11institutetext:  INAF-Osservatorio Astronomico di Capodimonte, via Moiariello
16, 80131 Napoli, Italy 22institutetext: INAF-Osservatorio Astronomico di
Roma, Via di Frascati 33, 00078 Monte Porzio Catone, Italy 33institutetext:
INAF-Osservatorio Astrofisico di Catania, via S. Sofia 78, 95123 Catania,
Italy 44institutetext: INAF-Osservatorio Astronomico di Padova – Via
dell’Osservatorio 8, 36012, Asiago (VI), Italy 55institutetext: Fundación
Galileo Galilei – INAF – Telescopio Nazionale Galileo, 38700, Breña Baja,
Santa Cruz de Tenerife, Spain 66institutetext: European Southern Observatory,
Karl Schwarzschild Str. 2, 85748 Garching, Germany

# GIARPS High-resolution Observations of T Tauri stars (GHOsT). III. A pilot
study of stellar and accretion properties ††thanks:  Based on observations
made with the GIARPS instrument at the Telescopio Nazionale Galileo under
program A36TAC_22 (PI: Antoniucci).

J.M. Alcalá 11 M. Gangi 22 K. Biazzo 22 S. Antoniucci 22 A. Frasca 33 T.
Giannini 22 U. Munari 44 B. Nisini 22 A. Harutyunyan 55 C. F. Manara 66 F.
Vitali 22<EMAIL_ADDRESS>
(Received ; accepted )

The mass-accretion rate, $\dot{M}_{\rm acc}$, is a crucial parameter for the
study of the evolution of accretion disks around young low-mass stellar
objects (YSOs) and for planet formation studies. The Taurus star forming
region (SFR) is rich in pre-main sequence (PMS) stars, most of them of the T
Tauri class. A variety of methodologies have been used in the past to measure
mass accretion in samples of YSOs in Taurus, but despite being a general
benchmark for star formation studies, a comprehensive and systematic analysis
of the Taurus T Tauri population, where the stellar and accretion properties
are derived homogeneously and simultaneously, is still missing. As part of the
GIARPS High-resolution Observations of T Tauri stars (GHOsT) project, here we
present a pilot study of the stellar and accretion properties of seven YSOs in
Taurus using the spectrograph GIARPS at the Telescopio Nazionale Galileo
(TNG). Contemporaneous low-resolution spectroscopic and photometric ancillary
observations allow us to perform an accurate flux calibration of the high-
resolution spectra. The simultaneity of the high-resolution, wide-band
spectroscopic observations, from the optical to the near-infrared (NIR), the
veiling measurements in such wide spectral range, and many well-calibrated
emission line diagnostics allows us to derive the stellar and accretion
properties of the seven YSOs in a homogeneous and self-consistent way. The
procedures and methodologies presented here will be adopted in future works
for the analysis of the complete GHOsT data set. We discuss the accretion
properties of the seven YSOs in comparison with the 90% complete sample of
YSOs in the Lupus SFR and investigate possibilities for the origin of the
continuum excess emission in the NIR.

###### Key Words.:

Stars: pre-main sequence, low-mass – Accretion, accretion disks –
protoplanetary disks – stars: variables: T Tauri – individual objects: RY Tau,
DG Tau, DL Tau, HN Tau A, DO Tau, RW Aur A, CQ Tau

††offprints: J.M. Alcalá

##  1 Introduction

The way in which circumstellar disks evolve and form proto-planets is deeply
influenced by the processes of mass accretion onto the star, ejection of
outflows, and photo-evaporation of disk material through winds (Hartmann,
Herczeg & Calvet 2016; Ercolano & Pascucci 2017, and references therein). In
order to understand planet formation it is necessary to explain how optically
thick accretion disks surrounding the youngest low-mass
($M_{\star}$$\lesssim$2.0$M_{\odot}$) stars evolve into optically thin debris
disks (Morbidelli & Raymond 2016). In this framework, the mass accretion rate,
$\dot{M}_{\rm acc}$, is a fundamental parameter for the evolution of accretion
disks around young low-mass stellar objects (YSOs). $\dot{M}_{\rm acc}$
measurements set important constraints for disk evolution models (Hartmann et
al. 1998; Hartmann, Herczeg & Calvet 2016) and disk clearing mechanisms
(Alexander et al. 2014; Ercolano & Pascucci 2017, and references therein).

In the current magnetospheric accretion paradigm for classical T Tauri (CTT)
stars , the strong stellar magnetic fields truncate the inner disk at a few
stellar radii (Donati & Landstreet 2009; Johns-Krull et al. 2013). Gas flows
from this truncation radius onto the star along the stellar magnetic field
lines, crashing onto the star and forming an accretion shock. The $\sim$104 K
optically thick post-shock gas and optically thin pre-shock gas produce
emission in the Balmer and Paschen continua and in many lines, including the
Balmer and Paschen series and the Ca II IR triplet (Hartmann et al. 1998;
Hartmann, Herczeg & Calvet 2016) observed in the optical spectra of CTTs.

The mass accretion rate can be derived from the energy released in the
accretion shock (accretion luminosity $L_{\rm acc}$; see Gullbring et al.
1998; Hartmann 1998) given the stellar properties. Observationally, this
requires measurements of excess flux in continuum and lines with respect to
similar nonaccreting template stars. Such measurements are best performed at
ultraviolet (UV) wavelengths ($\lambda$ $\lesssim$ 4000 Å) with the Balmer
continuum excess emission and the Balmer jump (see Herczeg & Hillenbrand 2008;
Ingleby et al. 2013; Alcalá et al. 2014, 2017; Manara et al. 2017a, and
references therein). In the past, $L_{\rm acc}$ has been calculated using
veiling measurements in high-resolution optical spectra (e.g., Hartigan et al.
1991; Hartigan & Kenyon 2003; White & Hillenbrand 2004, and references
therein). Also, it is well known that $L_{\rm acc}$, and therefore
$\dot{M}_{\rm acc}$, is correlated with the line luminosity, $L_{\rm line}$,
of ${H\textsc{i}}$, ${He\textsc{i,}}$ and ${Ca\textsc{ii}}$ lines (e.g.,
Muzerolle et al. 1998; Calvet et al. 2004; Herczeg & Hillenbrand 2008;
Rigliaco et al. 2012; Alcalá et al. 2014, 2017, and references therein). These
latter works provide $L_{\rm acc}$–$L_{\rm line}$ correlations simultaneously
and homogeneously derived from the UV to the near-infrared (NIR), underlying
the importance of these emission features as accretion diagnostics. These
accretion tracers are key diagnostics with which to estimate $L_{\rm acc}$via
the correlations mentioned above when flux-calibrated spectra below
$\lambda$$\sim$3700 Å are missing.

On the other hand, accretion is a highly variable process (Basri & Batalha
1990; Jayawardhana et al. 2006; Cody & Hillenbrand 2010; Venuti et al. 2014),
which leads to a range of $\dot{M}_{\rm acc}$ values for a given object when
measured at different epochs (see Costigan et al. 2012, 2014; Biazzo et al.
2012). Variability in YSOs induces dispersion in the observed $\dot{M}_{\rm
acc}$–$M_{\star}$ and $\dot{M}_{\rm acc}$–$M_{\rm disk}$ scaling
relationships, but cannot explain the large scatter of more than 2 dex in
$\log{}$$\dot{M}_{\rm acc}$ at a given YSO mass. Such scaling relationships
are predicted by the theory of viscous disk evolution (Lynden-Bell & Pringle
1974; Hartmann, Herczeg & Calvet 2016; Rosotti et al. 2017, and references
therein), but the $\dot{M}_{\rm acc}$–$M_{\rm disk}$ relationship has been
confirmed observationally only recently by spectroscopic surveys in strong
synergy with ALMA surveys of disks in star forming regions (Ansdell et al.
2016; Manara et al. 2016; Pascucci et al. 2016; Mulders et al. 2017).

As concluded in previous works (e.g., Rigliaco et al. 2012; Alcalá et al.
2014), the average $L_{\rm acc}$ and $\dot{M}_{\rm acc}$ derived from several
diagnostics, measured simultaneously, has a significantly reduced error. This
suggests the need to use spectroscopic observations simultaneously performed
from visible to NIR wavelengths and with the highest possible resolution to
overcome problems due to line blending. These requirements can be achieved
with the GIARPS (GIAno and haRPS, Claudi et al. 2017) high-resolution
spectrograph at the Telescopio Nazionale Galileo (TNG) in the Canary Islands,
Spain. The spectral coverage and resolution of GIARPS allows one to probe the
properties of the accretion columns, hot spots, the inner gaseous disk, the
stellar and disk winds, and the collimated jets (see Gangi et al. 2020;
Giannini et al. 2019), making TNG/GIARPS a powerful instrument with which to
investigate accretion in YSOs of the northern hemisphere, such as the Taurus-
Auriga star forming region (SFR).

The Taurus SFR contains a rich population of pre-main sequence (PMS) stars,
most of them T Tauri stars (see Kenyon et al. 2008, and references therein).
Several works have addressed the problem of measuring $\dot{M}_{\rm acc}$ in
the Taurus population using the different methodologies mentioned above (see
Herczeg & Hillenbrand 2008, 2014, and references therein). Also, a large
number of CTTs have already been observed with ALMA (Andrews et al. 2018; Long
et al. 2019), probing the outer regions of their disk, and allowing the
scaling relationships predicted by the viscous disk evolution theory to be
investigated further. However, despite being a general benchmark for star
formation studies, a comprehensive and systematic analysis of the Taurus
population, where the relevant stellar and accretion parameters are derived
simultaneously with sufficient accuracy, is still missing. As a first step in
filling this gap, here we present a pilot study of the accretion of seven YSOs
in Taurus observed with TNG/GIARPS as part of the GHOsT (GIARPS High-
resolution Observations of T Tauri stars) project. GHOsT is a survey of a
flux-limited complete sample of T Tauri stars in the Taurus star forming
region that is to be used to derive, in a homogeneous fashion (thus avoiding
systematic errors due to the use of different sets of nonsimultaneous
observations), the stellar, accretion, and outflow parameters, and to
constrain the properties of both the inner disk and the associated winds and
jets. The ultimate goal of GHOsT is to provide reliable measures of the mass-
accretion and mass-loss rates of the Taurus population and to put them in
relation with the properties of the central star and its disk, in synergy with
the complementary ALMA observations (Andrews et al. 2018; Long et al. 2019).

A comprehensive study of the jet line emission of the targets investigated in
this paper was published by Giannini et al. (2019, henceforth Paper I) and an
investigation of the link between atomic and molecular winds was published in
Gangi et al. (2020, henceforth Paper II), while the results of the complete
GHOsT survey will be presented in forthcoming papers. One of the main goals of
the present paper is the definition and assessment of the methodologies for
the determination of the stellar and accretion properties, in a homogeneous
and self-consistent way, to be adopted for the analysis of the complete set of
GHOsT data.

The paper is organized as follows. In Sect. 2 we present the target selection,
the observations, and the data processing. In Section 3 we show the procedures
used for the determination of the stellar parameters, and veiling estimates
both in the optical and in the NIR. In Sect. 4 the methodologies to derive the
accretion parameters are presented, while in Sect. 5 we discuss results on the
stellar and accretion properties of the studied sample, comparing with those
of the 90% complete sample of Lupus YSOs. The results of the veiling
measurements are also reported and discussed in the same section. Conclusions
are outlined in Sect. 6.

##  2 Target selection, observations, and data processing

The targets, observations, and data reduction are extensively described in
Paper I and Paper II, and are briefly summarized in this section.

###  2.1 The targets

For the pilot study, we selected six well-known CTTs in Taurus-Auriga with
clear signatures of accretion. The sources are listed in Table 1 together with
relevant properties from the literature (see also Paper I). Noteworthy is the
range of values for both the stellar physical parameters and mass accretion
rate, which is likely due to variability, but also to the distinct
methodologies used to derive them in previous works. The extreme CTT RW Aur A
(Alencar et al. 2005) was included in the sample as a case of highly veiled
object spectrum (Herczeg & Hillenbrand 2014) to test the limits of our
procedures. In addition, we also study the well-known intermediate-mass CTT CQ
Tau. This object was recently investigated in detail with ALMA (Ubeira
Gabellini et al. 2019) and has a low level of accretion (e.g., Mendigutía et
al. 2011); therefore, it has been included to test the ability of our methods
to trace very low accretion rates. However, this object displays a remarkable
UX Ori-type variability (Shakhovskoj et al. 2005), which complicates the
analysis of the data (Dodin & Suslina 2021). Several of the selected CTTs have
been included in the recent ALMA survey by Long et al. (2019). Hereafter, we
use the terms CTT and YSO interchangeably to refer to the objects in our
sample.

Table 1:  Selected CTTs for this study with their physical and accretion
properties from the literature.

Source | SpT | $T_{\rm eff}$ | $A_{\rm V}$ | $L_{\star}$ | $R_{\star}$ | $M_{\star}$ | Ref. |  $\log$$\dot{M}_{\rm acc}$ | Method for $\dot{M}_{\rm acc}$ | Ref. | d
---|---|---|---|---|---|---|---|---|---|---|---
|  | (K) | (mag) | ($L_{\odot}$) | ($R_{\odot}$) | ($M_{\odot}$) |  | ($M_{\odot}$ / yr) | determination | $\dot{M}_{\rm acc}$ | (pc)
RY Tau | G1 | 5945 | 2.20 | 9.60 | 2.9 | 2.00 | 1 |  $-$7.04/$-$7.19 | UV-excess | 1 | 138
|  | 5750 | 0.6-1.7 | 6.30 |  | 1.90 | 2 |  $-$7.30 |  | 15 |
| F7 | 6220 | 1.95 | 12.30 |  | 2.04 | 6 |  |  |  |
|  | 5920 | 2.35 |  |  |  | 18 |  $-$7.21 | H$\alpha$, He i6678 | 18 |
| K1 | 5080 |  | 7.60 | 2.92 | 2.00 | 19 |  $-$7.11 | H$\alpha$ | 19 |
DG Tau | K7.0 |  | 1.60 | 0.51 |  | 0.76 | 3 |  $-$8.20 | H$\alpha$ | 3 | 125
| K6 |  |  |  |  |  | 17 |  $-$7.00 | Br$\gamma$ | 4 |
|  |  |  |  |  |  |  |  $-$6.30 | UV-excess | 5 |
|  | 4350 | 2.20 |  |  |  | 18 |  $-$7.30 | H$\alpha$, He i6678 | 18 |
| M0 | 3890 |  | 1.70 | 2.87 | 0.30 | 19 |  $-$6.39 | H$\alpha$ | 19 |
| K3 | 4775 |  | 3.62 | 2.80 | 2.20 | 20 |  $-$6.13 | Excess emiss. | 21 |
DL Tau | K5.5 | 4277 | 1.80 | 0.65 |  | 0.98 | 6 |  $-$8.6 | H$\alpha$ | 3 | 160
| K5.5 |  | 1.80 | 0.50 |  | 0.92 | 3 |  $-$6.3 | UV-excess | 5 |
|  |  |  |  |  | 0.75 | 16 |  |  |  |
HN Tau A | K3 |  | 1.15 | 0.17 |  | 0.70 | 3 |  $-$8.69 | H$\alpha$ | 3 | 134
| K3 | 4730 | 1.15 | 0.16 |  | 1.53 | 6 |  $-$8.89 | UV-excess | 7 |
| K5 |  | 0.65 | 0.19 | 0.76 | 0.81 | 7 |  $-$8.37 | Several line lum. | 8 |
|  |  |  |  |  | 0.78 | 16 |  |  |  |
DO Tau | M0 |  | 2.27 | 1.01 | 2.25 | 0.37 | 7 |  $-$6.84 | UV-excess | 7 | 139
| M0.3 | 3806 | 0.75 | 0.23 |  | 0.59 | 6 |  $-$8.21 | H$\alpha$ | 3 |
|  |  |  |  |  | 0.56 | 16 |  |  |  |
RW Aur A | K3 |  | 0.5 | 0.50 | 1.10 | 0.90 | 9 |  $-$7.70 | UV-excess | 9 | 183
| K0-K3 | 5082 | 0.4 | 1.70 |  | 1.34 | 10 |  $-$7.50 | UV-excess | 10 |
| K0 | 5250 | 0.0 | 0.99 |  | 1.20 | 6 |  $-$7.39 | Several line lum. | 11 |
| K2 | 4955 |  | 1.70 | 1.70 | 1.34 | 20 |  $-$7.51 | Excess emiss. | 21 |
CQ Tau | F2 |  | 1.90 | 10.0 |  | 1.67 | 12 |  $<-$8.3 | UV-excess | 13 | 149
|  |  |  |  |  |  |  |  $-$7.0 | Br$\gamma$ | 14 |
| F3 | 6900 | 1.40 | 3.4 |  |  | 22 |  |  |  |

111
– Parameters of Long et al. are revisited values of Herczeg & Hillenbrand
(2014).
– $A_{\rm V}$, SpT, $L_{\star}$ in Simon et al. (2016) are those in Herczeg &
Hillenbrand (2014).
– Distances in the last column are from Gaia EDR3 (Gaia Collaboration et al.
2016a, 2020b).

References:
(1) Calvet et al. (2004); (2) Garufi et al. (2019); (3) Simon et al. (2016);
(4) Agra-Amboage et al. (2011); (5) Gullbring et al. (2000); (6) Long et al.
(2019); (7) Gullbring et al. (1998); (8) Fang et al. (2018); (9) Ingleby et
al. (2013); (10) White & Genz (2011); (11) Facchini et al. (2016); (12) Ubeira
Gabellini et al. (2019); (13) Mendigutía et al. (2011); (14) Donehew &
Brittain (2011); (15) Skinner et al. (2018);(16) Rigliaco et al. (2015); (17)
Hessman & Guenther (1997); (18) Frasca et al. (2018); (19) Isella et al.
(2009, and references therein); (20) Akeson et al. (2005, and references
therein); (21) White & Hillenbrand (2004); (22) Meeus et al. (2012).

###  2.2 Observations and data reduction

The GIARPS observing mode combines the HARPS-N (Pepe et al. 2002; Cosentino et
al. 2012) and GIANO-B (Oliva et al. 2012; Origlia 2014) high-resolution
(resolving power of 115,000 and 50,000, respectively) spectrographs,
simultaneously covering a wide spectral range of 390–690 nm for HARPS-N, and
940–2420 nm for GIANO-B. In order to perform a flux calibration as accurately
as possible, avoiding additional uncertainties due to variability, the GHOsT
survey is complemented with simultaneous/contemporaneous (within less than two
days of the GIARPS observations) low-resolution spectroscopy in the optical,
as well as with optical and NIR photometry (see Paper I).

The TNG/GIARPS observations were performed in 2017 during two nights, one on
October 29 and the other on November 13. The journal of the GIARPS
observations is reported in Paper I. The reduction steps of the GIARPS spectra
are thoroughly described in Paper I and Paper II, but a summary is provided
here.

The HARPS-N spectra were reduced using the latest version (Nov. 2013) of the
HARPS-N instrument Data Reduction Software and applying the appropriate mask
depending on the spectral type of the object (Pepe et al. 2002). The basic
processing steps for the data reduction consist in bias and dark subtraction,
flat fielding, wavelength calibration, spectrum extraction, and cross-
correlation computation. For the removal of the spurious features caused by
the telluric lines we first used the molecfit tool (Smette et al. 2015; Kausch
et al. 2015) to produce a synthetic telluric spectrum and then the package
telluric in IRAF222IRAF is distributed by the National Optical Astronomy
Observatory, which is operated by the Association of the Universities for
Research in Astronomy, inc. (AURA) under cooperative agreement with the
National Science Foundation. to remove the telluric lines.

In order to flux-calibrate the HARPS-N spectra, the contemporaneous absolute
flux-calibrated spectroscopy was acquired within 2 nights of our GHOsT runs
with the 1.22m telescope at the Asiago observatory, Italy. The spectra cover
the wavelength range 330–790 nm and were fully reduced and flux-calibrated
against a spectrophotometric standard observed during the same night. Their
flux zero-point was also checked with $BVR_{C}I_{C}$ photometric measurements
collected during the same nights with the ANS Collaboration telescopes (see
Munari et al. 2012). The photometry is reported in Paper I. Given the short
temporal distance between the two datasets we assume that the continuum shape
did not change significantly between the Asiago and TNG observations. Thus,
for each source we first fitted the continuum of the Asiago spectrum and then
multiplied it for the continuum-normalized HARPS-N spectrum.

The GIANO-B spectra were extracted following the data-reduction prescriptions
described in Carleo et al. (2018). Halogen lamp exposures were employed to map
the order geometry and for flat-field correction, while wavelength calibration
was based on lines from a U-Ne lamp acquired at the end of each observing
night. The molecfit tool (Smette et al. 2015) was used for removing the
telluric contribution in the near infrared.

To flux-calibrate the GIANO-B spectra, NIR photometry in the $JHK_{S}$ bands
was acquired with the REMIR instrument on the Rapid-Eye-Mount (REM) telescope
(Vitali et al. 2003), at the La Silla Observatory, Chile, during the night of
November 11, 2017. We assume that the NIR magnitudes did not change
significantly between TNG, Asiago, and REM observations. We then performed an
interpolation between the considered flux measurements using a spline function
to derive a smooth continuum function in the wavelength range 940–2420 nm,
that is a response function, which was then applied to flux-calibrate the
various (continuum-normalized) segments of the GIANO-B spectrum. Finally, the
flux-calibrated spectral segments most relevant for this pilot study of
accretion were selected.

We estimate that the flux calibration of the GIARPS spectra is precise within
20%. The final products do not contain the region of the Balmer Jump, but
include 17 well-resolved accretion diagnostics (12 in the optical and 5 in the
NIR) that form the basis for our measurements of accretion in the sample (see
Sect. 4).

##  3 Stellar parameters

A first step in any study of accretion is the determination of the YSO
physical properties. Estimates of the physical parameters, derived using a
number of methodologies, exist in the literature for all the YSOs in our
sample. In order to minimize uncertainties due to the different procedures
used in the literature, and in view of the forthcoming GHOsT data, we need to
adopt a methodology that allows us to determine the YSO properties in a self-
consistent and homogeneous way.

Table 2:  Properties of the CTT sample derived in this work

Name |  $T_{\rm eff}$ ($\pm$err) | SpT |  $A_{\rm V}$ a |  $A_{\rm V}$ b | $L_{\star}$ | $R_{\star}$ | $M_{\star}$
---|---|---|---|---|---|---|---
| (K) |  | (mag) | (mag) | ($L_{\odot}$) | ($R_{\odot}$) | ($M_{\odot}$)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
RY Tau | 5856 (151) | G1 | 2.25 | 2.32 | 8.87 | 2.89 | 1.80
DG Tau | 4004 (153) | K7 | 1.50 | 1.79 | 0.44 | 1.38 | 0.70
DL Tau | 4188 (100) | K5 | 1.50 | 1.45 | 0.40 | 1.20 | 0.90
HN Tau A† | 4617 (97) | K4 | 1.25 | 1.53 | 0.15 | 0.60 | 0.80⋆
DO Tau | 3694 (104) | M1 | 1.40 | 1.69 | 0.42 | 1.58 | 0.50
RW Aur A | 4870 | K0 | 1.00 | 0.57 | 1.64 | 1.80 | 1.50
CQ Tau‡ | 6823 (136) | F4 | 0.50 | 0.60 | 2.71 | 1.18 | 1.50⋆
333
a: extinction derived using spectral templates only.
b: extinction derived using spectral templates and veiling.
$\dagger$ : subluminous YSO (Sect. 3.4). The $L_{\star}$, $R_{\star}$, and
$M_{\star}$ values are underestimated.
$\ddagger$ : UX Ori type variable (Sect. 3.4). Parameters affected by variable
circumstellar extinction.
$\star$: corrected values of $L_{\star}$, $R_{\star}$, and $M_{\star}$ for the
two subluminous objects are estimated in Sect. 4.3.1. The mass reported here
is that of the closest PMS track on the HR diagram, with the uncorrected
values of $L_{\star}$.

###  3.1 Effective temperature and optical veiling

We used the ROTFIT code to determine effective temperature, $T_{\rm eff}$,
surface gravity, $\log{g}$, radial velocity, $RV$, projected rotational
velocity, $v\sin{i}$, and veiling as a function of wavelength, $r_{\lambda}$.
The code has been successfully applied on YSOs optical spectra at different
resolutions (Frasca et al. 2006, 2015), and is particularly well suited for
the HARPS-N spectra. In short, the code finds the best photospheric
rotationally broadened template spectrum that reproduces the target spectrum
by minimizing the $\chi^{2}$ of the difference between the observed and
template spectra in specific spectral segments. The spectral segments ($\sim
100$ Å each) are normalized to unity, and therefore a measure of extinction is
not provided by the code. We adopted as templates a grid of high-resolution
spectra of slowly rotating, low-activity stars with well-known atmospheric
parameters, which were retrieved from the ELODIE Archive (Moultaka et al.
2004). The HARPS-N spectra were degraded to the ELODIE resolution ($R=42,000$)
before running the analysis code. We have chosen this template grid because
real spectra are best suited for the determination of veiling and $v\sin i$
(Frasca et al. 2015, 2019). Moreover, they allow us to perform a careful
subtraction of the photospheric spectrum (see Section 4.1). The spectral
intervals analyzed with ROTFIT contain features that are sensitive to the
effective temperature and/or $\log{g}$.

The whole set of physical parameters derived with ROTFIT ($T_{\rm eff}$,
$\log{g}$, $RV$, $v\sin{i}$, and veiling) for the complete GHOsT sample will
be presented in a forthcoming paper, while the effective temperature,
essential for this work, is provided in Table 2. Optical veiling values, also
crucial for this pilot study, are given in Table 3. The spectral types,
determined using the $T_{\rm eff}$ from ROTFIT and the relation between
spectral type versus $T_{\rm eff}$ by Herczeg & Hillenbrand (2014), are also
reported in column 3 of Table 2.

For RW Aur A it was not possible to derive the parameters using the ROTFIT
method, as the spectrum is totally crossed by emission lines that hide the
photospheric lines at optical wavelengths. As discussed in Sect. 3.2, the
templates best matching the NIR spectrum have a spectral type between K1 and
K0, the latter being consistent with the determination by Herczeg &
Hillenbrand (2014) for this star. We therefore adopted the $T_{\rm eff}$ value
as determined from the K0 spectral type and the SpT versus $T_{\rm eff}$
relationship by these authors. For this star, Herczeg & Hillenbrand (2014)
report a veiling of 0.5 at $\lambda=$750 nm. Based on a linear relationship
between the veiling at 580 nm and 710 nm drawn from our previous studies of
the Lupus population (Alcalá et al. 2014, 2017), we estimate that the veiling
at $\lambda=$600 nm is $r600\approx 2.3\times r710$, where r710 is the veiling
at $\lambda=$710 nm. Within the errors, this is consistent with the measured
veiling in Frasca et al. (2017) where $r620\approx 2.0\times r710$. For RW Aur
A, we calculate a value of $r600\sim 1.2$. We find a similar value of veiling
considering the equivalent width of the lithium line at 6708 Å and applying
the method described in Biazzo et al. (2011). However, we consider this a
tentative value only, as the veiling of this CTT may be strongly variable
(0.3$<r_{\lambda}<$6.1, for $\lambda$ in the range 500–650 nm, Stout-Batalha
et al. 2000).

The corresponding $T_{\rm eff}$ values derived from ROTFIT are in good
agreement, within the errors, with those drawn from the Herczeg & Hillenbrand
(2014) spectral types. As a logical consequence, the spectral types are also
in good agreement, within a spectral subclass. We note that the values for CQ
Tau, which have not been included in the Herczeg & Hillenbrand (2014) study,
are in agreement with those published in Mendigutía et al. (2011) and Meeus et
al. (2012). Also, the negligible veiling at optical wavelengths for this star
is in agreement with the recent results by Dodin & Suslina (2021).

Table 3:  Veiling in the optical from ROTFIT and in the NIR with the procedure described in text. The projected rotational velocity determined with this procedure is also given in the last column. Name | $r450$ | $r500$ | $r550$ | $r600$ | $r650$ | $r968$ | $r983$ | $r1178$ | $r1256$ | $r1298$ | $r1565$ | $r1597$ | $r1666$ | $r1741$ | $r2130$ | $r2255$ | $r2322$ |  $v\sin{i}$ ($\pm$err)
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | (km/s)
RY Tau | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.2 | 0.6 | 0.4 | 0.7 | 0.3 | 0.5 | 0.4 | 0.5 | 0.9 | 1.4 | 1.2 | … | 49.8 (1.6)
DG Tau | … | … | 2.0 | 1.5 | 1.0 | 1.6 | 1.2 | 1.8 | 1.4 | 1.7 | 1.8 | 1.6 | 1.7 | 2.4 | 3–4 | 3–4 | … | 26.3 (3.3)
DL Tau | 3.0 | 2.5 | 2.0 | 1.2 | 1.5 | 1.1 | 1.1 | 1.1 | 1.0 | 1.0 | 0.9 | 0.6 | 0.8 | 1.7 | 2.5 | 2.1 | 2.5 | 12.0 (3.0)
HN Tau A | … | 0.8 | 0.8 | 0.8 | 0.5 | … | … | 1.1 | 1.2 | 1.5 | 1.8 | 1.6 | 1.3 | 2.3 | 3.3 | 5.0 | … | 50.7 (2.7)
DO Tau | 1.8 | 1.5 | 1.5 | 1.0 | 1.5 | 0.5 | 0.6 | 0.7 | 1.4 | 1.4 | 1.9 | 1.7 | 1.8 | 2.1 | 3.4 | 3.7 | 2.7 | 12.0 (2.2)
RW Aur A | … | … | … | 1.2 | … | … | … | … | 1.5 | … | … | 2.5 | 2.7 | 3.5 | 3.6 | 5.7 | 5.4 | 20.0 (3.4)
CQ Tau | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | … | 0.5 | 1.0 | 0.8 | … |  $<$3.0 | 2.0 | … | … | … | … | … | 79.0 (5.0)

###  3.2 Veiling and $v\sin i$ estimates in the NIR

The veiling of IR photospheric lines is usually attributed to the emission of
the inner edge of the dusty disk, where the dust is heated by stellar and
accretion radiation. As such, it can be used to infer properties of the
emission in excess of the stellar photosphere originating in the inner disk
and complementary to the UV and optical excess. In addition, veiling may have
an important impact on extinction (see Fischer et al. 2011; Herczeg &
Hillenbrand 2014, and references therein).

Figure 1: Two portions of the continuum-normalized spectrum of HN Tau A (black
solid line) in the $HK$ bands, with the rotationally broadened and veiled
spectrum of the stellar template overplotted (red dashed line). Absorption
features, mainly of the iron-peak group, are indicated with small vertical
lines. We refer to Rayner et al. (2009) for the details on the absorption
features. Emission lines such as the H2 line, indicated with the blue dotted
lines, are excluded from the analysis. The value of veiling, which minimizes
residuals with respect of the rotationally broadened and veiled template, is
indicated in the lower left.

The procedure we used to measure veiling of the photospheric lines in the NIR
follows the prescription thoroughly described in Antoniucci et al. (2017).
Briefly, we use template spectra acquired with GIANO-B and with similar
spectral types to the targets. The templates are chosen to have very low
$v\sin{i}$ values. Each template spectrum is broadened by convolution with a
rotational profile (Gray 2005) by increasing $v\sin{i}$ and it is artificially
veiled by adding a continuum excess, with both $v\sin i$ and $r_{\lambda}$ as
free parameters (see Eq. 1 in Antoniucci et al. 2017), until the photospheric
features match those of the target and minimum residuals between the target
spectrum and the rotationally broadened and veiled template are obtained.
Figure 1 shows an example of the result of the fitting procedure for HN Tau A
in two spectral intervals. The $r_{\lambda}$ values are assumed to be constant
within each spectral order. Values of $r_{\lambda}$ derived from this
procedure are given in Table 3. The procedure also yields an estimate of
$v\sin{i}$, which is also given in Table 3. The errors in veiling are on the
order of 20%.

As mentioned in the previous section, the optical HARPS-N spectrum of RW Aur A
is heavily veiled and crossed by numerous emission lines. Yet its NIR GIANO-B
spectrum shows some photospheric lines making it possible to estimate veiling
and $v\sin i$ . During this process, we were also able to determine that the
spectral type of the template best matching the photospheric lines corresponds
to a type between K1 and K0. We stress that in the case of DG Tau, the $r2130$
and $r2255$ estimates are rather uncertain, and so we were only able to
determine a range of values (see Table 3).

###  3.3 Extinction

As a first step to derive the visual extinction, $A_{\rm V}$, we adopt the
methods described in our previous works (Alcalá et al. 2014, 2017; Manara et
al. 2017a). As input data we use our primary flux calibrated spectra, that is
the Asiago spectra, which cover a sufficient wavelength range (330–790 nm) for
the purpose. To derive $A_{\rm V}$ for a given YSO, its spectrum was compared
with the spectra of nonaccreting YSOs best matching in spectral type. All our
nonaccreting templates were taken from Manara et al. (2013, 2017) and have
very low or negligible extinction ($A_{\rm V}<$ 0.5 mag; see Manara et al.
2013, 2017). The templates were rebinned to the Asiago spectra and then
artificially reddened by $A_{\rm V}$ in the range 0.0–4.0 mag in steps of 0.25
mag until the best match to the continuum slope of the YSO spectrum was found.
To redden the spectra we used the extinction law by Weingartner & Draine
(2001) for R${}_{\rm V}=5.5$, which has been found to be particularly well
suited for YSOs in general (Evans et al. 2009, and references therein). The
$A_{\rm V}$ values derived in this way are listed in column 4 of Table 2.

The main sources of uncertainty on $A_{\rm V}$ are the errors in spectral type
when associating a template to a given YSO, the error in the extinction of the
templates, and the errors in flux calibration. The combined effect leads to an
error of $\sim$0.35 mag, except for the case of RW Aur A for which we estimate
a larger error of about 0.5 mag. Adopting extinction laws by different authors
yields results consistent, within the errors of about 0.35 mag, with those of
Herczeg & Hillenbrand (2014). For instance, the latter authors find that for a
star with their measured $A_{\rm V}$$=$1.0 mag, adopting R${}_{\rm V}=$5 from
Cardelli et al. (1989) or R${}_{\rm V}=$5.1 from Weingartner & Draine (2001)
would yield $A_{\rm V}$$=$ 1.2 and 1.15 mag, respectively.

Figure 2: Plots of $2.5\cdot\log{[(1+r_{\lambda})\cdot
F^{T}_{\lambda}/F^{O}_{\lambda}]}$ vs. $A_{\lambda}/$$A_{\rm V}$ for the YSOs
in the sample (blue squares). The best linear fit for each object is shown as
a black line. The value of the slope $A_{\rm V}$ is shown in each panel. In
the case of CQ Tau the $r1565$ value is shown as an upper limit.

As mentioned in Section 3.2, another source of uncertainty is strong veiling,
which makes the YSO spectra intrinsically bluer than the templates. The
extinction as derived above is not severely affected by the veiling, as soon
as the analysis is restricted to wavelengths longer than about 450 nm (see
analysis in Appendix B of Alcalá et al. 2014), but also shorter than about 800
nm to avoid the effects of veiling in the NIR (Fischer et al. 2011). Thus, to
minimize the impact of veiling, the extinction was derived only from the red
portion of the Asiago spectra, starting at 500 nm. In this case, the effects
of NIR veiling are automatically excluded as the Asiago spectra do not cover
wavelengths longer than 790 nm.

We also applied an alternative method to derive $A_{\rm V}$ using the
prescription explained in Fischer et al. (2011, see their Eq. 4), originally
proposed in Gullbring et al. (1998, their Eq. 5). This requires measurements
of the veiling, $r_{\lambda}$, of the observed flux of the spectral template,
$F^{T}_{\lambda}$, and of the observed flux of the object, $F^{O}_{\lambda}$,
as a function of wavelength. The method is based on the fact that the quantity
$\Gamma_{\lambda}=2.5\cdot\log{[(1+r_{\lambda})\cdot
F^{T}_{\lambda}/F^{O}_{\lambda}]}$ is a linear function of the extinction
curve, $A_{\lambda}/$$A_{\rm V}$, and is equal to $A_{\lambda}/$$A_{\rm
V}$$\cdot$($A_{\rm V}$${}^{O}-$$A_{\rm V}$T)$-2.5\cdot\log{C}$, where $A_{\rm
V}$O and $A_{\rm V}$T are the visual extinction of the object and template,
respectively, and $C$ is a constant. The slope of a linear fit to the
$\Gamma_{\lambda}$ versus ($A_{\lambda}/$$A_{\rm V}$) relationship yields the
difference between the extinction of the object and the template, assuming the
same extinction law for both. In our case, $A_{\rm V}$T is always very close
to zero and therefore the slope of the linear fit yields $A_{\rm V}$O.

Figure 2 shows the plots of $\Gamma_{\lambda}$ versus $A_{\lambda}/$$A_{\rm
V}$ for the YSOs in the sample. For every YSO, we used the $r_{\lambda}$
values of Table 3, and the corresponding continuum $F^{T}_{\lambda}$ and
$F^{O}_{\lambda}$ values reported in Tables 7–13 in Appendix A. In these
tables, we also report the $r_{\lambda}$ values for convenience. The plots
show the best linear fit and the corresponding slope $A_{\rm V}$O. The error
on $A_{\rm V}$ indicated in each panel of Figure 2 is only the error on the
slope of the fit and does not represent the full error on $A_{\rm V}$, which
we estimate to be also on the order of 0.35 mag based mainly on flux
calibration errors and mismatch in spectral type of the templates and the
CTTs. The $A_{\rm V}$ results using this method are reported in column 5 of
Table 2.

In the case of RW Aur A, where the fit is not well constrained because only
one rough estimate of veiling in the optical was possible, the error may be as
high as 0.5 mag. Nevertheless, the resulting extinction values as derived from
both methods are consistent, within the errors. We also stress that the UX
Ori-type variability of CQ Tau may lead to large uncertainties on the $A_{\rm
V}$ value, as part of the extinction may be gray (Dodin & Suslina 2021).

The $A_{\rm V}$ derived from the spectral templates alone and those including
the veiling measurements (respectively columns 4 and 5 in Table 2) are in very
good agreement within the error of about 0.35 mag, although the veiling method
provides systematically higher values by up to $\sim$30%. As discussed in
Fischer et al. (2011), the adoption of different values of the total-to-
selective extinction, RV, has little impact on the results. We adopt the
$A_{\rm V}$ values derived from the ”veiling” method for the subsequent
analysis.

The veiling methodologies used in the NIR by Fischer et al. (2011) yielded
$A_{\rm V}$ values systematically higher than those derived from other
previous measurements. Yet, applying the same methods here, but extended to
the optical veilings, provides $A_{\rm V}$ values that are significantly lower
than those in Fischer et al. (2011) for the same stars. Herczeg & Hillenbrand
(2014) also calculate much lower $A_{\rm V}$ values than Fischer et al. (2011)
and interpret the higher values by the latter authors as possibly due to
spectral mismatch between the templates and the CTTs and to the lower
sensitivity of NIR spectra to extinction. Our extinction values are slightly
higher than those of Herczeg & Hillenbrand (2014), but still consistent within
the small amount of about 0.5 mag, and in some cases the agreement is very
good. This is consistent with the fact that the veiling method gives $A_{\rm
V}$ values that are systematically higher by $\sim$30% with respect to the
templates method alone.

###  3.4 Luminosity and mass

The stellar luminosity, $L_{\star}$, was derived as follows. For a given
object, we extracted first the BTsettl model (Allard et al. 2012) best
matching the $T_{\rm eff}$ values derived with ROTFIT above (see Sect. 3.1).
The model was then normalized to the extinction corrected flux,
$F^{corr}_{600}$, of the Asiago spectrum at $\lambda=$600 nm, where the
veiling estimates are expected to be more reliable, and corrections subject to
less uncertainty. To take into account the contribution of veiling, the
extinction-corrected flux at 600 nm was multiplied by the factor $1/(1+r600)$,
where $r600$ is the veiling at $\lambda=$600 nm derived from ROTFIT and listed
in Table 3 (see example for DL Tau in Figure 3). This factor, which is always
$\leq$1, effectively reduces the observed flux to that emitted by the stellar
photosphere only, excluding the emission due to accretion.

We therefore assume that the BT-settl model normalized in this way best
represents the spectral energy distribution (SED) of the object’s photosphere
at the star distance. Integration of the normalized model at all wavelengths
yields the bolometric flux corresponding to the object’s photosphere. The
stellar luminosity was then calculated using this flux and adopting the
distance reported in Table 1. The main sources of uncertainty on $L_{\star}$
are the errors in flux calibration of the Asiago spectra and the error on the
veiling correction. On this basis, we estimate an average uncertainty of about
0.2 dex in $\log$$L_{\star}$. We verified that using veiling values at other
wavelengths yields consistent results of the veiling-corrected bolometric
flux. For instance, in the case of DL Tau, which has the strongest veiling at
450 nm, we derive a corrected bolometric flux of 5$\times$10-10 erg s-1 cm-2
and 4.55$\times$10-10 erg s-1 cm-2 when using the $r600$ and $r450$ values,
respectively. The stellar radius, $R_{\star}$, was calculated from the
effective temperature and stellar luminosity.

Figure 3: Example of BT-settl model normalization. The extinction-corrected
Asiago spectrum of DL Tau is shown with the red line, while the BT-settl model
normalized to DL Tau at $\lambda=$600 nm is plotted with the blue line. We
note the increase of excess emission of DL Tau at wavelengths shorter than
about 450 nm. The veiling-corrected BT-settl model is plotted with the black
line. See text for details

In some cases (e.g., DG Tau) the $L_{\star}$ values from the oldest literature
may be overestimated most likely because such determinations did not consider
the contribution of veiling and/or overestimate extinction. Our stellar
luminosities are well consistent with those derived in Herczeg & Hillenbrand
(2014) within the error of about 0.2 dex in $\log$$L_{\star}$. It is worth
noting that in the case of RY Tau our $T_{\rm eff}$, $A_{\rm V}$, and
$L_{\star}$ values are in good agreement, within the errors, with those
reported in the recent and thorough study by Garufi et al. (2019). These
values are also fairly consistent with those reported in the paper by Calvet
et al. (2004).

We note that HN Tau A is subluminous on the HR diagram with both the value of
Herczeg & Hillenbrand (2014) for $L_{\star}$ and the one derived here. This is
likely due to obscuration of the stellar photosphere by the highly inclined
disk ($i\approx 70^{\circ}$; Long et al. 2019). The $L_{\star}$, $R_{\star}$,
and $M_{\star}$ values for this star may be underestimated by a factor of
$\sim$17, $\sim$4.3, and $\sim$2, respectively (see Sect. 4.3.1). Likewise,
our derived luminosity for CQ Tau places the star slightly below the main
sequence, most likely as a consequence of the fact that during the periods of
dimming, the extinction may be gray, and therefore the luminosity is
underestimated. The GHOsT observations of this star were performed when it was
in a faint stage, that is, $B=$10.89 mag as compared with $B=$9 mag in its
bright phase (Grinin et al. 2008), and therefore its luminosity may be
underestimated by a factor of about six (see also Sect. 4.3.1).

Finally, the mass, $M_{\star}$, of the seven CTTs was estimated by comparison
of the position of the objects on the HR diagram with the theoretical PMS
evolutionary tracks by Siess et al. (2000). The uncertainties on $L_{\star}$
and $T_{\rm eff}$ lead to a typical uncertainty of $\sim$0.15 dex in
$M_{\star}$. The derived $L_{\star}$, $R_{\star}$, and $M_{\star}$ values for
the sample are given in Table 2. The mass reported in this table for the
subluminous objects HN Tau A and CQ Tau corresponds to that of the
evolutionary track closest to these stars on the HR diagram, but corrected
values are estimated in Section 4.3.1.

##  4 Accretion diagnostics

The GIARPS spectra include several emission lines that are well correlated
with $L_{\rm acc}$ (Alcalá et al. 2014, 2017) and will be the basis of our
measurements of accretion in the sample. In particular, we extracted 17
spectral portions with well-resolved and flux-calibrated accretion
diagnostics, namely, eight hydrogen recombination lines (H$\alpha$, H$\beta$,
H$\gamma$, H$\delta$, Pa$\beta$, Pa$\gamma$, Pa$\delta$, Pa8), eight helium
lines (He i4026, He i4471, He i4713, He i4922, He i5016, He i5876, He i6678,
He i10830), and the Ca ii3934 line.

Figure 4: Examples of GIARPS spectra showing the line profiles of CTTs in our
sample

Figure 4 shows examples of GIARPS spectra for several emission lines of every
CTT star in our sample. For comparison, the spectra are normalized to the
local continuum and shifted in velocity to the rest wavelength. The latter was
determined from the profiles of the Li I $\lambda 6708$ Å photospheric line,
assuming weighted $\rm\lambda=670.7876nm$, and in the NIR from the Al I lines
at $\lambda=2019.884,2116.958,2121.396$ nm. All the spectra are shown in the
same velocity range for comparison.

There is a variety of line profiles with a range of widths and intensities,
typical of accreting YSOs. The widest lines are from RY Tau, RW Aur A, and HN
Tau A, while DG Tau and DL Tau show lines with intermediate width. The
narrowest lines are from DO Tau, yet the width of the H$\alpha$ line at 10% of
the line peak that we measure for the latter is more than 400 km/s, pointing
to significant accretion activity (White & Basri 2003; Natta et al. 2006).
Within the qualitative classification scheme of the Balmer lines proposed by
Antoniucci et al. (2017a), RY Tau, RW Aur A, and HN Tau A display wide and
multi-peak profiles, DG Tau and DL Tau show multi-peak profiles, while DO Tau
shows narrow and almost symmetric profiles. All these morphologies are
displayed by the Lupus sample studied by Antoniucci et al. (2017a). Two
exceptions in our sample are RY Tau and CQ Tau, where many lines are dominated
by the photospheric absorption and therefore the subtraction of the
photospheric spectrum is needed in order to measure the residual emission (see
Sect. 4.1).

###  4.1 Flux and luminosity of lines

The flux at Earth in permitted lines was computed by directly integrating the
GIARPS flux-calibrated spectra using the splot package under IRAF. Three
independent measurements per line were made, considering the lowest, highest,
and the middle position of the local continuum, depending on the local noise
level of the spectra. The flux and its error were then computed as the average
and standard deviation of the three independent measurements, respectively.

Figure 5: Examples of photospheric line subtraction for the H$\alpha$ and
H$\beta$ lines in CQ Tau and RY Tau. The black, red, and blue lines represent
the observed, photospheric, and photospheric-subtracted spectra, respectively.
See text for details.

In the case of RY Tau and CQ Tau, we performed the photospheric subtraction in
the following way: the spectral templates used to derive the stellar
parameters and NIR veiling were artificially broadened for $v\sin i$ and
veiled at the same values derived from ROTFIT and the NIR veiling procedure.
The rotated and veiled templates were then subtracted from the YSO spectra. In
this procedure, both the YSO and template spectra were normalized to the
continuum around the selected lines to be analyzed. Three measurements of the
equivalent widths of the corrected lines were made and the average was
computed. The error was estimated by the standard deviation of the observed
fluxes on the difference spectra in two spectral regions near the line.
Finally, the flux of the corrected lines was computed as the product of the
equivalent width times the absolute continuum flux adjacent to the lines. The
procedure, illustrated in Figure 5 for the H$\alpha$ and H$\beta$ lines and in
Figure 6 for the Pa$\beta$ line, was applied to lines strongly affected by the
photospheric contribution namely the Balmer, Paschen, and the He I $\lambda
10830$ Å lines. We note that in some cases a residual contribution of
nonphotospheric self-absorptions remained, in particular in the case of some
Paschen and the He I $\lambda 10830$ Å lines (see example in Figure 6). Lines
with strong self-absorption may underestimate $L_{\rm acc}$ and therefore the
measurement was not considered when such a contribution was more than
$\sim$30% of the flux. The procedure adopted here to measure the integrated
flux is the same adopted in Alcalá et al. (2017), where the $L_{\rm line}$
versus $L_{\rm acc}$ calibrations were derived.

Figure 6: Examples of photospheric line subtraction for the Pa$\beta$ line for
CQ Tau (upper panels) and RY Tau (lower panels). The red lines represent the
photospheric templates. The left and right panels show, in black lines, the
observed and photospheric-subtracted spectra, respectively. The green vertical
lines mark the intervals for the equivalent width measurement. The equivalent
widths of the emission line before and after the subtraction are also
indicated.

Not all the 17 lines in the GIARPS spectral range were detected or could be
measured in every CTT star. A summary of the number of lines with flux
measurements in every CTT in our sample is provided in the first column of
Table 4, and every panel of Figure 7 shows the lines detected and measured.
The absence of a point in these plots means that the line was not detected or
could not be extracted with the photospheric subtraction, mainly because of
large residuals of telluric lines and/or a strong contribution of the
nonphotospheric self-absorption component. DL Tau is the only star for which
the complete set of lines could be detected and measured, while CQ Tau has the
lowest number of lines with measured fluxes. For most stars, fluxes have been
measured for more than 12 lines. In the case of RW Aur A, the Balmer lines
higher than H4 (H$\gamma$, H$\delta$) are dominated by a nonphotospheric self-
absorption component. Therefore, we did not attempt a measurement of the flux
of those lines. Also, the H$\alpha$ and H$\beta$ lines in this star may be
affected by a similar self-absorption, but we measured their flux with the
awareness that it may be underestimated. A contribution of absorption
components in the emission lines of DG Tau, DL Tau, HN Tau A, and DO Tau is
not significant, and therefore we use the flux measured directly by the
integration of the lines. The observed fluxes, equivalent widths, and their
errors are reported in several tables provided in Appendix B (Tables
LABEL:tab:fluxes_EWs_Had to LABEL:tab:fluxes_EW_CaI3934) 444The flux errors
reported in these tables are those resulting from the uncertainty in continuum
placement. The estimated $\sim$20% uncertainty of flux calibration (see Sect.
2.2) should be added in quadrature..

Figure 7: Plots of $L_{\rm acc}$ as a function of the different accretion
diagnostic as labeled for the seven targets (blue dots). The vertical error
bars consider the error in $L_{\rm line}$ as well as the errors in the $L_{\rm
acc}$–$L_{\rm line}$ relationships. The horizontal red lines in each panel
represent the average $L_{\rm acc}$.

The luminosity of the different emission lines was computed as $L_{\rm line}$
$=4\pi d^{2}\cdot f_{\rm line}$, where $d$ is the YSO distance listed in Table
1 and $f_{\rm line}$ is the extinction-corrected flux of the lines.

###  4.2 Accretion luminosity

We derived $L_{\rm acc}$ via empirical relationships between accretion
luminosity and the luminosity of permitted emission lines. Such relationships
have been derived by several authors (e.g., Herczeg & Hillenbrand 2008;
Rigliaco et al. 2012; Alcalá et al. 2014, 2017). Here we used the most recent
ones by Alcalá et al. (2017), where the relationships are simultaneously
derived for lines from the UV to the NIR for a more than 90% complete sample
of Lupus YSOs.

In Figure 7 the derived $L_{\rm acc}$ values are plotted as a function of the
line diagnostics for the seven targets. The error bars include the errors in
$L_{\rm line}$, as well as the errors in each $L_{\rm acc}$–$L_{\rm line}$
calibration. The individual $L_{\rm acc}$ values corresponding to each
diagnostic are reported in the various tables in the Appendix B (Tables
LABEL:tab:fluxes_EWs_Had to LABEL:tab:fluxes_EW_CaI3934) for every CTT in the
sample. An average accretion luminosity, $\langle$$L_{\rm acc}$$\rangle$, was
then calculated for each target. These values are reported in Table 4 together
with the corresponding $\langle$$L_{\rm acc}$$\rangle$/$L_{\star}$ ratio.

The typical standard deviation of $\sim$0.25 dex on $\log$$\langle$$L_{\rm
acc}$$\rangle$ is within the expected error estimated from the fit of the UV
continuum excess emission in other samples using slab models (see Alcalá et
al. 2014, 2017; Manara et al. 2017a), although the error on $L_{\rm acc}$ for
the individual diagnostics is larger than this value. This confirms that the
average $L_{\rm acc}$, derived from several diagnostics measured
simultaneously, has a significantly reduced error.

###  4.3 Mass accretion rate

The average accretion luminosity of each target (see Table 4) was converted
into mass accretion rate, $\dot{M}_{\rm acc}$, using the relation

$\dot{M}_{acc}=(1-\frac{R_{\star}}{R_{\rm in}})^{-1}\leavevmode\nobreak\
\frac{\langle L_{acc}\rangle R_{\star}}{GM_{\star}}\approx
1.25\leavevmode\nobreak\ \frac{\langle L_{acc}\rangle R_{\star}}{GM_{\star}},$
(1)

assuming $\frac{R_{\star}}{R_{\rm in}}=\frac{1}{5}$, where $R_{\star}$ and
$R_{\rm in}$ are the stellar radius and inner-disk radius, respectively (see
Gullbring et al. 1998; Hartmann 1998), and using the stellar parameters
reported in Table 2. The resulting $\dot{M}_{\rm acc}$ values are reported in
Table 4.

Table 4:  Summary of the number of lines used to derive the average $L_{\rm
acc}$ and accretion properties.

Name | No. lines |  $\log$$\langle$$L_{\rm acc}$$\rangle$ ($\pm\sigma$ dex) |  $\langle$$L_{\rm acc}$$\rangle/$$L_{\star}$ |  $\log$$\dot{M}_{\rm acc}$
---|---|---|---|---
|  | ($L_{\odot}$) |  | ($M_{\odot}$ yr-1)
RY Tau | 12 |  $-$0.38 (0.15) | 0.05 |  $-$7.57
DG Tau | 14 |  $-$0.25 (0.18) | 1.28 |  $-$7.35
DL Tau | 17 |  $-$0.35 (0.18) | 1.12 |  $-$7.62
HN Tau A† | 15 |  $-$0.99 (0.23) | 0.68 |  $-$8.50
DO Tau | 16 |  $-$0.84 (0.16) | 0.34 |  $-$7.73
RW Aur A | 15 |  $+$0.39 (0.30) | 1.50 |  $-$6.93
CQ Tau | 9 |  $-$1.18 (0.17) | 0.02 |  $-$8.68
555
$\dagger$ : subluminous YSO. The values for the accretion properties may be
underestimated (see Sect. 4.3.1). Corrected values are provided in Table 5.

The sources of error in $\dot{M}_{\rm acc}$ are the uncertainties on $L_{\rm
acc}$, stellar mass, and radius. Propagating these, we estimate an average
error of $\sim$0.35 dex in $\dot{M}_{\rm acc}$ (see Appendix A of Alcalá et
al. 2017). However, additional errors on these quantities come from the
uncertainty in distance, as well as from differences in the adopted
evolutionary tracks. The largest uncertainty on the YSOs distance from the
Gaia EDR3 is estimated to be less than $\sim$10%, yielding relative
uncertainty of $\sim$0.2 dex in the mass accretion rate666We note that
$\dot{M}_{\rm acc}$ $\propto$ d3, as $L_{\rm acc}$ $\propto$ d2 and
$R_{\star}$ $\propto$ d.. On the other hand, it has been shown (see Appendix A
in Alcalá et al. 2017) that using different sets of PMS evolutionary tracks
leads to uncertainties of 0.04 dex to 0.3 dex in $\dot{M}_{\rm acc}$. We
therefore estimate that the cumulative relative uncertainty in $\dot{M}_{\rm
acc}$ is about 0.4 dex.

We note that our $L_{\rm acc}$$=0.08$ $L_{\odot}$ for CQ Tau is more than an
order of magnitude lower than the value reported in Donehew & Brittain (2011,
$L_{\rm acc}$$=$3.8 $L_{\odot}$; see also Tables 1 and 4 for the $\dot{M}_{\rm
acc}$ estimates). Yet, using the Br$\gamma$ luminosity reported by these
authors and the Alcalá et al. (2017) relationships we derive a $L_{\rm
acc}$$=$0.15 $L_{\odot}$, which is only a factor two our value and within the
limits of long-timescale variable accretion ($<$0.4 dex, see Costigan et al.
2012, 2014). A correction estimate due to UX Ori-type variability yields a
$L_{\rm acc}$$\sim 0.38$ $L_{\odot}$ for CQ Tau (see Section 4.3.1), which is
still lower by an order of magnitude than the Donehew & Brittain (2011)
determination. It is worth noting that our estimate of $\log$$\dot{M}_{\rm
acc}$$=-8.68$ for this star is consistent with the upper limit derived by
Mendigutía et al. (2011, $\log$$\dot{M}_{\rm acc}$$<-$8.3), suggesting that
these latter authors also observed the star in its faint phase.

We also stress that the $L_{\rm acc}$ values derived here for RY Tau, DL Tau,
HN Tau A, and DO Tau are consistent, within the errors, with those by Ingleby
et al (2009) and Ingleby et al. (2012), although in the case of RY Tau our
value is a factor of about four lower. We think this may be due to variable
accretion. It is also worth mentioning that our $\dot{M}_{\rm acc}$ estimates
for RY Tau and DG Tau are in good agreement with the range of values derived
by Frasca et al. (2018) based on the H$\alpha$ and He i6678 emission lines.

####  4.3.1 The cases of HN Tau A and CQ Tau

The highly inclined disk of HN Tau A may occult, at least partially, the
emission from the accretion flows and from the shock onto the stellar surface,
and therefore $L_{\rm acc}$ for this star will be underestimated in a similar
way to the $L_{\star}$ value (see Sect. 3.4). Nevertheless, the $L_{\rm
acc}$/$L_{\star}$ ratio for this star is at the level of the highest
accretors, possibly showing that both $L_{\rm acc}$ and $L_{\star}$ of the
star are obscured in the same manner. This interpretation has proven to be
correct for subluminous objects in Lupus (see Sect. 7.4 in Alcalá et al.
2014).

Following the same reasoning as in Alcalá et al. (2020, their Appendix C), we
can use the luminosity of the $[{O\textsc{i}}]\leavevmode\nobreak\ \lambda
6300$ line to estimate a correction factor on $L_{\rm acc}$ and $L_{\star}$.
The [O i] line is found to originate relatively far from the star and
therefore should not be significantly affected by obscuration effects from the
inner disk, and the line luminosity is also correlated with $L_{\rm acc}$ and
$L_{\star}$ (Natta et al. 2014; Nisini et al. 2018). From the HARPS-N spectrum
of HN Tau A, we measure a line flux F${}_{[{O\textsc{i}}]}=9\times 10^{-14}$
erg s-1 cm-2 and derive the extinction corrected ($A_{\rm V}$$=$1.53 mag) flux
F${}_{[{O\textsc{i}}]}^{\rm corr}=3\times 10^{-13}$ erg s-1 cm-2. From Paper I
we estimate that about one-third of the flux comes from the low-velocity
component (LVC), and therefore we derive a line luminosity, in solar units, of
$\log L_{[{O\textsc{i}}]}^{LVC}=-4.2$. Using the $L_{\rm acc}$-$L_{\rm line}$
and $L_{\rm acc}$-$L_{\star}$ relationships for the LVC777We use only the LVC
because the HVC may be affected by the fact that the jet is extended. In this
case, the relationships found in Nisini et al. (2018) on a sample observed
with the X-Shooter instrument might not give a correct value because of the
different instrumental FOV used. The LVC does not suffer from this problem
because it forms in a compact region. derived by Nisini et al. (2018) we
estimate the $\log$$L_{\rm acc}$ and $\log$$L_{\star}$ values given in Table
5, which are a factor of approximately 7 and 17 the subluminous values,
respectively, meaning that both $L_{\rm acc}$ and $L_{\star}$ are affected by
a similar obscuration factor, which is consistent with the interpretation for
subluminous objects (Alcalá et al. 2014). For comparison, we also include the
measured values in Table 5. The corrected stellar luminosity implies a stellar
radius a factor about 4.3 larger (i.e., 2.6 $R_{\odot}$), and places the star
on the HR diagram in a position consistent with the other CTTs.

Table 5:  Accretion and stellar properties of HN Tau A after and before correction for obscuration effects and upper limits for CQ Tau derived as explained in Section 4.3.1. | HN Tau A | CQ Tau
---|---|---
| Corrected | Measured | Upper lim. | Measured
Quantity | with $L_{[{O\textsc{i}}]}^{LVC}$ | values | with $\Delta B$ | values
$\log$$L_{\rm acc}$ |  $-$0.12 |  $-$0.99 |  $<-$0.42 |  $-$1.18
$\log$$L_{\star}$ |  $+$0.42 |  $-$0.82 |  $<+$1.18 |  $+$0.43
$\log$$R_{\star}$ |  $+$0.41 |  $-$0.22 |  $<+$0.44 |  $+$0.07
$\log$$M_{\star}$ |  $+$0.20 |  $-$0.10 |  $<+$0.30 |  $+$0.18
$\log$$\dot{M}_{\rm acc}$ |  $-$7.19 |  $-$8.68 |  $<-$7.70 |  $-$8.68

Using the corrected $L_{\star}$ value and the Siess et al. (2000) evolutionary
tracks, we estimate a mass of 1.6 $M_{\odot}$ for HN Tau A, which is a factor
of about two higher than the value provided in Table 2. The $\log{g}=3.8$
calculated from the corrected radius and mass is consistent with the typical
gravity for YSOs, while the subluminous values yield a much higher gravity of
$\log{g}=4.7$. The corrected $L_{\rm acc}$, $R_{\star}$, and $M_{\star}$
values and Eq. 1 would imply a $\log$$\dot{M}_{\rm acc}$$\approx-7.3$, that
is, HN Tau A would be among the strongest solar-mass accretors in Taurus.

The work by Nisini et al. (2018) also provides $L_{\rm line}$–$M_{\star}$ and
$L_{\rm line}$–$\dot{M}_{\rm acc}$ relationships allowing us to estimate
$M_{\star}$ and $\dot{M}_{\rm acc}$ indirectly from the $\log
L_{[{O\textsc{i}}]}^{LVC}$ value. The results are also provided in Table 5 and
are in agreement with the values derived from the evolutionary tracks and Eq.
1.

We warn the reader about the uncertainties on extinction in high-inclination
objects. The above calculations for HN Tau A in this section are based on the
assumption that the visual extinction of the LVC of the $[{O\textsc{i}}]$ line
is the same as measured for the star, i.e., $A_{\rm V}$$=$1.53 mag, which is
not necessarily true. However, we note that adopting $A_{\rm V}$$=$0 mag
yields a corrected $L_{\star}$ a factor of about three lower than when
assuming $A_{\rm V}$$=$1.53 mag, which is still underluminous on the HR
diagram. On the other hand, a much higher value of $A_{\rm V}$ would make the
star unreliably luminous. We therefore conclude that a reasonable value for
the visual extinction of the LVC of the $[{O\textsc{i}}]$ line should be in
the range from about 0.7 mag to 2 mag. As explained above, adopting $A_{\rm
V}$$=$1.53 mag yields a corrected $L_{\star}$$=$2.6 $L_{\odot}$, which leads
to consistent results on the stellar parameters. We therefore used this value,
but warn the reader that the genuine $L_{\star}$ value might be in the range
between $\sim$1.5 $L_{\odot}$ and $\sim$3.5 $L_{\odot}$.

For CQ Tau, the $[{O\textsc{i}}]$ line is barely seen, and therefore we cannot
use the above methodologies to correct the stellar and accretion parameters
for obscuration effects. However, we can estimate upper limits based on the
photometric variations and assuming gray extinction. As pointed out by Dodin &
Suslina (2021), CQ Tau did not show variations before 1940 and was
approximately constant at $B\sim$9 mag (Grinin et al. 2008). Adopting this
value as the unobscured magnitude of the star and based on our $B=$10.9 mag
measurement during the GHOsT observations, we estimate a correction factor on
the bolometric flux of the star of $\sim$5.7. This correction provides a
maximum bolometric flux, yielding upper limits of 15 $L_{\odot}$, 2
$M_{\odot}$ and 2.8 $R_{\odot}$ for $L_{\star}$, $M_{\star}$, and $R_{\star}$,
respectively. These corrected values of $R_{\star}$ and $M_{\star}$ yield a
$\log{g}=3.9$, which is more consistent with the gravity of a YSO than the
$\log{g}=4.5$ derived from the observed $R_{\star}$ and $M_{\star}$ values in
Table 2. Assuming that $L_{\rm acc}$ is affected by the same obscuration
factor as $L_{\star}$ (see Section 7.4 in Alcalá et al. 2014), we derive an
upper limit of $-$7.7 for $\log$$\dot{M}_{\rm acc}$. The estimated upper
limits are listed in Table 5.

##  5 Results and Discussion

The results of the previous sections show that the studied CTTs in Taurus are
highly accreting objects. The novel science products and aspects of this pilot
study are as follows.

  * •

Contemporaneous low-resolution spectroscopic and photometric observations,
allowing an accurate flux calibration of the high-resolution spectroscopy;

  * •

simultaneity of the high-resolution, wide-band spectroscopic observations,
from the optical to the NIR;

  * •

simultaneous use of veiling measurements, both in the optical and NIR, to
determine $A_{\rm V}$;

  * •

use of more than ten line diagnostics to estimate accretion luminosity,
yielding a much reduced error in $L_{\rm acc}$ as compared with determinations
using single diagnostics.

All of the above was achieved using well-defined and assessed procedures for
deriving the stellar physical and accretion parameters in a self-consistent
and homogeneous way. Therefore, the properties derived here can be considered
as more robust and reliable than in previous studies. Some limitations to the
application of our procedures are related to the extremely veiled CTTs like RW
Aur A, but this type of object is not common. We are therefore confident that
the same procedures can be applied to the entire GHOsT data sample, which will
be presented in forthcoming papers (Gangi et al., in preparation). In the
following, we discuss a few aspects of the stellar and accretion properties of
our sample, as well as of the continuum excess emission in the NIR of these
CTTs.

###  5.1 Stellar and accretion properties

This GIARPS/TNG pilot study confirms the high levels of accretion of the
selected CTTs. It is worth noting from Table 4 that the $L_{\rm
acc}$/$L_{\star}$ ratio for every CTT in this sample is well above the level
of chromospheric noise emission in YSOs (max ($L_{\rm
acc}$/$L_{\star}$)${}_{\rm noise}\approx$0.01 Manara et al. 2017). We point
out that in three sources, namely, DG Tau, DL Tau, and RW Aur A, the total
luminosity is accretion dominated (i.e., $L_{\rm acc}$/$L_{\star}$ $>$ 1),
which is more typical of the class I stage of evolution (e.g., Antoniucci et
al. 2008, Fiorellino et al., in press ).

The most actively accreting object in this sample is RW Aur A. Noteworthy, the
recent study by Takami et al. (2020) shows that the star was in its bright
stage during the GIARPS observations (13 Nov. 2017). Moreover, from Paper I we
know that the magnitude of the star was 10.44 mag in the $V$-band and this is
consistent with the high-accretion activity scenario by Takami et al. (2020).

The apparently least active object in the sample is CQ Tau. This might be
mostly related to the much higher photospheric flux in comparison with the
other objects, as CQ Tau is an intermediate-mass YSO with $T_{\rm
eff}$$\sim$6800 K. Nevertheless, its $\dot{M}_{\rm acc}$ is comparable with
that of many actively accreting stars of similar mass in other star forming
regions. Confirming the upper limits derived in Section 4.3.1 as true values
would suggest CQ Tau has a similar level of accretion activity to RY Tau. On
the other hand, if the determination of $L_{\rm acc}$ based on the
$[{O\textsc{i}}]\leavevmode\nobreak\ \lambda 6300$ line for HN Tau A is
correct (see Sect. 4.3.1), this would also be one of the most actively
accreting objects in Taurus.

To investigate the levels of accretion in the Taurus subsample in more detail,
we use in the following the 90% complete Lupus sample studied in Alcalá et al.
(2017) for comparison purposes, but using the rescaled values reported in
Appendix A of Alcalá et al. (2019). Given the very small number statistics of
this pilot study, we cannot provide any result on the sample as a whole, but
only at the level of the individual objects.

####  5.1.1 Accretion luminosity versus stellar luminosity

Figure 8 shows the accretion luminosity as a function of stellar luminosity
for the Lupus sample and the seven Taurus CTTs. While most Lupus objects lie
at $L_{\rm acc}$/$L_{\star}$ values between 0.01 and 0.1, five of the Taurus
CTTs have higher values, between 0.3 and 1.5 (see Table 4). The two CTTs with
values compatible with most of the Lupus YSOs are RY Tau and CQ Tau. We note
that recent ALMA data have shown that the dusty disk of the latter has a large
cavity (R${}_{cavity}=$53 au, Ubeira Gabellini et al. 2019), likely suggesting
a transitional disk. Also, in the case of RY Tau, submillimeter data show
evidence for a protoplanetary disk with structures such as rings and an inner
cavity (Isella et al. 2010; Pinilla et al. 2018; Long et al. 2018). The
$L_{\rm acc}$/$L_{\star}$ ratio for both CQ Tau and RY Tau is compatible with
those of other transitional disks in Lupus.

Figure 8: Accretion luminosity as a function of stellar luminosity for the
stars in Lupus (black symbols) and the seven Taurus CTTs studied here (blue
circles). The latter are labeled with their names. The Lupus transitional
disks are shown with crossed squares. The continuous lines represent the three
$L_{\rm acc}$ vs. $L_{\star}$ relations as labeled. The long-dashed line
represents the shift of HN Tau A on the diagram when correcting its $L_{\rm
acc}$ and $L_{\star}$ values for obscuration effects by the disk. The
corrected values are shown with the red dot. The leftward and downward red
arrows represent the upper limits on $L_{\star}$ and $L_{\rm acc}$ for CQ Tau,
respectively. The average errors for the Taurus sample are shown in the upper
left. Figure adapted from Alcalá et al. (2017).

Tilling et al. (2008) presented simplified stellar evolution calculations for
stars subject to time-dependent accretion history, and derived evolutionary
tracks on the $L_{\rm acc}$– $L_{\star}$ diagram for a variety of fractional
disk masses, $f_{disk}\equiv M_{disk}$/$M_{\star}$, and YSO masses. Alcalá et
al. (2014) showed that the relation of the Lupus data in Figure 8 is steeper
than the $L_{\rm acc}$/$L_{\star}$ $=$constant lines, more or less following
the slope of the Tilling et al. (2008) tracks. These latter authors also
concluded that the disks of the Lupus objects with the lowest masses should
have masses lower than 0.014 $\times$ $M_{\star}$. The five high accretors in
Taurus (DG, DL, HN, DO, and RW) fall, instead, in the region of the diagram
consistent with the Tilling et al. (2008) tracks for YSOs of one solar mass
and $f_{disk}=$0.2. These five stars have indeed masses on the order of
1$M_{\odot}$ hence, according to such tracks one would expect their disk mass
to be on the order of 0.2 $\times$ $M_{\star}$. Although a correlation between
the total mass of gas$+$dust in the disk and the stellar mass has not yet been
confirmed, correlations between the dust mass in the disk and the stellar mass
of YSOs in the Lupus and Chameleon star forming regions have been found
(Ansdell et al. 2016; Pascucci et al. 2016).

In this scenario, the most massive disk would be RY Tau. The presence of the
important jet in RY Tau was recently explained in terms of a very massive disk
around this intermediate-mass T Tauri star (Garufi et al. 2019), which might
still be fed by the interstellar matter in which the object is embedded. For
DG Tau, Podio et al. (2013) estimate a total disk mass in the range 0.015–0.1
$M_{\odot}$, depending on the assumed dust size distribution. The upper limit
would be consistent with the results from the Tilling et al. (2008) tracks. We
note that in the case of HN Tau A, the $L_{\rm acc}$ and $L_{\star}$ values
corrected for obscuration effects would still yield similar results for the
estimated fractional disk mass, while confirmation of the upper limits for CQ
Tau would imply a disk mass similar to that of RY Tau.

####  5.1.2 Mass accretion rate versus stellar mass

The relationship between mass accretion rate and stellar mass is a fundamental
aspect of the study of disk evolution in YSOs. During the CTT phase,that is,
after the protostar has almost entirely dispersed its envelope but is still
actively accreting from the optically thick accretion disk, the stellar mass
undergoes negligible changes. Therefore, the $\dot{M}_{\rm acc}$ versus
$M_{\star}$ relation represents a diagnostic tool for the evolution of
$\dot{M}_{\rm acc}$ (Clarke & Pringle 2006) and for the process driving disk
evolution (Ercolano et al. 2017).

Figure 9 shows the accretion rate as a function of stellar mass for the seven
CTTs in Taurus as compared with the Lupus sample. The Taurus CTTs populate the
upper right part of the diagram. Most of the Lupus YSOs fall well below the
theoretical prediction by Vorobyov & Basu (2009, short-dashed black line), but
the latter is relatively consistent with the upper envelope of the Lupus data
points distribution. The few Lupus YSOs on the upper envelope of the
$\dot{M}_{\rm acc}$–$M_{\star}$ relationship are the strongest Lupus accretors
at a given mass and are also among the most luminous on the HR diagram.
Interestingly, the five Taurus CTTs with the highest $L_{\rm acc}$/$L_{\star}$
ratios tend to follow the upper envelope888Here we considered the obscuration
corrected quantities for HN Tau A., which qualitatively is well fitted by the
theoretical prediction. These results demonstrate that the level of accretion
of these five CTTs is as high as that of the strongest accretors in Lupus
Alcalá et al. (2017).

On the other hand, CQ Tau falls in the lower envelope of the $\dot{M}_{\rm
acc}$–$M_{\star}$ relationship, with its accretion properties more closely
resembling those of transitional disks than those of the full disks, while RY
Tau follows the $\dot{M}_{\rm acc}$–$M_{\star}$ trend for the most massive
Lupus stars with full disks. Should the upper limits for CQ Tau be confirmed,
its accretion properties will be similar to those of RY Tau.

Figure 9: Mass accretion rate as a function of stellar mass for the seven
Taurus CTTs studied (blue circles) compared with stars in Lupus (black
symbols). The Lupus transitional disks are shown with crossed squares. Lupus
objects classified as weak or negligible accretors are plotted with downward
arrows. The long-dashed black line represents the shift of HN Tau A on the
diagram when correcting its $\dot{M}_{\rm acc}$ and $M_{\star}$ values for
obscuration effects by the disk. The corrected values are shown with the red
dot. The leftward and downward red arrows represent the upper limits on
$M_{\star}$ and $\dot{M}_{\rm acc}$ for CQ Tau, respectively. The black dashed
line shows the double power law theoretically predicted by Vorobyov & Basu
(2009), and the continuous magenta lines represent the fits to the data as in
Eqs. (4) and (5) of Alcalá et al. (2017). The average errors for the Taurus
sample are shown in the upper left. Figure adapted from Alcalá et al. (2019).

###  5.2 The continuum NIR excess emission

Clear evidence of continuum excess emission or veiling increasing with
wavelength, from the optical to the NIR, was found in CTTs over a decade
ago(Fischer et al. 2011, and references therein). As mentioned in Sect. 3.2,
the behavior of IR veiling with wavelength can provide information on the
physical properties of the dust in the inner edge of the disk.

Figure 10 shows the NIR veiling as a function of wavelength for the seven CTTs
in the sample. The increase of veiling with wavelength in the NIR is evident
in all the objects. Adopting the same strategies as in Antoniucci et al.
(2017), a fit of rλ versus $\lambda$ with a black-body power law yields the
temperature, $T_{\rm eff}^{\rm BB}$, for each CTT indicated in the
corresponding panel of Figure 10 and in Table 6. We also include in this table
the results for DR Tau and XZ Tau from Antoniucci et al. (2017). Typical
errors on the $T_{\rm eff}^{\rm BB}$ are on the order of 100–150 K. The
fitting procedure requires another parameter, $F_{factor}^{BB}$, namely the
factor by which the black-body must be multiplied to fit the data. Such a
factor is based on the ratio of the areas of the stellar disk and the emitting
region producing the NIR veiling. The results using this factor are also given
in Table 6. We warn the reader that the fit for DG Tau must be taken with care
because only a range of values for the two reddest points could be determined
(see Sect. 3.2).

Table 6:  Results on the veiling emission in the NIR.

Name | $T_{\rm eff}^{\rm BB}$ | $F_{factor}^{BB}$ |  $R_{sublim}$ ($\pm$err) |  $R_{in}^{cont}$ ($\pm$err) a
---|---|---|---|---
| (K) |  | (au) | (au )
RY Tau | 1500 | 51 | 0.22 (0.05) | 0.18 (0.01)
DG Tau | 1700 | 39 | 0.06 (0.01) | 0.17 (0.01)
DL Tau | 1600 | 36 | 0.06 (0.01) |
HN Tau A | 2100 | 23 | 0.07 (0.01)† |
DO Tau | 1800 | 25 | 0.04 (0.01) |
RW Aur A | 2150 | 38 | 0.07 (0.01) | 0.10 (0.01)
CQ Tau | 2050 | 65 | 0.07 (0.01) |
” | ” | ” |  $<$0.15‡ |
DR Tau | 2350 | 28 | 0.03 (0.01) | 0.12 (0.01)
XZ Tau | 1600 | 29 | 0.06 (0.01) |
999
$\dagger$ : computed with the $L_{\star}$ and $L_{\rm acc}$ values in Table 5
$\ddagger$ : computed with the upper limits on $L_{\star}$ and $L_{\rm acc}$
in Table 5
$a$: Interferometric measurements by Eisner et al. (2010)
The values for DR Tau and XZ Tau are taken from Antoniucci et al. (2017)

While the resulting temperatures for RY Tau, DG Tau, DL Tau, and within errors
DO Tau, are consistent with the origin of the NIR continuum excess emission
being the inner rim of the dusty disk, the derived $T_{\rm eff}^{\rm BB}$
value for the other two CTTs is significantly higher than the dust sublimation
temperature ($\sim$1500 K) and is more difficult to interpret in the same way,
although temperatures as high as 2000 K may be expected for the sublimation of
silicate dust (Pollack et al. 1994).

In the simple model by Dullemond et al. (2001), where the inner disk is
directly irradiated by the central star, the inner disk edge is located at a
radius, $R_{sublim}$, which is given by the following equation:

$\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\
R_{sublim}=\sqrt{(1+f)\left(\frac{L_{\star}+L_{acc}}{4\pi\sigma
T_{sublim}^{4}}\right)}\leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \\\ ,$ (2)

where $f$ is the ratio of the inner edge height to its radius, and is
estimated to be 0.1 for T Tauri stars. Assuming this model and using the
$L_{\star}$ and $L_{\rm acc}$ results of the previous sections, and adopting
$T_{\rm eff}^{\rm BB}$ in Table 6 as sublimation temperature, we computed the
$R_{sublim}$ values listed in Table 6 for our sample of CTTs in Taurus. The
error in $R_{sublim}$ was calculated by error propagation in Eq. 2 and
adopting errors of 0.2 dex, 0.25 dex, and 150 K on $\log$$L_{\star}$
$\log$$L_{\rm acc}$, and $T_{\rm eff}^{\rm BB}$, respectively. We can compare
these values with the inner radius, $R_{in}^{cont}$, derived from
interferometric observations of the continuum NIR emission by Eisner et al.
(2010) for a few of the CTTs in common. These values are listed in the last
column of Table 6. We note that except for RY Tau, where $R_{sublim}$ and
$R_{in}^{cont}$ are in very good agreement, the $R_{sublim}$ values for the
other four stars with interferometric observations are lower than the
$R_{in}^{cont}$ measurements. Interestingly, the upper limits on $L_{\star}$
and $L_{\rm acc}$ for CQ Tau would yield a $R_{sublim}$ value more similar to
those typically found using interferometric observations (see Table 6).

Previous works (i.e., Eisner et al. 2007; Anthonioz et al. 2015) have shown
that the irradiated disk model for CTTs predicts radii for the inner rim of
the dusty disk that are underestimated with respect to interferometric
measurements. We therefore expect the $R_{sublim}$ values in Table 6 for DL
Tau, HN Tau A, DO Tau, CQ Tau, and XZ Tau to be underestimated by a factor of
between about two and three. However, one possibility is that the $T_{\rm
eff}^{\rm BB}$ we measure is not the sublimation temperature, but being
instead related to the excess emission in the NIR, may be the temperature of
hot gas inside the sublimation radius.

Figure 10: Plots of NIR veiling as a function of wavelength for the stars in
our sample (blue dots). The red dashed lines show the black body fits to the
data with T${}_{\rm eff}^{\rm BB}$ as labeled. See text for details.

Several authors (e.g., Fischer et al. 2011) discussed possible scenarios for
the NIR continuum emission. Among the suggested contributions that may enhance
the NIR continuum excess at the shorter $IYJ$ wavelengths there are warm
annuli around accretion hot spots, hot gas inside the dust sublimation radius,
and hot gas in the accretion flows and/or winds. Fischer et al. (2011) modeled
and discussed the presence of multiple temperature components in the shocked
photosphere. Also, detailed multiple-component modeling of the accretion
emission has been performed by Ingleby et al. (2013).

The results in Paper I showed that DG Tau and HN Tau A share similar physical
conditions in their jets. The temperature and ionization gradients of the jets
in these two objects would favor a magneto-hydrodynamical shock heating in
which the warm and ionized streamlines originate in the internal and mainly
gaseous disk, while the low-velocity and almost neutral stream lines come from
the dusty regions of the outer disk. Therefore, the hypothesis of a gaseous
hot disk inside the dust sublimation radius in HN Tau A and the similarity of
the physical conditions of its jet with those in the DG Tau jet would also
favor a much higher accretion rate in HN Tau A than what is measured without
obscuration correction. The possibility for the formation of the jets in DO
Tau and RW Aur A in a gaseous inner disk was also explored in Paper I. In this
context, jets signify the presence of dense hot regions inside the gaseous
inner disk.

In conclusion, it may be possible that some of the NIR continuum excess
emission of the CTTs, in particular in the case of HN Tau A, RW Aur A, and DR
Tau, originates in a thick gaseous disk inside the dust sublimation radius, as
already suggested by Fischer et al. (2011) and Antoniucci et al. (2017) for
other similar cases. In fact, the size of an emitting region estimated as
$R_{emiss}^{cont}\sim$ $R_{\star}$$\cdot\sqrt{F_{factor}^{BB}}$ is always
smaller than the typical inner rim radius of $\sim$0.1 au in CTTs measured
from interferometric observations in the NIR. This is consistent with the
results by Koutoulaki et al. (2019) who detected ro-vibrational emission of CO
in the NIR X-Shooter spectrum of RW Aur A. The modeling presented by these
latter authors of five band-heads shows that the CO emission comes from a
region at a distance of $\sim$0.06–0.08 au from the star.

##  6 Conclusions

In this pilot study, we report GIARPS@TNG high-resolution observations of
seven CTTs in the Taurus-Auriga star forming region, namely RY Tau, DG Tau, DL
Tau, HN Tau A, DO Tau, RW Aur A, and CQ Tau. The spectra simultaneously cover
a wide spectral range from the optical to the NIR. Contemporaneous
spectrophotometric and photometric observations were also performed, allowing
us to flux-calibrate the high-resolution spectra with an estimated accuracy of
$<$20%. We show that the GIARPS@TNG data, together with the ancillary
observations, allows the stellar and accretion parameters of YSOs to be
derived in a self-consistent and homogeneous way.

High-resolution spectroscopy was used to derive the veiling throughout the
wide spectral range. The impact of veiling on the estimates of extinction was
accounted for. Deriving extinction on the basis of well-flux-calibrated
spectral templates alone may lead to underestimation of $A_{\rm V}$ by up to
$\sim$30%, if veiling is neglected. Best matching the spectral type of
templates and YSOs reduces errors in the $A_{\rm V}$ estimates. Simultaneously
deriving veiling, stellar parameters, and $v\sin i$ avoids degeneracy, which
in turn allows more accurate stellar parameters to be obtained.

A large number of emission line diagnostics were used to calculate the
accretion luminosity in the seven CTTs via accretion luminosity versus line
luminosity relationships. We confirmed that the average $L_{\rm acc}$ derived
from several diagnostics measured simultaneously has a significantly reduced
error.

We therefore conclude that the GHOsT data sets and the procedures adopted here
yield more robust results on the stellar and accretion parameters than those
in previous studies of Taurus CTTs. However, in the case of extremely veiled
objects, our procedures may fail or provide uncertain results, although this
type of object is expected to be rare.

Assuming magnetospheric accretion, we calculated the mass accretion rate of
the CTTs in the sample, confirming the high-levels of accretion in these
objects. Being in its bright stage during the GIARPS observations, RW Aur A is
the most actively accreting object in this sample, which is consistent with
the high-accretion activity scenario by Takami et al. (2020). The apparently
least active objects in the sample are CQ Tau and HN Tau. We identify these
two objects as subluminous on the HR diagram, the former because of its UX
Ori-type variability and the latter because of the high inclination of its
disk. Correction for disk obscuration makes HN Tau one of the most actively
accreting objects in the sample, at a level close to RW Aur A.

A comparison of the accretion properties of the Taurus CTTs with those of
Lupus YSOs yields the following results: the Taurus CTTs have values of
$L_{\rm acc}$/$L_{\star}$ of between 0.3 and 1.5, which are normally higher
than those of the Lupus YSOs. The two Taurus objects classified as
transitional disks, namely RY Tau and CQ Tau, have values similar to those of
the Lupus transitional disks. The five CTTs with the highest $L_{\rm
acc}$/$L_{\star}$ ratios, namely DG Tau, DL Tau, HN Tau A, DO Tau, and RW Aur
A, tend to follow the upper envelope of the $\dot{M}_{\rm acc}$ – $M_{\star}$
relationship for the Lupus population, and have accretion rates comparable to
those of the strongest accretors in Lupus.

The NIR veiling increases with wavelength in all the studied CTTs. The
analysis of this behavior shows that these CTTs display a significant
continuum excess emission in the NIR. In some cases, such excess can be
ascribed to the thermal emission from the inner rim of the dusty disk, while
in others may be more compatible with emission from a thick gaseous disk
inside the dust sublimation radius. The origin of the jets studied in Paper I
is compatible with the latter possibility.

###### Acknowledgements.

We very much thank the anonymous referee for her/his comments and suggestions.
This work has been supported by PRIN-INAF-MAIN-STREAM 2017 ”Protoplanetary
disks seen through the eyes of new-generation instruments” and by PRIN-INAF
2019 ”Spectroscopically tracing the disk dispersal evolution (STRADE)”. We
warmly thank the GAPS team for sharing the solar spectrum acquired with
GIARPS, and the TNG personnel for their help during the observations. We
dedicate this work to Mr. G.Atusino, whose premature loss deeply saddened all
of us; for his immense presence, unconditional support and long-life great
friendship. This research made use of the SIMBAD database, operated at the CDS
(Strasbourg, France). This work has made use of data from the European Space
Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the
Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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##  Appendix A Measurements of continuum fluxes for the CTTs and templates

In Tables 7 to 13 we report the observed continuum fluxes for the CTTs and the
spectral templates adopted for the determination of the extinction according
to the methods described in Fischer et al. (2011). We define the quantity:

$\Gamma_{\lambda}\equiv
2.5\cdot\log{\rm[(1+r_{\lambda})\cdot\frac{F^{T}_{\lambda}}{F^{O}_{\lambda}}]},$
(3)

where ${\rm r_{\lambda}}$, ${\rm F^{T}_{\lambda}}$, and ${\rm
F^{O}_{\lambda}}$ are the veiling, the observed continuum flux of the spectral
template, and the observed continuum flux of the object, as a function of
wavelength, respectively. As mentioned in Sect. 3.3, the method is based on
the fact that

$\Gamma_{\lambda}={\rm(A_{v}^{O}-A_{v}^{T})\cdot\frac{\rm A_{\lambda}}{\rm
A_{v}}-2.5\cdot\log{C}},$ (4)

so that $\Gamma_{\lambda}$ is a lineaar function of $\frac{\rm
A_{\lambda}}{\rm A_{v}}$, where ${\rm A_{v}^{O}}$ and ${\rm A_{v}^{T}}$ are
the visual extinction of the the object and template, respectively, and $C$ is
a constant. The tables also provide $\Gamma_{\lambda}$ as a function of
wavelength and the rλ values are also included for convenience.

Table 7:  $\Gamma_{\lambda}$ versus Aλ/Av for RY Tau. Wavelength | Aλ/$A_{\rm V}$ | $F^{T}_{\lambda}$ | $F^{O}_{\lambda}$ | rλ | $\Gamma_{\lambda}$
---|---|---|---|---|---
(nm) |  | erg/s/cm2/nm | erg/s/cm2/nm |  |
450.0 | 1.169 | 1.70e-11 | 2.00e-12 | 0.0 | 2.324
500.0 | 1.080 | 2.10e-11 | 2.20e-12 | 0.0 | 2.449
550.0 | 0.990 | 2.10e-11 | 2.60e-12 | 0.0 | 2.268
600.0 | 0.900 | 1.90e-11 | 3.00e-12 | 0.0 | 2.004
650.0 | 0.820 | 1.80e-11 | 3.20e-12 | 0.0 | 1.875
968.0 | 0.450 | 8.60e-12 | 5.00e-12 | 0.2 | 0.787
983.0 | 0.430 | 8.40e-12 | 5.10e-12 | 0.6 | 1.052
1178.0 | 0.300 | 5.60e-12 | 5.30e-12 | 0.4 | 0.425
1256.0 | 0.264 | 4.90e-12 | 5.10e-12 | 0.7 | 0.533
1298.0 | 0.250 | 4.60e-12 | 4.90e-12 | 0.3 | 0.216
1565.0 | 0.178 | 2.90e-12 | 3.50e-12 | 0.5 | 0.236
1597.0 | 0.173 | 2.80e-12 | 3.30e-12 | 0.4 | 0.187
1666.0 | 0.163 | 2.40e-12 | 2.90e-12 | 0.5 | 0.235
1741.0 | 0.151 | 2.00e-12 | 2.40e-12 | 0.9 | 0.499
2130.0 | 0.114 | 1.00e-12 | 1.60e-12 | 1.4 | 0.440
2255.0 | 0.110 | 8.30e-13 | 2.20e-12 | 1.2 | 0.202
2322.0 | 0.100 | 7.50e-13 | 2.80e-12 | … | …
Table 8:  $\Gamma_{\lambda}$ versus Aλ/Av for DG Tau. Wavelength | Aλ/$A_{\rm V}$ | $F^{T}_{\lambda}$ | $F^{O}_{\lambda}$ | rλ | $\Gamma_{\lambda}$
---|---|---|---|---|---
(nm) |  | erg/s/cm2/nm | erg/s/cm2/nm |  |
450.0 | 1.169 | 4.20e-14 | 2.20e-13 | … | …
500.0 | 1.080 | 4.70e-14 | 2.40e-13 | … | …
550.0 | 0.990 | 6.90e-14 | 3.20e-13 | 2.0 | -0.473
600.0 | 0.900 | 7.70e-14 | 3.90e-13 | 1.5 | -0.767
650.0 | 0.820 | 8.60e-14 | 4.60e-13 | 1.0 | -1.068
968.0 | 0.450 | 1.00e-13 | 9.60e-13 | 1.6 | -1.418
983.0 | 0.430 | 9.00e-14 | 9.80e-13 | 1.2 | -1.736
1178.0 | 0.300 | 7.00e-14 | 1.10e-12 | 1.8 | -1.873
1256.0 | 0.264 | 6.70e-14 | 1.10e-12 | 1.4 | -2.088
1298.0 | 0.250 | 6.50e-14 | 1.10e-12 | 1.7 | -1.993
1565.0 | 0.178 | 5.50e-14 | 1.00e-12 | 1.8 | -2.031
1597.0 | 0.173 | 5.40e-14 | 9.90e-13 | 1.6 | -2.121
1666.0 | 0.163 | 5.10e-14 | 9.60e-13 | 1.7 | -2.108
1741.0 | 0.151 | 4.50e-14 | 9.30e-13 | 2.4 | -1.959
2130.0 | 0.114 | 2.70e-14 | 7.90e-13 | 3.0 | -2.161
2255.0 | 0.110 | 2.20e-14 | 7.70e-13 | 4.0 | -2.113
2322.0 | 0.100 | 2.00e-14 | 7.70e-13 | … | …
Table 9:  $\Gamma_{\lambda}$ versus Aλ/Av for DL Tau. Wavelength | Aλ/$A_{\rm V}$ | $F^{T}_{\lambda}$ | $F^{O}_{\lambda}$ | rλ | $\Gamma_{\lambda}$
---|---|---|---|---|---
(nm) |  | erg/s/cm2/nm | erg/s/cm2/nm |  |
450.0 | 1.169 | 6.10e-13 | 1.40e-13 | 3.0 | 3.103
500.0 | 1.080 | 6.20e-13 | 1.50e-13 | 2.5 | 2.901
550.0 | 0.990 | 8.90e-13 | 2.00e-13 | 2.0 | 2.814
600.0 | 0.900 | 9.00e-13 | 2.50e-13 | 1.5 | 2.386
650.0 | 0.820 | 9.60e-13 | 2.90e-13 | 1.5 | 2.295
968.0 | 0.450 | 9.50e-13 | 4.90e-13 | 1.1 | 1.524
983.0 | 0.430 | 1.00e-12 | 4.90e-13 | 1.1 | 1.580
1178.0 | 0.300 | 1.10e-12 | 4.70e-13 | 1.1 | 1.729
1256.0 | 0.264 | 1.00e-12 | 4.70e-13 | 1.0 | 1.572
1298.0 | 0.250 | 9.70e-13 | 4.60e-13 | 1.0 | 1.563
1565.0 | 0.178 | 8.60e-13 | 4.20e-13 | 0.9 | 1.475
1597.0 | 0.173 | 8.00e-13 | 4.10e-13 | 0.6 | 1.236
1666.0 | 0.163 | 7.80e-13 | 4.00e-13 | 0.8 | 1.363
1741.0 | 0.151 | 6.90e-13 | 3.90e-13 | 1.7 | 1.698
2130.0 | 0.114 | 3.70e-13 | 2.90e-13 | 2.5 | 1.625
2255.0 | 0.110 | 3.10e-13 | 2.60e-13 | 2.1 | 1.419
2322.0 | 0.100 | 2.70e-13 | 2.40e-13 | 2.5 | 1.488
Table 10:  $\Gamma_{\lambda}$ versus Aλ/Av for HN Tau A. Wavelength | Aλ/$A_{\rm V}$ | $F^{T}_{\lambda}$ | $F^{O}_{\lambda}$ | rλ | $\Gamma_{\lambda}$
---|---|---|---|---|---
(nm) |  | erg/s/cm2/nm | erg/s/cm2/nm |  |
450.0 | 1.169 | 7.50e-13 | 6.40e-14 | … | …
500.0 | 1.080 | 7.60e-13 | 7.40e-14 | 0.8 | 3.167
550.0 | 0.990 | 8.60e-13 | 8.80e-14 | 0.8 | 3.113
600.0 | 0.900 | 9.00e-13 | 1.00e-13 | 0.8 | 3.024
650.0 | 0.820 | 8.70e-13 | 1.10e-13 | 0.5 | 2.686
968.0 | 0.450 | 5.90e-13 | 1.50e-13 | … | …
983.0 | 0.430 | 5.80e-13 | 1.50e-13 | … | …
1178.0 | 0.300 | 4.60e-13 | 1.50e-13 | 1.1 | 2.022
1256.0 | 0.264 | 4.00e-13 | 1.40e-13 | 1.2 | 1.996
1298.0 | 0.250 | 3.80e-13 | 1.40e-13 | 1.5 | 2.079
1565.0 | 0.178 | 3.00e-13 | 1.40e-13 | 1.8 | 1.945
1597.0 | 0.173 | 2.90e-13 | 1.40e-13 | 1.6 | 1.828
1666.0 | 0.163 | 2.70e-13 | 1.30e-13 | 1.3 | 1.698
1741.0 | 0.151 | 2.20e-13 | 1.30e-13 | 2.3 | 1.867
2130.0 | 0.114 | 1.20e-13 | 1.30e-13 | 3.3 | 1.497
2255.0 | 0.110 | 1.00e-13 | 1.20e-13 | 5.0 | 1.747
2322.0 | 0.100 | 8.30e-14 | 1.20e-13 | … | …
Table 11:  $\Gamma_{\lambda}$ versus Aλ/Av for DO Tau. Wavelength | Aλ/$A_{\rm V}$ | $F^{T}_{\lambda}$ | $F^{O}_{\lambda}$ | rλ | $\Gamma_{\lambda}$
---|---|---|---|---|---
(nm) |  | erg/s/cm2/nm | erg/s/cm2/nm |  |
450.0 | 1.169 | 4.60e-14 | 1.50e-13 | 1.8 | -0.165
500.0 | 1.080 | 5.30e-14 | 1.60e-13 | 1.5 | -0.205
550.0 | 0.990 | 7.10e-14 | 1.80e-13 | 1.5 | -0.015
600.0 | 0.900 | 7.80e-14 | 2.10e-13 | 1.0 | -0.323
650.0 | 0.820 | 8.70e-14 | 2.30e-13 | 1.5 | -0.061
968.0 | 0.450 | 9.90e-14 | 5.00e-13 | 0.5 | -1.318
983.0 | 0.430 | 8.90e-14 | 5.10e-13 | 0.6 | -1.385
1178.0 | 0.300 | 7.10e-14 | 5.80e-13 | 0.7 | -1.704
1256.0 | 0.264 | 6.60e-14 | 6.00e-13 | 1.4 | -1.446
1298.0 | 0.250 | 6.40e-14 | 6.00e-13 | 1.4 | -1.479
1565.0 | 0.178 | 5.50e-14 | 6.10e-13 | 1.9 | -1.456
1597.0 | 0.173 | 5.50e-14 | 6.10e-13 | 1.7 | -1.534
1666.0 | 0.163 | 5.20e-14 | 6.00e-13 | 1.8 | -1.537
1741.0 | 0.151 | 4.70e-14 | 5.90e-13 | 2.1 | -1.518
2130.0 | 0.114 | 2.70e-14 | 4.90e-13 | 3.4 | -1.538
2255.0 | 0.110 | 2.10e-14 | 4.50e-13 | 3.7 | -1.647
2322.0 | 0.100 | 1.90e-14 | 4.30e-13 | 2.7 | -1.966
Table 12:  $\Gamma_{\lambda}$ versus Aλ/Av for RW Aur A. Wavelength | Aλ/$A_{\rm V}$ | $F^{T}_{\lambda}$ | $F^{O}_{\lambda}$ | rλ | $\Gamma_{\lambda}$
---|---|---|---|---|---
(nm) |  | erg/s/cm2/nm | erg/s/cm2/nm |  |
450.0 | 1.169 | 7.70e-13 | 2.20e-12 | … | …
500.0 | 1.080 | 7.50e-13 | 2.30e-12 | … | …
550.0 | 0.990 | 7.60e-13 | 2.20e-12 | 1.2 | -0.298
600.0 | 0.900 | 7.10e-13 | 2.20e-12 | … | …
650.0 | 0.820 | 6.70e-13 | 2.30e-12 | … | …
968.0 | 0.450 | 3.80e-13 | 1.80e-12 | … | …
983.0 | 0.430 | 3.70e-13 | 1.80e-12 | … | …
1178.0 | 0.300 | 2.60e-13 | 1.40e-12 | … | …
1256.0 | 0.264 | 2.30e-13 | 1.30e-12 | 1.5 | -0.886
1298.0 | 0.250 | 2.20e-13 | 1.30e-12 | … | …
1565.0 | 0.178 | 1.60e-13 | 1.00e-12 | … | …
1597.0 | 0.173 | 1.50e-13 | 1.00e-12 | 2.5 | -0.700
1666.0 | 0.163 | 1.30e-13 | 9.50e-13 | 2.7 | -0.739
1741.0 | 0.151 | 1.10e-13 | 9.10e-13 | 3.5 | -0.661
2130.0 | 0.114 | 5.50e-14 | 6.60e-13 | 3.6 | -1.041
2255.0 | 0.110 | 4.40e-14 | 5.70e-13 | 5.7 | -0.716
2322.0 | 0.100 | 3.70e-14 | 5.10e-13 | 5.4 | -0.833
Table 13:  $\Gamma_{\lambda}$ versus Aλ/Av for CQ Tau. Wavelength | Aλ/$A_{\rm V}$ | $F^{T}_{\lambda}$ | $F^{O}_{\lambda}$ | rλ | $\Gamma_{\lambda}$
---|---|---|---|---|---
(nm) |  | erg/s/cm2/nm | erg/s/cm2/nm |  |
450.0 | 1.169 | 7.90e-12 | 4.90e-12 | 0.0 | 0.519
500.0 | 1.080 | 7.00e-12 | 4.60e-12 | 0.0 | 0.456
550.0 | 0.990 | 6.00e-12 | 4.30e-12 | 0.0 | 0.362
600.0 | 0.900 | 5.30e-12 | 3.90e-12 | 0.0 | 0.333
650.0 | 0.820 | 4.50e-12 | 3.40e-12 | 0.0 | 0.304
968.0 | 0.450 | 1.90e-12 | 2.60e-12 | … | …
983.0 | 0.430 | 1.80e-12 | 2.50e-12 | 0.5 | 0.084
1178.0 | 0.300 | 1.10e-12 | 2.00e-12 | 1.0 | 0.103
1256.0 | 0.264 | 9.50e-13 | 1.90e-12 | 0.8 | -0.114
1298.0 | 0.250 | 8.60e-13 | 1.80e-12 | … | …..
1565.0 | 0.178 | 5.00e-13 | 1.50e-12 |  $<$3.0 |  $<$0.312
1597.0 | 0.173 | 4.80e-13 | 1.50e-12 | 2.0 | -0.044
1666.0 | 0.163 | 4.10e-13 | 1.50e-12 | … | …
1741.0 | 0.151 | 3.50e-13 | 1.40e-12 | … | …
2130.0 | 0.114 | 1.70e-13 | 1.20e-12 | … | …
2255.0 | 0.110 | 1.30e-13 | 1.10e-12 | … | …
2322.0 | 0.100 | 1.20e-13 | 1.10e-12 | … | …

##  Appendix B Individual fluxes, equivalent widths and $L_{\rm acc}$
estimates

Tables LABEL:tab:fluxes_EWs_Had to LABEL:tab:fluxes_EW_CaI3934 report the
observed fluxes, equivalent widths, for every CTTs in the sample, as well as
the corresponding $L_{\rm acc}$ values derived from the individual accretion
diagnostics and using the $L_{\rm acc}$–$L_{\rm line}$ relationships by Alcalá
et al. (2017).

Table 14:  Measured fluxes and equivalent widths of Balmer lines and accretion luminosity for the CTTs sample: H$\alpha$ (H3) to H$\delta$ (H6). Object | $f_{\rm H\alpha}$ | $EW_{\rm H\alpha}$ | $f_{\rm H\beta}$ | $EW_{\rm H\beta}$ | $f_{\rm H\gamma}$ | $EW_{\rm H\gamma}$ | $f_{\rm H\delta}$ | $EW_{\rm H\delta}$
---|---|---|---|---|---|---|---|---
| (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å)
RY Tau | 4.78($\pm$0.22)e$-$12 |  $-$14.49$\pm$0.54 | 3.30($\pm$0.56)e$-$13 |  $-$1.72$\pm$0.13 | 2.44($\pm$0.30)e$-$13 |  $-$1.36$\pm$0.20 | 1.54($\pm$0.46)e$-$13 |  $-$0.95$\pm$0.14
DG Tau | 6.30($\pm$0.09)e$-$12 |  $-$108.43$\pm$7.28 | 1.01($\pm$0.06)e$-$12 |  $-$43.72$\pm$8.80 | 5.02($\pm$0.35)e$-$13 |  $-$33.92$\pm$8.01 | 3.20($\pm$0.27)e$-$13 |  $-$24.81$\pm$6.66
DL Tau | 3.19($\pm$0.06)e$-$12 |  $-$91.93$\pm$6.09 | 5.41($\pm$0.30)e$-$13 |  $-$39.20$\pm$6.85 | 3.73($\pm$0.33)e$-$13 |  $-$33.30$\pm$9.29 | 2.65($\pm$0.21)e$-$13 |  $-$30.15$\pm$7.32
HN Tau A | 1.42($\pm$0.02)e$-$12 |  $-$113.60$\pm$7.57 | 2.39($\pm$0.10)e$-$13 |  $-$32.39$\pm$4.53 | 1.36($\pm$0.13)e$-$13 |  $-$25.86$\pm$6.27 | 9.25($\pm$0.96)e$-$14 |  $-$19.64$\pm$5.24
DO Tau | 1.92($\pm$0.07)e$-$17 |  $-$64.87$\pm$6.99 | 3.10($\pm$0.29)e$-$13 |  $-$19.87$\pm$4.51 | 2.03($\pm$0.39)e$-$13 |  $-$12.69$\pm$8.19 | 1.51($\pm$0.39)e$-$13 |  $-$10.13$\pm$8.38
RW Aur A | 1.74($\pm$0.02)e$-$11 |  $-$69.88$\pm$2.47 | 2.28($\pm$0.20)e$-$12 |  $-$10.18$\pm$1.29 | … | … | … | …
CQ Tau | 2.29($\pm$0.18)e$-$12 |  $-$7.53$\pm$0.42 | 3.09($\pm$0.45)e$-$13 |  $-$0.83$\pm$0.17 | 2.18($\pm$0.29)e$-$13 |  $-$0.56$\pm$0.32 | 1.29($\pm$0.31)e$-$13 |  $-$0.29$\pm$0.10
Object |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$
| ${\rm H\alpha}$ | (dex) | ${\rm H\beta}$ | (dex) | ${\rm H\gamma}$ | (dex) | ${\rm H\delta}$ | (dex)
RY Tau |  $-$0.33 | 0.15 |  $-$0.51 | 0.18 |  $-$0.38 | 0.15 |  $-$0.49 | 0.21
DG Tau |  $-$0.45 | 0.15 |  $-$0.29 | 0.16 |  $-$0.38 | 0.14 |  $-$0.50 | 0.16
DL Tau |  $-$0.67 | 0.16 |  $-$0.52 | 0.16 |  $-$0.46 | 0.15 |  $-$0.53 | 0.16
HN Tau A |  $-$1.23 | 0.17 |  $-$1.08 | 0.17 |  $-$1.10 | 0.16 |  $-$1.17 | 0.18
DO Tau |  $-$0.98 | 0.17 |  $-$0.84 | 0.17 |  $-$0.78 | 0.17 |  $-$0.82 | 0.21
RW Aur A |  $-$0.29 | 0.14 |  $-$0.38 | 0.16 | … | … | … | …
CQ Tau |  $-$1.20 | 0.17 |  $-$1.29 | 0.17 |  $-$1.23 | 0.17 |  $-$1.37 | 0.21
Table 15:  Measured fluxes and equivalent widths of Paschen lines and accretion luminosity for the CTTs sample: Pa$\beta$ (Pa5) to Pa$\epsilon$ (Pa8). Object | $f_{\rm Pa\beta}$ | $EW_{\rm Pa\beta}$ | $f_{\rm Pa\gamma}$ | $EW_{\rm Pa\gamma}$ | $f_{\rm Pa\delta}$ | $EW_{\rm Pa\delta}$ | $f_{\rm Pa\epsilon}$ | $EW_{\rm Pa\epsilon}$
---|---|---|---|---|---|---|---|---
| (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å)
RY Tau | 1.20($\pm$0.08)e$-$12 |  $-$2.66$\pm$0.32 | 4.92($\pm$1.16)e$-$13 |  $-$1.05$\pm$0.35 | 3.71($\pm$0.71)e$-$13 |  $-$0.80$\pm$0.22 | … | …
DG Tau | 1.98($\pm$0.07)e$-$12 |  $-$18.50$\pm$0.98 | 1.40($\pm$0.02)e$-$12 |  $-$13.33$\pm$0.83 | 1.00($\pm$0.06)e$-$12 |  $-$10.15$\pm$0.89 | 8.01($\pm$1.01)e$-$13 |  $-$7.93$\pm$1.67
DL Tau | 1.03($\pm$0.07)e$-$12 |  $-$22.01$\pm$2.15 | 6.86($\pm$0.53)e$-$13 |  $-$14.29$\pm$1.67 | 5.37($\pm$0.06)e$-$13 |  $-$10.76$\pm$1.72 | 4.35($\pm$0.81)e$-$13 |  $-$8.19$\pm$2.43
HN Tau A | 2.28($\pm$0.12)e$-$13 |  $-$16.06$\pm$1.26 | 1.52($\pm$0.17)e$-$13 |  $-$10.41$\pm$1.56 | 9.80($\pm$2.40)e$-$14 |  $-$6.67$\pm$2.13 | … | …
DO Tau | 3.97($\pm$0.33)e$-$13 |  $-$6.64$\pm$0.75 | 2.16($\pm$0.27)e$-$13 |  $-$3.85$\pm$0.65 | 1.42($\pm$0.03)e$-$13 |  $-$2.80$\pm$0.76 | … | …
RW Aur A | 2.80($\pm$0.10)e$-$12 |  $-$21.37$\pm$1.24 | 1.91($\pm$0.11)e$-$12 |  $-$12.99$\pm$1.12 | 1.80($\pm$0.15)e$-$12 |  $-$10.71$\pm$1.26 | 1.13($\pm$0.25)e$-$12 |  $-$6.46$\pm$1.88
CQ Tau | 3.02($\pm$0.40)e$-$13 |  $-$1.66$\pm$0.38 | … | … | … | … | … | …
Object |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$
| ${\rm Pa\beta}$ | (dex) | ${\rm Pa\gamma}$ | (dex) | ${\rm Pa\delta}$ | (dex) | ${\rm Pa\epsilon}$ | (dex)
RY Tau |  $-$0.36 | 0.24 |  $-$0.45 | 0.27 |  $-$0.31 | 0.34 | … | …
DG Tau |  $-$0.25 | 0.23 |  $-$0.05 | 0.22 |  $+$0.04 | 0.30 |  $-$0.18 | 0.40
DL Tau |  $-$0.36 | 0.23 |  $-$0.22 | 0.23 |  $-$0.08 | 0.31 |  $-$0.30 | 0.41
HN Tau A |  $-$1.22 | 0.28 |  $-$1.22 | 0.27 |  $-$1.17 | 0.40 | … | …
DO Tau |  $-$0.91 | 0.27 |  $-$1.00 | 0.26 |  $-$0.90 | 0.38 | … | …
RW Aur A |  $+$0.19 | 0.21 |  $+$0.36 | 0.21 |  $+$0.56 | 0.28 |  $+$0.16 | 0.38
CQ Tau |  $-$1.08 | 0.28 | … | … | … | … | … | …
Table 16:  Measured fluxes and equivalent widths of He i lines and accretion luminosity for the CTTs sample: He i4026 to He i4922. Object | $f_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 4026}$ | $EW_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 4026}$ | $f_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 4471}$ | $EW_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 4471}$ | $f_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 4713}$ | $EW_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 4713}$ | $f_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 4922}$ | $EW_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 4922}$
---|---|---|---|---|---|---|---|---
| (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å)
RY Tau | 1.02($\pm$0.51)e$-$14 |  $-$0.07$\pm$0.06 | … | … | … | … | 5.28($\pm$2.56)e$-$14 |  $-$0.25$\pm$0.05
DG Tau | 3.89($\pm$3.08)e$-$14 |  $-$3.98$\pm$1.56 | 9.36($\pm$0.90)e$-$14 |  $-$5.23$\pm$0.75 | … | … | … | …
DL Tau | 4.54($\pm$2.60)e$-$14 |  $-$12.04$\pm$1.15 | 6.99($\pm$3.52)e$-$14 |  $-$6.59$\pm$3.30 | 1.35($\pm$1.07)e$-$14 |  $-$1.18$\pm$1.00 | 9.19($\pm$1.86)e$-$14 |  $-$6.81$\pm$2.28
HN Tau A | 1.61($\pm$0.74)e$-$14 |  $-$4.51$\pm$3.50 | 2.73($\pm$0.89)e$-$14 |  $-$5.35$\pm$2.47 | … | … | 3.70($\pm$1.04)e$-$14 |  $-$5.55$\pm$2.26
DO Tau | 1.22($\pm$0.43)e$-$14 |  $-$1.27$\pm$0.82 | 2.93($\pm$0.69)e$-$14 |  $-$1.83$\pm$0.80 | 7.47($\pm$5.83)e$-$15 |  $-$0.56$\pm$0.50 | 4.08($\pm$1.23)e$-$14 |  $-$3.00$\pm$1.43
RW Aur A | 5.41($\pm$1.63)e$-$13 |  $-$2.79$\pm$0.99 | 4.48($\pm$1.99)e$-$13 |  $-$2.18$\pm$1.13 | 1.71($\pm$0.35)e$-$13 |  $-$0.85$\pm$0.18 | 8.33($\pm$1.20)e$-$13 |  $-$3.97$\pm$0.81
CQ Tau | … | … | … | … | … | … | … | …
Object |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$
| ${{He\textsc{i}}\leavevmode\nobreak\ \lambda 4026}$ | (dex) | ${{He\textsc{i}}\leavevmode\nobreak\ \lambda 4471}$ | (dex) | ${{He\textsc{i}}\leavevmode\nobreak\ \lambda 4713}$ | (dex) | ${{He\textsc{i}}\leavevmode\nobreak\ \lambda 4922}$ | (dex)
RY Tau |  $-$0.64 | 0.30 | … | … | … | … |  $-$0.33 | 0.27
DG Tau |  $-$0.37 | 0.41 |  $-$0.20 | 0.18 | … | … | … | …
DL Tau |  $-$0.25 | 0.32 |  $-$0.27 | 0.29 |  $-$0.73 | 0.46 |  $-$0.32 | 0.19
HN Tau A |  $-$0.87 | 0.29 |  $-$0.85 | 0.25 | … | … |  $-$0.84 | 0.22
DO Tau |  $-$0.87 | 0.26 |  $-$0.70 | 0.22 |  $-$0.98 | 0.46 |  $-$0.70 | 0.22
RW Aur A |  $+$0.61 | 0.21 |  $+$0.34 | 0.26 |  $+$0.04 | 0.31 |  $+$0.42 | 0.16
CQ Tau | … | … | … | … | … | … | … | …
Table 17:  Measured fluxes and equivalent widths of He i lines and accretion luminosity for the CTTs sample: He i5016 to He i10830. Object | $f_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 5016}$ | $EW_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 5016}$ | $f_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 5876}$ | $EW_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 5876}$ | $f_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 6678}$ | $EW_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 6678}$ | $f_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 10830}$ | $EW_{\rm{He\textsc{i}}\leavevmode\nobreak\ \lambda 10830}$
---|---|---|---|---|---|---|---|---
| (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å) | (erg s-1 cm-2) | (Å)
RY Tau | … | … | 1.24($\pm$0.29)e$-$13 |  $-$0.45$\pm$0.10 | 2.09($\pm$0.59)e$-14$ |  $-$0.07$\pm$0.05 | 1.02($\pm$0.10)e$-$12 |  $-$0.25$\pm$0.02
DG Tau | … | … | 1.27($\pm$0.16)e$-$13 |  $-$3.57$\pm$0.61 | 5.84($\pm$3.57)e$-14$ |  $-$1.17$\pm$0.78 | 1.65($\pm$0.07)e$-$12 |  $-$1.70$\pm$0.15
DL Tau | 2.55($\pm$0.45)e$-$14 |  $-$1.84$\pm$0.56 | 1.52($\pm$0.18)e$-$13 |  $-$6.55$\pm$1.12 | 5.98($\pm$3.40)e$-14$ |  $-$2.06$\pm$1.34 | 1.21($\pm$0.06)e$-$12 |  $-$2.49$\pm$0.22
HN Tau A | 1.29($\pm$0.23)e$-$14 |  $-$1.88$\pm$0.45 | 4.23($\pm$0.99)e$-$14 |  $-$4.76$\pm$1.44 | 1.62($\pm$0.94)e$-14$ |  $-$1.53$\pm$0.98 | 3.78($\pm$0.21)e$-$13 |  $-$2.61$\pm$0.25
DO Tau | 7.44($\pm$1.67)e$-$15 |  $-$0.55$\pm$0.18 | 6.31($\pm$0.72)e$-$14 |  $-$3.02$\pm$0.57 | 2.59($\pm$0.33)e$-14$ |  $-$1.00$\pm$0.18 | 2.04($\pm$0.16)e$-$13 |  $-$0.59$\pm$0.08
RW Aur A | 7.22($\pm$0.72)e$-$13 |  $-$3.20$\pm$0.40 | 5.00($\pm$0.56)e$-$13 |  $-$2.33$\pm$0.31 | 4.72($\pm$0.83)e$-13$ |  $-$2.21$\pm$0.45 | 3.00($\pm$0.24)e$-$12 |  $-$1.91$\pm$0.21
CQ Tau | … | … | 5.97($\pm$1.70)e$-$14 |  $-$0.15$\pm$0.05 | 8.63($\pm$4.58)e$-15$ |  $-$0.03$\pm$0.02 | 4.92($\pm$0.67)e$-$13 |  $-$0.22$\pm$0.04
Object |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$
| ${{He\textsc{i}}\leavevmode\nobreak\ \lambda 5016}$ | (dex) | ${{He\textsc{i}}\leavevmode\nobreak\ \lambda 5876}$ | (dex) | ${{He\textsc{i}}\leavevmode\nobreak\ \lambda 6678}$ | (dex) | ${{He\textsc{i}}\leavevmode\nobreak\ \lambda 10830}$ | (dex)
RY Tau | … | … |  $-$0.14 | 0.21 |  $-$0.57 | 0.32 |  $-$0.63 | 0.38
DG Tau | … | … |  $-$0.42 | 0.19 |  $-$0.29 | 0.43 |  $-$0.54 | 0.36
DL Tau |  $-$0.54 | 0.21 |  $-$0.22 | 0.19 |  $-$0.13 | 0.41 |  $-$0.50 | 0.36
HN Tau A |  $-$0.97 | 0.22 |  $-$1.03 | 0.23 |  $-$1.02 | 0.44 |  $-$1.24 | 0.43
DO Tau |  $-$1.10 | 0.23 |  $-$0.72 | 0.20 |  $-$0.66 | 0.30 |  $-$1.47 | 0.46
RW Aur A |  $+$0.71 | 0.16 |  $+$0.19 | 0.18 |  $+$0.83 | 0.25 |  $-$0.02 | 0.33
CQ Tau | … | … |  $-$1.11 | 0.25 |  $-$1.58 | 0.43 |  $-$1.13 | 0.42
Table 18:  Measured fluxes and equivalent widths of the ${Ca\textsc{i}}\leavevmode\nobreak\ \lambda 3934$ line and accretion luminosity for the CTTs sample. Object | $f_{\rm{Ca\textsc{i}}\leavevmode\nobreak\ \lambda 3934}$ | $EW_{\rm{Ca\textsc{i}}\leavevmode\nobreak\ \lambda 3934}$ |  $\log$($L_{\rm acc}$/$L_{\odot}$) | $\pm\sigma$
---|---|---|---|---
| (erg s-1 cm-2) | (Å) | ${\rm{Ca\textsc{i}}\leavevmode\nobreak\ \lambda 3934}$ | (dex)
RY Tau | 2.57($\pm$0.29)e$-$13 | -6.61$\pm$2.97 |  $-$0.26 | 0.16
DG Tau | 7.45($\pm$0.72)e$-$13 | -40.05$\pm$16.00 |  $-$0.12 | 0.15
DL Tau | 2.43($\pm$0.39)e$-$13 | -56.38$\pm$15.00 |  $-$0.57 | 0.17
HN Tau A | 3.29($\pm$0.49)e$-$13 | -94.81$\pm$25.50 |  $-$0.58 | 0.17
DO Tau | 2.14($\pm$0.49)e$-$13 | -25.94$\pm$10.40 |  $-$0.66 | 0.19
RW Aur A | 2.72($\pm$0.33)e$-$12 | -13.27$\pm$2.86 |  $+$0.24 | 0.15
CQ Tau | 3.30($\pm$0.64)e$-$13 | -2.71$\pm$0.70 |  $-$0.95 | 0.19