11institutetext: European Southern Observatory, Karl-Schwarzschild-Strasse 2,
85748 Garching bei München, Germany
11email<EMAIL_ADDRESS>22institutetext: INAF - Osservatorio Astrofisico di
Catania, via S. Sofia, 78, 95123 Catania, Italy 33institutetext: School of
Cosmic Physics, Dublin Institute for Advanced Studies, 31 Fitzwilliam Place,
Dublin 2, Ireland 44institutetext: INAF – Osservatorio Astronomico di
Capodimonte, via Moiariello 16, 80131 Napoli, Italy 55institutetext: Purple
Mountain Observatory, Chinese Academy of Sciences, 10 Yuanhua Road,
Nanjing210023, China 66institutetext: University of Science and Technology of
China, Hefei 230026, China 77institutetext: Center for Astrophysics, Harvard &
Smithsonian, 60 Garden Street, Cambridge, MA 02138-1516, USA 88institutetext:
Institut für Astronomie und Astrophysik, Eberhard Karls Universität Tübingen,
Sand 1, 72076 Tübingen, Germany 99institutetext: SETI Institute, 339 Bernardo
Ave., Suite 200, Mountain View, CA 94043, USA 1010institutetext: Institute of
Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

# FitteR for Accretion ProPErties of T Tauri stars (FRAPPE):
A new approach to use Class III spectra to derive
stellar and accretion properties††thanks: Based on observations collected at
the European Southern Observatory under ESO programmes 085.C-0764(A),
093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001,
110.23P2.001

R.A.B. Claes FitteR for Accretion ProPErties of T Tauri stars (FRAPPE): A new
approach to use Class III spectra to derive stellar and accretion
properties††thanks: Based on observations collected at the European Southern
Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004,
106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for Accretion
ProPErties of T Tauri stars (FRAPPE): A new approach to use Class III spectra
to derive stellar and accretion properties††thanks: Based on observations
collected at the European Southern Observatory under ESO programmes
085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008,
109.23D4.001, 110.23P2.001 J. Campbell-White FitteR for Accretion ProPErties
of T Tauri stars (FRAPPE): A new approach to use Class III spectra to derive
stellar and accretion properties††thanks: Based on observations collected at
the European Southern Observatory under ESO programmes 085.C-0764(A),
093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001,
110.23P2.001FitteR for Accretion ProPErties of T Tauri stars (FRAPPE): A new
approach to use Class III spectra to derive stellar and accretion
properties††thanks: Based on observations collected at the European Southern
Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004,
106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001 C.F. Manara FitteR for
Accretion ProPErties of T Tauri stars (FRAPPE): A new approach to use Class
III spectra to derive stellar and accretion properties††thanks: Based on
observations collected at the European Southern Observatory under ESO
programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006,
106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for Accretion ProPErties of T
Tauri stars (FRAPPE): A new approach to use Class III spectra to derive
stellar and accretion properties††thanks: Based on observations collected at
the European Southern Observatory under ESO programmes 085.C-0764(A),
093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001,
110.23P2.001 A. Frasca FitteR for Accretion ProPErties of T Tauri stars
(FRAPPE): A new approach to use Class III spectra to derive stellar and
accretion properties††thanks: Based on observations collected at the European
Southern Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A),
106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for
Accretion ProPErties of T Tauri stars (FRAPPE): A new approach to use Class
III spectra to derive stellar and accretion properties††thanks: Based on
observations collected at the European Southern Observatory under ESO
programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006,
106.20Z8.008, 109.23D4.001, 110.23P2.001 A. Natta FitteR for Accretion
ProPErties of T Tauri stars (FRAPPE): A new approach to use Class III spectra
to derive stellar and accretion properties††thanks: Based on observations
collected at the European Southern Observatory under ESO programmes
085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008,
109.23D4.001, 110.23P2.001FitteR for Accretion ProPErties of T Tauri stars
(FRAPPE): A new approach to use Class III spectra to derive stellar and
accretion properties††thanks: Based on observations collected at the European
Southern Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A),
106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001 J.M.
Alcalá FitteR for Accretion ProPErties of T Tauri stars (FRAPPE): A new
approach to use Class III spectra to derive stellar and accretion
properties††thanks: Based on observations collected at the European Southern
Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004,
106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for Accretion
ProPErties of T Tauri stars (FRAPPE): A new approach to use Class III spectra
to derive stellar and accretion properties††thanks: Based on observations
collected at the European Southern Observatory under ESO programmes
085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008,
109.23D4.001, 110.23P2.001
A. Armeni FitteR for Accretion ProPErties of T Tauri stars (FRAPPE): A new
approach to use Class III spectra to derive stellar and accretion
properties††thanks: Based on observations collected at the European Southern
Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004,
106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for Accretion
ProPErties of T Tauri stars (FRAPPE): A new approach to use Class III spectra
to derive stellar and accretion properties††thanks: Based on observations
collected at the European Southern Observatory under ESO programmes
085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008,
109.23D4.001, 110.23P2.001 M. Fang FitteR for Accretion ProPErties of T Tauri
stars (FRAPPE): A new approach to use Class III spectra to derive stellar and
accretion properties††thanks: Based on observations collected at the European
Southern Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A),
106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for
Accretion ProPErties of T Tauri stars (FRAPPE): A new approach to use Class
III spectra to derive stellar and accretion properties††thanks: Based on
observations collected at the European Southern Observatory under ESO
programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006,
106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for Accretion ProPErties of T
Tauri stars (FRAPPE): A new approach to use Class III spectra to derive
stellar and accretion properties††thanks: Based on observations collected at
the European Southern Observatory under ESO programmes 085.C-0764(A),
093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001,
110.23P2.001FitteR for Accretion ProPErties of T Tauri stars (FRAPPE): A new
approach to use Class III spectra to derive stellar and accretion
properties††thanks: Based on observations collected at the European Southern
Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004,
106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001 J.B. Lovell FitteR for
Accretion ProPErties of T Tauri stars (FRAPPE): A new approach to use Class
III spectra to derive stellar and accretion properties††thanks: Based on
observations collected at the European Southern Observatory under ESO
programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006,
106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for Accretion ProPErties of T
Tauri stars (FRAPPE): A new approach to use Class III spectra to derive
stellar and accretion properties††thanks: Based on observations collected at
the European Southern Observatory under ESO programmes 085.C-0764(A),
093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001,
110.23P2.001 B. Stelzer FitteR for Accretion ProPErties of T Tauri stars
(FRAPPE): A new approach to use Class III spectra to derive stellar and
accretion properties††thanks: Based on observations collected at the European
Southern Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A),
106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for
Accretion ProPErties of T Tauri stars (FRAPPE): A new approach to use Class
III spectra to derive stellar and accretion properties††thanks: Based on
observations collected at the European Southern Observatory under ESO
programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006,
106.20Z8.008, 109.23D4.001, 110.23P2.001 L. Venuti FitteR for Accretion
ProPErties of T Tauri stars (FRAPPE): A new approach to use Class III spectra
to derive stellar and accretion properties††thanks: Based on observations
collected at the European Southern Observatory under ESO programmes
085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008,
109.23D4.001, 110.23P2.001FitteR for Accretion ProPErties of T Tauri stars
(FRAPPE): A new approach to use Class III spectra to derive stellar and
accretion properties††thanks: Based on observations collected at the European
Southern Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A),
106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001 M. Wyatt
FitteR for Accretion ProPErties of T Tauri stars (FRAPPE): A new approach to
use Class III spectra to derive stellar and accretion properties††thanks:
Based on observations collected at the European Southern Observatory under ESO
programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006,
106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for Accretion ProPErties of T
Tauri stars (FRAPPE): A new approach to use Class III spectra to derive
stellar and accretion properties††thanks: Based on observations collected at
the European Southern Observatory under ESO programmes 085.C-0764(A),
093.C-0506(A), 106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001,
110.23P2.001 A. Queitsch FitteR for Accretion ProPErties of T Tauri stars
(FRAPPE): A new approach to use Class III spectra to derive stellar and
accretion properties††thanks: Based on observations collected at the European
Southern Observatory under ESO programmes 085.C-0764(A), 093.C-0506(A),
106.20Z8.004, 106.20Z8.006, 106.20Z8.008, 109.23D4.001, 110.23P2.001FitteR for
Accretion ProPErties of T Tauri stars (FRAPPE): A new approach to use Class
III spectra to derive stellar and accretion properties††thanks: Based on
observations collected at the European Southern Observatory under ESO
programmes 085.C-0764(A), 093.C-0506(A), 106.20Z8.004, 106.20Z8.006,
106.20Z8.008, 109.23D4.001, 110.23P2.001

###### Abstract

Context. Studies of the stellar and accretion properties of classical T Tauri
stars (CTTS) require comparison with photospheric spectral templates. The use
of low-activity, slowly-rotating field dwarfs or model spectra can be
advantageous for the determination of stellar parameters, but it can lead to
an overestimate of mass accretion rate, since both classes of templates do not
include the emission of the active chromosphere present in young stars.
Observed spectra of non-accreting young stars are best suited to this purpose.
Using such templates comes with the downside of a limited number of available
templates and observational uncertainties on the properties of the templates.

Aims. Here we aim at expanding the currently available grid of wide-wavelength
coverage observed spectra of non-accreting stars with additional new spectra
and an interpolation method that allows us to obtain a continuous grid of low
resolution spectra ranging from spectral type G8 to M9.5, while also
mitigating observational uncertainties. This interpolated grid is then
implemented in the self-consistent method to derive stellar and accretion
properties of CTTS. With the new templates, we aim to estimate a lower limit
on the accretion luminosities that can be obtained through a study of the UV
excess emission using observed templates.

Methods. We analyse the molecular photospheric features present in the
VLT/X-Shooter spectra of the targets to perform a spectral classification,
including estimates of their extinction.

We apply a non-parametric fitting method to the full grid of observed
templates to obtain an interpolated grid of templates. Both the individual
templates and interpolated grid are provided to the community. We implement
this grid to improve the method to self-consistently derive stellar and
accretion properties of accreting stars. We use the uncertainties on our
interpolated grid to estimate a lower limit on the accretion luminosity that
we can measure with this method.

Results. Our new method, which uses a continuous grid of templates, provides
results that are consistent with using individual templates but it
significantly improves the reliability of the results in case of degeneracies
associated to the peculiarities of individual observed templates. We find that
the measurable accretion luminosities ranges from $\sim 2.7$ dex lower than
the stellar luminosity in M5.5 stars to $\sim 1.3$ dex lower for G8 stars. For
young stars with masses of $\sim 1M_{\odot}$ and ages of 3-6 Myr this limit
translates into an observational limit of mass accretion rate on the order of
$10^{-10}\rm M_{\odot}/yr$. This limit is higher than the lower limit on the
measurable mass accretion rate when using the various emission lines present
in the spectra of young stars to estimate the accretion rate. An analysis of
these emission lines allows us to probe lower accretion rates, pending a
revised calibration of the relationships between line and accretion
luminosities at low accretion rates

Conclusions. The implementation of an interpolated grid of observed templates
allows us to better disentangle degenerate solutions, leading to a more
reliable estimate of accretion rates in young accreting stars.

###### Key Words.:

Accretion, accretion disks - Protoplanetary disks - Stars: pre-main sequence -
Stars: variables: T Tauri, Herbig Ae/Be

##  1 Introduction

Young stars are surrounded by circumstellar disks in which planets form (e.g.,
Williams & Cieza 2011). These disks dissipate in a few Myr (e.g., Fedele et
al. 2010). The processes governing their evolution and dispersal, and their
impact on planet formation remain open questions (e.g., Manara et al. 2023,
for a review). The first proposed mechanism involves the gradual spread of the
disk due to viscosity, resulting in most of the material accreting onto the
central star, with a small fraction of material carrying the angular momentum
outward (Lynden-Bell & Pringle 1974; Hartmann et al. 1998). An alternative
scenario sees the evolution dominated by the ejection of angular momentum from
the disk in MHD winds (Blandford & Payne 1982; Lesur 2021b, a; Tabone et al.
2022). At the same time, high-energy radiation from the star, such as far-
ultraviolet (FUV), extreme ultraviolet (EUV), or X-ray radiation, removes
material from the inner disk in the form of photoevaporative winds. This
process may potentially create a gap in the inner disk and ultimately lead to
the dissipation of the disk (e.g., Clarke et al. 2001; Alexander et al. 2014;
Ercolano & Pascucci 2017). Understanding the impact of viscosity, MHD winds
and internal photoevaporation is critical for our understanding planet
formation. Indeed, while these processes are ongoing, the dust grains present
in the disks are expected to grow from small grains into planetesimals (e.g.;
Johansen et al. 2007; Booth & Clarke 2016; Carrera et al. 2017, 2021). These
planetesimals can further grow into planetary systems (e.g.; Alibert et al.
2005; Liu et al. 2019; Lyra et al. 2023), or may be revealed in the form of
collisionally active debris disks once the gas in the disk has dissipated
(e.g.; Wyatt 2008; Hughes et al. 2018; Lovell et al. 2021).

Each of these disk evolution mechanisms makes specific predictions about the
time evolution of accretion rates through the disk, and thus on the central
star. Determining the mass accretion rate of young stars is therefore a key
parameter to shed light on whether viscous or MHD-wind driven evolution
dominates disk evolution and which role photevaporation plays in dissipating
the disk (e.g., Mulders et al. 2017; Lodato et al. 2017; Somigliana et al.
2020, 2023).

Numerous studies attempted to constrain disk evolution by analyzing
theoretically expected and observed relationships between mass accretion rate
and stellar or disk properties, such as disk and stellar mass (e.g., Dullemond
et al. 2006; Hartmann et al. 2006; Alexander et al. 2006; Ercolano et al.
2014; Mulders et al. 2017; Rosotti et al. 2017; Manara et al. 2020). Currently
no definitive conclusions have been drawn in favor of either model.

Recently, Alexander et al. (2023) showed that the distribution of $\gtrsim
300$ homogeneous accretion rate measurements of young stars in the $0.5-1.0$
$M_{\odot}$ range should suffice to distinguish between a
viscous+photoevaporation and a MHD-wind driven disk evolution scenario.
Currently, only $\sim 100$ accretion rate measurements are available in this
mass range, and this sample lacks homogeneous upper limits for the non
detections. Providing such upper limits could enable even stronger statistical
approaches to further constrain model parameters. Ercolano et al. (2023) used
the accretion rate distribution of a sample of potential extreme low accretors
presented by Thanathibodee et al. (2022, 2023) to discern between different
types of photoevaporation that could dissipate the disk at the end of a
viscously driven evolution scenario. This sample was limited as it only
contained 24 sources. A thorough characterisation of more low accretors can
therefore provide valuable constraints on disk evolution processes.

Tracers of the accretion and outflow processes can be found in the spectra of
young stars. The current paradigm for accretion in young, low-mass ($\lesssim
1$ $M_{\odot}$) stars is known as magnetospheric accretion (Hartmann et al.
2016, for a review). In this scenario, accreting material is funneled by the
star’s magnetosphere onto its surface, creating hotspots that emit excess
continuum radiation in the ultraviolet and optical spectra (Calvet & Gullbring
1998). The hot gas associated with the accretion streamers leads to the
appearance of various prominent emission lines (e.g., $\rm H\alpha$, $\rm
H\beta$ Ca K, $\rm Pa\beta$,…) in the spectra (e.g., Muzerolle et al. 2001a;
Campbell-White et al. 2021).

The spectroscopic study of young stars can, therefore, provide vital
constraints on the physics governing disk evolution. Accurately representing
the emission from the central star is crucial in these investigations. Several
methods are employed to estimate accretion rates in young stars. As a first
option one can fit the line profile using magnetospheric accretion flow models
(Muzerolle et al. 2001b; Thanathibodee et al. 2023). The downside of these
models is that they assume the stellar magnetic field to be both dipolar,
aligned with the stellar rotation axis and disk, which is not necessarily
accurate (e.g., Donati et al. 2008; Alencar et al. 2012; Singh et al. 2024).
In a second method, the line luminosity of various emission lines is converted
into an accretion luminosity using empirical relations (e.g., Herczeg &
Hillenbrand 2008; Alcalá et al. 2014, 2017). These relations are calibrated
using the third method which is the only one that directly probes the energy
released at the accretion shock. This method consists of measuring the UV
continuum excess emission (e.g., Valenti et al. 1993; Calvet et al. 2004;
Herczeg & Hillenbrand 2008; Rigliaco et al. 2012; Ingleby et al. 2013; Pittman
et al. 2022; Robinson et al. 2022). In order to self-consistently determine
both the stellar and accretion parameters, the UV-excess and the spectral
features in the optical part of medium-resolution flux-calibrated spectra must
be fit simultaneously (Manara et al. 2013a). For this aim, both the
photospheric and chromospheric emission in the UV part of the spectrum must be
correctly accounted for (Ingleby et al. 2011a; Manara et al. 2013b).

Available synthetic spectra (e.g., Allard et al. 2011) do not fully reproduce
the observed spectra of chromospherically active low gravity objects, such as
pre-main sequence low-mass stars. In particular, none of the current models
contain emission originating in the chromospheres of young stars, since only
the stellar photospheres are modeled, which dominate only at wavelengths
longer than the Balmer Jump. At shorter wavelengths, bound free and free free
emission originating in the chromosphere starts to dominate the continuum
(Houdebine et al. 1996; Franchini et al. 1998). The chromosphere also emits in
several spectral lines that are used to constrain accretion properties of
accreting young stellar objects (YSOs, Stelzer et al. 2013). The spectra of
field dwarfs will also poorly represent those of young stars as the former
have a significantly higher $\log{g}$. The best solution appears to use
spectra of non-accreting young stars. Class III stars (Greene et al. 1994),
which are defined according to their infrared classification where they
display a lack of infrared excess emission $d\log(\nu
F_{\nu})/d\log(\nu)<-1.6$ (Williams & Cieza 2011), make ideal candidates for
such templates, as this category often overlaps with Weak lined T Tauri Stars
(WTTS), which present much fainter emission lines than CTTS.

A grid of Class III templates with broad wavelength coverage medium-resolution
spectra obtained with the X-Shooter spectrograph on the ESO Very Large
Telescope (VLT) was previously provided to the community by Manara et al.
(2013b) (hereafter MTR13) and further expanded by Manara et al. (2017a)
(hereafter MFA17). This grid includes 41 spectra and contains spectral types
ranging from G4 to M8. Both MTR13 and MFA17 used these spectra to estimate the
contribution of chromospheric emission to the emission lines that are commonly
used for the determination of mass accretion rates. To study the contribution
of the chromosphere to the UV continuum emission, Ingleby et al. (2011b)
compared the spectrum of the M0 Class III RECX-1 to the photospheric spectrum
of a standard dwarf star. Here it was found that attributing this excess to
accretion would result in an estimated accretion luminosity of $\log(L_{\rm
acc}/L_{\star})=-1.3$. The chromospheres of young stars can therefore
significantly affect measured accretion rates in low accretors. Moreover, the
Balmer continuum excess emission and the Balmer Jump are more difficult to
detect in the spectra of early-type (¡K3) YSOs than in the later types due to
the lower contrast between photospheric emission and accretion induced
continuum excess emission (Herczeg & Hillenbrand 2008). Constraints on the
influence of the chromospheric emission in the UV on measurements of (low)
accretion rates is still lacking. A better understanding of the chromospheres
of young stars is therefore needed to characterise the lowest accretors to
better understand the late phases of disk dispersal and hence, provide
constraints on disk evolution models.

Here we expand the library of X-Shooter Class III templates previously
provided by MTR13 and MFA17 by an additional 18 templates and present a method
for interpolating between them. We also aim to constrain the influence of the
UV continuum chromospheric emission on determination of mass accretion rates.
The paper is structured as follows. The sample selection, observations and
data reduction are described in Sect. 2. The analysis of the stellar
properties of our sample is described in Sect. 3. In Sect. 4 the final grid
and our method for interpolating it are discussed. Sect. 5 discusses an
application of this interpolated grid using a self consistent method to derive
the mass accretion rates and validate this method on a set spectra of
accreting young stars in the Chamaeleon I star-forming region. In Sect. 6 we
obtain a lower limit on the mass accretion rates that we can measure from the
UV excess, taking into account uncertainties on the chromospheric emission and
discuss the implications for studies of mass accretion rate ($\dot{M}_{\rm
acc}$) in CTTS. Finally, we summarize our conclusions in Sect. 7.

##  2 Sample, observations, and data reduction

The new targets considered in this work come mainly from the sample of Lovell
et al. (2021), who studied 30 Class III stars (age $\lesssim$10 Myr) using the
Atacama Large Millimeter Array (ALMA). Lovell et al. (2021) reaffirmed that
these sources are Class III YSO through a comparison of the K-band (2MASS) and
either 12$\mu$m (WISE) or 24$\mu$m (Spitzer) fluxes. In addition to this
Lovell et al. (2021) fitted the SEDs of these targets and found no significant
NIR excess emission. These stars are likely members of of the Lupus star
forming region, although their membership still needs to be confirmed (Lovell
et al. 2021; Michel et al. 2021). A total of 19 objects of this sample were
recently observed using X-shooter (Pr.ID. 109.23D4.001, 110.23P2.001, PI
Manara), a broad-band, medium-resolution, high-sensitivity spectrograph
mounted on the ESO/VLT. The two components of a binary system, THA15-36A and
THA15-36B, were observed simultaneously in the slit. Three additional archival
X-Shooter spectra were available for the targets MT Lup and NO Lup (Pr.ID.
093.C-0506(A), PI Caceres) and MV Lup (Pr.ID. 085.C-0764(A), PI Günther).
Other targets in the sample of Lovell et al. (2021) were already included in
the grid of MTR13 and MFA17. In addition to this, we use in this work two
targets observed with VLT/X-shooter in the PENELLOPE Large Program (Pr.ID.
106.20Z8, Manara et al. 2021), namely RECX-6 and RXJ0438.6+1546. RECX-6 was
identified as a class III YSO by Sicilia-Aguilar et al. (2009) based on a fit
of its SED. RXJ0438.6+1546 was already included in the grid of MFA17, who
selected their targets based on available Spitzer data. The latter was already
observed with X-Shooter and included in the sample of MFA17, but the new
observations are used here. In total the targets considered in the analysis in
this work are 24, observed in 23 observations.

The wavelength range covered with X-Shooter is divided into three arms, the
UVB arm ($\lambda\lambda\sim 300-550$nm), the VIS arm ($\lambda\lambda\sim
500-1050$nm), and the NIR arm ($\lambda\lambda\sim 1000-2500$nm). Different
slit widths were used for the different arms and for fainter or brighter
targets. For brighter sources, we used $1\aas@@fstack{\prime\prime}0$,
$0\aas@@fstack{\prime\prime}4$, $0\aas@@fstack{\prime\prime}4$ wide slits in
the UVB, VIS and NIR arm respectively. These slit widths provide typical
spectral resolutions of $R\sim 5400$, $18400$ and $11600$ in the three arms.
Fainter, later spectral type objects were observed using
$1\aas@@fstack{\prime\prime}0$, $0\aas@@fstack{\prime\prime}9$,
$0\aas@@fstack{\prime\prime}9$ in the three arms, providing resolutions of
$R\sim 5400$, $8900$ and $5600$. For MV lup, RXJ0438.6+1546, MT Lup and NO
Lup, the $0\aas@@fstack{\prime\prime}5$ wide slits were used in the UVB arm,
resulting in spectra with resolution $R\sim 9700$. The observations with the
slits with the aforementioned widths were preceded by short exposures with a
slit with the significantly larger width of $5\aas@@fstack{\prime\prime}0$ in
all arms to obtain spectra not affected by slit losses to be used for absolute
flux calibration. The only exception of the use of the wide slits were MV Lup,
MT Lup, and NO Lup.

Appendix A contains a log of the observations presented here. In the observing
log, several targets are highlighted as spatially unresolved binaries. We
exclude these spectra from our sample since they can not be used as templates
to represent the stellar emission of individual targets and an analysis of
these spectra is outside the scope of this paper. In particular, we exclude
CD-39 10292, THA15-38, CD-35 10498, V1097 Sco and NN Lup. NN Lup was
discovered to be SB2 binaries in our analysis with the ROTFIT tool (see Sect.
3.2). CD-39 10292 is an SB2 binary first identified by Melo et al. (2001).
V1097 Sco and CD-35 10498 were identified as binaries by Zurlo et al. (2021)
and were not spatially resolved in the X-Shooter slit. THA15-38 was resolved
as a binary in the acquisition image of ESPRESSO observations that are part of
the PENELLOPE program. This was possible due to the excellent seeing
conditions ($\lesssim 0\aas@@fstack{\prime\prime}6$) during the night of the
ESPRESSO observations.

The data reduction was performed using the ESO X-Shooter pipeline v.4.2.2
(Modigliani et al. 2010) in the Reflex workflow (Freudling et al. 2013). The
pipeline executes the standard reduction steps: flat fielding, bias
subtraction, extraction and combination of orders, rectification, wavelength
calibration, flux calibration using a standard star observed during the same
night and the final extraction of the 1D spectrum. The telluric lines were
removed from the narrow slit observations using the molecfit tool (Smette et
al. 2015). This was done by fitting the telluric features on the spectra
themselves, rather than by using a telluric standard star. As a final step,
the narrow slit observations are rescaled to the continuum flux of the wide
slit spectra to get flux-calibrated spectra, using the procedure developed for
the PENELLOPE program (see Manara et al. 2021). For the UVB arm this was done
using a correction factor constant with wavelength. The VIS and NIR arms were
rescaled using a factor with a linear dependency on wavelength. To test the
flux calibration of our spectra they were compared to archival photometry. The
overall agreement between the spectra and photometry is excellent ($\Delta{\rm
mag}<0.2$ mag) with the exception of 2MASSJ16090850-3903430 and THA15-36. This
is however within the typical variation range at optical wavelength which is
mostly due to starspots rotational modulation. A description of how we flux
calibrated targets with $\Delta{\rm mag}>0.2$ mag can be found in Appendix A.
Appendix A also contains a description of how we obtained an accurate flux
calibration for the apparent visual binary THA15-36, which was spatially
resolved in the X-Shooter slit. Zurlo et al. (2021) resolved this system using
VLT/NACO, and argued that both components are unbound given their different
Gaia distances ($146.5\pm 0.8$ pc for the primary and $154.3\pm 1.8$ pc for
the secondary).

##  3 Stellar Parameters of the new Class III spectra

In this section, we derive the stellar parameters for all the 19 resolved
stars whose spectra are presented here for the first time. This is done by
first determining the spectral type from atomic and molecular features present
in the spectra, then comparing these estimates with results from the fitting
of individual absorption lines, and finally determining the stellar luminosity
to place the targets on the Hertzsprung-Russel Diagram (HRD) to derive their
stellar masses.

###  3.1 Spectral type and extinction determination

Table 1: Spectral types and extinction obtained in this work.

Name | $A_{V}$ | SpT | Uncertainty | literature | HH14 | TiO | Riddick et al.
---|---|---|---|---|---|---|---
CD-31_12522 | 0.0 | K0.5 | $\pm 1$ | K2a | K0.7 | K4.7 | …
RXJ1608.9-3905 | 0.0 | K2.0 | $\pm 1$ | K2b | K1.7 | K4.5 | …
MV Lup | 0.0 | K2.0 | $\pm 1$ | K2c | K2.0 | K4.5 | …
RXJ0438.6+1546 | 0.0 | K2.0 | $\pm 1$ | K2d | K1.3 | K4.6 | …
2MASSJ15552621-3338232 | 0.1 | K6.0 | $\pm 1$ | K5e | K8 | K5.6 | …
MT Lup | 0.1 | K5.5 | $\pm 1$ | K5f | K8.7 | K4.9 | …
MX Lup | 0.0 | K6.0 | $\pm 0.5$ | K6c | K9.0 | K5.2 | …
RXJ1607.2-3839 | 0.35 | K7.5 | $\pm 0.5$ | K7c | K9.0 | K7.7 | …
MW Lup | 0.0 | K7.5 | $\pm 0.5$ | K7c | K11.9 | K7.4 | …
NO Lup | 0.35 | K7.5 | $\pm 0.5$ | K7c,g | K9.9 | K7.5 | …
THA15-43 | 0.0 | K7.5 | $\pm 0.5$ | M0h | M3.6 | K7.7 | …
THA15-36A | 0.0 | M0.5 | $\pm 1$ | … | M1.1 | M0.8 | …
THA15-36B | 0.5 | M2.0 | $\pm 1$ | … | M2.7 | M2.0 | …
RECX-6 | 0.0 | M3.0 | $\pm 0.5$ | M3i | M3.6 | M3.4 | M3.6
Sz67 | 0.0 | M3.0 | $\pm 0.5$ | M4c | M3.8 | M3.7 | M3.8
2MASSJ16090850-3903430 | 0.3 | M5.0 | $\pm 0.5$ | M5c | M5.3 | M5.4 | M5.3
2MASSJ16075888-3924347 | 0.25 | M4.5 | $\pm 0.5$ | M5c | M5.0 | M4.8 | M5.1
2MASSJ16091713-3927096 | 0.75 | M5.5 | $\pm 0.5$ | M5c | M5.8 | M6.0 | M5.7
V1191 Sco | 0.4 | M5.5 | $\pm 0.5$ | M5c | M6.2 | M5.8 | M5.9

111The spectral types and extinction obtained in this work from comparing to
available templates are reported in column 2 and 3, with the uncertainty on
the SpT reported in column 4. The other columns report previous literature SpT
values, and those obtained using the spectral indices from HH14, Jeffries et
al. (2007), and Riddick et al. (2007). The uncertainty on the SpT is given in
subclasses. Refrences: a: Torres et al. (2006), b: Galli et al. (2015),c:
Padgett et al. (2006), d: MFA17,e: Köhler et al. (2000),f: Krautter et al.
(1997),g: Hardy et al. (2015),h: Merín et al. (2008),i: Rugel et al. (2018)

Determining spectral types (SpT) for (non-accreting) young stellar objects is
a complex process that is best performed by comparison with other targets of
well known SpT. In this case, we consider the grid of non-accreting Class III
young stellar object of MTR13 and MFA17 as a starting point, and later also
check and refine their grids using the new spectra presented here.

The first estimate of the SpT of our targets was obtained applying to the new
spectra the same spectral indices used by MTR13 and MFA17, namely the spectral
indices presented by Riddick et al. (2007), the TiO index of Jeffries et al.
(2007) and the indices presented by Herczeg & Hillenbrand (2014, hereafter
HH14). The indices of Riddick et al. (2007) are accurate for spectral types
later than M3. The indices by Jeffries et al. (2007) hold for spectral types
later than K6, since the used TiO feature disappears for earlier SpTs. The
indices of HH14 are accurate for SpTs from early K to late M stars. The
results for these different methods are listed in Table 1. Spectral indices
are less reliable estimates of the SpT in cases in which the extinction is
substantial since they are based on ratios of features at different wavelength
ranges. In general, extinction is low for our targets, but it can still
introduce additional uncertainty to the SpT estimates obtained from the
spectral indices.

Therefore, to obtain a simultaneous extinction and SpT estimate, we performed
a comparison of the spectra in our sample with the spectra of MTR13 and MFA17,
which have negligible extinction. We obtained the first estimates of SpT and
$A_{V}$ using a simple $\chi^{2}$-like comparison. The final values of both
the spectral type and extinction are derived through a visual comparison
between the spectra presented here and those presented by MTR13 and MFA17. The
main indicators used in this comparison are the depths of various molecular
bands. The K6 to M9.5 spectra include a variety of molecular features whose
depth increases almost monotonically for later SpTs in the spectral region
between 580 and 900 nm. This includes various absorption bands from TiO
($\lambda\lambda$ 584.7-605.8, 608-639, 655.1-685.2, 705.3-727, 765-785,
820.6- 856.9, 885.9-895 nm), CaH ($\lambda\lambda$ 675-705 nm) and VO
($\lambda\lambda$ 735-755, 785-795, 850-865 nm). Fig. 1 displays spectra with
SpTs ranging from M1 to K7.5. Similar figures for the other spectra with SpT
later than K5 can be found in Appendix G. The previously mentioned molecular
features can be seen to increase in depth for later spectral types.

Figure 1: X-Shooter spectra of Class III YSOs with spectral type ranging from
M1 to K7. All the spectra are normalized at 731 nm and offset in the vertical
direction for clarity. The spectra are also smoothed to the resolution of 2500
at 750 nm to make easier the identification of the molecular features. The
black colors indicate spectra presented by MTR13 and MFA17. The red color is
used for spectra presented for the first time here.

For SpT earlier than K6 a MgH and Mg b absorption feature ($\lambda\lambda$
505-515 nm) is used to assess the spectral type. The use of this feature was
first discussed by HH14 who present it in the context of a spectral index. The
depth of this absorption feature is best determined by comparing the flux at
510nm to the flux expected at the same wavelength from a linear fit between
the median flux of the spectral regions of $\lambda\lambda$ 460-470 nm and
$\lambda\lambda$540-550nm. Fig. 2 displays this feature for spectral types
from K1 to K6. Here the linear fit between $\lambda\lambda$ 460-470 nm and
$\lambda\lambda$540-550 nm is also indicated. Additionally, a linear fit for
the regions of $\lambda\lambda$ 488-492 nm and $\lambda\lambda$514-516 nm is
included in this figure to highlight the increasing depth of this feature with
SpT. We perform this comparison at different values of extinction to estimate
it simultaneously. The results are listed in Table 1, where we have rounded
the SpT to half a subclass.

Our estimates are typically consistent within at most 1.5 subclass of the
literature values. The TiO spectral indices agrees within 1 subclass for
targets later than K5. The spectral indices of HH14 agree within a subclass at
all spectral types except for the K5 to M0 range. Finally the indices of
Riddick et al. (2007) have a similar agreement for the targets later than M3.
We note that the use of features in the NIR region ($\lambda\lambda>1000$ nm)
can give rise to significantly different spectral types. On top of the fact
that the NIR indices are based on features covering a larger wavelength range
and thus are more affected by extinction and by imperfect telluric removal and
or flux calibration in that wavelength range (e.g., MTR13), the likely
explanation for this deviation is the presence of cold spots on the stellar
surface (e.g., Stauffer et al. 2003; Vacca & Sandell 2011; Pecaut 2016; Gully-
Santiago et al. 2017; Gangi et al. 2022).

We adopt similar uncertainties on the SpT as MFA17. For objects later than K6
we estimate the uncertainties to be 0.5 subclass. For objects earlier than K6
we estimate the uncertainties to be 1 subclass. For the binary components of
THA15-36 we assume larger uncertainties of 1 subclass due to the less certain
flux calibration of the spectra. We estimate the uncertainty on the extinction
to be 0.2 mag. A description of how we confirmed the uncertainties on the SpT
and estimated those on the extinction follows in Sect. 4 and Appendix C.

Figure 2: X-Shooter spectra of Class III YSOs with SpT ranging from K6 to K2.
The spectra have been normalized at 460 nm and an offset has been added for
clarity. The spectra have been smoothed to have a resolution of $\sim$2500 at
750nm. The observations presented here are displayed in red, while the spectra
of MTR13 and MFA17 are indicated in black. We highlight the R510 spectral
index feature using the solid blue line. The dashed blue line indicates the
slope of the surrounding continuum.

###  3.2 Photospheric properties from ROTFIT

A large number of absorption lines are resolved in the spectra, allowing us to
obtain photospheric properties. We analyse the absorption lines in the VIS arm
of the X-Shooter spectra using the ROTFIT tool (e.g., Frasca et al. 2015,
2017) to derive the effective temperature ($T_{\rm{eff}}$), surface gravity
($\log{g}$), projected rotational velocity ($v\sin{i}$), radial velocities
(RV), and veiling at three wavelengths ($\lambda\,620\,\rm{nm}$,
$\lambda\,710\,\rm{nm}$ and $\lambda\,970\,\rm{nm}$). The veiling is given by
$r=EW(template)/EW(observation)-1$, where EW is the equivalent width of
absorption lines near the wavelength of interest. ROTFIT searches, within a
grid of templates, for the spectrum that minimizes the $\chi^{2}$ to the
target spectrum in different spectral regions. The templates consist of a grid
of BT-Settl model spectra (Allard et al. 2011) of solar metallicity, $\log{g}$
ranging from 0.5 to 5.5 dex and an effective temperature ranging from 2000 to
6000 K. ROTFIT achieves this by first deriving the radial velocity of the star
cross-correlating the target and template spectrum and uses this information
to shift the observed spectrum to the rest frame. ROTFIT then convolves the
templates with both a Gaussian to match the X-Shooter resolution. Then the
templates are iteratively broadened by convolution with a rotational profile
with increasing $v\sin{i}$ until a minimum $\chi^{2}$ is attained. ROTFIT
analyses spectral intervals that contain features sensitive to $\log{g}$
and/or the $T_{\rm{eff}}$ such as the KI doublet at $\lambda\>\approx
766-770\>\rm{nm}$ and the NaI doublet at $\lambda\>\approx 819\>\rm{nm}$. An
additional continuum emission component is added to the template in order to
estimate the veiling. As for the $v\sin{i}$, per each template, the veiling is
also a free parameter in the fit.

We did not set this continuum component and therefore the veiling to 0 despite
most of our targets being non-accretors. We preferred to let the veiling vary
for our Class III stars as a check. As expected, we always found zero or low
veiling values, which could be the result of small residuals in the scattered
light subtraction or the effect of the interplay between different parameters.
The largest value of r=0.4 is found at 620 nm for three K-type stars. A
possible explanation could be the effect of starspots on the spectra. Another
possible explanation is that of an undetected companion. Apart from these
extreme values, we do not consider veiling values as small as 0.2 to be
significant. The photospheric parameters, $v\sin{i}$, veiling measurements,
and RV derived with ROTFIT can be found in Table 2. As stated in Sect. 2,
during this analysis, we found two targets to be double lined spectroscopic
binaries, namely NN Lup and CD-39 10292. We excluded these from our analysis.
Fig. 3 shows the comparison between the $T_{\rm{eff}}$ derived using ROTFIT
and obtained using different SpT -$T_{\rm eff}$ conversions. Here it can be
seen that the effective temperature obtained from the SpT agrees best with
ROTFIT when using the SpT -$T_{\rm eff}$ relation by HH14. The low $\log g$
found are mostly compatible with that of young objects ($\lesssim$10 Myr).

Figure 3: Comparison between the temperatures obtained with ROTFIT and from
the spectral type for the targets presented here. The relation of Herczeg &
Hillenbrand (2014) is labeled as HH14, the one by Pecaut & Mamajek (2013) as
PM13, that of Kenyon & Hartmann (1995) asn KH95 and the relationship of Luhman
et al. (2003) as Luh03. The relations are only applied to spectral type ranges
where they are valid. The solid line represents the one-to-one relation. Table
2: Photospheric parameters derived using ROTFIT.

Name | $T_{\rm{eff}}$ | $\sigma(T_{\rm{eff}})$ | $\log{g}$ | $\sigma(\log{g})$ | $v\sin{i}$ | $\sigma(v\sin{i})$ | $RV$ | $\sigma(RV)$ | $r_{970\rm{nm}}$ | $r_{710\rm{nm}}$ | $r_{620\rm{nm}}$
---|---|---|---|---|---|---|---|---|---|---|---
| $[K]$ | $[K]$ | $[cgs]$ | $[cgs]$ | $[km/s]$ | $[km/s]$ | $[km/s]$ | $[km/s]$ |  |  |
CD-31_12522 | 4920 | 223 | 4.04 | 0.12 | 30.2 | 1.0 | 2.2 | 0.8 | 0.00 | 0.00 | 0.00
RXJ0438.6+1546 | 4851 | 111 | 4.08 | 0.23 | 21.0 | 1.0 | 18.9 | 0.7 | 0.30 | 0.00 | 0.40
RXJ1608.9-3905 | 4552 | 124 | 4.27 | 0.14 | 43.6 | 1.0 | -0.7 | 0.9 | 0.00 | 0.00 | 0.40
MV Lup | 4513 | 96 | 4.83 | 0.25 | 1.0 | 6.0 | 2.4 | 0.7 | 0.00 | 0.00 | 0.00
MT Lup | 4411 | 77 | 4.41 | 0.12 | 7.9 | 1.4 | 2.7 | 0.6 | 0.40 | 0.20 | 0.30
J15552621-3338232 | 4295 | 112 | 4.88 | 0.24 | 1.0 | 11.0 | 0.8 | 0.6 | 0.10 | 0.00 | 0.20
MX Lup | 4216 | 61 | 4.45 | 0.21 | 10.0 | 1.0 | 2.4 | 0.6 | 0.00 | 0.00 | 0.20
MW Lup | 4032 | 54 | 5.03 | 0.29 | 15.2 | 3.2 | 3.4 | 0.6 | 0.00 | 0.00 | 0.00
RXJ1607.2-3839 | 3954 | 86 | 4.53 | 0.11 | 32.8 | 2.0 | -0.4 | 1.0 | 0.00 | 0.00 | 0.40
NO Lup | 3907 | 98 | 4.43 | 0.11 | 11.2 | 1.0 | -2.3 | 0.8 | 0.10 | 0.20 | 0.30
THA15-43 | 3885 | 23 | 5.19 | 0.18 | 9.4 | 2.0 | 1.6 | 0.7 | 0.10 | 0.00 | 0.30
THA15-36A | 3650 | 60 | 4.57 | 0.12 | 19.2 | 1.0 | 2.2 | 0.8 | 0.10 | 0.20 | 0.30
THA15-36B | 3465 | 43 | 4.92 | 0.11 | 21.1 | 1.0 | 1.8 | 0.7 | 0.10 | 0.20 | 0.30
RECX-6 | 3419 | 36 | 4.68 | 0.12 | 23.4 | 1.9 | 16.3 | 0.7 | 0.00 | 0.00 | 0.00
Sz67 | 3226 | 57 | 4.53 | 0.20 | 70.3 | 1.0 | -0.6 | 3.6 | 0.00 | 0.00 | 0.10
J16075888-3924347 | 3054 | 93 | 4.24 | 0.15 | 25.0 | 11.0 | 2.4 | 0.9 | 0.00 | 0.00 | 0.00
J16090850-3903430 | 3000 | 64 | 4.25 | 0.13 | 4.1 | 10.2 | -1.6 | 1.0 | 0.20 | 0.00 | 0.10
V1191Sco | 2883 | 105 | 3.59 | 0.11 | 33.5 | 9.7 | -0.2 | 1.0 | 0.00 | 0.00 | 0.00
J16091713-3927096 | 2876 | 130 | 4.73 | 0.13 | 69.0 | 13.0 | 2.8 | 4.3 | 0.00 | 0.00 | 0.00

222 $r_{970\rm{nm}}$, $r_{710\rm{nm}}$ and $r_{620\rm{nm}}$ is the veiling
measured around 970nm ,710 nm and 620 nm respectively.

###  3.3 Luminosity determination

The stellar luminosities are obtained using a method similar to that used by
MTR13. In this method, the dereddened spectra are extrapolated to wavelengths
not covered by the spectra and integrated to compute the bolometric flux.

The X-Shooter spectra are extrapolated using a BT-Settl (Allard et al. 2011)
synthetic spectrum appropriate for the target. We use the effective
temperature obtained from the SpT$-T_{\rm eff}$ relation of HH14. We prefer
this $T_{\rm eff}$, since in Sect. 5.1 we will use the obtained SpT to compute
the luminosity. For the metallicity of the synthetic spectra we assumed solar
values, typical for targets in the Lupus region (Biazzo et al. 2017), and for
the surface gravity we chose $\log{g}=4.0$ in all cases. This parameter has
very limited impact on the global luminosity estimate, since most of the
stellar emission is covered by the X-Shooter spectra and the synthetic spectra
are used to measure a minor fraction of the global emission. The synthetic
spectra are then matched to the spectra at 400.5 nm and 2300 nm and used to
represent the flux at wavelengths shorter and longer than these respective
values. The wavelengths chosen here differ from those used by MTR13. We chose
these wavelengths in order to avoid the high noise level at short wavelengths
and poor flux calibration at the end of the $K$-band present in some spectra.
Due to this difference, we also re-applied this method to the sample of MTR13
and MFA17. We also performed a linear interpolation across the strong telluric
absorption features between the $J$,$H$, and $K$ band ($\lambda\lambda$
1330-1550 nm, $\lambda\lambda$ 1780-2080 nm) in order to account for the
stellar flux in these regions. An example of a prolonged spectrum created in
this way is shown in Appendix D. The bolometric flux is then computed by
integrating over the prolonged spectrum.

We used the photogeometric distances of Bailer-Jones et al. (2021) to convert
the fluxes to luminosities for all targets with exception of TWA 26. For this
star we used the geometric distance of the same authors since a photogeometric
distance is unavailable. The distances provided by Bailer-Jones et al. (2021)
are based on the Gaia DR3 (Gaia Collaboration et al. 2016, 2023) parallaxes
but include a photometric and geometric prior to improve the distance
estimate. The inclusion of these priors significantly improves the
uncertainties for the most distant targets (namely those in $\sigma$ Orionis).
For more nearby targets the distance estimate and its uncertainty do not
change significantly from the inverse Gaia parallaxes.

The uncertainties on these estimates are computed by propagating the
uncertainties of matching the BT-Settl models to the observations, the
distance, the extinction, and the photometric flux. We adopt an extinction
uncertainty of $\sigma_{A_{V}}=0.2mag$. For the targets calibrated using wide
slit spectra, we assumed the uncertainties on the photometric flux 5% of the
total flux, which is slightly more conservative than the 4% of Rugel et al.
(2018). For the spectra calibrated using the available photometry we assume an
uncertainty of 0.2 dex on the luminosity, the same as that of MTR13.

We also computed the luminosities of the grid using the bolometric correction
of HH14. This correction uses the flux measured at 751 nm to estimate the
total flux of the star. We notice a small but systematic discrepancy between
the luminosities derived from the two methods at effective temperatures lower
than $\leavevmode\nobreak\ 4500\rm K$. We therefore propose a correction to
the relationship provided by HH14 which is further discussed in Appendix D.
This new relation is assumed in this work.

Figure 4: HR Diagram of the objects analysed here (highlighted with larger
black outlined star symbols) and those analysed by MTR13 and MFA17. The model
isochrones and evolutionary tracks by Baraffe et al. (2015a) are also shown.
The isochrones are the 1.2, 3, 10 and 30 Myr ones.

Fig. 4 shows our sample in a Hertzsprung-Russell diagram together with the
samples of MTR13 and MFA17. Here, we used the luminosities obtained by
integrating the extended spectrum and the effective temperature is obtained
from the spectral type using the relationship of HH14. The isochrones and
evolutionary tracks of Baraffe et al. (2015a) are also plotted. The isochronal
age of the targets in our sample appears to be dependent on the stellar mass.
Targets with $M_{\star}\gtrsim 0.7M_{\odot}$ tend to be $\sim
10\rm\;to\;30\;\rm Myrs$ old according to the isochrones, whereas those with
lower mass have ages of $\sim 1\rm\;to\;10\;Myrs$, despite all except one
target being members of the Lupus star forming region. This trend is also
present in the samples of MTR13 and MFA17 as well as other star samples such
as those of Bell et al. (2014), Herczeg & Hillenbrand (2015), and Pecaut
(2016). Stelzer et al. (2013) see a similar trend when comparing their sample
to isochrones in the $\log{g}-T_{\rm eff}$ diagram. It is unclear what causes
this discrepancy but possible origins include the presence of starspots
affecting the position in the HRD (e.g., Gangi et al. 2022; Pérez Paolino et
al. 2024) or affecting overall evolution (Somers & Pinsonneault 2015), the
effect of accretion during earlier stages of the star’s evolution (Baraffe et
al. 2017) or the effect of the stellar magnetic field on the subphotospheric
convective motions in the stars (Feiden 2016). The evolutionary tracks by
Feiden (2016) include the later effect and are similar to the models of
Baraffe et al. (2015a) in the non-magnetic case. The SPOTS models of Somers et
al. (2020) includes the influence of starspots at different filling factors on
the isochrones. An analysis of the spot coverage of our sample and comparison
with the SPOTS isochrones is beyond the scope of this work and deferred to a
future work.

##  4 New combined grid

The first goal of this work is to improve upon the grid of template spectra of
YSOs presented by MTR13 and MFA17 by adding new templates to the grid and
interpolating the spectra to generate a continuous grid. This is discussed in
this section.

###  4.1 Description of the new grid

We combine the observations presented here with those of MTR13 and MFA17 to
create an enhanced library of spectral templates that is made available to the
community. We add one additional spectrum presented by Manara et al. (2016),
that of the K0 star HBC407. The sources selected by MTR13 and MFA17 were
classified to be Class III YSOs and using Spitzer data (e.g., Evans et al.
2009). Manara et al. (2014) presented additional X-Shooter observations of
Class III targets, namely IC348-127, T21, CrA75. These targets were highly
extincted, with $A_{V}\sim 6\>\rm mag$, $A_{V}=3.2\>\rm mag$ and
$A_{V}=1.5\>\rm mag$, respectively. This high extinction causes additional
uncertainties in the dereddened spectra due to the uncertainties in the
assumed extinction law. Therefore we do not include these spectra in our grid.

There are 6 stars from our new observations that are not included in the grid.
The 5 unresolved binaries previously mentioned in Sect. 2 are excluded from
our grid since they cannot be used to represent the stellar emission of
individual stars. To avoid potential accretors in our sample we we use the
$H\alpha$ equivalent width criterion of White & Hillenbrand (2004) and Barrado
y Navascués & Martín (2003), among others. The spectrum of
2MASSJ16075888-3924347 shows evidence of ongoing accretion, therefore we
exclude it from our grid. This is further discussed in Appendix B.

From the grid of MTR13, Sz121 and Sz122 are excluded since they are likely
spectroscopic binaries or ultrafast rotators (MTR13, Stelzer et al. 2013). For
RXJ0438.6+1546 a spectrum was presented by MFA17. This target was also
observed as a part of the PENELLOPE VLT Large Program (Manara et al. 2021). We
only use the more recent PENELLOPE spectrum since the observations were
performed with better sky transparency conditions.

We confirm the spectral types of all except for one target of MTR13 and MFA17
through visual inter-comparison. The TiO absorption bands of CD 36-7429A
appear to best match that of the K7 templates. We re-assign the spectral type
of CD 36-7429A from K5 (MTR13) to K7. This spectral type is further confirmed
by the TiO index of Jeffries et al. (2007) which yields a spectral type of
K7.0 and the analysis of Fang et al. (2017, 2021) who also adopted a SpT of K7
for this target. Pecaut & Mamajek (2013) also adopted a SpT of K7 for this
source. Interestingly, the estimate of $T_{\rm eff}$ from the ROTFIT analysis
of the absorption lines lead to a result more consistent with a SpT of K5
(Stelzer et al. 2013). It is possible that spots covering the stellar surface
lead to this discrepancy (e.g., Stauffer et al. 2003; Vacca & Sandell 2011;
Pecaut 2016; Gully-Santiago et al. 2017; Gangi et al. 2022). We however assume
K7 as the SpT for this target based on the molecular features. The spectra
first presented in this work have been dereddened using the values listed in
Table 1 to provide an extinction-less grid. This grid can be found on
GitHub333https://github.com/RikClaes/FRAPPE.

The uncertainties on both $A_{V}$ and SpT are estimated by fitting the spectra
of targets within 1 spectral type subclass of other targets in the combined
grid. In this procedure, we search for the best fitting template spectrum in
the remainder of the grid at different values of extinction. The best fit
template and extinction are found by searching for the minimum of a
$\chi^{2}$-like metric that includes the spectral features discussed in Sect.
3.1.

For both the difference in spectral type and extinction we find a distribution
with a median value of 0 and standard deviations of $\sim
0.5\>\rm{subclasses}$ and $\sim 0.25\>\rm{mag}$ respectively. We note that the
standard deviation is larger for spectra earlier than K6, in part due to the
lack of spectra of similar spectral type. We therefore estimate the
uncertainties on SpT’s earlier than K6 to be $\sim 1\>\rm{subclasses}$, those
at later SpT to be $\sim 0.5\>\rm{subclasses}$. For the extinction we adopt an
uncertainty of $0.2\>\rm{mag}$. THA15-36B appears as a strong outlier with
$\Delta\rm SpT=-1.5$ and $\Delta\rm A_{V}=0.8$. This supports our decision to
provide higher uncertainties on both THA15-36A and THA15-36B. Because of this
we also exclude THA15-36A and THA15-36B when constructing our interpolated
grid in Sect. 4.2.

The final grid of templates is reported in Table 3. Fig. 5 shows the spectral
type distribution of all the spectra in our final grid. Our final grid of
templates includes 57 targets and spans a range of spectral types from G5 to
M9.5. The spectral types later than K6 appear to be well represented. The
earlier spectral types appear less well sampled, with the most prominent gaps
between G5 to G8 and K4 to K5.5.

Figure 5: Histogram of SpT for the grid of Class III templates. Table 3: The final grid of spectral templates and their stellar properties. Name | Region | SpT | $\rm T_{\rm eff}[K]$ | distance [pc] | $\log(L/L_{\sun})$ | reference
---|---|---|---|---|---|---
RXJ0445.8+1556 | Taurus | G5 | 5430 | $167.3_{-3.8}^{+3.2}$ | $0.64\pm 0.07$ | MFA17
RXJ1508.6-4423 | Lupus | G8 | 5180 | $145.7\pm 0.4$ | $0.01\pm 0.07$ | MFA17
RXJ1526.0-4501 | Lupus | G9 | 5025 | $150.1\pm 0.3$ | $-0.07\pm 0.06$ | MFA17
HBC407 | Taurus | K0 | 4870 | $249.1_{-29.7}^{+43.5}$ | $0.05_{-0.12}^{+0.17}$ | Manara et al. (2014)
PZ99J160843.4-260216 | Upper Scorpius | K0.5 | 4830 | $137.4_{-1.0}^{+1.1}$ | $0.09\pm 0.06$ | MFA17
CD-31_12522 | Lupus | K0.5 | 4830 | $127.4\pm 0.5$ | $-0.12\pm 0.06$ | This work
RXJ1515.8-3331 | Lupus | K0.5 | 4830 | $115.4\pm 0.2$ | $-0.14\pm 0.06$ | MFA17
PZ99J160550.5-253313 | Upper Scorpius | K1 | 4790 | $105.1\pm 0.2$ | $-0.29\pm 0.06$ | MFA17
RXJ0457.5+2014 | Taurus | K1 | 4790 | $122.2\pm 0.3$ | $-0.27\pm 0.06$ | MFA17
RXJ0438.6+1546 | Taurus | K2 | 4710 | $139.1\pm 0.3$ | $0.02\pm 0.06$ | This work
RXJ1608.9-3905 | Lupus | K2 | 4710 | $156.0\pm 0.4$ | $0.14\pm 0.06$ | This work
MV Lup | Lupus | K2 | 4710 | $137.1\pm 0.3$ | $-0.21\pm 0.2$ | This work
RXJ1547.7-4018 | Lupus | K3 | 4540 | $130.2\pm 0.3$ | $-0.21\pm 0.06$ | MFA17
RXJ1538.6-3916 | Lupus | K4 | 4375 | $122.5\pm 0.4$ | $-0.40\pm 0.06$ | MFA17
MT Lup | Lupus | K5.5 | 4163 | $133.1\pm 0.3$ | $-0.52\pm 0.2$ | This work
2MASSJ15552621-3338232 | Lupus | K6 | 4115 | $119.0\pm 0.2$ | $-0.70\pm 0.05$ | This work
RXJ1540.7-3756 | Lupus | K6 | 4115 | $134.3\pm 0.3$ | $-0.50\pm 0.05$ | MFA17
RXJ1543.1-3920 | Lupus | K6 | 4115 | $133.6_{-6.2}^{+5.4}$ | $-0.50_{-0.07}^{+0.06}$ | MFA17
MX Lup | Lupus | K6 | 4115 | $128.8_{-0.2}^{+0.3}$ | $-0.58\pm 0.05$ | This work
SO879 |  $\sigma$ Ori. | K7 | 4020 | $395.6_{-2.2}^{+3.4}$ | $-0.21\pm 0.2$ | MTR13
TWA6 | TW Hya | K7 | 4020 | $65.5\pm 0.1$ | $-0.75\pm 0.2$ | MTR13
CD -36 7429A | TW Hya | K7 | 4020 | $76.3\pm 0.1$ | $-0.52\pm 0.2$ | MTR13
RXJ1607.2-3839 | Lupus | K7.5 | 3960 | $167.9\pm 2.7$ | $-0.23\pm 0.05$ | This work
MWlup | Lupus | K7.5 | 3960 | $129.6_{-0.3}^{+0.2}$ | $-0.75\pm 0.05$ | This work
NO Lup | Lupus | K7.5 | 3960 | $132.8_{-0.2}^{+0.3}$ | $-0.46\pm 0.2$ | This work
THA15-43 | Lupus | K7.5 | 3960 | $125.1\pm 0.3$ | $-0.75\pm 0.05$ | This work
Tyc7760283_1 | TW Hya | M0 | 3900 | $53.5\pm 0.1$ | $-0.62\pm 0.2$ | MTR13
TWA14 | TW Hya | M0.5 | 3810 | $92.0_{-0.1}^{+0.2}$ | $-0.87\pm 0.2$ | MTR13
THA15-36A | Lupus | M0.5 | 3810 | $145.6_{-0.6}^{+0.9}$ | $-0.86\pm 0.2$ | This work
RXJ1121.3-3447_app2 | TW Hya | M1 | 3720 | $59.7\pm 0.1$ | $-0.70\pm 0.2$ | MTR13
RXJ1121.3-3447_app1 | TW Hya | M1 | 3720 | $59.7\pm 0.1$ | $-0.61\pm 0.2$ | MTR13
THA15-36B | Lupus | M2 | 3560 | $150.9_{-1.5}^{+1.6}$ | $-1.07\pm 0.2$ | This work
CD -29 8887A | TW Hya | M2 | 3560 | $45.9_{-0.5}^{+0.4}$ | $-0.50\pm 0.2$ | MTR13
CD -36 7429B | TW Hya | M3 | 3410 | $76.1\pm 0.2$ | $-1.06\pm 0.2$ | MTR13
TWA15_app2 | TW Hya | M3 | 3410 | $114.7\pm 0.2$ | $-0.92\pm 0.2$ | MTR13
TWA7 | TW Hya | M3 | 3410 | $34.05\pm 0.03$ | $-0.97\pm 0.2$ | MTR13
Sz67 | LupusI | M3 | 3410 | $103.2_{-0.9}^{+1.0}$ | $-0.86\pm 0.04$ | This work
RECX-6 | LupusI | M3 | 3410 | $97.9\pm 0.1$ | $-0.99\pm 0.04$ | This work
TWA15_app1 | TW Hya | M3.5 | 3300 | $114.2\pm 0.2$ | $-0.93\pm 0.2$ | MTR13
Sz94 | Lupus | M4 | 3190 | $114.6\pm 0.3$ | $-1.25\pm 0.2$ | MTR13
SO797 |  $\sigma$ Ori. | M4.5 | 3085 | $385.9_{-10.6}^{+11.5}$ | $-1.20\pm 0.2$ | MTR13
SO641 |  $\sigma$ Ori. | M5 | 2980 | $374.6_{-14.8}^{+10.6}$ | $-1.50\pm 0.2$ | MTR13
Par_Lup3_2 | Lupus | M5 | 2980 | $157.2\pm 1.0$ | $-0.96\pm 0.2$ | MTR13
2MASSJ16090850-3903430 | LupusIII | M5 | 2980 | $156.5_{-0.9}^{+1.3}$ | $-1.29\pm 0.$ | This work
SO925 |  $\sigma$ Ori. | M5.5 | 2920 | $371.5_{-19.4}^{+25.8}$ | $-1.56\pm 0.2$ | MTR13
SO999 |  $\sigma$ Ori. | M5.5 | 2920 | $387.7_{-15.7}^{+16.5}$ | $-1.21\pm 0.2$ | MTR13
V1191Sco | LupusIII | M5.5 | 2920 | $168.4_{-2.4}^{+2.2}$ | $-1.01\pm 0.04$ | This work
2MASSJ16091713-3927096 | LupusIII | M5.5 | 2920 | $133.7_{-2.8}^{+2.6}$ | $-2.00\pm 0.04$ | This work
Sz107 | Lupus | M5.5 | 2920 | $152.4_{-1.8}^{+1.9}$ | $-1.03\pm 0.2$ | MTR13
Par_Lup3_1 | Lupus | M6.5 | 2815 | $159.7_{-4.1}^{+4.2}$ | $-1.38\pm 0.2$ | MTR13
LM717 | ChaI | M6.5 | 2815 | $190.6_{-2.5}^{+2.6}$ | $-1.58\pm 0.04$ | MFA17
J11195652-7504529 | ChaI | M7 | 2770 | $189.2_{-4.2}^{+4.7}$ | $-2.01\pm 0.04$ | MFA17
LM601 | ChaI | M7.5 | 2720 | $186.1_{-4.6}^{+4.8}$ | $-2.09\pm 0.04$ | MFA17
CHSM17173 | ChaI | M8 | 2670 | $191.5_{-4.2}^{+4.6}$ | $-1.83\pm 0.04$ | MFA17
TWA26 | TW Hya | M9 | 2570 | $46.6\pm 0.5$ | $-2.63\pm 0.2$ | MTR13
DENIS1245 | TW Hya | M9.5 | 2520 | $83.1_{-2.8}^{+2.3}$ | $-2.78\pm 0.2$ | MTR13

###  4.2 Interpolation

The grid presented in Sect. 4.1 is limited in two key ways. First, the grid is
sparse and possesses gaps at a number of spectral types. Secondly, individual
spectra have intrinsic uncertainties. Directly applying one of these spectra
to represent the photosphere of a Class II star or to analyse other Class III
targets may therefore bias the results. In order to mitigate these downsides
we interpolate the grid of template spectra for the characterization of young
stellar photospheres.

Figure 6: Example of a local polynomial fit to the normalized fluxes (black
points) extracted in the wavelength range of 399 to 402 nm. The red point have
been excluded from the fit due to the low SNR of this spectrum. The blue line
indicates the median fit resulting from the Monte Carlo simulation. The
transparent blue region indicates the 1-$\sigma\,$ uncertainty interval. The
residuals are computed using only the uncertainties on the non-parametric fit.

We first start by normalizing the dereddened spectra to the flux measured at
731 nm in order to remove the dependency of individual target’s distance and
luminosity. We choose 731 nm as our reference region, since it is free of
strong telluric features, avoids features dependent on $\log g$ and the
photospheric emission dominates at this wavelength. Median normalized fluxes
are then computed in a wavelength interval of choice for each of the spectra.
To compute the uncertainty on this flux, we propagate the uncertainties on the
flux in the normalization range ($\sim 731$ nm) and the flux in the wavelength
range. We also propagate the uncertainties on the extinction. The spectra of
some of the later spectral type stars in our sample have a signal to noise of
$\sim 0$ at the shortest wavelengths in the UVB arm. In this case, we exclude
these normalised fluxes from the procedure. This procedure results in a set
containing a normalized flux $f_{\lambda}/f_{731\rm nm}$ and associated
uncertainty for each template in our library.

We use a non-parametric local polynomial fit (Cleveland 1979) to interpolate
between these fluxes as a function of SpT. In this type of interpolation, the
value at a given position (spectral type in our case) is obtained by fitting a
polynomial to a weighted version of the data points, this is expressed in Eq.
1.. The polynomial at a given $x$, representing SpT subclass, is defined by
the parameters ${\hat{a}_{1}(x),...,\hat{a}_{n}(x)}$ as:

${\hat{a}_{1}(x),...,\hat{a}_{n}(x)}=argmin_{a_{0},...,a_{n}}\sum_{i}K\left(\frac{x-x_{i}}{h}\right)\left(y_{i}-\sum_{k=0}^{n}a_{n}\cdot
x_{i}^{k}\right)^{2}$ (1)

Here $x_{i}$ represents the SpTs of our set of median fluxes in a given
wavelength range and $y_{i}$ is the values of the normalized fluxes
themselves. $K$ is a chosen kernel used for weighting the values that are
fitted and $h$ is the selected bandwidth. We used a polynomial of degree 2, a
bandwidth of 2.5 SpT subclasses, and a Gaussian kernel.

To obtain the value of the local polynomial fit ($y$) at spectral type
position (x) the expression:

$y=\sum_{k=0}^{n}\hat{a}_{n}\cdot x$ (2)

is evaluated. This procedure is repeated at several equally spaced $x$ values
representing spectral types from G8 to M9.5, allowing us to retrieve the
interpolated value at any SpT within this range. We limited our interpolation
to range from G8 to M9.5 because of the large gap between our only G5 spectrum
and the rest of our grid. We make use of the implementation provided by the
localreg PYTHON package 444https://github.com/sigvaldm/localreg/tree/master.

To account for the heteroscedastic uncertainties we used a Monte-Carlo
simulation of 1000 iterations. In each iteration, we resample the normalised
flux and SpT of each data point by adding a value sampled from a Gaussian
distribution with a standard deviation equal to the respective error and a
mean of zero. The non-parametric fit is computed for each iteration. At each
of the spectral type points we adopt the median values of these fits as the
final interpolated model spectrum and for the error we adopt the 1-$\sigma\,$
interval around this median. Fig. 6 shows an example of this procedure for one
wavelength range.

We repeat this procedure for multiple wavelength ranges. An interpolated
spectrum is then obtained by evaluating the values of these multiple non-
parametric fits at a given spectral type. We applied it to wavelength ranges
of 1 nm width over the entire UVB and VIS arms. A comparison between our
interpolated spectra and Class III templates of the same spectral type is
shown in Fig. 7. Here it can be seen that individual templates can have a flux
that is lower (PZ99J160843.4-260216) or higher (Par Lup 2) than that of the
interpolated templates at short wavelengths. This effect could be a
consequence of the uncertainties on the SpT and/or $A_{V}$ of the spectra
and/or differing levels of chromospheric activity. We find that roughly half
of the Class III spectra have a Balmer continuum flux higher than that of the
interpolated templates while the other half have a lower flux. Fig. 7 also
shows that the interpolation can deviate significantly from the observed
spectra in the region around 950 nm. This is a consequence of a poor telluric
correction in several template spectra. This extinction-less interpolated grid
can be found on GitHub 555https://github.com/RikClaes/FRAPPE along with the
Python script used to generate it and obtain the interpolated templates.

Figure 7: Comparison between individual Class III templates and the
interpolated spectra of the same spectral type. The templates are plotted in
black and the interpolated spectra in blue/orange. The transparent blue/orange
regions represent the 1-$\sigma$ uncertainties in the interpolated spectra.
The blue and orange colours correspond to the wavelength ranges of the
X-Shooter VIS and UVB arms respectively. The templates have been convolved
with a Gaussian kernel for clarity.

##  5 Interpolated spectra for spectral fitting

In this section we will apply the new Class III interpolated grid to the
classic problem of deriving in a self-consistent way the stellar (SpT,
$A_{V}$, $L_{\star}$) and accretion properties ($L_{\rm acc}$) of an actively
accreting TTS. In particular, we will compare our results to those obtained
using a method in which the individual template spectra (those listed in Table
3) are used to account for the stellar contribution.

Determining accretion and stellar properties in YSOs is not trivial. Excess
continuum emission due to accretion and extinction alters the observed
spectrum in opposite ways, although with a different wavelength dependence. A
self consistent method for deriving stellar properties, accretion luminosity,
and extinction simultaneously was previously presented by Manara et al.
(2013a). The method presented here is a further development of this
prescription, but with a different approach to the way the stellar photosphere
is accounted for when modeling an observed spectrum. This also implies changes
in how the stellar luminosity is calculated. We refer to this method as
FRAPPE: FitteR for Accretion ProPErties. We apply here this method to the 14
accreting T Tauri stars in the Chamaeleon I star-forming region observed with
X-Shooter during the VLT/PENELLOPE Large Program (Manara et al. 2021).

###  5.1 Fitting the UV excess

The fitting procedure used here combines three components to fit an observed
spectrum: 1) A continuum slab model is used to represent the emission from the
accretion shock; 2) a reddening law to account for extinction; 3) our
interpolated templates are used to represent the stellar contribution. Our
fitting procedure consists of a Python code that searches in a grid of
parameters the combination that best reproduces the observed spectrum of the
input accreting YSO.

For the continuum excess emission we use the grid of isothermal hydrogen slab
models developed by Rigliaco et al. (2012) and Manara et al. (2013a), the
details of which details are described in Manara (2014). Prior to these works,
such an approach was used by Valenti et al. (1993) and Herczeg & Hillenbrand
(2008). Here we describe the key parts of the model. The models assume local
thermodynamic equilibrium (LTE) and include emission from both $\rm H$ and
$\rm H^{-}$. A given models are described by an electron density ($n_{e}$),
electron temperature ($T_{\rm e^{-}}$), and the optical depth at 300 nm
($\tau$). The grid contains slab models for $n_{e}$ ranging from $10^{-11}\rm
cm^{-3}$ to $10^{-16}\rm cm^{-3}$, $T_{\rm e^{-}}$ ranging from 5000 to 11000
K and $\tau$ from 0.01 to 5. The slab models are matched to the observed,
dereddened spectrum of an accreting YSO using a scaling factor ($H_{\rm
slab}$). The models extend below the minimum wavelength of X-Shooter
($\lesssim 330\rm nm$), allowing us to compute $L_{\rm acc}$ from the total
flux of the slab model when scaled to match the observed spectrum during the
fitting procedure.

We use the Cardelli extinction law (Cardelli et al. 1989) to account for
extinction in our procedure. We fix the total-to-selective extinction value
$R_{V}$ to the average interstellar value of $R_{V}=3.1$ for all of the fits
performed in this work. To find the best fitting $A_{V}$ value we let the
extinction free to vary from 0.0 to 2.0 mag in steps of 0.1 mag. When an
extinction value is found at the upper edge of this range, we re-run the
procedure for larger $A_{V}$.

The main difference with respect to the method presented by Manara et al.
(2013a) is the use of an interpolated grid of templates created with the
method described in Sect. 4.2., while Manara et al. (2013a) used the
individual spectra in the grid of Class III templates from MTR13 (and later
MFA17) to represent the photospheric and chromospheric contribution of the
central star. During the fitting procedure, this grid is sampled at specific
SpT values. We run our procedure for SpTs at steps of 0.5 subclasses. The
interpolated spectra are scaled to the observed, dereddened spectrum of the
accreting YSO using a scaling factor ($K_{\rm cl3}$) which sets the stellar
luminosity.

The best fit is found by minimizing the likelihood function given in equation
3.

$\chi^{2}_{like}=\sum_{W.L.ranges}\frac{(f_{mod.}-f_{obs,dered})^{2}}{\sigma_{obs,dered}^{2}+\sigma_{mod.}^{2}}$
(3)

Here $f_{mod.}$ is the flux density of the model spectrum, which comprises the
sum of the scaled slab model and scaled interpolated Class III template,
within one of the selected wavelength range. $f_{obs,dered}$ is the flux of
the observed spectrum in the corresponding range after dereddening,
$\sigma_{obs}$ is the noise of the dereddened observation in the same range.
This expression is different than that from Manara et al. (2013a) in that it
includes $\sigma_{mod.}$, the uncertainties on the interpolated grid, taking
into account the scaling applied to match the observations (i.e.
$\sigma_{mod.}=K_{\rm cl3}\cdot\sigma_{interp.}$ ). At the edges of the
interpolations SpT range its uncertainties become larger in all wavelength
ranges. This will bias the results towards the edges of our spectral type
range. To prevent this, we set the errors at SpT’s earlier than K0 equal to
those obtained at K0.

We select a limited number of wavelength ranges to create an interpolated grid
of templates using the method presented in Sect. 4.2. These wavelength ranges
are selected starting from those used by Manara et al. (2013a), but with some
additions, as they carry information about the SpT and about the excess
emission due to accretion. Wavelength ranges not considered by Manara et al.
(2013a) are highlighted in Table 6. We note that the way Manara et al. (2013a)
used the information in these ranges differs from ours. In the best fit
determination of Manara et al. (2013a) the slopes of the observed Balmer and
Paschen continuum and the flux ratio at both sides of the Balmer jump are
matched to the model. We, however, choose to directly match the flux within
these wavelength ranges. We also modified some of the regions adopted from
Manara et al. (2013a) to prevent an overlap in wavelength. We included a
number of TiO bandheads around $\sim 710\>\rm nm$ to constrain the spectral
type of targets ranging from K6 to M9.5. To constrain targets with SpT from G5
to K6 we include wavelength ranges around $\sim 465$, $\sim 510$, and $\sim
540\>\rm nm$. These are based on the ones used in the R515 index presented by
HH14 with slight adjustments being made to avoid the sharp edges of features
which are present in the spectra of later type stars.

To constrain the accretion spectrum we include two wavelength ranges that
carry information about the size of the Balmer jump to be constrained ($\sim
361\>\rm nm$ and $\sim 400.5\>\rm nm$), three additional ranges to further
constrain the Balmer continuum ($\sim 335\>\rm nm$, $\sim 340\>\rm nm$ and
$\sim 355\>\rm nm$ ) and three more to constrain the Paschen continuum ($\sim
414.5\>\rm nm$, $\sim 450\>\rm nm$, and $\sim 475\>\rm nm$). At longer
wavelengths, the inner disk of Class II YSO can contribute to the observed
flux (e.g.; Pittman et al. 2022). Since our models do not include such a
component, we omit the use of wavelength ranges in the NIR arm. Suboptimal
telluric correction of both the templates and spectra being analysed can
affect the analysis when included. Wavelength regions that include telluric
lines are therefore also omitted. The exact wavelength ranges can be found in
Table 6.

The accretion emission is known to veil photospheric absorption features in
the observed YSO spectrum. Therefore we compare the Ca I line at $\sim 420\rm
nm$ in the observed spectrum with that of a veiled Class III template to
verify the goodness of our fits. We use a random Class III template with the
SpT nearest to the best fit solution and the best fitting slab model for this
test.

Fig. 8 shows how the normalized TiO 710 nm features vary as a function of SpT
in our interpolated grid. Here it can be seen that the different wavelength
rages disperse at late spectral types, showing the usefulness of this feature
to classify M stars.

Table 4: Wavelength ranges included in the interpolated grid used in our
fitting procedure.

Name | wavelength ranges
---|---
Balmer jump | 359-362b
| 399-402 b
Balmer continuum | 337.5-342.5
| 352-358 b
Paschen continuum | 414-415 a
| 448-452
| 474-476
TiO 710 nm | 702.5-703.5
| 706.5-707.5
| 709.5-710.5
| 713.5-714.5
R515 | 464-466 b
| 510-515 a
| 539-544 a
666Wavelength ranges that are newly introduced with respect to Manara et al.
(2013a) are indicated with $a$. Wavelength ranges that have been modified with
respect to Manara et al. (2013a) are reported with $b$.

Figure 8: Example of several interpolated normalized fluxes and their
associated uncertainties. The values of the fluxes in the TiO 710 nm
absorption band can be seen to diverge at late spectral types, indicating its
usefulness to constrain the spectral type of these later than K5. The shaded
areas indicate the respective 1 sigma uncertainties.

The procedure works as follows. For each spectral type we dereddened the
observed spectrum for each value of $A_{V}$. Then for each of these
combinations, we consider all of the slab models. The scaling factor for each
combination is obtained by having the combined model match the dereddened
observation at $\sim 355\>\rm nm$ and $\sim 731\>\rm nm$. We note that the
latter wavelength range is the same one as used to normalise our grid of
interpolated spectra. $K_{clIII}$ therefore corresponds to the stellar flux at
731 nm. In other words, we solve the following system of equations numerically
for $K_{\rm cl3}$ and $H_{\rm slab}$.

$\cases{f}_{355}&=K_{\rm cl3}\cdot f_{clIII,355}+H_{\rm slab}\cdot
f_{slab,355}\vspace{{0.3cm}}\\\ \par f_{731}=K_{\rm cl3}\cdot
f_{clIII,731}+H_{\rm slab}\cdot f_{slab,731}\\\ =K_{\rm cl3}\cdot 1+H_{\rm
slab}\cdot f_{slab,731}{}$ (4)

We then use the parameters to calculate $\chi^{2}_{like}$. This is done for
every point in the grid. When this is done for the entire grid of parameters
we select the model with the lowest $\chi^{2}_{like}$ as the best fit. This
optimization procedure is the same as that used by Manara et al. (2013a).

From this procedure, we directly obtain SpT and $A_{V}$. The accretion
luminosity is calculated by first integrating the scaled slab model over its
entire wavelength range ($\lambda\lambda=$ 50 nm to 2500 nm). This results in
the total accretion flux $F_{acc}$ which can then be converted to $L_{acc}$
using $L_{acc}=4\pi d^{2}F_{acc}$, with $d$ being the distance to the target.
$T_{\rm eff}$ is obtained from the SpT using the relationship by HH14.

Due to our use of interpolated spectra, our stellar luminosity calculation
differs from that of Manara et al. (2013a). To obtain the stellar luminosity
we first compute the stellar flux at 751 nm, the reference wavelength of our
bolometric correction. We obtain $f_{751}$ by first computing the flux at this
wavelength in the dereddened observed spectrum and then subtracting the scaled
slab model flux at the same wavelength. For sources with $T_{\rm eff}<3500\rm
K$ we apply the same interpolation over the VO feature as discussed in
Appendix D. The bolometric flux $F_{bol.}$ is then computed using our adjusted
relationship of HH14 and converted to $L_{\star}$ using $L_{\star}=4\pi
d^{2}F_{\rm bol}$.

The stellar radius is computed from $T_{\rm eff}$ and $L_{\star}$ using
$R_{\star}=L_{\star}/(4\pi\sigma_{\rm Boltz}T_{\rm eff}^{4})$. The stellar
mass ($M_{\star}$) and age are derived by placing the target on the HRD and
interpolating evolutionary tracks at its position. We preferred to use to more
recent models of Baraffe et al. (2015b). However, for 5 targets the $T_{\rm
eff}$ and/or $L_{\star}$range of the Baraffe et al. (2015b) models did not
extend to the found values, in these cases we used the tracks of Siess et al.
(2000) instead. Finally, we can obtain the mass accretion rate $\dot{M}_{\rm
acc}$ using

$\dot{M}_{acc}=\frac{L_{acc}R_{\star}}{GM_{\star}}\Bigg{(}1-\frac{R_{\star}}{R_{in}}\Bigg{)}^{-1},$
(5)

where we use the typical assumption for the inner disk radius of
$R_{in}=5R_{\star}$ (Gullbring et al. 1998).

Figure 9: Accretion luminosities vs. spectral type as obtained using FRAPPE
(gray squares) and obtained using the method of Manara et al. (2013b) (red
triangles). Results obtained for the same target with the two methods are
connected with a blue line. The green triangle indicates the M5 solution of WZ
Cha. The light blue circles are the nearly complete Chamaeleon I sample
presented by Manara et al. (2013a). The black errorbars indicate the
uncertainties on the accretion luminosity. The gray arrows indicate sources
listed as upper limits by Manara et al. (2023).

###  5.2 Accretion rates in accreting young stars in the Chamaeleon I region

To test our method we apply it to the sample of 14 Chamaeleon I targets
observed with the VLT/X-Shooter spectrograph as part of the VLT/PENELLOPE
Large Programme (see Manara et al. 2021, for details on the survey). The
results are listed in Table 7, and are presented here for the first time. In
Appendix F comparisons between the dereddened observations and best fit models
are shown. For the purpose of comparison, we applied the procedure of Manara
et al. (2013a) to the same sample and list the results in Table 8. In Fig. 9
the results of both methods are plotted on a $L_{\rm acc}$-SpT diagram. Fig.
10 displays both the obtained stellar luminosity and accretion luminosity.
Results obtained for the same target are connected with a blue line to make
the comparison easier. The values for the nearly complete sample of accreting
young stars in the Chamaeleon I star-forming region presented by Manara et al.
(2017a), using the values from Manara et al. (2023), is also shown with blue
circles.

It can be seen that the results obtained here are generally in agreement
within the typical uncertainties for the fitting procedure of Manara et al.
(2013a) ($\sigma_{A_{V}}\approx 0.2{\,\rm mag}$, $\sigma_{L_{\rm acc}}\approx
0.25{\,\rm dex}$ and $\sigma_{\dot{M}_{\rm acc}}\approx 0.35{\,\rm dex}$,
Manara et al. 2023). For the SpT we expect typical uncertainties of half a
subclass for SpTs later than K6, for earlier SpTs we expect uncertainties of
about 1 subclass. For 3 targets we find differences larger than the typical
uncertainties. These targets are WZ Cha, CV Cha and VZ Cha. We describe the
results for these targets in Appendix E.

The derived accretion luminosities of all targets agree within the
aforementioned uncertainties. The obtained stellar luminosities are also in
good agreement.

Fig. 11 displays the resulting $\dot{M}_{\rm acc}$\- $M_{\star}$ diagram. For
WZ Cha we obtained two degenerate solutions using the method of Manara et al.
(2013a) one at SpT M3 (indicated in red) and one at SpT M5 (indicated in
green). We prefer the M5 solution as the Class III template to which the M3
solution was fitted appears to be an outlier (see Appendix E). Here it can be
seen that, with exception of the M3 solution of WZ Cha, our results are within
the typical uncertainties.

The result obtained for WZ Cha and VZ Cha illustrates the benefits of our
method (see Appendix E). For WZ Cha, FRAPPE breaks a degeneracy between
spectral types and in the case of VZ Cha the Paschen continuum appears better
reproduced. The analysis for CV Cha highlights the need for improved
constraints when fitting late G to early K stars. Such constraints can not
only be obtained from the inclusion of Class III spectra around these spectral
types in our grid but also from additional information on the emission and
absorption lines present in the spectra of the Class II YSOs.

Figure 10: Accretion luminosities vs. stellar luminosity as obtained using
FRAPPE (red triangles) and obtained using the method of Manara et al. (2013b)
(gray squares). Results obtained for the same target with the two methods are
connected with a blue line. The green triangle indicates the M5 solution of WZ
Cha. The light blue dots is the nearly complete Chamaeleon I sample presented
by Manara et al. (2013a). The black errorbars indicate the uncertainties on
the stellar luminosity and accretion luminosity. The gray arrows indicate
sources listed as upper limits by Manara et al. (2023). Figure 11: Mass
accretion rate vs. stellar mass as obtained using FRAPPE (red triangles) and
obtained using the method of Manara et al. (2013b) (gray squares). Results
obtained for the same target with the two methods are connected with a blue
line. The green triangle indicates the M5 solution of WZ Cha. The light blue
dots are the nearly complete Chamaeleon I sample presented by Manara et al.
(2013a). The blue errorbars indicate the uncertainties on the stellar mass and
mass accretion rate. The gray arrows indicate sources listed as upper limits
by Manara et al. (2023). Table 5: Accretion properties of the Chameleon I
PENELLOPE targets obtained with FRAPPE.

Name | Dist | SpT | $T_{\rm eff}$ | $A_{V}$ | $L_{\star}$ | $\log(L_{acc}/L_{\odot})$ |  $M_{\star}$_B15 |  $M_{acc}$_B15 |  $M_{\star}$_S00 |  $M_{acc}$_S00
---|---|---|---|---|---|---|---|---|---|---
| [pc] |  | [K] | [mag] | $[L_{\odot}]$ |  | [$M\odot$] | [$M_{\odot}$/yr] | [$M\odot$] | [$M_{\odot}$/yr]
CHX18N | 192.0 | K5.5 | 4164 | 0.70 | 1.40 | -1.42 | 0.77 | $4.48\cdot 10^{-9}$ | 0.85 | $4.06\cdot 10^{-9}$
CHX18N_ep2 | 192.0 | K5.5 | 4164 | 0.70 | 1.41 | -1.22 | 0.77 | $7.11\cdot 10^{-9}$ | 0.86 | $6.40\cdot 10^{-9}$
CSCha | 190.0 | K5.5 | 4164 | 0.40 | 1.79 | -1.13 | 0.76 | $9.81\cdot 10^{-9}$ | 0.85 | $8.75\cdot 10^{-9}$
CVCha | 192.0 | K3.0 | 4540 | 1.10 | 4.03 | 0.14 | 1.19 | $1.52\cdot 10^{-7}$ | 1.47 | $1.23\cdot 10^{-7}$
Hn5 | 195.0 | M5.0 | 2980 | 0.80 | $1.79\cdot 10^{-1}$ | -2.30 | … | … | 0.15 | $2.14\cdot 10^{-9}$
INCha | 193.0 | M5.0 | 2980 | 0.00 | $2.18\cdot 10^{-1}$ | -2.75 | … | … | 0.16 | $7.91\cdot 10^{10}$
IPTau | 129.4 | M0.0 | 3900 | 1.10 | $3.96\cdot 10^{-1}$ | -1.21 | 0.63 | $5.43\cdot 10^{-9}$ | 0.64 | $5.31\cdot 10^{-9}$
SYCha | 181.0 | K7.5 | 3960 | 0.70 | $5.63\cdot 10^{-1}$ | -0.80 | 0.63 | $1.58\cdot 10^{-8}$ | 0.67 | $1.52\cdot 10^{-8}$
Sz10 | 184.0 | M4.5 | 3084 | 0.70 | $1.46\cdot 10^{-1}$ | -2.04 | 0.15 | $3.17\cdot 10^{-9}$ | 0.17 | $2.87\cdot 10^{-9}$
Sz19 | 189.0 | G8.5 | 5104 | 1.50 | 7.17 | -1.083 | … | … | 2.36 | $4.79\cdot 10^{-9}$
Sz45 | 192.0 | M0.0 | 3900 | 0.50 | $4.57\cdot 10^{-1}$ | -1.56 | 0.61 | $2.64\cdot 10^{-9}$ | 0.61 | $2.62\cdot 10^{-9}$
VWCha | 190.0 | K7.0 | 4020 | 2.10 | 2.32 | -0.194 | … | … | 0.71 | $1.13\cdot 10^{-7}$
VZCha | 191.0 | K7.5 | 3960 | 1.20 | $6.83\cdot 10^{-1}$ | -0.29 | 0.63 | $5.79\cdot 10^{-8}$ | 0.67 | $5.40\cdot 10^{-8}$
WZCha | 193.0 | M5.0 | 2980 | 0.60 | $1.97\cdot 10^{-1}$ | -1.83 | … | … | 0.15 | $6.37\cdot 10^{-9}$
XXCha | 192.0 | M2.5 | 3484 | 0.50 | $2.38\cdot 10^{-1}$ | -2.14 | 0.33 | $1.16\cdot 10^{-9}$ | 0.35 | $1.11\cdot 10^{-9}$

777The stellar mass and mass accretion rates are computed with both the
isochrones of Baraffe et al. (2015b) (marked as B15) and Siess et al. (2000)
(marked as S00). CV Cha and CS Cha are binaries (Reipurth et al. 2002;
Guenther et al. 2007, respectively). We do not report values that are outside
of the ranges of the Baraffe et al. (2015b) isochrones.

Table 6: Accretion properties of the Chameleon I PENELLOPE targets obtained
with the method presented by Manara et al. (2013a).

Name | Dist. [pc] | SpT | Teff [K] |  $A_{V}$ [mag] |  $L_{\star}$ [$L_{\odot}$] | $\log(L_{\rm acc}/L_{\odot})$ | $M_{\star}$ |  $\dot{M}_{\rm acc}$ [$M_{\odot}$/yr] | Model
---|---|---|---|---|---|---|---|---|---
CHX18N | 192 | K6 | 4115 | 0.7 | 1.23 | -1.236 | 0.73 | $6.90\cdot 10^{-9}$ | B15
CHX18N_ep2 | 192 | K6 | 4115 | 0.8 | 1.48 | -1.248 | 0.72 | $7.49\cdot 10^{-9}$ | B15
CSCha | 190 | K6 | 4115 | 0.4 | 1.51 | -0.808 | 0.72 | $2.08\cdot 10^{-8}$ | B15
CVCha | 192 | K0.5 | 4830 | 1.1 | 3.43 | 0.166 | 1.40 | $1.10\cdot 10^{-7}$ | B15
Hn5 | 195 | M5 | 2980 | 1.1 | 0.20 | -2.093 | 0.15 | $3.55\cdot 10^{-9}$ | S00
INCha | 193 | M5 | 2980 | 0.2 | 0.18 | -2.732 | 0.15 | $7.93\cdot 10^{-10}$ | S00
SYCha | 181 | K7 | 4020 | 0.8 | 0.60 | -0.775 | 0.70 | $1.53\cdot 10^{-8}$ | B15
Sz10 | 184 | M5 | 3125 | 1.0 | 0.20 | -1.849 | 0.17 | $4.87\cdot 10^{-9}$ | B15
Sz19 | 189 | G9 | 5025 | 1.5 | 7.04 | -0.623 | 2.37 | $1.40\cdot 10^{-8}$ | S00
Sz45 | 189 | M0 | 3900 | 0.7 | 0.48 | -1.344 | 0.60 | $4.54\cdot 10^{-9}$ | B15
VWCha | 190 | K7 | 4020 | 2.3 | 2.58 | -0.019 | 0.70 | $1.80\cdot 10^{-7}$ | S00
VZCha | 191 | K7.5 | 3960 | 1.7 | 0.63 | 0.040 | 0.64 | $1.16\cdot 10^{-7}$ | B15
WZCha | 193 | M3 | 3410 | 1.0 | 0.21 | -1.881 | 0.29 | $2.37\cdot 10^{-9}$ | B15
WZCha | 193 | M5 | 3060 | 0.8 | 0.26 | -1.706 | 0.18 | $7.73\cdot 10^{-9}$ | S00
XXCha | 192 | M3 | 3410 | 0.3 | 0.31 | -2.344 | 0.29 | $9.78\cdot 10^{-10}$ | B15

888The degenerate solution of WZ Cha is marked as *WZ Cha.

Figure 12: SpT and $T_{\rm eff}$ depedency of the accretion noise
$\log(L_{acc,noise}/L_{\star})$ values obtained from interpreting the
uncertainties in the Balmer and Paschen continuum ($<500$ nm) on our model
Class III spectra as accretion (Green dots). The blue dots illustrate the
$\log(L_{acc,noise}/L_{\star})$ values obtained when fitting the Class III
spectra with an accretion slab model. The results obtained for the PENELLOPE
Chamaeleon I sample is indicated with orange dots. The black line shows the
$L_{\rm acc,noise}$ relationship measured from the emission lines by MFA17 and
the red lines on the left show the uncertainty thereon. On the right, the red
line illustrates the best fit to the $\log(L_{acc,noise}/L_{\star})$ values.

##  6 Limits on accretion luminosity measurements from the UV excess

The study of the Class III spectra is important not just because they are used
as templates of the photospheres of accreting stars, but also because they
provide essential information on the limitations introduced by the stellar
chromospheric activity to the measurements of low accretion luminosities.
MTR13 and MFA17 discussed how chromospheric activity in the form of line
emission defines the lower boundaries to $L_{\rm acc}$ derived from the well-
established correlation between line emission and accretion luminosity, and
named this $L_{\rm acc,noise}$. Here we will examine how the noise in the
Balmer continuum emission in Class III objects sets an upper boundary to the
values of $L_{\rm acc}$ derived from the Balmer excess.

A variety of factors such as the uncertainties on the spectral type,
extinction, and levels of chromospheric activity may contribute to the
uncertainties on our interpolated model spectra. While such uncertainties may
only cause minor contributions to the accretion luminosity measured in strong
accretors, in weakly accreting objects such noise may have an important
impact. Therefore, to characterise the limitations of our method we derive the
accretion luminosities that correspond to the 1 $\sigma$ uncertainties on our
interpolated spectra, and we refer to this value as $L_{\rm acc,noise}$. To do
this, we create a set of artificial spectra that include a UV excess
equivalent to the 1 $\sigma$ uncertainties and fit these with FRAPPE.

Templates later than SpT M5.5 have a S/N ¡ 1 in the Balmer and Paschen
continuum. Therefore, including these templates in our analysis would strongly
affect the uncertainty of the continuum UV flux. We therefore limit the
analysis presented here to spectral types ranging from G8 to M5.5. We generate
another interpolated grid based on our templates but excluding templates later
than M5.5. We use this grid to create a set of blue enhanced artificial
spectra. For wavelength ranges in the Balmer and Paschen continuum (¡ 500nm)
we set the value of the artificial spectrum equal to the interpolation spectra
plus $1\sigma$ of the uncertainty thereon. The $1\sigma$ uncertainty is
obtained from the Monte Carlo simulation discussed in Sect 4.2. For longer
wavelengths, we simply adopt the values of the interpolated spectrum. The
artificial spectra are unitless since our interpolation is normalized to have
the flux at 731 nm equal to 1. We therefore multiply the artificial spectra
with a random value on the order of $0.1\times 10^{-14}$ to $100\times
10^{-14}$ erg nm-1s-1cm-2 so that they have a ”realistic” flux. We create such
artificial spectra for each half subclass ranging from G8 to M5.5.

During this fitting procedure, we keep the SpT fixed to the value used for
constructing the spectrum. The extinction is fixed to $A_{V}=0$ mag. In doing
so we obtain the accretion luminosities corresponding to spectra whose Balmer
and Paschen continuum are 1$\sigma$ interval above the interpolation. Here we
assumed that the uncertainties in the Balmer and Paschen continuum are fully
correlated.

The $L_{\rm acc,noise}$ and $L_{\star}$ obtained with this method are
arbitrary as they scale with the multiplicative factor used to create the
artificial spectra. Therefore we do not report the obtained values of $L_{\rm
acc,noise}$ and $L_{\star}$. Instead, we report the ratio $L_{\rm
acc,noise}/L_{\star}$ which is independent of this scaling and representative
of the contrast down to which we can accurately measure a UV excess. The
results are listed in Table 7. The dependence of $L_{acc,noise}/L_{\star}$ as
a function of SpT is shown in Fig. 12. Assuming the SpT-$T_{\rm eff}$ relation
of HH14, we also plot $L_{acc,noise}/L_{\star}$ as a function of $T_{\rm eff}$
in Fig. 12. Here it can be seen that the trend as a function of $T_{\rm eff}$
can be well approximated as a simple linear relation. This relationship can be
expressed as:

$\log(L_{\rm acc,noise}/L_{\star})=(5.9\pm 0.2)\cdot\log(\rm T_{\rm
eff}[K])-(23.3\pm 0.7)$ (6)

The relationships in Eq. 6 and Table 7 can be seen as a criterion for the
lowest measurable accretion luminosities. If the $\log(L_{\rm
acc,noise}/L_{\star})$ measured for a CTTS is of a similar order of magnitude
or falls below it, then we can not conclude if a target is accreting based on
the UV excess measurement. Several relations between the effective temperature
and spectral type have been presented in the literature (e.g.; HH14, Pecaut &
Mamajek 2013; Kenyon & Hartmann 1995; Luhman et al. 2003). Due to this lack of
uniformity, we recommend to directly use the values of $L_{\rm acc,noise}$ at
each SpT reported in Table 7.

Figure 12 also includes results obtained by fitting the Class III templates
themselves with FRAPPE. Here we once again kept the SpT fixed to the SpT of
the respective Class III and kept $A_{V}=0$ mag. In this way, we obtain a
similar $L_{\rm acc,noise}$ measurements. Only half of the Class III templates
provide a $L_{\rm acc,noise}$ measurement since half have a Balmer continuum
below the interpolation. The $L_{\rm acc,noise}$ values obtained from the
class III templates display a large scatter, this is a natural consequence of
the scatter in the residuals between the templates and the interpolation in
the Balmer and Paschen continuum. These results demonstrate how different the
Balmer continua, and therefore the inferred UV-excess, of the various
templates are. Using individual templates one may derive accretion luminosity
that can change by fractions of the stellar luminosity of up to 10% relative
to that found by using the interpolated spectra. The most extreme case is for
late G SpT targets. This uncertainty is significantly weaker at later SpTs and
in most cases it is only on the order of 1% of the stellar luminosity or
lower.

We also plot the results for the Class II targets presented in Sect. 5.2. One
target, Sz19, clearly falls below the relationship in Eq. 6. Its measured mass
accretion rate can therefore be highly affected by uncertainties on the
chromospheric emission. Finally, for comparison, we also plot a similar
relationship derived by MFA17 for the lowest accretion luminosities that one
can measure by studying the emission lines. MFA17 measured the luminosities of
several chromospheric emission lines in Class III stars and converted them to
accretion luminosities using the relations of Alcalá et al. (2014). We
converted their results obtained as a function of spectral type to effective
temperature using the SpT-$T_{\rm eff}$ of HH14 for consistency. It can be
seen that the $1\sigma$ threshold that we derive for the UV continuum excess
is higher in the entire SpT/$T_{\rm eff}$ range than the threshold obtained
from the line luminosities. This implies that an analysis of accretion tracing
emission lines allows us to measure lower accretion luminosities than the UV
excess. However, the empirical relationships used to convert line luminosities
to accretion luminosities (Alcalá et al. 2014, 2017) have been calibrated
using measurements of the UV excess. It is therefore uncertain whether these
relationships can be extrapolated to accretion luminosities below the
threshold on the measurable UV excess. A more detailed modeling of the $\rm
H\alpha$ emission lines, such as performed by Thanathibodee et al. (2023) may
yet allow for the characterisation of accretion properties of stars with low
accretion rates, even well below the threshold of MFA17. Here we need to add
the caveat that new work is currently being done on the influence of
chromospheric emission lines on accretion rate measurements (Stelzer et al. in
prep.), which will update the limit of MFA17 using the relationship between
line and accretion luminosity of Alcalá et al. (2017).

We note that our criterion for measurable accretion luminosities and that of
MFA17 are different in nature. The criterion of MFA17 represents typical
chromospheric line luminosities, whereas ours represents the 1 sigma
uncertainty on the stellar and chromospheric UV continuum emission in our
interpolated Class III model spectrum. The interpretation of both therefore
differs. If the line luminosity measured in a CTTS is of a similar order of
magnitude to the criterion of MFA17, then the chomospheric emission likely
provides a dominant contribution to the measured $L_{\rm acc}$. On the other
hand, if a $L_{\rm acc}$ obtained from the UV excess is smaller than the limit
presented here, then the uncertainties on this $L_{\rm acc}$ is dominated by
the uncertainties on the stellar emission.

Table 7: Accretion noise values as a function of SpT and $T_{\rm eff}$.

SpT | $\rm T_{\rm eff}[K]$ | $\log(L_{\rm acc,noise}/L_{\star})$
---|---|---
G8.0 | 5180 | -1.3
G8.5 | 5102 | -1.3
G9.0 | 5025 | -1.3
G9.5 | 4947 | -1.3
K0.0 | 4870 | -1.4
K0.5 | 4830 | -1.4
K1.0 | 4790 | -1.4
K1.5 | 4750 | -1.5
K2.0 | 4710 | -1.5
K2.5 | 4625 | -1.5
K3.0 | 4540 | -1.5
K3.5 | 4457 | -1.5
K4.0 | 4375 | -1.5
K4.5 | 4292 | -1.6
K5.0 | 4210 | -1.7
K5.5 | 4162 | -1.7
K6.0 | 4115 | -1.8
K6.5 | 4067 | -1.9
K7.0 | 4020 | -1.9
K7.5 | 3960 | -1.9
M0.0 | 3900 | -2.0
M0.5 | 3810 | -2.0
M1.0 | 3720 | -2.0
M1.5 | 3640 | -2.0
M2.0 | 3560 | -2.1
M2.5 | 3485 | -2.2
M3.0 | 3410 | -2.3
M3.5 | 3300 | -2.3
M4.0 | 3190 | -2.5
M4.5 | 3085 | -2.6
M5.0 | 2980 | -2.7
M5.5 | 2920 | -2.7
999The accretion noise values are obtained from interpreting the 1$\sigma$
level of uncertainty on the Balmer and Paschen continua ($<500$ nm) on our
interpolated Class III spectra at a given spectral type as accretion
luminosity. $T_{\rm eff}$ obtained from the relationship from HH14 are also
listed for convenience.

Table 8: The stellar and accretion luminosities obtained for the Class III templates when fitted with FRAPPE using $A_{V}=0$ and the spectral type of the respective Class III template. Name | $\log{L_{\star}}$ | $\log{L_{acc}}$ | $\log(L_{\rm acc}/L_{\star\rm})$
---|---|---|---
RXJ1508.6-4423 | -0.06 | -1.09 | -1.07
RXJ1526.0-4501 | -0.03 | -2.293 | -2.23
PZ99J160843.4-260216 | 0.09 | -1.817 | -1.91
CD-31_12522 | -0.14 | -1.449 | -1.31
RXJ1547.7-4018 | -0.18 | -2.128 | -1.94
RXJ1538.6-3916 | -0.36 | -2.795 | -2.43
2MASSJ15552621-3338232 | -0.69 | -2.485 | -1.80
RXJ1543.1-3920 | -0.48 | -3.165 | -2.68
RXJ1607.2-3839 | -0.21 | -3.586 | -3.38
NOlup | -0.45 | -1.968 | -1.52
Tyc7760283_1 | -0.61 | -3.401 | -2.79
THA15-36B | -1.11 | -3.352 | -2.24
Sz67 | -1.16 | -4.837 | -2.97
RECX-6 | -1.05 | -3.237 | -2.50
CD_36_7429B | -0.99 | -4.134 | -4.63
TWA7 | -0.84 | -5.616 | -4.00
TWA15_app2 | -0.95 | -3.553 | -2.29
TWA15_app1 | -1.01 | -2.786 | -1.78
Sz94 | -1.23 | -3.225 | -1.99
Par_Lup3_2 | -0.96 | -3.753 | -2.79
2MASSJ16091713-3927096 | -1.83 | -4.887 | -3.05
Sz107 | -1.06 | -3.538 | -2.48
J11195652-7504529 | -2.07 | -5.451 | -3.38
CHSM17173 | -1.86 | -4.790 | -2.93

###  6.1 Implications for mass accretion rate estimates.

The limitations on measuring $L_{\rm acc}$ through the UV excess in turn
reflects on the $\dot{M}_{\rm acc}$ values that we can reliably measure. It is
of particular interest to investigate how these limitations affect the
$\dot{M}_{\rm acc}-M_{\star}$ relation. We use the values of $L_{\rm
acc,noise}$ from Eq. 6 to compute the lower limit of $\dot{M}_{\rm acc}$ as a
function of stellar mass using the non-magnetic isochrones of Feiden (2016) at
1, 2, 3, and 6 Myr. The results are shown in Fig. 13. We use these isochrones
since they extend to higher masses than those of Baraffe et al. (2015b) and
therefore better cover the spectral types in Table 7. The isochrones of Feiden
(2016) are mostly consistent with those of Baraffe et al. (2015b).

We also applied the relationship of Eq. 6 directly to the measured $L_{\rm
acc}$ and $L_{\star}$ of the Chamaeleon I sample from Manara et al. (2023) and
the sample presented in Sect. 5.2. The results are also plotted in Fig. 13.
The majority of Class II targets fall well above the UV excess measurement
limit. However, a considerable fraction appears to fall below the limit. The
measured accretion rates of these targets are therefore dominated by the
uncertainties on the stellar UV-continuum emission. More detailed analyses are
needed to disentangle the possible low accretion rate in these targets from
the stronger chromospheric emission.

Manara et al. (2017b) used the Chamaeleon I sample shown here in combination
with a sample of targets in Lupus (from Alcalá et al. 2017) to discuss whether
the correlation between $\dot{M}_{\rm acc}$ and $M_{\star}$ is driven by the
detection limits and if the observed scatter in $\dot{M}_{\rm acc}$ fills the
observable range. Only 3 sources from the sample of Manara et al. (2023) that
fall below our detection limit were previously not indicated as upper limits.
These targets all fall in a locus were upper limits were already present. Our
limit on the measurable mass accretion rate therefore does not change the
conclusion reached by Manara et al. (2017b). Namely, that this correlation is
real and not a consequence of detection limits.

Figure 13: Mass accretion rate vs. stellar mass for the Chamaeleon I sample
presented by Manara et al. (2023) (blue dots) and the Chamaeleon I sample
analysed in this work. Objects that have an accretion luminosity lower than
the criterion given in equation 6 are marked with a red dot. The limits we
derived based on the uncertainties on the chromospheric emission are shown
with the blue, orange, and green lines for 1.2, 3, and 6 Myr old objects
respectively. The red errorbars indicate the uncertainties on the stellar mass
and mass accretion rate. The gray arrows indicate sources listed as upper
limits by Manara et al. (2023).

##  7 Summary and conclusions

We presented the analysis of 24 new VLT/X-shooter spectra of Class III young
stars for their use as photospheric templates to complement the previous
samples of MTR13 and MFA17. All spectra are available in reduced and
dereddened form on GitHub 101010https://github.com/RikClaes/FRAPPE_ClassIII.
We obtained the spectral type through the use of spectral indices and by
comparing the relative strength of photospheric features to the samples of
MTR13 and MFA17.

We employed ROTFIT to derive the photospheric properties ($\log{g}$, $\rm
T_{eff}$, $v\sin{i}$, RV) of the sample. The results of both methods are
generally in agreement with each other and the photospheric properties confirm
the young nature of these targets. As previously noted in the literature
(e.g., Bell et al. 2014; Herczeg & Hillenbrand 2015; Manara et al. 2017a;
Pecaut 2016), we see a mass dependent trend of the derived isochronal ages for
targets in the same star forming region. We compared the stellar luminosities
obtained through extending and integrating the X-Shooter spectra in our sample
with luminosities obtained by applying the bolometric correction of HH14. We
found a small but systematic difference between the results of both methods
for effective temperatures lower than about 4500 K, leading us to propose an
adjustment to the bolometric correction of HH14.

To remove the non-uniform SpT sampling of the templates and mitigate the
uncertainties associated with their use, we proposed a method of interpolating
between the templates. We applied this type of interpolation to the entire
wavelength range covered by the spectra in 1nm wide bins and made the results
publicly available on GitHubnote1. We also applied the method to specific
regions in the spectra that are useful to obtain the stellar and accretion
properties of Class II targets. This empirical method has been implemented in
a code that self consistently measures the extinction, stellar, and accretion
properties. We verified this framework by analysing the Chamaeleon I sample
observed as part of the PENELLOPE program and compared the results to those
obtained using the method presented by Manara et al. (2013a) on the same
spectra. We found good agreement in the results obtained with the two methods.
Several future improvements, such as additional Class III templates at early
SpTs or the inclusion of veiling measurements in the best fit determination,
can still be made to FRAPPE. Such improvements are particularly useful to
constrain the stellar properties stars with a spectral type earlier than K6
and will make FRAPPE more user friendly.

We measured the typical accretion to stellar luminosity ratios that would be
obtained if the 1 $\sigma$ uncertainties in our model spectra were interpreted
as excess emission due to accretion. This ratio is representative of the
typical lower limit on the measurable mass accretion rates in young stars when
using continuum UV excess. The value has a strong dependency on the spectral
type. This trend is likely a consequence of the worse constraints on earlier
SpT stellar emission within our sample of Class III sources, as well as of a
worse contrast with the UV excess due to earlier stars having the peak of the
photospheric emission at bluer wavelengths, hampering the detection of an
excess for contrast reasons. This limit is higher than the lower limit
presented for accretion rates derived from emission lines presented by MFA17.
We, therefore, conclude that an in-depth analysis of emission lines is needed
to obtain accurate measurements of mass accretion rates in low accreting
objects. We applied our lower limit to the Chamaeleon I sample of Manara et
al. (2023). The majority of objects in this region were found to have
accretion rates well above our lower limit.

This shows that the uncertainties associated with the use of Class III
templates do not significantly affect the observed correlations between mass
accretion rate and disk mass or stellar mass (see Manara et al. 2023 for a
review). Our improved methodology for self consistently deriving accretion
properties will facilitate further studies into these relations.

###### Acknowledgements.

We thank the anonymous referee for the useful comments to our submitted
manuscript. R. Claes acknowledges the PhD fellowship of the International Max-
Planck-Research School (IMPRS) funded by ESO This work was partly funded by
the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in the
framework of the YTTHACA Project 469334657 under the project code MA 8447/1-1.
Funded by the European Union (ERC, WANDA, 101039452). Views and opinions
expressed are however those of the author(s) only and do not necessarily
reflect those of the European Union or the European Research Council Executive
Agency. Neither the European Union nor the granting authority can be held
responsible for them. J. B. Lovell acknowledges the Smithsonian Institute for
funding via a Submillimeter Array (SMA) Fellowship. J.M. Alcalá acknowledges
financial support from PRIN-MUR 2022 20228JPA3A “The path to star and planet
formation in the JWST era (PATH)” funded by NextGeneration EU and by INAF-GoG
2022 “NIR-dark Accretion Outbursts in Massive Young stellar objects (NAOMY)”.
J.M. Alcalá and A. Frasca acknowledge financial support from Large Grant INAF
2022 “YSOs Outflows, Disks and Accretion: towards a global framework for the
evolution of planet forming systems (YODA)”. This work benefited from
discussions with the ODYSSEUS team (HST AR-16129),
https://sites.bu.edu/odysseus/. 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. This research has made use
of the SIMBAD database, operated at CDS, Strasbourg, France.

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##  Appendix A Observations and data reduction

Table 9: Night log of the observations |  | Slit width [$"\times 11"$] | Exp. Time[$N_{\rm exp}\times{\rm s}$] | Exp. time [$N_{\rm exp}\times NDIT\times{\rm s}$]
---|---|---|---|---
Name | Date of observation [UT] | UVB | VIS | NIR | UVBexpT | VISexpT | NIRexpT
CD-31_12522 | 2022-06-03T00:41:42.9278 | 1.0 | 0.4 | 0.4 | 2 $\times$ 250 | 2 $\times$ 160 | 2 $\times$ 2 $\times$ 150
RXJ1608.9-3905 | 2022-05-03T08:35:32.8475 | 1.0 | 0.4 | 0.4 | 2 $\times$ 180 | 2 $\times$ 90 | 2 $\times$ 2 $\times$ 100
MV Lup | 2010-05-05T08:30:21.1291 | 0.5 | 0.4 | 0.4 | 4 $\times$ 150 | 8 $\times$ 60 | 12 $\times$ 1 $\times$ 100
RXJ0438.6+1546 | 2021-12-08T02:10:32.3906 | 0.5 | 0.4 | 0.4 | 2 $\times$ 110 | 2 $\times$ 20 | 2 $\times$ 4 $\times$ 30
J15552621-3338232 | 2022-05-03T06:04:01.0328 | 1.0 | 0.4 | 0.4 | 4 $\times$ 180 | 4 $\times$ 90 | 4 $\times$ 2 $\times$ 100
MT Lup | 2014-04-28T05:33:01.1666 | 0.5 | 0.4 | 0.4 | 4 $\times$ 179 | 4 $\times$ 80 | 4 $\times$ 20 $\times$ 10
MX Lup | 2022-06-03T02:34:14.6760 | 1.0 | 0.4 | 0.4 | 4 $\times$ 180 | 4 $\times$ 90 | 4 $\times$ 2 $\times$ 100
RXJ1607.2-3839 | 2022-06-24T04:15:05.3699 | 1.0 | 0.4 | 0.4 | 4 $\times$ 180 | 4 $\times$ 90 | 4 $\times$ 2 $\times$ 100
MW Lup | 2022-06-03T01:52:44.9932 | 1.0 | 0.4 | 0.4 | 4 $\times$ 200 | 4 $\times$ 110 | 4 $\times$ 2 $\times$ 100
NO Lup | 2014-04-28T08:07:12.0366 | 0.5 | 0.4 | 0.4 | 4 $\times$ 219 | 4 $\times$ 120 | 4 $\times$ 20 $\times$ 12
THA15-43 | 2022-07-19T03:13:14.3819 | 1.0 | 0.4 | 0.4 | 4 $\times$ 200 | 4 $\times$ 110 | 4 $\times$ 2 $\times$ 100
THA15-36A | 2022-06-24T05:03:13.4256 | 1.0 | 0.4 | 0.4 | 4 $\times$ 210 | 4 $\times$ 120 | 4 $\times$ 3 $\times$ 80
THA15-36B | 2022-06-24T05:03:13.4256 | 1.0 | 0.4 | 0.4 | 4 $\times$ 210 | 4 $\times$ 120 | 4 $\times$ 3 $\times$ 80
RECX-6 | 2022-03-02T03:22:05.3962 | 1.0 | 0.4 | 0.4 | 2 $\times$ 440 | 2 $\times$ 350 | 2 $\times$ 5 $\times$ 100
Sz67 | 2022-06-16T03:55:17.2951 | 1.0 | 0.4 | 0.4 | 2 $\times$ 280 | 2 $\times$ 190 | 2 $\times$ 3 $\times$ 100
J16090850-3903430 | 2022-06-24T05:34:42.3279 | 1.0 | 0.9 | 0.9 | 4 $\times$ 600 | 4 $\times$ 510 | 4 $\times$ 3 $\times$ 200
16075888-3924347 | 2022-07-13T23:46:15.8273 | 1.0 | 0.9 | 0.9 | 4 $\times$ 600 | 4 $\times$ 510 | 4 $\times$ 3 $\times$ 200
J16091713-3927096 | 2022-06-03T04:01:34.0592 | 1.0 | 0.9 | 0.9 | 4 $\times$ 700 | 4 $\times$ 610 | 4 $\times$ 3 $\times$ 250
V1191Sco | 2022-06-02T07:50:32.4620 | 1.0 | 0.9 | 0.9 | 4 $\times$ 550 | 4 $\times$ 460 | 4 $\times$ 3 $\times$ 200
Binaries |  |  |  |  |  |  |
CD-39_10292 | 2022-07-25T01:02:17.1203 | 1.0 | 0.4 | 0.4 | 2 $\times$ 250 | 2 $\times$ 160 | 2 $\times$ 3 $\times$ 100
THA15-38 | 2022-07-22T02:23:20.5225 | 1.0 | 0.4 | 0.4 | 4 $\times$ 210 | 4 $\times$ 120 | 4 $\times$ 3 $\times$ 80
CD-35_10498 | 2023-03-06T07:52:55.5080 | 1.0 | 0.4 | 0.4 | 2 $\times$ 200 | 2 $\times$ 110 | 2 $\times$ 2 $\times$ 100
V1097Sco | 2022-06-05T00:47:31.7504 | 1.0 | 0.4 | 0.4 | 4 $\times$ 210 | 4 $\times$ 120 | 4 $\times$ 3 $\times$ 80
NN Lup | 2022-06-16T04:16:09.4443 | 1.0 | 0.4 | 0.4 | 4 $\times$ 200 | 4 $\times$ 110 | 4 $\times$ 2 $\times$ 100
Table 10: Photometry available for our targets.

Band | MVlup | NOlup | MTlup | THA15-36 | 2MASSJ16090850
---|---|---|---|---|---
U | 11.98 (2) | 15.13 (2) | … | … | …
B | 12.59 (3) | 14.65(2) | … | 15.30 (6) | 18.00 (8)
V | 11.28(3) | 12.86 (5) | 12.32 (6) | 13.89 (6) | 16.60 (8)
R | 10.02 (2) | 12.14 (2) | 12.10 (6) | 13.57 (6) | 16.43 (8)
G | 11.04 (1) | 12.21 (1) | 11.99(1) | … | 15.66 (1)
I | 9.5210.02 (4) | 11.15 (5) | 11.01 (5) | 11.68 (7) | 14.16 (8)
J | 9.56 (4) | 9.90 (4) | 10.11 (4) | 10.47 (4) | 12.20 (4)
H | 9.02 (4) | 9.29 (4) | 9.57 (4) | 9.77(4) | 11.64 (4)
Ks | 8.88 (4) | 9.12 (4) | 9.38 (4) | 9.53 (4) | 11.36 (4)
SDSS_g | … | … | 12.90 (6) | 14.61 (6) | …
SDSS_r | … | … | 11.86 (6) | 13.29 (6) | …
SDSS_i | … | … | 11.42 (6) | 12.26 (6) | …
111111(1): Gaia Collaboration et al. (2020), (2): Makarov (2007), (3): Høg et
al. (2000), (4): Cutri et al. (2003) (5): Kiraga (2012) (6): Zacharias et al.
(2012) (7): Cieza et al. (2007) (8): Merín et al. (2008)

Table 11: Signal to noise ratios at different wavelengths. name | 416 nm | 448 nm | 490 nm | 701 nm | 750 nm | 801nm | 1217.5 nm | 1600 nm | 2214 nm
---|---|---|---|---|---|---|---|---|---
RXJ0445.8+1556 | 15.93 | 12.99 | 14.77 | 56.26 | 53.54 | 115.46 | 48.87 | 14.27 | 273.74
RXJ1508.6-4423 | 16.24 | 14.61 | 16.63 | 69.86 | 50.61 | 136.19 | 50.14 | 30.65 | 88.64
RXJ1526.0-4501 | 6.60 | 8.07 | 7.86 | 24.60 | 21.29 | 116.23 | 106.00 | 16.40 | 131.51
HBC407 | 6.06 | 7.47 | 7.57 | 19.43 | 16.57 | 104.87 | 84.71 | 14.47 | 160.83
PZ99J160843.4-260216 | 7.63 | 8.95 | 8.65 | 28.02 | 24.43 | 135.80 | 109.30 | 19.15 | 150.05
CD-31_12522 | 7.67 | 9.09 | 8.26 | 24.71 | 21.82 | 74.21 | 123.74 | 16.71 | 367.12
RXJ1515.8-3331 | 6.24 | 7.26 | 7.15 | 22.46 | 18.48 | 109.48 | 72.32 | 20.20 | 239.62
PZ99J160550.5-253313 | 5.73 | 6.83 | 6.73 | 19.68 | 16.02 | 91.52 | 94.63 | 11.15 | 124.80
RXJ0457.5+2014 | 6.75 | 7.53 | 7.41 | 25.51 | 22.08 | 105.95 | 101.53 | 13.02 | 172.28
RXJ0438.6+1546 | 6.15 | 7.26 | 7.07 | 20.07 | 19.44 | 61.56 | 95.07 | 16.04 | 252.33