# Modeling of CO ro-vibrational line emission of HD 141569

Stanley K. Jensen Jr  Department of Physics and Astronomy, 118 Kinard
Laboratory, Clemson University, Clemson, SC 29634-0978  Sean D. Brittain
Department of Physics and Astronomy, 118 Kinard Laboratory, Clemson
University, Clemson, SC 29634-0978  Joan R. Najita  NSF’s NOIRLab, 950 North
Cherry Avenue, Tucson, AZ 85719  John S. Carr  Department of Astronomy,
University of Maryland, College Park, MD 20742, USA

###### Abstract

HD 141569 is a Herbig Ae/Be star that straddles the boundary between the
transition disks and debris disks. It is a low dust mass disk that reveals
numerous structural elements (e.g. gaps and rings) that may point to young
planets. It also exhibits a reservoir of CO gas observed at both millimeter
and IR wavelengths. Previous observations (Goto et al., 2006) reported a
possible asymmetry in the CO gas emission. Herein the IR ro-vibrational
emission lines are analyzed and modeled both spectroscopically and
spectroastrometrically. We find emission features from both 12CO and 13CO
isotopologues heated to a temperature of approximately 200 K in the radial
extent of 13 to 60 au. We do not see evidence of the previously reported
asymmetry in CO emission, our results being consistent with a Keplerian,
axisymmetric emitting region. This raises the question of whether the emission
profile may be evolving in time, possibly as a result of an orbiting feature
in the inner disk such as a planet.

##  1\. Introduction

During the early stages of formation, stars are frequently surrounded by
protoplanetary disks. These disk are shaped by a variety of factors, such as
their host stars or planets that may form within them. Planets in the process
of forming can affect the disk in potentially dramatic and observable ways,
such as inducing gaps, spiral arms, and disk eccentricities (e.g. Kley &
Dirksen 2006; Dong et al. 2015a, b). Observations of the gas and dust within
these disks can give insight into the kind of processes at work in this early
stage of stellar and planetary development.

Transition disks in particular are a subclass of interest. While
protoplanetary disks create an IR excess, resulting from emission of the dust,
transition disks lack a NIR excess. This is understood as a gap or cavity in
the extent of the dust near the central star. It may also be the case, though
it is not strictly necessary, that gas also is lacking in these regions. The
cause of such observed gaps is the subject of ongoing research, both generally
and for specific systems, with the most exciting explanation being a planet or
planets in the act of formation (e.g. Strom et al. 1989; Najita et al. 2007,
2015; Espaillat et al. 2014; van der Marel et al. 2016).

Definitively detecting planets within disks has proven difficult, although
recently a companion of PDS 70 was detected by Keppler et al. (2018) using the
VLT instrument SPHERE. In general, direct imaging to identify high-mass
planets and their circumplanetary disk (CPD) or envelope has been less
successful than expected. As a result, there is a need for alternatives such
as potential signposts that are more readily observable. Possible alternatives
are indirect signatures of planet-disk interaction, such as the aforementioned
gaps/holes in disks or spiral structure. However, these signposts can be
generated by other mechanisms (e.g. photoevaporation and gravitational
instability, respectively), so the direct detection of a massive companion is
crucial in order to validate these signposts.

A complementary approach to detecting forming planets is through the line
emission formed in their circimplanetary disks. Circumplanetary disks are
intrinsically three-dimensional structures with complicated flow patterns
(e.g., Tanigawa et al., 2012; Ayliffe & Bate, 2012; Gressel et al., 2013;
Szulágyi et al., 2017). Simulations indicate the size of the disk can be
anywhere from one-third to the full extent of the Hill sphere Quillen et al.
(2004); Ayliffe & Bate (2009b, a); Martin & Lubow (2011); Szulágyi et al.
(2014, 2016) with temperatures $\gtrsim 1000$ K in steady state (Szulágyi,
2017) and perhaps much higher during an outburst (Zhu, 2015). At these sizes
and temperatures, ro-vibrational emission of CO in the NIR is detectable
(e.g., Najita et al., 2003). An example of the potential of this method comes
from HD 100546 (Brittain et al., 2019), where we have inferred the presence of
the inner companion from a component of the $v=1-0$ ro-vibrational CO emission
that varies relative to the stable hot band (i.e., $v^{\prime}\geq 2$, where
$v^{\prime}$ is the upper vibrational state) emission. The variation of the
observed Doppler shift and the spectroastrometric signal can be explained by
an emission source in a Keplerian orbit near the edge of the disk gap. Here we
present a similar study of the ro-vibrational CO emission emerging from HD
141569.

HD 141569 is a 5.9 Myr old (Wichittanakom et al., 2020) Herbig Ae/Be star
110.6$\pm$0.54 parsecs away (Gaia Collaboration et al., 2016, 2018). A low-
mass transition disk on the cusp of becoming a debris disk, the disk in the
system is a few hundred au in total extent (Weinberger et al., 1999; Wyatt et
al., 2015). Observations in the (sub)millimeter show the gas extending to
$\sim$270 au through rotational 12CO lines and dust to nearly 400 au using
continuum emission (Di Folco et al., 2020). It also shows signs of belonging
to the $\lambda$ Boö group of stars in its photospheric abundances (Gray &
Corbally, 1998). This group is marked by a depletion in refractory elements,
indicating accretion of the surrounding disk material, which has undergone
some degree of gas-dust separation, onto the star (e.g. King 1994; Murphy et
al. 2015).

Various structural aspects have been observed, some of which show asymmetries.
Marsh et al. (2002) noted a decrease in optical depth inside of 30 au based on
mid-infrared imaging. The SED of HD 141569 indicates that the inner 10 au has
been cleared (Malfait et al., 1998). Tightly wound, large-scale spirals with
radii of a few hundred au were observed with the ACS on HST by Clampin et al.
(2003), with both planets and tidal interactions from HD 141569’s stellar
companions being put forth as possible causes. More recently Perrot et al.
(2016) observed ring-like structures within 40 and 100 au using SPHERE.
Observations with the STIS instrument on HST by Konishi et al. (2016) detected
an additional component of the disk inward of, and separated by a gap from,
those seen by Clampin et al. (2003). This component partially overlaps the
inner region discussed by Marsh et al. (2002) and shows spiral structure at
$\sim$120 au.

CO is one of the most abundant molecules in protoplanetary disks. While
millimeter emission lines result from pure rotational transitions of CO which
are sensitive to the cool gas, observations of the near infrared lines from
ro-vibrational CO transitions are sensitive to the warm gas in the inner disk
regions. Within the disk, the rotational population is determined by thermal
excitation, while the vibration population is due to UV fluorescence from
stellar irradiation (e.g. Brittain et al. 2007). These infrared emission
features can provide useful information as to the distribution and physical
properties of the gas within the disk. Previous studies of HD 141569 have
observed the infrared CO ro-vibration emission to investigate the physical
conditions and extent of the disk, such as inner/outer radii and temperature
(e.g. Brittain & Rettig 2002; Brittain et al. 2003; Goto et al. 2006; Brittain
et al. 2007; Thi et al. 2014; van der Plas et al. 2015).

More recent ALMA observations by Flaherty et al. (2016) using CO(3-2) and
CO(1-0) emission determined an inner radius of 29${}^{+14}_{-20}$ au. Imaging
by Miley et al. (2018) of the midplane with ALMA using 13CO (2-1) emission
found the gas to be asymmetrically distributed. They also found a midplane
counterpart to a ring previously discovered in scattered light (Biller et al.,
2015) at $\sim$220 au, and found the CO gas, particularly 13CO, extends to
approximately the same region. Thus the size of the gas disk is smaller than
the radial extent of the dust, which extends to $\sim$400 au (Clampin et al.,
2003). This is highly unusual as the dust component of most disks is smaller
than the gas disk. This is generally understood to be the result of the inward
migration of dust due to gas drag. This population of dust that extends beyond
the gas may indicate that it is second generation dust in keeping with the
suggestion that HD 141569 bridges the transition from transition disk to
debris disk.

The derived inclination of the disk of HD 141569 has varied somewhat with
different observations. Near-infrared observations with the Hubble Space
Telescope (HST) instrument NICMOS by Weinberger et al. (1999) found an
inclination of $51^{\circ}\pm 3^{\circ}$. Optical images taken with HST
instrument STIS by Mouillet et al. (2001) found $55^{\circ}\pm 1.2^{\circ}$.
Observations using sub-millimeter facilities also found differing inclinations
of $60^{\circ}\pm 3^{\circ}$ (Submillimeter Array, CARMA; Flaherty et al.
2016) and $53.4^{\circ}$${}^{+1.2^{\circ}}_{-0.9^{\circ}}$ (ALMA; White et al.
2016).

Investigations of the double-peaked CO ro-vibration lines in the disk of HD
141569 have shown a region deficient or entirely devoid of gas inside of 9-15
au (Goto et al., 2006; Brittain et al., 2007) and the CO emission likely
results from a population of gas beyond 17 au with a rotational temperature
$\sim$200 K (Brittain & Rettig, 2002; Brittain et al., 2003). Thi et al.
(2014) found the gas of the inner region of the disk to be in the range of 100
to 300 K. This is cooler than is found for the near-infrared CO emission from
many other transition disks such as HD 100546 ($\sim$1000 K, Brittain et al.
2009), HD 97058 ($\sim$1300, van der Plas et al. 2015), and HD 179218 (600-700
K, Brittain et al. 2018). An example of a disk with a more similar rotational
temperature is Oph IRS 48 at 260 K (Brown et al., 2012).

A possible north-south asymmetry is observed in the spatially resolved ro-
vibrational spectrum of CO. Goto et al. (2006) reported an inner hole size of
11$\pm$2 au using a distance of 108 pc based on Merín et al. (2004).
Correcting for the current Gaia distance of 110 pc makes a marginal difference
to the cavity radius ($\sim$11.25 au). Such asymmetries may be caused by, for
instance, giant planets which induce vortices (Hammer et al., 2017) or by an
eccentric disk induced by a massive planet (Kley & Dirksen, 2006). These
features may be useful in the discovery of planets as a way to differentiate
from a transition disk cavity that is created by photoevaporation or grain
growth. In the case of an eccentric disk induced by a massive planet, the
orientation will precess very slowly ( 1∘ per 100 orbits, Kley & Dirksen
2006), and thus a resulting line asymmetry will be observable over decadal
timescales.

In this paper we present high resolution ($\lambda$/$\Delta\lambda\sim$
75,000) M-band spectroscopy of HD 141569. We also measure the
spectroastrometric signal of the emission lines. Spectroastrometry is a
technique for determining spatial information via spectroscopic observations
originally described by Beckers (1982) and Christy et al. (1983). Specifically
it involves the measurement of the centroid of the PSF of the spectrum on the
detector as a way of determining the center of light (in analogy to, for
instance, center of mass) of the observed object. The presence of a close
companion or rotating disk around a point-like star will shift the centroid
away from the position of the central object in a characteristic pattern as a
function of velocity. On longer timescales and with multiple observations,
this technique can be used to identify variable features, including potential
(proto-) planetary companions (Brittain et al., 2014, 2015, 2019) or disk
winds (Whelan & Garcia, 2008; Pontoppidan et al., 2008, 2011). We compare the
CO line profiles and CO temperature to previous observations, and use the
spectroastrometric signal to test whether the emission is consistent with gas
arising in Keplerian orbit.

##  2\. Observations and Reductions

The data were obtained on April 19, 2017 between 11:59 and 16:05 UT with the
iSHELL cross-dispersion echelle spectrograph at the Infrared Telescope
Facility (IRTF) (Rayner et al., 2016). The date was chosen to ensure that the
target CO emission lines would be shifted out of corresponding telluric
absorption features. Observations used the M2 mode (16 orders with wavelength
range 4.52-5.25 $\mu$m; roughly 1910-2220 cm-1) with an ABBA nodding pattern
which allowed us to combine the images in an A-B-B+A pattern so as to remove
sky emission to first order. Seeing for the night was approximately
0′′.8-0′′.9. Targets included the science star HD 141569 in three sets, each
of which was further separated into position angles (PAs) of 356∘ and 176∘
along the semi-major axis of the disk, and additional standard stars HR 6556
and HR 5793, the former standard associated with the first science set and the
latter for the other two. Observations for HD 141569 were taken in 15 second
exposures with four coadds at two position angles, 356∘ and 176∘, in each of
the three sets for a total integration time of 180 minutes. The two position
angles are necessary in order to correct any instrumental artifacts that may
affect the spectroastrometric centroid measurement. Both standards were also
observed with 15 second exposures and 4 coadds. Flats were taken after
observations were completed for each target. The slit width in all cases was
0′′.375 providing a spectral resolution of $\sim$75,000. Information regarding
the details of the observations are summarized in Table 1.

The obtained data were reduced using a standard procedure, described in
Brittain et al. (2018). General reductions were carried out order-by-order
using custom IDL code. The ABBA nodding in addition to removing sky emission
also resulted in an A and B beam spectrum in each order. The A and B beams
were individually fit to polynomials to rectify the order. After
rectification, dispersion correction was applied using the Spectrum Synthesis
Program (SSP) telluric atmospheric radiance model (Kunde & Maguire, 1974).
Then the spectrum was extracted from a rectangular region by selecting high-
signal rows of each beam and summing columns into new single-row elements to
form each beam’s spectrum. Following this, the resulting A and B beams were
combined. After reductions were complete for both the science target and the
telluric standard to this point, the ratio of the two was taken to remove
telluric features from the science target.

The wavelength calibration was refined after combining beams (using SSP) and
after ratioing (using the standard) as necessary. In the event that any large
scale variation in the continuum remained after telluric correction, a low-
order polynomial was used to flatten the continuum.

In order to compare the fully reduced data with the model (described in
section 4), which generates flux in physical units erg/s/cm2/cm-1, the data
continuum level must be properly converted from the relative flux of the
science-to-standard ratio. This requires knowledge of the continuum level of
the star in the relevant wavelength range. For the case here, 4.6 $\mu$m
ALLWISE photometry (Wright et al., 2010; Cutri et al., 2013) was used,
obtained through the VizieR database (Ochsenbein et al., 2000), yielding a
continuum value of 1.86$\times 10^{-13}$ erg/s/cm2/cm-1.

Centroid measurements were performed using the rectified orders generated
before spectral extraction with MPFITEXPR, a part of the IDL code MPFIT
(Markwardt, 2009), iteratively for each column of each beam. Here, a skewed
Moffat function was used, of the form below:

$f=p_{0}\left(\frac{(x-p_{1})^{2}}{u^{2}}+1\right)^{-p_{4}}+p_{5}$ (1)
$u=\frac{2\cdot p_{2}}{1+e^{p_{3}(x-p_{1})}}$ (2)

Where $p_{0}$ is the amplitude, $p_{1}$ is the center, $p_{2}$ is the half-
width at half-maximum (HWHM), $p_{3}$ is the skew parameter, $p_{4}$ is
controls with broadness of the wings, and $p_{5}$ is the zero-level of the
function. The skewed Moffat function was used because a Gaussian was
determined to not be as accurate a description of the shape of the point
spread function (PSF; see Fig. 1 for comparison). An average PSF was
determined using the regions of the continuum identified during the reduction
process. The PSF was used to determine a “typical” fit as a basis for the
fitting of the individual columns. Once the typical fit was found, all
parameters were fixed except for those pertaining to the height and centroid
position. The PSF for each column was then fit across the entirety of each
beam. This was repeated for each position angle and order. An additional
attempt was made to look for variation in the width of the PSF across the
continnum and the emission features. However, no consistent variation across
the spectrum was found. Any underlying variation requires higher signal-to-
noise and resolution than were obtained here.

Artifacts that affect the measurement of the centroid of the spectrum may
result from the instrument itself and must be corrected. This is accomplished
by the rotation of the slit position during observations. Since the observed
position angles have a 180∘ difference, the spectroastrometric signal is
inverted in one compared to the other while any instrumental artifacts should
remain unchanged. Thus averaging one position angle with the negative of the
other removes these artifacts. (e.g. Whelan & Garcia 2008; Pontoppidan et al.
2008)

Once all three sets of data were reduced as described, the spectra and
centroids were averaged together to create the final versions (Figs. 2, 3, 4,
5, 6, 7, 8, 9, 10, and 11).

Spectral and spectroastrometric CO line profiles were created by stacking
individual lines within each vibrational band in order to improve the signal-
to-noise ratio. Figures 12 and 13 show the spectroscopic and
spectroastrometric average profiles along with a model to be elaborated on in
section 4.

##  3\. Results

The wavenumber range from 1950 to 2200 cm-1 (approximately 4.5 to 5.1 $\mu$m)
was examined, which provides ample access to numerous CO ro-vibrational lines.
This includes coverage of isotopolgues such as 13CO and C18O, though the
latter was not observed here. The non-detection of C18O has previously been
noted in ALMA observations by Miley et al. (2018), who suggested selective
photodissociation for the isotopologue as a possible cause. Figures 2, 3, 4,
5, 6, 7, 8 9, 10, and 11 show the spectrum and centroid for HD 141569. The
stronger 12CO v=1-0 and v=2-1 emission features show a clear double-peaked
profile. 12CO lines from up to v=5-4 vibrational transitions are readily
visible in the spectrum. A few v=6-5 and v=7-6 lines were found as well,
though often with confounding aspects such as high local noise and possible
blending with weak lines. Additional lines are also evident from 13CO v=1-0
and v=2-1 transitions. Any possible lines from additional CO isotopologues or
vibrational bands are either too weak to identify reliably or are blended with
much stronger features. When measuring the equivalent widths, lines were
ignored if they showed signs of being strongly blended, or having lost
significant portions to telluric absorption. The measured equivalent widths
are shown in Table LABEL:tab:eqw_long.

The line profiles obtained by line stacking provide some immediate insight.
These can be seen in Figure 12 for the spetroscopic profiles, and Figure 13
for the spectroastrometric profiles. The 12CO v=1-0 profile is symmetric.
Depending on the adopted stellar mass, here the assumed range varies from 2 to
2.4 M⊙ in line with previous results such as those from Merín et al. (2004)
and White et al. (2016), respectively, the wings at HWZI ($\sim$10 km s-1)
imply an inner edge to the emitting region of approximately 12-15 au, and the
two peaks an outer edge of 50-90 au for Keplerian orbits.

The spectroastrometric signal, from by-eye inspection of individual lines
(Figures 7, 8, 9, 10, and 11), seems indicative of primarily or solely
axisymmetric Keplerian rotation of the disk. This is reinforced, again through
by-eye inspection, in the line stacking (Figure 13) which also produces the
characteristic ”s”-shaped curve of differential rotation by an axisymmetric
Keplerian disk.

Assuming that the gas responsible for the observed emission is optically thin,
the population of each level is related to the line flux by

$F_{ij}=\frac{hc\tilde{\nu}_{ij}A_{ij}N_{j}}{4\pi d^{2}}$ (3)

where $h$ is the Planck constant, $c$ the speed of light, $\tilde{\nu}_{ij}$
the wavenumber of the transition between states $i$ and $j$, $A_{ij}$ the
Einstein coefficient, $N_{j}$ the population of state $j$, and $d$ is the
distance to the object. The relative population of the rotational levels is

$N_{j}=\frac{g_{j}Ne^{-\frac{E^{\prime}}{k_{B}T}}}{Q}$ (4)

where $g_{j}$ is the degeneracy of state $j$, $N$ is the source population,
$E^{\prime}$ is the energy of the upper level, $k_{B}$ is the Boltzmann
constant, $T$ is the temperature, and $Q$ is the partition function. This can
be rearranged into a linear form such that

$\ln\left(\frac{N_{j}}{g_{j}}\right)=-\frac{E^{\prime}j}{k_{B}T}+\ln\left(\frac{N}{Q}\right).$
(5)

The vibrational lines follow a similar form.

For the linear fitting, we adopt the likelihood-based method of Kelly (2007)
through the IDL code LINMIX_ERR due to its treatment of both measurement
errors and upper limits. The results for majority of the vibrational bands
observed for 12CO are consistent at approximately 200 K. However, the derived
rotational temperature from the upper-limit-dominated v=7-6 band is highly
uncertain. The results from all the fits are summarized in Table 3. The
rotational fits are likewise shown in Figure 14.

The vibrational temperature, using simple linear regression with the results
of the method of Kelly (2007), is 4540$\pm$440 K. The high vibrational
temperature compared to its rotational counterpart is indicative of UV
fluorescence and consistent with the value of 5600$\pm$800 K found by Brittain
et al. (2007). The new result incorporates more lines at a higher resolution,
which allows for better line separation and thus a smaller uncertainty in the
vibrational temperature.

##  4\. Modeling

In examining the spectrum of HD 141569, two separates models were used. The
first is a 1+1D slab fluorescence model, of the kind used by Brittain et al.
(2009), that generates CO emission features from a disk of given parameters.
The disk itself is assumed to be Keplerian and axisymmetric in nature as well
as vertically isothermal. The radial rotational temperature is described by a
power law. A constant turbulent velocity was included for the material in the
disk. The UV luminosity parameter, which determines the amount of ultraviolet
emission from the star illuminating the disk, was also included to account for
UV fluorescence in the disk. The relative fluxes of the isotopologues
considered (12CO, 13CO, and C18O) are determined by scaling factors rather
than explicitly taking into account effects such as selective dissociation or
dust opacity (see, e.g., Brittain et al. 2007, 2009 for more details).

Parameters for the fluorescence model were iteratively determined by
individual single-model runs as well as by $\chi^{2}$ minimization through
running multiple models. Single-model instances were primarily used for rough
determination of parameter space and incremental adjustments between automated
runs. The $\chi^{2}$ minimization runs generated random combinations within
the parameter space, compared the model results with the data, and returned
the $\chi^{2}$ values and the best fit model spectrum and centroid. These
results were used to inform parameter space adjustments and the process
repeated.

Each $\chi^{2}$ minimization run allowed for variation of multiple parameters.
Free parameters included inner and outer radii of emitting region, fiducial
rotational temperature, the slope of the radial rotational temperature
dependence $\alpha_{rot}$, fiducial hydrogen density, slope of the radial
hydrogen density dependence $\alpha_{H}$, UV luminosity, turbulence velocity,
and number of layers, where fiducial parameters were taken as the relevant
parameter value at 1 au and the $\alpha$-values are the power law indices for
the radial distribution of the respective quantities. The UV luminosity is
based on extinction corrected data from the International Ultraviolet Explorer
(IUE) (Brittain et al. (2007) and references therein). The original data
assumed a distance of 99 pc. In this paper, we adopt the distance inferred
from Gaia measurements 110.6 pc (Gaia Collaboration et al., 2016, 2018) and
the flux increased by twenty percent.

The number of layers was set to 7000, corresponding to a total column density
of $1.9\times 10^{17}$ cm-2, at which point the gas grows optically thick to
the UV radiation, for the material excited by UV emission along the star-disk
line of sight. Accounting for the inclination of the disk, the column density
along the observed line of sight is $5.3\times 10^{16}$ cm-2. Additional
parameters were occasionally included, such as stellar mass, inclination,
inner wall area, and disk PA relative to slit. These latter parameters were
typically informed by various literature values or to assess their effect on
the fit. The stellar mass was ultimately set at 2.39 M⊙, consistent with White
et al. (2016), and the disk PA was set as aligned with the slit. The final
inclination was fixed to 51∘, in line with Weinberger et al. (1999). In the
case of $\chi^{2}$ minimization runs, the parameters were generated randomly
within ranges based on values found in the literature, results of individual
model iteration, and results of other minimization runs.

The final parameters include an emission region with 13$\pm$2 au and 60$\pm$5
au for the inner-outer radii, respectively, a fiducial rotational temperature
of 495$\pm$5 K at 1 au, and a temperature $\alpha_{rot}$ value of
0.275$\pm$0.020. The full line list can be found in Table LABEL:tab:eqw_long.
Average profiles for both the spectrum and spectroastrometric signal of the
12CO, 13CO, and C18O lines can be seen in Figs. 12 and 13.

The fluorescence model’s temperature profile as a function of radius dips
below the average rotational temperature of $\sim$200 K, as can be seen in
Fig. 16. This likewise would bring the annulus-averaged temperature well below
that established temperature. However, as can be seen in Figs. 17 and 18 the
majority of the emission is coming from the inner regions. When the
temperature is weighted by the annuli luminosity, the average temperature is
found to be 202 K.

The line profiles of warm gas in a disk may be asymmetric for various reasons,
including emission from a circumplanetary disk or emission from an eccentric
disk (e.g. Kley & Dirksen 2006; Regály et al. 2011; Liskowsky et al. 2012). In
order to further verify that there is no evidence of asymmetry in the line
profile, a second model for eccentric disks was used. The eccentric disk model
is much simpler than the fluorescence model previously described. The disk in
this model has an eccentric inner rim, with the azimuthally averaged
eccentricity decreasing with radius. The geometry of the disk (eccentricity
profile, inner and outer radii), stellar mass, and radial intensity profile
are the free parameters. Rather than generating an entire spectrum as in the
fluorescence model only a single line profile in velocity space was produced
per run. This profile was compared with the average profile from observations,
with the final fit determined through $\chi^{2}$ minimization.

While the model itself does not capture the finer details of the physics of
molecular emission, the resulting line profile is sufficient for investigating
the possibility of disk eccentricity and allows for a more rapid exploration
of the parameter space (hundreds of thousands or millions of runs compared to
hundreds or thousands in the same time for the fluorescence model). From this
we find an eccentricity upper limit of 0.02, while a sample model fit with
eccentricity of 0 can be found in Figure 15. The disk geometry parameters are
consistent with those found using the fluorescence model.

##  5\. Discussion and Conclusions

The results presented here do not confirm the possible asymmetry noted by Goto
et al. (2006). Our data indicates that any asymmetry at the time of the
observations would be less than 5%. There are a few possibilities as to why an
asymmetry may have been evident in previous data but not here. The first is
that the previous asymmetry was not real. The cause may have been, for
instance, artifacts in the original data.

Alternatively, it is possible that a source of asymmetric emission may have
rotated in the disk over time. An eccentric disk induced by a giant planet has
the ability to create an asymmetric emission profile. Though this is not
consistent with the presented data as the precession of an eccentric disk is
slow, on the order of 1∘ per 1000 orbits (Kley & Dirksen, 2006). There simply
is not enough time for multiple orbits between the two observations.

If instead the original asymmetry were caused by the circumplanetary disk of a
forming planet, then it would evolve on the planet’s orbital timescale. At the
inner rim with a 12 year difference, such a feature would move more than 100∘.
In principle this would allow it to become hidden behind the inner rim of the
circumstellar disk, similar to the case of HD 100546. However, that the gas in
the disk of HD 141569 is optically thin (with emission arising from an
extended, tenuous upper layer, Brittain et al. 2007) renders this unlikely as
it would still be visible. For instance, Thi et al. (2014) notes that the
continuum emission is optically thin in both vertical and radial directions
over a range of wavelengths, to the point that the SED was not dependent on
the inclination. As such, it does not seem tenable that the molecular emission
from a circumplanetary disk would be hidden by the inner edge of the
circumstellar disk.

An additional possibility is that the asymmetry was caused by a vortex.
Vortices can be created from something as simple as perturbations within the
disk (e.g. Barranco & Marcus 2005) or may be induced by a planet near the
inner rim of the disk (e.g. Espaillat et al. 2014). Additionally, these
features can be dispersed fairly rapidly due to various factors such as
elliptical instability (Lesur & Papaloizou, 2009; Barge et al., 2016),
vertical shear (Barranco & Marcus, 2005), and dust feedback (Fu et al., 2014;
Crnkovic-Rubsamen et al., 2015). The mechanism or mechanisms of dispersal will
vary depending on the local conditions within the disk, as well as the
vortex’s radial and vertical position and structure. A deteriorating or now-
destroyed vortex could result in a loss of asymmetry as observed here. The
rapidity of dissipation is a key point, and there is a wide range of lifetimes
for vortices. One parameter that can affect this is the aspect ratio, a
measure of elongation. For vortices with aspect ratios less than 4,
dissipation can occur in less than an orbit. More elongated (aspect ratios
larger than 10) can survive for hundreds of orbits. (e.g. Lesur & Papaloizou
2009). The formation of a vortex with the correct aspect ratio is a problem in
and of itself. One might be created as a result of the influence of a massive
planet, however it may also imply that the planet formed rapidly (Hammer et
al., 2019).

It should be noted that a lack of direct evidence for a CPD does not imply the
absence of a planet, as it may have finished accreting or entered a period of
quiescence and thus be too dim to observe. A hypothetical planet may also be
too small, or the surrounding disk may be too tenuous, for it to support a
full CPD. Indeed, Di Folco et al. (2020) infer that the total mass of the
circumstellar disk of HD 141569 is $\rm\sim 10^{-4}M_{\odot}$. However,
inferences of disk masses are highly uncertain (e.g., Dong et al., 2018).

We have confirmed that the rotational temperature of CO gas is $\sim$200 K and
a rotational temperature of $\sim$4500, consistent with previous results
Brittain & Rettig (2002); Brittain et al. (2003, 2007); Thi et al. (2014). The
difference in the two temperatures implies that the gas is UV fluoresced. The
spectral and spectroastrometric profiles of the CO emission is consistent with
Keplerian material in an axisymmetric disk. The possibility of non-
axisymmetric structure is testable by additional observations at different
position angles.

## Acknowledgements

This publication makes use of data products from the Wide-field Infrared
Survey Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration.

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

These observations were obtained as visiting astronomers at the Infrared
Telescope Facility, which is operated by the University of Hawaii under
contract 80HQTR19D0030 with the National Aeronautics and Space Administration.

The authors would like to thank Jeffery Fung for his assistance and advice
regarding the creation and destruction of vortices in disks.

## References

  * Ayliffe & Bate (2009a) Ayliffe, B. A., & Bate, M. R. 2009a, MNRAS, 397, 657
  * Ayliffe & Bate (2009b) —. 2009b, MNRAS, 393, 49
  * Ayliffe & Bate (2012) —. 2012, MNRAS, 427, 2597
  * Barge et al. (2016) Barge, P., Richard, S., & Le Dizès, S. 2016, A&A, 592, A136
  * Barranco & Marcus (2005) Barranco, J. A., & Marcus, P. S. 2005, ApJ, 623, 1157
  * Beckers (1982) Beckers, J. M. 1982, Optica Acta, 29, 361
  * Biller et al. (2015) Biller, B. A., Liu, M. C., Rice, K., et al. 2015, MNRAS, 450, 4446
  * Brittain et al. (2018) Brittain, S. D., Carr, J. S., & Najita, J. R. 2018, PASP, 130, 074505
  * Brittain et al. (2014) Brittain, S. D., Carr, J. S., Najita, J. R., Quanz, S. P., & Meyer, M. R. 2014, ApJ, 791, 136
  * Brittain et al. (2009) Brittain, S. D., Najita, J. R., & Carr, J. S. 2009, ApJ, 702, 85
  * Brittain et al. (2015) —. 2015, Ap&SS, 357, 54
  * Brittain et al. (2019) —. 2019, ApJ, 883, 37
  * Brittain & Rettig (2002) Brittain, S. D., & Rettig, T. W. 2002, Nature, 418, 57
  * Brittain et al. (2003) Brittain, S. D., Rettig, T. W., Simon, T., et al. 2003, ApJ, 588, 535
  * Brittain et al. (2007) Brittain, S. D., Simon, T., Najita, J. R., & Rettig, T. W. 2007, ApJ, 659, 685
  * Brown et al. (2012) Brown, J. M., Herczeg, G. J., Pontoppidan, K. M., & van Dishoeck, E. F. 2012, ApJ, 744, 116
  * Christy et al. (1983) Christy, J. W., Wellnitz, D. D., & Currie, D. G. 1983, Lowell Observatory Bulletin, 9, 28
  * Clampin et al. (2003) Clampin, M., Krist, J. E., Ardila, D. R., et al. 2003, AJ, 126, 385
  * Crnkovic-Rubsamen et al. (2015) Crnkovic-Rubsamen, I., Zhu, Z., & Stone, J. M. 2015, MNRAS, 450, 4285
  * Cutri et al. (2013) Cutri, R. M., Wright, E. L., Conrow, T., et al. 2013, Explanatory Supplement to the AllWISE Data Release Products, Tech. rep.
  * Di Folco et al. (2020) Di Folco, E., Péricaud, J., Dutrey, A., et al. 2020, A&A, 635, A94
  * Dong et al. (2018) Dong, R., Najita, J. R., & Brittain, S. 2018, ApJ, 862, 103
  * Dong et al. (2015a) Dong, R., Zhu, Z., Rafikov, R. R., & Stone, J. M. 2015a, ApJ, 809, L5
  * Dong et al. (2015b) Dong, R., Zhu, Z., & Whitney, B. 2015b, ApJ, 809, 93
  * Espaillat et al. (2014) Espaillat, C., Muzerolle, J., Najita, J., et al. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning, 497
  * Flaherty et al. (2016) Flaherty, K. M., Hughes, A. M., Andrews, S. M., et al. 2016, ApJ, 818, 97
  * Fu et al. (2014) Fu, W., Li, H., Lubow, S., Li, S., & Liang, E. 2014, ApJ, 795, L39
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1
  * Goto et al. (2006) Goto, M., Usuda, T., Dullemond, C. P., et al. 2006, ApJ, 652, 758
  * Gray & Corbally (1998) Gray, R. O., & Corbally, C. J. 1998, AJ, 116, 2530
  * Gressel et al. (2013) Gressel, O., Nelson, R. P., Turner, N. J., & Ziegler, U. 2013, ApJ, 779, 59
  * Hammer et al. (2017) Hammer, M., Kratter, K. M., & Lin, M.-K. 2017, MNRAS, 466, 3533
  * Hammer et al. (2019) Hammer, M., Pinilla, P., Kratter, K. M., & Lin, M.-K. 2019, MNRAS, 482, 3609
  * Kelly (2007) Kelly, B. C. 2007, ApJ, 665, 1489
  * Keppler et al. (2018) Keppler, M., Benisty, M., Müller, A., et al. 2018, A&A, 617, A44
  * King (1994) King, J. R. 1994, MNRAS, 269, 209
  * Kley & Dirksen (2006) Kley, W., & Dirksen, G. 2006, A&A, 447, 369
  * Konishi et al. (2016) Konishi, M., Grady, C. A., Schneider, G., et al. 2016, ApJ, 818, L23
  * Kunde & Maguire (1974) Kunde, V. R., & Maguire, W. C. 1974, J. Quant. Spec. Radiat. Transf., 14, 803
  * Lesur & Papaloizou (2009) Lesur, G., & Papaloizou, J. C. B. 2009, A&A, 498, 1
  * Liskowsky et al. (2012) Liskowsky, J. P., Brittain, S. D., Najita, J. R., et al. 2012, ApJ, 760, 153
  * Malfait et al. (1998) Malfait, K., Bogaert, E., & Waelkens, C. 1998, A&A, 331, 211
  * Markwardt (2009) Markwardt, C. B. 2009, in Astronomical Society of the Pacific Conference Series, Vol. 411, Astronomical Data Analysis Software and Systems XVIII, ed. D. A. Bohlender, D. Durand, & P. Dowler, 251
  * Marsh et al. (2002) Marsh, K. A., Silverstone, M. D., Becklin, E. E., et al. 2002, ApJ, 573, 425
  * Martin & Lubow (2011) Martin, R. G., & Lubow, S. H. 2011, ApJ, 740, L6
  * Merín et al. (2004) Merín, B., Montesinos, B., Eiroa, C., et al. 2004, A&A, 419, 301
  * Miley et al. (2018) Miley, J. M., Panić, O., Wyatt, M., & Kennedy, G. M. 2018, A&A, 615, L10
  * Mouillet et al. (2001) Mouillet, D., Lagrange, A. M., Augereau, J. C., & Ménard, F. 2001, A&A, 372, L61
  * Murphy et al. (2015) Murphy, S. J., Corbally, C. J., Gray, R. O., et al. 2015, Publications of the Astronomical Society of Australia, 32, e036
  * Najita et al. (2003) Najita, J., Carr, J. S., & Mathieu, R. D. 2003, ApJ, 589, 931
  * Najita et al. (2015) Najita, J. R., Andrews, S. M., & Muzerolle, J. 2015, MNRAS, 450, 3559
  * Najita et al. (2007) Najita, J. R., Strom, S. E., & Muzerolle, J. 2007, MNRAS, 378, 369
  * Ochsenbein et al. (2000) Ochsenbein, F., Bauer, P., & Marcout, J. 2000, A&AS, 143, 23
  * Perrot et al. (2016) Perrot, C., Boccaletti, A., Pantin, E., et al. 2016, A&A, 590, L7
  * Pontoppidan et al. (2011) Pontoppidan, K. M., Blake, G. A., & Smette, A. 2011, ApJ, 733, 84
  * Pontoppidan et al. (2008) Pontoppidan, K. M., Blake, G. A., van Dishoeck, E. F., et al. 2008, ApJ, 684, 1323
  * Quillen et al. (2004) Quillen, A. C., Blackman, E. G., Frank, A., & Varnière, P. 2004, ApJ, 612, L137
  * Rayner et al. (2016) Rayner, J., Tokunaga, A., Jaffe, D., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, 990884
  * Regály et al. (2011) Regály, Z., Sándor, Z., Dullemond, C. P., & Kiss, L. L. 2011, A&A, 528, A93
  * Strom et al. (1989) Strom, K. M., Strom, S. E., Edwards, S., Cabrit, S., & Skrutskie, M. F. 1989, AJ, 97, 1451
  * Szulágyi (2017) Szulágyi, J. 2017, ApJ, 842, 103
  * Szulágyi et al. (2016) Szulágyi, J., Masset, F., Lega, E., et al. 2016, MNRAS, 460, 2853
  * Szulágyi et al. (2017) Szulágyi, J., Mayer, L., & Quinn, T. 2017, MNRAS, 464, 3158
  * Szulágyi et al. (2014) Szulágyi, J., Morbidelli, A., Crida, A., & Masset, F. 2014, ApJ, 782, 65
  * Tanigawa et al. (2012) Tanigawa, T., Ohtsuki, K., & Machida, M. N. 2012, ApJ, 747, 47
  * Thi et al. (2014) Thi, W. F., Pinte, C., Pantin, E., et al. 2014, A&A, 561, A50
  * van der Marel et al. (2016) van der Marel, N., Verhaar, B. W., van Terwisga, S., et al. 2016, A&A, 592, A126
  * van der Plas et al. (2015) van der Plas, G., van den Ancker, M. E., Waters, L. B. F. M., & Dominik, C. 2015, A&A, 574, A75
  * Weinberger et al. (1999) Weinberger, A. J., Becklin, E. E., Schneider, G., et al. 1999, ApJ, 525, L53
  * Whelan & Garcia (2008) Whelan, E., & Garcia, P. 2008, Spectro-astrometry: The Method, its Limitations, and Applications, ed. F. Bacciotti, L. Testi, & E. Whelan, 123
  * White et al. (2016) White, J. A., Boley, A. C., Hughes, A. M., et al. 2016, ApJ, 829, 6
  * Wichittanakom et al. (2020) Wichittanakom, C., Oudmaijer, R. D., Fairlamb, J. R., et al. 2020, MNRAS, 493, 234
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868
  * Wyatt et al. (2015) Wyatt, M. C., Panić, O., Kennedy, G. M., & Matrà, L. 2015, Ap&SS, 357, 103
  * Zhu (2015) Zhu, Z. 2015, ApJ, 799, 16

Figure 1.—  Sample PSF (HD 141569 set 2, PA 356∘, order 108, A beam) with
three different function fits. The normalized, column-averaged counts are
shown as black plus-signs. Gaussian fit in red, Moffat fit in purple, and
skewed Moffat fit in turquoise. The Gaussian and Moffat fits were generated by
MPFITPEAK while the final skewed Moffat fit was found with MPFITEXPR. Figure
2.—  Partial spectrum for HD 141569 with model fit from 2200 to 2150 cm-1.
Black lines are data and dotted red lines are the final model. Regions without
data are either segments where more than 40% of flux was lost to absorption
features or are gaps between orders. The locations of various ro-vibrational
lines are marked. They are, from top to bottom, 12CO bands v=1-0 to 6-5, then
13CO bands v=1-0 and 2-1, and finally C18O band v=1-0. The color of each band
is indicated in the first panel. Figure 3.—  Similar to Figure 2 for the
wavenumber range of 2150 to 2100 cm-1. Figure 4.—  Similar to Figure 2 for the
wavenumber range of 2100 to 2050 cm-1. Figure 5.—  Similar to Figure 2 for the
wavenumber range of 2050 to 2000 cm-1. Figure 6.—  Similar to Figure 2 for the
wavenumber range of 2000 to 1950 cm-1. Figure 7.—  Partial spectroastrometric
data for HD 141569 with model fit fit from 2200 to 2150 cm-1. Black lines are
data and dotted red lines are the final model. Regions without data are
segments where more than 40% of flux was lost to absorption features. The
locations of various ro-vibrational lines are marked. They are, from top to
bottom, 12CO bands v=1-0 to 6-5, then 13CO bands v=1-0 and 2-1, and finally
C18O band v=1-0. The same color scheme used in figure 1 is used here. Figure
8.—  Similar to Figure 7 for the wavenumber range of 2150 to 2100 cm-1. Figure
9.—  Similar to Figure 7 for the wavenumber range of 2100 to 2050 cm-1. Figure
10.—  Similar to Figure 7 for the wavenumber range of 2050 to 2000 cm-1.
Figure 11.—  Similar to Figure 7 for the wavenumber range of 2000 to 1950
cm-1. Figure 12.—  Gallery of average spectroscopic line profiles for both the
data and fluorescence model. The top row, from left to right, contains 12CO
v=1-0, 2-1, and 3-2 vibrational bands. The middle row contains 12CO v=4-3,
5-4, and 6-5 bands. The bottom row contains 13CO v=1-0 and 2-1 bands, and the
C18O v=1-0 band. In all cases the data profile is in black and the model
profile in blue. The apparent excess in the 12CO v=4-3 plot is the result of a
large feature unrelated to the vibrational band which was not completely
averaged out during line stacking. Figure 13.—  Similar to Fig. 12 with the
average spectroastrometric profile for the various vibrational bands. The top
row, from left to right, contains 12CO v=1-0, 2-1, and 3-2 vibrational bands.
The middle row contains 12CO v=4-3, 5-4, and 6-5 bands. The bottom row
contains 13CO v=1-0 and 2-1 bands, and the C18O v=1-0 band. In all cases the
data profile is in black and the model profile in blue. Figure 14.—
Excitation diagram for CO lines. 12CO measurements are shown in filled black
circles. 13CO measurements in blue. Upper limits are given by downward-
pointing triangles, red for 12CO and green for 12CO. Vibrational band
increases from left to right starting with v=1-0. The fits, orange, are those
derived from the results of the method of Kelly (2007). Figure 15.—  Eccentric
disk model results for HD 141569. Below is the stacked line profile in black
and model in red. Above are residuals in black and zero line in red. The
eccentricity has been set to zero for this plot. Figure 16.—  Final model
temperature as a function of radius. Calculated as a power law, with fiducial
(1 au) temperature of 495 K and exponent of 0.275. Figure 17.—  Final model
cumulative luminosity as a function of radius. Figure 18.—  Final model total
emission fraction as a function of radius.

Table 1HD 141569 observation information Date | April 19, 2017
---|---
Seeing | 0.8-0.9″
Position angles | 356∘, 176∘
Int. time (HD 141569) | 180 min
Int. time (HR 6556) | 6 min
Int. time (HR 5793) | 10 min

Table 2HD 141569 CO Equivalent Width Data Line ID | Wavenumber | Equivalent width
---|---|---
| (cm-1) | (cm-1)
1-0 R(12) | 2190.02 | $0.03049\pm 0.00935$
1-0 R(10) | 2183.22 | $0.04278\pm 0.01087$
1-0 R(8) | 2176.28 | $0.04682\pm 0.00730$
1-0 R(7) | 2172.76 | $0.05099\pm 0.00305$
1-0 R(6) | 2169.20 | $0.05845\pm 0.00342$
1-0 R(5) | 2165.60 | $0.06448\pm 0.00365$
1-0 R(4) | 2161.97 | $0.07791\pm 0.00233$
1-0 R(2) | 2154.60 | $0.06634\pm 0.00229$
1-0 R(1) | 2150.86 | $0.08847\pm 0.00645$
1-0 P(2) | 2135.55 | $0.07270\pm 0.00417$
1-0 P(5) | 2123.70 | $0.12240\pm 0.00994$
1-0 P(6) | 2119.68 | $0.11881\pm 0.00397$
1-0 P(7) | 2115.63 | $0.13156\pm 0.00567$
1-0 P(8) | 2111.54 | $0.11382\pm 0.01156$
1-0 P(11) | 2099.08 | $0.08902\pm 0.01263$
1-0 P(12) | 2094.86 | $0.06629\pm 0.01340$
1-0 P(13) | 2090.61 | $0.04340\pm 0.01529$
1-0 P(14) | 2086.32 | $0.03946\pm 0.01391$
1-0 P(17) | 2073.26 | $<0.00663$
1-0 P(20) | 2059.91 | $<0.00300$
1-0 P(21) | 2055.40 | $<0.00639$
1-0 P(22) | 2050.85 | $<0.00190$
1-0 P(23) | 2046.28 | $<0.00206$
1-0 P(24) | 2041.67 | $<0.00325$
2-1 R(20) | 2188.49 | $<0.00283$
2-1 R(19) | 2185.45 | $<0.00306$
2-1 R(18) | 2182.36 | $<0.00252$
2-1 R(15) | 2172.89 | $0.00807\pm 0.00247$
2-1 R(14) | 2169.66 | $0.01839\pm 0.00251$
2-1 R(13) | 2166.39 | $0.02628\pm 0.00344$
2-1 R(12) | 2163.08 | $0.02909\pm 0.00287$
2-1 R(9) | 2152.94 | $0.04470\pm 0.00577$
2-1 R(8) | 2149.49 | $0.05101\pm 0.02383$
2-1 R(6) | 2142.47 | $0.05986\pm 0.00354$
2-1 R(5) | 2138.91 | $0.07514\pm 0.01071$
2-1 R(4) | 2135.31 | $0.05277\pm 0.01074$
2-1 R(2) | 2128.01 | $0.05586\pm 0.01133$
2-1 R(0) | 2120.57 | $<0.00311$
2-1 P(1) | 2112.98 | $0.03020\pm 0.00635$
2-1 P(2) | 2109.14 | $0.05808\pm 0.00613$
2-1 P(3) | 2105.26 | $0.06359\pm 0.01916$
2-1 P(5) | 2097.39 | $0.07426\pm 0.00441$
2-1 P(6) | 2093.41 | $<0.00212$
2-1 P(7) | 2089.39 | $0.06654\pm 0.01019$
2-1 P(11) | 2072.99 | $0.04170\pm 0.01059$
2-1 P(16) | 2051.73 | $0.01715\pm 0.00323$
2-1 P(20) | 2034.14 | $<0.00299$
2-1 P(21) | 2029.66 | $<0.00179$
3-2 R(22) | 2167.25 | $<0.00149$
3-2 R(21) | 2164.31 | $<0.00100$
3-2 R(20) | 2161.34 | $<0.00114$
3-2 R(18) | 2155.28 | $<0.00179$
3-2 R(17) | 2152.20 | $<0.00091$
3-2 R(16) | 2149.08 | $<0.00101$
3-2 R(14) | 2142.72 | $0.01384\pm 0.00619$
3-2 R(12) | 2136.21 | $0.02080\pm 0.01076$
3-2 R(11) | 2132.91 | $0.02213\pm 0.00294$
3-2 R(10) | 2129.56 | $<0.00323$
3-2 R(9) | 2126.18 | $0.03317\pm 0.00402$
3-2 R(8) | 2122.76 | $0.04266\pm 0.00879$
3-2 R(7) | 2119.30 | $0.03226\pm 0.00524$
3-2 R(5) | 2112.29 | $0.04211\pm 0.00482$
3-2 R(4) | 2108.72 | $0.04307\pm 0.01304$
3-2 R(3) | 2105.13 | $0.03380\pm 0.01698$
3-2 R(1) | 2097.82 | $0.03703\pm 0.00435$
3-2 R(0) | 2094.12 | $0.02131\pm 0.00680$
3-2 P(1) | 2086.60 | $0.02656\pm 0.00684$
3-2 P(3) | 2078.95 | $0.03738\pm 0.02623$
3-2 P(5) | 2071.15 | $0.05154\pm 0.00548$
3-2 P(6) | 2067.21 | $0.05525\pm 0.01392$
3-2 P(9) | 2055.16 | $0.03221\pm 0.01300$
3-2 P(10) | 2051.08 | $0.03998\pm 0.00820$
3-2 P(11) | 2046.96 | $0.03404\pm 0.00875$
3-2 P(14) | 2034.41 | $0.01792\pm 0.01090$
3-2 P(15) | 2030.16 | $0.00704\pm 0.00685$
3-2 P(17) | 2021.56 | $<0.00187$
3-2 P(20) | 2008.42 | $<0.00161$
3-2 P(21) | 2003.98 | $<0.00481$
3-2 P(22) | 1999.50 | $<0.00217$
3-2 P(23) | 1994.99 | $<0.00198$
3-2 P(24) | 1990.45 | $<0.00264$
4-3 R(21) | 2137.20 | $<0.00690$
4-3 R(19) | 2131.29 | $<0.00229$
4-3 R(18) | 2128.27 | $<0.00782$
4-3 R(17) | 2125.22 | $<0.00177$
4-3 R(16) | 2122.14 | $<0.00856$
4-3 R(15) | 2119.01 | $<0.00167$
4-3 R(13) | 2112.65 | $0.00819\pm 0.00366$
4-3 R(12) | 2109.41 | $0.01689\pm 0.00627$
4-3 R(11) | 2106.14 | $<0.00183$
4-3 R(10) | 2102.83 | $<0.01172$
4-3 R(9) | 2099.48 | $0.02340\pm 0.00849$
4-3 R(8) | 2096.10 | $0.02407\pm 0.00653$
4-3 R(7) | 2092.68 | $0.02295\pm 0.00599$
4-3 R(6) | 2089.22 | $0.01877\pm 0.00679$
4-3 R(5) | 2085.73 | $0.02908\pm 0.00608$
4-3 R(3) | 2078.64 | $<0.01046$
4-3 R(1) | 2071.40 | $0.02445\pm 0.00407$
4-3 R(0) | 2067.74 | $0.01236\pm 0.01187$
4-3 P(3) | 2052.71 | $0.03673\pm 0.01844$
4-3 P(7) | 2037.12 | $0.03544\pm 0.01078$
4-3 P(8) | 2033.14 | $0.03008\pm 0.00774$
4-3 P(9) | 2029.13 | $0.02965\pm 0.00634$
4-3 P(11) | 2021.00 | $0.01574\pm 0.00808$
4-3 P(15) | 2004.34 | $<0.00172$
4-3 P(16) | 2000.09 | $<0.00302$
4-3 P(17) | 1995.81 | $<0.00159$
4-3 P(20) | 1982.78 | $<0.00202$
4-3 P(21) | 1978.37 | $<0.00151$
4-3 P(22) | 1973.93 | $<0.00158$
4-3 P(23) | 1969.45 | $<0.00317$
4-3 P(24) | 1964.95 | $<0.00350$
5-4 R(21) | 2110.15 | $<0.00167$
5-4 R(19) | 2104.31 | $<0.00165$
5-4 R(17) | 2098.32 | $<0.00245$
5-4 R(16) | 2095.26 | $<0.00266$
5-4 R(15) | 2092.17 | $0.00869\pm 0.00847$
5-4 R(14) | 2089.05 | $<0.00146$
5-4 R(13) | 2085.88 | $<0.00379$
5-4 R(11) | 2079.44 | $0.00759\pm 0.00550$
5-4 R(10) | 2076.17 | $<0.00196$
5-4 R(9) | 2072.85 | $0.01265\pm 0.01087$
5-4 R(8) | 2069.51 | $0.01840\pm 0.01024$
5-4 R(7) | 2066.12 | $0.01955\pm 0.01380$
5-4 R(4) | 2055.75 | $0.02450\pm 0.00645$
5-4 R(3) | 2052.22 | $0.04551\pm 0.01377$
5-4 R(2) | 2048.66 | $0.02031\pm 0.00439$
5-4 P(1) | 2034.05 | $0.00982\pm 0.00519$
5-4 P(2) | 2030.31 | $0.01924\pm 0.00980$
5-4 P(6) | 2015.00 | $0.02174\pm 0.01102$
5-4 P(7) | 2011.09 | $0.02277\pm 0.00494$
5-4 P(8) | 2007.14 | $0.02341\pm 0.00958$
5-4 P(9) | 2003.17 | $<0.00253$
5-4 P(10) | 1999.15 | $<0.00682$
5-4 P(11) | 1995.10 | $0.01221\pm 0.00753$
5-4 P(14) | 1982.76 | $<0.00183$
5-4 P(15) | 1978.58 | $<0.00156$
5-4 P(16) | 1974.37 | $0.01206\pm 0.00333$
5-4 P(17) | 1970.13 | $<0.00226$
5-4 P(19) | 1961.54 | $<0.00628$
5-4 P(20) | 1957.20 | $<0.00242$
5-4 P(21) | 1952.82 | $<0.00200$
6-5 R(22) | 2086.00 | $<0.00393$
6-5 R(20) | 2080.31 | $<0.00200$
6-5 R(18) | 2074.46 | $<0.00298$
6-5 R(17) | 2071.48 | $<0.00397$
6-5 R(16) | 2068.46 | $<0.00157$
6-5 R(15) | 2065.41 | $<0.00373$
6-5 R(14) | 2062.32 | $<0.00311$
6-5 R(11) | 2052.81 | $<0.00392$
6-5 R(10) | 2049.57 | $0.01325\pm 0.00558$
6-5 R(8) | 2042.98 | $0.00982\pm 0.00797$
6-5 R(7) | 2039.63 | $0.01580\pm 0.00971$
6-5 R(6) | 2036.25 | $0.01719\pm 0.00582$
6-5 R(2) | 2022.35 | $0.01539\pm 0.01396$
6-5 R(0) | 2015.18 | $<0.00289$
6-5 P(2) | 2004.17 | $<0.00595$
6-5 P(3) | 2000.43 | $0.01395\pm 0.00848$
6-5 P(4) | 1996.66 | $0.01938\pm 0.00988$
6-5 P(6) | 1989.01 | $0.01743\pm 0.01661$
6-5 P(9) | 1977.27 | $0.01457\pm 0.01252$
6-5 P(10) | 1973.29 | $<0.00118$
6-5 P(11) | 1969.28 | $<0.00341$
6-5 P(12) | 1965.24 | $<0.00441$
6-5 P(14) | 1957.05 | $<0.00465$
6-5 P(15) | 1952.90 | $<0.00150$
7-6 R(22) | 2059.06 | $<0.00144$
7-6 R(21) | 2056.27 | $<0.00465$
7-6 R(19) | 2050.57 | $<0.00412$
7-6 R(18) | 2047.66 | $<0.00261$
7-6 R(16) | 2041.73 | $<0.00516$
7-6 R(15) | 2038.71 | $<0.00393$
7-6 R(14) | 2035.66 | $<0.00101$
7-6 R(13) | 2032.56 | $<0.00106$
7-6 R(11) | 2026.26 | $<0.00253$
7-6 R(9) | 2019.81 | $<0.00227$
7-6 R(7) | 2013.22 | $0.01040\pm 0.00949$
7-6 R(6) | 2009.87 | $0.00843\pm 0.00777$
7-6 R(4) | 2003.06 | $0.03692\pm 0.03516$
7-6 R(3) | 1999.60 | $<0.00248$
7-6 R(2) | 1996.11 | $0.00499\pm 0.00488$
7-6 R(0) | 1989.01 | $<0.00632$
7-6 P(1) | 1981.78 | $<0.00238$
7-6 P(2) | 1978.11 | $<0.00162$
7-6 P(3) | 1974.40 | $<0.00119$
7-6 P(4) | 1970.66 | $<0.00209$
7-6 P(6) | 1963.08 | $0.02082\pm 0.00560$
7-6 P(7) | 1959.24 | $<0.00154$
7-6 P(8) | 1955.36 | $<0.00678$
7-6 P(9) | 1951.45 | $<0.00269$
(13)1-0 R(22) | 2171.31 | $<0.00230$
(13)1-0 R(21) | 2168.42 | $<0.00128$
(13)1-0 R(19) | 2162.54 | $<0.00105$
(13)1-0 R(17) | 2156.51 | $<0.00431$
(13)1-0 R(16) | 2153.44 | $<0.00129$
(13)1-0 R(15) | 2150.34 | $<0.00179$
(13)1-0 R(13) | 2144.03 | $0.00831\pm 0.00450$
(13)1-0 R(11) | 2137.59 | $0.01118\pm 0.00536$
(13)1-0 R(9) | 2131.00 | $0.01725\pm 0.00391$
(13)1-0 R(5) | 2117.43 | $0.02828\pm 0.00892$
(13)1-0 R(4) | 2113.95 | $0.02591\pm 0.00348$
(13)1-0 R(3) | 2110.44 | $0.01988\pm 0.00258$
(13)1-0 R(2) | 2106.90 | $0.02079\pm 0.00745$
(13)1-0 R(0) | 2099.71 | $0.01035\pm 0.00993$
(13)1-0 P(1) | 2092.39 | $0.01080\pm 0.00937$
(13)1-0 P(2) | 2088.68 | $0.02318\pm 0.00828$
(13)1-0 P(7) | 2069.66 | $0.03204\pm 0.00815$
(13)1-0 P(9) | 2061.82 | $0.03615\pm 0.00746$
(13)1-0 P(10) | 2057.86 | $0.02184\pm 0.00709$
(13)1-0 P(11) | 2053.86 | $0.02056\pm 0.00546$
(13)1-0 P(12) | 2049.83 | $0.01428\pm 0.00528$
(13)1-0 P(14) | 2041.69 | $<0.00597$
(13)1-0 P(15) | 2037.57 | $<0.00411$
(13)1-0 P(16) | 2033.42 | $<0.00363$
(13)1-0 P(17) | 2029.24 | $<0.00387$
(13)1-0 P(19) | 2020.78 | $<0.00198$
(13)1-0 P(21) | 2012.21 | $<0.00121$
(13)1-0 P(22) | 2007.88 | $<0.00467$
(13)1-0 P(23) | 2003.51 | $<0.00313$
(13)1-0 P(24) | 1999.12 | $<0.00832$
(13)2-1 R(21) | 2142.39 | $<0.00117$
(13)2-1 R(19) | 2136.57 | $<0.00203$
(13)2-1 R(18) | 2133.60 | $<0.00094$
(13)2-1 R(17) | 2130.61 | $<0.00108$
(13)2-1 R(15) | 2124.50 | $<0.01001$
(13)2-1 R(13) | 2118.26 | $<0.00187$
(13)2-1 R(12) | 2115.09 | $<0.00349$
(13)2-1 R(11) | 2111.88 | $<0.00143$
(13)2-1 R(9) | 2105.36 | $<0.00874$
(13)2-1 R(7) | 2098.71 | $0.01535\pm 0.00418$
(13)2-1 R(6) | 2095.33 | $0.01329\pm 0.00491$
(13)2-1 R(5) | 2091.92 | $0.01841\pm 0.00330$
(13)2-1 R(2) | 2081.49 | $0.01540\pm 0.01090$
(13)2-1 R(0) | 2074.36 | $0.00770\pm 0.00705$
(13)2-1 P(6) | 2048.41 | $0.02421\pm 0.00403$
(13)2-1 P(8) | 2040.70 | $0.02197\pm 0.01111$
(13)2-1 P(9) | 2036.80 | $0.01567\pm 0.00570$
(13)2-1 P(11) | 2028.91 | $0.01185\pm 0.00624$
(13)2-1 P(13) | 2020.89 | $<0.00236$
(13)2-1 P(18) | 2000.30 | $<0.00189$
(13)2-1 P(19) | 1996.09 | $0.01091\pm 0.00787$
(13)2-1 P(21) | 1987.58 | $<0.00724$
(13)2-1 P(22) | 1983.28 | $<0.00227$
(13)2-1 P(23) | 1978.95 | $<0.00162$
(13)2-1 P(24) | 1974.59 | $<0.00090$
Table 3Rotational tempeatures Ro-vibrational | Temperature
---|---
band | (K)
12CO v=1-0 | 195$\pm$25
12CO v=2-1 | 217$\pm$13
12CO v=3-2 | 193$\pm$16
12CO v=4-3 | 196$\pm$30
12CO v=5-4 | 251$\pm$47
12CO v=6-5 | 219$\pm$116
12CO v=7-6 | 149$\pm$587
13CO v=1-0 | 209$\pm$28
13CO v=2-1 | 144$\pm$42
12CO Vibrational | 4537$\pm$436
Table 4Final model parameters Parameter | Value
---|---
Fixed |
M⋆ | 2.39 M⊙
Lrel | 1.2
$i$ | 51∘
$v_{obs}$ | -21.4 km/s
Varied |
Rin | 13$\pm$2 au
Rout | 60$\pm$5 au
Trot,0 | 495$\pm$5 K
$\alpha_{rot}$ | 0.275$\pm$0.020
vturb | 2.5$\pm$ 0.5 km/s
Flare angle |  $16^{\circ}$${}^{+13^{\circ}}_{-15^{\circ}}$