# Towards a comprehensive view of accretion, inner disks, and extinction in
classical T Tauri stars: an ODYSSEUS study of the Orion OB1b association

Caeley V. Pittman Institute for Astrophysical Research, Department of
Astronomy, Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA
Catherine C. Espaillat Institute for Astrophysical Research, Department of
Astronomy, Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA
Connor E. Robinson Department of Physics & Astronomy, Amherst College,
Amherst, MA 01002, USA  Thanawuth Thanathibodee Institute for Astrophysical
Research, Department of Astronomy, Boston University, 725 Commonwealth Avenue,
Boston, MA 02215, USA  Nuria Calvet Department of Astronomy, University of
Michigan, 311 West Hall, 1085 S. University Avenue, Ann Arbor, MI 48109, USA
John Wendeborn Institute for Astrophysical Research, Department of Astronomy,
Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA  Jesus
Hernández Instituto de Astronomía, Universidad Autónoma de México Ensenada,
B.C, México  Carlo F. Manara European Southern Observatory, Karl-
Schwarzschild-Strasse 2, 85748 Garching, Germany  Fred Walter Department of
Physics and Astronomy, Stony Brook University, Stony Brook NY 11794-3800, USA
Péter Ábrahám Konkoly Observatory, Research Centre for Astronomy and Earth
Sciences, Eötvös Loránd Research Network, Konkoly-Thege Miklós út 15-17, 1121
Budapest, Hungary  ELTE Eötvös Loránd University, Institute of Physics,
Pázmány Péter Sétány 1/A, 1117 Budapest, Hungary  CSFK, MTA Centre of
Excellence, Konkoly-Thege Miklós út 15-17, 1121 Budapest, Hungary  Juan M.
Alcalá Osservatorio Astronomico di Capodimonte, via Moiariello 16, 80131
Napoli, Italy  Sílvia H. P. Alencar Departamento de Fisica, Universidade
Federal de Minas Gerais, Av. Antonio Carlos 6627, 30270-901 Belo Horizonte,
MG, Brazil  Nicole Arulanantham Space Telescope Science Institute, 3700 San
Martin Drive, Baltimore, MD 21218, USA  Sylvie Cabrit Observatoire de Paris,
PSL University, Sorbonne University, CNRS, LERMA, 61 Av. de l’Observatoire,
75014 Paris, France  Jochen Eislöffel Thüringer Landessternwarte, Sternwarte
5, D-07778 Tautenburg, Germany  Eleonora Fiorellino Konkoly Observatory,
Research Centre for Astronomy and Earth Sciences, Eötvös Loránd Research
Network, Konkoly-Thege Miklós út 15-17, 1121 Budapest, Hungary  CSFK, MTA
Centre of Excellence, Konkoly-Thege Miklós út 15-17, 1121 Budapest, Hungary
Osservatorio Astronomico di Capodimonte, via Moiariello 16, 80131 Napoli,
Italy  Kevin France Laboratory for Atmospheric and Space Physics, University
of Colorado Boulder, Boulder, CO 80303, USA  Manuele Gangi Osservatorio
Astronomico di Roma, via di Frascati 33, 00078 Monte Porzio Catone, Italy
Konstantin Grankin Crimean Astrophysical Observatory, Department of Stellar
Physics, Nauchny, 298409, Crimea  Gregory J. Herczeg Kavli Institute for
Astronomy and Astrophysics, Peking University, Yiheyuan 5, Haidian Qu, 100871
Beijing, China  Department of Astronomy, Peking University, Yiheyuan 5,
Haidian Qu, 100871 Beijing, China  Ágnes Kóspál Konkoly Observatory, Research
Centre for Astronomy and Earth Sciences, Eötvös Loránd Research Network,
Konkoly-Thege Miklós út 15-17, 1121 Budapest, Hungary  ELTE Eötvös Loránd
University, Institute of Physics, Pázmány Péter Sétány 1/A, 1117 Budapest,
Hungary  CSFK, MTA Centre of Excellence, Konkoly-Thege Miklós út 15-17, 1121
Budapest, Hungary  Max Planck Institute for Astronomy, Königstuhl 17, 69117
Heidelberg, Germany  Ignacio Mendigutía Centro de Astrobiología (CSIC-INTA),
ESA-ESAC Campus, 28692, Villanueva de la Cañada, Madrid, Spain  Javier Serna
Instituto de Astronomía, Universidad Autónoma de México Ensenada, B.C, México
Laura Venuti SETI Institute, 339 Bernardo Ave, Suite 200, Mountain View, CA
94043, USA

(Received 15 June 2022; Revised 2 August 2022; Accepted 7 August 2022)

###### Abstract

The coevolution of T Tauri stars and their surrounding protoplanetary disks
dictates the timescales of planet formation. In this paper, we present
magnetospheric accretion and inner disk wall model fits to NUV-NIR spectra of
nine classical T Tauri stars in Orion OB1b as part of the Outflows and Disks
around Young Stars: Synergies for the Exploration of ULLYSES Spectra
(ODYSSEUS) Survey. Using NUV-optical spectra from the Hubble UV Legacy Library
of Young Stars as Essential Standards (ULLYSES) Director’s Discretionary
Program and optical-NIR spectra from the PENELLOPE VLT Large Programme, we
find that the accretion rates of these targets are relatively high for the
region’s intermediate age of 5.0 Myr; rates range from 0.5–$17.2\times
10^{-8}$ M☉ yr-1, with a median value of $1.2\times 10^{-8}$ M☉ yr-1. The NIR
excesses can be fit with 1200–1800 K inner disk walls located at 0.05–0.10 AU
from the host stars. We discuss the significance of the choice in extinction
law, as the measured accretion rate depends strongly on the adopted extinction
value. This analysis will be extended to the complete sample of T Tauri stars
being observed through ULLYSES to characterize accretion and inner disks in
star-forming regions of different ages and stellar populations.

Stellar accretion disks; Protoplanetary disks; Star formation; Pre-main
sequence stars; Reddening law; Interstellar extinction

††journal: AJ

##  1 Introduction

The coevolution of T Tauri stars (TTS) and their surrounding protoplanetary
disks is one of the most important subjects in the field of planet formation
(Manara et al., 2022). Accretion of disk material onto the star can be traced
by continuum excesses in the near-ultraviolet to optical region of the
spectrum (Valenti et al., 1993; Gullbring et al., 2000; Herczeg & Hillenbrand,
2008). Emission from the frontally-illuminated inner wall of the disk can be
traced by continuum excesses in the near-to mid-infrared region (Natta et al.,
2001; Tuthill et al., 2001; D’Alessio et al., 2005). A model that can self-
consistently reproduce the spectra of actively-accreting T Tauri stars from
the ultraviolet to the infrared is a vital tool for understanding the
coevolution of the star and inner disk. To reproduce the NUV-NIR spectra of
CTTS, one can combine accretion shock and inner disk wall models to create a
consistent description of the physical mechanisms producing the observed
spectra, as has been demonstrated in GM Aurigae by Ingleby et al. (2015).

The magnetospheric accretion model (Koenigl, 1991; Shu et al., 1994; Hartmann
et al., 1994; Calvet & Gullbring, 1998; Muzerolle et al., 1998, 2001) has been
widely used in explaining observations of UV-excesses and emission lines in
CTTS (for a review, see Hartmann et al., 2016). Bouvier et al. (2020) and the
Gravity Collaboration (2020) confirmed that hydrogen Br$\gamma$ emission
associated with the magnetospheric accretion paradigm originates well within
TTS corotation radii, reinforcing the hypothesis that the emission comes from
accretion columns rather than a wind farther away from the star. When modeling
this emission, it is important to fit the optical spectra in addition to the
NUV, as accretion estimates that fit excesses only at blue wavelengths
underestimate the accretion rates by a factor of $\sim$2 (Fischer et al.,
2011). To account for both NUV and optical continuum excesses in classical T
Tauri stars (CTTS), Ingleby et al. (2013) found that a multi-column accretion
shock model should be used (based on the shock model of Calvet & Gullbring,
1998).

D’Alessio et al. (2005) found that the spectrum of a heated inner wall of a
dusty disk located at the dust sublimation radius dominates the emission at
NIR-MIR wavelengths. The structure and intensity of emission from the inner
wall of protoplanetary disks are determined primarily by the wall’s geometry
and the mineralogy of the dust (e.g. Muzerolle et al., 2003; McClure et al.,
2013). Gas accretion onto the star is likely driven by turbulence in this
inner disk, which also necessarily causes diffusion of dust particles that are
coupled to the gas; the strength of this diffusion dictates the shape of the
inner wall, independent of dust composition, with the wall geometry ranging
from short and curved, to tall and vertical (Schobert & Peeters, 2021). The
primary implication of this is that observed emission from a curved wall does
not depend heavily on disk inclination $i$, whereas emission from a vertical
wall depends strongly on $i$. McClure et al. (2013) best fit the 2–10 $\mu$m
continuum excesses of four TTS by approximating a curved wall using two
vertical walls at different radii, each with a different height, dust size
distribution, and composition.

The Hubble UV Legacy Library of Young Stars as Essential Standards (ULLYSES)
DDT program (Roman-Duval et al., 2020), combined with the PENELLOPE Very Large
Telescope (VLT) Large Program (Manara et al., 2021), provides an ideal sample
for exploring the variation in CTTS system properties across ranges of
spectral types, ages, and masses. The Outflows and Disks around Young Stars:
Synergies for the Exploration of ULLYSES Spectra (ODYSSEUS) collaboration
(Espaillat et al., 2022) is maximizing the scientific impact of these data by
studying accretion, outflows, and disk chemistry in the largest sample of TTS
observed with the Hubble Space Telescope (HST) to date. This paper focuses on
modeling the accretion and inner disks of the first sample of TTS observed by
ULLYSES.

ULYSSES began observations with Orion OB1, located about 400 pc away (Briceño
et al., 2019). Here, we study nine CTTS in the Orion OB1b star-forming region,
which has a mean age of 5.0 Myr and a disk fraction of 12% (Briceño et al.,
2019). This is intermediate between Cloud B (2.5 Myr, 31% CTTS) and OB1a (10.8
Myr, 6% CTTS), indicating an intermediate level of disk evolution in the
region.

In this work, we model the same Orion OB1b sample of CTTS as Manara et al.
(2021) to demonstrate the significance of using NUV spectra to determine the
accretion and extinction properties of these targets. For the first time, we
model both accretion and inner disks in a sample of CTTS using contemporaneous
spectra from 2000–24000 Å. Once this analysis is extended to the full ULLYSES
sample of $\sim$60 CTTS in nine star-forming regions, we can constrain the
relationships between stellar parameters and accretion and inner disk
properties to an extent that has not been done before.

This paper is organized as follows. In Section 2, we discuss the sample of
TTS, multiplicity in the sample, stellar parameters, and observations. In
Section 3, we describe the accretion shock and disk models used to fit the
NUV-NIR continua of the CTTS. Section 4 presents the modeling results. In
Section 5, we compare our results to those of previous studies and discuss the
significance of the choice in extinction law and the wavelength range of data
available. Finally, in Section 6 we present a summary of our findings and
future work that will be possible through ODYSSEUS.

##  2 Sample and Observations

The ULLYSES program (Roman-Duval et al., 2020) began observations with a
sample of eight CTTS in the Orion OB1b subassociation (Briceño et al., 2001,
2005, 2019) and two WTTS (weak-lined TTS, non-accreting sources) in the 25 Ori
cluster, which are used as template photospheres in this analysis (see Figure
3 in Appendix A for a justification of their classification as WTTS). Each
target was observed with both HST and the VLT contemporaneously. One of these
targets, CVSO 165, was discovered to be a binary system composed of two CTTS,
so 11 TTS were observed in total spanning spectral types M3.5–K6 and masses
0.3–0.9 M☉.

###  2.1 Objects and stellar parameters

CVSO 17, CVSO 36, and CVSO 109 are known to be physical binaries (Tokovinin et
al., 2020), and CVSO 104 and CVSO 165 have visual companions with which they
are not kinematically associated (Manara et al., 2021). The primary component
of CVSO 104 was found to be a spectroscopic binary (Kounkel et al., 2019;
Manara et al., 2021; Frasca et al., 2021), but these components are not
resolved in the HST observations. Proffitt et al. (2021) found that the
primary component of CVSO 165 is also itself a binary. The ULLYSES HST
observations of this object are able to resolve the two components, which both
show signatures of active accretion and are thus both modeled in this
analysis.

Stellar parameters for all CTTS targets and WTTS photospheric templates used
in this work are listed in Table 2. For targets not affected by unresolved
binarity in their X-Shooter observations, values for spectral type (SpT), mass
(M⋆), distance ($d$), and veiling ($r$) are adopted from Manara et al. (2021),
and their values for stellar radius (R⋆) and V-band extinction ($A_{V}$) are
included for comparison with the values we derive. Effective temperatures for
all targets except the CVSO 165 binary system come from the temperature-
spectral type relation given for 5–30 Myr stars in Pecaut & Mamajek (2013).
Manara et al. (2021) derive distances from Gaia Early Data Release 3
parallaxes that have reliable astrometric solutions (typically RUWE $<$ 1.4).
For those without reliable solutions, the mean distance to the association is
used and an uncertainty of 10% assumed.

####  2.1.1 CVSO 165 binary

We obtain the effective temperature ($T_{eff}$) and the visual extinction
($A_{V}$) for each component of the CVSO 165 system by comparing the HST
spectra against the PHOENIX synthetic spectral library (Husser et al., 2013).
We use values of surface gravity adequate for PMS stars (e.g., $3.0<{\rm
log(g)}<4.5$) and interpolate the spectral library to obtain theoretical grids
with intervals of 50 K in $T_{eff}$. For each theoretical spectrum, we apply
values of $A_{V}$ from 0 to 5 in steps of 0.01 using the standard interstellar
reddening law (RV=3.1) from Cardelli et al. (1989). Minimizing $\chi^{2}$, we
obtain the $T_{eff}$ and the $A_{V}$ from the best match between the observed
HST spectra and the reddened synthetic spectra. To avoid contamination from
accretion flux, we use the spectral range from 6000–9000 Å. We also avoid the
region around H$\alpha$, fitting a Gaussian function to the line profile and
ignoring the spectral range between -5$\sigma$ and +5$\sigma$ from the center
of the line. Finally, the uncertainties in the estimated values are obtained
using the Monte Carlo (MC) method of error propagation (Anderson, 1976),
varying the HST spectra fluxes randomly 500 times within their reported
uncertainties. The values reported in Table 2 are the median and standard
deviation of the 500 MC results.

We derive V magnitudes for each component of CVSO 165 by multiplying the HST
spectrum by the Johnson V-filter transmission curve. We obtained ${\rm
V}=13.875\pm 0.002$ for CVSO 165A and ${\rm V}=15.775\pm 0.004$ for CVSO 165B.
The RUWE astrometric parameter is highly sensitive to unresolved binary
systems; the high RUWE value of 14.3 for CVSO 165 indicates a poor astrometric
solution (Lindegren, 2020). Therefore, we assume a distance of $400\pm 40$ pc
(Briceño et al., 2019) to estimate the stellar luminosity for CVSO 165A and
CVSO 165B using the visual magnitude corrected by extinction. Finally,
comparing the location on the H-R diagram with the MIST evolutionary model
(Dotter, 2016), we obtained the stellar masses reported in Table 2 for each
component. The uncertainties in the masses were obtained using the MC method
of error propagation and the uncertainties estimated for the luminosity and
$T_{eff}$.

####  2.1.2 Veiling

Veiling measurements are necessary to set the flux of the WTTS template
photosphere relative to the CTTS spectrum, with the relationship given by
$F_{{\rm phot},\lambda}=F_{{\rm CTTS},\lambda}/(1+r_{\lambda})$. In our
analysis, we scale the WTTS template spectrum to the data using the observed
veiling at one wavelength, $\lambda_{0}$. First, the WTTS spectrum is scaled
to the observed CTTS spectrum at $\lambda_{0}$ with a $\frac{F_{\rm
obs}(\lambda_{0})}{F_{\rm phot}(\lambda_{0})}$ term. Then, it is scaled to the
observed veiling with a $\frac{1}{1+r_{\lambda_{0}}}$ term such that the
contribution of the photosphere to the data’s continuum flux at $\lambda_{0}$
is equivalent to the contribution implied by the veiling measurement. Only the
absolute flux of the WTTS template spectrum is changed, not the shape of the
WTTS spectrum. This scaling process allows us to use the observed veiling to
determine the amount of continuum excess emission for which we need to account
with the accretion shock and inner disk wall models.

Three epochs of veiling measurements at $\lambda_{0}$=5500 Å (r5500) are
available for 7 out of 9 of the CTTS from VLT/UVES and VLT/ESPRESSO (Manara et
al., 2021), and we use the value from the epoch closest in time to the
HST/STIS observations for these targets. CVSO 90 has VLT/X-Shooter veiling
available at $\lambda_{0}$=7100 Å, so this is used in place of r5500 for this
target. The veiling measured from the unresolved CVSO 165 spectrum is split
between the two components according to the ratio of their U-band fluxes. CVSO
104 has not yet been formally modeled at the wavelengths relevant to
accretion; however, its r5500 has been estimated from modeling the UVES
spectrum when the objects are nearly in conjunction (A. Frasca, priv. comm.).
The observations used to measure the veiling for each target are shown in
Table 1, and the veiling values are included in Table 2.

Table 1: Observation Log

Object | Telescope/Instrument | Date (MJD)
---|---|---
CVSO 58 |  HST/STISa | 59184.97
| VLT/X-Shooterb | 59185.25
| VLT/UVESb,c | 59185.09
CVSO 90 |  HST/STISa | 59199.60
| VLT/X-Shooterb,c | 59198.06
CVSO 104 |  HST/STISa | 59180.21
| VLT/X-Shooterb | 59180.13
| VLT/UVESb,c | 59179.12
CVSO 107 |  HST/STISa | 59188.02
| VLT/X-Shooterb | 59187.08
| VLT/UVESb,c | 59188.14
CVSO 109 |  HST/STISa | 59181.20
| VLT/X-Shooterb | 59181.15
| VLT/UVESb,c | 59181.17
CVSO 146 |  HST/STISa | 59192.85
| VLT/X-Shooterb | 59192.08
| VLT/ESPRESSOb,c | 59193.09
CVSO 165 |  HST/STISa | 59197.82
| VLT/X-Shooterb | 59197.08
| VLT/ESPRESSOb,c | 59198.10
CVSO 176 |  HST/STISa | 59182.86
| VLT/X-Shooterb | 59185.17
| VLT/UVESb,c | 59183.15

Note. — aObserved through the ULLYSES HST DDT Program (Roman-Duval et al.,
2020). bObserved through the PENELLOPE VLT Large Programme (Manara et al.,
2021). cUsed for veiling measurement.

Table 2: Adopted Stellar Properties of Orion OB1 Targets

Object | SpT | Temperature | Luminosity | Radius | Mass | Distance | $A_{V}$ | $r$ | Template
---|---|---|---|---|---|---|---|---|---
|  | (K) | (L☉) | (R☉) | (M☉) | (pc) | (mag) |  |
Single CTTS
CVSO 58 | K7 | 3970 | 0.32 | 1.19 | 0.81 | 349.00$\pm 2.8$ | 0.8 | $0.81\pm 0.04$ | HBC 427+TWA 6
CVSO 90 | M0.5 | 3700 | 0.13 | 0.88 | 0.62 | 338.70${}^{+3.8}_{-3.7}$ | 0.1 | $1.8\pm 0.4^{*}$ | TWA 7+TWA 14
CVSO 107 | M0.5 | 3700 | 0.32 | 1.38 | 0.53 | 330.40$\pm 2.5$ | 0.3 | $0.98\pm 0.11$ | TWA 7+TWA 14
CVSO 146 | K6 | 4020 | 0.80 | 1.84 | 0.86 | 332.00$\pm 1.7$ | 0.6 | $0.44\pm 0.10$ | HBC 427+RXJ1543.1-3920
CVSO 176 | M3.5 | 3260 | 0.34 | 1.83 | 0.25 | 302.40${}^{+2.9}_{-2.8}$ | 1.0 | $0.34\pm 0.16$ | CVSO 17/36+TWA 15A
Binary CTTS
CVSO 104† | M2 | 3490 | 0.37 | 1.66 | 0.37 | 360.70${}^{+3.9}_{-3.8}$ | 0.2 | $0.8^{\star}$ | CVSO 17/36+TWA 2A
CVSO 109Aa | M0$\pm 0.5$ | 3767.6$\pm 81.2$ | $0.59^{+0.17}_{-0.13}$ | $1.81\pm 0.25$ | 0.50${}_{-0.05}^{+0.07}$ | 400$\pm 40$ | 0.06${}_{-0.24}^{+0.24}$ | $0.90\pm 0.08$ | TWA 7+TWA 14
CVSO 165A | K5.5$\pm 1.0$ | 4221$\pm 28$ | 0.90${}_{-0.15}^{+0.19}$ | 1.78$\pm 1.07$ | 0.84$\pm 0.05$ | 400$\pm 40$ | 0.32$\pm 0.05$ | $0.21\pm 0.03^{**}$ | RECX 1+RXJ1543.1-3920
CVSO 165B | M1$\pm 1.5$ | 3849$\pm 7$ | 0.47${}_{-0.08}^{+0.10}$ | 1.55$\pm 0.93$ | 0.58$\pm 0.23$ | 400$\pm 40$ | 1.35$\pm 0.12$ | $0.15\pm 0.02^{**}$ | TWA 7+TWA 14
WTTS
RECX 1b | K5 | 4140 | 1.0 | 1.8 | 0.9 | 97 | 0.0 | … | …
RXJ1543.1-3920c | K6 | 4020 | 0.40 | 1.19 | … | 150 | $0.1\pm 0.1$ | … | …
HBC 427b | K7 | 3970 | 0.8 | 1.9 | 0.8 | 140 | 0.0 | … | …
TWA 6d | K7 | 3970 | 0.11 | 0.67 | 0.66 | 51 | … | … | …
TWA 14d | M0.5 | 3700 | 0.15 | 0.90 | 0.73 | 96 | … | … | …
TWA 7b | M1 | 3630 | 0.5 | 1.8 | 0.5 | 50 | 0.0 | … | …
TWA 2Ad | M2 | 3490 | 0.33 | 1.51 | 0.55 | 47 | … | … | …
CVSO 17† | M2 | 3490 | 0.30 | 1.50 | 0.37 | 414.2${}^{+9.3}_{-8.9}$ | 0.0 | … | …
CVSO 36† | M2 | 3490 | 0.22 | 1.28 | 0.39 | 335.5$\pm 3.0$ | 0.1 | … | …
TWA 15Ad | M3.5 | 3260 | 0.11 | 1.00 | 0.30 | 111 | … | … | …

Note. — The following stellar parameters for the CTTS come from Manara et al.
(2021) unless otherwise noted: spectral type, luminosity, mass, distance
(derived from GAIA Early Data Release 3 parallaxes when reliable solutions
were available, see Gaia Collaboration et al., 2021), $A_{V}$, $r$. All
veilings are at 5500 Å unless otherwise noted. The adopted temperature comes
from the temperature-spectral type relation for 5-30 Myr stars in Pecaut &
Mamajek (2013, Table 6), with an average used for intermediate spectral types.
The radius is calculated from the luminosity and temperature using the Stefan-
Boltzmann relation. Italicized WTTS come from X-Shooter; otherwise, they come
from HST/STIS. The average of CVSO 17 and CVSO 36, weighted by their
uncertainties, is used because the individual spectra have low SNR in the NUV.
a Espaillat et al. (2022) b Ingleby et al. (2013) cManara et al. (2017) d
Manara et al. (2013)

†Unresolved spectroscopic binary system

∗Veiling at 7100 Å from X-Shooter

∗∗Veiling for the primary and secondary components of CVSO 165 attained by
scaling the ESPRESSO veiling of $0.36\pm 0.05$ for CVSO 165 to the ratio of
the components’ U-band fluxes

⋆ Veiling at 5500 Å estimated from modeling the UVES spectrum when the binary
components are nearly in conjunction (A. Frasca, priv. comm.)

###  2.2 HST/STIS observations

HST Space Telescope Imaging Spectrograph (STIS) and Cosmic Origins
Spectrograph (COS) observations of these targets were taken as part of the
ULLYSES DDT program through proposals GO16113, GO16114, and GO16115 (Roman-
Duval et al. 2020, PI: Julia Roman-Duval). This paper utilizes observations of
each target with the following gratings: STIS/G230L (spectral resolution
500-1010, plate scale 0.025”/pixel, and NUV-MAMA pixel size of 25 $\mu$m),
STIS/G430L (spectral resolution 530-1040, plate scale 0.051”/pixel, and CCD
pixel size of 21 $\mu$m), and STIS/G750L (spectral resolution 530-1040, plate
scale 0.051”/pixel, and CCD pixel size of 21 $\mu$m), all using the 52X2 slit.
These spectra span a total wavelength range of $1710-10,000$ Å after they are
combined and trimmed. See Table 1 for the times of observations. Values of
$\lambda F_{\lambda}$ that are less than $1\times 10^{-15}$ erg/s/cm2 are
removed. The spectra analyzed here come from ULLYSES Data Release 4, which
separates spectra for the resolvable binary systems (CVSO 36, CVSO 104, CVSO
109, and CVSO 165) into their constituent components. The data between 1710
and 3300 Å are dereddened with our derived $A_{V}$ using the Whittet et al.
(2004) extinction law based on HD 29647 in Taurus (normalized to the Cardelli
et al. (1989) standard ISM law), as the Whittet et al. (2004) law removes a
potential overcorrection of the 2175 Å bump that is present in standard ISM
extinction laws. From 3300 Å onwards, the data are dereddened using the
Cardelli et al. (1989) law to align with the analysis of Manara et al. (2021).
Both laws assume an interstellar reddening of R${}_{V}=3.1$.

###  2.3 VLT/X-Shooter observations

Contemporaneous VLT/X-Shooter observations were taken through the ESO
PENELLOPE Large Programme (Manara et al., 2021, PI: Carlo Manara; see their
Figures F.1 and F.2 for the X-Shooter data overplotted with the HST data). See
Table 1 for the times of observations. Though observations were taken in the
UVB, VIS, and NIR arms, we use only the NIR spectra (spectral resolution
$\sim$11600, plate scale 0.248”/pixel, using the 0.4” slit) for modeling the
inner disk wall because HST data are available out to 1 $\mu$m. As described
in Manara et al. (2021), these flux-calibrated data are dereddened using the
Cardelli et al. (1989) extinction law and corrected for telluric absorption
using molecfit v3.0.3 (Smette et al., 2015; Kausch et al., 2015). Again,
points with $\lambda F_{\lambda}$$<1\times 10^{-15}$ erg/s/cm2 are removed.

The X-Shooter data for the binary targets CVSO 109 and CVSO 165 are
unresolved, so it is necessary to split the total flux between the two
components to achieve a better representation of the resolved NIR spectra. As
described in Espaillat et al. (2022), the X-Shooter spectrum of CVSO 109A is
scaled by the J-band fluxes of the two components and their difference found
by Tokovinin et al. (2020). The J-band flux difference is not available for
CVSO 165A and CVSO 165B, so these spectra are simply scaled down to align with
the HST continua. This is just an approximation given that the two components
have different spectral types. However, our inferred NIR flux ratio of the
primary to the secondary of 2.4 is reasonably consistent with our measured V-
and R-band flux ratios of 2.6 and 2.7, respectively.

The HST and X-Shooter observations of CVSO 176 were separated by about 65
hours, and this seems to have produced a significant discontinuity between the
data. This can likely be attributed to variability, as variations on the order
of hours to days are expected from magnetosphere-disk interactions (Venuti et
al., 2017; Sergison et al., 2020; Fischer et al., 2022). Both the flux and
slope of the HST and X-Shooter continua do not agree. However, if the
X-Shooter spectrum is scaled up by a factor of 1.75 (corresponding to a change
of 0.6 mag), it aligns with the HST spectrum. This agrees with contemporaneous
photometry from AAVSOnet that shows a decrease in Sloan $i$-band flux of 0.6
mag between MJD
9182.67–9189.84.111http://www.astro.sunysb.edu/fwalter/SMARTS/Odysseus/cvso176.phot.html
This likely indicates a change in the emission from the inner disk wall. Both
the scaled and unscaled X-Shooter data are shown in the model fits to CVSO
109A, CVSO 165A, CVSO 165B, and CVSO 176 presented in Figure 1.

###  2.4 TESS observations

TESS, the Transiting Exoplanet Survey Satellite (Ricker et al., 2014), has
observed these targets on two occasions, in Sector 6 (2018 Dec 11 through 2019
Jan 07) and in Sector 32 (2020 Nov 19 through Dec 17). The latter coincided
with the observations reported here, and these data were used to estimate the
stellar rotation periods of our targets (expected of order 4–9 days, Percy et
al., 2010). We note that the 27 day viewing window of TESS samples only a few
of the expected periods, so this analysis only reveals gross trends in very
complex light curves.

We download the full frame image data from the MAST archives using the TESScut
software (Brasseur et al., 2019). TESS images, while photometrically stable
and of continuous cadence, suffer from coarse spatial resolution (21′′
pixels). TESS is a single-channel photometer with a 600–1000 nm bandpass. The
temporal resolution was 10 minutes in Sector 32 and 30 minutes in Sector 6.

We extract the data using aperture photometry with a 1.5 pixel radius. The
background is extracted from an annulus between 5 and 10 pixels from the
source. Because there are often other sources in the background annulus, we
iterate on the background pixels, removing those more than 3$\sigma$ from the
median level until we converge on the median background level. We assume that
the background is spatially flat in this region.

###  2.5 WTTS photospheric templates

The template photospheres constructed for each of the CTTS targets are
composed of two WTTS spectra stitched together: the wavelength range between
2000 and $\sim$6,000 Å comes from the HST/STIS spectrum closest in spectral
type to the CTTS, and the remaining data out to 24,000 Å come from the
VLT/X-Shooter spectrum that provided the best photospheric fit in Manara et
al. (2021) (except for CVSO 165B, which has a spectral type different than
that assigned to the unresolved CVSO 165 system). All targets have HST WTTS
within $\pm 1$ spectral subtype except for CVSO 176, which is fit with a WTTS
1.5 subtypes earlier. Each pair of WTTS stitched together as photospheric
templates for each CTTS target are listed in the “Template” column of Table 2.
Note that there are four X-Shooter WTTS for which extinction estimates are
unavailable. $A_{V}$ for these targets is assumed to be zero because they were
chosen from regions of low extinction (Manara et al., 2013). This should not
have a significant effect on the fitted $A_{V}$ and $\dot{M}$ values because
extinction is most important at wavelengths shorter than these X-Shooter WTTS
spectra cover.

##  3 Accretion and Disk Models

The accretion and disk wall models used in this work are computed and fit in
order to be consistent with one another. First the accretion shock model is
calculated for the specific stellar parameters of each target and fit to the
data. Then, the output stellar radius, accretion rate, and shock temperature
are used as inputs to the disk wall model, which is then calculated for the
given stellar parameters and fit to the data. In Sections 3.1–3.2, we describe
our implementation of the Calvet & Gullbring (1998) accretion shock model and
the D’Alessio Irradiated Accretion Disk radiative transfer model (DIAD,
D’Alessio et al. 1998, 1999, 2001, 2004, 2005, 2006).

###  3.1 Multi-column accretion shock model

We model the NUV and optical HST continua using the Calvet & Gullbring (1998)
accretion shock model, updated to include three accretion columns of varying
energy fluxes. These approximate a flow with a density gradient, as was
recently found in GM Aurigae (Espaillat et al., 2021). Following Calvet &
Gullbring (1998), we assume a magnetospheric truncation radius ($R_{\rm i}$)
of 5 R⋆ for all objects but CVSO 109A.222Modeling of H$\alpha$ and H$\beta$
lines of CVSO 109A showed a smaller $R_{\rm i}$ of 2.3 R⋆ (see Espaillat et
al., 2022), but this analysis is still in preparation for the other objects
(Thanathibodee et al., in prep.). We note that changing $R_{\rm i}$ to 2.3 R⋆
from 5 R⋆ increases the calculated accretion rate by a factor of 1.4. $R_{\rm
i}$, R⋆, and M⋆ determine the infall velocity of the accreted material, which
is assumed to be the freefall velocity. The updated model is solved for
individual parameter combinations rather than interpolating over a presolved
grid of solutions. We add V-band extinction $A_{V}$ as a free parameter in the
Markov chain Monte Carlo (MCMC) fitting process, then calculate the stellar
radius R⋆ from the fluxes of the dereddened CTTS spectrum and its associated
X-shooter WTTS template scaled by the measured veiling. For details regarding
the updates applied to the model, see Robinson & Espaillat (2019).

The complete shock model is composed of: a WTTS template photosphere $F_{\rm
phot}(\lambda)$ scaled to the veiling measured by Manara et al. (2021)
$r_{\lambda_{0}}$ (shown in Table 2), plus three accretion columns of low,
medium, and high flux densities (${\cal F}$ = $1\times 10^{10}$, $1\times
10^{11}$, and $1\times 10^{12}$ erg s-1 cm-2, respectively). The emission from
these columns is scaled by the stellar radius R⋆, the distance $d$, and
filling factors $f$, which represent the fraction of the stellar surface that
is covered by each accretion column. Thus, the total dereddened model flux is
given by

$F_{\rm tot}(\lambda)=10^{0.4A_{\lambda_{0}}}\left[\frac{F_{\rm
obs}(\lambda_{0})}{F_{\rm phot}(\lambda_{0})}\frac{F_{\rm
phot}(\lambda)}{1+r_{\lambda_{0}}}\right]+\left(\frac{R_{\star}}{d}\right)^{2}\sum_{i}^{n}f_{i}{\cal
F}_{i}(\lambda)$ (1)

where $A_{\lambda_{0}}$ is the extinction as described in Sections 2.2 and
2.3; $F_{\rm phot}(\lambda)$ is the WTTS template photosphere scaled by
$F_{\rm obs}(\lambda_{0})/F_{\rm phot}(\lambda_{0})$ to the observed STIS
spectrum at $\lambda_{0}$; $n$ sums over the three accretion columns of
different energy-flux densities; $f_{i}$ are the filling factors associated
with each accretion column; and ${\cal F}_{i}$ are the accretion shock spectra
calculated as the sum of the emission from the heated photosphere and the
preshock region of the system for each accretion column.

Equation 1 is fit to the HST continuum (with emission lines masked out)
between 2000-10,000 Å for each object using an MCMC with 2,000 steps, 100
walkers, and a burn-in of 550. $A_{V}$ has a tophat prior ranging between 0
and 2 on account of the low extinction reported for Orion OB1 (median
$A_{V}=0.65$ mag, Briceño et al., 2019), and the sum of the filling factors is
restricted between 0 and 40% of the stellar surface, as modeling has
demonstrated that the footprint of the accretion column can produce detectable
emission that covers up to 39% of the TTS surface (Ingleby et al., 2013, 2014;
Robinson & Espaillat, 2019). Once the best-fit model is obtained, the average
temperature of the shock ($T_{\rm shock}$) is calculated by fitting blackbody
curves to the three columns’ spectra, then weighting each column’s associated
accretion luminosity by its fractional filling factor according to

$T_{\rm shock}=\left[\frac{f_{1E10}}{f_{\rm
tot}}T_{1E10}^{4}+\frac{f_{1E11}}{f_{\rm
tot}}T_{1E11}^{4}+\frac{f_{1E12}}{f_{\rm
tot}}T_{1E12}^{4}\right]^{\frac{1}{4}}.$ (2)

The blackbody given by $T_{\rm shock}$ is an important input to the inner disk
wall model, as both the stellar and the accretion luminosities irradiate the
wall.

###  3.2 DIAD

We also model the protoplanetary disk’s frontally-illuminated inner dust wall,
which is located at the dust sublimation radius, using the D’Alessio
Irradiated Accretion Disk radiative transfer models (DIAD, D’Alessio et al.
1998, 1999, 2001, 2004, 2005, 2006). The inner dust wall begins contributing
significantly at 1 $\mu$m, after which the total model consists primarily of
emission from the photosphere and the disk, with non-zero but less significant
emission from the accretion columns at these longer wavelengths. Because our
data extend only to 2.4 $\mu$m, our model includes only the inner wall, not
the disk behind it.

For details regarding the DIAD model used here, see the ODYSSEUS I paper
(Espaillat et al., 2022, Section 6.1.2). In short, we model the inner dust
wall assuming a fractional abundance of graphite and pyroxine-type silicates
of 0.0025 and 0.004, respectively, in accordance with the Draine & Lee (1984)
model for the diffuse ISM. The grains are spherical with a size distribution
that scales as $a^{-p}$ between grain radii of $a_{\rm min}$ and $a_{\rm max}$
and $p$ of 3.5 (Mathis et al., 1977). The minimum grain size is held at 0.005
$\mu$m. Since the NIR spectra do not extend to 10 $\mu$m, we cannot
confidently constrain the 10 $\mu$m silicate feature. Instead, we assume an
$a_{max}$ of 10 $\mu$m because Maucó et al. (2018) fit the 10 $\mu$m silicate
feature well with this value for the three objects from this analysis that
were included in their study (CVSO 104, CVSO 107, and CVSO 109). The wall is
illuminated by the stellar luminosity and the accretion luminosity, which is
given by the $T_{\rm shock}$ derived for each target from its best-fit
accretion shock model.

To obtain the best fit to the SED of each target, we adjust the height of the
inner wall ($z\rm_{wall}$) between 0.5 and 20 gas scale heights (H), noting
that the larger values of $z\rm_{wall}$ are indicative of excess emission
likely originating from an optically-thin dust cavity in a pre-transitional
disk for which we do not account in this model (Maucó et al., 2018). We adjust
the temperature of the optically thin wall atmosphere ($T\rm_{wall}$) between
1200 and 1800 K. Disk inclination $i$ is estimated as described in Section
3.3.

Note that in the case of a vertical wall, the inner disk wall height is
degenerate with the inclination of the system. Since these disks are
unresolved, we cannot distinguish between a high wall and a highly inclined
viewing angle (we receive maximum wall emission from a disk inclined at
60-80∘, see Dullemond et al. 2001; Calvet et al. 2005).

The radius in the disk at which the wall is located ($R_{\rm wall}$) is
derived using the best-fitting $T_{\rm wall}$ following

$R_{\rm wall}\sim\left[{\frac{(L_{*}+L_{\rm
acc})}{16\pi\sigma_{R}}}(2+{\frac{\kappa_{s}}{\kappa_{d}}})\right]^{1/2}{1\over
T_{\rm wall}^{2}},$ (3)

which assumes that the thickness of the atmosphere is negligible compared to
the radius (Muzerolle et al., 2003; D’Alessio et al., 2004), where
$\sigma_{R}$ is the Stefan-Boltzmann constant; $\kappa_{s}$ and $\kappa_{d}$
are the mean opacities to the incident and local radiation, respectively;
$L_{\star}$ is the stellar luminosity; and $L_{\rm acc}$ is the luminosity of
the stellar accretion shock as given by the output accretion rate ($\dot{M}$)
and $R_{\star}$ of the multi-column accretion shock model described in Section
3.1, with

$L_{\rm acc}=(1-1/R_{\rm i})(GM_{\star}\dot{M}/R_{\star}).$ (4)

As described in Section 3.1, $R_{\rm i}$ is taken to be 2.3R⋆ for CVSO 109A
and 5R⋆ for all other targets. Disk models with $R_{\rm wall}$ located at the
dust sublimation radius predict values of $R_{\rm wall}$ between 0.07-0.54 AU,
with stronger accretors having larger values of $R_{\rm wall}$ as indicated by
Equation 3 (Muzerolle et al., 2003).

###  3.3 Inclinations

We infer the inclinations of our targets by estimating their stellar rotation
periods from their TESS light curves and taking measurements of $v\sin i$ from
Manara et al. (2021) and Kounkel et al. (2019). Temporal analysis of the light
curves uses the Scargle periodogram analysis (Scargle, 1982; Horne & Baliunas,
1986) as implemented in IDL333Jörn Wilms 2005: http://astro.uni-
tuebingen.de/software/idl/aitlib/timing/scargle.html. We look for peaks in the
power spectral density (PSD) between 1 to 10 days in excess of a 99%
confidence level.

When power is found, we fold the data on the periods that show significant
power. To minimize long-term secular variability, we construct a running mean
of width 1.5 times the period, and subtract that from the light curve prior to
folding. We bin the data into 20 phase bins, setting the uncertainty in each
phase bin to the variance in that bin and test the binned light curve against
the null hypothesis.

We also examine the auto-correlation of the light curve. The width of the
correlation peak is proportional to the duration of the typical features
contributing to the variations. We also consider the positive and negative
excursions in the light curve separately: positive excursions may be due to
bright patches on the photosphere; negative excursions may be due to
occultations of the surface by circumstellar material, or by starspots. To
define positive and negative excursions, we de-trend the light curve with a
polynomial fit (3rd to 6th order, depending on the number of points) and
retain only those points above or below the trend. Brief discussions of the
individual targets can be found in Appendix B.

##  4 Analysis and Results

Figure 1: Fitting the NUV–NIR continua of Orion OB1b targets. We show the HST
(0.2–1 $\mu$m) and X-Shooter (1–2.4 $\mu$m) data (black) along with the
photospheric template (grey), which is scaled using the optical veiling
derived from VLT spectra listed in Table 2. The single model with the highest
likelihood is shown in red. The median model parameter values and their
associated 1$\sigma$ uncertainties are listed in Tables 3 and 5. The best fit
model is a combination of the accretion shock model (consisting of the three
columns with energy fluxes of 1$\times 10^{10}$, 1$\times 10^{11}$, and
1$\times 10^{12}$ erg/s/cm2—cyan, sea-green, and brown dotted lines,
respectively—with filling factors as indicated in the legend) and the DIAD
model (consisting of the emission from the inner disk wall; lime green dashed
line). Residuals are shown in the bottom panel of each figure. Emission lines
were excluded from the fit, and regions significantly affected by telluric
absorption were excluded from both the observed spectra and model fitting;
this produces the gaps seen in the residual plots.

Figure 1 shows the best fits of the accretion shock and accretion disk models
to the full NUV–NIR spectra of the nine CTTS analyzed here. Tables 3 and 5
list, respectively, the accretion and disk model parameters associated with
each fit. Using our accretion shock model, we derive V-band extinction,
stellar radius, accretion rate, and accretion column structure for each
target.

Our results indicate that accretion remains strong in TTS longer than
originally expected. Hartmann et al. (2016) predict an accretion rate on the
order of $3\times 10^{-9}$ M☉ yr-1 for a 0.7 M☉ star of 5 Myr (the median age
of the Orion OB1b region). However, Ingleby et al. (2014) measured accretion
rates on the order of $1\times 10^{-8}$ M☉ yr-1 for CVSO 58, CVSO 90, and CVSO
109. Similarly, our derived accretion rates range from 0.5–17.2$\times
10^{-8}$ M☉ yr-1, with a median value of 1.2$\times 10^{-8}$ M☉ yr-1. These
accretion rates are comparable to those of the 1–2 Myr regions Taurus and
Chamaeleon I (Ingleby et al., 2013). These high accretion rates produce
associated accretion luminosities that range from 0.07–1.96 $L_{\star}$, with
a median accretion luminosity of 0.25 $L_{\star}$. Given that the accretion
luminosities are comparable to the stellar luminosities for these targets, the
accretion rates from the accretion shock model are important inputs to the
inner disk wall model.

The average accretion shock temperatures range from 4800 K to 10542 K, in
agreement with the range predicted by Calvet & Gullbring (1998). With a mean
temperature of 6511 K, these targets have $T_{\rm shock}$ notably lower than
the typically-assumed temperature of 8000–10000 K for a single accretion
column (e.g., D’Alessio et al., 1998; Fischer et al., 2011). The average
temperatures of the three accretion columns are 4274 K for the low flux-
density column; 6695 K for the medium flux-density column; and 10786 K for the
high flux-density column. See Table 7 in the appendix for the best-fit
temperatures for each column of each target.

We are able to attain satisfactory fits to the NIR excesses of five targets,
though there are a number of cases in which the photosphere goes above the
data around 1 $\mu$m and thus forces the total model fit to be above the data
(CVSO 58, CVSO 104, CVSO 107, CVSO 109A, CVSO 165B, and CVSO 176). In the
cases of CVSO 107, CVSO 109A, CVSO 165B, and CVSO 176, there is no clear NIR
excess above the photospheric and accretion shock emission, so no inner disk
wall is fitted to these targets. This may result from variability in the
veiling, which dictates the scaling of the WTTS photospheric template. This
will be examined further in future work.

The lack of NUV spectra of WTTS templates with the same spectral subtype as
some of the CTTS may produce scaling that results in mismatches in the NIR.
Four out of the five targets that are fit with an inner wall require a wall
height in excess of 5 gas scale heights to produce enough emission to account
for the excess. These targets are likely pre-transitional disks, which have
extra emission from an optically-thin dust component in their inner disk
cavities (Maucó et al., 2018). Our future work will examine whether this
additional component produces a better fit to the data.

###  4.1 Uncertainties

The average accretion shock model uncertainty, quantified by an MCMC nuisance
parameter, is 14%. This statistical goodness-of-fit is a lower limit to the
actual uncertainty as it does not take the uncertainties of the input
parameters, the photospheric templates, or the extinction curve into account.
When accretion rates are calculated considering the uncertainties in R⋆ and
the filling factors, and assuming an uncertainty of 2R⋆ for the magnetospheric
truncation radius Ri, the median percent error increases from 4% to 32%.

Uncertainties in our derived stellar radii take into account the error in the
data fluxes, CTTS distance, veiling, visual extinction, and an assumed 10%
error in the WTTS template fluxes. Our estimates have an average percent error
of 8%. The updated luminosity measurements included in Table 3 propagate our
derived error in R⋆, but no uncertainty is assumed for the stellar
temperature. The uncertainties in the average shock temperature are dominated
by the errors in the filling factors. Since the errors are often asymmetric,
the larger of the upper and lower uncertainties is taken as the error in
propagation.

A significant source of systematic uncertainty comes from the availability and
scaling of the WTTS photospheric templates. There are seven total WTTS
templates with NUV spectra available between SpTs K5 and M2, and there are no
templates of type K6 or M0. All CTTS studied here are fit with a template
within 1.5 subtypes of their own spectral classification, but even this
difference in spectral type introduces some amount of error. Fitting each
target CTTS with the next closest template on either side, when available,
changes the best-fit visual extinction by 0.37 mag on average.

Once a template is chosen, it must be scaled to the data by the veiling
measurement, which has its own variability and uncertainty. Three measurements
of veiling, each separated by a day, were available for all targets except
CVSO 90 and CVSO 104. The measured veiling for a given target varied, on
average, by a factor of 1.6 across the three epochs. By choosing the epoch
closest in time to the HST observations, we minimize the influence of veiling
variability, but it cannot be completely removed.

Our derivation of inclinations are rough estimates given that the stellar
rotation periods in the TESS data can easily be obscured by other processes,
such as occultation dips and discrete accretion events. Uncertainties have not
been determined for the period measurements, so the quoted uncertainties in
inclinations come from errors in $v\sin i$ and R⋆. We note that if the
inclination estimates are wrong, the only parameter that would be affected is
the height of the inner disk wall $z_{\rm wall}$.

Table 3: Best-fit Accretion Shock Model Parameters of Orion OB1 CTTS

Object | $A_{V}$ | $R_{\star}$ | $L_{\star}$ | $L_{\rm acc}$ | $\dot{M}$ | $f_{1E10}$ | $f_{1E11}$ | $f_{1E12}$ | $T_{\rm shock}$
---|---|---|---|---|---|---|---|---|---
| (mag) | (R☉) | (L☉) | (L☉) | (10-8 M☉ yr-1) | (fraction of stellar surface covered) | (K)
CVSO 58 | $1.39^{+0.04}_{-0.04}$ | $1.05^{+0.07}_{-0.07}$ | 0.25$\pm$0.03 | $0.202^{+0.011}_{-0.011}$ | $1.03^{+0.05}_{-0.06}$ | $0.231^{+0.010}_{-0.022}$ | $0.00020^{+0.0017}_{-0.00013}$ | $0.0092^{+0.0007}_{-0.0007}$ | 5493$\pm$96
CVSO 90 | $0.92^{+0.03}_{-0.30}$ | $0.84^{+0.09}_{-0.09}$ | 0.12$\pm$0.03 | $0.234^{+0.011}_{-0.08}$ | $1.25^{+0.06}_{-0.4}$ | $0.053^{+0.016}_{-0.03}$ | $0.00031^{+0.024}_{-0.00023}$ | $0.0202^{+0.0011}_{-0.010}$ | 7975$\pm$1105
CVSO 104 | $0.05^{+0.05}_{-0.03}$ | $1.64^{+0.13}_{-0.12}$ | 0.36$\pm$0.06 | $0.0655^{+0.003}_{-0.0021}$ | $1.14^{+0.05}_{-0.04}$ | $0.0304^{+0.0027}_{-0.004}$ | $0.0074^{+0.0005}_{-0.0004}$ | $0.00049^{+0.00006}_{-0.00003}$ | 5239$\pm$105
CVSO 107 | $1.16^{+0.03}_{-0.05}$ | $1.97^{+0.15}_{-0.15}$ | 0.66$\pm$0.10 | $0.331^{+0.012}_{-0.021}$ | $4.84^{+0.17}_{-0.3}$ | $0.076^{+0.004}_{-0.007}$ | $0.00015^{+0.0027}_{-0.00008}$ | $0.00456^{+0.00024}_{-0.0004}$ | 5656$\pm$128
CVSO 109A | $0.83^{+0.04}_{-0.32}$ | $2.55^{+0.20}_{-0.20}$ | 1.18$\pm$0.19 | $0.61^{+0.04}_{-0.23}$ | $17.2^{+1.0}_{-7}$ | $0.0006^{+0.011}_{-0.0005}$ | $0.0073^{+0.0026}_{-0.0021}$ | $0.0051^{+0.0005}_{-0.0026}$ | 8877$\pm$1910
CVSO 146 | $0.28^{+0.03}_{-0.02}$ | $1.25^{+0.09}_{-0.09}$ | 0.37$\pm$0.05 | $0.0926^{+0.003}_{-0.0027}$ | $0.530^{+0.017}_{-0.015}$ | $0.155^{+0.005}_{-0.006}$ | $0.0159^{+0.0011}_{-0.0010}$ | $0.00058^{+0.00005}_{-0.00004}$ | 4975$\pm$27
CVSO 165A | $0.33^{+0.02}_{-0.02}$ | $1.69^{+0.20}_{-0.20}$ | 0.56$\pm$0.13 | $0.0617^{+0.0017}_{-0.0015}$ | $0.708^{+0.020}_{-0.017}$ | $0.1020^{+0.0024}_{-0.003}$ | $0.00287^{+0.0004}_{-0.00028}$ | $0.0000485^{+0.000007}_{-0.0000023}$ | 4800$\pm$14
CVSO 165B | $1.23^{+0.02}_{-0.02}$ | $2.00^{+0.25}_{-0.25}$ | 1.14$\pm$0.29 | $0.176^{+0.005}_{-0.006}$ | $1.65^{+0.05}_{-0.06}$ | $0.00013^{+0.0004}_{-0.00007}$ | $0.00009^{+0.00015}_{-0.00003}$ | $0.00275^{+0.00008}_{-0.00012}$ | 10542$\pm$343
CVSO 176 | $1.44^{+0.03}_{-0.03}$ | $3.26^{+0.31}_{-0.31}$ | 1.08$\pm$0.21 | $0.0815^{+0.0023}_{-0.0020}$ | $4.18^{+0.12}_{-0.10}$ | $0.0108^{+0.0019}_{-0.004}$ | $0.00106^{+0.00026}_{-0.00020}$ | $0.000267^{+0.000017}_{-0.000015}$ | 5043$\pm$254

Note. — Figure 1 continued. The unscaled X-Shooter spectrum of CVSO 109 is
shown in light grey.

Note. — Figure 1 continued. The X-Shooter data for CVSO 165 are unresolved, so
the NIR spectra have been scaled to align with the HST continuum of each
component. This is just an approximation given that the two components have
different spectral types. The X-Shooter spectrum of CVSO 176 has been scaled
up to the HST continuum by a factor of 1.75 to account for the discontinuity
between the continua, which is likely due to variability given that the
observations were $\sim$65 hours apart. The unscaled X-Shooter spectra are
shown in light grey.

Note. — Best-fit accretion shock model parameters for each CTTS. To calculate
the models, the stellar mass, distance, temperature, and veiling are adopted
as given in Table 2. $R_{\rm i}$ is taken to be 5R⋆ for all targets except
CVSO 109A, which has $R_{\rm i}=2.3$R⋆ as described in Section 3.1. For the
best-fit temperatures of individual accretion columns, see Table 7 in the
appendix.

Table 4: Periods and Inclinations of Orion OB1 CTTS

Object | $v\sin i$ | Period | $v$ | $i$
---|---|---|---|---
| (km/s) | (days) | (km/s) | (∘)
CVSO 58 | 17.9$\pm$1.3 | 5.7 | 9.3$\pm$0.5 | …
CVSO 90 | 8.3$\pm$1.6 | 5.1 | 8.3$\pm$0.9 | …
CVSO 104 | 7.5$\pm$1.0 | 4.7 | 17.7$\pm$1.3 | 25.1$\pm$4.1
CVSO 107 | 5.9$\pm$0.9 | 6.4 | 15.6$\pm$0.9 | 22.3$\pm$3.9
CVSO 109A | 3.2$\pm$0.9 | 6.5 | 19.8$\pm$1.2 | 9.3$\pm$2.7
CVSO 146 | 5.0$\pm$0.8 | 5.5 | 11.5$\pm$0.7 | 25.8$\pm$4.8
CVSO 165A | 15.4$\pm$0.9 | 4.3 | 19.9$\pm$1.4 | 50.8$\pm$6.5
CVSO 165B | 15.4$\pm$0.9 | 4.3 | 23.5$\pm$1.9 | 40.9$\pm$4.9
CVSO 176 | 18.4$\pm$1.2 | 7.1 | 23.2$\pm$1.9 | 52.4$\pm$7.8

Note. — Calculated inclinations $i$ for our targets. $v\sin i$ comes from the
VLT modeling that produced the veilings used in this paper (Manara et al.,
2021) for all targets except CVSO 90, which takes $v\sin i$ from Kounkel et
al. (2019). Stellar rotational velocities $v$ are calculated using the radii
we derive here. The derived $v$ for CVSO 58 is smaller than its $v\sin i$, and
the calculated $i$ for CVSO 90 has an error of almost $\pm 180^{\circ}$; thus,
inclination is assumed to be a standard 60∘ for these targets, corresponding
to cos($i)=0.5$.

Table 5: Best-fit Accretion Disk Model Parameters of Orion OB1 CTTS

Object | $z_{\rm wall}$ | $T_{\rm wall}$ | $R_{\rm wall}$
---|---|---|---
| (H) | (K) | (AU)
CVSO 58 | 5 | 1200 | 0.10
CVSO 90 | 5.5 | 1600 | 0.06
CVSO 104 | 5.5 | 1200 | 0.07
CVSO 146 | 18 | 1800 | 0.05
CVSO 165A | 8 | 1400 | 0.07

Note. — Best-fit parameters for the the accretion disk models given input
parameters as shown in Tables 2 and 3. We adopt $a_{\rm min}=0.005$ $\mu$m,
$a_{\rm max}=10$ $\mu$m, and $p=3.5$. Disk inclinations $i$ are taken from
Table 4.

##  5 Discussion

In Section 5.1, we place our results in the context of previous studies. In
Section 5.2, we examine the significance of the choice of extinction law and
the wavelength range of data available.

###  5.1 Comparison to previous results

Table 6: Literature comparison

Object | $\dot{M}_{\rm C05}$ |  $A_{V}$,C05 | $\dot{M}_{\rm I14}$ |  $A_{V}$,I14 | $\dot{M}_{\rm M18}$ |  $A_{V}$,M18 | $\dot{M}_{\rm M21}$ |  $A_{V}$,M21 | BC∗ | $\dot{M}_{\rm P22}$ |  $A_{V}$,P22
---|---|---|---|---|---|---|---|---|---|---|---
| ($\times 10^{-8}$) | (mag) | ($\times 10^{-8}$) | (mag) | ($\times 10^{-8}$) | (mag) | ($\times 10^{-8}$) | (mag) |  | ($\times 10^{-8}$) | (mag)
CVSO 58 | 0.45 | 0.12 | 1.60 | 0.8$\pm 0.5$ | … | … | 0.43 | 0.8 |  | $1.03^{+0.06}_{-0.06}$ | $1.39^{+0.04}_{-0.04}$
CVSO 90 | 1.77 | 0.00 | 1.00 | 0.0$\pm 0.4$ | … | … | 0.25 | 0.1 |  | $1.25^{+0.05}_{-0.5}$ | $0.92^{+0.03}_{-0.30}$
CVSO 104 | 0.75 | 0.00 | … | … | 0.56 | 0.1 | 0.32 | 0.2 |  | $1.14^{+0.06}_{-0.04}$ | $0.05^{+0.05}_{-0.03}$
CVSO 107 | 1.09 | 0.32 | 0.25 | 0.7$\pm 0.4$ | 0.29 | 0.4 | 5.01 | 0.3 |  | $4.83^{+0.19}_{-0.29}$ | $1.16^{+0.03}_{-0.05}$
CVSO 109 | 2.52 | 0.00 | 3.00 | 0.8$\pm 0.5$ | 0.67 | 0.0 | 3.24 | 0.1 | A | $17.2^{+1.0}_{-6}$ | $0.83^{+0.04}_{-0.32}$
CVSO 146 | 0.81 | 0.37 | … | … | … | … | 0.27 | 0.6 |  | $0.529^{+0.016}_{-0.015}$ | $0.28^{+0.03}_{-0.02}$
CVSO 165 | 0.37 | 0.00 | … | … | … | … | 0.08 | 0.2 | A | $0.708^{+0.021}_{-0.017}$ | $0.33^{+0.02}_{-0.02}$
| … | … | … | … | … | … | … | … | B | $1.65^{+0.05}_{-0.06}$ | $1.23^{+0.02}_{-0.02}$
CVSO 176 | 0.43 | 0.00 | … | … | … | … | 1.45 | 1 |  | $4.19^{+0.12}_{-0.11}$ | $1.44^{+0.03}_{-0.03}$

Note. — Comparison between the accretion rates and visual extinctions derived
here and those derived by Calvet et al. (2005) (C05), Ingleby et al. (2014)
(I14), Maucó et al. (2018) (M18), and Manara et al. (2021) (M21). ∗For the
binary targets that are resolved in this study, the BC column indicates which
binary component is being referenced.

Robinson & Espaillat (2019) applied the multi-column accretion shock model
from Ingleby et al. (2013) to multi-epoch observations of five CTTS and found
that mass accretion rates vary with a spread of a factor of $\sim$2 for a
given object. Similarly, Venuti et al. (2014) found that the accretion rate
for a given object has a spread of 0.5 dex (a factor of $\sim$3) from studying
about 200 CTTS in NGC 2264. Rather than merely representing this intrinsic
variability, the best-fit values for accretion rate and visual extinction
presented in this work are systematically higher than those found by previous
studies of objects in this sample (Calvet et al., 2005; Ingleby et al., 2014;
Maucó et al., 2018; Manara et al., 2021). See Table 6 for the individual
values found by each work.

Calvet et al. (2005) modeled all CTTS analyzed here (though their observations
of binaries CVSO 109 and CVSO 165 were unresolved), obtaining accretion rates
for each using photometric excesses in U–B and U–V. They cite an overall
uncertainty of a factor of 3 for each measured accretion rate, with the
largest contribution coming from uncertainty in the extinction. They calculate
$A_{V}$ from the $V-I_{C}$ color using the Cardelli et al. (1989) extinction
law with $R_{V}=3.1$. The accretion rates measured here are 0.6-9.7 times that
of those presented in Calvet et al. (2005), with a median ratio of 2.3. This
cannot be attributed to different flux levels, as all of our observed U–V
colors are redder than those presented in Calvet et al. (2005). Additionally,
our measured extinctions are systematically larger than those of Calvet et al.
(2005), with a median difference of 0.8 mag. Because our accretion rates are
systematically higher, it is likely that the different accretion rates result
from systematic effects in the different modeling techniques and adopted
extinctions rather than solely from true variability.

The closest analogue to our modeling technique is that of Ingleby et al.
(2014), who modeled CVSO 58, CVSO 90, CVSO 107, and the unresolved CVSO 109
system. They used the veiling at V and I to estimate extinction by comparing
the observed photospheric V-IC colors to the standard colors in Kenyon &
Hartmann (1995). They note that their inferred V-band extinctions would
decrease by 0.2-0.4 mag had they used the colors of Pecaut & Mamajek (2013),
and this in turn would decrease their $\dot{M}$s by a factor of 1.8–2.4. They
then deredden their data using the Whittet et al. (2004) law towards HD 29647,
as we do here. The MagE and MIKE spectra they used for these four targets
covered only 3400–9000 Å, so their fitting does not include the NUV.

Ingleby et al. (2014) thus fit the excess shock emission beyond the Balmer
jump using a five-column accretion shock model also based on Calvet &
Gullbring (1998) (the three columns used here plus two intermediate columns).
However, instead of using the standard accretion shock model, they found that
they needed to increase the low-density preshock emission by up to a factor of
five to accurately reproduce the bluest regions of the excess emission
spectra. This likely explains why the structure of their accretion columns,
specifically the area they cover, is notably different from this work. Some of
our model fits show a trend of underestimating the flux near the Balmer jump;
future work will examine whether increasing this preshock emission produces a
better fit to the data, or whether this is merely an effect of Balmer-line
crowding that is not accounted for by our continuum model.

The ratios of our accretion rates to that of Ingleby et al. (2014) are 0.7
(CVSO 58), 1.2 (CVSO 90), 19.3 (CVSO 107), and 5.7 (CVSO 109). Note that had
they used the same spectral type–color conversion as we did (Pecaut & Mamajek,
2013), these ratios would have been higher as described above. The differences
in our derived accretion rates correspond to the differences in U- and V-band
magnitudes between our respective observations. CVSO 58 was dimmer in both
bands in our epoch of observations ($\Delta U=0.70$ mag, $\Delta V=0.38$ mag),
and we find a lower accretion rate. The other three CTTS were brighter in both
bands in our epoch — CVSO 90 ($\Delta U=-0.48$ mag, $\Delta V=-0.53$ mag),
CVSO 107, ($\Delta U=-0.61$ mag, $\Delta V=-0.04$ mag), and CVSO 109A ($\Delta
U=-1.11$ mag, $\Delta V=-0.09$ mag) — and we found higher accretion rates for
these. The greatest increase in U-band belongs to CVSO 109A, which is
consistent with the TESS light curve that shows that our HST observation
occurred near a local maximum in CVSO 109’s light curve (Espaillat et al.,
2022). These magnitudes come from observed, rather than dereddened, data, so
differences in our treatments of extinction have no effect. Thus, our
accretion rates are in broad agreement with those of Ingleby et al. (2014).

Maucó et al. (2018) estimated accretion rates for CVSO 104, CVSO 107, and the
unresolved CVSO 109 system using the H$\alpha$-$\dot{M}$ relation found for
Taurus CTTS by Ingleby et al. (2013): log($\dot{M}$)=1.1($\pm
0.3$)log(L${}_{{\rm H}\alpha})-5.5(\pm 0.8$), where the value of the H$\alpha$
line luminosity was estimated as its equivalent width times the continuum
flux. Espaillat et al. (2022) found that for CVSO 109 this method produces a
lower accretion rate than do the accretion shock models. This is what we find
here, as the ratios of our accretion rates to theirs are 2.0 (CVSO 104), 16.7
(CVSO 107), and 25.7 (CVSO 109). The discrepancy may result from 1) the small
number of sources used to determine this relation (10 CTTS), or 2) the
assumption of a uniform distance for all Taurus CTTS (140 pc) in the
determination of $L_{{\rm H}\alpha}$.

Manara et al. (2021) analyzed X-Shooter spectra of all of the ULLYSES Orion
targets, using a hydrogen slab model to obtain their accretion properties.
They fit for $A_{V}$ using the Cardelli et al. (1989) extinction law.
X-Shooter spectra are available only beyond 3000 Å, so the NUV is not included
in their analysis. Our multi-column accretion shock model finds higher
accretion rates for all targets except CVSO 107, which has the highest
accretion rate in the analysis of Manara et al. (2021). The median ratio of
our accretion rates to theirs is 3.5.

Six of our CTTS targets have stellar radii from Manara et al. (2021) included
in Table 2. There are no individual uncertainties available for the Manara et
al. (2021) spectral types and luminosities, but previous work using their
method of determining stellar radii showed that objects with spectral types
earlier than M4.5 have percent errors less than 25% (Alcalá et al., 2017).
Assuming a percentage error of 25% for the radii calculated from the Manara et
al. (2021) spectral types and luminosities, we find that our best-fit radii
for CVSO 58, CVSO 90, and CVSO 104 are consistent within the errors; those fit
for CVSO 107 and CVSO 176 are larger by a factor of 1.4 and 1.8, respectively;
and that fit for CVSO 146 is lower by a factor of 1.5.

The systematically higher accretion rates presented in this work can in large
part be attributed to a) our use of the accretion shock model as opposed to
H$\alpha$ luminosity or an isothermal hydrogen slab model, and b) the larger
NUV wavelength coverage of these data, as the NUV is the most important region
for constraining the highest energy-flux density accretion column. The latter
has the important implication that all ground-based measurements of CTTS
accretion rates may be underestimated. Since HST has a finite lifetime, future
work should examine whether a correction factor can be determined to account
for the systematic underestimation of accretion rates caused by the lack of
NUV coverage.

###  5.2 Extinction law

When modeling NUV observations of CTTS, the choice of extinction law is
incredibly important because of the strong attenuation by grains at UV
wavelengths and the constraint imposed by the 2175 Å bump. If a law produced
for the general ISM is used, such as Cardelli et al. (1989) or Fitzpatrick et
al. (2019), the absorption bump feature is strong and will bias results
towards lower values of $A_{V}$. If, by contrast, the Whittet et al. (2004)
law towards HD 29647 (which is embedded in Taurus) is used, the absorption
feature is much less pronounced and the fitted $A_{V}$ will be higher.

No single interstellar extinction law can describe all star-forming regions
equally well. This is supported by the finding that Taurus and Ophiuchus
exhibit very different ultraviolet extinction functions, which Whittet et al.
(2004) suggest is likely caused by their different populations of massive
stars. Ophiuchus’s significant population of OB stars produce radiation that
maintains the strength of the 2175 Å bump, so the Cardelli et al. (1989) law
is better suited for use there than is the Whittet et al. (2004) law. Thus,
NUV data for specific TTS provide an important constraint on the
characteristics of both the individual stars themselves and their surrounding
environments. Data from HST are vital for probing the ISM of star-forming
regions to distinguish between grain populations that significantly attenuate
around 2175 Å and those that do not.

Figure 2: Spectra of CVSO 90 dereddened with the best-fit V-band extinction
when modeled with the Whittet et al. (2004) law (black solid line) and
Cardelli et al. (1989) law (red dashed line, shown scaled to the Whittet et
al. (2004) law spectrum at 3000 Å). The overcorrected 2175 Å bump is apparent
in the red curve.

For these targets in Orion, the fits produced by the Whittet et al. (2004) law
are better than those produced by the Cardelli et al. (1989) law, which
overcorrects for the 2175 Å bump (see Figure 2). This indicates that Orion
OB1b is likely more similar to Taurus than Ophiuchus in terms of its
interstellar extinction function. This is supported by an analysis of the
ultraviolet interstellar radiation field (ISRF) of the region. The Habing
field parameter $G_{0}$ gives the ratio of the local field enhanced by a
neighboring OB star to the typical ISRF ($F_{0}$) according to

$G_{0}=\frac{1}{F_{0}}\frac{L_{\rm FUV}}{4\pi r^{2}},$ (5)

where $F_{0}$ is assumed to be $1.6\times 10^{-3}$ erg/s/cm2 (Habing, 1968),
$L_{\rm FUV}$ is approximated as the OB star’s luminosity, and $r$ is the true
distance between the OB star and the CTTS target of interest (Anderson et al.,
2013; Maucó et al., 2016).

Liseau et al. (1999) found that the $\rho$ Ophiuchi star-forming region has
$G_{0}=20$–140. In contrast, $G_{0}$ values for our OB1b CTTS targets are much
lower. Assuming that the seven most significant OB stars around Orion OB1b
($\zeta$ Ori, $\epsilon$ Ori, $\delta$ Ori, $\eta$ Ori, 22 Ori, 25 Ori, and
$\psi^{2}$ Ori) are all at the median OB1b distance of 400 pc, $G_{0}$ for our
targets has a median value of 0.7 and a maximum value of 67. This, in
combination with the low $A_{V}$ of the region, demonstrates that though Orion
OB1b is an OB region, its interstellar extinction function should align more
with that of quiescent Taurus than of hotter, dustier $\rho$ Ophiuchi. This
can in part explain the relatively high accretion rates of this region in
spite of its intermediate age, as these disks have not been externally
photoevaporated by an enhanced ISRF. This is also consistent with the disk
models from Calvet et al. (2005), which could not reproduce the low long-
wavelength infrared fluxes observed in Orion OB1 using small outer disk radii
consistent with external photoevaporation ($\sim$30 AU). Instead, they
concluded that the disks must be flatter and have larger maximum grain sizes
than those in Taurus ($a_{\rm max}$=1 mm). For an analysis of the effect of an
enhanced ISRF on circumstellar disk evolution, see Anderson et al. (2013).

The ULLYSES survey, which will provide over 80 custom-calibrated NUV spectra
of CTTS in nine star-forming regions, will allow us to examine the goodness-
of-fit of different extinction laws in different environments. Beyond this, it
would be ideal to attain extinction curves for all nearby star-forming regions
rather than using either a general ISM curve or the curve calculated to the
specific environment of Taurus.

##  6 Summary

  * •

Accretion rates for the 9 CTTS studied here range from $0.5-17.2\times
10^{-8}$ M☉ yr-1, relatively high for the intermediate age of Orion OB1b.

  * •

Our accretion rates and V-band extinctions are systematically higher than
those calculated from optical data in previous works, in large part due to our
wavelength coverage that extends into the NUV.

  * •

The NIR excesses of the five targets in which an excess is present are fit
with 1200–1800 K inner disk walls located at 0.05–0.10 AU from the host stars.

  * •

The choice of extinction law significantly affects the calculated accretion
rate and introduces uncertainty that is difficult to quantify. Our analysis
indicates that the environment of Orion OB1b is more similar to quiescent
Taurus than to hot $\rho$ Ophiuchi. Ideally, extinction curves can be
calculated for each star-formation region in the near future.

  * •

This multi-column shock and DIAD analysis will be applied to all nine star-
forming regions being observed through ULLYSES, allowing us to extend the
analysis across distinct stellar populations and search for correlations
between accretion and disk properties in a larger sample. Additionally, it
will be applied to the four CTTS being monitored by the ULLYSES program (GM
Aur, TW Hya, BP Tau, and RU Lup).

Support for this work comes from HST AR-16129, as well as NASA through grant
number AR 16129 from the Space Telescope Science Institute, which is operated
by AURA, Inc., under NASA contract NAS 5-26555. This work benefited from
discussions with the ODYSSEUS team (https://sites.bu.edu/odysseus/); see
Espaillat et al. (2022) for an overview of the ODYSSEUS survey. J.H.
acknowledges support from CONACyT project No. 86372 and the UNAM-DGAPA-PAPIIT
project IA102921. P.A., E.F. and Á.K. acknowledge support from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme under grant agreement No 716155 (SACCRED). C.F.M.
acknowledges funding by the European Union under the European Union’s Horizon
Europe Research & Innovation Programme 101039452 (WANDA). 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. Neither
the European Union nor the granting authority can be held responsible for
them. C.F.M., J.M.A, M.G. and E.F. acknowledge support from the project PRIN-
INAF 2019 “Spectroscopically Tracing the Disk Dispersal Evolution”. S.H.P.A.
acknowledges support from CNPq, CAPES and Fapemig. Based on observations
obtained with the NASA/ESA Hubble Space Telescope, retrieved from the Mikulski
Archive for Space Telescopes (MAST) at the Space Telescope Science Institute
(STScI). STScI is operated by the Association of Universities for Research in
Astronomy, Inc. under NASA contract NAS 5-26555. This paper utilizes the
D’Alessio irradiated accretion disk (DIAD) code. We wish to recognize the work
of Paola D’Alessio, who passed away in 2013. Her legacy and pioneering work
live on through her substantial contributions to the field.

## References

  * Alcalá et al. (2019) Alcalá, J. M., Manara, C. F., France, K., et al. 2019, A&A, 629, A108, doi: 10.1051/0004-6361/201935657
  * Alcalá et al. (2017) Alcalá, J. M., Manara, C. F., Natta, A., et al. 2017, A&A, 600, A20, doi: 10.1051/0004-6361/201629929
  * Anderson (1976) Anderson, G. M. 1976, Geochim. Cosmochim. Acta, 40, 1533, doi: 10.1016/0016-7037(76)90092-2
  * Anderson et al. (2013) Anderson, K. R., Adams, F. C., & Calvet, N. 2013, ApJ, 774, 9, doi: 10.1088/0004-637X/774/1/9
  * Bouvier et al. (2020) Bouvier, J., Perraut, K., Le Bouquin, J. B., et al. 2020, A&A, 636, A108, doi: 10.1051/0004-6361/202037611
  * Brasseur et al. (2019) Brasseur, C. E., Phillip, C., Fleming, S. W., Mullally, S. E., & White, R. L. 2019, Astrocut: Tools for creating cutouts of TESS images, Astrophysics Source Code Library, record ascl:1905.007.  http://ascl.net/1905.007
  * Briceño et al. (2005) Briceño, C., Calvet, N., Hernández, J., et al. 2005, AJ, 129, 907, doi: 10.1086/426911
  * Briceño et al. (2001) Briceño, C., Vivas, A. K., Calvet, N., et al. 2001, Science, 291, 93, doi: 10.1126/science.291.5501.93
  * Briceño et al. (2019) Briceño, C., Calvet, N., Hernández, J., et al. 2019, AJ, 157, 85, doi: 10.3847/1538-3881/aaf79b
  * Calvet et al. (2005) Calvet, N., Briceño, C., Hernández, J., et al. 2005, AJ, 129, 935, doi: 10.1086/426910
  * Calvet & Gullbring (1998) Calvet, N., & Gullbring, E. 1998, ApJ, 509, 802, doi: 10.1086/306527
  * Cardelli et al. (1989) Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245, doi: 10.1086/167900
  * D’Alessio et al. (2001) D’Alessio, P., Calvet, N., & Hartmann, L. 2001, ApJ, 553, 321, doi: 10.1086/320655
  * D’Alessio et al. (2006) D’Alessio, P., Calvet, N., Hartmann, L., Franco-Hernández, R., & Servín, H. 2006, ApJ, 638, 314, doi: 10.1086/498861
  * D’Alessio et al. (1999) D’Alessio, P., Calvet, N., Hartmann, L., Lizano, S., & Cantó, J. 1999, ApJ, 527, 893, doi: 10.1086/308103
  * D’Alessio et al. (2004) D’Alessio, P., Calvet, N., Hartmann, L., Muzerolle, J., & Sitko, M. 2004, in IAU Symposium, Vol. 221, Star Formation at High Angular Resolution, ed. M. G. Burton, R. Jayawardhana, & T. L. Bourke, 403
  * D’Alessio et al. (1998) D’Alessio, P., Cantö, J., Calvet, N., & Lizano, S. 1998, ApJ, 500, 411, doi: 10.1086/305702
  * D’Alessio et al. (2005) D’Alessio, P., Hartmann, L., Calvet, N., et al. 2005, ApJ, 621, 461, doi: 10.1086/427490
  * Dotter (2016) Dotter, A. 2016, ApJS, 222, 8, doi: 10.3847/0067-0049/222/1/8
  * Draine & Lee (1984) Draine, B. T., & Lee, H. M. 1984, ApJ, 285, 89, doi: 10.1086/162480
  * Dullemond et al. (2001) Dullemond, C. P., Dominik, C., & Natta, A. 2001, ApJ, 560, 957, doi: 10.1086/323057
  * Espaillat et al. (2021) Espaillat, C. C., Robinson, C. E., Romanova, M. M., et al. 2021, Nature, 597, 41, doi: 10.1038/s41586-021-03751-5
  * Espaillat et al. (2022) Espaillat, C. C., Herczeg, G. J., Thanathibodee, T., et al. 2022, The ODYSSEUS Survey. Motivation and First Results: Accretion, Ejection, and Disk Irradiation of CVSO 109.  https://arxiv.org/abs/2201.06502
  * Fischer et al. (2011) Fischer, W., Edwards, S., Hillenbrand, L., & Kwan, J. 2011, ApJ, 730, 73, doi: 10.1088/0004-637X/730/2/73
  * Fischer et al. (2022) Fischer, W. J., Hillenbrand, L. A., Herczeg, G. J., et al. 2022, Accretion Variability as a Guide to Stellar Mass Assembly, arXiv, doi: 10.48550/ARXIV.2203.11257
  * Fitzpatrick et al. (2019) Fitzpatrick, E. L., Massa, D., Gordon, K. D., Bohlin, R., & Clayton, G. C. 2019, 886, 108, doi: 10.3847/1538-4357/ab4c3a
  * France et al. (2012) France, K., Schindhelm, R., Herczeg, G. J., et al. 2012, ApJ, 756, 171, doi: 10.1088/0004-637X/756/2/171
  * Frasca et al. (2021) Frasca, A., Boffin, H. M. J., Manara, C. F., et al. 2021, A&A, 656, A138, doi: 10.1051/0004-6361/202141686
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1, doi: 10.1051/0004-6361/202039657
  * Gravity Collaboration (2020) Gravity Collaboration. 2020, Nature, 584, 547, doi: 10.1038/s41586-020-2613-1
  * Gullbring et al. (2000) Gullbring, E., Calvet, N., Muzerolle, J., & Hartmann, L. 2000, ApJ, 544, 927, doi: 10.1086/317253
  * Habing (1968) Habing, H. J. 1968, Bull. Astron. Inst. Netherlands, 19, 421
  * Hartmann et al. (2016) Hartmann, L., Herczeg, G., & Calvet, N. 2016, ARA&A, 54, 135, doi: 10.1146/annurev-astro-081915-023347
  * Hartmann et al. (1994) Hartmann, L., Hewett, R., & Calvet, N. 1994, ApJ, 426, 669, doi: 10.1086/174104
  * Herczeg & Hillenbrand (2008) Herczeg, G. J., & Hillenbrand, L. A. 2008, ApJ, 681, 594, doi: 10.1086/586728
  * Horne & Baliunas (1986) Horne, J. H., & Baliunas, S. L. 1986, ApJ, 302, 757, doi: 10.1086/164037
  * Husser et al. (2013) Husser, T. O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6, doi: 10.1051/0004-6361/201219058
  * Ingleby et al. (2014) Ingleby, L., Calvet, N., Hernández, J., et al. 2014, ApJ, 790, 47, doi: 10.1088/0004-637X/790/1/47
  * Ingleby et al. (2015) Ingleby, L., Espaillat, C., Calvet, N., et al. 2015, ApJ, 805, 149, doi: 10.1088/0004-637X/805/2/149
  * Ingleby et al. (2013) Ingleby, L., Calvet, N., Herczeg, G., et al. 2013, ApJ, 767, 112, doi: 10.1088/0004-637X/767/2/112
  * Kausch et al. (2015) Kausch, W., Noll, S., Smette, A., et al. 2015, A&A, 576, A78, doi: 10.1051/0004-6361/201423909
  * Kenyon & Hartmann (1995) Kenyon, S. J., & Hartmann, L. 1995, ApJS, 101, 117, doi: 10.1086/192235
  * Koenigl (1991) Koenigl, A. 1991, ApJ, 370, L39, doi: 10.1086/185972
  * Kounkel et al. (2019) Kounkel, M., Covey, K., Moe, M., et al. 2019, AJ, 157, 196, doi: 10.3847/1538-3881/ab13b1
  * Lindegren (2020) Lindegren, L. 2020, A&A, 633, A1, doi: 10.1051/0004-6361/201936161
  * Liseau et al. (1999) Liseau, R., White, G. J., Larsson, B., et al. 1999, A&A, 344, 342
  * Manara et al. (2022) Manara, C. F., Ansdell, M., Rosotti, G. P., et al. 2022, arXiv e-prints, arXiv:2203.09930.  https://arxiv.org/abs/2203.09930
  * Manara et al. (2017) Manara, C. F., Frasca, A., Alcalá, J. M., et al. 2017, A&A, 605, A86, doi: 10.1051/0004-6361/201730807
  * Manara et al. (2021) Manara, C. F., Frasca, A., Venuti, L., et al. 2021, PENELLOPE – X-Shooter spectra of targets in the Orion OB1 and sigma-Orionis regions, Zenodo, doi: 10.5281/zenodo.4477091
  * Manara et al. (2013) Manara, C. F., Testi, L., Rigliaco, E., et al. 2013, A&A, 551, A107, doi: 10.1051/0004-6361/201220921
  * Manara et al. (2021) Manara, C. F., Frasca, A., Venuti, L., et al. 2021, A&A, 650, A196, doi: 10.1051/0004-6361/202140639
  * Mathis et al. (1977) Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425, doi: 10.1086/155591
  * Maucó et al. (2016) Maucó, K., Hernández, J., Calvet, N., et al. 2016, ApJ, 829, 38, doi: 10.3847/0004-637X/829/1/38
  * Maucó et al. (2018) Maucó, K., Briceño, C., Calvet, N., et al. 2018, ApJ, 859, 1, doi: 10.3847/1538-4357/aabf40
  * McClure et al. (2013) McClure, M. K., D’Alessio, P., Calvet, N., et al. 2013, ApJ, 775, 114, doi: 10.1088/0004-637X/775/2/114
  * Muzerolle et al. (1998) Muzerolle, J., Calvet, N., & Hartmann, L. 1998, ApJ, 492, 743, doi: 10.1086/305069
  * Muzerolle et al. (2001) —. 2001, ApJ, 550, 944, doi: 10.1086/319779
  * Muzerolle et al. (2003) Muzerolle, J., Calvet, N., Hartmann, L., & D’Alessio, P. 2003, ApJ, 597, L149, doi: 10.1086/379921
  * Natta et al. (2001) Natta, A., Prusti, T., Neri, R., et al. 2001, A&A, 371, 186, doi: 10.1051/0004-6361:20010334
  * Pecaut & Mamajek (2013) Pecaut, M. J., & Mamajek, E. E. 2013, ApJS, 208, 9, doi: 10.1088/0067-0049/208/1/9
  * Percy et al. (2010) Percy, J. R., Grynko, S., Seneviratne, R., & Herbst, W. 2010, PASP, 122, 753, doi: 10.1086/654826
  * Proffitt et al. (2021) Proffitt, C. R., Roman-Duval, J., Taylor, J. M., et al. 2021, Research Notes of the American Astronomical Society, 5, 36, doi: 10.3847/2515-5172/abe852
  * Ricker et al. (2014) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9143, Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave, ed. J. Oschmann, Jacobus M., M. Clampin, G. G. Fazio, & H. A. MacEwen, 914320, doi: 10.1117/12.2063489
  * Robinson & Espaillat (2019) Robinson, C. E., & Espaillat, C. C. 2019, ApJ, 874, 129, doi: 10.3847/1538-4357/ab0d8d
  * Roman-Duval et al. (2020) Roman-Duval, J., Proffitt, C. R., Taylor, J. M., et al. 2020, Research Notes of the AAS, 4, 205, doi: 10.3847/2515-5172/abca2f
  * Roman-Duval et al. (2020) Roman-Duval, J., Proffitt, C. R., Taylor, J. M., et al. 2020, Research Notes of the American Astronomical Society, 4, 205, doi: 10.3847/2515-5172/abca2f
  * Scargle (1982) Scargle, J. D. 1982, ApJ, 263, 835, doi: 10.1086/160554
  * Schobert & Peeters (2021) Schobert, B. N., & Peeters, A. G. 2021, A&A, 651, A27, doi: 10.1051/0004-6361/202039398
  * Sergison et al. (2020) Sergison, D. J., Naylor, T., Littlefair, S. P., Bell, C. P. M., & Williams, C. D. H. 2020, MNRAS, 491, 5035, doi: 10.1093/mnras/stz3398
  * Shu et al. (1994) Shu, F., Najita, J., Ostriker, E., et al. 1994, ApJ, 429, 781, doi: 10.1086/174363
  * Smette et al. (2015) Smette, A., Sana, H., Noll, S., et al. 2015, A&A, 576, A77, doi: 10.1051/0004-6361/201423932
  * Tokovinin et al. (2020) Tokovinin, A., Petr-Gotzens, M. G., & Briceño, C. 2020, AJ, 160, 268, doi: 10.3847/1538-3881/abc2d6
  * Tuthill et al. (2001) Tuthill, P. G., Monnier, J. D., & Danchi, W. C. 2001, Nature, 409, 1012, doi: 10.1038/35059014
  * Valenti et al. (1993) Valenti, J. A., Basri, G., & Johns, C. M. 1993, AJ, 106, 2024, doi: 10.1086/116783
  * Venuti et al. (2014) Venuti, L., Bouvier, J., Flaccomio, E., et al. 2014, A&A, 570, A82, doi: 10.1051/0004-6361/201423776
  * Venuti et al. (2017) Venuti, L., Bouvier, J., Cody, A. M., et al. 2017, A&A, 599, A23, doi: 10.1051/0004-6361/201629537
  * Whittet et al. (2004) Whittet, D. C. B., Shenoy, S. S., Clayton, G. C., & Gordon, K. D. 2004, ApJ, 602, 291, doi: 10.1086/380837

##  Appendix A CVSO 17 and CVSO 36

As shown in Figure 3, we find that CVSO 17 and CVSO 36 show no significant UV
continuum excess in their HST spectra that would indicate active accretion,
which aligns with the analysis of their X-Shooter spectra by Manara et al.
(2021) and confirms their photometric characterization as WTTS by Calvet et
al. (2005). Additionally, an analysis of their far-UV spectra shows no
fluorescent H2 emission, which is a clear delineation between CTTS and WTTS
(France et al., 2012; Alcalá et al., 2019).

Figure 3:  The photospheric template shown is the M1 WTTS TWA 7.

##  Appendix B TESS object notes

CVSO 58: In Sector 6 there was significant power at 2.87 and 5.31 days. The
2.9 day period folds well, but the likelihood that the amplitude of the period
is significant is only 0.12. In Sector 32 significant power exists at 6.45 and
1.41 days, but neither looks periodic after folding. The auto-correlation
functions in both sectors show a peak near 5.7 days. This peak is strongest
for the dips; during Sector 6 the positive excursions (brightenings) show a
less well-defined peak at a period near 6 days.

CVSO 90: The Sector 6 PSD peaks at 3.15 days, but there is no significant
period seen in the folded light curve. The Sector 32 PSD shows a strong and
broad peak at 5.11 days. The folded light curve is not significant due to lots
of scatter in the half of the period dominated by deep dips. The
autocorrelation function shows a peak at a lag of about 4.4 days for the
absorption dips, and a peak at a 5.7 day period for the brightenings.

CVSO 104: This star has a peak in the PSD near 4.7 days in each sector. It is
not clear whether the light curve is dominated by bright or dark excursions.
We do not attempt to fold the two sectors together because it it impossible to
keep track of the phases over this time.

CVSO 107: The Sector 6 light curve is dominated by two deep dips spaced 12
days apart. The periodogram finds power at 6.3 days, or half that spacing.
Power at the same period also dominates in Sector 32. The brightenings show a
preferred lag of 6.5 days, while the dips lag at 7.7 days. There are three
possible short flares of 2-3 hour duration in Sector 6.

CVSO 109: The two light curves look similar, with strongest power near 6 days
(6.0 days in Sector 6; 6.6 days in Sector 32). After subtracting an 8 day
running mean, the folded light curves look sinusoidal, with amplitudes of
about 0.07 mag. The autocorrelation functions are broad, consistent with a
sinusoidal modulation.

CVSO 146: This star is partially blended with the brighter A2 star HD 290671
in the $TESS$ images (4.8 pixel separation). The A star has a low amplitude
1.56 day period. There is power at about 9 days in each sector; there is
additional power at 5.5 days in Sector 6 and 4.4 days in Sector 32. None of
these appear periodic. The autocorrelation power in Sector 6 is strongest for
the dips, at a period of 10-12 days; the brightenings show a correlation at
7-8 days; in Sector 32 both the brightenings and fadings show power near 5
days, with comparable peaks near 7 days (brightenings) and 8 days (fadings).

CVSO 165: $TESS$ cannot resolve this pair. The periodograms at both epochs
show strongest power at 4.3 days; in the latter half of Sector 32 there are
two prominent (0.1 mag) dips, and possibly 2 others cut off, at this spacing,
but that period is not obvious at other times. There is substructure in Sector
6, with the brightenings correlating with lags of 7.7 and 13 days and the
fadings correlating at 8.8 days (twice the strongest period) and 11.6 days. In
Sector 32 the brightenings and fadings correlate on the 4.3 day period.

CVSO 176: This was not observed by TESS in Sector 32. In Sector 6 the
character is clearly that of a dipper, with fadings up to 0.2 mag. Despite the
periodogram placing most of the power at 3.6 days, the autocorrelation shown
the strongest peak at 7.3 days, in both brightenings and dips.

##  Appendix C Accretion column temperatures and mass flux rates

Blackbodies are individually fit to the three accretion column spectra of each
target, then a weighted average is taken by scaling the associated accretion
luminosities by each column’s fractional filling factor according to Equation
2. Table 7 shows the individual temperatures fit to each accretion column.

Table 7: Accretion column temperatures

Object | T1E10 | T1E11 | T1E12 | Tshock
---|---|---|---|---
| (K) | (K) | (K) | (K)
CVSO 58 | 4422$\pm$1 | 6880$\pm$3 | 10916$\pm$3 | 5493$\pm$96
CVSO 90 | 4171$\pm$2 | 6816$\pm$3 | 10870$\pm$3 | 7975$\pm$1105
CVSO 104 | 4051$\pm$2 | 6634$\pm$3 | 10698$\pm$3 | 5239$\pm$105
CVSO 107 | 4187$\pm$2 | 6696$\pm$3 | 10679$\pm$3 | 5656$\pm$128
CVSO 109A | 4255$\pm$2 | 6506$\pm$2 | 10714$\pm$2 | 8877$\pm$1910
CVSO 146 | 4459$\pm$1 | 6871$\pm$3 | 10973$\pm$3 | 4975$\pm$27
CVSO 165A | 4675$\pm$1 | 6853$\pm$3 | 10760$\pm$3 | 4800$\pm$14
CVSO 165B | 4309$\pm$1 | 6690$\pm$3 | 10729$\pm$3 | 10542$\pm$343
CVSO 176 | 3938$\pm$2 | 6310$\pm$1 | 10736$\pm$2 | 5043$\pm$254

Note. — Best-fit temperatures for the three accretion columns and the
resultant weighted-average temperature. Uncertainties on T1E10, T1E11, and
T1E12 are one standard deviation on the temperature. The error on Tshock comes
from the propagated accretion column temperature and filling factor
uncertainties. Since the filling factor uncertainties are not symmetric, the
larger of the two uncertainties is used in the error propagation.

Table 8 shows the mass flux rates of the individual accretion columns for each
target. We find no clear correlations between the column that contributes the
most to the total mass flux and either the stellar mass or the total mass
accretion rate. Our future analysis of the entire ULLYSES sample will allow us
to expand this analysis and look for correlations with stellar age.

Table 8: Accretion column mass flux rates

Object | M⋆/R⋆ | $\dot{M}_{1E10}$ | $\dot{M}_{1E11}$ | $\dot{M}_{1E12}$ | $\dot{M}_{\rm tot}$
---|---|---|---|---|---
| (M⊙/R⊙) | (10-8 M☉ yr-1) | (10-8 M☉ yr-1) | (10-8 M☉ yr-1) | (10-8 M☉ yr-1)
CVSO 176 | 0.08 | $0.93^{+0.17}_{-0.4}$ | $0.92^{+0.22}_{-0.18}$ | $2.31^{+0.15}_{-0.13}$ | $4.18^{+0.11}_{-0.12}$
CVSO 104 | 0.23 | $0.227^{+0.021}_{-0.03}$ | $0.55^{+0.04}_{-0.03}$ | $0.360^{+0.05}_{-0.022}$ | $1.14^{+0.06}_{-0.03}$
CVSO 109A | 0.20 | $0.018^{+0.28}_{-0.015}$ | $2.1^{+0.7}_{-0.6}$ | $15.1^{+1.5}_{-5}$ | $17.2^{+1.0}_{-4}$
CVSO 107 | 0.27 | $0.69^{+0.04}_{-0.06}$ | $0.012^{+0.23}_{-0.007}$ | $4.11^{+0.23}_{-0.4}$ | $4.83^{+0.19}_{-0.3}$
CVSO 165A | 0.34 | $0.531^{+0.012}_{-0.017}$ | $0.150^{+0.020}_{-0.014}$ | $0.0253^{+0.004}_{-0.0013}$ | $0.708^{+0.020}_{-0.017}$
CVSO 90 | 0.74 | $0.032^{+0.010}_{-0.019}$ | $0.0018^{+0.16}_{-0.0014}$ | $1.21^{+0.06}_{-0.6}$ | $1.25^{+0.05}_{-0.4}$
CVSO 58 | 0.77 | $0.206^{+0.009}_{-0.019}$ | $0.0018^{+0.016}_{-0.0012}$ | $0.82^{+0.06}_{-0.07}$ | $1.03^{+0.06}_{-0.06}$
CVSO 165B | 0.42 | $0.0007^{+0.0026}_{-0.0004}$ | $0.0053^{+0.010}_{-0.0020}$ | $1.64^{+0.05}_{-0.07}$ | $1.65^{+0.05}_{-0.07}$
CVSO 146 | 0.69 | $0.220^{+0.007}_{-0.008}$ | $0.226^{+0.015}_{-0.014}$ | $0.082^{+0.007}_{-0.006}$ | $0.529^{+0.018}_{-0.016}$

Note. — Mass flux rates of individual accretion columns with targets listed in
order of increasing stellar mass. There is no clear correlation between the
column that dominates the mass flux and either the stellar mass or the total
accretion rate.