/variables/.is family, /variables/.unknown/.style = //.initial = #1

11institutetext: Max-Planck-Institut für Astronomie (MPIA), Königstuhl 17,
D-69117 Heidelberg, Germany
11email<EMAIL_ADDRESS>22institutetext: Department of Chemistry, Ludwig-
Maximilians-Universität, Butenandtstr. 5-13, D-81377 München, Germany
33institutetext: LAB, Université de Bordeaux, B18N, Allée Geoffroy, Saint-
Hilaire, CS 50023, 33615 Pessac Cedex 44institutetext: CNRS, Université de
Bordeaux, B18N, Allée Geoffroy, Saint-Hilaire, CS 50023, 33615 Pessac Cedex
55institutetext: IRAM, 300 Rue de la Piscine, F-38046 Saint Martin d’Hères,
France 66institutetext: Max-Planck-Institut für extraterrestrische Physik
(MPE), Gießenbachstr. 1, D-85741 Garching bei München, Germany
77institutetext: IPAG, Université Grenoble Alpes, CNRS, F-38000 Grenoble,
France 88institutetext: Centro de Astrobiología (CAB), CSIC-INTA, Ctra Ajalvir
Km 4, Torrejón de Ardoz, 28850 Madrid, Spain 99institutetext: Department of
Astronomy, The University of Texas at Austin, 2500 Speedway, Austin, TX,
78712, USA 1010institutetext: I. Physikalisches Institut, Universität zu Köln,
Zülpicher Str. 77, 50937 Köln, Germany

# PRODIGE - Planet-forming disks in Taurus with NOEMA

I. Overview and first results for 12CO, 13CO, and C18O

D. Semenov 1122 Th. Henning 11 S. Guilloteau 3344 G. Smirnov-Pinchukov 11 A.
Dutrey 3344 E. Chapillon 55 V. Piétu 55 R. Franceschi 11 K. Schwarz 11 S. van
Terwisga 11 L. Bouscasse 55 P. Caselli 66 C. Ceccarelli 77 N. Cunningham 77 A.
Fuente 88 C. Gieser  66 T.-H. Hsieh 66 A. Lopez-Sepulcre 5577 D. M. Segura-Cox
NSF Astronomy and Astrophysics Postdoctoral Fellow9966 J. E. Pineda 66 M. J.
Maureira 66 Th. Möller 1010 M. Tafalla 88 M. T. Valdivia-Mena 66

###### Abstract

Context. The physics and chemistry of planet-forming disks are far from being
fully understood. To make further progress, both broad line surveys and
observations of individual tracers in a statistically significant number of
disks are required.

Aims. Our aim is to perform a line survey of eight planet-forming Class II
disks in Taurus with the IRAM NOrthern Extended Millimeter Array (NOEMA), as a
part of the MPG-IRAM Observatory Program PRODIGE (PROtostars and DIsks: Global
Evolution; PIs: P. Caselli and Th. Henning).

Methods. Compact and extended disks around T Tauri stars CI, CY, DG, DL, DM,
DN, IQ Tau, and UZ Tau E are observed in $\sim 80$ lines from $>20$ C-, O,-
N-, and S-bearing species. The observations in four spectral settings at
210-280 GHz with a $1\sigma$ rms sensitivity of $\sim 8-12$ mJy/beam at a
$0.9\arcsec$ and 0.3 km s-1 resolution will be completed in 2024. The $uv$
visibilities are fitted with the DiskFit model to obtain key stellar and disk
properties.

Results. In this first paper, the combined 12CO, 13CO, and C18O $J=2-1$ data
are presented. We find that the CO fluxes and disk masses inferred from dust
continuum tentatively correlate with the CO emission sizes. We constrained
dynamical stellar masses, geometries, temperatures, the CO column densities,
and gas masses for each disk. The best-fit temperatures at 100 au are $\sim
17-37$ K, and decrease radially with the power-law exponent $q\sim 0.05-0.76$.
The inferred CO column densities decrease radially with the power-law exponent
$p\sim 0.2-3.1$. The gas masses estimated from 13CO (2-1) are $\sim
0.001-0.2\leavevmode\nobreak\ M_{\odot}$.

Conclusions.  Using NOEMA, we confirm the presence of temperature gradients in
our disk sample. The best-fit CO column densities point to severe CO freeze-
out in these disks. The DL Tau disk is an outlier, and has either stronger CO
depletion or lower gas mass than the rest of the sample. The CO isotopologue
ratios are roughly consistent with the observed values in disks and the low-
mass star-forming regions. The high 13CO/C18O ratio of $\sim 23$ in DM Tau
could be indicative of strong selective photodissociation of C18O in this
disk.

###### Key Words.:

ISM: individual objects: CI Tau, CY Tau, DG Tau, DL Tau, DM Tau, DN Tau, IQ
Tau, UZ Tau \- Line: profiles - Protoplanetary disks - Radio lines: planetary
systems - Stars: variables: T Tauri - Techniques: interferometric

##  1 Introduction

A diversity of discovered exoplanets calls for a better understanding of the
physical and chemical processes in their natal planet-forming disks (e.g.,
Mordasini et al. 2012; Turrini et al. 2021; Mollière et al. 2022). Recently,
young planets have been imaged inside the gas-rich PDS 70 disk for the first
time (e.g., Keppler et al. 2018; Haffert et al. 2019; Facchini et al. 2021).
However, despite extensive progress achieved with the powerful Very Large
Telescope (VLT), Spitzer, James Webb Space Telescope (JWST), Herschel, Atacama
Large Millimeter/Submillimeter Array (ALMA), extended Jansky Very Large Array
(eVLA), and NOrthern Extended Millimeter Array (NOEMA), our understanding of
the disk physics and chemical composition is still limited. Among the key disk
properties, we have only begun to determine their (1) mass measurements, (2)
dust-to-gas ratios, (3) temperature structures, and (4) elemental ratios and
molecular abundances in the gas and ice phases (e.g., Andrews 2020; Öberg et
al. 2021; Benisty et al. 2023; Manara et al. 2023; Miotello et al. 2023; Öberg
et al. 2023).

The majority of the disk masses have been inferred from the dust continuum
data, often by using fixed dust emissivities and/or dust temperatures, and
ill-constrained gas-to-dust ratios (see, e.g., Bergin & Williams 2018; Manara
et al. 2023, and references therein). Gas masses in a limited number of disks
have been obtained by more direct methods. By observing HD emission with
Herschel and performing disk temperature modeling, the gas masses of TW Hya,
DM Tau, and GM Aur disks have been directly inferred (Bergin et al. 2013;
McClure et al. 2016; Trapman et al. 2017). Using CO emission observed with
ALMA, Lodato et al. (2023) have constrained the self-gravity of the IM Lup and
GM Aur disks, and derived gas masses of $\sim 0.1M_{\odot}$ and $\sim
0.26M_{\odot}$, respectively. Yoshida et al. (2022) have measured the pressure
broadening of the 12CO (3-2) line and inferred high gas densities in the inner
TW Hya disk midplane. Modeling the dust emission sizes at multiple wavelengths
has also provided constraints on the gas surface densities, suggesting that
the disks could be more massive than previously thought (Birnstiel et al.
2018; Powell et al. 2019; Trapman et al. 2020; Franceschi et al. 2022; Tazzari
et al. 2021).

Disk temperatures at distinct vertical layers are usually probed via a
combination of the optically thick and thin lines, such as CO, and they often
show the presence of radial and vertical gradients (e.g., Dartois et al. 2003;
Williams & Best 2014; Cleeves et al. 2016; Miotello et al. 2018; Teague et al.
2018b; Calahan et al. 2021b, a; Schwarz et al. 2021; Miotello et al. 2023).
For edge-on or well-resolved disks, the vertical temperature profile can be
derived directly from the line observations (e.g., Dutrey et al. 2017; Pinte
et al. 2018; Law et al. 2021b; Paneque-Carreño et al. 2022). Such studies
require combined physical, chemical, and radiative transfer modeling, and
hence considerable effort to reach a balance between the model feasibility and
its computational costs (Haworth et al. 2016).

In addition to temperatures, turbulent properties of the gas in disks can be
estimated from the high signal-to-noise ratio (S/N) line data by accounting
for the Keplerian shear and thermal broadening, which requires a good
understanding of the underlying thermal structures (e.g., Guilloteau et al.
2012; Teague et al. 2016; Flaherty et al. 2020; Paneque-Carreño et al. 2023).
Subsonic turbulence has only been firmly detected in the DM Tau and IM Lup
disks so far. The deviations from Keplerian rotation have been found in
various disks, which could be signatures of embedded planets or disk winds
(e.g., Teague et al. 2018a; Pinte et al. 2019; Boehler et al. 2021; Teague et
al. 2021; Stadler et al. 2023).

To better understand the cause of the apparent lack of turbulence in disks,
studies of disk ionization are important. Usually, the combination of the HCO+
and N2H+ isotopologues are used to probe the disk ionization degree, which is
driven by the interstellar or stellar X-rays and cosmic ray particles (Dutrey
et al. 2007; Öberg et al. 2011; Cleeves et al. 2015; Teague et al. 2015;
Aikawa et al. 2021). The impact of the impinging stellar far-ultraviolet (FUV)
radiation on disk properties and molecular composition can be characterized
via observations of FUV tracers such as C2H, c-C3H2, CN, HCN, and HNC,
combined with disk chemistry models (e.g., Bergin et al. 2003; Henning et al.
2010; Chapillon et al. 2012; Guzmán et al. 2015; Bergner et al. 2021).

The inferred abundances of CO isotopologues, light hydrocarbons (e.g., C2H),
and sulfur-bearing species have revealed substantial depletion of the
elemental sulfur and oxygen in some disks, and the nonsolar elemental C/O
ratios in their molecular layers (e.g., Bergin et al. 2016; Kama et al. 2016;
Semenov et al. 2018; Le Gal et al. 2019; Miotello et al. 2019; Fedele & Favre
2020; Rivière-Marichalar et al. 2020; Bosman et al. 2021; Cleeves et al. 2021;
Le Gal et al. 2021; Phuong et al. 2021; Ruaud et al. 2022; Anderson et al.
2022; Furuya et al. 2022a; Pascucci et al. 2023). A possible reason for the
excessive volatile depletion in the disk molecular layers is the chemical
processing and sequestration into refractory ices, which sediment toward the
disk midplanes along with the growing dust grains (Favre et al. 2013; Öberg &
Bergin 2016; Krijt et al. 2020; Eistrup & Henning 2022; Van Clepper et al.
2022). Still, the overall chemical composition and partitioning of the
elemental C, O, N, and S into various species remain poorly constrained in
disks. Therefore, a homogeneous study of the disk composition in many chemical
species is necessary, and to begin with we need the high S/N CO isotopologue
data.

Last but not least, ubiquitous $\sim 1-100$ au substructures, such as inner
holes, gaps, rings, spirals visible in both the gas and dust emission are
indicative of the planet formation, planet-disk interactions, or disk
instabilities, which further complicates the analysis and interpretation of
the observations (e.g., ALMA Partnership et al. 2015; Long et al. 2017;
Andrews et al. 2018; Smirnov-Pinchukov et al. 2020; Law et al. 2021a; Bae et
al. 2023; Jennings et al. 2022; Zhang et al. 2023). The “Molecules with ALMA
at Planet-forming Scales” (MAPS) collaboration has performed the high-
resolution, multiband ALMA observations of the IM Lup, GM Aur, AS 209, HD
163296, and MWC 480 disks down to the $\sim 10-20$ au scales (Öberg et al.
2021, and references therein). The MAPS team has found a variety of small-
scale dust and chemical substructures in these disks, characterized their
molecular complexity and the C/O ratios, and revealed complex disk dynamics
suggestive of the planet-disk interactions and disk winds.

With the goal of better constraining the physical and chemical structures in
the Class 0/I and Class II sources, we have conceived the MPG-IRAM large
observing project PRODIGE (PROtostars to DIsks: Global Evolution) at NOEMA.
The first studies of the Class 0/I protostars in Perseus have been published
in Valdivia-Mena et al. (2022) and Hsieh et al. (2023). Here, we present the
first paper about Class II disks in Taurus. This paper focuses on the analysis
and modeling of the CO isotopologue data to unveil the geometry, physical
structure, and CO depletion of the targeted disks, which are needed for the
future analysis and modeling of other emission lines. The overview of the
project, its scientific goals, and sample selection are described in Section
2. The observations and CO line data are presented in Sections 3 and 4,
respectively. The results of the parametric fitting and empirical trends
between various disk and stellar parameters are presented and discussed in
Section 5. Our summary and conclusions are provided thereafter.

##  2 PRODIGE overview, scientific goals, and sample

The recently upgraded NOEMA interferometer with $12\times 15$-m antennas
operating at $70-280$ GHz with up to $\sim 1\,800$ m long baselines is a
powerful facility111https://www.iram.fr/GENERAL/NOEMA-Phase-A.pdf (see
Schuster et al. 2024, in prep.). The PolyFiX correlator can be tuned to
include up to 64 62.5 kHz spectral windows in dual polarization, or used with
a uniform 250 kHz resolution across the full 15.5 GHz bandwidth (Gentaz 2019).
In the high-resolution mode, one can target four times more molecular lines
compared to the ALMA correlator, which makes NOEMA on par with ALMA for the
line surveys at $\sim 0.5-1\arcsec$ resolution.

In light of these considerations, we have devised the large program PRODIGE at
NOEMA to study in a coherent manner the physics and chemistry at $\sim 100$ au
scales in 8 protoplanetary disks in Taurus (PI: Th. Henning; 260 h) and in 30
low-mass protostars in Perseus (PI: P. Caselli; 260 h). The observations began
in 2020 and will be completed in 2024. Below we describe the science goals,
the sample, and the strategy of the Class II disk part of the PRODIGE project.

###  2.1 Sample

In contrast to the MAPS project that has targeted 2 T Tauri and 3 Herbig Ae
disks from various star-forming regions (SFRs) (Öberg et al. 2021), we decided
to focus on both the large ($>300$ au) and compact ($<300$ au) T Tauri disks
in Taurus SFR. We chose the T Tauri systems with the stellar masses of
$M_{*}\lesssim 1M_{\odot}$, outside the $\sim 1.1-2.1M_{\odot}$ mass range
targeted in the MAPS project (Öberg et al. 2021). By focusing on the disks
that have been formed in the same star-forming region from similar initial
conditions, we are able to perform a less biased comparison of the disk
properties between the sources (Ansdell et al. 2018; Luhman 2018; Miotello et
al. 2023).

The Taurus SFR is young, $\sim 1-5$ Myr (Luhman 2023), nearby ($\sim 140-170$
pc; Gaia Collaboration et al. 2018), and has solar-like metallicities
(Cartledge et al. 2006; D’Orazi et al. 2011; Nieva & Przybilla 2012), which
together with a large, $>200$ population of Class II disks (Esplin & Luhman
2019) and a lack of massive stars make it an attractive environment to study
the evolution of protoplanetary disks.

To optimize the available observing time at NOEMA, we decided to target a
limited number of sources but with a high enough sensitivity to detect as many
weak lines of multiple species as possible. Our sample selection criteria
were: 1) Class II sources in Taurus with ages of $\sim 1-5$ Myr, 2) isolated
stars without severe foreground extinction ($A_{V}<3$ mag), 3) T Tauri stars
only, $M_{*}\sim 0.4-1.0\leavevmode\nobreak\ M_{\odot}$, 4) compact and
extended disks without severe substructures visible in the ALMA continuum
images (Long et al. 2018, 2019), 5) disks with 1.3 mm continuum fluxes of
$>60$ mJy to allow self-calibration, 6) disks with previous molecular line
detections (Guilloteau et al. 2016), and 7) at least one disk with measured
gas mass via the HD lines.

Thus, we have selected the following eight systems:

  * •

DM Tau: a large, moderately inclined disk ($\sim 35\degr$) with a gas mass
measured via the HD emission with Herschel (Piétu et al. 2007; McClure et al.
2016);

  * •

DL Tau, CI Tau, CY Tau, IQ Tau, DN Tau: less extended disks with inclinations
up to $55\degr$ (Guilloteau et al. 2011; Long et al. 2018);

  * •

UZ Tau E: a compact, circumbinary disk with a small inner hole and an
inclination of $\sim 56\degr$ (Long et al. 2018);

  * •

DG Tau: a Class I/II object with a jet and an outflow, and an inclination of
$\sim 32\degr$ (perhaps, part of a wide binary system with DG Tau B;
Guilloteau et al. 2011).

Only some of the targeted disks have been observed with ALMA in the CO
isotopologue lines with the sensitivity and resolution comparable to our
PRODIGE NOEMA survey (in particular, C18O). Furthermore,  CY Tau, DM Tau, DL
Tau, DN Tau, and DG Tau have been observed with JWST in Cycle 1 in the
framework of the GTO program “MIRI EC Protoplanetary and Debris Disks Survey”
(GTO 1282; PI: Th. Henning222https://www.stsci.edu/jwst/science-
execution/program-information.html?id=1282).

The basic properties of our disk sample are summarized in Tables 1 and 2. The
additional information about individual sources can be found in Appendix A.

Table 1: Stellar properties.

Source | R.A. | Dec | SpTy | $T_{\rm eff}$ | $M_{*}$ | $\log_{10}(M_{\mathrm{acc}})$ | $\log_{10}(L_{*})$ | Distance | References
---|---|---|---|---|---|---|---|---|---
| ($\degr$ $\arcmin$ $\arcsec$) | ($\degr$ $\arcmin$ $\arcsec$) |  | (K) | ($M_{\odot}$) | ($\log_{10}[M_{\odot}$ yr${}^{-1}]$) | ($\log_{10}L_{\odot}$) | (pc) |
CI Tau | 04 33 52.014 | +22 50 30.094 | K5.5 | 4277 | $0.90\pm 0.02$ | -7.28 | -0.09 | 158.7 | (1,4,5)
CY Tau | 04 17 33.728 | +28 20 46.810 | M2.3 | 3560 | $0.30\pm 0.02$ | -8.85 | -0.61 | 128.9 | (2,3,4,5)
DG Tau∗ | 04 27 04.691 | +26 06 16.042 | K7 | 4000 | $0.70$ | -7.35 | -0.58 | 121.2 | (2,3,5,6)
DL Tau | 04 33 39.077 | +25 20 38.098 | K5.5 | 4277 | $1.04\pm 0.02$ | -7.62 | -0.19 | 159.3 | (1,4,5)
DM Tau | 04 33 48.734 | +18 10 09.974 | M1 | 3720 | $0.55\pm 0.02$ | -7.99 | -0.82 | 145.1 | (2,3,4,6,7)
DN Tau | 04 35 27.378 | +24 14 58.909 | M0.3 | 3806 | $0.87\pm 0.15$ | -9.04 | -0.16 | 128.2 | (1,5,7)
IQ Tau | 04 29 51.557 | +26 06 44.855 | M1.1 | 3690 | $0.74\pm 0.02$ | -8.54 | -0.67 | 131.3 | (1,4,5)
UZ Tau E∗ | 04 32 43.078 | +25 52 30.672 | M1.9 | 3574 | $1.20\pm 0.03$ | -8.05 | -0.46 | 131.2 | (1,5,7)

333The $J=2000$ coordinates and distances are based on the Gaia DR2 catalog
(Gaia Collaboration et al. 2018). The DR2 distances have uncertainties of
$\approx 0.7-1.2$ pc. Spectral types, $T_{\rm eff}$ and Log$(L_{*})$ for CI,
DL, DN, IQ Tau and UZ Tau E are adopted from Long et al. (2018). For CY, DG,
and DM Tau, the distance-corrected values are taken from Luhman et al. (2010)
and Herczeg & Hillenbrand (2014). The dynamical stellar masses for CI, CY, DL,
DM and IQ Tau were taken from Simon et al. (2019). The stellar masses for DN
Tau and the UZ Tau E binary stars were taken from Long et al. (2022). The
stellar mass of DG Tau is taken from Gangi et al. (2022) (no uncertainties
provided). The mass accretion rates, except for DM Tau, are from Gangi et al.
(2022). The mass accretion rate for DM Tau is taken from Ricci et al. (2010).
∗ denotes the bynary systems. References are (1) Long et al. (2018), (2)
Luhman et al. (2010), (3) Herczeg & Hillenbrand (2014), (4) Simon et al.
(2019), (5) Gangi et al. (2022), (6) Ricci et al. (2010), and (7) Long et al.
(2022).

Table 2: Disk properties.

Source | VLSR | Incl. | P.A. | $R_{\rm disk}$ | $M^{\rm dust}_{\rm disk}\times 100$ |  $S_{\nu}$(1.3mm) | Age | References
---|---|---|---|---|---|---|---|---
| (km s-1) | ($\degr$) | ($\degr$) | (au) | ($M_{\odot}$) | (mJy) | (Myr) |
CI Tau | 5.74 | $49.99^{+0.11}_{-0.12}$ | $281.22^{+0.13}_{-0.13}$ | $520\pm 13$ | 0.016 | $125.3\pm 6.2$ | $2.5^{+2.0}_{-1.1}$ | (1,4,6)
CY Tau | 7.25 | $34\pm 3$ | $63\pm 5$ | $295\pm 11$ | 0.019 | $111.1\pm 2.9$ | $2.3^{+0.7}_{-0.6}$ | (1,3)
DG Tau | 5.5 | $32\pm 2$ | $60\pm 4$ | $300\pm 50$ | 0.036 | $389.9\pm 4.6$ | $0.28^{+0.12}_{-0.08}$ | (2,3)
DL Tau | 6.10 | $44.95^{+0.09}_{-0.09}$ | $322.14^{+0.15}_{-0.14}$ | $463\pm 6$ | 0.025 | $204.4\pm 1.9$ | $3.5^{+2.8}_{-1.6}$ | (1,4,6)
DM Tau | 6.05 | $-34.7\pm 0.7$ | $64.7\pm 0.2$ | $900\pm 10$ | 0.025 | $108.5\pm 2.4$ | 1-5 | (1,5,7)
DN Tau | 6.38 | $35.18^{+0.2}_{-0.22}$ | $349.19^{+0.36}_{-0.38}$ | $241\pm 7$ | 0.013 | $88.61^{+0.09}_{-0.2}$ | $0.9^{+0.6}_{-0.4}$ | (1,4,6)
IQ Tau | 5.47 | $58.2\pm 0.2$ | $313.8\pm 0.22$ | $220\pm 15$ | 0.009 | $64.11^{+0.25}_{-0.34}$ | $4.2^{+4.1}_{-2.0}$ | (1,4,6)
UZ Tau E | 5.70 | $56.15\pm 0.07$ | $0.39\pm 0.08$ | $300\pm 20$ | 0.018 | $149.9\pm 1.4$ | $1.3^{+1.0}_{-0.6}$ | (1,4,6)

444The systemic velocities, the outer gas radii, and the disk masses measured
from the dust emission for all disks but DG Tau are adopted from Guilloteau et
al. (2016), and for DG Tau from Güdel et al. (2018) and Guilloteau et al.
(2011). The $S_{\nu}$(1.3mm) continuum fluxes for all disks but IQ and DN Tau
are taken from Guilloteau et al. (2016) and for the IQ Tau and DN Tau from
Long et al. (2018). The inclination and positional angle (PA) for CI, DL, DN,
IQ and UZ Tau E are taken from Long et al. (2018), for DM Tau from Piétu et
al. (2007), and for CY and DG Tau from Guilloteau et al. (2011). Position
angles are those of the disk rotation axis. The disk ages for CI, DL, DN, IQ
Tau and UZ Tau E are taken from Long et al. (2019), for CY and DG Tau from
Guilloteau et al. (2011), and for DM Tau from Law et al. (2022). References
are (1) Guilloteau et al. (2016), (2) Güdel et al. (2018), (3) Guilloteau et
al. (2011), (4) Long et al. (2018), (5) Piétu et al. (2007), (6) Long et al.
(2019), and (7) Law et al. (2022).

###  2.2 Main science goals

In this first paper, we aim to derive the disk temperature and density
structures, using the optically thick and thin CO isotopologue data, and the
power-law radiative transfer model DiskFit (e.g., Piétu et al. 2007). The
best-fit radial temperature and column density profiles that are presented in
this paper were also utilized as priors to reconstruct 1+1D radial and
vertical disk structures using the physical, chemical and line radiative
transfer model DiskCheF (presented in Franceschi et al. 2024).

In the next study, we aim to constrain the disk ionization from a combination
of the optically thick and thin HCO+ (3-2) and N2H+ (3-2) isotopologue lines,
using the best-fit disk physical structures obtained from the CO data. The
disk turbulence (or the upper limits) will be constrained from the CS data to
minimize the thermal broadening contribution to the local line profiles.

After that, using the reconstructed best-fit physical structures and a variety
of detected molecules, the CHNOS chemistry, the volatile budget, and the
presence of the large-scale radial chemical substructures in the disk sample
will be studied. We will infer the gas-phase elemental ratios and depletion
factors, and will investigate the impact of the high-energy FUV and X-ray
radiation on disk chemistry from the combination of C2H, CN, HCN, and HNC. The
efficiency of the D-, 13C-, and 18O-fractionation will be inferred from the
analysis of the observed ratios of DCN/HCN, DNC/HNC, N2D+/N2H+, etc., coupled
with the chemical model with fractionation processes. The inferred chemical
abundances, elemental ratios, depletion factors and isotopic ratios will be
correlated with the key stellar and disk physical quantities (mass, size, gas
temperature, etc.).

##  3 Observations and methods

We observed the GO Tau disk in a pilot 1 mm line survey with NOEMA, using 9
antennas in C configuration ($\sim 0.9\arcsec$ beam), reaching the sensitivity
of $8-12$ mJy/beam at $0.3$ km s-1 resolution after $\sim 4-6$ hours of the
on-source integration (Guilloteau et al., in prep.). This combination between
the resolution and integration time allowed us detecting and at least
partially resolving the line emission from key CHONS species and their
isotopologues, and is optimal for the line surveys in nearby protoplanetary
disks. The four PolyFiX spectral settings in the 210-280 GHz range with a
total 62 GHz coverage were required to target the majority of the detected or
potentially detectable molecular transitions. We employed the same observing
strategy for the PRODIGE project, where each disk is observed for $4-6$ hours
using the same spectral setup and antenna configuration each year (four
different spectral setups between 2020 and 2024).

###  3.1 PolyFiX/NOEMA observations

Observations of the eight T Tau disks were carried out at the NOEMA
interferometer with the PolyFiX correlator in Band 3 (1.3 mm) between 2020,
January 9 and 2020, November 30 (project L19ME; PI: Thomas Henning, co-PI P.
Caselli and S19AW for DN Tau and CI Tau). We used high-resolution, 62.5kHz
spectral chunks to target specific emission lines over the $\sim 15.5$ GHz
PolyFiX bandwidth in dual polarization (other spectral windows had a 2 MHz
resolution). The first observing run covered the main CO isotopologues in
order to better characterize the disk physics, which is needed for the further
analysis and chemical modeling. In addition to 12CO, 13CO, C18O and 13C17O
(2-1), the lines of para-H2CO, DCO+, DCN, DNC, 13CN, cyclic C3H2, C2D, HC3N,
N2D+, and other rare species were targeted. The spectral setup was centered at
$\sim 225$GHz and covered, in total, $\sim 40$ molecular lines in 27 high
resolution spectral windows. The spectral setup is shown in Fig. 11 and
targeted molecular lines and their spectroscopic parameters are listed in
Table 7 in Appendix B. In 2021-23, two other spectral setups were observed,
covering CN, 13CN, cyclic C3H2, ortho-H2CO, HCN isotopologues and HCO+
isotopologues, CS, H2CO, and other species, respectively (the data will be
presented in a future paper).

Observations were carried out with ten antennas in the C configuration. Each
source was observed independently (no track-sharing) with one to three tracks,
using the quasars J0438+300 and 0507+179 as phase calibrators. 3C84 was the
bandpass calibrator in all the tracks but the last one on UZ Tau E, where
3C454.3 was used instead. To ensure good relative flux calibration, LkHa 101
served as a flux calibrator in all datasets but one on UZ Tau E (this last
track was calibrated using the common calibrator with the first track observed
on this source the day before). MWC349 and 2010+723 have been additional flux
calibrators on some tracks (for more detail, see 8). Absolute flux calibration
uncertainties for our CO data are within 10% or better. Mean on-source
integration time was 5.5 hours per source. The $1\sigma$ rms noise varies from
source to source and is $3.7-9.2$ mJy at 0.3 km s-1 resolution.

###  3.2 Data reduction

The raw data were reduced and calibrated at IRAM, using GILDAS/CLIC package
(version 24sep19 02:05 cest)555http://www.iram.fr/IRAMFR/GILDAS. For each
track, we ran the CLIC reduction pipeline and, based on the astronomer on
duty’s notes and after data inspection, corrected for failures (via flagging)
or inaccurate baseline measurements (using measurements taken after the
original observation). The calibrator fluxes (and their time variations) were
bootstrapped and applied to each dataset through a final round of amplitude
calibration. The $uv$ tables were generated at full spectral resolution for
each source and spectral window.

###  3.3 Line imaging

Self-calibration and imaging were performed with the Imager
software666https://imager.oasu.u-bordeaux.fr, using an automatic pipeline, a
custom-built line catalog, and third-party Python tools. Before any
processing, we accounted for the source proper motions by using the Gaia DR2
measurements and the UV_PROPER_MOTION command on each UV table. After self-
calibration, the solutions were applied to the line spectra in the respective
sidebands to improve their signal-to-noise ratios. To increase the S/N ratio,
the line data were resampled to 0.3 km s-1 spectral resolution before imaging
and deconvolution. To further maximize the sensitivity, the data were cleaned
using natural weighting with the Hogbom algorithm. After that, channel and
moment maps were created. The synthesized beams are $\approx
1.1-1.5\arcsec\times 0.5-0.7\arcsec$, for the major and minor beam axis,
respectively. The corresponding positional angles are $\sim 15-20\degr$. Even
in the worst case, the beam major axis is at most at 45$\degr$ from the disk
minor axis, making the disks properly spatially resolved.

To further increase the S/N of the data, we used the Kepler pixel deprojection
technique presented in Teague et al. (2016); Yen et al. (2016); Matrà et al.
(2017). This technique allows shifting and stacking individual spectra by
taking the disk geometry, distance and Keplerian velocities into account,
boosting the signal-to-noise for detected emission. It also allows recovering
the emission radial profile. We use the implementation available through the
KEPLER command in the Imager package. It is similar to that available through
the GoFish777https://github.com/richteague/gofish tool (Teague 2019). The
Imager implementation provides the radial brightness profile distribution by
slicing the data into radial bins, and for each bin, computing the average
spectrum over azimuth, thereby producing a Radius-Velocity diagram. The radial
profile is obtained by retaining the maximum brightness found as a function of
velocity, and an error estimate is derived from the spectra. This peak
brightness estimator is more reliable than the line integrated flux, as faint
line wings are always difficult to properly fit to derive such flux
accurately. However, in the inner part of disk, which remains spatially
unresolved, the peak brightness is reduced compared to the intrinsic source
brightness due to beam dilution. The method works well because geometrical
parameters (including the projected Keplerian velocities) are well defined
from the bright lines such as 12CO (2-1). The only exception was DG Tau due to
its complex structure and the presence of the outflow and shocks, hence only
the standard line imaging was done for this source.

###  3.4 DiskFit model

The radiative transfer code DiskFit was used to fit the observed
$uv$-visibilities (see e.g., Piétu et al. 2007). Rotationally symmetric disk
structure was assumed, with power laws used to describe disk surface density,
temperature, molecular column density radial profiles, etc. The disk was
assumed to be vertically isothermal, with vertically uniform relative
molecular abundances and Gaussian density distribution for the total gas
density. The LTE excitation conditions have been assumed, and the ray tracing
was used to calculate synthetic line emission. The observational data were
fitted in Fourier space by the Levenberg–Marquardt $\chi^{2}$ minimization,
using the same $uv$ sampling in the model as in the observed data. The
symmetric $1\sigma$ error bars that include thermal noise and phase
calibration errors were obtained through the covariance matrix. This
minimization method is sufficient despite the large number of model parameters
(up to 17), because as discussed by Piétu et al. (2007), except for the
rotation velocity-inclination pair coupled through $v\sin{i}$, parameters are
only weakly coupled as can be seen from the MCMC fitting done by Simon et al.
(2017), their Fig.B11.

The validity of the power law assumptions in the DiskFit model relies on rapid
decrease of the disk surface density with radius, the known Keplerian rotation
pattern for the gas, and power-law-like radial decrease of the temperature as
probed from the CO emission. As was discussed in Piétu et al. (2007) and
Phuong et al. (2020), these are reasonable assumptions for outer, $\gtrsim
50-100$ au regions in low-mass, Class II T Tauri disks without severe
substructures, as considered in the present study. In inner, $\lesssim 30-80$
au disk regions, temperature distributions could become flatter, as was found,
for example, by the modeling of the CO ALMA data from MAPS large program (Law
et al. 2022).

While these assumptions apply reasonably well for at least CO and its
isotopologues in the sample of disks studied here, the assumption of a power-
law radial decrease in molecular column density for other species could be
less justified due to the presence of chemical and/or excitation effects,
which will be investigated in subsequent papers. The azimuthally averaged CO
intensity profiles presented below do not show large-scale substructures. We
have further tested applicability of the power-law DiskFit model for
recovering the underlying disk physical parameters. For that, we have
generated synthetic CO isotopologue datacubes with a 2D-line radiative
transfer model URANIA, assuming a power-law surface density profile,
hydrostatic equilibrium in vertical direction, thermal structure computed by
radiative transfer, and using a full gas-grain chemistry, and found that the
DiskFit model can recover the underlying disk properties well (Pavlyuchenkov
et al. 2007).

To facilitate the fitting, we used the stellar masses and geometric parameters
(position, inclination, orientation) from the previous studies and the CO data
(see Tables 1-2). In a first iteration, a fit of the optically thick 12CO
(2-1) line was used to determine the gas temperature, assuming it follows a
power law distribution ($T_{k}(r)=T_{0}\times(r/100\leavevmode\nobreak\
\mathrm{au})^{-q}$). High enough 12CO column densities were assumed to ensure
optical thickness of the synthetic 12CO (2-1) emission (e.g.,
$N(\textrm{CO})>10^{16}$ cm-2 at 100 au). The temperature $T_{k}(r)$ derived
from fitting the optically thick 12CO line was used to fit mostly optically
thin 13CO (2-1) data and to determine the 13CO column density distribution
($N(\mathrm{CO};r)=N_{0}\times(r/100\leavevmode\nobreak\ \mathrm{au})^{-p}$).
As an initial guess for the 13CO column densities, the inferred 12CO column
densities scaled down by a factor of 70 were utilized. We then iterated
between 12CO and 13CO data in order to optimize the fit results. Finally, to
successfully fit the weakest C18O (2-1) emission, the stellar masses,
geometric parameters, and temperature profiles had to be fixed, using the
best-fit values derived from the 13CO fitting. The results of the modeling are
presented below in Sec. 5.1.

##  4 Results

###  4.1 CO line images

Figure 1: Observations of 12CO (2-1) emission in the DM Tau disk. Shown are
the channel map of the observed line brightness distribution (left), the
moment-zero map (top right), and the integrated spectrum (bottom right). The
channel map shows 16 velocity channels with a step of $0.5$ km s-1 in the
[-4.5, +4.5] km s-1 range around the systemic velocity. The contour lines
start at $2$ K, with a step of $2$ K. The color bar shows line brightness
temperatures (K). The contour lines in the moment-zero plot start at 3, 6, and
$9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms noise (mJy km
s-1) is shown in the upper left corner of the moment-zero plot, and the
synthesized beam is depicted by the dark ellipse in the left bottom corner.
Figure 2: Observations of 12CO (2-1) emission in the DM Tau disk. Shown is a
pixel-deprojected Keplerian plot consisting of the three panels: (left) the
radial profile of the line brightness temperature (K) with observations and
errorbars in black, and profile derived from the best-fit disk model in red.
The magenta dashed curve indicates the expected brightness temperature of an
optically thick line derived from temperature power law. (Top) the integrated
spectrum (black line) overlaid with the best-fit Gaussian profile (red line).
(Bottom right) aligned and stacked line intensity (K) as a function of disk
radius (Y-axis; au) and velocity (X-axis; km s-1). The color bar units are in
Kelvin.

We present the 12CO (2-1) moment map, channel maps, integrated spectrum, and
Keplerian plot for the bright and large DM Tau disk in Figs. 1-2. These plots
look overall similar for the other CO isotopologues and for the other disks
(although, usually, with more noise and, in some cases, contamination by
molecular cloud, see Appendix C). The 12CO channel map in Fig. 1 shows a
“butterfly” pattern characteristic of rotating Keplerian disks. The DM Tau
12CO observations are not affected by the foreground cloud absorption, which
is also true for DN Tau and IQ Tau (see Appendix C). In contrast, the
optically thick emission lines in CI, CY, DG, DL Tau, and UZ Tau E are
partially obscured at $\sim 4-6$ km s-1. This absorption leads to asymmetric
emission distributions in the integrated intensity maps and skewed double-
peaked integrated spectra. For example, the NW half of the CI Tau disk appears
much less pronounced than its SE half on the CI Tau integrated intensity map
(see Fig. 12).

The Keplerian deprojection transforms the double-peaked 12CO (2-1) integrated
spectrum of the DM Tau disk with a $\sim 2$ km s-1 FWHM width and a peak value
of $\sim 9.5$ Jy into a single peaked spectrum with a FWHM width of $\sim 0.5$
km s-1 and a peak value of $\sim 27.7$ Jy (see Fig. 2, top panel). This
single-peaked integrated spectrum is well-fitted by a single Gaussian. The
“teardrop” pattern visible in the bottom right panel of Fig. 2 is a
characteristic signature of molecular emission from a Keplerian disk (e.g.,
Teague et al. 2016). It is fully symmetric with respect to the systemic
velocity of $6.05$ km s-1. The high-velocity “halo” visible at the inner
$\lesssim 100$ au radii in the teardrop plot represents the CO emission from
the innermost disk region with the strongest gradients of physical conditions.
It falls within a single beam and hence suffers from beam smearing and
dilution.

The radial profile of the 12CO (2-1) line brightness temperature depicted in
red in left panel in Fig. 2 is derived from the best-fit disk model, while the
magenta dashed line shows the expected brightness of a completely optically
thick line. The overall agreement between these curves and the observed
profile indicates that CO is mostly optically thick and that the power-law
approximation for the temperature is appropriate at this scale. The line
brightness temperature distribution has a skewed Gaussian-like profile, with
an inner “hole” inside $r\sim 150$ au, followed by an extended bell-like peak
with $T_{\mathrm{B}}\sim 16$ K, and a steady decline until $r\sim 1,000$ au.
The apparent drop within the inner $r\lesssim 150$ au is a result of beam
dilution. The radial extent of the 12CO (2-1) line brightness temperature of
$\sim 1,000$ au is larger than the CO gas radius estimate of $\sim 900\pm 10$
au (Table 2) due to our limited angular resolution.

The line brightness radial profiles look similar in the other disks and for
the other CO isotopologue lines, and do not show any significant
substructures. The targeted disks do not have prominent inner holes with sizes
of $\sim 50-100$ au, neither in the dust nor gas distributions, and the $\sim
100$ au spatial resolution of our data does not permit us to infer the
presence of smaller substructures in the disks. The typical peak
$T_{\mathrm{B}}$ values are $\sim 6.5-16$ K for 12CO (2-1), $1.2-7.5$ K for
13CO (2-1), and $0.2-1.8$ K for C18O (2-1), respectively. The $\approx
0.8-0.9\arcsec$ beam ($\sim 100-150$ au spatial scale) leads to the radially
smooth $T_{\mathrm{B}}(r)$ profiles, without any significant substructures
visible in the plots. The emission radii vary from disk to disk and differ for
each CO isotopologue, with the most extended emission in the 12CO (2-1) lines.
As noted above, the inner “holes” with radii $\lesssim 100-150$ au in the
brightness temperature profiles are due to the beam dilution.

While the analysis of the large disk around DM Tau shows that the DiskFit
modeling in terms of power laws is reasonably appropriate, the parameters
derived from such models do start suffering from unavoidable degeneracy when
the disk radius is small due to the limited angular resolution. For the
smaller disks (DN Tau, IQ Tau and UZ Tau E), deriving both the column density
and the temperature law becomes impossible as the optically thick core cannot
be well separated from the optically thin outer part. The geometric parameters
are, however, unaffected. Temperature can be derived from 12CO, while 13CO and
C18O column densities can be derived assuming the same temperature as given
from 12CO. Furthermore, in the relevant temperature range (20-30 K), the
derived column densities are rather insensitive to the temperature. We provide
below more specific details for each source.

##### CI Tau:

Both the moment-zero map and the integrated spectrum of the 12CO (2-1)
emission are affected by the foreground absorption at 4.2-6.5 km s-1 (12). It
also causes the asymmetry of the teardrop plot and the slightly skewed
deprojected integrated spectrum that cannot be fitted with a single Gaussian
(Fig. 13). The radial profile of the line brightness temperature is fainter
than the best fit profile because of the absorption, and extends only up to
$\sim 600-650$ au. In contrast, the 13CO and C18O (2-1) data unaffected by the
cloud show smooth profiles and a broader extent of the line brightness
temperature up to radius of $\sim 900$ au (Figs. 14-17).

##### CY Tau:

The 12CO (2-1) emission is also affected by the foreground absorption that is
visible as stripes in the channel map at $V_{\mathrm{LSR}}\sim 4.5$ and $5$ km
s-1 (LABEL:fig:CY_Tau-CO_comp). This is far from the systemic velocity of
$7.3$ km s-1, and thus both the moment-zero map and integrated spectrum are
not strongly affected by the absorption. The asymmetry of the teardrop plot
toward the redshifted wing at radii $\lesssim 100$ au is due to the cloud
contamination (Fig. LABEL:fig:CY_Tau-CO_kepl). The CO emission for all
isotopologues is compact, $R_{\mathrm{CO}}\sim 300$ au. Deriving a temperature
profile from the CO data is ambiguous because of the combination of cloud
contamination and relatively compact ($R_{\mathrm{CO}}\sim 300$ au) disk.

##### DG Tau:

The 12CO (2-1) emission in the channel map reveals a complex structure, which
consists of a large-scale envelope with filamentary structure, a bow shock at
velocities of $\sim 2.5-4$ km s-1, and a Keplerian disk (Fig.
LABEL:fig:DG_Tau-CO_comp). The large-scale outflow emission is not directly
visible on the 12CO (2-1) map, partly due to the lack of short spacing data.
Strong foreground cloud and envelope absorption lead to the multiple
absorption dips in the integrated spectrum. The same complex structure is
present in more optically thin 13CO and C18O (2-1) emission maps (Figs.
LABEL:fig:DG_Tau-13CO_comp-LABEL:fig:DG_Tau-C18O_comp). The C18O emission
indicates a possible small ($\lesssim 100$ au radius) disk, but with no
obvious signature for Keplerian rotation, given the weak S/N.

##### DL Tau:

The 12CO (2-1) emission shows strong foreground absorption at
$V_{\mathrm{LSR}}\sim 5-6.5$ km s-1, which is visible in the moment-0th map
and integrated spectrum (Fig. LABEL:fig:DL_Tau-CO_comp). Even more optically
thin 13CO (2-1) emission is affected, and shows an arc-like integrated
intensity distribution that is located off the center (Fig.
LABEL:fig:DL_Tau-13CO_comp, top right). The C18O (2-1) emission is weak and
barely visible in the Keplerian deprojected plot (Fig.
LABEL:fig:DL_Tau-C18O_kepl). The CO line brightness temperatures are low in
this disk, in particular for optically thin 13CO and C18O (2-1) lines. The
peak $T_{\mathrm{B}}$ values are $\sim 7.2$ K for 12CO (2-1), $\sim 1.3$ K for
13CO (2-1), and only $\sim 0.2$ K for C18O (2-1), respectively. The observed
12CO (2-1) radial brightness profile differs from the fitted one because of
cloud contamination around the systemic velocity. The 12CO (2-1) emission is
clearly optically thick, and declines more steeply at the disk edge than for
the minor CO isotopologues.

##### DM Tau:

The 12CO (2-1) emission is not affected by the foreground absorption. The
corresponding line brightness distribution $T_{\mathrm{B}}(r)$ has an inner
hole inside $r\sim 130$ au, followed by a peak brightness, and a 3-step
decline until the radius of $\sim 1\,050$ au, with the two turn-over points at
$r\leavevmode\nobreak\ \sim 340$ au and $\sim 700$ au, respectively (Fig. 2).
The steeper profile between $r\sim 800$ au and $\sim 1\,000$ au could be
caused by the tapered surface density distribution at the disk edge. The C18O
(2-1) emission looks noisy because the DM Tau observations were done under
suboptimal conditions during late April, leading to higher noise compared to
the other disks in the sample (Fig. LABEL:fig:DM_Tau-C18O_comp).

##### DN Tau and IQ Tau:

The CO isotopologue emission is compact, $R_{\mathrm{CO}}\sim 200-300$ au
(Figs. LABEL:fig:DN_Tau-CO_comp-LABEL:fig:IQ_Tau-C18O_kepl). The C18O (2-1)
emission is weak. The IQ Tau disk shows low line brightness temperatures that
are similar to those in the DL Tau disk. The peak $T_{\mathrm{B}}$
temperatures are $\sim 9.5$ K for 12CO (2-1), $\sim 1.2$ K for 13CO (2-1), and
only $\sim 0.2$ K for C18O (2-1), respectively. The FWHM widths of the CO
deprojected spectra in the IQ Tau disk are $\sim 1.5$ km s-1. For DN Tau, the
DiskFit analysis requires a central hole of 15-20 au (or substantially fainter
emission within this radius) in all CO isotopologues to best represent the
emission. An alternate solution is a rather flat temperature distribution
(exponent $q\approx 0$), which is less physically realistic. Both solutions
result in a relative lack of emission at high velocities and can explain the
faintness of the line wings.

##### UZ Tau E:

The CO isotopologue emission maps show the presence of the prominent disk
around the spectroscopic binary in the center, accompanied by the compact
binary system UZ Tau W (Figs. LABEL:fig:UZ_Tau-CO_comp-
LABEL:fig:UZ_Tau-C18O_kepl). Emission is also visible toward UZ Tau W in all
CO isotopologues. The disk around UZ Tau E is clearly asymmetric in 12CO
(2-1), with a tail of emission opposite to the position of the UZ Tau W
binary. It extends to a similar distance as the apparent E-W star separation,
clearly suggesting that all these stars were born in a common disk. The best-
fit DiskFit analysis results in a compact CO disk with an outer radius of 200
au, which does not represent the extended emission at all. Moreover, there is
a strong degeneracy between the assumed CO column density profile and the
derived kinetic temperature profile, which is further influenced by the non-
represented outer disk emission. High-temperature solutions (37 K at 100 au,
with a steep exponent of $-0.85$) are possible for 12CO, but require lower
column densities ($<10^{17}$ cm-2) and relatively flat distribution with an
exponent of 0.8). The emission from the minor CO isotopologues is more
compact, with an outer radius around 140 au.

###  4.2 Fluxes

Table 3: Parameters of the observed CO isotopologue lines.

Molecule | Transition | Source | $V_{\rm LSR}$ | $\Delta V_{\rm FWHM}$ | $S_{\rm peak}$ | $\int S_{\nu}\Delta V$
---|---|---|---|---|---|---
|  |  | (km/s) | (km/s) | (Jy) | (Jy km s-1)
CO | (2-1) | CI Tau | $5.88\pm 0.004$ | $0.97\pm 0.01$ | $4.35\pm 0.04$ | $4.48\pm 0.04$
|  | CY Tau | $7.26\pm 0.01$ | $0.70\pm 0.01$ | $2.94\pm 0.04$ | $2.18\pm 0.03$
|  | DL Tau | $6.10\pm 0.01$ | $0.70\pm 0.01$ | $4.43\pm 0.06$ | $3.30\pm 0.05$
|  | DM Tau | $6.05\pm 0.004$ | $0.49\pm 0.004$ | $27.66\pm 0.10$ | $14.37\pm 0.05$
|  | DN Tau | $6.41\pm 0.01$ | $0.93\pm 0.02$ | $3.18\pm 0.05$ | $3.16\pm 0.05$
|  | IQ Tau | $5.53\pm 0.01$ | $1.47\pm 0.02$ | $2.26\pm 0.03$ | $3.53\pm 0.04$
|  | UZ Tau E | $5.85\pm 0.01$ | $1.57\pm 0.01$ | $4.97\pm 0.04$ | $8.31\pm 0.07$
13CO | (2-1) | CI Tau | $5.76\pm 0.004$ | $0.66\pm 0.01$ | $5.32\pm 0.06$ | $3.75\pm 0.04$
|  | CY Tau | $7.26\pm 0.01$ | $0.65\pm 0.02$ | $1.20\pm 0.03$ | $0.83\pm 0.02$
|  | DL Tau | $6.09\pm 0.01$ | $0.53\pm 0.03$ | $1.01\pm 0.04$ | $0.56\pm 0.02$
|  | DM Tau | $6.04\pm 0.004$ | $0.44\pm 0.01$ | $9.63\pm 0.13$ | $4.53\pm 0.06$
|  | DN Tau | $6.41\pm 0.01$ | $0.93\pm 0.02$ | $0.62\pm 0.01$ | $0.61\pm 0.01$
|  | IQ Tau | $5.55\pm 0.02$ | $1.31\pm 0.05$ | $0.21\pm 0.01$ | $0.29\pm 0.01$
|  | UZ Tau E | $5.72\pm 0.01$ | $2.23\pm 0.01$ | $0.50\pm 0.004$ | $1.18\pm 0.01$
C18O | (2-1) | CI Tau | $5.74\pm 0.01$ | $0.83\pm 0.03$ | $0.95\pm 0.03$ | $0.84\pm 0.03$
|  | CY Tau | $7.27\pm 0.02$ | $0.70\pm 0.05$ | $0.30\pm 0.02$ | $0.22\pm 0.01$
|  | DL Tau | $6.23\pm 0.03$ | $0.63\pm 0.07$ | $0.13\pm 0.01$ | $0.08\pm 0.01$
|  | DM Tau | $6.05\pm 0.01$ | $0.40\pm 0.02$ | $1.77\pm 0.06$ | $0.76\pm 0.03$
|  | DN Tau | $6.49\pm 0.08$ | $1.48\pm 0.19$ | $0.06\pm 0.01$ | $0.09\pm 0.01$
|  | IQ Tau | $7.40\pm 0.10$ | $1.56\pm 0.24$ | $0.040\pm 0.01$ | $0.07\pm 0.01$
|  | UZ Tau E | $5.61\pm 0.02$ | $2.26\pm 0.04$ | $0.11\pm 0.004$ | $0.27\pm 0.01$

888The observed values along with the $1\sigma$ uncertainties obtained from
the Gaussian fitting of the Kepler-deprojected integrated spectrum. Column 4:
LSR velocity. Column 5: Full width half maximum line width. Column 6: Peak
flux density. Column 7: Integrated flux (line area).

The observed peak and integrated CO fluxes, along with the systemic velocities
and the line widths, are presented in Table 3. The $1\sigma$ flux
uncertainties were estimated from the rms noise in the emission-free channels.
The system velocities have been derived with a precision of $\approx 4-100$ m
s-1 (with the uncertainties stemming from the Gaussian fit of the spectra).
They vary between about 5.5 and 7.4 km s-1, depending on the source, which are
typical values for the Taurus disks. The line widths corrected for the disk
orientation, but not for Keplerian rotation for 12CO (2-1) are $0.49-1.58$ km
s-1, for 13CO (2-1) are $0.45-2.24$ km s-1, and for C18O (2-1) are $0.40-2.31$
km s-1. The lines are the widest for the disks around IQ Tau and UZ Tau E,
which are the smallest disks and have the highest inclination angles above
$55\degr$, plus their C18O data have low S/N and noisy.

The integrated fluxes vary between 2.94 and 15.35 Jy km s-1 for 12CO (2-1),
4.82 and 0.38 Jy km s-1 for 13CO (2-1), and 0.81 and 0.06 Jy km s-1 for C18O
(2-1), respectively. Similarly, the peak fluxes (flux densities) vary between
2.95 and 29.54 Jy for 12CO (2-1), 9.95 and 0.27 Jy for 13CO (2-1), and 1.89
and 0.05 Jy for C18O (2-1), respectively. The observed peak and integrated
fluxes rescaled to the same 150 pc distance, as well as their uncertainties
estimated from the rms noise in the emission-free channels are shown in Figs.
3-4.

The large ($\sim 800$ au) and massive ($\sim 0.01-0.045M_{\odot}$) disk around
DM Tau is the brightest disk in our sample, with the 13CO and C18O (2-1)
fluxes that are comparable with the 12CO and 13CO (2-1) fluxes from the other
disks. The next brightest disk is CI Tau (with partly blocked 12CO (2-1)
emission), followed by the CY Tau and UZ Tau E disks, and then by the rest of
the sample. The weakest optically thin 13CO and C18O (2-1) emission comes from
DL Tau, DN Tau and IQ Tau. The $\sim 500$ au DL Tau disk is twice as large as
the compact, $\sim 200-250$ au DN Tau and IQ Tau disks (Table 2). Moreover,
the DL Tau disk is about $\sim 2-3$ times more massive ($\sim 0.025M_{\odot}$)
than the DN Tau ($\sim 0.013M_{\odot}$) and IQ Tau ($\sim 0.009M_{\odot}$)
disks, which have the lowest masses in the sample. Thus, the low 13CO and C18O
(2-1) fluxes and the low line brightness temperatures in the DL Tau disk
indicate that either the DL Tau disk mass has been previously overestimated or
that CO is severely depleted in this system (see below). The low 13CO and C18O
(2-1) fluxes as well as line brightness temperatures in DN Tau and IQ Tau
disks are likely due to their low disk masses.

The integrated fluxes obtained with NOEMA are equal to within the absolute
flux calibration accuracy with the previous observations. For example, Rota et
al. (2022) have measured the integrated 12CO and 13CO (2-1) fluxes with ALMA
in UZ Tau E, and found values of $7.58\pm 0.1$ and $1.33\pm 0.04$ Jy km/s,
respectively. These values agree well with the integrated 12CO and 13CO (2-1)
fluxes of $8.31\pm 0.07$ and $1.18\pm 0.01$ Jy km/s measured in this study.
Long et al. (2022) have used ALMA and SMA and derived the integrated 12CO
(2-1) fluxes for DL Tau, DM Tau and UZ Tau E to be 7.05, 15.21, and 7.32 Jy km
s-1, respectively. Our values are 3.32, 14.37, and 8.32 Jy km s-1,
respectively. The discrepancy between the NOEMA and ALMA/SMA data is $\sim
10-15\%$ for DM Tau and UZ Tau E, and a factor of 2 for DL Tau. The reason for
such a  discrepancy for the heavily cloud-contaminated DL Tau system is most
likely due to a different degree of filtering of the extended emission. The
integrated 13CO (2-1) fluxes in DL Tau, DM Tau, DN Tau, IQ Tau and UZ Tau E
measured by Guilloteau et al. (2013) with the IRAM 30-m antenna agree with our
13CO (2-1) fluxes within a range of $\sim 10\%$ \- a factor of 2. Finally, our
integrated 12CO, 13CO, and C18O (2-1) fluxes from CI Tau, CY Tau, DL Tau, and
IQ Tau agree within $\sim 10-80\%$ with the SMA observations of Williams &
Best (2014).

Figure 3: Observed CO-integrated fluxes rescaled to the same distance of 150
pc. The $\pm 3\sigma$ rms noise is depicted by the vertical lines with caps.
The Y-axis has a $\log$ scale. Figure 4: Same as Fig. 3 but for the peak
fluxes.

##  5 Discussion

###  5.1 Best-fit disk parameters derived with DiskFit

####  5.1.1 Stellar properties and disk geometries

Table 4:  Best-fit parameters of the stellar properties and disk geometry.

Source | Line | $V_{\mathrm{LSR}}$ | $M_{*}$ | PA | Inclination | Gas radius
---|---|---|---|---|---|---
|  | (km/s) | (M☉) | (deg) | (deg) | (au)
CI Tau |  12CO (2-1) | $5.78\pm 0.01$ | $1.035$ | $281.7\pm 0.1$ | $48.4\pm 0.2$ | $518\pm 1$
|  13CO (2-1) | $5.74\pm 0.01$ | $0.973$ | $281.7\pm 0.1$ | $46.6\pm 0.9$ | $517\pm 14$
| C18O (2-1) | [$5.73$] | [$0.965$] | [$282.0$] | [$46.9$] | [$511$]
CY Tau |  12CO (2-1) | $7.31\pm 0.01$ | $0.543$ | $64.7\pm 0.2$ | $27.8\pm 3.9$ | $251\pm 1$
|  13CO (2-1) | $7.31\pm 0.01$ | $0.492$ | $63.9\pm 0.2$ | $25.5\pm 0.2$ | $220\pm 5$
| C18O (2-1) | [$7.27$] | [$0.522$] | [$65.0$] | [$28.1$] | [$214$]
DL Tau |  12CO (2-1) | $6.05$ | $1.283$ | $320.4\pm 0.2$ | $36.7\pm 18.1$ | $621\pm 17$
|  13CO (2-1) | $6.04\pm 0.01$ | $1.047$ | $320.2\pm 0.7$ | $44.7\pm 4.8$ | $499\pm 16$
| C18O (2-1) | [$6.04$] | [$1.047$] | [$320.2$] | [$44.7$] | [$499$]
DM Tau |  12CO (2-1) | $6.05\pm 0.01$ | $0.496$ | $65.5\pm 0.4$ | $-33.7\pm 0.2$ | $900\pm 10$
|  13CO (2-1) | $6.02\pm 0.01$ | $0.515$ | $65.9\pm 0.2$ | $-34.8\pm 7.5$ | $688\pm 9$
| C18O (2-1) | $6.04\pm 0.01$ | $0.501$ | $66.3\pm 1.4$ | [$-36.0$] | $530\pm 10$
DN Tau |  12CO (2-1) | $6.40\pm 0.00$ | $0.756$ | $172.0\pm 0.2$ | $32.7\pm 0.7$ | $287\pm 2$
|  13CO (2-1) | $6.37\pm 0.03$ | $0.657$ | $170.9\pm 0.8$ | $36.3\pm 1.6$ | $168\pm 2$
| C18O (2-1) | [$6.37$] | [$0.657$] | [$170.9$] | [$36.3$] | $168\pm 2$
IQ Tau |  12CO (2-1) | $5.51\pm 0.02$ | $0.639$ | $311.2\pm 0.2$ | $62.2\pm 0.6$ | $203\pm 4$
|  13CO (2-1) | $5.54\pm 0.11$ | $0.658$ | $311.8\pm 2.2$ | $60.0\pm 3.7$ | $207\pm 11$
| C18O (2-1) | [$5.54$] | [$0.658$] | [$311.8$] | [$60.0$] | $207\pm 11$
UZ Tau E |  12CO (2-1) | $5.83\pm 0.01$ | $1.298$ | $-2.9\pm 0.1$ | $56.8\pm 1.3$ | $212\pm 1$
|  13CO (2-1) | $5.77\pm 0.04$ | $1.294$ | $-6.6\pm 0.2$ | $60.5\pm 4.1$ | $190\pm 1$
| C18O (2-1) | [$5.77$] | [$1.294$] | [$-6.6$] | [$60.5$] | [$190$]
999The best-fit values along with the $1\sigma$ uncertainties obtained by the
DiskFit modeling. The values in square brackets have been kept fixed during
fitting. The distances from Table 1 have been used. Column 3: Systemic
velocity. Column 4: stellar mass. Column 6: Positional angle (PA).

We used the DiskFit model and obtained the best-fit parameters for the seven
disks (excluding the complex DG Tau system). The best-fit geometric parameters
are presented in Table 4. To fit weak C18O (2-1) emission, the stellar masses,
geometric parameters, and temperature profiles were fixed to the best-fit 13CO
values (they are indicated by the square brackets in Table 4). As can be
clearly seen, for each disk the systemic velocities derived from the CO
isotopologues agree with each other, as well as with the literature values.
The accuracy of the systemic velocities derived from the 12CO and 13CO lines
varies between $4$ and $20$ m s-1 (Table 2). The agreement with the best-fit
values derived by the Gaussian fitting of the Kepler-integrated spectra is in
general within $\lesssim 20$ m s-1 for all cases, except for the disks
affected by the strong cloud confusion (where Kepler-deprojected spectrum is
biased), and the very weak C18O (2-1) emission of IQ Tau.

The best-fit inclination and positional angles agree with the literature
values, and are within $\lesssim 1-4\degr$ for the 12CO and 13CO data for all
the sources but CY Tau (inclination) and DN Tau (PA), see Table 2. The PA and
inclination derived from the 12CO data in DN Tau are larger than those
obtained from the 13CO data by $\approx 2$ and $3.6\degr$, respectively. For
DL Tau, the 12CO (2-1)-based inclination angle is smaller than the 13CO
(2-1)-based value by $\approx 8\degr$, but it has a large uncertainty of $\sim
18\degr$ due to the asymmetry of emission caused by the foreground absorption.

The discrepancy in the best-fit orientation and the inclination of the CO
emitting layers affects the best-fit dynamical stellar masses. This leads to
the difference of $\lesssim 5-10\%$ in the inferred masses of CI Tau, CY Tau,
DM Tau, IQ Tau and UZ Tau E. The best-fit stellar masses of DL Tau and DN Tau
derived from 12CO (2-1) are larger by $\sim 15-20\%$ than those obtained from
13CO (2-1), see Table 4.

Furthermore, the best-fit stellar masses agree within $\sim 10\%$ with the
literature values (Table 1) for CI Tau, DL Tau (disregarding the 12CO
estimate), DM Tau, IQ Tau and UZ Tau E. The best-fit dynamical mass of DN Tau,
$\approx 0.66-0.76M_{\odot}$ agrees with the literature value of $0.87\pm
0.15M_{\odot}$ within the uncertainties. The strongest disagreement between
the best-fit mass derived with DiskFit ($0.49-0.54M_{\odot}$) and the
dynamical value from the literature ($0.30\pm 0.02M_{\odot}$ Simon et al.
2017) is found for the CY Tau disk. In contrast to our $\approx 0.9\arcsec$
observations with NOEMA, the CY Tau mass in Simon et al. (2017) has been
derived by the DiskFit modeling of the ALMA 12CO (2-1) data with a higher
$\approx 0.23\arcsec$ resolution. Given a low inclination of $\lesssim
30\degr$ and a small disk size of $\sim 200-250$ au, it becomes difficult to
precisely constrain the inclination from the CO data when the angular
resolution is only twice better than the disk radius. In this case, the
DiskFit fitting of the NOEMA data resulted in $i\sim 24-28\degr$, while for
the Simon et al. (2017) ALMA data the DiskFit converged to $i\sim 30\pm
2\degr$. The strong absorption toward CY Tau further complicates the fitting
of the NOEMA 12CO data.

Finally, the best-fit CO gas radii and the literature values shown in Table 2
agree within $\sim 10-20\%$ for the entire sample. The smallest CO emission
sizes are found for the DN Tau ($\sim 170-290$ au), UZ Tau E ($\sim 190-210$
au), and IQ Tau ($\sim 200-210$ au) systems. The DL Tau and DM Tau disks are
the largest, with $R_{\mathrm{CO}}\sim 500-800$ au, which could be explained
by their high initial sizes followed by efficient viscous spreading during
their evolution (e.g., Shakura & Sunyaev 1973; Lynden-Bell & Pringle 1974;
Manara et al. 2023). For CI Tau, CY Tau, IQ Tau and UZ Tau E, the difference
between various best-fit $R_{\mathrm{CO}}$ is $\lesssim 40$ au. In contrast,
for DL Tau, DM Tau, and DN Tau, the disk sizes derived from 12CO (2-1) differ
significantly from the sizes inferred from the less bright CO isotopologue
lines (by $\gtrsim 100$ au). Besides the cloud absorption affecting the
observed 12CO emission and the noise affecting minor CO isotopologue data,
another reason could be the structure of the disk, namely, the steepness of
the surface density profile and the degree of tapering toward the outer edge.
For strongly tapered disks, the $R_{\mathrm{CO}}$ sizes should be less
affected by the S/N of the respective CO data, as well as the
photodissociation of CO and opacity effects. Interestingly, in the study of
Guilloteau et al. (2011), it has been found from the continuum data modeling
that the disks around DM Tau and DL Tau should be less tapered than the disks
around CI Tau, CY Tau, and UZ Tau E, supporting our NOEMA observations.

####  5.1.2 CO temperatures, column densities, isotopic ratios, and disk gas
masses

The best-fit CO excitation temperature and column density profiles are
presented in Table 5 and compared in Fig. 5. The (sub)millimeter CO lines in
disks are usually thermalized, and their excitation temperatures are thus
close to the gas kinetic temperatures. As can be clearly seen, the derived CO
temperatures in the outer disks at $r\sim 100$ au are low, $\sim 17-37$ K.
Some of the derived temperatures at $r=100$ au are below the freeze-out
temperature of CO of 20 K. From a theoretical perspective, temperatures below
20 K are expected in the outer, $\gtrsim 100-200$ au midplane regions in the
disks around cool T Tauri stars (e.g., Kenyon & Hartmann 1987; Birnstiel et
al. 2010; Woitke et al. 2016). Moreover, the presence of cold, $\lesssim 20$ K
CO gas in the outer disks due to the grain evolution, nonthermal photo- or
chemical desorption, or transport processes has been predicted by various
detailed disk thermochemical models (e.g., Semenov et al. 2006; Piétu et al.
2007; Krijt et al. 2020; Woitke et al. 2022; Gavino et al. 2023).
Alternatively, these low temperatures could be caused by the single power-law
description of the disk temperatures in the DiskFit model, whereas in other
disk models aiming at fitting the CO isotopologue or dust continuum emission,
a temperature floor values have often been assumed to keep the disk midpane or
CO layer temperatures above a certain thermal threshold value (see, e.g.,
Andrews et al. 2009; Rosenfeld et al. 2013; Williams & Best 2014; Zhang et al.
2017; Schwarz et al. 2018; Tazzari et al. 2021; Miotello et al. 2023; Law et
al. 2022).

The best-fit temperature exponents $q$ are usually $\sim 0.4-0.7$. The 13CO
and C18O lines in CI Tau are an exception, and are more consistent with flat
temperature profiles. These values are typical for outer disk regions around
cool T Tauri stars (e.g. Henning & Semenov 2013; Dutrey et al. 2014; Miotello
et al. 2023). The less optically thin minor CO isotopologues probe a deeper,
cooler part of the CO molecular layer, and thus show lower gas temperatures
(depending on the vertical structure), see, e.g. Dutrey et al. (2017); Flores
et al. (2021). The warmest CO gas is in the CI, DN, DM Tau and UZ Tau E disks,
with $T\sim 32-37$ K. The CI Tau and DN Tau have the highest stellar
luminosities in our sample, $L_{*}\approx 0.8$ and $0.69L_{\odot}$,
respectively, and, hence, should have the warmest disk atmospheres (Table 1).
The disk of DM Tau is flared and hence could be more efficiently heated by the
central M dwarf star, leading to a stronger temperature gradient (Piétu et al.
2007). The UZ Tau E disk may have a low gas mass of $\lesssim 0.003M_{\odot}$
(see Appendix A), but this should not necessarily lead to a warmer CO
molecular layer in this disk. A more plausible explanation is that the
luminosity of this binary system is higher than $\sim 0.35L_{\odot}$ shown in
Table 1. Indeed, a higher luminosity value of $\sim 0.8-2.2L_{\odot}$ have
been adopted in other works (Ricci et al. 2010; Guilloteau et al. 2016;
Tripathi et al. 2017; Manara et al. 2023).

Rather similar CO temperatures have been found for our disks in other studies.
Law et al. (2022) have constrained vertical structures of the CI Tau and DM
Tau disks, using archival $\approx 0.1-0.4\arcsec$ ALMA data. They have found
that the DM Tau disk has an elevated CO emission surface, and inferred the
12CO temperatures between $\sim 20$ K in the outer disk and up to $\sim 35$ K
in the inner disk at $r\lesssim 100$ au. These DM Tau temperatures are also
similar to those obtained in the earlier studies of Piétu et al. (2007) and
Flaherty et al. (2020). In Law et al. (2023), a detailed analysis of the
vertical emission distribution and the gas temperatures using better $\approx
0.1-0.2\arcsec$ ALMA observations of the three main CO isotopologues have been
performed for several disks, including DM Tau. It has been found that the C18O
emission comes from the cold midplane, while the 12CO and 13CO emission comes
from elevated heights, $z/r\sim 0.2-0.4$ (and the 12CO emitting surface is
located higher than the 13CO surface). They derived the best-fit 12CO and 13CO
temperatures at $r=100$ au of $38\pm 0.5$ and $26\pm 0.4$ K, respectively,
which our DiskFit values of $31.6\pm 0.1$ and $21.4\pm 0.2$ K match rather
well (see Table 5). The best-fit power-law exponents for the gas temperature
profiles of $q\approx 0.42-0.56$ have been obtained by Law et al. (2023),
which again are well matched by our DiskFit $q\approx 0.51-0.58$ values
(within uncertainties).

In contrast to DM Tau, the 12CO temperature at $r=100$ au in CI Tau derived by
Law et al. (2022) is $\sim 48$ K, which is warmer than the best-fit 12CO
temperature of $\sim 34$ K derived in this study (see Table 5). One of the
reasons for that is a lower spatial resolution of our $0.9\arcsec$ NOEMA CO
data compared to the $\sim 0.1\arcsec$ ALMA data used by Law et al., which
makes it impossible for the DiskFit model to probe gas properties in the
innermost $\sim 50-80$ au regions resolved with ALMA. Another reason is that
the CO temperature profile constrained from the high-resolution ALMA data
deviates from a simple power law in CI Tau, with prominent gas temperature
dips at the radii of 70 and 120 au, and a local gas temperature peak at 90 au
(this peak coincides with a strong change in the CO surface emission profile
and is close to a dust continuum emission ring), see Law et al. (2022). Our
coarser NOEMA CO observations do not show these substructures, see Fig. C.1.
Hence, the DiskFit model that is not sensitive to these localized temperature
deviations and is more strongly dominated by the CO data from the colder,
$>100$ au region tends to underestimate the gas temperature in the inner disk.

Table 5:  Best-fit gas thermal and CO column density profiles.

Source | Line | Temperature at 100 au | Temperature exp. | Column density at 100 au | Column density exp.
---|---|---|---|---|---
|  | (K) | $q$ | (cm-2) | $p$
CI Tau |  12CO (2-1) | $34.1\pm 0.8$ | $0.69\pm 0.01$ | $17.97$ | $1.32$
|  13CO (2-1) | $18.6\pm 0.9$ | $0.05\pm 0.03$ | $16.18\pm 0.02$ | $1.67\pm 0.11$
| C18O (2-1) | [$18.7$] | $0.09$ | $15.22\pm 0.01$ | $1.59$
CY Tau |  12CO (2-1) | $17.0\pm 0.1$ | $0.65\pm 0.01$ | $17.00$ | $1.40$
|  13CO (2-1) | $18.2\pm 0.1$ | $0.76\pm 0.01$ | $16.12\pm 0.06$ | $1.75\pm 0.07$
| C18O (2-1) | [$18.2$] | [$0.76$] | $14.88\pm 0.13$ | $1.51\pm 0.09$
DL Tau |  12CO (2-1) | $19.9\pm 0.1$ | $0.66\pm 0.01$ | $16.93$ | $0.47$
|  13CO (2-1) | $18.2\pm 0.1$ | $0.50\pm 0.01$ | $14.95\pm 0.05$ | $0.18\pm 0.06$
| C18O (2-1) | [$18.2$] | [$0.50$] | $13.92\pm 0.08$ | [$0.18$]
DM Tau |  12CO (2-1) | $31.6\pm 0.1$ | $0.58\pm 0.05$ | $17.85\pm 0.39$ | $2.75\pm 0.02$
|  13CO (2-1) | $21.4\pm 0.2$ | $0.51\pm 0.01$ | $16.29\pm 0.02$ | $1.57\pm 0.04$
| C18O (2-1) | [$21.5$] | [$0.5$] | $14.92\pm 0.02$ | $0.53\pm 0.07$
DN Tau |  12CO (2-1) | $25.8\pm 3.4$ | $0.62\pm 0.05$ | $16.36\pm 0.02$ | $3.08\pm 0.08$
|  13CO (2-1) | $24.3\pm 0.1$ | $0.65\pm 0.01$ | $15.52\pm 0.02$ | $0.85\pm 0.05$
| C18O (2-1) | [$24.3$] | [$0.65$] | $14.64\pm 0.03$ | [$0.85$]
IQ Tau |  12CO (2-1) | $20.3\pm 0.2$ | $0.41\pm 0.01$ | $16.85$ | $1.40$
|  13CO (2-1) | $20.4\pm 0.1$ | $0.37\pm 0.01$ | $14.96\pm 0.03$ | $1.34\pm 0.59$
| C18O (2-1) | [$20.4$] | [$0.37$] | $14.04\pm 0.12$ | $1.34\pm 0.59$
UZ Tau E |  12CO (2-1) | $36.6\pm 0.9$ | $0.67\pm 0.19$ | $16.65\pm 0.02$ | $1.28\pm 0.01$
|  13CO (2-1) | $27.9\pm 0.1$ | $0.55\pm 0.01$ | $16.10\pm 0.06$ | $0.45\pm 0.04$
| C18O (2-1) | [$27.9$] | [$0.55$] | $15.34\pm 0.01$ | [$0.50$]

101010The parameters in square brackets have been kept fixed during the
fitting. The best-fit temperatures are the excitation temperatures of the
corresponding CO transitions. Please note that the best-fit column densities
derived from the optically thick 12CO data can be underestimated.

The column density profiles at $r=100$ au are compared in Fig. 6 and are $\sim
2\times 10^{16}-10^{18}$ cm-2 for 12CO, $\sim 10^{15}-2\times 10^{16}$ cm-2
for 13CO, and $\sim 10^{14}-2\times 10^{15}$ cm-2 for C18O, respectively. The
power-law exponents of the column density profiles $p$ are $\sim 0.5-3.2$ for
12CO and vary between $0.2$ and $1.8$ for 13CO and C18O. The 12CO (2-1)
emission is optically thick, and thus the best-fit 12CO column densities could
be underestimated. (Constraints on the 12CO column density come in part from
the optically thin line wings, and in part from the power law assumption). The
highest 12CO surface densities of $\sim 10^{18}$ cm-2 were found in the CI Tau
and DM Tau disks, whereas the lowest values of $\lesssim 10^{17}$ cm-2 were
found in the disks around CY, DL, DN, IQ Tau, and UZ Tau E. The column
densities derived from the less optically thick 13CO (2-1) are the highest for
CI Tau, CY Tau, and DM Tau ($\sim 2\times 10^{16}$ cm-2), and the lowest in DL
Tau and IQ Tau ($\lesssim 10^{15}$ cm-2). For C18O (2-1), the highest column
densities were obtained for CI Tau, DM Tau, and UZ Tau E ($\sim 10^{15}$
cm-2), while the lowest values were found in DL Tau and IQ Tau ($\sim 10^{14}$
cm-2). Thus, both the DL Tau and IQ Tau disks have the lowest CO surface
densities in our sample. While for the IQ Tau disk it can be explained by its
low disk mass of $0.009M_{\odot}$, the situation for DL Tau is more
interesting. The combined [CI] and CO observations of DL Tau with ALMA and ACA
by Sturm et al. (2022) have revealed that carbon could be severely depleted by
a factor of $\sim 50-150$ in the outer DL Tau molecular layer. This is
consistent with the apparently old age of the DL Tau disk, $\sim 4-8$ Myr, as
well as a measured high CO/dust size ratio, indicative of efficient radial
drift and dust evolution, and associated chemical processing of CO (Krijt et
al. 2020; Powell et al. 2022; Sturm et al. 2022). Another estimate of the CO
depletion for our sample has been derived for DM Tau by McClure et al. (2016),
who found that the depletion is mild, within a factor of 5 or less.

We used the best-fit column densities and calculated the corresponding
isotopic ratios and the $1\sigma$ uncertainties for 12CO/13CO and 13CO/C18O
(see Fig. 7). Both the 12CO/13CO and 13CO/C18O ratios roughly fall within the
ranges observed in disks and the ISM of $\sim 20-165$ and $\sim 8-12$,
respectively (e.g. Piétu et al. 2007; Booth et al. 2019; Furuya et al. 2022b;
Yoshida et al. 2022). The only exception is the 13CO/C18O ratio in DM Tau,
where the C18O column density could be underestimated due to the noisy C18O
(2-1) data or, perhaps, could be the result of strong selective
photodissociation of C18O in the very extended, outer flared disk region (see
Fig. LABEL:fig:DM_Tau-C18O_comp).

Finally, we used the best-fit power-law profiles of the 13CO column densities
to estimate disk gas masses. Since the best-fit 12CO column densities could be
underestimated by DiskFit due to the optical thickness of the 12CO line, we
assumed a range of $[20-69]$ for the 12CO/13CO ratios and used it to
recalculate the 12CO column densities. CO is heavily frozen-out in the
midplane of the cold, $>100$ au disk regions probed by our NOEMA observations,
hence we have adopted a non-ISM 12CO/H2 ratio of $\sim 10^{-6}$ to constrain
the underlying gas surface density profile (e.g., Semenov & Wiebe 2011;
Miotello et al. 2018; Krijt et al. 2020; Trapman et al. 2022). By taking all
these assumptions into account, the resulting disk gas masses vary between
$\sim 10^{-3}-0.2\leavevmode\nobreak\ M_{\odot}$ with considerable
uncertainties, see Table 6. Compared to the rescaled dust masses adopted from
the previous studies (see Table 2), the gas masses calculated from our 13CO
data are somewhat higher by a factor of $\sim 2-3$, except for the disks
around DL Tau, DN Tau and IQ Tau, which have lower CO-derived masses compared
to their rescaled dust-derived masses. This is not surprising because the DL
Tau, DN Tau, and IQ Tau disks have low C18O (2-1) fluxes and low best-fit C18O
column densities, indicating a low amount of CO gas. The CO-derived mass of
the extended, $R_{\rm CO}\sim 620$ au disk around DL Tau deviates the most
from its dust mass, once again suggesting that this peculiar system may have
more severe CO depletion than in other disks (see also Sturm et al. 2022),
while the compact disks around DN Tau and IQ Tau have low total gas masses.
The most massive disk in our sample is DM Tau with a CO-derived mass of $\sim
0.06-0.2M_{\odot}$, which is somewhat higher than its mass of $\lesssim
0.045M_{\odot}$ derived from the Herschel HD observations (McClure et al.
2016; Trapman et al. 2017). A more detailed study of the gas densities and
masses in PRODIGE sources derived by the physical-chemical modeling will be
presented in Franceschi et al. (2024).

Table 6: Disk gas masses derived from the 13CO (2-1) column densities.

Source |  12CO/13CO = 20 |  12CO/13CO = 69 | $M^{\rm dust}_{\rm disk}\times 100$
---|---|---|---
| ($M_{\odot}$) | ($M_{\odot}$) | ($M_{\odot}$)
CI Tau | $0.04$ | $0.15$ | 0.016
CY Tau | $0.04$ | $0.12$ | 0.019
DL Tau | $0.005$ | $0.02$ | 0.036
DM Tau | $0.06$ | $0.2$ | 0.025
DN Tau | $0.003$ | $0.01$ | 0.013
IQ Tau | $0.001$ | $0.004$ | 0.009
UZ Tau E | $0.01$ | $0.04$ | 0.018
111111Columns 2 and 3: Disk masses derived assuming two different 12CO/13CO
ratios. Column 4: Disk masses derived from the dust continuum that were taken
from Table 2.

Figure 5: Best-fit gas temperatures and their $1\sigma$ uncertainties for the
observed 12CO and 13CO isotopologues at a disk radius of 100 au are shown.
Figure 6: Best-fit column densities and their $1\sigma$ uncertainties for the
observed CO isotopologues at a disk radius of 100 au are shown. The 12CO
column densities can be underestimated due to the optical thickness of the
12CO emission.

Figure 7: Column density ratios of 12CO/13CO (top) and 13CO/C18O (bottom) at a
disk radius of 100 au. The shaded area shows the isotopic ratios measured in
disks or the ISM. The local ISM isotopic ratios are shown by the thick red
line.

###  5.2 Correlations between disk physical and chemical properties

In this subsection, we discuss trends among the various disk physical and
chemical parameters. Given a modest size of our disk sample with $<10$ systems
and a biased selection procedure, the results of such analysis should be taken
with care. We compared the dust continuum fluxes, CO emission radii, CO
temperatures, disk masses derived from dust masses rescaled by an assumed
gas/dust ratio of 100, and stellar masses versus the absolute and normalized
integrated and peak fluxes, CO column densities, ages, etc., and found only a
few potential correlations. For each correlation, we calculated the
corresponding coefficient of determination, which is equal to the Pearson
coefficient $r$ squared, by taking the data uncertainties when necessary.

First, we compare the 1.3 mm continuum and the rescaled disk dust masses in
Fig. 8. As can be clearly seen, despite the fact that dust masses are derived
from continuum emission, there is no strong correlation between these
quantities due to significant uncertainties in the derived dust masses and a
limited disk sample size. A similar absence of a clear correlation was found
between the CO-derived gas masses and the dust continuum, again due to gas
mass uncertainties.

Next, we compare the best-fit CO emission radii with the corresponding
integrated and peak fluxes in Fig. 9. While the optically thick 12CO (2-1)
data show a potential correlation between the peak flux $S_{\nu}$ and the disk
gas radius $R_{\mathrm{CO}}$ (bottom right panel), for the optically thin CO
isotopologues there is a dependence between both the peak and integrated
fluxes, and the disk gas radius. In all these cases, the DL Tau disk with its
very low CO fluxes (wrt its large, $\sim 600$ au CO radius) appears as an
outlier. The same trend is visible for the CO fluxes normalized to the dust
continuum vs $R_{\mathrm{CO}}$. The likely interpretation of this potential
trend is a combination of similar cold temperatures in the outer regions of
our T Tau disk sample, coupled with similar radial CO density profiles off-set
by distinct (but yet not too different) absolute CO column densities.

Interestingly, the correlation between the disk radius $R$ and the disk
luminosity/flux $F$, $R\propto F^{0.5}$, has been observationally inferred for
the dust continuum for many disks in Chamaeleon, Lupus, Ophiuchus, and Taurus,
and for the 12CO emission in the Lupus and Upper Scorpius disks (Manara et al.
2023, and references therein). Such a correlation should in general hold when
1) emission is optically thick and 2) the temperature spread is relatively
narrow. Manara et al. have mentioned several explanations for such
correlation, such as (1) dust grain growth and radial drift in a low viscosity
regime or when slowed by pressure bumps in the disk substructures, or (2) the
presence of optically thick dust substructures. In the recent study by Zagaria
et al. (2023), semi-analytic and detailed DALI thermo-chemical modeling of the
disk CO fluxes have been performed, assuming a viscous accretion model and an
MHD-wind-based accretion model. They have found that indeed the CO fluxes
correlate with the disk radii, which can be constrained from the fluxes even
when the disks are not spatially resolved. They have also found that the disk
models are able to reproduce the CO fluxes observed in the Lupus star-forming
region only when a CO depletion factor of $\sim 40-100$ is introduced in the
model atop of the ISM abundance $x_{\mathrm{CO}}=10^{-4}$, which is
representative of severe CO depletion and photodissociation in the outer disk
regions.

Another quantity that could correlate with the CO isotopologue emission radius
in our sample is the dust-derived disk mass (see Fig. 10). A naive
explanaition for such a trend could be again the radial dust drift and slower
depletion of the mm dust reservoirs in larger disks compared to the compact
ones. Better statistics regarding disk gas properties from larger, $\gtrsim
30-50$ disks’ observational surveys is needed to verify or falsify our
findings.

Figure 8:  Correlation between the thermal dust continuum fluxes at $1.3$ mm
and the disk gas masses derived by rescaling disk dust masses. The size of the
disk symbol reflects the disk size, and the color of the symbol designates the
luminosity of the central star (darker colors correspond to lower
luminosities). The coefficient of determination (corresponding to the Pearson
coefficient $r$ to the power of two) was calculated by taking the data
uncertainties into account and is shown in the top right corner.

Figure 9:  Correlation between the CO gas radii and the integrated (left) and
peak (right) fluxes. The 12CO-, 13CO-, and C18O-based data are shown from
bottom to top. The size of the disk symbol reflects the disk emission size for
the given CO isotopologue, and the color of the symbol designates the
luminosity of the central star (darker colors correspond to lower
luminosities). The coefficients of determination (corresponding to the Pearson
coefficients $r$ to the power of two) were calculated by taking the data
uncertainties into account and are shown in the top right corner of each
subplot. Figure 10:  Same as Fig. 9 but for the correlation between the CO gas
radii and the disk masses.

##  6 Summary and conclusions

We presented the large MPG-IRAM Observatory Program PRODIGE at NOEMA (L19ME;
PIs: P. Caselli and Th. Henning), which is aimed at characterizing the
properties of eight Class II T Tauri disks in Taurus via a 1 mm line survey
(2020-2024). The chosen CI Tau, CY Tau, DG Tau, DL Tau, DM Tau, DN Tau, IQ
Tau, and UZ Tau E systems include both compact and extended disks without
severe substructures. To deal with a large volume of interferometric data in a
coherent manner, we developed the automatic Gildas/Imager pipeline for line
selection, imaging, self-calibration, Kepler deprojection, and the S/N
boosting. For this first paper, the combined 12CO, 13CO, and C18O $J=2-1$ data
taken at the $0.9\arcsec$ and 0.3 km s-1 resolution with the $8-12$ mJy/beam
sensitivity were analyzed and modeled.

We detected the emission of the three main CO isotopologues in all the disks
(though C18O (2-1) was only marginally detected in IQ Tau). The foreground
cloud absorption affects the optically thick 12CO (2-1) emission in CI Tau, CY
Tau, DG Tau, DL Tau, and UZ Tau E, and also in 13CO in DL Tau. We spatially
resolved the CO emission in all of the disks, and inferred their outer gas
radii, ranging from $\sim 200$ to 900 au. The peak line brightness
temperatures are $\sim 7-16$ K for 12CO (2-1), $1-8$ K for 13CO (2-1), and
$0.2-2$ K for C18O (2-1), respectively, indicating that the outer disk gas is
cold and that the 13CO (2-1) and C18O (2-1) lines are mostly optically thin.

We found that the CO (2-1) fluxes may scale with the disk outer radius (except
that of DL Tau). This may suggest that the assumed radial distribution of the
gas is similar in all of our disks, which differ only by the normalization (a
total gas mass). The DL Tau system stands out with a large CO radius but faint
13CO and C18O emission. Homogeneous depletion of CO cannot account for this
discrepancy and its gas radial distribution should differ from those in the
other targeted disks. The UZ Tau E disk shows evidence of non-Keplerian
motions, most likely due to the tidal interactions with its UZ Tau W binary
companion located $\sim 600$ au away.

We fit each line in the Fourier space using the power-law DiskFit model. The
discerned gas temperatures at 100 au are low, $\sim 17-37$ K, and close or
slightly above the CO evaporation temperature. The temperatures of the CO
molecular layers decline radially with a power-law exponent of $\sim 0.5-0.7$.
When strong enough, the 13CO (2-1) emission is indicative of a flatter
temperature profile with an exponent of $\sim 0-0.4$, and it usually has lower
temperatures than the temperatures probed by the 12CO line in the extended
disks, consistent with the vertical temperature gradients. The difference
between the 12CO and 13CO temperatures is not systematic though.

We found that the 12CO, 13CO, and C18O column densities at $r=100$ au are
$\sim 10^{17}-10^{18}$ cm-2, $\sim 10^{15}-10^{16}$ cm-2, and $\lesssim
10^{14}-10^{15}$ cm-2, respectively. The lowest 13CO and C18O column densities
were found in the DL Tau and IQ Tau disks. Most disks have a 13CO column
density exponent $p$ of about $1.5$, with a notable exception for DL Tau,
where it is almost zero. The inferred CO column densities point to CO
depletion in the outer disk regions. In addition, there could be selective
depletion of carbon inside the inner, $\lesssim 150-200$ au, region in the DL
Tau disk, making the overall CO budget of this extended $\sim 600$ au sized
disk much lower than in the other sources. These results support the previous
finding based on ALMA observations that CO can be strongly depleted in the DL
Tau disk by a factor of $\gtrsim 100-200$ (atop of the depletion due to CO
photodissociation and freeze-out).

The best-fit isotopic 12CO/13CO ratios of $\sim 5-80$ and the 13CO/C18O ratios
of $\sim 6-23$ broadly agree within the uncertainties with the previously
discerned isotopic values in disks and the local ISM of $\sim 20-165$ and
$\sim 8-12$, respectively. For CI Tau, CY Tau, DM Tau, and UZ Tau E, the disk
gas masses estimated from the best-fit 13CO radial profiles and the disk gas
radii are $\sim 0.001-0.2\leavevmode\nobreak\ M_{\odot}$ (with large
uncertainties), and they are a factor of two to three higher than the rescaled
dust disk masses.

Finally, we investigated the dependences between various distinct disk and
stellar parameters. Owing to the limited size of our sample, the only clear
trends that we could identify are between the CO emission sizes and the CO
fluxes or disk masses. Similar relations have been found for the 12CO emission
observed in the Lupus and Upper Scorpius disks, as well as for the dust
continuum observations of disks in the Chamaeleon, Lupus, Ophiuchus, and
Taurus star-forming regions.

###### Acknowledgements.

This work is based on observations carried out under project numbers L19ME and
S19AW (for DN Tau and CI Tau) with the IRAM NOEMA Interferometer. IRAM is
supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). D. S., Th. H.,
G. S.-P., R. F, K. S., and S. vT acknowledge support from the European
Research Council under the Horizon 2020 Framework Program via the ERC Advanced
Grant No. 832428-Origins. A. F. acknowledges funding from the European
Research Council via the ERC advanced grant SUL4LIFE (GAP-101096293). A. F.
also thanks the Spanish MICIN for funding from PID2019-106235GB-I00. This work
was partly supported by the Programme National “Physique et Chimie du Milieu
Interstellaire” (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES.
This research made use of NASA’s Astrophysics Data System. Some of the figures
in this paper were made with the matplotlib package (Hunter 2007).

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##  Appendix A Additional information about the disk sample

##### CI Tau:

The CI Tau system consists of a single star surrounded by a $\sim 175$ au dust
disk and a $\sim\leavevmode\nobreak\ 520$ au CO gas disk (Long et al. 2018,
2019; Law et al. 2022). The stellar dynamical mass is $0.9M_{\odot}$, while
other mass estimates derived from the stellar models are $0.8-1.29M_{\odot}$
(Ricci et al. 2010; Simon et al. 2019; Gangi et al. 2022). A hot Jupiter
planet with a 9-day orbital period has been found in this system (Johns-Krull
et al. 2016; Flagg et al. 2019), making it a (pre-)transitional system. The
high-resolution ALMA observations by Clarke et al. (2018); Konishi et al.
(2018); Long et al. (2018); Rosotti et al. (2021) have revealed several
emission rings and gaps in the dust continuum. The dust gaps with widths of
$\sim 9-22$ are located at radii of $\sim 12-14$, $39-48$ and $100-120$ au,
suggesting that there could be up to four planets interacting with the disk.
There is a hint for the presence of a 13CO gap at $\sim 60$ au (Rosotti et al.
2021). The disk mass derived from dust emission varies between $\sim 0.015$
and $0.05$ solar masses (Andrews & Williams 2007; Ricci et al. 2010;
Guilloteau et al. 2016; Ribas et al. 2020).

##### CY Tau:

CY Tau is the lowest mass star in our sample, with a dynamical mass of only
$0.3M_{\odot}$ (Simon et al. 2019). Its mass estimates derived by various
stellar models deviate considerably from the dynamical mass, and are $\sim
0.35-0.5M_{\odot}$ (Ricci et al. 2010; Simon et al. 2019; Pegues et al. 2021).
The single CY Tau star is surrounded by a prominent disk with a dust radius of
$\sim 100$ au and a gas radius of $\sim 200-300$ au (Guilloteau et al. 2014;
Herczeg & Hillenbrand 2014; Guilloteau et al. 2016; Powell et al. 2019). The
disk mass derived from dust emission is $\sim 0.01-0.077M_{\odot}$ (Ricci et
al. 2010; Guilloteau et al. 2011, 2016; Ribas et al. 2020). The disk gas mass
derived from the fitting the dust lane locations and the disk surface density
is $0.06M_{\odot}$ (Powell et al. 2019).

##### DG Tau:

DG Tau is a young, $\sim 0.3-0.5$ Myr Class I/II object, partly enshrouded by
an extended envelope. It shows both thermal and nonthermal radio emission
associated with a bipolar jet, an outflow, and shocks (Guilloteau et al. 2012;
Purser et al. 2018; Garufi et al. 2022). The stellar mass of the targeted DG
Tau star is about $0.8M_{\odot}$ (Banzatti et al. 2019). The DG Tau disk has a
CO gas radius of $\sim 200-300$ au (Guilloteau et al. 2011). The disk mass
estimates vary wildly, $\sim 0.03-0.4M_{\odot}$ (Isella et al. 2009;
Guilloteau et al. 2011; Ribas et al. 2020).

##### DL Tau:

DL Tau is the most massive star in our sample, with a dynamical mass
$M_{*}\approx 1\,M_{\odot}$ (non-dynamical mass estimates vary between 0.8 and
$1.1M_{\odot}$), see Ricci et al. (2010); Long et al. (2018); Simon et al.
(2019); Gangi et al. (2022). The DL Tau system has a dust disk with a radius
of $\sim 150$ au and a gas disk with a radius of $\leavevmode\nobreak\ \sim
500$ au (Long et al. 2018, 2022). The $0.1\arcsec$ ALMA observations by Long
et al. (2018) and Long et al. (2020) have revealed three dust gaps with widths
of $\sim 7-26$ au, located at $\sim 40$, $67$, and $89$ au (Long et al. 2018).
Fainter substructures at $\gtrsim 150$ au have been found in the dust emission
(Jennings et al. 2022). The derived disk mass from dust observations is $\sim
0.01-0.1M_{\odot}$ (Andrews & Williams 2007; Ricci et al. 2010; Guilloteau et
al. 2011). The age of this system is poorly estimated. While Ricci et al.
(2010) have derived an age of $\sim 2.2$ Myr, which is in agreement with other
estimates, McClure (2019) has estimated that the DL Tau system could be much
older, $\sim 7.8$ Myr.

##### DM Tau:

The well-studied DM Tau system is a single star with a dynamical mass of
$0.55M_{\odot}$ surrounded by a large $\sim 200$ au dust and a $\sim 600-800$
au gas disk (Guilloteau et al. 2011; Simon et al. 2019; Long et al. 2020). The
age of DM Tau is $\sim 1-5$ Myr (Guilloteau et al. 2011). The DM Tau disk
shows two prominent gaps in dust emission at $\sim 3$ and $21$ au, with more
shallow gaps at $\sim 70$, $83$ and $\sim 112$ au (Kudo et al. 2018; Hashimoto
et al. 2021; Francis et al. 2022). The DM Tau disk is turbulent, with
discerned $\alpha\sim 10^{-2}-8\times 10^{-2}$ (Guilloteau et al. 2012;
Flaherty et al. 2020; Francis et al. 2022). The disk gas mass derived from the
modeling HD (1-0) emission is $\sim 0.004-0.045M_{\odot}$, depending on the
assumed disk thermal structure (McClure et al. 2016; Trapman et al. 2017).

##### DN Tau:

DN Tau has a dynamical mass of $0.87M_{\odot}$ and is surrounded by a disk
with a $\sim 100$ au dust and a $\sim 240$ au gas radius (Ricci et al. 2010;
Long et al. 2018; Simon et al. 2019). The dust emission shows the presence of
a $\sim 23$ au wide gap at $\sim 60$ au (Long et al. 2018). The disk mass
derived from dust continuum data is $\sim 0.01-0.04M_{\odot}$ (Guilloteau et
al. 2016; Ribas et al. 2020).

##### IQ Tau:

IQ Tau has a dynamical mass of $0.74M_{\odot}$ and is surrounded by a disk
with a $\sim 100$ au dust and a $\sim 220$ au gas radius (Ricci et al. 2010;
Long et al. 2018; Simon et al. 2019). The non-dynamical mass estimates span a
broad range, $0.4-0.7M_{\odot}$. The IQ Tau disk shows the presence of a $\sim
7$ au dust continuum gap at $\sim 40$ au (Long et al. 2018). The disk mass
derived from dust continuum data is $\sim 0.007-0.02M_{\odot}$ (Ricci et al.
2010; Guilloteau et al. 2016; Ribas et al. 2020).

##### UZ Tau E:

UZ Tau E is a spectroscopic binary EXOr system with a separation of $\sim
0.03$ au, which is gravitationally linked with another close binary UZ Tau W
system at a $3.6\arcsec$ separation (Hales et al. 2020; Long et al. 2022). The
combined mass of the UZ Tau E is $1.2M_{\odot}$. The UZ Tau E is surrounded by
a disk with a $\sim 80$ au dust and a $\sim 200-300$ au gas radius (Ricci et
al. 2010; Long et al. 2022). It has a small inner cavity with a radius of
$\lesssim 10$ au and a shallow, $\leavevmode\nobreak\ \sim 7$ au gap at the
radius of $\sim 70$ au (Long et al. 2018; Jennings et al. 2022). The dust disk
mass is estimated to be $\sim 1-2.2\times 10^{-4}M_{\odot}$, while the gas
mass derived from the fitting optically thin CO data is $\sim 3.2\times
10^{-3}M_{\odot}$ (Ricci et al. 2010; Guilloteau et al. 2016; Long et al.
2018; Hales et al. 2020). The high, $\sim 0.03-0.07$ dust/gas ratio in the UZ
Tau E disk is similar to the values found in other EXors as well as Lupus
disks (Hales et al. 2020).

##  Appendix B Spectral setup 1 (2019-2020)

Figure 11:  First NOEMA/PolyFiX setup with an LO frequency of $\approx 224.9$
GHz that has been observed during 2020. The following key disk molecular
species have been targeted at the native 62.5 kHz ($\sim 0.1$ km s-1) spectral
resolution: 12CO, 13CO, C18O, p-H2CO, DCO+, DCN, DNC, c-C3H2, HC3N, N2D+, etc.
Table 7: Spectroscopic line parameters for the PolyFiX setup 1 observations
(2019-2020).

Frequency | Molecule | Transition | $E_{u}$ | $S_{ij}\mu^{2}$ | Catalog
---|---|---|---|---|---
(GHz) |  |  | (K) | (D2) |
213.360650 | HCS+ | 5-4 | 30.72 | 19.2 | CDMS
214.357039 | SO $3\Sigma$ $\nu=0$ | 7(8)-7(7) | 81.24 | 0.44 | CDMS
214.573873 |  13C17O | J=2-1, F=5/2-5/2 | 15.45 | 0.05 | CDMS
214.778436 | H2C18O | 3(1,2)-2(1,1) | 32.48 | 43.50 | SLAIM
215.220653 | SO $3\Sigma$ $\nu=0$ | 5(5)-4(4) | 44.10 | 11.31 | CDMS
216.112582 | DCO+ | 3-2 | 20.74 | 142.00 | CDMS
216.278756 | c-HCCCH | 3(3,0)-2(2,1) | 19.47 | 45.62 | CDMS
216.372830 | C2D ∗ | N=3-2, J=7/2-5/2, F=9/2-7/2 | 20.77 | 2.53 | CDMS
216.373320 | C2D ∗ | N=3-2, J=7/2-5/2, F=5/2-3/2 | 20.77 | 1.87 | CDMS
216.568651 | H2CO | 9(1,8)-9(1,9) | 174.00 | 3.48 | JPL
216.710436 | H2S | 2(2,0)-2(1,1) | 84.00 | 2.06 | CDMS
217.104938 | SiO | 5-4 | 31.25 | 47.99 | CDMS
217.238400 | DCN | J=3-2, F=2-1 | 20.85 | 18.11 | JPL
217.238631 | DCN | J=3-2, F=2-2 | 20.85 | 38.81 | JPL
217.443722 |  13CN ∗ | N=2-1, J=5/2-3/2, F1= 2-1, F=1-1 | 15.68 | 1.09 | CDMS
217.822148 | c-HCCCH | 6(1,6)-5(0,5) | 38.61 | 64.13 | JPL
218.222188 | H2CO | 3(0,3)-2(0,2) | 20.97 | 16.31 | CDMS
218.324723 | HC3N | 24-23 | 130.98 | 334.19 | CDMS
218.475641 | H2CO | 3(2,2)-2(2,1) | 68.09 | 9.06 | CDMS
218.732732 | c-HCCCH | 7(1,6)-7(0,7) | 61.17 | 33.00 | CDMS
218.760066 | H2CO | 3(2,1)-2(2,0) | 68.11 | 9.06 | CDMS
218.903357 | OCS | 18-17 | 99.81 | 9.21 | CDMS
219.560328 | C18O | 2-1 | 15.81 | 0.02 | CDMS
219.908525 | H${}_{2}^{13}$CO | 3(1,2)-2(1,1) | 32.94 | 43.50 | JPL
219.949442 | SO $3\Sigma$ $\nu=0$ | 6(5)-5(4) | 34.98 | 14.01 | CDMS
220.398688 |  13CO | 2-1 | 15.87 | 0.02 | CDMS
220.709016 | CH3CN $\nu=0$ | 12(3)-11(3) | 133.16 | 476.93 | JPL
220.730261 | CH3CN $\nu=0$ | 12(2)-11(2) | 97.44 | 247.32 | JPL
220.743011 | CH3CN $\nu=0$ | 12(1)-11(1) | 76.01 | 252.57 | JPL
220.747261 | CH3CN $\nu=0$ | 12(0)-11(0) | 68.87 | 254.41 | JPL
228.910489 | DNC | 3-2 | 21.97 | 27.90 | CDMS
229.347630 | SO2 $\nu=0$ | 11(5,7)-12(4,8) | 122.01 | 3.13 | CDMS
230.537984 |  12CO | 2-1 | 16.57 | 0.02 | CDMS
230.778011 | l-H2CCC | 11(1,10)-10(1,9) | 79.81 | 550.09 | CDMS
231.060983 | OCS | 19-18 | 110.90 | 9.72 | CDMS
231.220766 |  13CS | 5-4 | 33.29 | 20.91 | CDMS
231.321828 | N2D+ ∗ | 3-2 | 22.20 | 191.48 | CDMS
231.410259 | D2CO | 4(0,4)-3(0,3) | – | – | Lovas
235.789641 | CO+ | 2-1 | – | – | Lovas
236.452293 | SO $3\Sigma$ $\nu=0$ | 1(2)-2(1) | 15.81 | 0.03 | CDMS
236.512844 | HC3N | 26-25 | 153.25 | 362.07 | CDMS

121212An asterisk denotes the lines with hyper-fine components. Column 4:
Upper state energies. Column 5: Line strengths. Column 6: The line catalogs
from which the line data are taken, based on the online v3 of Splatalogue
http://www.cv.nrao.edu/php/splat/.

Source | date | Calibrators | # antennas and | on-source telescope
---|---|---|---|---
|  | Bandpass | Phase | Flux | configuration | time1 (h)
CI Tau | 07-apr-2020 | 3c84 | J0438+300 0507+179 | LkHa101 MWC349 | 10 C | 2.6
| 13-jan-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 4.1
CY Tau | 28-feb-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 2.2
| 28-mar-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 4.5
DG Tau | 26-mar-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 2.2
| 06-apr-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 4.8
DL Tau | 31-mar-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 1.9
| 08-apr-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 4.0
DM Tau | 07-apr-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 3.8
| 09-apr-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 6.8
DN Tau | 09-jan-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 3.0
| 11-jan-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 2.2
| 02-apr-2020 | 3c84 | J0438+300 0507+179 | LkHa101 | 10 C | 2.0
IQ Tau | 22-nov-2020 | 3c84 | J0438+300 0507+179 | LkHa101 2010+723 | 10 C | 5.6
UZ Tau E | 29-nov-2020 | 3c84 | J0438+300 0507+179 | LkHa101 2010+723 | 10 C | 3.8
| 30-nov-2020 | 3C454.3 | J0438+300 0507+179 | MWC349 2010+723 | 10 C | 1.5

1 \- from number of scan on source, not from uvt table after QA

Table 8: Summary of the observations.

##  Appendix C Channel maps, moment $0$-th maps, and Kepler plots

Figure 12: Observed 12CO (2-1) emission in the CI Tau disk. Shown are the
channel map of the observed line brightness distribution (top left), the
moment-zero map (top right), and the integrated spectrum (top middle). The
channel map shows 16 velocity channels with a step of $0.5$ km s-1 in the
[-4.5, +4.5] km s-1 range around the systemic velocity. The contour lines
start at $2$ K, with a step of $2$ K. The color bar shows line brightness
temperatures (K). The contour lines in the moment-zero plot start at 3, 6, and
$9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms noise (mJy km
s-1) is shown in the upper left corner of the moment-zero plot, and the
synthesized beam is depicted by the dark ellipse in the left bottom corner.
The 12CO (2-1) spectrum shows a nearly absent blueshifted velocity component
due to the cloud absorption. Figure 13: Observations of 12CO (2-1) emission in
the CI Tau disk. Shown is a pixel-deprojected Keplerian plot consisting of the
three panels: (left) the radial profile of the line brightness temperature
(K), (top) the integrated spectrum (black line) overlaid with the best-fit
Gaussian profile (red line), and (bottom right) aligned and stacked line
intensity (K) as a function of disk radius (Y-axis; au) and velocity (X-axis;
km s-1). The color bar units are in Kelvin. The zigzag behavior of the
$T_{\mathrm{B}}(r)$ curve at $\sim 200-500$ au is caused by the foreground
cloud absorption. Figure 14: Same as Fig. 12 but for 13CO (2-1) emission.
Figure 15: Same as Fig. 13 but for 13CO (2-1) emission. Figure 16: Same as
Fig. 12 but for C18O (2-1) emission. Figure 17: Same as Fig. 13 but for C18O
(2-1) emission.

/variables/disk = CY_Tau /variables/name = CY Tau /variables/mol = CO
/variables/line = 12CO (2-1)

Figure 18: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner. Figure 19: Observations of /variables/line emission in the
/variables/name disk. Shown is a pixel-deprojected Keplerian plot consisting
of the three panels: (left) the radial profile of the line brightness
temperature (K), with observations and errorbars in black, and profile derived
from the best-fit disk model in red, (top) the integrated spectrum (black
line) overlaid with the best-fit Gaussian profile (red line), and (bottom
right) aligned and stacked line intensity (K) as a function of disk radius
(Y-axis; au) and velocity (X-axis; km s-1). The color bar units are in Kelvin.

/variables/mol = 13CO /variables/line = 13CO (2-1)

Figure 20: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner. Figure 21: Observations of /variables/line emission in the
/variables/name disk. Shown is a pixel-deprojected Keplerian plot consisting
of the three panels: (left) the radial profile of the line brightness
temperature (K), with observations and errorbars in black, and profile derived
from the best-fit disk model in red, (top) the integrated spectrum (black
line) overlaid with the best-fit Gaussian profile (red line), and (bottom
right) aligned and stacked line intensity (K) as a function of disk radius
(Y-axis; au) and velocity (X-axis; km s-1). The color bar units are in Kelvin.

/variables/mol = C18O /variables/line = C18O (2-1)

Figure 22: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner. Figure 23: Observations of /variables/line emission in the
/variables/name disk. Shown is a pixel-deprojected Keplerian plot consisting
of the three panels: (left) the radial profile of the line brightness
temperature (K), with observations and errorbars in black, and profile derived
from the best-fit disk model in red, (top) the integrated spectrum (black
line) overlaid with the best-fit Gaussian profile (red line), and (bottom
right) aligned and stacked line intensity (K) as a function of disk radius
(Y-axis; au) and velocity (X-axis; km s-1). The color bar units are in Kelvin.

/variables/disk = DG_Tau /variables/name = DG Tau /variables/mol = CO
/variables/line = 12CO (2-1)

Figure 24: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner.

/variables/mol = 13CO /variables/line = 13CO (2-1)

Figure 25: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner.

/variables/mol = C18O /variables/line = C18O (2-1)

Figure 26: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner.

/variables/disk = DL_Tau /variables/name = DL Tau /variables/mol = CO
/variables/line = 12CO (2-1)

Figure 27: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner. Figure 28: Observations of /variables/line emission in the
/variables/name disk. Shown is a pixel-deprojected Keplerian plot consisting
of the three panels: (left) the radial profile of the line brightness
temperature (K), with observations and errorbars in black, and profile derived
from the best-fit disk model in red, (top) the integrated spectrum (black
line) overlaid with the best-fit Gaussian profile (red line), and (bottom
right) aligned and stacked line intensity (K) as a function of disk radius
(Y-axis; au) and velocity (X-axis; km s-1). The color bar units are in Kelvin.

/variables/mol = 13CO /variables/line = 13CO (2-1)

Figure 29: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner. Figure 30: Observations of /variables/line emission in the
/variables/name disk. Shown is a pixel-deprojected Keplerian plot consisting
of the three panels: (left) the radial profile of the line brightness
temperature (K), with observations and errorbars in black, and profile derived
from the best-fit disk model in red, (top) the integrated spectrum (black
line) overlaid with the best-fit Gaussian profile (red line), and (bottom
right) aligned and stacked line intensity (K) as a function of disk radius
(Y-axis; au) and velocity (X-axis; km s-1). The color bar units are in Kelvin.

/variables/mol = C18O /variables/line = C18O (2-1)

Figure 31: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner. Figure 32: Observations of /variables/line emission in the
/variables/name disk. Shown is a pixel-deprojected Keplerian plot consisting
of the three panels: (left) the radial profile of the line brightness
temperature (K), with observations and errorbars in black, and profile derived
from the best-fit disk model in red, (top) the integrated spectrum (black
line) overlaid with the best-fit Gaussian profile (red line), and (bottom
right) aligned and stacked line intensity (K) as a function of disk radius
(Y-axis; au) and velocity (X-axis; km s-1). The color bar units are in Kelvin.

/variables/disk = DM_Tau /variables/name = DM Tau

/variables/mol = 13CO /variables/line = 13CO (2-1)

Figure 33: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,
and the synthesized beam is depicted by the dark ellipse in the left bottom
corner. Figure 34: Observations of /variables/line emission in the
/variables/name disk. Shown is a pixel-deprojected Keplerian plot consisting
of the three panels: (left) the radial profile of the line brightness
temperature (K), with observations and errorbars in black, and profile derived
from the best-fit disk model in red, (top) the integrated spectrum (black
line) overlaid with the best-fit Gaussian profile (red line), and (bottom
right) aligned and stacked line intensity (K) as a function of disk radius
(Y-axis; au) and velocity (X-axis; km s-1). The color bar units are in Kelvin.

/variables/mol = C18O /variables/line = C18O (2-1)

Figure 35: Observations of /variables/line emission in the /variables/name
disk. Shown are the channel map of the observed line brightness distribution
(left), the moment-zero map (top right), and the integrated spectrum (bottom
right). The channel map shows 16 velocity channels with a step of $0.5$ km s-1
in the [-4.5, +4.5] km s-1 range around the systemic velocity. The contour
lines start at $2$ K, with a step of $2$ K. The color bar shows line
brightness temperatures (K). The contour lines in the moment-zero plot start
at 3, 6, and $9\sigma$, with a step of $6\sigma$ afterward. The $1\sigma$ rms
noise (mJy km s-1) is shown in the upper left corner of the moment-zero plot,