that protoplanetary
disks are engaged in accretion, the process(es) responsible remain unclear.
Here we present evidence for redshifted molecular absorption in the spectrum
of a Class I source that indicates rapid inflow at the disk surface. High
resolution mid-infrared spectroscopy of GV Tau N reveals a rich absorption
spectrum of individual lines of $\rm C_{2}H_{2}$, HCN, $\rm NH_{3}$, and $\rm
H_{2}O$. From the properties of the molecular absorption, we can infer that it
carries a significant accretion rate $\dot{M}_{\rm abs}\sim
10^{-8}-10^{-7}{M_{\odot}\,{\rm yr}^{-1}},$ comparable to the stellar
accretion rates of active T Tauri stars. Thus we may be observing disk
accretion in action. The results may provide observational evidence for
supersonic “surface accretion flows,” which have been found in MHD simulations
of magnetized disks. The observed spectra also represent the first detection
of $\rm NH_{3}$ in the planet formation region of a protoplanetary disk. With
$\rm NH_{3}$ only comparable in abundance to HCN, it cannot be a major missing
reservoir of nitrogen. If, as expected, the dominant nitrogen reservoir in
inner disks is instead N2, its high volatility would make it difficult to
incorporate into forming planets, which may help to explain the low nitrogen
content of the bulk Earth.

T Tauri stars, protoplanetary disks, stellar accretion disks, circumstellar
disks, planet formation, interstellar molecules

##  1 Introduction

Stars form surrounded by disks, the repositories of excess angular momentum
inherited from the molecular cloud that cannot be contained within the star
alone. Physical processes that redistribute or remove disk angular momentum
can drive mass accretion onto the star and affect the outcome of planet
formation; e.g., giant planets that form in the disk may be swept inward along
with the accretion flow. Although it is as yet unclear what physical
mechanism(s) generate accretion flows, the process(es) must be robust: T Tauri
stars (i.e., young stars surrounded by disks) commonly show excess UV emission
produced by mass flows that reach the stellar surface (Hartmann et al. 2016).

One clue to the nature of disk accretion comes from the sizes of gaseous
disks. Whereas disks in the embedded “Class I” phase of pre-main-sequence
evolution are modest in size (typically $<100$ au in radius), gas disks in the
more evolved “Class II” phase, when infall from the molecular cloud has
ceased, span a range of sizes including many much larger than 300 au (Najita &
Bergin 2018; Ansdell et al. 2018). The existence of such large disks is
remarkable given the multiple processes that can act to reduce disk sizes
(e.g., FUV photoevaporation, companion formation, disk winds). Their existence
suggests that internal angular momentum redistribution plays a large enough
role in driving accretion that a significant fraction of disks grow
substantially in size from the Class I to Class II phases (Najita & Bergin
2018). However there have been few observational clues to date as to the
nature of the process that redistributes the angular momentum. Disk spectral
line diagnostics offer the opportunity to probe the dynamics of disks for
potential new insights.

Spectral features in the mid-infrared (MIR) offer the opportunity to study the
dynamics and chemistry of planet formation environments. Class II (T Tauri)
disks commonly reveal a MIR spectrum that is rich in emission from water and
organic molecules ($\rm CO_{2}$, HCN, $\rm C_{2}H_{2}$; Carr & Najita 2008,
2011; Salyk et al. 2011). The emitting areas, line profiles, and thermal-
chemical properties of the emitting gas are consistent with emission from an
irradiated disk atmosphere within a few au of the star, i.e., the terrestrial
planet region of the disk (e.g., Najita & Ádámkovics 2017; Najita et al.
2018). In contrast to the frequent detection of MIR molecular emission, MIR
molecular absorption is detected only rarely from young stars at low spectral
resolution. Observations with the Spitzer Space Telescope detected molecular
absorption features of HCN, $\rm C_{2}H_{2}$, and $\rm CO_{2}$ from IRS 46
(Lahuis et al. 2006) and GV Tau (e.g., Bast et al. 2013), and $\rm CO_{2}$
from DG Tau B (Kruger et al. 2011; Pontoppidan et al. 2008). The similar
molecular species and gas temperatures detected in emission and absorption
suggested that the absorption features also arise in a disk atmosphere but
viewed close to edge on (Bast et al. 2013; Doppmann et al. 2008).

Here we report high resolution MIR spectroscopy of the Class I source GV Tau
N, which reveals a rich molecular absorption spectrum of individual lines of
$\rm C_{2}H_{2}$ and HCN, as well as $\rm H_{2}O$ and the first detection of
$\rm NH_{3}$ in the planet formation region of a protoplanetary disk. The
resolved line profiles, which have a significant redshifted component, may
provide observational evidence for a new accretion mechanism: supersonic
“surface accretion flows,” which have been found in MHD simulations of
magnetized disks (Zhu & Stone 2018; see also Stone & Norman 1994; Beckwith et
al. 2009; Guilet & Ogilvie 2012, 2013).

A young stellar binary in the Taurus molecular cloud (d=140 pc), GV Tau
(a.k.a. Haro 6–10, IRAS 04263+2426) comprises a bright optical source, GV Tau
S, and an infrared companion located 1.2′′ away, GV Tau N, which dominates the
MIR flux of the system (e.g., Leinert & Haas 1989; Sheehan & Eisner 2014).
While GV Tau has the strongly rising 2–25 $\rm\,\mu{\rm m}$ continuum
characteristic of Class I sources (e.g., Furlan et al. 2008), its relatively
weak gas and dust emission compared to other low-mass embedded YSOs suggests
that the system lacks a significant envelope (Hogerheijde et al. 1998). That
property and the poorly defined molecular outflow structure of the system
(Hogerheijde et al. 1998) suggest that it is a more evolved Class I source.
Spatially resolved millimeter imaging further suggests modest solid disk
masses for both GV Tau N and S (Sheehan & Eisner 2014) and small dust disk
sizes ($\sim 15$ au; Guilloteau et al. 2011).

In addition to the molecular absorption bands of HCN, $\rm C_{2}H_{2}$, and
$\rm CO_{2}$ detected with Spitzer (Bast et al. 2013), the spectrum of GV Tau
N also shows individual near-infrared (NIR) absorption lines of HCN, $\rm
C_{2}H_{2}$, CH4, and CO (Gibb et al. 2007; Doppmann et al. 2008; Gibb & Horne
2013; Davis et al. 2015). While CO absorption has been detected toward both
Class I and Class II sources at high spectral resolution (Brittain et al.
2005; Rettig et al. 2006; Horne et al. 2012; Kruger et al. 2011; Smith et al.
2015, Lee et al. 2016), organic absorption features are rarely seen. Here we
report a high spectral resolution observation of the MIR spectrum of GV Tau N.
The observations are described in Section 2, and the detected features are
analyzed in Section 3. In Section 4, we discuss the origin of the absorption
features and the possible support they provide for the existence of surface
accretion flows. We also comment on the detection of $\rm NH_{3}$ and its
implications for our understanding of the nitrogen reservoir in disks.

##  2 TEXES Observations

We observed GV Tau N with TEXES, the Texas Echelon-cross-Echelle spectrograph
(Lacy et al. 2002), on the Gemini-North 8m telescope during observing
campaigns in November 2006 and October 2007. We used the high resolution,
cross-dispersed mode for all observations with a slit width of 0.54′′. The
spectral resolving power in this instrumental configuration is
R$\approx$100,000. We nodded the object on the slit every $\sim$10 seconds to
facilitate background subtraction and removal of night-sky emission. TEXES
does not use the chopping secondary mirror. During the first visit to GV Tau
on (UT) 19 November 2006, we observed both GV Tau S and GV Tau N to confirm
that the mid-IR flux originated almost entirely with GV Tau N. Subsequent to
that observation, we concentrated solely on GV Tau N.

The spectral coverage in a single setting with TEXES is roughly 0.5% of the
central wavenumber. Therefore, we targeted specific molecular transitions in
each setting based on the telluric atmosphere, the source Doppler shift, and a
desire to cover a range of lower state levels and molecules. We used the
night-sky emission features to evaluate and adjust the spectral setting to
avoid desired features falling into gaps in the coverage; for $\lambda\geq 11\
\mu m$, the TEXES spectral orders are larger than the detector.

The standard observation sequence with TEXES includes observing an ambient
temperature blackbody roughly every 7 minutes as a flatfield. We also observed
a telluric calibrator, either a hot star or a featureless continuum source,
immediately before or after GV Tau N. The telluric calibrator helps to reduce
the impact of atmospheric absorption and to flatten the continuum beyond what
division by the blackbody alone provides. A log of the observations, including
the telluric calibrator used, is given in Table 1.

The data were reduced using the standard TEXES pipeline. The pipeline removes
spikes, rectifies the cross-dispersed echellograms, flatfields the data,
aligns and combines nod pairs, optimally extracts the spectrum of the
continuum object, and does a wavelength calibration using a night-sky emission
line. We subsequently divided the GV Tau N spectra by a scaled version of the
telluric calibrator spectrum to remove residual atmospheric lines.

The wavelength scale was refined using telluric absorption lines in the
spectrum of GV Tau N. For each setting, a dispersion function was fit to all
measureable telluric lines in each order, using the IRAF task
ecidentify.111IRAF was distributed by the National Optical Astronomy
Observatory, which was managed by the Association of Universities for Research
in Astronomy (AURA) under a cooperative agreement with the National Science
Foundation. The fits had an average rms residual of $0.15\,{\rm\,km\,s^{-1}}$
and an average maximum residual of $0.3\,{\rm\,km\,s^{-1}}$. Two observations
have larger uncertainties. The signal-to-noise for the $814\,{\rm\,cm^{-1}}$
setting from 2007 was too low to use telluric lines in the GV Tau N spectrum.
Instead, the dispersion function was fit to lines in the telluric standard
(rms $0.06\,{\rm\,km\,s^{-1}}$), and this solution was applied to GV Tau N.
Three measurable telluric lines in the GV Tau N spectrum were used to assign a
zero-point (wavelength shift) uncertainty of $0.5\,{\rm\,km\,s^{-1}}$. The
$932\,{\rm\,cm^{-1}}$ setting from 2007 only contains three telluric lines;
hence an independent dispersion solution was not possible. In this case, the
pipeline wavelength scale was retained, with an assumed uncertainty of
$1\,{\rm\,km\,s^{-1}}$.

Model telluric transmission spectra were utilized for a few of the settings.
Because the S/N for the $780\,{\rm\,cm^{-1}}$ setting was degraded due to
insufficient S/N in the telluric calibrator, corrections for atmospheric lines
were made using the software package TERRASPEC (Bender 2010). TERRASPEC was
also used to improve the correction for telluric water lines in the 767 and
$807\,{\rm\,cm^{-1}}$ settings. For all of the observations, additional
continuum normalization was carried out for each order of interest by fitting
a low-order polynomial to the continuum outside the intervals of absorption
from known molecular transitions in GV Tau N.

##  3 Analysis

In the TEXES spectra we detect numerous absorption lines of $\rm NH_{3}$, HCN,
and $\rm C_{2}H_{2}$, a few lines of $\rm H_{2}O$ in absorption, and $\rm
H_{2}$ in emission (Table 2). The $\rm H_{2}$ emission from GV Tau was
previously reported in Bitner et al. (2008) and is not discussed further here.
Most of the HCN and $\rm C_{2}H_{2}$ lines were measured in 2006, with
additional lines measured in 2007. The unexpected detection in 2006 of
numerous $\rm NH_{3}$ absorption lines was followed up in 2007 with grating
settings that probed lower energy $\rm NH_{3}$ transitions. Weak absorption
lines of water were also detected in the 2007 spectra. The entire set of
pipeline-reduced spectra for GV Tau N are shown in Figure A1. The positions
and identifications of the detected lines are indicated.

Figure 1: $\rm C_{2}H_{2}$ spectra (top) and normalized line profiles (bottom)
in 2006 (left) and 2007 (right). For reference, in the bottom panels, the
vertical lines mark the velocity of the molecular cloud core from Hogerheijde
et al. (1998). In the bottom panels, the profiles are scaled to extend from 0
at the bottom of the absorption to 1 in the continuum. The lines have an
absorption core at $v_{\rm helio}\simeq 20{\rm\,km\,s^{-1}}$ and a red wing
extending to $\sim 40{\rm\,km\,s^{-1}}.$ In both epochs, the strength of the
red wing relative to the core is greater in the higher energy lines (above
R23) than the lower energy lines.

While the $\rm H_{2}O$ lines are pure rotational transitions within the ground
vibrational state, the $\rm NH_{3}$, HCN, and $\rm C_{2}H_{2}$ absorption
lines are predominantly ro-vibrational transitions out of the ground
vibrational state to a higher vibrational state; the $\rm C_{2}H_{2}$
$\nu_{4}$+$\nu_{5}$ – $\nu_{4}$ line is an exception (see section 3.1).

The HCN $\nu_{2}$ vibrational mode is the bending mode. The $\nu_{5}$ mode of
$\rm C_{2}H_{2}$ (HCCH) is the symmetric bending mode, in which the two H
atoms vibrate together, and the $\nu_{4}$ mode is the antisymmetric bending
mode. In the R5 transition, for example, the rotational transition is J=5 to
J=6, Q5 is J=5 to J=5, and P5 is J=5 to J=4. For $\rm C_{2}H_{2}$, the H atom
spin statistics cause the odd-J (ortho) lines to be three times as strong as
the even-J lines, and Q-branch lines are approximately twice as strong as P-
and R-branch lines. Since HCN and $\rm C_{2}H_{2}$ are linear molecules in
their ground vibrational states, only the quantum number J is required to
label their rotational states, although the excited bending modes are split
into e and f states depending on the relative orientation of the rotational
axis and the bending motion.

For $\rm NH_{3}$, the $\nu_{2}$ vibrational mode is the ‘umbrella’ mode in
which the three H atoms vibrate together. The ground and $\nu_{2}$ states are
split by inversion splitting, with lines from the symmetric and anti-symmetric
states labelled s and a. For this symmetric top molecule the rotational state
is described by two quantum numbers, J (the total angular momentum) and K (the
angular momentum about the symmetry axis). Line strengths depend on both J and
K, but typically states with K=3n are twice as strong as those with
K=3n$\pm$1\. J can change in a radiative transition, but K does not.
Transitions are labelled by the lower state J and K.

###  3.1 HCN and $\rm C_{2}H_{2}$

We detect a total of 8 lines of the HCN $\nu_{2}$ band, 14 lines of the $\rm
C_{2}H_{2}$ $\nu_{5}$ band, and one line from the $\rm C_{2}H_{2}$
$\nu_{4}$+$\nu_{5}$ – $\nu_{4}$ band (i.e., absorption out of the $\nu_{4}$
vibrational level; Figure A1). In 2006, we detected 12 $\rm C_{2}H_{2}$ lines
between R5 and R37 and 6 HCN lines between R10 and R34. In 2007, we detected 6
$\rm C_{2}H_{2}$ lines between R15 and R37, as well as three HCN transitions
(R17, R18, R32) with limits on two additional HCN transitions (R33 and R34).
The lower energy levels of the observed lines range from $E_{\ell}<100$ K to
$\sim 1600$ K.

The absorption features range in strength from $\sim 1$% deep at high
excitation down to a maximum of $\sim 20$% deep at intermediate-$J$ values
(Fig. 1 and Fig. 2). Figure 1 shows representative line profiles of $\rm
C_{2}H_{2}$ over a range of excitation for 2006 (left) and 2007 (right), both
as observed (top) and with the absorption features scaled to the same depth
(bottom) in order to compare relative velocity profiles. In the bottom panels,
vertical lines indicate the velocity of the gaseous envelope surrounding GV
Tau (dashed line; $v_{\rm helio}=17.3\pm 0.5{\rm\,km\,s^{-1}}$; or $v_{\rm
LSR}=7.0\,{\rm\,km\,s^{-1}}$; Hogerheijde et al. 1998). The MIR molecular
absorption is clearly redshifted with respect to the molecular cloud velocity.

Figure 2: HCN spectra (top) and normalized line profiles (bottom) in 2006.
Like the $\rm C_{2}H_{2}$ lines, higher energy HCN lines show a red wing that
is stronger relative to the core than lower energy HCN lines. Figure 3: The
HCN and $\rm C_{2}H_{2}$ lines showed similar profiles at low-$J$ (top) and
high-$J$ (bottom) in 2006 and 2007 (not shown), suggesting that the HCN and
$\rm C_{2}H_{2}$ absorption arise in the same gas along the line of sight.

Figure 2 shows the HCN spectra and normalized profiles from the 2006 data; the
HCN profiles from 2007 are similar. Figure 3 compares the $\rm C_{2}H_{2}$ and
HCN profiles for low (top) and high (bottom) excitation lines. The $\rm
C_{2}H_{2}$ and HCN lines have nearly identical velocity profiles.

At low-$J$, the HCN and $\rm C_{2}H_{2}$ lines profiles both have a “single
dip” core absorption component centered at 21–22 $\rm\,km\,s^{-1}$ with a FWHM
of $\sim 8-10{\rm\,km\,s^{-1}}$, and a red wing extending to $\sim
40{\rm\,km\,s^{-1}}$ (Figs. 1, 2, 3). When scaled to the same depth, the $\rm
C_{2}H_{2}$ and HCN profiles show a trend in which the red wing becomes
stronger (relative to the core) at high $J$ (Fig. 1 and Fig. 2), i.e., the
high velocity gas is more highly excited or is more optically thick. While low
and intermediate rotational levels (e.g., R15 of $\rm C_{2}H_{2}$) tend to
show a wing that smoothly decreases in strength to the red, higher excitation
lines show more velocity structure. For example, the $\rm C_{2}H_{2}$ R37 line
could be fit with velocity components at 21, 28, and 36 $\rm\,km\,s^{-1}$. The
velocity structure of the $\rm NH_{3}$ (§3.2) and $\rm H_{2}O$ (§S3.3) lines
is similar to that seen in the HCN and $\rm C_{2}H_{2}$ lines, suggesting that
the molecular absorption is composed of multiple velocity components.

Figure 4: Comparison of $\rm C_{2}H_{2}$ ortho and para lines in 2006. If the
absorbing gas is optically thin, the odd-J lines should be approximately 3
times stronger than the adjacent even-J lines. The more modest ratio of the
absorption depths implies that the absorbing gas is marginally optically
thick. The relative absorption depths approach unity in the red wing,
indicating larger optical depths than in the line core.

If the absorbing gas is optically thin, the odd-$J$ $\rm C_{2}H_{2}$ lines
should be approximately 3 times stronger than the adjacent even-$J$ lines. For
several of the stronger $\rm C_{2}H_{2}$ lines observed (R14 vs. R15; R21 vs.
the average of R20 and R22; R23 vs. the average of R22 and R24), the ratio of
the absorption depths of the ortho and para lines is lower, $\sim 2$ in the
absorption core (Fig. 4), indicating that the odd-$J$ lines have optical
depths of $\sim 1$ or greater. The relative depths of the neighboring ortho-
para lines also differ between the core and the wing. The ratio of the
absorption depths declines from $\sim 2$ within the absorption core to $\sim
1$ in the red wing beyond 30 $\rm\,km\,s^{-1}$ (Fig. 4), indicating that the
even-$J$ $\rm C_{2}H_{2}$ lines are also optically thick in the high velocity
gas. Interestingly, the observed depths of the $\rm C_{2}H_{2}$ lines ($<20$%)
are far less than expected for optically thick lines. This suggests that the
line strengths are significantly diluted, or an intrinsically narrow line is
highly broadened by macroscopic motions, or some combination of these two
effects.

Figure 5: Spectra of $\rm NH_{3}$ absorption lines. The top panel shows the
aP(6,K) transitions observed in 2006. The two strongest lines have twice the
statistical weight of the others but similar profiles. The bottom panel shows
a selection of Q-branch lines of various strengths observed in 2007. The
weaker lines have a more flat-bottomed profile and a bluer velocity centroid.

###  3.2 $\rm NH_{3}$

We detect a total of 34 lines of the $\rm NH_{3}$ $\nu_{2}$ band (Figure A1):
12 transitions in 2006 with lower energy levels from $358{\rm\,cm^{-1}}$ to
$888{\rm\,cm^{-1}}$, and 27 transitions in 2007 with lower energy levels from
$17{\rm\,cm^{-1}}$ to $1581{\rm\,cm^{-1}}$. The $\rm NH_{3}$ absorption
strengths are similar to those of the $\rm C_{2}H_{2}$ and HCN lines and range
in strength from $\sim 1$% deep for the weakest measured lines to a maximum of
$\sim 30$% deep for the aQ(3,3) transition measured in 2007. Example spectra
for individual $\rm NH_{3}$ lines are shown in Figure 5 for several P-branch
lines from 2006 and Q-branch lines from 2007.

Figure 6: Comparison of the 2006 $\rm NH_{3}$ aP(6,K) average profile with
that of the $\rm C_{2}H_{2}$ R15 reveals similar profiles, suggesting that the
$\rm NH_{3}$ and $\rm C_{2}H_{2}$ arise in the gas along similar lines of
sight.

The profiles of the $\rm NH_{3}$ P-branch lines are roughly similar to the
$\rm C_{2}H_{2}$ and HCN profiles, although there are differences in detail.
Figure 6 compares the $\rm C_{2}H_{2}$ R15 line ($E_{\ell}=282\,{\rm
cm^{-1}}$) with the average of four aP(6,K) $\rm NH_{3}$ lines from 2006
($E_{\ell}=384-417\,{\rm cm^{-1}}$). Like the HCN and $\rm C_{2}H_{2}$ line
profiles discussed in the previous section, the P-branch $\rm NH_{3}$ line
profiles also have an absorption core at $\sim 22{\rm\,km\,s^{-1}}$ and a red
wing extending to $\sim 40{\rm\,km\,s^{-1}}$. However, the shape of the $\rm
NH_{3}$ core is more square bottomed, with a small shift in the velocity of
the blue edge. In addition, the aP(6,K) $\rm NH_{3}$ lines from 2006 show weak
emission blueward of the absorption. A similar emission component is not seen
in the line profiles of the other molecules, nor in the profiles of other $\rm
NH_{3}$ lines (including the aP(6,K) lines from 2007); however, the latter
could be due to lower signal-to-noise of the other spectra. Similar line
profiles are predicted in radiative transfer models of disk atmospheres with
modest radial flows (see Section 4.2).

Figure 7: Comparison of the $\rm NH_{3}$ aP(6,K) average profile
($E_{\ell}\sim 400\,{\rm\,cm^{-1}}$) and the sP(8,3) profile ($E_{\ell}$ = 679
$\rm\,cm^{-1}$) observed in 2007 shows that, like the $\rm C_{2}H_{2}$ and HCN
lines, the high velocity wing is stronger in the higher energy transitions.
Figure 8: Comparison of $\rm NH_{3}$ profiles for an average of seven Q-branch
lines and four aP(6,K) lines of similar energy in 2007. The line shapes differ
markedly, with the Q-branch $\rm NH_{3}$ lines lacking much of a red wing.

Similar to $\rm C_{2}H_{2}$ and HCN, the higher velocity red wing of the $\rm
NH_{3}$ profiles becomes stronger, relative to the core, for higher excitation
lines. Figure 7 compares the average 2007 profile of the aP(6,K) lines
($E_{\ell}=384-417\,{\rm cm^{-1}}$) with that of the sP(8,3) line
($E_{\ell}=679\,{\rm cm^{-1}}$). The higher energy line clearly shows enhanced
absorption at higher velocities in the red wing.

Perhaps surprisingly, the Q-branch lines show the $\sim 22\,{\rm\,km\,s^{-1}}$
core absorption component (FWHM $\sim 8\,{\rm\,km\,s^{-1}}$) but lack the red
wing. Figure 8 compares the average 2007 line profiles of the Q-branch
($E_{\ell}=17-423\,{\rm cm^{-1}}$) and aP(6,K) lines. The profile shapes
differ markedly, with the higher velocity absorption in the red wing absent in
the Q-branch lines. The average Q-branch profile is sharper and centered more
to the red than the flat-bottomed P-branch lines. However, the Q-branch
profiles also vary with line strength (see Fig. 5, bottom), with the weaker
Q-branch lines closer in shape and velocity to those of the aP(6,K) lines. The
absence of the red wing in the Q-branch lines may have something to do with
the fact that the Q-branch transitions overlap the 10 $\rm\,\mu{\rm m}$
silicate absorption feature, while the measured P-branch lines fall between 12
and 13 $\rm\,\mu{\rm m}$. Detailed radiative transfer models that include
these opacity differences may be able to help us understand the origin of the
differences in the profiles.

###  3.3 $\rm H_{2}O$

We detected 4 high excitation lines of $\rm H_{2}O$ in the 2007 spectra
(Figure A1), with lower energy levels ranging from 2631 $\rm\,cm^{-1}$ to 3211
$\rm\,cm^{-1}$. All of the lines are very weak, $\sim$ 2–3% deep. In contrast
to the $\rm C_{2}H_{2}$, HCN, and $\rm NH_{3}$ lines, which have a prominent
absorption core at $\sim 22\,{\rm\,km\,s^{-1}}$, the $\rm H_{2}O$ absorption
is deepest at $\sim 37{\rm\,km\,s^{-1}}$.

Figure 9: Comparison of spectra (top) and normalized line profiles (bottom) of
water lines in 2007 to $\rm C_{2}H_{2}$ lines. The short solid vertical line
marks the position of the telluric water absorption. The vertical dotted line
marks the velocity of the molecular cloud core.  Figure 10: The similar
strengths of ortho and para water lines in 2007 reveals that the absorption is
optically thick. The short solid vertical line marks the position of the
telluric water absorption.

Figure 9 compares the average spectrum and profile of the four detected $\rm
H_{2}O$ lines with spectra and profiles of high-excitation (average of R31 and
R33) and low-excitation (R15) lines of $\rm C_{2}H_{2}$ in the 2007 data. The
comparison shows that the $\rm H_{2}O$ absorption profile is strongest in the
far red wing of the low-$J$ $\rm C_{2}H_{2}$ absorption profile. The $\rm
H_{2}O$ absorption is very weak in the region of the the 22 $\rm\,km\,s^{-1}$
component and intermediate in strength at $\sim 28{\rm\,km\,s^{-1}}.$ The
profile of the higher energy $\rm C_{2}H_{2}$ line, whose overall strength is
weak, like the $\rm H_{2}O$ absorption, is intermediate between the two
profiles: it has the same velocity components as $\rm H_{2}O$ (at roughly 22
$\rm\,km\,s^{-1}$, 28 $\rm\,km\,s^{-1}$, and 36 $\rm\,km\,s^{-1}$) but with
more equal depths.

Figure 10 compares the profiles of the 163,13–152,14 and 164,13–151,14 water
lines, which are an ortho-para pair; they have nearly identical Einstein
A-values and lower level energies (Table 2) but differ by a factor of 3 in
their statistical weights. The absorption strengths of the two transitions are
essentially the same, which shows that the absorption is optically thick. At
the same time, the absorption depths are very small, which implies that the
absorption is highly diluted, either because the absorber covers a small
fraction (filling factor) of the background continuum and/or an intrinsically
narrow, deeper absorption feature is broadened by macroscopic motions. A
similar, but less extreme, result was found for the $\rm C_{2}H_{2}$
absorption.

Table 2 lists 4 the detected water lines as well as an additional 4 undetected
water lines that were used to constrain the properties of the water
absorption.

###  3.4 Variability

There are some differences in the absorption strength and velocity profiles of
the lines observed in 2006 and 2007. Figure 11 compares the 2006 and 2007
spectra of $\rm C_{2}H_{2}$ for the R15 line and the average of two high
excitation lines. In 2007 the core of the R15 line decreased in strength,
while the red wing has increased. In the high excitation lines, the wing also
increased in strength in 2007 while the 22 $\rm\,km\,s^{-1}$ core remained
about the same. The same behavior is seen for HCN. The increase in the depth
of the red wing relative to the core is common to all transitions and to all
three molecules, including the P-branch $\rm NH_{3}$ lines observed in both
epochs.

A more subtle change is a small redward shift in the blue edge of the lower
excitation $\rm C_{2}H_{2}$ and HCN lines, resulting in a change of the line
centroid from 22 to 23 $\rm\,km\,s^{-1}$. These velocities differ from the
average velocity of 19 $\rm\,km\,s^{-1}$ that Doppmann et al. (2008) found for
the 3 $\rm\,\mu{\rm m}$ HCN lines, in spectra with 13 $\rm\,km\,s^{-1}$
resolution that did not resolve the line profiles. Hence, velocity variations
may be common, but the TEXES data show that this can be produced by changes in
the velocity structure of the absorption, rather than just a simple velocity
shift of the entire profile.

Figure 11: Comparison of profiles of high-$J$ (top) and low-$J$ (bottom)
profiles of $\rm C_{2}H_{2}$ lines in 2006 and 2007.

###  3.5 Equivalent Widths and Absorption Properties

The equivalent widths (EWs) of the absorption features were used to infer the
temperatures and column densities of the absorbing molecules. Because there
are differences in absorption strengths and profiles between 2006 and 2007,
the EWs measured in the two epochs were analyzed separately.

As noted in previous sections, the “core” and “wing” components of the line
profiles show different behaviors as a function of line excitation energy,
both in the observed ortho-para ratio of $\rm C_{2}H_{2}$ absorption depths
and in the interesting absence of a red wing in the Q-branch $\rm NH_{3}$
lines. We therefore measured and analyzed the absorption as that of two
velocity components, simply defined: one redward of $\sim 26{\rm\,km\,s^{-1}}$
and the other blueward of the same velocity. A possible alternative would have
been to decompose the profile into two Gaussians. However, because the
profiles are not strictly Gaussian, and they in fact appear to be composed of
multiple components with possibly complex behavior, we adopted the simpler
approach, with the goal of capturing the essence of the difference between the
lower and higher velocity absorption.

The measured EWs for the two velocity components and their combined EW are
given in Tables 3 and 4 for all lines measured in 2006 and 2007, respectively.
The uncertainties include both the spectral pixel-to-pixel noise, which comes
from the continuum signal-to-noise, and an estimate of the uncertainty in the
continuum placement. The average line depth over the velocity interval is also
listed for both components. In analyzing the detected $\rm H_{2}O$ absorption,
we found it useful to also include upper limits on a few additional $\rm
H_{2}O$ lines that could become detectable at very high column density and
lower temperatures. These lines are listed in Table 4 along with their
2-$\sigma$ upper limits on EW for the high-velocity component.

In the case of a uniform absorbing medium that lies in front of an opaque
continuum source, the absorption equivalent width, which is a simple function
of the line optical depth $\tau_{\nu},$ can be diluted by unobscured continuum
emission (e.g., if the absorber does not completely cover the background MIR
continuum source) and/or by emission from the absorber. That is, if the
emission from a background source $B_{\nu,b}(T_{b})$ with temperature $T_{b}$
is absorbed by a medium with opacity $\tau_{\nu}$ and source function
$S_{\nu,a}$, the emergent intensity is

$I_{\nu}=B_{\nu,b}\,e^{-\tau_{\nu}}+\left(1-e^{-\tau_{\nu}}\right)S_{\nu,a}$
(1)

at a frequency $\nu$ in the line and $I_{\nu}=B_{\nu,b}$ in the neighboring
continuum. The fractional intensity decrement in the line relative to the
continuum is then

$\left(B_{\nu,b}-I_{\nu}\right)/B_{\nu,b}=\left(1-e^{-\tau_{\nu}}\right)\left(1-S_{\nu,a}/B_{\nu,b}\right),$
(2)

and the equivalent width

$EW=f_{c}\int\left(1-I_{\nu}/B_{\nu,b}\right)d\nu\,=f_{d}\int\left(1-e^{-\tau_{\nu}}\right)d\nu,$
(3)

where the quantity

$f_{d}=f_{c}\left(1-S_{\nu,a}/B_{\nu,b}\right)$ (4)

combines the effects of the covering fraction of the absorber $f_{c}$ and the
average dilution by emission from the absorber across the line
$f_{e}=\left(1-S_{\nu,a}/B_{\nu,b}\right).$ In LTE, $S_{\nu}=B_{\nu}(T)$ where
$T$ is the temperature of the absorbing medium. However, as a result of the
high critical density for vibrational LTE, the vibrational temperature $T_{\rm
vib}$ may be less than $T,$ and both $S_{\nu}$ and $T_{\rm vib}$ can be
affected by the radiation field.

Here we model the absorbing gas as a uniform slab. The line optical depths are
determined by the gas temperature ($T$), and the ratio of the column density
of the molecule ($N$) to the intrinsic line width, which includes thermal and
microturbulent components. If the absorption is approximated as a Gaussian
line profile with FWHM $\Delta v$, the line center optical depth is

$\tau_{0}={g_{u}A\bar{\nu}^{3}\over 8\pi}{e^{-E_{\ell}/kT}\over Q(T)}{N\over
1.0645\,\Delta v}\left(1-e^{-hc\bar{\nu}/kT}\right)$ (5)

where $\bar{\nu}$ is the wavenumber of the transition, $g_{u}$ is the
multiplicity of the upper state, $E_{\ell}$ is the energy of the transition,
$Q$ is the partition function, and the factor 1.0645 relates the product of
the FWHM and peak height of a Gaussian to its area. All of the molecular
parameters and data for the partition functions are from HITRAN (Rothman et al
2013; Fischer et al. 2003). We assume that the lower energy levels are in LTE.

For each molecule and velocity component, we plot a curve-of-growth (COG) as
ln(EW) versus the logarithm of a quantity proportional to $\tau_{0}$ and then
determine the model parameters that minimize $\chi^{2}$. The first two
parameters, $T$ and $N/\Delta v$, determine the line optical depths and the
shape of the COG; equivalently, these two parameters set the relative EWs of
the lines. The third parameter in this approach, $f_{d}\Delta v$, is a scaling
factor that best matches the absolute EWs for all lines. From these three
parameters, the value of $f_{d}N$ automatically follows.

Note that $f_{d}$ and $\Delta v$ are not independently determined, although it
is possible to place physical limits on $\Delta v$ (and hence $f_{d}$). If all
lines are optically thin (all points fall on the linear part of the COG),
$N/\Delta v$ is not constrained and the only determined parameters are $T$ and
$f_{d}N$. The results from the COG analysis are given in Tables 5 and 6. The
parameter uncertainties represent 1-$\sigma$, i.e., a 68% confidence interval,
where the joint confidence region for the parameters is the space enclosed by
the surface of constant $\chi^{2}$ that corresponds to the confidence level
and the number of free parameters. Note that there is correlation between
parameters, such that the upper bound on temperature generally corresponds to
lower column density and larger intrinsic line width, and visa versa. The
uncertainties depend on the number of lines used, the signal-to-noise of the
EWs, and the range in optical depth and lower energy level covered by the
measured transitions.

In Figure 12, example COGs are plotted for both the low- and high-velocity
components of $\rm C_{2}H_{2}$ from 2006. The COG analysis shows
quantitatively the conclusion reached from visual examination of the $\rm
C_{2}H_{2}$ spectra; the high-velocity (HV) component (the red wing) has a
higher optical depth than the low-velocity (LV) component (the 22
$\rm\,km\,s^{-1}$ core), as indicated by the greater curvature in its COG. The
line with the highest opacity is the R15, which has an optical depth of 2 for
the LV and 6 for the HV component. Remarkably, the temperatures of the HV and
LV components are about the same, $\sim 450$ K. Thus, our finding that higher
rotational transitions are more prominent in the HV component is not due to a
higher temperature for the high-velocity gas but to greater optical depth
(larger $N/\Delta v$).

Figure 12: Curves of growth for the low-velocity (blue points) and high-
velocity (red points) components of $\rm C_{2}H_{2}$ in 2006. The solid lines
are the best-fit model curves of growth.

Despite its higher optical depth, the EWs and absorption depths of the HV
component are smaller than those of the LV component, indicating a larger
dilution factor. Because the LV and HV components share the same temperature
(Tables 5, 6), the contribution of line emission by the warm absorber to the
value of $f_{d}$ (through the quantity $f_{e}$ in eq. 1) is the same for both
components. Thus, the greater dilution of the HV component (i.e., smaller
$f_{d}$) compared to the LV component indicates that the covering fraction of
the background continuum is smaller for the high-velocity gas than the low-
velocity gas.222Small values of $f_{d}$ reflect small covering fractions
rather than significant emission from the absorbing gas. The vibrational
temperature of the absorber $T_{\rm vib}$ and the temperature of the
background continuum $T_{b}$ would have to be very similar for emission to
have a significant impact. In LTE, $T_{\rm vib}$ is the same as the rotational
temperature of the absorber, which is here $\sim 450$ K. For $T_{\rm vib}$=450
K, reducing $f_{e}$ to 0.16–0.21, the range of dilution factors inferred for
the LV component (Tables 5 and 6), requires a background continuum temperature
of $T_{b}$=480–490 K. Such similar foreground and background temperatures seem
implausible; with temperatures that similar, the foreground gas is as likely
to produce emission as absorption.

For $\rm H_{2}O$, the absorption is dominated by the HV component (Section
3.3); the observed redward velocity of the absorption shifts it out of the
telluric water absorption, enabling its detection. The $20\,{\rm\,km\,s^{-1}}$
component is clearly detected in the average spectrum (Fig. 9), but it is too
weak in individual lines to be useful in determining the absorption
parameters. Therefore, the analysis was restricted to the HV component.
Furthermore, because all four of the detected lines are optically thick, we
are unable to constrain the absorption properties using these lines alone. We
therefore also included in the analysis the upper limits on several additional
water lines covered by our spectra. Because these additional lines, shown in
Table 4, would become strong enough to detect at very high column density
and/or low temperature, including their upper limits places an upper bound on
the water column density. The 2-$\sigma$ upper limits were included in the
$\chi^{2}$ fit using the approach discussed in Sawicki (2012). The best-fit
COG for the $\rm H_{2}O$ absorption is shown in Figure 13. The resulting
analysis yields the best-fit properties shown in Table 6.

Figure 13: Curve of growth for $\rm H_{2}O$. Detected water lines (solid
points) and upper limits (downward arrows) are indicated along with the best
fit (red line).

Using the above procedure, we derived gas temperatures of $\sim 450$ K for
both velocity components of all molecules, with one clear exception discussed
below. For molecules other than water, the derived values for $N/\Delta v$ are
in the range $10^{16}-10^{17}{\rm\,cm^{-2}}\,{\rm km^{-1}\,s}$, with the value
for the HV component consistently 3–7 times greater than that for the LV
component. For the HV component of water, $N/\Delta v$ is much larger,
$2.9\times 10^{19}{\rm\,cm^{-2}}\,{\rm km^{-1}\,s}$.

Because radiative transitions between rotational levels of $\rm C_{2}H_{2}$
are forbidden, collisions will control the rotational populations in the
ground vibrational state. Therefore, LTE should be a good approximation for
$\rm C_{2}H_{2}$ and the derived temperature a measure of the gas kinetic
temperature. For HCN, the critical densities for our measured transitions
range from $10^{8}-10^{9}\,{\rm\,cm^{-3}}$. The derived excitation temperature
is the same as that of $\rm C_{2}H_{2}$ (for the 2006 data), indicating that
the gas densities are at least this high. The measured rotational levels for
$\rm NH_{3}$ have comparable critical densities. However, the critical
densities for the measured water lines are higher, $\sim 4\times
10^{10}\,{\rm\,cm^{-3}}.$ Models of disk atmospheres predict that warm
molecules are present at high densities ($\gtrsim 10^{11}\,{\rm\,cm^{-3}}$),
making LTE a reasonable assumption (e.g., Bruderer 2014; Najita & Ádámkovics
2017).

To determine the line-of-sight column density $N$ from the constrained
quantity $N/\Delta v$ requires an assumption about the local line broadening
$\Delta v.$ A lower limit on $N$ comes from assuming that the local line
broadening is thermal, which for the observed molecules is $\sim
1\,{\rm\,km\,s^{-1}}$ at 450 K. For an upper limit to $N,$ we can adopt for
$\Delta v$ the observed width of the absorption component ($\sim
8\,{\rm\,km\,s^{-1}}$), which would be appropriate if the absorbing medium is
highly turbulent. However, this is unlikely, because the profiles of the R15
and R14 lines of $\rm C_{2}H_{2}$ are identical across the LV component, i.e.,
the ortho-para ratio and hence the optical depth is nearly constant across the
LV core of the lines. If the absorption was due to a single intrinsically
broad ($\sim 8\,{\rm\,km\,s^{-1}}$) profile, then the optical depth would be
highest at the absorption minimum and decrease away from line center, in
contrast to the observed profiles.

More likely, the observed width of the absorption feature is produced by
multiple lines of sight through the rotating disk atmosphere that pass through
gas at different velocities. In this case, the local line broadening $\Delta
v$ is substantially less than the full observed width, implying a smaller
line-of-sight column density. In Tables 5 and 6 we list values for $N$ for an
assumed width of $2\,{\rm\,km\,s^{-1}},$ a value between the approximate
thermal width of hydrogen ($4.5\,{\rm\,km\,s^{-1}}$) and that of water ($\sim
1\,{\rm\,km\,s^{-1}}$) at the temperature of the absorption (450 K), implying
some amount of microturbulent broadening for the observed molecules. We
interpret these values of $N$ in the next section.

Although we find a $\sim 450$ K temperature for the velocity components of
almost all molecules, we derive a much lower temperature for $\rm NH_{3}$ in
2007 (250 K) than in 2006 (455 K) for the LV component. Because the addition
of the Q branch in the 2007 data adds a large number of lines, which cover a
greater range in optical depth, the temperature from the COG is well
constrained. Setting the temperature to 250 K for the 2006 data gives a
extremely bad fit. One could be concerned that the Q branch probes different
gas, given its different behavior, i.e., the absence of the red wing in the
Q-branch lines. In Figure 14, we plot the COG for the 2007 LV component, where
the model COG is the best fit to the combined Q- and P-branch lines. The
P-branch lines are plotted with a different color, and follow the same trend
as the Q-branch lines. In addition, fitting the Q- and P-branch lines
separately yields consistent temperatures.

Figure 14: Curve of growth for the 2007 low-velocity component of $\rm
NH_{3}$. The Q-branch (black) and P-branch (pink) lines follow the same trend
and are fit with similar temperatures. The solid line is the best-fit model
curve of growth.

Comparison with Previous Results. We can compare our results for HCN to the
findings of Doppmann et al. (2008), who measured the 3 $\rm\,\mu{\rm m}$
absorption lines of HCN and $\rm C_{2}H_{2}$ in GV Tau N at a resolution of 13
$\rm\,km\,s^{-1}$ using NIRSPEC on Keck. They fit the $\nu_{1}$ HCN spectrum
with a temperature of 550 K and an HCN column density of $1.5\times
10^{17}{\rm\,cm^{-2}}$, using a microturbulent velocity of 3 $\rm\,km\,s^{-1}$
(FWHM = 5.0 $\rm\,km\,s^{-1}$). This is equivalent to $N/\Delta v=3\times
10^{16}{\rm\,cm^{-2}}\,{\rm km^{-1}\,s}$. Hence, their result is in reasonable
agreement with the values we obtained with the MIR lines for the LV component
of HCN.

We can also compare the results from our spectrally resolved molecular spectra
with the analysis by Bast et al. (2013) of the Spitzer/IRS spectrum of GV Tau.
Our study differs from that of Bast et al. in two important ways. Firstly, the
TEXES data spatially resolve the N and S components of the binary, whereas
Bast et al. did not account for dilution by GV Tau S. Our TEXES observations
confirm that the S component lacks MIR molecular absorption, a result similar
to that found in $L$-band molecular spectroscopy of GV Tau N and S (Doppmann
et al. 2008; Gibb et al. 2007). Secondly, the high spectral resolution of the
TEXES data allows us to resolve the profiles and to infer dilution of the line
equivalent widths.

For comparison to Bast et al., we use the $f_{d}\,N$ values from our analysis
with $f_{d}$ = 1, i.e., the column densities we would derive without taking
dilution into account. For $\rm C_{2}H_{2}$ and HCN, our column densities are
somewhat larger, by factors of 1–3, than those reported by Bast et al. The
temperature for HCN is in agreement, but their temperature for $\rm
C_{2}H_{2}$ (720 K) is higher. For $\rm NH_{3}$, our values of $f_{d}\,N\sim
2\times 10^{16}{\rm\,cm^{-2}}$ are similar to the upper limit reported by Bast
et al. ($1.9\times 10^{16}{\rm\,cm^{-2}}$ for 500 K). All of our derived
column densities would be larger for $f_{d}<1$. Some of the observed
differences may be due to variability, because the Spitzer and TEXES data were
taken at different times.

To summarize, the TEXES spectra reveal warm ($\sim 450\,K$), redshifted MIR
molecular absorption in GV Tau N, with larger column densities than inferred
in previous studies. The HV component of the absorption is more optically
thick than the LV component, has a column density 3–6 times larger, and is
more highly diluted (by a factor $\sim 5$) than the LV component due to a
smaller covering fraction of the background MIR continuum.

##  4 Discussion

###  4.1 Origin of the Absorption

The working hypothesis in the literature is that the molecular absorption in
GV Tau N occurs in gas in the disk atmosphere observed against the hotter dust
continuum from smaller radii in a disk viewed close to edge-on (Gibb et al.
2007; Doppmann et al. 2008; Bast et al. 2013). Here we discuss the origin of
the absorbing gas in light of our results on the temperature, column
densities, and line profiles of the molecular absorption.

Clues from Temperature and Column Density. We find that the absorbing gas is
warm ($\sim 450$ K) and the detected molecular species show profiles that can
be modeled as multiple velocity components that probe gas along the same lines
of sight to the 12 $\rm\,\mu{\rm m}$ continuum. The rotational temperatures
derived for the HCN, $\rm C_{2}H_{2}$, and $\rm H_{2}O$ absorption are similar
to (but at the cool end of) the excitation temperatures derived for the same
molecules from the MIR molecular emission observed from T Tauri disks
(400–1000 K; Carr & Najita 2011; Salyk et al. 2011). The latter is thought to
arise from the heated disk atmosphere within an au of the star (e.g., Najita
et al. 2011; Najita & Ádámkovics 2017).

The relative column densities of the molecular species detected in absorption
in GV Tau N are also consistent with the ratios derived for the MIR molecular
emission from T Tauri disks. For the high-velocity absorption component
measured for GV Tau N in 2007, for which a $\rm H_{2}O$ column density could
be determined, the column density ratios are $N({\rm C_{2}H_{2}})/N({\rm
H_{2}O})$ = 0.002, $N({\rm HCN})/N({\rm H_{2}O})$ = 0.005, and $N({\rm
C_{2}H_{2}})/N({\rm HCN})$ = 0.4. Figure 15 compares the GV Tau N column
density ratios (blue star) with the emission column density ratios of T Tauri
disks derived from high and low resolution spectra (squares). The GV Tau N
values are similar to the ratios derived from T Tauri star emission spectra
using slab models that make assumptions similar to those adopted here. The
similar column density ratios are consistent with the interpretation that the
GV Tau N absorption arises in a disk atmosphere.

Figure 15: Molecular absorption column density ratios reported here for GV Tau
N (blue star) compared with emission column density ratios from T Tauri disk
spectra studied at high spectral resolution with TEXES (blue squares; Najita
et al. 2018) and low spectral resolution with Spitzer/IRS (purple squares;
Carr & Najita 2011; Najita et al. 2018). The estimates from Spitzer assume
equal emitting areas for all molecules. Also shown are the abundances of
comets (orange dots; Dello Russo et al. 2016), and the average properties of
hot cores (green cross; see Carr & Najita 2011 for details). The GV Tau N
absorption column density ratios are similar to the emission column density
ratios of T Tauri disks, consistent with the interpretation that the
absorption arises in a disk atmosphere viewed at high inclination.

At the same time, the absolute column densities of the MIR absorption are much
higher than the column densities seen in emission. Here we compare
specifically to results for AS205 N and DR Tau, two high accretion rate disks
viewed at low inclination. As the only sources whose HCN and $\rm C_{2}H_{2}$
emission has been measured at high spectral resolution, their velocity-
resolved spectra enable tighter constraints on the properties of the emitting
gas (Najita et al. 2018). For a valid comparison (apples to apples), we assume
thermal local linewidths for the GV Tau N absorption, as assumed in the
earlier emission line analysis. The column densities of $\rm H_{2}O$, HCN, and
$\rm C_{2}H_{2}$ in the HV absorption component of GV Tau N are 40 times
greater on average than the emission column densities of AS205 N and DR Tau,
and the (HCN and $\rm C_{2}H_{2}$) column densities of the LV component of GV
Tau N are $\sim 10$ times greater. The roughly order-of-magnitude larger line-
of-sight column densities observed in absorption vs. emission are expected if
the warm molecular layer responsible for the T Tauri star emission is viewed
at high inclination in GV Tau N, as in an edge-on disk.

There is little definitive information available on the orientation of the GV
Tau N disk. Modeling of MIR interferometric observations made with VLTI/MIDI
favored a high inclination for GV Tau N ($i\sim 80$ degrees; Roccatagliata et
al 2011). In addition, the CO overtone emission from the inner disk of GV Tau
N is broad ($\sim 95\,{\rm\,km\,s^{-1}}$) suggesting the disk is not close to
face on (Doppmann et al. 2008). In contrast, modeling that fits the spectral
energy distribution (SED) and scattered light images of GV Tau N with a disk +
envelope model favors a lower inclination ($i\sim 30$ degrees; Sheehan &
Eisner 2014). However, the SED modeling may not provide a strong constraint on
the orientation of the inner disk of GV Tau N; because the modeling weights
large-scale phenomena prominently in the fit, the preferred solution may be
influenced primarily by the envelope properties rather than the inner disk
($<10$ au) properties where the warm absorption arises.

Clues from Line Profiles. While the results above echo previous results from
the literature, the high velocity resolution of the TEXES data lends new
insights into the dynamics of the absorbing gas. The $R$=600 Spitzer spectra
detected molecular bands but did not resolve individual lines. The
NIRSPEC/Keck spectra studied by Doppmann et al. (2008) and Gibb et al. (2007)
marginally resolved individual HCN lines in the $L$-band. In comparison, the
TEXES data, with a resolution of $\sim 3\,{\rm\,km\,s^{-1}},$ measure the
profiles of individual lines.

In interpreting the line profiles, we adopt as the system velocity for GV Tau
N the velocity measured for the gaseous envelope surrounding GV Tau ($v_{\rm
helio}=17.3\pm 0.5{\rm\,km\,s^{-1}}$ or $v_{\rm LSR}=7.0\,{\rm\,km\,s^{-1}}$;
Hogerheijde et al. 1998). The stellar radial velocity of GV Tau N is not well
known. One estimate, based on an absorption component detected in the CO
overtone emission from the source ($v_{\rm helio}=5.8\pm
4.0{\rm\,km\,s^{-1}}$), is blueshifted relative to both the cloud and envelope
velocity, suggesting that the central source may be a spectroscopic binary
(Doppmann et al. 2008).

As described in Section 3, the GV Tau N line profiles have single-dipped,
$\sim 10{\rm\,km\,s^{-1}}$ FWHM absorption line profiles; the absorption core
has a velocity offset redward of the system velocity and a red wing extending
to higher velocities. The redward offset of the core and red wing are not
expected for a simple rotating disk and suggests gas that is radially
inflowing. The redshifted absorption we observe is reminiscent of earlier
Keck/NIRSPEC results for GV Tau N. Doppmann et al. (1998) found that the NIR
HCN absorption toward GV Tau N, centered at $19{\rm\,km\,s^{-1}},$ is $\sim
2{\rm\,km\,s^{-1}}$ redward of the system velocity.

Assuming that all of the absorbing gas resides at $\sim 19{\rm\,km\,s^{-1}}$,
Doppmann et al. (2008) argued that the NIR warm molecular absorption is
unlikely to arise from gas in an infalling envelope. Given the inferred mass
of the stellar component(s) of GV Tau N ($0.8{M_{\odot}}$), the envelope
infall velocity $v_{in}=(2G{\rm M_{\star}}/r)^{1/2}$ would reach the observed
$2{\rm\,km\,s^{-1}}$ velocity shift at a distance of 360 au. In contrast,
models of infalling protostellar envelopes predict that the gas temperature
reaches 500 K only within 2 au of the star at the $\sim 7\,{\rm L_{\odot}}$
accretion luminosity of GV Tau (Ceccarelli et al. 1996, their Fig. 4), i.e.,
well within the distance of 360 au that would be inferred for the infalling
gas based on its velocity relative to the molecular envelope. If the NIR
molecular absorption arises in infalling gas at 360 au, an additional, non-
traditional source of heating is need to explain the observed temperature of
the absorbing gas.

A similar argument applies to the MIR absorption. At the higher resolution and
signal-to-noise of the TEXES spectrum compared to the NIRSPEC results, we find
that the core of the MIR molecular absorption, centered at 21–22
$\rm\,km\,s^{-1}$, is $\sim 4{\rm\,km\,s^{-1}}$ redward of the system
velocity, with the red wing of the absorption extending to larger velocities,
$\sim 15-20{\rm\,km\,s^{-1}}$ redward of the system velocity. Infalling gas
would reach the $\sim 4{\rm\,km\,s^{-1}}$ redshifted velocity of the
absorption core at $\sim 90$ au and the $\sim 17{\rm\,km\,s^{-1}}$ wing
velocity at $\sim 5$ au from an $0.8{M_{\odot}}$ star. While some of the high
velocity gas (arising within $\sim 10$ au) might be warm enough to explain the
observed absorption, the bulk of the infalling gas at $\sim 90$ au would be
too cool to explain the observed absorption.

Moreover, because of angular momentum conservation, it may be very difficult
for infall to reach the inner few au of a Class I system. For rotating infall,
angular momentum prevents direct accretion onto the star and its vicinity,
instead causing the infalling material to reach the disk near the centrifugal
radius (20–40 au). The difficulty of reaching the inner few au through infall
is even more true for late accretion sources in which the infall is
increasingly dominated by high angular momentum material. GV Tau, which has a
weak molecular envelope, is such a late accretion source, i.e., transitioning
from a Class I source to a Class II source.

Another general argument against infall (and in favor of an inner disk
atmosphere) is the molecular composition of the absorption and its rarity.
Figure 15 shows that the GV Tau ratios of $\rm C_{2}H_{2}$, HCN, and water are
similar to those of T Tauri disk atmospheres seen in emission. Such absorption
is rare. GV Tau N is the only Class I source known to show $\rm C_{2}H_{2}$,
HCN, water, and $\rm NH_{3}$ in absorption. One other source shows $\rm
C_{2}H_{2}$ and HCN absorption in its Spitzer spectrum (IRS46; Lahuis et al.
2006).

If the temperature and composition we observe in GV Tau N were typical of
infalling envelopes, we would commonly observe these features in Class I
sources. Compared to a disk atmosphere, gas in an infalling envelope would
cover a much larger fraction of the star, approximately the range of polar
angles between the disk surface and the inner cavity carved out by outflow. As
a result, absorption from infall would be detected over a much wider range of
viewing angles than disks viewed nearly edge on. The rarity of molecular
absorption like that seen in GV Tau N argues against its origin in an
infalling envelope.

Disk Origin. Unlike the infalling envelope scenario, a nearly edge-on rotating
disk can account for almost all of the properties of the observed molecular
absorption: the temperature and column density (as discussed above) and its
line width. Single-dipped absorption line profiles can arise when a disk
atmosphere is seen in absorption against the MIR continuum arising from
smaller radii. While both the line absorption and the continuum emission
likely arise over a range of radii, for simplicity in the discussion below, we
assume that the continuum arises from a compact region $r<r_{c},$ and the
absorption occurs at larger radii $r_{a}>r_{c}$. Because the MIR continuum is
compact compared to $r_{a}$, only the portion of the disk atmosphere at
$r_{a}$ that is close to the line-of-sight to the continuum is seen in
absorption, i.e., within an azimuthal angle $\pm\phi$ where
$\sin\phi=r_{c}/r_{a}$ (Fig. 16)

Figure 16: Left: Schematic (not to scale) illustrating the likely observing
geometry of GV Tau N. The line of sight to the MIR disk continuum (orange
region) passes through the warm molecular atmosphere at larger radii (pink
region), producing molecular absorption that samples a range of radii in the
atmosphere (between the blue dots). Right: Top down view of the warm molecular
absorption velocities. Absorption by gas at a given radius $r_{a}$ (heavy blue
arc) along the line of sight to the warmer MIR continuum at $r<r_{c}$ (yellow-
orange region) has velocity components from both rotation (blue arrows) and
inflow (green arrows). The absorption velocities (red arrows) are shifted to
the red and span a range of velocities.

Gas at $r_{a}$ along the line-of-sight to the MIR continuum has a maximum
projected radial velocity of $v_{los}=\pm v_{a}\sin\phi\,\sin i$ where $v_{a}$
is the disk rotational velocity at $r_{a}$ and $i$ is the disk inclination.
For a disk in Keplerian rotation, where the projected radial velocity due to
rotation at $r_{c}$ is $v_{c}$ and the projected radial velocity at $r_{a}$ is
$v_{a}=v_{c}\left(r_{c}/r_{a}\right)^{1/2},$ $v_{los}=\pm\ v_{c}\sin
i(r_{c}/r_{a})^{3/2}.$ If the 12 $\rm\,\mu{\rm m}$ continuum arises within
$r_{c}=0.3$ au of the star, where $v_{c}=49{\rm\,km\,s^{-1}}$ for an
$0.8{M_{\odot}}$ star, maximum absorption velocities of $v_{los}=\pm
5{\rm\,km\,s^{-1}}$ would arise at a modestly larger radius of $r_{a}=1.4$ au
$(\sin i)^{2/3}.$ (That is, gas at this radius would absorb background
continuum emission from $\sim 0.3$ au over the $10{\rm\,km\,s^{-1}}$ FWHM of
the observed absorption features.) Higher velocity absorption would arise from
gas at smaller radii. Lower velocity absorption arises from both gas at larger
radii as well as gas at smaller radii that are close to the line of sight to
the star. At a disk radius of 4 au, the maximum absorption velocity would be
$\pm 1{\rm\,km\,s^{-1}}\,(\sin i).$

Thus, a conventional rotating, edge-on disk can account for almost all of the
properties of the observed molecular absorption (the temperature, column
density, and its line width), except for its redshift from the system
velocity. We can also account for the redward offset of the absorption core if
the gas in the disk atmosphere is also radially inflowing along the disk
surface (Fig. 16). Such “surface accretion” flows are found in simulations of
rotating magnetized disks.

###  4.2 Surface accretion in GV Tau N?

In their global ideal MHD simulations of thin disks threaded by a vertical
magnetic field, Zhu & Stone (2018) found that accretion occurs primarily in a
surface accretion flow in the upper, magnetically dominated disk surface. (See
also earlier theoretical work by Stone & Norman 1994; Beckwith et al. 2009;
Guilet & Ogilvie 2012, 2013.) The accretion is supersonic, reaching inward
velocities $v_{r}=2$–4 $c_{s}$ where $c_{s}$ is the sound speed.

In their simulation, the rapid accretion at the disk surface (primarily due to
the magnetic $B_{r}B_{\phi}$ stress) carries the magnetic field inward,
pinching it inward at the disk surface. As a result, the disk atmosphere is
connected magnetically to the midplane at larger radii, which spins down the
atmosphere, producing significantly sub-Keplerian rotation—as small as 60% of
Keplerian rotation—in the atmosphere. The inward pinching of the magnetic
field also launches a disk wind, although the torque due to the wind at the
disk surface plays only a small role in driving accretion.

The expected properties of the accreting atmosphere are roughly consistent
with the observed properties of the molecular absorption in GV Tau N. For
molecular gas at 500 K, supersonic accretion at $v_{r}=2$–4 $c_{s}$
corresponds to $v_{r}\simeq 3$–5 km/s, qualitatively similar to the redshift
of the absorption core ($\sim 4$ km/s); the velocities of the red wing ($\sim
15$–20 km/s) correspond to higher velocities $\sim 13c_{s}$. For gas in sub-
Keplerian rotation at a disk radius $r_{a}$ along the line of sight to the MIR
continuum (which arises within $r_{c}$), its projected radial velocity spans
the range $v_{los}=\pm\ \beta\,\sin i\ v_{c}(r_{c}/r_{a})^{3/2}$, as described
above, where $\beta$ is a factor that accounts for possible deviations from
Keplerian rotation. If $\beta=0.6$ and $r_{c}=0.3$ au so that
$v_{c}=49{\rm\,km\,s^{-1}}$ for a stellar mass of $0.8{M_{\odot}}$, an
observed absorption core with a FWHM of $\pm 5{\rm\,km\,s^{-1}}$ would
correspond to absorbing gas at $r_{a}=1$ au $(\sin i)^{2/3}.$

Preliminary work on a detailed radiative transfer model of a rotating disk
with radial inflow, viewed nearly edge on, appears to be able to account for
the properties of the molecular absorption observed in the GV Tau N spectrum.
The modeling, which builds on the previous results of Lacy (2013), can
plausibly account for the shape of the absorption components as well as the
slightly blueshifted emission seen in the $\rm NH_{3}$ P-branch profiles. In
one promising scenario, rapidly inflowing gas near the inner rim of the disk
is seen against the continuum from the inner rim, and more slowly inflowing
gas located near the disk surface at larger radii is seen against the disk
continuum at smaller radii (Lacy et al., in preparation).

If the observed absorption arises in a surface accretion flow, the flow may
carry a significant mass accretion rate. For an inward flow with velocity
$v_{\rm in}$ and vertical column density $N_{\perp}$ at a characteristic
radius $r_{a}$, the mass accretion rate is

$\dot{M}_{\rm abs}=2\pi r_{a}m_{\rm H}\,v_{\rm in}\,N_{\perp}.$ (6)

If we assume

$N_{\perp}=N_{\rm abs}\eta/x_{\rm mol}$ (7)

where $N_{\rm abs}$ is the observed line-of-sight molecular absorption column
(e.g., values in the final column in Tables 5 and 6), $\eta$ is the ratio of
the vertical to the line-of-sight molecular column densities, and $x_{\rm
mol}$ is the abundance of the tracer molecule relative to hydrogen, the
associated accretion rate is

$\dot{M}_{\rm abs}=10^{-9}{M_{\odot}\,{\rm yr}^{-1}}\,\left({v_{\rm
in}\over{4{\rm\,km\,s^{-1}}}}\right)\left({N_{\rm abs}\over
10^{16}{\rm\,cm^{-2}}}\right)\left({r_{a}\over 1\,{\rm
au}}\right)\left({\eta\over 0.1}\right)\left({x_{\rm mol}\over
10^{-6}}\right)^{-1}.$ (8)

For the observed HCN absorption, the properties of its LV component are
$v_{\rm in}=4{\rm\,km\,s^{-1}}$, $N_{\rm abs}=7\times
10^{16}\,{\rm\,cm^{-2}}.$ Assuming an abundance in the warm disk atmosphere of
$x_{\rm HCN}\sim 10^{-6}$ at $\sim 1$ au, as found in disk chemistry models
that account for the MIR molecular emission properties of T Tauri disks
(Najita & Ádámkovics 2017), and $\eta=0.1$, the corresponding vertical column
density and accretion rate are $N_{\perp}=7\times 10^{21}\,{\rm\,cm^{-2}}$ and
$\dot{M}_{\rm abs}\sim 7\times 10^{-9}{M_{\odot}\,{\rm yr}^{-1}}.$

Similarly, given the inferred properties of the HV HCN absorption component,
$v_{\rm in}=20{\rm\,km\,s^{-1}}$, $N_{\rm abs}=3\times
10^{17}\,{\rm\,cm^{-2}},$ the corresponding vertical column density is
$N_{\perp}=3\times 10^{22}\,{\rm\,cm^{-2}},$ and the accretion rate associated
with the HV component is 20 times larger than that of the LV, or $\dot{M}_{\rm
abs}\sim 1.5\times 10^{-7}{M_{\odot}\,{\rm yr}^{-1}}.$ Using the properties of
the HV water absorption ($N_{\rm abs}=5.8\times 10^{19}{\rm\,cm^{-2}}$) and a
conservative water abundance estimate of $x_{{\rm H_{2}O}}\sim 3\times
10^{-4}$ (Najita & Ádámkovics 2017) yields a similarly large estimate of the
accretion rate of the HV component, $1\times 10^{-7}{M_{\odot}\,{\rm
yr}^{-1}}.$

In adopting abundances for this estimate, we want to select values from model
atmospheres that are able to match the properties of the Spitzer molecular
emission from inner disks and use abundance values appropriate for the warm
atmosphere region that is responsible for the emission. The models in Najita &
Ádámkovics (2017) do a fair job reproducing the properties of many of the
molecules detected with Spitzer. To make a conservative estimate of the
accretion rate, we have adopted model abundances at the high end of the
predicted values within the layer responsible for the emission. The properties
of the Walsh et al. (2015) and Woitke et al. (2018) models differ from those
of Najita & Ádámkovics in detail (e.g., the molecular atmosphere of Woitke et
al. is much cooler), but their model abundances, if adopted, would imply
similar or larger accretion rates. For example, Walsh et al. find a peak HCN
abundance of $\sim 10^{-7}$ which would imply a much larger accretion rate for
the LV component of $\dot{M}_{\rm abs}\sim 7\times 10^{-8}{M_{\odot}\,{\rm
yr}^{-1}}.$ The peak water abundances for all of the models are similar $\sim
10^{-4}.$ Thus, the molecular abundances of current disk atmosphere models
suggest large accretion rates for both the LV and HV components.

The assumed value of $\eta=0.1$ is plausible for the geometry of a highly
inclined disk viewed close to edge on. A more accurate value could be obtained
from a more complete model of the physical, thermal, and chemical disk
conditions.

The above discussion assumed a local line broadening of $2\,{\rm\,km\,s^{-1}}$
(Tables 6 and 7) and that the full absorption width we measure is actually the
result of observing absorption along multiple lines of sight through the
rotating disk atmosphere, encountering gas at different projected velocities.
The column densities and accretion rates above would be smaller by a factor of
two, or larger by a factor of 4, if we assumed that the local line broadening
is instead thermal width or the full observed width of the absorption
component, respectively.

The resulting vertical column densities ($7\times 10^{21}\,{\rm\,cm^{-2}}$ for
LV; $2\times 10^{22}\,{\rm\,cm^{-2}}$ for HV) are similar to and larger than
the vertical column densities thought to be responsible for the emission from
T Tauri disks. The resulting accretion rates ($7\times
10^{-9}\,{M_{\odot}\,{\rm yr}^{-1}}$ for LV; $1\times
10^{-7}\,{M_{\odot}\,{\rm yr}^{-1}}$ for HV) span the range observed from
typical to very active T Tauri stars. While there are substantial
uncertainties associated with the above estimates (including the fact that we
only measure gas columns where the molecular tracers are abundant and atomic
gas is not probed), the inferred accretion rates are substantial and fall
within the expectations for T Tauri stars. Thus, the observed radial inflow
does appear capable of explaining the observed accretion rates of very active
T Tauri stars and Class I objects.

The idea of accretion at the disk surface dates back at least to Gammie
(1996), who described a “layered accretion” picture of T Tauri disks, in which
only the surface region of the disk that is sufficiently ionized to couple to
magnetic fields participates in accretion via the magnetorotational
instability (the “active layer”), and the deeper layers of the disk are a non-
accreting “dead zone.” In Gammie (1996), the active layer was $\sim 100\,{\rm
g~{}cm^{-2}}$ thick, and an equivalent viscosity parameter $\alpha=0.01$ was
sufficient to account for observed T Tauri stellar accretion rates ($\sim
10^{-8}\,{M_{\odot}\,{\rm yr}^{-1}}$). In the intervening years, more detailed
models of disk ionization and our improved understanding of the role of non-
ideal MHD processes have shrunk theoretical expectations for the vertical
extent of the accreting layer to smaller and smaller column densities,
requiring larger equivalent values of $\alpha$ and larger inflow velocities to
deliver the same accretion rate. Here T Tauri-like accretion rates appear to
be transported over vertical columns of only $\sim 0.01\,{\rm g~{}cm^{-2}}.$

Supersonic surface accretion flows—which differ from previous disk accretion
mechanisms in that accretion is driven not by turbulence or a wind, but
primarily by large-scale net magnetic fields in the disk atmosphere (Zhu &
Stone 2018)—may help resolve the open question of how protoplanetary disks
accrete at planet formation distances ($\sim$0.3–10 au). Because of the low
ionization fractions of disks below their surfaces, it is increasing unclear
whether turbulence generated by the magnetorotational instability (MRI) can
drive a significant accretion rate in protoplanetary disks (e.g., Turner et
al. 2014).

The apparent evidence for a supersonic surface accretion flow in the disk of
GV Tau N suggests an alternative pathway for disk accretion. As a mechanism
that redistributes angular momentum within the disk rather than removing it
from the system—as in a disk wind—the supersonic surface accretion flows
studied by Zhu & Stone (2018) contribute to disk spreading: angular momentum
from the disk surface is transported to the midplane at larger radii, which
induces the surface to accrete and the midplane to spread to larger radii. As
an “in-disk” transport mechanism, such surface accretion flows may help
explain the larger sizes of gas disks surrounding Class II sources (as large
as $\sim 500-800$ au) compared to those of Class I sources (typically $<100$
au). The striking size difference has been interpreted as evidence that some
“in disk” angular momentum transport process is active in the Class II (T
Tauri) phase (Najita & Bergin 2018).

Our results may also be related to magnetothermal wind-driven accretion.
Because the winds rely on relatively weak magnetic fields, their magnetic
lever arms are small; as a result, transporting disk material from large radii
to small (over a factor of 30 in radius, from 10 au to 0.3 au) is an
inefficient process requiring large wind mass loss rates, comparable to or
greater than the accretion rate (Bai & Stone 2013). Although strong
observational evidence for such massive, angular momentum-removing disk winds
is currently lacking, the winds are also predicted to produce accretion in
narrow current sheets, which can reach high velocities near the disk surface
under certain conditions (Bai 2013). If the net vertical field is anti-aligned
with disk rotation, near-sonic to supersonic inflow can develop on one side of
the disk surface over some range of radii; under other conditions, the
accretion flow reaches much lower velocities or occurs close to the midplane
(Bai & Stone 2013, Bai 2017). The accretion flow we observe in GV Tau N may be
related to the predicted high-velocity flows.

Thus, our spectroscopic results appear to capture disk accretion in action and
provide observational support for supersonic surface accretion, a potentially
important mode of accretion in protoplanetary disks. To explore this
possibility further, we need future spectroscopic searches for redshifted warm
molecular absorption from other Class I sources; the incidence rate of the
absorption, which constrains its covering fraction, can distinguish between an
origin in a disk atmosphere (small covering fraction) or an infalling envelope
(large covering fraction). Detailed radiative transfer (RT) modeling is needed
to understand whether the line profiles we observe can actually be produced in
disk atmospheres undergoing surface accretion. Similarly, thermal-chemical-RT
modeling of infalling envelopes is needed to explore that alternative scenario
as an explanation for the observed line profiles.

In addition, future theoretical work is needed to understand whether surface
accretion flows can be driven under realistic ionization conditions in
protoplanetary disks; the Zhu & Stone (2018) simulations were carried out
assuming ideal MHD. At the observed inflow velocities of $\sim
5\,{\rm\,km\,s^{-1}}$, the accreting material will travel an au in a year,
implying that the flow must be rapidly replenished in order to sustain it over
protostellar lifetimes ($\sim 10^{5}$ yr). Whether and how the replenishment
occurs—from disk inflows at larger radii and/or from deeper in the disk—is an
open question. The results reported by Fuente et al. (2020) may provide a
clue. They find evidence for redshifted absorption at modest inflow velocities
($\lesssim 3\,{\rm\,km\,s^{-1}}$) in cool molecular gas at larger distances
from GV Tau N, as traced in 13CO (J=3-2).

It would also be useful to obtain additional observational evidence for
surface accretion flows. As discussed above, even if disks do commonly accrete
through their sub-Keplerian surfaces at supersonic speeds, such flows are
unlikely to be commonly observed. Nearly edge-on disks, like that inferred for
GV Tau N, are advantageous systems in which to search for surface accretion
flows because the modest inward motions (few times the sound speed) are more
readily detected from that viewing angle. However, edge-on disks are
intrinsically rare because of their special orientation. Consistent with this
picture, GV Tau N is one of the few YSOs to show molecular absorption in
Spitzer/IRS spectra, and yet its SED is similar to that of other Class I
sources (Furlan et al. 2008). That is, GV Tau N appears to be a typical Class
I source viewed at an unusual inclination.

Although GV Tau N is rare in its molecular absorption properties, radial
inflows have been reported in several other disk systems. As described by
Zhang et al. (2015), the classical T Tauri star AA Tau, whose inner disk is
highly inclined ($\sim 70$–75 degrees), shows very broad CO fundamental
emission lines, with narrow absorption superposed near the line center.
Following a photometric dimming event in 2011, the molecular absorption
component increased in strength and showed a constant redshift of $\sim
6\,{\rm\,km\,s^{-1}}$ with respect to the star. The observed velocity shift,
temperature of the absorbing gas ($\sim 500$ K), and inferred column density
of the absorber ($N_{\rm H}\sim 3\times 10^{22}\,{\rm\,cm^{-2}}$) are
comparable to the properties of the absorption in GV Tau N.

Perhaps most dramatically, Boogert et al. (2002) reported redshifted
absorption in the 5 $\rm\,\mu{\rm m}$ CO absorption spectrum of the Class I
protostar L1489 IRS. The CO spectrum revealed redshifted absorption profiles
similar to those seen here, but with a red wing extending to
$100\,{\rm\,km\,s^{-1}}$ produced by warm ($\sim 250$ K) gas. The absorption
was interpreted as inward flowing gas at the warm disk surface, although at
the time the phenomenon was reported, the physical origin of the gas was
unclear. It is tempting to speculate that the CO absorption in L1489 IRS also
arises in a disk surface accretion flow, albeit one with a very high inflow
velocity.

As another possible example of a surface accretion flow but on a larger scale,
spatially resolved CO $J$=3–2 imaging with ALMA of the Herbig Ae star HD100546
shows deviations from Keplerian rotation which have been interpreted as
indicating either a severely warped and twisted inner disk or radially
infalling gas within 100 au (Walsh et al. 2017). The lack of evidence for a
disk warp from high contrast imaging of the dust disk favors the latter
explanation. To explain the CO spatial and spectral structure, the required
inward velocities are several times the sound speed, similar to the inflow
speeds found in simulations that report surface accretion flows (Zhu & Stone
2018). Walsh et al. found reasonable fits to the HD100546 data with a radial
flow that is 63% of the Keplerian velocity within 84 au. Given the $\sim
4.6\,{\rm\,km\,s^{-1}}$ Keplerian velocity of HD100546 at 84 au (assuming a
$2{M_{\odot}}$ star), the radial flow velocity is $2.6{\rm\,km\,s^{-1}}.$ If
the gas temperature in the disk atmosphere at 84 au is 30 K, the expected
inward flow velocity from a surface accretion flow is approximately
$4c_{s}=2.2{\rm\,km\,s^{-1}},$ similar to the radial flow velocity inferred
from the observations.

Similarly, ALMA imaging of HCO+ emission from the classical T Tauri star AA
Tau has a twist (within the innermost ring at 40 au) in the projected velocity
field relative to the velocity field at larger radii, which is also
interpreted as a warp or an inward radial flow (Loomis et al. 2017). Thus,
although radial inflows have not been much reported to date, studies of
detailed disk dynamics with ALMA and high resolution studies of nearly edge-on
disks, carried out for larger samples than have been explored to date, can
clarify this picture.

Another way to detect surface accretion flows may be through their sub-
Keplerian rotation. While disk rotation at planet formation distances ($<10$
au) has been demonstrated using velocity-resolved molecular emission line
profiles (e.g., CO fundamental emission), demonstrating that the rotation is
sub-Keplerian requires spatial constraints on the observed velocities (i.e.,
spatially and spectrally resolved emission or spectroastrometry; e.g.,
Pontoppidan et al. 2011) as well as independently determined stellar masses.
The latter may be challenging to obtain. One of the “gold standard” methods
for measuring pre-main-sequence stellar masses is to spatially resolve the
rotation of outer disks assuming pure Keplerian rotation (e.g., Simon et al.
2000).

###  4.3 First Detection of $\rm NH_{3}$ in an Inner Disk?

Although ammonia has been previously reported in the outer disk of one young
star (TW Hya, in data taken with the Herschel Space Observatory; Salinas et
al. 2016), it has not been previously reported in inner disks, in either
emission or absorption. In their analysis of Spitzer molecular emission
spectra taken at low resolution, Salyk et al. (2011) reported upper limits on
the column density of ammonia, based on simple slab modeling and an assumed
temperature of 400 K. The results correspond to upper limits on the ratio of
ammonia to water of [$\rm NH_{3}$/$\rm H_{2}O$] $\lesssim 0.005$. The analysis
by Bast et al. (2013) of the Spitzer absorption spectrum of GV Tau led to an
upper limit on its $\rm NH_{3}$ absorption column density of $2\times
10^{16}{\rm\,cm^{-2}}$ assuming a temperature of 500 K. Our measured
absorption columns for $\rm NH_{3}$ towards GV Tau N are consistent with these
upper limits.

Ammonia upper limits have also been derived from high resolution spectra of
inner T Tauri disks. Mandell et al. (2012) reported upper limits on warm $\rm
NH_{3}$ emission corresponding to [$\rm NH_{3}$/$\rm H_{2}O$] $\lesssim 0.2,$
based on VLT/CRIRES spectra at 3$\rm\,\mu{\rm m}$. Summarizing the results of
a Gemini/TEXES program to search for $\rm NH_{3}$ Q-branch emission at 10.75
$\rm\,\mu{\rm m}$ from inner T Tauri disks, Pontoppidan et al. (2019) found a
lower average abundance upper limit of [$\rm NH_{3}$/$\rm H_{2}O$] $<0.003$.
When compared with the HCN abundance measured in the same disks, the $\rm
NH_{3}$ upper limit corresponds to [$\rm NH_{3}$/HCN] $<0.1.$

Here we find a much larger [$\rm NH_{3}$/HCN] ratio for GV Tau N, which shows
comparable absorption column densities in $\rm NH_{3}$ and HCN. Using the best
constrained values, that of $f_{d}\,N$ for the low velocity component of each
molecule at each epoch, our inferred ratio of [$\rm NH_{3}$/HCN] is $\sim
0.5,$ much larger than the [$\rm NH_{3}$/HCN]$\sim 0.1$ upper limits obtained
by Pontoppidan et al. (2019) from the molecular emission spectrum of three T
Tauri disks.

Whereas conspicuous $\rm NH_{3}$ emission is absent in the Spitzer IRS spectra
of T Tauri stars (e.g., Salyk et al. 2011, Carr & Najita 2011), detectable
emission is expected if $\rm NH_{3}$ is co-located with the HCN (i.e., has the
same temperature; $\sim 600$ K in emission) and has an abundance similar to
that of HCN. To illustrate this discrepancy, we show in Figure 17 examples of
predicted molecular emission spectra for simple slab models of T Tauri disks.
The predictions adopt the HCN column densities that have been derived for
these disks assuming that the HCN emission has the same temperature and
emitting area as the $\rm H_{2}O$ emission (Carr & Najita 2011; Najita et al.
2018). At the GV Tau N column density ratio of [$\rm NH_{3}$/HCN]=0.5 and a
temperature of 600 K, the resulting $\rm NH_{3}$ emission would be measureable
(solid red line). At the lower ratio of [$\rm NH_{3}$/HCN]=0.1, corresponding
to the high-resolution limits from Pontoppidan et al. (2019), the $\rm NH_{3}$
emission would not be detectable (blue line).

Figure 17: Observed spectra (black line) compared with simple slab emission
models for $\rm NH_{3}$ emission from inner T Tauri disks assuming [$\rm
NH_{3}$/HCN] abundance ratios of 0.5 (red lines) and 0.1 (blue line) and HCN
columns from Carr & Najita (2011) that assume optically thin emission, i.e.,
the HCN emission has the same emitting area as the water emission. Models at
the higher abundance ratio are for temperatures of 600 K (solid red), 450 K
(dotted red), and 300 K (dashed red); the model with the lower abundance ratio
assumes 600 K. The three stars shown are ordered from low (AA Tau) to medium
(BP Tau) to high (DR Tau) stellar accretion rate.

The much higher [$\rm NH_{3}$/HCN] column density ratio observed in absorption
GV Tau N compared to that seen in emission in T Tauri disks might be expected
if the emission and absorption features probe the conditions at different disk
heights. In their thermal-chemical models of irradiated disk atmospheres,
Najita & Ádámkovics (2017) find that $\rm NH_{3}$ is abundant deeper in the
atmosphere, and at lower gas temperature, than the region in which HCN and
$\rm C_{2}H_{2}$ are abundant. Thus, we expect a low [$\rm NH_{3}$/HCN] ratio
in the HCN-emitting gas (Figure 17, blue line). Abundant but cool $\rm NH_{3}$
located below the HCN-emitting gas would also produce weak to negligible
emission (Figure 17, dashed red line).

In contrast, cool gas could still be readily detected in absorption in
transitions out of the ground vibrational state, particularly with the large
slant column densities for a disk viewed at high inclination. The cooler
temperatures we measure for the $\rm NH_{3}$, HCN, and $\rm C_{2}H_{2}$
absorption (450 K), compared to the typical temperatures of the HCN and $\rm
C_{2}H_{2}$ emission from T Tauri stars (600-1200 K; Carr & Najita 2011; Salyk
et al. 2011) are consistent with the idea that the GV Tau N absorption probes
a deeper layer in the disk atmosphere than the region responsible for the MIR
molecular emission from T Tauri disks. The low temperatures we find for the
$\rm NH_{3}$ absorption (250 K in 2007 and 450 K in 2006) are roughly
consistent with this explanation for the lack of detectable $\rm NH_{3}$
emission from T Tauri disks and with the cooler temperatures anticipated for
$\rm NH_{3}$ compared to HCN from the disk thermal-chemical models.

The measured column densities of $\rm NH_{3}$ and HCN in GV Tau N add to our
current understanding of the nitrogen reservoir in disks. As described by
Pontoppidan et al. (2019), nitrogen is highly depleted in the bulk Earth, by
5–6 orders of magnitude, compared to its cosmic abundance. The low abundance
suggests that the bulk carrier of nitrogen in the material that formed the
Earth was much more volatile than water, favoring a nitrogen-bearing molecule
like N2, which has a low binding energy (430 K) compared to other potentially
abundant molecules such as HCN and $\rm NH_{3}$ (3610 K and 3130 K
respectively; Walsh et al. 2015). Our results for GV Tau N are consistent with
this picture. Because the measured column of $\rm NH_{3}$ is modest, only
comparable to that of HCN, it cannot be a major missing reservoir of nitrogen,
and a molecule like N2 is instead the likely dominant nitrogen reservoir.

##  5 Summary and Conclusions

The mid-infrared spectra of GV Tau N reported here were obtained with the
original goal of studying the physical properties and molecular content of a
disk viewed edge-on. The opportunity to study an unusually large column
density of disk gas in absorption offered the potential to detect new
molecular species. Consistent with that expectation, the TEXES spectra
revealed the first evidence for $\rm NH_{3}$ in the planet formation region of
disks. The measured temperatures, molecular column densities, and column
density ratios of the detected species ($\rm C_{2}H_{2}$, HCN, $\rm NH_{3}$,
and $\rm H_{2}O$) are consistent with the properties of a disk atmosphere
within a few au of the star viewed at high inclination. While the $\rm NH_{3}$
abundance measured here is higher than the upper limits obtained from
molecular emission studies of disks, our results do confirm the expectation
that $\rm NH_{3}$ is not a major missing reservoir of nitrogen. If, as
expected, the dominant nitrogen reservoir in inner disks is instead N2, its
high volatility would make it difficult to incorporate into forming planets, a
situation that may help to explain the low nitrogen content of the bulk Earth.

More interestingly, the TEXES spectra reveal an unexpected and significant
redshift to the detected molecular absorption features, indicative of inflow
at the disk surface. From the properties of the molecular absorption (column
density, velocity shift), we can infer that the redshifted absorption carries
a significant accretion rate: $\dot{M}_{\rm abs}\sim
10^{-8}-10^{-7}{M_{\odot}\,{\rm yr}^{-1}},$ comparable to the stellar
accretion rates of active T Tauri stars. Thus we may be observing disk
accretion in action. The results may provide observational evidence for a new
disk accretion pathway for young protoplanetary disks: supersonic “surface
accretion flows.” These flows have been found in MHD simulations of magnetized
disks (e.g., Zhu & Stone 2018), but their potential role in young
protoplanetary disks has received limited attention to date. The observed
flows may also be related to accretion flows generated by magnetothermal
winds. Future spectroscopy of the dynamics of other edge-on disks would help
establish whether supersonic inward flows are common among young disks. In
addition, future simulations are needed to understand whether supersonic
surface accretion flows can be sustained under realistic ionization conditions
in protoplanetary disks.

##  Appendix A TEXES Spectra of GV Tau N

The figures in this section show the entire set of spectra of GV Tau N used in
this study. Each panel shows the pipeline-reduced spectra on the observed
wavelength scale before additional corrections were made to remove low-order
structure in the continuum. Detected lines are annotated at the velocity of
the gaseous envelope surrounding GV Tau, $v_{\rm
helio}=17.3\,{\rm\,km\,s^{-1}}$ (or $v_{\rm LSR}=7.0\,{\rm\,km\,s^{-1}}$;
Hogerheijde et al. 1998). The molecular absorption features are clearly
redshifted with respect to the envelope velocity.

Figure A1a: TEXES pipeline-reduced spectra of GV Tau N, shown before
additional corrections were made to remove low-order structure in the
continuum. Absorption lines of $\rm C_{2}H_{2}$ (red), HCN (purple), $\rm
NH_{3}$ (green), and water (blue) are marked in each panel, as is the 12
$\rm\,\mu{\rm m}$ H2 emission line (blue). This panel shows the GV Tau N
spectrum observed in 2006 at the setting centered at 765.5 ${\rm cm^{-1}}$.
Figure A1b: As in Figure A1a, for the setting centered at 744.8 ${\rm
cm^{-1}}$ observed in 2006.  Figure A1c: As in Figure A1a, for the setting
centered at 780.5 ${\rm cm^{-1}}$ observed in 2006.  Figure A1d: As in Figure
A1a, for the setting centered at 787.0 ${\rm cm^{-1}}$ observed in 2006.
Figure A1e: As in Figure A1a, for the setting centered at 814.0 ${\rm
cm^{-1}}$ observed in 2006.  Figure A1f: As in Figure A1a, for the setting
centered at 767.0 ${\rm cm^{-1}}$ observed in 2007.  Figure A1g: As in Figure
A1a, for the setting observed in 2007 centered one order to the red of the
other setting at 767.0 ${\rm cm^{-1}}$ shown in the previous panel.  Figure
A1h: As in Figure A1a, for the setting centered at 932.0 ${\rm cm^{-1}}$
observed in 2007.  Figure A1i: As in Figure A1a, for the setting centered at
807.0 ${\rm cm^{-1}}$ observed in 2007.  Figure A1j: As in Figure A1a, for the
setting centered at 814.5 ${\rm cm^{-1}}$ observed in 2007.

We gratefully thank Zhaohuan Zhu for introducing us to his 2018 paper and for
helpful discussion and advice. We also thank the referee for helpful comments
that improved the manuscript. This work was performed in part at the Aspen
Center for Physics which is supported by the National Science Foundation grant
PHY-1607611. Work by SDB was performed in part at the National Optical
Astronomy Observatory. NOAO is operated by the Association of Universities for
Research in Astronomy (AURA), Inc. under a cooperative agreement with the
National Science Foundation. SDB also acknowledges support from this work by
NASA Agreement No. NXX15AD94G; NASA Agreement No. NNX16AJ81G; and NSF-AST
1517014. The authors wish to recognize and acknowledge the very significant
cultural role and reverence that the summit of Mauna Kea has always had within
the indigenous Hawaiian community. We are most fortunate to have the
opportunity to conduct observations from this mountain. We thank the Gemini
staff, and John White in particular, for their support of TEXES observations
on Gemini North. The development of TEXES was supported by grants from the NSF
and the NASA/USRA SOFIA project. Modification of TEXES for use on Gemini was
supported by Gemini Observatory. Observations with TEXES were supported by NSF
grant AST 06-07312. M. J. R. acknowledges support from NSF grant AST 07-08074,
NASA grant NNG04GG92G, and NASA Collaborative Agreement 80NSSC19K1701. This
work is based on observations obtained at the international Gemini
Observatory, a program of NSF’s NOIRLab, which is managed by the Association
of Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation on behalf of the Gemini Observatory
partnership: the National Science Foundation (United States), National
Research Council (Canada), Agencia Nacional de Investigación y Desarrollo
(Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina),
Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and
Korea Astronomy and Space Science Institute (Republic of Korea).

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