# A Multi-wavelength, Multi-epoch Monitoring Campaign of Accretion Variability
in T Tauri Stars from the ODYSSEUS Survey. I.  _HST_ FUV and NUV Spectra

John Wendeborn 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  Sophia
Lopez Institute for Astrophysical Research, Department of Astronomy, Boston
University, 725 Commonwealth Avenue, Boston, MA 02215, USA  Thanawuth
Thanathibodee 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, C025 Science
Center 25 East Drive, Amherst, MA 01002, USA  Caeley V. Pittman Institute for
Astrophysical Research, Department of Astronomy, Boston University, 725
Commonwealth Avenue, Boston, MA 02215, USA  Nuria Calvet Department of
Astronomy, University of Michigan, 1085 South University Avenue, Ann Arbor, MI
48109, USA  Nicole Flors Institute for Astrophysical Research, Department of
Astronomy, Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA
Fredrick M. Walter Department of Physics and Astronomy, Stony Brook
University, Stony Brook NY 11794-3800, USA  Ágnes Kóspál Konkoly Observatory,
HUN-REN Research Centre for Astronomy and Earth Sciences, CSFK, MTA Centre of
Excellence, Konkoly-Thege Miklós út 15-17  Institute of Physics and Astronomy,
ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest,
Hungary  Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg,
Germany  Konstantin N. Grankin Crimean Astrophysical Observatory, 298409
Nauchny, Republic of Crimea  Ignacio Mendigutía Centro de Asrobiología, (CSIC-
INTA), Departamento de Astrofísica, ESA-ESAC Campus,E-28691 Madrid, Spain
Hans Moritz Günther Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge MA,
02139  Jochen Eislöffel Thüringer Landessternwarte, Sternwarte5, D-07778
Tautenburg, Germany  Zhen Guo Instituto de Física y Astronomía, Universidad de
Valparaíso, ave. Gran Bretaña, 1111, Casilla 5030, Valparaíso, Chile  Kevin
France Laboratory for Atmospheric and Space Physics, University of Colorado
Boulder, Boulder, CO 80303,USA  Eleonora Fiorellino INAF-Osservatorio
Astronomico di Capodimonte, via Moiariello 16, 80131 Napoli, Italy  William J.
Fischer Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,
MD 21218, USA  Péter Ábrahám Konkoly Observatory, HUN-REN Research Centre for
Astronomy and Earth Sciences, CSFK, MTA Centre of Excellence, Konkoly-Thege
Miklós út 15-17  ELTE Eötvös Loránd University, Institute of Physics, Pázmány
Péter sétány 1/A, 1117 Budapest, Hungary  University of Vienna, Dept. of
Astrophysics, Türkenschanzstr. 17, 1180, Vienna, Austria  Gregory J. Herczeg
Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing
100871, People’s Republic of China  Department of Astronomy, Peking
University, Beijing 100871, People’s Republic of China

###### Abstract

The Classical T Tauri Star (CTTS) stage is a critical phase of the star and
planet formation process. In an effort to better understand the mass accretion
processes, which can dictate future stellar evolution and planet formation, a
multi-epoch, multi-wavelength photometric and spectroscopic monitoring
campaign of four CTTSs (TW Hya, RU Lup, BP Tau, and GM Aur) was carried out in
2021 and 2022/2023 as part of the Outflows and Disks Around Young Stars:
Synergies for the Exploration of ULLYSES Spectra (ODYSSEUS) program. Here we
focus on the $HST$ UV spectra obtained by the $HST$ Director’s Discretionary
Time UV Legacy Library of Young Stars as Essential Standards (ULLYSES)
program. Using accretion shock modeling, we find that all targets exhibit
accretion variability, varying from short increases in accretion rate by up to
a factor of 3 within 48 hours, to longer decreases in accretion rate by a
factor of 2.5 over the course of 1 year. This is despite the generally
consistent accretion morphology within each target. Additionally, we test
empirical relationships between accretion rate and UV luminosity and find
stark differences, showing that these relationships should not be used to
estimate the accretion rate for an individual target. Our work reinforces that
future multi-epoch and simultaneous multi-wavelength studies are critical in
our understanding of the accretion process in low-mass star formation.

Stellar accretion disks, Star formation, Protoplanetary disks, Pre-main
sequence stars

††facilities: $HST$, LCOGT, $TESS$, AAVSO, ZTF, ASAS-SN, Konkoly Observatory,
CrAO††software: Python, Specutils, AstroPy, emcee

##  1 Introduction

Classical T Tauri Stars (CTTSs) are young ($<$10 Myr), low-mass ($<$2 M⊙)
stars that are actively accreting from a surrounding protoplanetary disk. This
disk is the reservoir from which planets will form (or in some cases have
already formed, e.g., Keppler et al., 2018; Haffert et al., 2019; Pérez et
al., 2019; Zhou et al., 2022), and dictates much of the future evolution of
the system. The process of disk-to-star mass accretion, which takes place at
the star-disk boundary, typically within $\sim$10 R∗, is highly energetic,
emitting X-rays and UV radiation (Kastner et al., 2002; Herbst et al., 1994;
Günther et al., 2007) which can have a profound impact on the disk. These
effects include modifying disk chemistry, modulating the presence and distance
of snowlines, inhibiting dust grain growth, annealing solid dust grains, and
depleting/dispersing disk material (see reviews by Fischer et al., 2023; Bae
et al., 2022; Miotello et al., 2023). As such, it is important to fully
understand the accretion process in order to paint a complete picture of the
star/planet formation processes.

Due to the strong magnetic fields in CTTSs (1–3 kG; Johns-Krull, 2007; Donati
et al., 2020), accretion occurs via magnetospheric accretion (see reviews by
Bouvier et al., 2007; Hartmann et al., 2016). The magnetic field truncates the
disk at some radius (the inner truncation radius, Rin, typically assumed to be
5 R⋆), where the hot plasma is bound to and travels along the magnetic fields
lines. Along its path, it eventually reaches super-sonic, free-fall velocities
(vff) until it reaches the photosphere, producing highly energetic shocks and
accretion hotspots.

Simulations show the accretion flow can vary in density (Romanova et al.,
2008; Kulkarni & Romanova, 2008; Romanova et al., 2012; Zhu et al., 2023b)
which affects the temperature of the resulting hotspot. Denser flows create
hotter hotspots which radiate more strongly at UV wavelengths, while less
dense flows (i.e. cooler hotspots) peak in the optical (Calvet & Gullbring,
1998; Ingleby et al., 2013; Pittman et al., 2022). This excess UV/optical
emission can be modeled, assuming it originates from accretion columns of
various energy densities (Calvet & Gullbring, 1998). Such modeling (often
using $HST$ UV-optical spectra) has revealed that the accretion structure is
not only time-variable, but also varies greatly from object to object. Some
stars are dominated by large, cooler hotspots driven by low density accretion
columns, while in others the accretion is dominated by high density columns
producing small but high temperature hotspots (Ingleby et al., 2013, 2015;
Robinson & Espaillat, 2019; Pittman et al., 2022).

The accretion onto CTTSs is known to be intrinsically variable on timescales
from minutes–hours (e.g. inhomogenous accretion flows, hotspot plasma
oscillations), days–weeks (e.g. inner disk inhomogeneity, inner disk thermal
instabilities), to months–years (e.g. MRI, gravitational instability); see
review by Bae et al. (2022). Observationally, the variable mass accretion
process is often associated with other sources of variability, including
stellar rotation, chromospheric activity, disk occultation, variable
extinction, winds/outflows, dark spots, and flares.

Accretion has been correlated with UV (Calvet et al., 2004; Ardila et al.,
2013; Robinson & Espaillat, 2019) and optical (Alcalá et al., 2014, 2017) line
luminosity, though there is typically notable scatter/outliers within these
empirical relationships, implying that they are an imperfect analogue for the
true accretion rate. One explanation for this scatter is intrinsic
variability, though until now no extensive multi-epoch FUV/NUV campaign has
been carried out to gauge how these relationships vary in individual stars as
the accretion varies over the span of several rotation periods.

In an effort to better understand accretion variability in CTTSs, and to
connect it to other observables in the UV-IR, a multi-wavelength, multi-epoch
observing campaign of the CTTSs TW Hya, RU Lup, BP Tau, and GM Aur was carried
out in 2021 and 2022. These observations include multi-epoch $HST$ Cosmic
Origins Spectrograph (COS) UV spectra taken as part of the ULLYSES (UV Legacy
Library of Young Stars as Essential Standards) $HST$ Director’s Discretionary
Time Program, moderate cadence multi-band $uBgVriz$ and Transiting Exoplanet
Survey Satellite ($TESS$, Ricker et al., 2015) photometry, and multi-epoch
high resolution optical spectra. In this paper (Paper I) we present the $HST$
COS FUV and NUV results of our multi-epoch, multi-wavelength study of these
four CTTSs. The photometry and optical spectra, partly obtained as part of the
Outflows and Disks Around Young Stars: Synergies for the Exploration of
ULLYSES Spectra (ODYSSEUS) collaboration and PENELLOPE Very Large Telescope
(VLT) program (Espaillat et al., 2022; Manara et al., 2021), will be presented
in follow-up works, Paper II and Paper III, respectively.

Here in Paper I, we describe our sample in Section 2 and then our observations
and data in Section 3. Section 4 describes our accretion shock model and the
results of our analyses. In Section 5 we discuss these results in more detail
and speculate on their implications. We summarize our final conclusions in
Section 6.

##  2 Sample

Our sample consists of TW Hya, RU Lup, BP Tau, and GM Aur, chosen by the
ULLYSES implementation team. This sample was chosen as they are well-studied,
prototypical CTTSs with well-known magnetic configurations and reasonably
constrained rotation periods. Below we provide more background information on
each target, with some properties summarized in Table 1.

###  2.1 TW Hya

TW Hya is a nearby ($d\sim 60$ pc Gaia Collaboration et al., 2023) CTTS of
spectral type K7 (Ingleby et al., 2013). Its surrounding disk has many
concentric gaps and rings (Andrews et al., 2012; Huang et al., 2018a), which
may have been carved out by an embedded planet (Nayakshin et al., 2020; Zhu et
al., 2023a). The star is viewed nearly pole-on (18°, from $v$sin$i$ Alencar &
Batalha, 2002) and the disk is viewed nearly face-on (5.5–7°, from scattered
light and (sub)millimeter continuum Debes et al., 2023; Qi et al., 2004; Huang
et al., 2018a). We adopt an inclination of 7° from millimeter observations
here and in Paper II and Paper III. Donati et al. (2011) estimate the star’s
magnetic obliquity, the angle between its rotation and dipolar magnetic axis,
to be low, at about 10°.

Despite its nearly pole-on geometry, TW Hya has shown photometric periodicity,
though at a wide and inconsistent range of periods (0.16-4.7 days; Siwak et
al., 2011, 2014, 2018). Radial velocity studies (Huélamo et al., 2008;
Sicilia-Aguilar et al., 2023) reveal a strong, stable, sinusoidal rotational
modulation at about 3.57-days.

TW Hya is old (8–10 Myr, Sokal et al., 2018), yet is still actively accreting
from a surrounding accretion disk beyond the assumed $\lesssim$5 Myr lifespan
of protoplanetary disks (Evans et al., 2009; Williams & Cieza, 2011) and
therefore challenges our understanding of disk dispersal mechanisms. The range
of measured accretion rates in TW Hya is 0.05–0.6$\times$10-8 M⊙ yr-1 (Ingleby
et al., 2013; Manara et al., 2014; Robinson & Espaillat, 2019; Sousa et al.,
2023; Herczeg et al., 2023). This accretion is thought to primarily occur
through a single, large, pole-ward flow (Donati et al., 2011; Sicilia-Aguilar
et al., 2023) along with many smaller, more sporadic accretion tongues near
the equator (Siwak et al., 2018).

###  2.2 RU Lup

Previous studies of RU Lup have shown it is a highly veiled (rK=6.3, rV=2–9;
Stempels & Piskunov, 2002; Stempels et al., 2007; Herczeg & Hillenbrand, 2008;
Sousa et al., 2023), strongly accreting ($\dot{M}$ $\sim$2–7$\times$10-8 M⊙
yr-1; Herczeg et al., 2005; Herczeg & Hillenbrand, 2008; Alcalá et al., 2017;
Stock et al., 2022) K7 (Sousa et al., 2023) CTTS with a powerful accretion-
driven outflow (Takami et al., 2001; Whelan et al., 2021). Its distance is
about 156 pc (Gaia Collaboration et al., 2023). The rotation period of RU Lup
is generally assumed to be 3.71 days (Stempels et al., 2007), detected via
radial velocity measurements. However, this period has not been recovered in
other time-dependant photometric studies of RU Lup, likely due to the
combination of stochastic accretion activity (Siwak et al., 2016; Stock et
al., 2022) and its low inclination angle.

RU Lup possesses a 63 au radius dust disk (with a gas disk extending to 120
au) with concentric gaps and rings (Andrews et al., 2018; Huang et al., 2018b)
and unique gas structure. The gas structure, primarily traced by 12CO, is a
large, clumpy 5-armed spiral that extends for $>$1000 au (Huang et al.,
2020a). Millimeter continuum (Huang et al., 2018b) and NIR (K-band)
interferometric (GRAVITY Collaboration et al., 2021) observations find disk
inclinations of 18.8° and 16°, respectively. Other observations of RU Lup have
placed the stellar inclination between 23–24° using line broadening (Herczeg
et al., 2005) and radial velocity variations (Stempels et al., 2007), slightly
higher than the millimeter observations, but still in line with a close-to
face-on disk. Here we assume an inclination of 16° from millimeter
observations.

###  2.3 BP Tau

BP Tau is a $\sim$3 Myr (Grankin, 2016) K7 (Ingleby et al., 2013) system in
the Taurus-Auriga complex at a distance of about 128 pc (Gaia Collaboration et
al., 2023). Previous studies have estimated a wide range of accretion rates
for BP Tau, between 0.09–3 $\times$10-8 M⊙ yr-1 (Gullbring et al., 1998;
Schmitt et al., 2005; Long et al., 2011; Ingleby et al., 2013). Its rotation
period has been estimated to be between 6.1–11 days (Vrba et al., 1986; Simon
et al., 1990; Osterloh et al., 1996; Gómez de Castro & Franqueira, 1997; Percy
& Palaniappan, 2006; Percy et al., 2006), but it is generally considered to be
either 7.6 or 8.2 days from photometric variability, assumed to originate from
accretion signatures rotating with the stellar surface.

Donati et al. (2008) performed a spectropolarimetric study of BP Tau in 2006
to map the structure of its magnetic field. Their study revealed a field
dominated by a dipolar component, but still with a strong octupolar component,
both tilted from the rotation axis by $\sim$10°, though in opposite
directions. They predicted accretion hotspots on its surface near the
octupoles that cover about 2% of the surface. Long et al. (2011) also
recovered similar accretion structure, revealing that the hotspots are mostly
symmetric in longitude but elongated in latitude.

Observations of BP Tau’s disk reveal a $\sim$60 au radius dust disk with 2–3
gap/ring pairs inclined at 37–39° (Long et al., 2019; Zhang et al., 2023). The
stellar inclination has also been estimated at 48–52° (Simon et al., 1990;
Johns-Krull et al., 1999) from estimates of $v$sin$i$ and an assumed rotation
period of 7.6 days. We adopt an inclination of 38.2° from the millimeter
observations of Zhang et al. (2023).

###  2.4 GM Aur

GM Aur is a young (2 Myr Jensen & Mathieu, 1997) K5 (Manara et al., 2014)
system in the Taurus-Auriga complex at a distance of about 155 pc (Gaia
Collaboration et al., 2023). It possesses a transitional disk with an inner
cavity of radius 20 au and multiple outer concentric rings (Espaillat et al.,
2011; Macías et al., 2018; Huang et al., 2020b). Such studies place the disk
inclination between 52.8–53.2°and we adopt 53°.

It is a moderate accretor, with accretion rates between 0.4–2.0$\times$10-8 M⊙
yr-1 (Ingleby et al., 2013; Manara et al., 2014; Robinson & Espaillat, 2019;
Espaillat et al., 2021). The accretion occurs primarily via a single, large
hotspot near the pole which, in combination with its moderate inclination and
rotation, causes a strong, stable periodicity of about 6 days (Percy et al.,
2010; Espaillat et al., 2021; Bouvier et al., 2023). The magnetic obliquity
has been estimated at 13° (McGinnis et al., 2020).

Espaillat et al. (2021) showed that short-wavelength photometry ($ug$) peaked
about a day prior to longer-wavelength bands ($ri/TESS$), which they attribute
to a large, asymmetric, and azimuthally stratified accretion hotspot. Bouvier
et al. (2023) recently conducted a multiwavelength study of GM Aur in 2021,
including optical/NIR photometry and spectra. They found a $\sim$6-day period
in their photometry, as well as at low red-shifted velocities ($\sim$0–100
km/s) in H$\alpha$, H$\beta$, and H$\gamma$, and in the wings ($\pm$200-400
km/s) of H$\alpha$ and H$\beta$. At moderate blue-shifted velocities (-200–0
km/s), where variable absorption is strongest, they found non-periodic
variability. They attribute these variability characteristics (both periodic
and non-periodic) to the presence of a stable, rotating accretion hotspot
along with stochastically variable outflows.

##  3 Observations and Data Reduction

$HST$ observations were carried out with the Cosmic Origins Spectrograph (COS)
instrument for TW Hya, RU Lup, BP Tau, and GM Aur as part of the ULLYSES DDT
program through proposals 16107–16110 and 16589–16592 (Roman-Duval et al.
2020, PI: Julia Roman-Duval). These spectra are presented in Figure 1. The
observations utilized the G160M and G230L gratings, which cover a wavelength
range of about 1400–3200 Å, with a gap between about 2100–2500 Å. Below about
1760 Å the spectral resolution, R, is $\sim$18,000 and elsewhere R$\sim$2,900.
All spectra have been de-reddened according to the Whittet et al. (2004)
extinction law and the extinction values from Table 1, assuming RV=3.1. The
spectra presented here were obtained via ULYSSES Data Release 6 (Roman-Duval
et al., 2020). Note that a portion of the TW Hya data used here is presented
in (Hinton et al., 2022) in a study of flaring in CTTSs.

Each target was observed approximately four times per rotation period for
three rotation periods in two epochs separated by about a year (see Table 2),
totaling 21–24 visits per target. All $HST$ spectra used in this work can be
found in MAST https://doi.org/10.17909/a530-qm96 (catalog 10.17909/a530-qm96).
For clarity, in this work “epoch” will refer to the different halves of the
monitoring (Epoch 1/E1, corresponding to 2021 and Epoch 2/E2, corresponding to
2022/2023), while “visit” will refer to individual $HST$ observations.

There were some changes to the observing schedule of the targets, typically
due to problems with guide star and/or target acquisition. Several visits of
TW Hya failed during the original scheduled window in E2 and were rescheduled
to 2022 April 25–26 (MJD: 59694.5-59695.4). $HST$ went offline during a visit
of GM Aur on 2021 October 5 (MJD: 59492) in E1. The remaining observations
were carried out from 2021 December 6–12 (MJD: 59554.3-59560.2). In other
cases, individual observations failed and were not re-observed, resulting in
less than 24 total observations for each target, except BP Tau for which all
24 total observations were carried out.

Table 1: Target Parameters

Object | RA/Dec | Distance | SpT | Period | M∗ | Teff | R∗ | AV | i |
---|---|---|---|---|---|---|---|---|---|---
| [J2000] | [pc] |  | [days] | [M⊙] | [K] | [R⊙] | [mag] | [∘] |
TW Hya | 11:01:51.905/ | 59.96${}^{+0.37}_{-0.11}$ a afootnotemark:  | K7bbfootnotemark:  | 3.57ccfootnotemark:  | 0.79ddfootnotemark:  | 4060ddfootnotemark:  | 0.93eefootnotemark:  | 0.00ddfootnotemark:  | 7fffootnotemark:  |
| -34:42:17.033 |  |  |  |  |  |  |  |  |
RU Lup | 15:56:42.311/ | 156.0${}^{+1.2}_{-1.1}$ a afootnotemark:  | K7ggfootnotemark:  | 3.71hhfootnotemark:  | 0.65iifootnotemark:  | 3950iifootnotemark:  | 1.83*i*ifootnotemark:  | 0.07iifootnotemark:  | 16jjfootnotemark:  |
| -37:49:15.474 |  |  |  |  |  |  |  |  |
BP Tau | 04:19:15.834/ | 128.3${}^{+0.7}_{-0.6}$ a afootnotemark:  | K7bbfootnotemark:  | 7.6kkfootnotemark: , 8.2llfootnotemark:  | 0.7mmfootnotemark:  | 4055nnfootnotemark:  | 1.77*n*nfootnotemark:  | 0.51mmfootnotemark:  | 38.2oofootnotemark:  |
| +29:06:26.927 |  |  |  |  |  |  |  |  |
GM Aur | 04:55:10.982/ | 155.0${}^{+1.4}_{-2.0}$ a afootnotemark:  | K5ddfootnotemark:  | 6.0eefootnotemark:  | 1.36ddfootnotemark:  | 4350ddfootnotemark:  | 2.00eefootnotemark:  | 0.6bbfootnotemark:  | 53ppfootnotemark:  |
| +30:21:59.574 |  |  |  |  |  |  |  |  |

††footnotetext: a: Gaia Collaboration et al. (2023), b: Ingleby et al. (2013),
c: Sicilia-Aguilar et al. (2023), d: Manara et al. (2014), e: Robinson &
Espaillat (2019) (from Manara et al. (2014) with updated Gaia distances), f:
Andrews et al. (2016), g: Sousa et al. (2023), h: Stempels et al. (2007), i:
Herczeg et al. (2005), j: GRAVITY Collaboration et al. (2021), k: Vrba et al.
(1986), l: Percy & Palaniappan (2006), m: Gullbring et al. (1998), n: Johns-
Krull et al. (1999), o: Zhang et al. (2023), p: Macías et al. (2018), *:
Updated with current Gaia distances

Table 2: $HST$ COS Observations

Object | Epoch | Date (UT) | MJD | # of
---|---|---|---|---
|  | [Begin/End] | [Begin-End] | Observations
TW Hya | 1 | 2021-03-29/2021-04-08 | 59302.7-59312.6 | 11
TW Hya | 2 | 2022-03-30/2022-04-27 | 59668.5-59695.4 | 10
RU Lup | 1 | 2021-08-10/2021-08-21 | 59436.9-59447.3 | 10
RU Lup | 2 | 2022-08-10/2022-08-24 | 59801.3-59815.4 | 12
BP Tau | 1 | 2021-08-20/2021-09-12 | 59446.8-59469.1 | 12
BP Tau | 2 | 2022-12-13/2023-01-06 | 59926.2-59950.5 | 12
GM Aur | 1 | 2021-10-13/2021-12-12 | 59500.5-59560.2 | 11
GM Aur | 2 | 2022-11-26/2022-12-12 | 59909.9-59925.2 | 11

Note. — All $HST$ spectra used in this work, including targets and templates,
can be found in MAST https://doi.org/10.17909/a530-qm96 (catalog
10.17909/a530-qm96).

Figure 1: $HST$ COS spectra of TW Hya, RU Lup, BP Tau, and GM Aur. The red-
colored spectra were taken in Epoch 1, while the blue-colored spectra were
taken in Epoch 2. Darker lines denote spectra obtained earlier in their
respective epoch. Spectra have not been dereddened here. For clarity, data
have been smoothed using a Savitzky-Golay filter. More details on the timing
of the observations are given in Table 2.

##  4 Analysis and Results

In the following sections we analyze and model the UV spectra presented in
Section 3. We characterize the accretion properties of TW Hya, RU Lup, BP Tau,
and GM Aur by fitting the data with accretion shock models. We measure the
luminosities of UV lines and features and compare these to the accretion rates
derived with the accretion shock models.

###  4.1 Accretion Shock Modeling

We use the accretion shock models of Calvet & Gullbring (1998) following
similar methods as Robinson & Espaillat (2019) (hereafter RE19, ). We adopt
the stellar parameters listed in Table 1.

To accurately estimate the excess emission caused by accretion, one must have
an estimate of the underlying photospheric+chromospheric emission
(F${}_{\rm{Phot,\ True}}$) of a non-accreting star (see Equation 1, where
FWTTS is the raw spectrum of non-accreting Weak T Tauri Star (WTTS) and VCTTS
and VWTTS are the flux of the CTTS and WTTS spectra at V-band (5500 Å),
$f_{i}$ is the surface coverage fraction of an individual accretion column,
$i$, and rV is the optical veiling). To estimate this, we utilize
contemporaneous optical veiling measurements (rV) to scale a raw WTTS spectrum
(FWTTS) to the appropriate $V$-band level for any visit with contemporaneous
$V$ photometry (see Paper II). We calculate veiling using medium–high
resolution (R$\sim$5,400–140,000) optical ($\lambda\sim 4000-8000\AA$) spectra
from SMARTS/CHIRON, VLT/ESPRESSO, VLT/XSHOOTER, VLT/UVES, Haute-
Provence/SOPHIE, and Tautenburg/TCES. We follow the basic procedure of
Hartigan et al. (1989). See Paper III, Section 3 for a more detailed
description of our procedure and findings. For TW Hya, RU Lup, and BP Tau, we
use $HST$ STIS spectra of the K7 WTTS HBC 427 (PID 11616) as the basis for the
photospheric template, while for GM Aur we use the K5 WTTS RECX-1 (PID 11616).

The result is the emission from the fraction of the stellar photosphere not
covered by accretion shocks (F${}_{\rm{Phot,\ Obs.}}$) that contributes
towards the observed CTTS spectrum for that particular visit. We can then fit
for the excess emission due to accretion (see below) and divide
F${}_{\rm{Phot,\ Obs.}}$ by the fraction of the stellar surface not covered by
hotspots to obtain F${}_{\rm{Phot,\ True}}$ that can be used for fitting. This
results in multiple photospheric templates for each target (with the exception
of RU Lup), one for each visit with contemporaneous V-band observation. For TW
Hya, we obtain 21 templates, 15 for BP Tau, and 14 for GM Aur.

$\mathrm{F}_{\rm{Phot,\
True}}=\mathrm{F}_{\rm{WTTS}}\left(\frac{V_{\rm{CTTS}}}{V_{\rm{WTTS}}}\right)\left(\frac{1}{1+r_{V}}\right)\left(\frac{1}{1-\sum
f_{i}}\right)$ (1)

In the case of RU Lup, we are unable to estimate rV for any visit, owing to
the numerous, strong emission lines in its optical spectra (see Paper III,
Gahm et al., 2008). We therefore cannot estimate F${}_{\rm{Phot,\ True}}$ as
above. Instead, we assume F${}_{\rm{Phot,\ True}}$ is the raw $HST$ spectrum
of HBC 427 (FWTTS) scaled to the distance and radius of RU Lup via Equation 2.
We discuss this further in Appendix A.

$F_{\rm{Phot,\
True}}=\mathrm{F}_{\rm{WTTS}}\left(\frac{d_{\rm{WTTS}}R_{\rm{CTTS}}}{d_{\rm{CTTS}}R_{\rm{WTTS}}}\right)^{2}$
(2)

.

To reproduce the excess emission, here we follow Ingleby et al. (2013) and use
multiple accretion columns. We employ a four-column model with energy fluxes,
${\mathcal{F}}=1/2\rho v_{s}^{3}$, of 1010 (low), 1011 (medium), 1012 (high),
and 3$\times$1012 (very high) erg s-1 cm-2. RE19 note that the inclusion of
this fourth, very high density column was necessary for several observations
of DM Tau and GM Aur to fit the spectrum near 1800 Å. Here we use four columns
for all of our fitting for consistency. The energy flux (${\mathcal{F}}$)
depends on $\rho$, the density of material in the accretion column, and
$v_{s}$, the infall velocity. The infall velocity is set to be the free-fall
velocity at the magnetospheric truncation radius (Rin) of 5 stellar radii. We
note that Rin has been measured in TW Hya (3.5 R⋆, Gravity Collaboration et
al. (2020) and 8.3–12.4 R⋆ depending on assumed magnetic field strength
Gravity Collaboration et al. 2023) and RU Lup (3.3–6.6 R⋆ depending on assumed
magnetic field strength Gravity Collaboration et al., 2023). We opt to use 5
R⋆ for all objects due to the uncertainties in these estimates and for
consistency; the free fall velocity changes little for any choice of Rin
within the measured uncertainties.

We use filling factors ($f_{i}$) to scale the resulting emission and these are
left as free parameters. These four filling factors ($f_{low}$, $f_{medium}$,
$f_{high}$, $f_{very~{}high}$) measure the fraction of the visible stellar
surface that is covered by the four accretion columns with the energy fluxes
noted above. We calculate $\dot{M}$ by adding the contributions of the four
accretion columns with

$\dot{M}=\frac{8\pi
R_{\ast}^{2}}{v_{s}^{2}}\sum_{i}\mathcal{F}_{i}f_{i}=\frac{8\pi
R_{\ast}^{2}}{v_{s}^{2}}\mathcal{F}_{\rm{weighted}}f_{\rm{total}}~{}~{}.$ (3)

One can additionally calculate the fractional accretion rate ($\dot{m}_{k}$)
for each column as the fraction of the total mass accretion rate contributed
by that individual column as

$\dot{m}_{k}=\frac{f_{k}\mathcal{F}_{k}}{\sum_{i}f_{i}\mathcal{F}_{i}},$ (4)

where $f$ is the filling factor and $\mathcal{F}$ is the associated energy
flux.

We re-sample our COS spectra to a lower resolution (R$\sim$1500, similar to
that of $HST$ STIS G230L grating used in Robinson & Espaillat 2019) and mask
notable lines (e.g. Mg II: 2800 Å). We also remove data below $\sim$1800 Å due
to the abundance of emission lines and added uncertainty in estimating the
continuum. Including some optical emission is important to constrain the
contribution from lower density columns, which can cover a large fraction of
the star and contribute significantly to the total mass accretion. While RE19
use $HST$ STIS NUV-optical spectra, which extend continuously from
$\sim$1800–5700 Å, our $HST$ COS spectra extend to just 3200 Å and so do not
span any optical wavelengths. Thus, we combine our COS spectra with
contemporaneous (within 6 hours) $BgV$ photometry (see Paper II). We do not
include anything redder than $V$ (such as $ri$) since we truncate our model at
5700 Å. Visits without contemporaneous photometry are still modeled in the
same manner and are noted in Tables 4 and 5, but should be considered
carefully and we discuss the reliability of these results in Appendix B.

Based on modeling that has shown that accretion hotspots can cover up to
$\sim$40% of the stellar surface (Romanova et al., 2003; Ingleby et al., 2013,
2015; Robinson & Espaillat, 2019), we allow individual $f_{i}$ to vary between
0 and 40% and limit the total surface coverage of all columns ($\Sigma f_{i}$)
to 50%. The accretion column filling factors are fit using a Markov Chain
Monte Carlo ($emcee$, Foreman-Mackey et al., 2013) technique.

Every $HST$ visit for a given target is fit with each template for that
target. For example, each of the 24 visits of BP Tau was fit using each of the
15 templates. The final value for a given parameter in a single fit is the
median of the posterior distribution, and the upper/lower uncertainties are
the difference between the 84th/16th percentile and the median
($\pm$1-$\sigma$). Finally, these values and uncertainties are averaged across
all templates, resulting in the values listed in Tables 4–5.

Figure 2 shows the results of our shock modeling, including accretion rates,
filling factors ($f$), and fractional accretion rates ($\dot{m}$) of the four
accretion columns. Individual fits for each $HST$ visit can be found in
Figures 7–14 in Appendix C. In most cases there are anti-correlations in the
posterior distributions of adjacent accretion columns (fLow/fMedium,
fMedium/fHigh, and fHigh/f${}_{\mathrm{Very\ High}}$) resulting from
degeneracies between the models. Some degeneracy is expected, given that the
emission from like-density accretion columns is similar. We discuss the
details of the fits for each individual object in the sections below.

Figure 2: Results of our shock model fitting for TW Hya (top left), RU Lup
(top right), BP Tau (bottom left), and GM Aur (bottom right). The top row of
each panel shows the mass accretion rate: the total height of the bar
represents the total accretion rate while the colored bars show the accretion
contributed by each respective accretion column. The errorbar atop each bar
represents the uncertainty on the total accretion rate. The subsequent rows
are the filling factors of the low, medium, high, and very high density
accretion columns. The left and right columns of each panel show Epochs 1 and
2. Note the additional break in the Date axes for TW Hya E2 and GM Aur E1 due
to the uneven sampling from $HST$.

####  4.1.1 Modeling Results for TW Hya

TW Hya’s accretion is primarily driven by the low density accretion column,
which generally covers 20–40% of the stellar surface and contributes 40–70% of
the total mass accretion. In some cases, the medium column becomes significant
(often when fLow is very low, likely due to their degeneracy) and can
contribute up to 90% of the mass accretion, though it typically covers
$\sim$1% of the surface and contributes 0–50% of the mass accretion. The high
density column consistently contributes 10–50% of the mass accretion, while
the very high density column is generally insignificant in TW Hya, except for
two visits of high $\dot{M}$ in E2.

While the total mass accretion is typically dominated by the lower density
columns, the variability in the accretion appears to be driven by the high
density columns. The Spearmann $r$ coefficient between
$\dot{m}_{\mathrm{Low+Medium}}$ and $\dot{M}$ is -0.74, while it is +0.74
between $\dot{m}_{\mathrm{High+Very\ High}}$, suggesting that changes in the
accretion are driven by higher density, hotter accretion flows. For reference,
$r=1$ implies a perfect positive correlation, $r=-1$ implies a perfectly
negative correlation, and $r=0$ implies no correlation.

Overall, the accretion rate (top left panel, uppermost row, Figure 2) varies
between 0.08–0.51$\times$10-8 M⊙ yr-1 peak-to-peak across both epochs, a
factor of 6.5 difference (0.80 dex), with a median accretion rate of
0.25$\times$10-8 M⊙ yr-1. The median accretion parameters and variability are
similar in E1 and E2, with TW Hya accreting more strongly in E2 (0.23 vs
0.35$\times$10-8 M⊙ yr-1).

####  4.1.2 Modeling Results for RU Lup

RU Lup (top right panel of Figure 2) is the strongest accretor in our sample,
with accretion rates between 11.8–17.0$\times$10-8 M⊙ yr-1 in E1, with a
median of 13.2$\times$10-8 M⊙ yr-1. The accretion rate drops considerably from
E1 to E2, with rates between 3.5–12.2$\times$10-8 M⊙ yr-1 in E2 and a median
of 6.0$\times$10-8 M⊙ yr-1. The peak-to-peak variability in RU Lup is a factor
of 4.9, or 0.69 dex.

The accretion is dominated by the medium density column in both E1 and E2. In
E1, it covers 18–26% of the stellar surfaces and contributes 85–98% of the
total mass accretion rate. In E2, it covers 6.9–19.4% of the surface and
contributes 80–97% to $\dot{M}$. The decrease in $\dot{M}$ from E1 to E2 is
driven entirely by the decrease in fMedium. No other accretion column
contributes more than 16% of the accretion in any visit. Combined,
$\dot{m}_{\mathrm{Low}}$, $\dot{m}_{\mathrm{High}}$, and
$\dot{m}_{\mathrm{Very\ High}}$ contribute just 4.6% of the mass accretion on
average.

####  4.1.3 Modeling Results for BP Tau

BP Tau is a moderate accretor, with accretion rates between
0.9–3.2$\times$10-8 M⊙ yr-1 in E1 and 0.9–1.7$\times$10-8 M⊙ yr-1 in E2, and
median accretion rates of 1.3 and 1.4$\times$10-8 M⊙ yr-1, respectively.
Overall, the accretion rate varies by a factor of 3.6 (0.55 dex) peak-to-peak.

The medium density column typically dominates the accretion in BP Tau,
covering 1–2% of the stellar surface and accounting for 40–60% of the mass
accretion. That said, each column, in at least one visit each, contributes
$>$50% to $\dot{M}$ in that visit, suggesting that all columns are important.
This is reinforced by the fact that the $r$ correlation coefficient does not
exceed 0.4 for the lower/higher columns in either E1 or E2, showing that no
one column consistently dominates the total accretion rate.

From E1 to E2, the accretion appears to become cooler/less dense. The low and
high density columns, on average, contribute more to the accretion while the
very high density column diminishes. This can be qualitatively observed in
Figures 11 and 12 in Appendix C, where the slope of the BP Tau spectra in E1
appears flatter than E2, implying a hotter/denser accretion flow in E1.

####  4.1.4 Modeling Results for GM Aur

GM Aur is dominated by low and medium density accretion columns which, save
for the accretion burst near MJD=59509 discussed in more detail below,
together fill up to 15% of the stellar surface and typically constitute 90% of
the total mass accretion. The high density accretion is largely insignificant,
generally contributing $<$1% to the total accretion, with visit 1.7 being the
only exception, when it jumps to 6.0%. While the very high density accretion
column only contributes $\sim$10% to $\dot{M}$ on average, it is highly
correlated with $\dot{M}$, with $r$ values of 0.56 and 0.93 in E1 and E2,
respectively. This is similar to TW Hya, where the bulk of the accretion comes
from lower density flows, but the variability is primarily driven by higher
density, hotter flows.

The accretion varies between 0.32–2.15$\times$10-8 M⊙ yr-1 in E1 (which
includes a burst) and 0.5–1.1$\times$10-8 M⊙ yr-1 in E2. The median accretion
rates are 0.58$\times$10-8 M⊙ yr-1 and 0.67$\times$10-8 M⊙ yr-1. Most of the
variability is driven by small bursts, with up to 4 seen in our $HST$
observations at MJD$\sim$59502, 59509, 59557, and 59912. With the exception of
the burst at MJD=59509, they persist across only one $HST$ visit (no more than
2 days) and increase $\dot{M}$ by about 0.5$\times$10-8 M⊙ yr-1 or a factor of
2.

$HST$ captured the beginning of the larger burst at MJD=59509 in at least 2
visits, but due to synchronization problems with the command flow went into
safe mode soon after and was unable to capture the end of the burst. The
accretion rate increased from a quiescent rate of $\sim$0.43–2.15$\times$10-8
M⊙ yr-1 within 4 days, a factor of 5.0 (0.70 dex) increase. This burst (and
the smaller ones discussed above) was driven by the very high density
accretion column, for which $\dot{m}_{\mathrm{Very\ High}}$ increased by about
a factor of 3.5 over that time.

###  4.2 UV Spectral Lines and Features

Table 3: UV Features

Line | $\ \ \ \ \ \ \lambda_{0}\ \ \ \ \ \ $ |  Approx.
---|---|---
| [Å] | Width [Å]
Mg ii∗ | 2798 | 20
Al iii] | 2670 | 10
C iii] | 1909 | 10
Si iii] | 1892 | 5
Si ii | 1808 | 10
O iii] | 1666 | 5
He ii | 1640 | 5
C iv∗† | 1548 | 8
C i† | 1463 | 2
Si iv† | 1403 | 4
Si iii† | 1399 | 2
H2 Bump | 1600 | 200

**footnotetext: We do not separate the doublet components of the Mg ii and C
iv lines. Central wavelengths noted here are the short wavelength component of
the doublet.

††footnotetext: These lines are blended with H2 lines (France et al., 2012).

UV line luminosities have previously been found to correlate with mass
accretion (Calvet et al., 2004; Yang et al., 2012; Ingleby et al., 2013;
Ardila et al., 2013; Robinson & Espaillat, 2019). Additionally, a broad region
near 1600 Å dubbed the “H2 bump,” (e.g., Herczeg et al., 2004; Bergin et al.,
2004) has also been linked with accretion (see Yang et al., 2012; Ingleby et
al., 2009, 2012; France et al., 2017; Thanathibodee et al., 2018; Espaillat et
al., 2019; France et al., 2023). Here we measure the luminosities of selected
UV lines, the FUV and NUV continua, and the H2 bump.

####  4.2.1 UV Line Luminosities

While these COS spectra are filled with many emission lines, we focus on 11 of
the brightest lines previously linked with accretion (see Table 3). Note that
many of these lines are blended and only approximate line centers are provided
in Table 3. Additionally, Mg ii is affected by wind absorption (Ardila et al.,
2002; Xu et al., 2021). To measure the line luminosities, we first subtract
the continuum from the dereddened spectra. Within $\sim$50 Å of the line
center, we mask outlying points above or below the median flux of the
spectrum, where the outlier threshold vary per line and per object. We then
fit a continuum to the remaining data using the specutils function
fit_generic_continuum and subtract this from the original spectrum. We then
integrate the flux of the continuum-subtracted spectrum within a narrow region
that varies by line. Finally, we convert these fluxes to luminosities.

Figure 3 shows our UV luminosities along with log-log linear relationships
with Lacc (Equation 5) derived here. We exclude non-detections (here defined
as SNR$<$2) in Figure 3 and in the associated linear fits. UV luminosities,
fit coefficients, and associated uncertainties are shown in Tables 6–9 and
Table 10.

$L_{acc}=\frac{GM_{*}\dot{M}}{R_{*}}(1-\frac{1}{R_{i}}),R_{i}=5R_{*}$ (5)

Looking at all objects together, only three lines exhibit moderate
correlations to Lacc: Mg ii ($r$=0.66), Al iii] ($r$=0.55), and Si iii]
($r$=0.61), though Si iii] is often only marginally detected, despite this
global correlation. The other lines show weak/no correlation and are often
skewed by either TW Hya and/or RU Lup. Lacc in TW Hya is comparable to BP Tau
and GM Aur, but in many cases it exhibits much brighter emission lines. Lacc
is much higher in RU Lup, but its lines are often significantly dimmer than
would be expected given its accretion rate (particularly He ii, C iv),
rendering those global correlations very weak.

Figure 3: Accretion luminosity vs luminosity for various UV lines/regions.
Red/orange circles, green/lime triangles, blue/cyan diamonds, and purple/pink
pluses are TW Hya, RU Lup, BP Tau, GM Aur, respectively. Open points are
visits without contemporaneous photometry. Colored, dashed lines are the
intra-object log-log linear fits for all observations of each target (see
Table 10). For all UV features besides the H2 Bump, we exclude data with
SNR$<$2\. For the H2 Bump, we only exclude data where the bump was not
visually detected, independent of SNR.

If instead we focus on the inter-object trends, many object-line pairs show
strong correlations that differ from the global trend or exist when a global
trend does not. TW Hya shows weak to moderate correlations in all lines except
He ii ($r$=0.85) and C iv ($r$=0.86), which are strongly correlated to Lacc.
In RU Lup, some lines (Al iii], Si iii], Si iv) show strong correlations to
Lacc, but others show no or even anti-correlation. He ii is actually
moderately anti-correlated with Lacc ($r$=$-$0.49) and is exceptionally dim
relative to other lines and targets. BP Tau in all cases shows weak
correlations between Lacc and LLine, though Mg ii is moderately correlated
($r$=0.59). The UV lines in GM Aur do not show any particularly strong
correlations with Lacc, with Mg ii, He ii and C iv showing the strongest
correlations at $r$=0.75, 0.67, and 0.81, respectively. The others are weakly
correlated or have large uncertainties due to so many visits being discarded
as non-detections (e.g., Al iii], C iii, Si iii], O iii]).

####  4.2.2 FUV and NUV Continuum Luminosities

For the FUV and NUV fluxes, we integrate the flux of the fitted, dereddened
continuum spectra between 1400–2100 and 2500–3200 Å, respectively. The FUV and
NUV luminosities and fit coefficients are listed in Tables 6–9 in the Appendix
and in Figure 3.

TW Hya shows a wide range of FUV luminosities, ranging between 0.005–0.040 L⋆
in both epochs, with a median of 0.014 L⋆ (0.003 L⊙). The NUV varies between
0.009–0.056 L⋆, with a median of 0.028 L⋆ (0.006 L⊙). RU Lup is generally
brighter than TW Hya, and varies between 0.008–0.026 L⋆ (median 0.020 L⋆,
0.015 L⊙) in the FUV and 0.052–0.238 L⋆ (median 0.169 L⋆, 0.124 L⊙) in the
NUV. BP Tau shows the least degree of continuum variability, varying between
0.002–0.011 L⋆ (median 0.004 L⋆, 0.003 L⊙) in the FUV and 0.007–0.016 L⋆
(median 0.010 L⋆, 0.008 L⊙) in the NUV. LFUV/LNUV is on average higher in E1
(0.52) than E2 (0.39), reinforcing the denser flow in E1 predicted by the
shock model. GM Aur is generally the dimmest amongst the four targets, ranging
between 0.0009–0.008 L⋆ (median 0.0014 L⋆, 0.002 L⊙) in the FUV and
0.003–0.010 L⋆ (median 0.005 L⋆, 0.006 L⊙) in the NUV.

The FUV/NUV luminosities also show stronger time variability than the
accretion rates, readily varying by a factor of 2 on day-long timescales. TW
Hya exhibits a factor of $\sim$5.1 increase in FUV flux within just 2 days,
from 7.3$\times$10-3 L⋆ in Visit 2.1 to 37.2$\times$10-3 L⋆ in Visit 2.2. The
FUV and NUV continua rise considerably in GM Aur during the burst near
MJD=59509, by a factor of 8.5 and 4.7, respectively, in about 4 days.

The FUV/NUV continuum luminosities show far stronger correlations with Lacc
than any of the lines, though some of the same trends persist. Globally, both
LFUV and LNUV are strongly correlated with Lacc, with $r$=0.85 and 0.96,
respectively. In the FUV, RU Lup again skews the fit, having either elevated
accretion rates or diminished FUV luminosities. In the NUV all 4 targets
exhibit similar slopes, though the y-intercept of the fitted line varies by
target. Individually, each target (with the exception of BP Tau) shows fairly
strong correlations with Lacc: r$\geq$0.88 in all cases. BP Tau is moderately
correlated (rFUV/NUV=0.55/0.66), but shows the same linear slope as the other
targets in the NUV.

####  4.2.3 H2 Bump Luminosities

For the H2 Bump near 1600 Å, we follow a similar method as France et al.
(2017) to extract the bump spectrum and calculate its luminosity. We first
hand-pick $\sim$110 points between 1400–1800 Å selected to avoid strong atomic
and molecular lines. The lines present in each target vary, and so we change
the selected points for each target. From these $\sim$110 points, we define a
binned spectrum whose flux and uncertainty are the mean and standard deviation
of the original spectrum within 0.75 Å of the selected points. This binned
spectrum is thus a pseudo-continuum, composed of the true, underlying
continuum plus the broad H2 Bump feature and so does not include bright
emission lines.

From this binned spectrum, we fit a continuum using a second-order polynomial
using the points away from the H2 Bump, between 1405–1490 Å and 1690–1800 Å.
Next we subtract this continuum from the binned spectrum. Finally, we
integrate this continuum-subtracted binned spectrum between 1490–1690 Å to
calculate the H2 Bump flux and convert to luminosity. The H2 Bump luminosities
are shown in Tables 6–9 and Figure 3 along with fit coefficients given in the
Appendix. For these correlations, we exclude data where the bump was not
visually distinct from the underlying continuum, regardless of the calculated
flux or SNR.

Note that while the measured uncertainties on the H2 Bump luminosities are low
(typically $<$5%), the true uncertainties are likely higher. The determination
of the continuum in each spectrum not only depends heavily on the number and
location of the chosen binned continuum points, but can also be affected by
any spurious emission lines. For this reason, we apply an additional 10%
uncertainty added in quadrature to the measured uncertainty for TW Hya, BP
Tau, and GM Aur. RU Lup exhibits uniquely strong, wide, and numerous
emission/absorption features, making its continuum particularly uncertain, so
we apply a 20% uncertainty.

The H2 Bump shows similar trends as the other lines. TW Hya is the only target
that shows a moderately positive correlation ($r$=0.54). Here, it is not an
outlier and shows very similar bump luminosities as BP Tau and GM Aur. RU Lup
shows a very weakly negative correlation and possesses much lower bump
luminosities than the other targets with comparatively high Lacc, though in
most cases the bump is not detected. Even ignoring Visit 1.7, with a
particularly low bump luminosity, there is still only a weakly positive
correlation in RU Lup. BP Tau shows a wide range of bump luminosities ($\sim$1
dex) with no correlation to Lacc, similar to many of the emission lines. The
H2 Bump in GM Aur shows a very weakly positive correlation with Lacc, with far
more spread in Lacc than L${}_{H2\ Bump}$. Globally, we see a weakly negative
correlation between Lacc and L${}_{H2\ Bump}$.

##  5 Discussion

Our shock model fitting finds diversity in accretion column structures between
objects, but these structures remain roughly consistent for individual objects
over the course of at least a year (i.e., the longest timescale probed in this
work) while the accretion rate changes on short timescales of about a day. In
TW Hya, the shock model predicts a large hotspot dominated by the low-density
accretion column while in RU Lup the accretion is dominated by the medium
density accretion column. GM Aur is primarily dominated by the low and medium
density columns, while BP Tau is marginally dominated by the medium density
column but sees strong contributions from the other columns at various times.
Besides the fraction of the star covered by each column, there are no
significant changes in these structures during the course of the $HST$
observations, even when the accretion rate itself changes. Despite this
relative stability in the accretion structure, there is variability in the
accretion rate up to a factor of four within two days. This is consistent with
previous reports that accretion is variable on all timescales probed (Costigan
et al., 2014; Hartmann et al., 2016; Zsidi et al., 2022; Herczeg et al.,
2023). Specifically, Venuti et al. (2014) find that accretion variability is
typically about 0.5 dex on timescales of days-weeks and our results are
consistent with this. Our accretion rates are also within the scatter seen in
accretion rate in larger samples (e.g., Manara et al., 2021). We see an
average total surface coverage of about 15%, in line with magnetospheric
accretion models that suggest total filling factors of about 20% (Zhu et al.,
2023b).

TW Hya and GM Aur have been studied by other researchers with datasets
overlapping the timing of the $HST$ observations presented here, allowing us
to directly compare our results. Herczeg et al. (2023) find that in over 25
yrs of TW Hya optical spectroscopic data, with some that overlap the times of
our dataset, that the average accretion rate is 0.25$\times$10-8 M⊙ yr-1,
which flickers over timescales of hours but is roughly stable over 25 yrs and
varies between 0.05 to 0.9$\times$10-8 M⊙ yr-1. Our results are consistent and
we find that the average accretion rate of TW Hya is about 0.3$\times$10-8 M⊙
yr-1 with a range of $\sim$0.1–0.5$\times$10-8 M⊙ yr-1. GM Aur was observed by
Bouvier et al. (2023) who performed an optical and NIR spectrophotometric
monitoring campaign overlapping some of the $HST$ observations, probing
timescales of days to months over a period of six months and covering 30
rotation periods. Bouvier et al. (2023) find evidence of rotational modulation
of accretion and a stable accretion funnel flow and accretion shock. Our
results are consistent with this study.

Some UV lines, such as the C iv line, have been seen to correlate with
accretion rate in larger samples (e.g., Calvet et al., 2004; Yang et al.,
2012; Ardila et al., 2013; Ingleby et al., 2013; Robinson & Espaillat, 2019),
but here we caution against using these lines alone to characterize the
accretion rate. Like RE19 and Calvet et al. (2004), we do generally find a
moderate, positive correlation between accretion rate and UV line
luminosities. That said, certain targets (i.e., TW Hya, RU Lup) often deviate
from these patterns. For some lines, the relationship between Lline and Lacc
in TW Hya is consistent with the other targets, but in others it is completely
removed from the other targets and the relationship described in RE19, and is
self-consistent between E1 and E2. In these cases, either the accretion rates
are lower than would be expected or the UV luminosity is higher than expected.
As for RU Lup, in only some cases (Mg ii, Al iii], Si iii], Si iv) does it
trend with other targets and previous studies. Even then, RU Lup exhibits a
much steeper relationship than either BP Tau, GM Aur, or the empirical
relationships of Calvet et al. (2004), Yang et al. (2012), or RE19. The bright
He ii line is interesting as it shows moderate anti-correlation and is rather
dim when considering that RU Lup is comparatively bright in most lines and in
Lacc. TW Hya and RU Lup are outliers and this may be linked to their viewing
geometry, which are both seen closer to face-on (Table 1). Ultimately, while
moderate correlations between Lacc and LUV are generally found, we emphasize
not only that there is considerable scatter in these relationships, but that
the variability trends in individual targets often differ from the global
trend. They should not be used to estimate accretion rates, at least on their
own.

In the majority of cases, the correlation between observed flux (line or
continuum) and accretion rate is positive. As more energy is available from a
larger accretion rate, more power is radiated in the continuum and the line.
If the structure of the accretion shock does not change with accretion rate,
one might expect that the observed flux and accretion rate are directly
proportional. However, in RU Lup, some line fluxes are observed to be anti-
correlated with the accretion rate. Detailed multi-dimensional modeling with
radiative transfer is beyond the scope of this work, but here we speculate on
how this fits into our knowledge of accretion shock emission. Decreasing
fluxes with increasing accretion luminosity are clearly seen in He ii and Si
iii and less clearly in the H2 Bump and C iii]. Thus, the conditions present
in the medium density accretion column (temperature, density, physical size,
etc.) may promote a high optical depth for these lines. When the accretion
rate increases in RU Lup, so does the size of the medium density column, which
may in turn increase the optical depth in these moderate temperature lines,
resulting in the negative relationships we see. Other lines, formed at lower
(C i, Mg ii) and higher (C iv) temperatures than the Si iii and He ii lines
would form in physically distinct locations and different conditions and may
not be subject to same optical depth effects as Si iii and He ii.

We also compare our results on the H2 Bump to those in the literature. The H2
Bump has been suggested to be driven by collisional excitation of H2 via X-ray
photons (Bergin et al., 2004), Ly$\alpha$ dissociation of H2O in the inner
disk (France et al., 2017), linked to the surface density of the inner disk
(Espaillat et al., 2019), or due to the H i 2-photon continuum (Bottorff et
al., 2006). Espaillat et al. (2019) found that there was no correlation
between L${}_{H2\ Bump}$ and contemporaneous X-ray data and France et al.
(2017) show that the H2 Bump spectrum itself is inconsistent with electron-
impact excitation, ruling out the first scenario. For the latter two
scenarios, there is an expected correlation between the H2 Bump luminosity and
Lacc, since accretion should produce Ly$\alpha$ photons (e.g., Alencar et al.,
2012). France et al. (2023) find strong correlations between the H2 Bump and
both Ly$\alpha$ and _WISE_ W3-W4 colors, which they suggest reinforces that
the H2 Bump originates in the inner disk, where Ly$\alpha$ photons can reach
and dissociate the H2O content of the inner disk. Espaillat et al. (2019)
suggest that the H2 Bump is driven by changes in the surface density in the
inner disk that propagate through the accretion column and lead to a change in
the accretion rate. They find a strong correlation ($r$=0.7) in a sample of 7
CTTSs (27 observations). Looking at all four targets in our sample together
(89 observations), we do not recover a strong (or even positive) correlation
($r$=-0.42) between the H2 Bump and Lacc. Individually, the only target that
shows even moderate correlation is TW Hya ($r$=0.54). The other 3 targets show
very weak correlations ($r\leq 0.31$). Therefore, we do not find strong
evidence supporting that the H2 Bump is due to Ly$\alpha$ dissociation of H2O
or surface density changes.

Lastly, the FUV luminosity can change by a factor of 2–5 on day timescales and
correlates well with accretion rate. While BP Tau shows comparatively little
variability, the other 3 targets exhibit strong FUV/NUV continuum variability,
about a factor of 10 peak-to-peak. The median FUV luminosity in our sample is
2.0$\times 10^{31}$ erg s-1, which is what is usually used in FUV
photoevaporation models (e.g., Gorti et al., 2009; Pascucci et al., 2023). FUV
radiation has also been shown to affect disk chemistry near planet-forming
radii (Bergin et al., 2004; Yang et al., 2012; Ádámkovics et al., 2016). The
FUV variability seen here implies that accretion-driven FUV radiation fields
can reach levels 10$\times$ those assumed in Bergin et al. (2004), showing
that accretion variability can drive disk chemistry dynamics.

##  6 Summary

We studied a multi-epoch $HST$ UV spectral monitoring campaign of four CTTSs:
TW Hya, RU Lup, BP Tau, and GM Aur. We use a magnetospheric accretion shock
model to estimate the accretion rates and accretion column filling factors for
roughly 24 observations of each target. From those same spectra we measure
luminosities of various UV lines, the 1600 Å H2 Bump, and the FUV/NUV
continuum. Our main findings are as follows:

  1. 1.

Our accretion shock modeling reveals an array of accretion structures in our
four targets. Accretion in TW Hya is primarily driven by the low density
column, but some visits see strong contribution from other columns. RU Lup is
dominated by medium density accretion columns, with little accretion coming
from other columns. BP Tau sees roughly equal contribution from all four
columns, with a preference for the low and medium density columns. GM Aur is
dominated by the low and medium density columns, with some contribution from
the very high density column when the accretion rate increases.

  2. 2.

All four targets show accretion variability of at least a factor of 3 (0.48
dex) during our monitoring. TW Hya and GM Aur exhibit variability in their
accretion rate of a factor of 3 or greater within two days. RU Lup, on the
other hand, shows a sustained decrease of a factor of 2.2 between 2021 and
2022, showing that CTTSs can undergo a sustained decrease in accretion rate on
timescales of over one year. BP Tau exhibited the least accretion variability
in our sample, varying by about a factor of 3.6 peak-to-peak across all
observations.

  3. 3.

UV line luminosities are generally only moderately correlated with accretion
rate, but TW Hya, RU Lup, and BP Tau often show scatter both with respect to
other targets in the sample and within a single object. In TW Hya, the UV line
luminosities are higher than expected given its low accretion rate. RU Lup is
very inconsistent, showing no, strongly positive, and weakly negative
correlations with accretion. We suggest this is due to its strong accretion-
driven outflow and/or near face-on inclination. BP Tau generally shows little
correlation to UV line luminosities; the accretion rate tends to vary
significantly less than the line luminosities.

  4. 4.

FUV and NUV continuum luminosities show strong correlations to accretion rate.
TW Hya is again an outlier, with low accretion rates and high UV luminosities.
Together, RU Lup, BP Tau, and GM Aur trend closely with one another. In
general, the FUV/NUV continua are even more variable than the overall
accretion rate, with both varying by factors of 2–5 within 1–2 days in all
four targets.

  5. 5.

We find generally comparable FUV luminosities to those used in previous works
to estimate the effect of FUV radiation on disk dynamics, but note that
accretion induced variability can exceed this by a factor of $\sim$10 in some
cases.

  6. 6.

With the exception of TW Hya, we do not find strong correlations between
accretion luminosity and the 1600 Å H2 Bump.

Our study further demonstrates that accretion in CTTSs is highly variable and
reinforces the importance of simultaneity in future multi-instrument/multi-
wavelength observations of CTTSs. Additionally, we show that each star in our
sample exhibits unique relationships between accretion rate and other UV
accretion tracers. These empirical relationships should not be utilized when
studying an individual CTTSs and should be used cautiously for small samples.

This work is supported by $HST$ AR-16129 from the Space Telescope Science
Institute, which is operated by AURA, Inc. This material is based upon work
supported by the National Science Foundation under Grant Number AST-2108446.
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. This work is supported by the ANID FONDECYT
Postdoctoral program No. 3220029. We acknowledge support by ANID, – Millennium
Science Initiative Program – NCN19_171. This work has been supported by the
project PRIN‐INAF 2019 “Spectroscopically Tracing the Disk Dispersal Evolution
(STRADE)” and by the INAF Large Grant 2022 “YSOs Outflow, Disks and Accretion
(YODA)”. This work was also supported by the NKFIH excellence grant
TKP2021-NKTA-64. IM is funded by grant PID2022-138366NA-I00, by the Spanish
Ministry of Science and Innovation/State Agency of Research
MCIN/AEI/10.13039/501100011033 and the European Union, and by a Ramón y Cajal
fellowship RyC2019-026992-I. We thank Jerome Bouvier for his suggestions that
improved this manuscript. We thank the ULLYSES team at STScI for planning and
implementing the $HST$ observations and creating data products, with guidance
from the research community.

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##  Appendix A Shock Modeling of RU Lup

As discussed in Section 4.1, our choice of template for RU Lup is complicated
by our lack of contemporaneous veiling estimates. The photospheric template we
employ in our modeling (F${}_{\rm{Phot,\ RU\ Lup}}$) is obtained by scaling
the raw WTTS spectrum to the radius and distance of RU Lup. While this can
introduce additional uncertainty from the stellar radii and distances, we
believe this is a reasonable estimate and is within upper and lower limits for
the true photosphere.

As a lower limit on the photospheric contribution (F${}_{\rm{Phot,\ Low}}$),
we can assume that all observed emission originates from accretion by imposing
F${}_{\rm{Phot,\ Low}}=0$. As an upper limit on the photospheric contribution
(F${}_{\rm{Phot,\ High}}$), we scale the raw WTTS template to the dimmest
observation of our $V$ light curve of RU Lup (see Paper II). This assumes that
all emission at $V$ originates from the photosphere, implying no contribution
from accretion at $V$. RU Lup is likely accreting at all times, even if only
very weakly, meaning the photospheric contribution to the observed spectrum is
likely smaller.

Figure 4: Top: Comparison between F${}_{\rm{Phot,\ High}}$ (red) and
F${}_{\rm{Phot,\ RU\ Lup}}$ (black). Recall that F${}_{\rm{Phot,\ Low}}$ is
zero, i.e., the photosphere does not contribute to the observed spectrum.
F${}_{\rm{Phot,\ RU\ Lup}}$ lays between F${}_{\rm{Phot,\ High}}$ and
F${}_{\rm{Phot,\ Low}}$. Bottom: Accretion rates for RU Lup when using
F${}_{\rm{Phot,\ High}}$ (red triangles), F${}_{\rm{Phot,\ RU\ Lup}}$ (black
squares), and F${}_{\rm{Phot,\ Low}}$ (blue circles) as photospheric
templates.

Figure 4 shows the comparison between F${}_{\rm{Phot,\ High}}$ and
F${}_{\rm{Phot,\ RU\ Lup}}$, along with accretion rates derived using each
template. In all cases, the accretion rates obtained using F${}_{\rm{Phot,\
RU\ Lup}}$ fall between those derived from the F${}_{\rm{Phot,\ High}}$ and
F${}_{\rm{Phot,\ Low}}$.

##  Appendix B Effect of No Contemporaneous Photometry on Shock Model Fits

10 of the 89 $HST$ visits do not have contemporaneous $BgV$ photometry. The
optical portion of the shock model fit is therefore less constrained and here
we discuss what effect that may have on the results for those visits. To gauge
this effect, we re-run our shock models for all visits but remove the
photometry, effectively fitting only the UV COS spectrum from $\sim$1800–3200
Å. A comparison between some of the resulting accretion parameters (accretion
rate and filling factors) for visits that have contemporaneous photometry is
shown in Figure 5.

Figure 5: Comparison of accretion shock model results when removing optical
photometry points from fitting. Left to right: $\dot{M}$, fLow, fMedium,
fHigh, and f${}_{Very\ High}$. Red circles, green triangles, blue diamonds,
and purple pluses are TW Hya, RU Lup, BP Tau, and GM Aur, respectively. Mean
Absolute Percent Error (MAPE) values between the parameters with and without
photometry are listed above each panel.

In general, when no optical photometry is present, the filling factors are
accurate to no better than about 50%. Fits without photometry show larger
filling factors for the low density column, with a Mean Absolute Percent Error
(MAPE) of 4584%. Much of this strong deviation comes from visits that are
normally fit with particularly low fLow (near 0%), but jump to the upper limit
of fLow=40% when the photometry is removed. In turn, this higher fLow results
in generally lower fMedium (MAPE=130%). The high and very high density columns
are generally consistent to within 47% and 263%, though for the very high
density column the strongest deviations occur when f${}_{Very\ High}$ is very
low and contributes little to the total mass accretion.

While the filling factors are largely inaccurate, the overall mass accretion
rate is typically consistent to within about 26%, generally being
overestimated due to the unconstrained fLow. These results suggest that while
some optical data is very important to constrain the filling factors, the
total accretion rate is fairly well constrained. Thus, for visits with no
contemporaneous optical photometry (which are noted in Tables 4-5), the
accretion rates are likely overestimated by up to about 30%. The associated
filling factors are likely inaccurate, with little consistency as to how
over/underestimated they are. Figure 6 shows that the correlations between
Lacc and LLine are largely consistent whether or not visits without
contemporaneous photometry are included.

Figure 6: Comparison of Lacc/L⋆ vs LLine/L⋆ correlation coefficients. Filled
circles are for all visits, regardless of whether they have contemporaneous
optical photometry (what is shown in Figure 3). Open diamonds are for only
visits with contemporaneous photometry.

##  Appendix C Shock Model Results

Tables 4 and 5 show the mass accretion rates and filling factors of the four
accretion columns obtained from our shock model fitting of TW Hya, RU Lup, BP
Tau, and GM Aur. Figures 7–14 show the shock model fits for each $HST$ visit.

For TW Hya, BP Tau, and GM Aur, the upper/lower uncertainties are the average
differences between the 84th/16th and 50th percentiles in the resulting
posterior distributions, except where the standard deviation of results from
all F${}_{Phot,\ True}$ is larger. For RU Lup, we only cite the difference
between the 84th/16th and 50th percentiles in the resulting posterior
distributions, as only one F${}_{Phot,\ True}$ was used. These uncertainties
thus underestimate the true uncertainty in the model parameters given the
uncertainty in the true, underlying F${}_{Phot,\ True}$. Additionally, the
uncertainties for all four targets only describe the widths of the posterior
distributions of each parameter. They do not properly account for non-
systematic uncertainties, such as R∗, M∗, and AV. RE19 note that the true
uncertainties are likely to be at least 10% when accounting for other sources
of error.

Table 4: Shock model results for TW Hya and RU Lup.

Object | Visit | Date | $\dot{M}$ | $f_{Low}$ | $f_{Medium}$ | $f_{High}$ | $f_{Very\ High}$
---|---|---|---|---|---|---|---
|  | [MJD] | [10-8 M⊙ yr-1 ] | [%] | [%] | [%] | [%]
TW Hya | 1.1 | 59302.69 | 0.078${}^{+0.012}_{-0.007}$ | 0.3${}^{+1.7}_{-0.2}$ | 0.9${}^{+0.05}_{-0.08}$ | 0.029${}^{+0.002}_{-0.006}$ | 0.0002${}^{+0.0011}_{-0.0002}$
TW Hya | 1.2 | 59303.68 | 0.25${}^{+0.04}_{-0.05}$ | 27.6${}^{+3.4}_{-4.1}$ | 0.4${}^{+0.4}_{-0.4}$ | 0.05${}^{+0.04}_{-0.04}$ | 0.007${}^{+0.008}_{-0.007}$
TW Hya | 1.3 | 59304.41 | 0.368${}^{+0.009}_{-0.011}$ | 39.5${}^{+0.4}_{-1.0}$ | 0.14${}^{+0.11}_{-0.08}$ | 0.165${}^{+0.004}_{-0.01}$ | 0.0002${}^{+0.002}_{-0.0002}$
TW Hya | 1.4 | 59305.47 | 0.24${}^{+0.03}_{-0.02}$ | 0.8${}^{+4.6}_{-0.7}$ | 1.9${}^{+0.2}_{-0.2}$ | 0.175${}^{+0.006}_{-0.023}$ | 0.0004${}^{+0.0046}_{-0.0004}$
TW Hya | 1.5 | 59306.53 | 0.12${}^{+0.01}_{-0.01}$ | 0.2${}^{+1.2}_{-0.2}$ | 1.27${}^{+0.08}_{-0.08}$ | 0.061${}^{+0.003}_{-0.015}$ | 0.0003${}^{+0.003}_{-0.0003}$
TW Hya | 1.6 | 59307.19 | 0.39${}^{+0.03}_{-0.04}$ | 28.4${}^{+4.1}_{-4.9}$ | 0.7${}^{+0.3}_{-0.3}$ | 0.253${}^{+0.006}_{-0.008}$ | 0.0001${}^{+0.0013}_{-0.0001}$
TW Hya | 1.7 | 59308.31 | 0.22${}^{+0.02}_{-0.02}$ | 21.1${}^{+3.1}_{-3.5}$ | 0.4${}^{+0.2}_{-0.2}$ | 0.095${}^{+0.003}_{-0.005}$ | 0.0001${}^{+0.0009}_{-0.0001}$
TW Hya | 1.8 | 59309.17 | 0.49${}^{+0.02}_{-0.02}$ | 39.4${}^{+0.4}_{-1.1}$ | 1.1${}^{+0.2}_{-0.1}$ | 0.262${}^{+0.007}_{-0.028}$ | 0.0005${}^{+0.0057}_{-0.0005}$
TW Hya | 1.9 | 59310.56 | 0.18${}^{+0.02}_{-0.02}$ | 16.7${}^{+2.4}_{-2.5}$ | 0.6${}^{+0.1}_{-0.1}$ | 0.06${}^{+0.003}_{-0.005}$ | 0.0001${}^{+0.001}_{-0.0001}$
TW Hya | 1.10 | 59311.56 | 0.1${}^{+0.02}_{-0.02}$ | 0.2${}^{+1.1}_{-0.2}$ | 1.2${}^{+0.1}_{-0.1}$ | 0.02${}^{+0.02}_{-0.02}$ | 0.003${}^{+0.004}_{-0.003}$
TW Hya | 1.11 | 59312.55 | 0.08${}^{+0.02}_{-0.02}$ | 5.8${}^{+2.0}_{-2.0}$ | 0.3${}^{+0.1}_{-0.1}$ | 0.039${}^{+0.003}_{-0.013}$ | 0.0004${}^{+0.0025}_{-0.0003}$
TW Hya | 2.1 | 59668.49 | 0.12${}^{+0.02}_{-0.02}$ | 5.5${}^{+2.3}_{-2.9}$ | 0.7${}^{+0.2}_{-0.1}$ | 0.056${}^{+0.002}_{-0.004}$ | 0.0001${}^{+0.0007}_{-0.0001}$
TW Hya | 2.2 | 59670.61 | 0.487${}^{+0.008}_{-0.007}$ | 39.8${}^{+0.2}_{-0.5}$ | 0.74${}^{+0.06}_{-0.07}$ | 0.001${}^{+0.009}_{-0.001}$ | 0.096${}^{+0.001}_{-0.002}$
TW Hya | 2.3 | 59671.47 | 0.2${}^{+0.02}_{-0.02}$ | 18.1${}^{+2.7}_{-3.0}$ | 0.4${}^{+0.2}_{-0.1}$ | 0.092${}^{+0.003}_{-0.004}$ | 0.0001${}^{+0.0005}_{-0.0001}$
TW Hya | 2.4 | 59673.58 | 0.35${}^{+0.03}_{-0.04}$ | 29.3${}^{+4.5}_{-5.0}$ | 0.6${}^{+0.3}_{-0.3}$ | 0.183${}^{+0.005}_{-0.007}$ | 0.0001${}^{+0.001}_{-0.0001}$
TW Hya | 2.5 | 59674.44 | 0.35${}^{+0.02}_{-0.02}$ | 35.1${}^{+2.2}_{-1.7}$ | 0.007${}^{+0.031}_{-0.005}$ | 0.19${}^{+0.01}_{-0.02}$ | 0.003${}^{+0.005}_{-0.002}$
TW Hya | 2.6 | 59675.77 | 0.46${}^{+0.04}_{-0.06}$ | 27.7${}^{+4.8}_{-7.7}$ | 0.3${}^{+0.5}_{-0.3}$ | 0.404${}^{+0.008}_{-0.012}$ | 0.0002${}^{+0.0013}_{-0.0001}$
TW Hya | 2.7 | 59676.49 | 0.39${}^{+0.01}_{-0.01}$ | 37.8${}^{+1.3}_{-1.5}$ | 0.009${}^{+0.047}_{-0.007}$ | 0.233${}^{+0.006}_{-0.014}$ | 0.001${}^{+0.0032}_{-0.0009}$
TW Hya | 2.8 | 59677.55 | 0.51${}^{+0.02}_{-0.02}$ | 39.2${}^{+0.6}_{-1.2}$ | 0.02${}^{+0.13}_{-0.02}$ | 0.19${}^{+0.01}_{-0.02}$ | 0.068${}^{+0.005}_{-0.004}$
TW Hya | 2.9 | 59678.35 | 0.239${}^{+0.009}_{-0.009}$ | 24.4${}^{+1.1}_{-1.2}$ | 0.008${}^{+0.042}_{-0.006}$ | 0.127${}^{+0.003}_{-0.008}$ | 0.0002${}^{+0.0017}_{-0.0002}$
TW Hya | 2.10 | 59695.41 | 0.444${}^{+0.005}_{-0.006}$ | 39.5${}^{+0.4}_{-0.9}$ | 0.008${}^{+0.032}_{-0.006}$ | 0.0007${}^{+0.003}_{-0.0005}$ | 0.099${}^{+0.001}_{-0.001}$
RU Lup | 1.1 | 59436.88 | 13.1${}^{+0.3}_{-0.3}$ | 0.1${}^{+0.6}_{-0.1}$ | 20.5${}^{+0.4}_{-0.4}$ | 0.14${}^{+0.02}_{-0.02}$ | 0.0002${}^{+0.003}_{-0.0002}$
RU Lup | 1.2 | 59438.80 | 12.7${}^{+0.7}_{-0.9}$ | 20.9${}^{+7.9}_{-10.7}$ | 18.2${}^{+0.7}_{-0.6}$ | 0.09${}^{+0.04}_{-0.08}$ | 0.007${}^{+0.016}_{-0.007}$
RU Lup | 1.3 | 59439.46a | 12.6${}^{+1.2}_{-0.6}$ | 3.5${}^{+18.8}_{-3.4}$ | 20.1${}^{+0.6}_{-0.7}$ | 0.07${}^{+0.03}_{-0.07}$ | 0.002${}^{+0.015}_{-0.002}$
RU Lup | 1.4 | 59440.38a | 11.8${}^{+1.4}_{-0.6}$ | 4.5${}^{+21.7}_{-4.4}$ | 18.6${}^{+0.5}_{-0.7}$ | 0.06${}^{+0.03}_{-0.06}$ | 0.001${}^{+0.012}_{-0.001}$
RU Lup | 1.5 | 59441.38a | 14.6${}^{+0.9}_{-0.6}$ | 1.1${}^{+13.6}_{-1.1}$ | 23.6${}^{+0.6}_{-0.7}$ | 0.06${}^{+0.04}_{-0.06}$ | 0.004${}^{+0.012}_{-0.004}$
RU Lup | 1.6 | 59442.43 | 13.3${}^{+0.3}_{-0.3}$ | 0.11${}^{+0.7}_{-0.09}$ | 21.0${}^{+0.4}_{-0.4}$ | 0.13${}^{+0.02}_{-0.02}$ | 0.0002${}^{+0.0023}_{-0.0002}$
RU Lup | 1.7 | 59443.43 | 12.9${}^{+0.5}_{-0.3}$ | 0.5${}^{+6.0}_{-0.4}$ | 21.3${}^{+0.4}_{-0.4}$ | 0.03${}^{+0.02}_{-0.03}$ | 0.002${}^{+0.006}_{-0.002}$
RU Lup | 1.8 | 59444.29 | 15.0${}^{+0.3}_{-0.3}$ | 0.1${}^{+1.1}_{-0.1}$ | 23.5${}^{+0.5}_{-0.5}$ | 0.16${}^{+0.02}_{-0.02}$ | 0.0002${}^{+0.0028}_{-0.0002}$
RU Lup | 1.9 | 59446.27 | 17.0${}^{+0.4}_{-0.6}$ | 19.8${}^{+3.0}_{-7.7}$ | 26.4${}^{+0.5}_{-0.5}$ | 0.008${}^{+0.026}_{-0.007}$ | 0.002${}^{+0.005}_{-0.001}$
RU Lup | 1.10 | 59447.26a | 16.0${}^{+1.1}_{-0.7}$ | 4.4${}^{+16.6}_{-4.3}$ | 25.6${}^{+0.7}_{-0.9}$ | 0.06${}^{+0.04}_{-0.06}$ | 0.004${}^{+0.013}_{-0.004}$
RU Lup | 2.1 | 59801.26 | 12.0${}^{+0.5}_{-0.5}$ | 32.0${}^{+1.6}_{-3.2}$ | 16.1${}^{+0.4}_{-0.5}$ | 0.03${}^{+0.07}_{-0.03}$ | 0.013${}^{+0.007}_{-0.013}$
RU Lup | 2.2 | 59804.04 | 6.4${}^{+0.1}_{-0.1}$ | 0.09${}^{+0.44}_{-0.07}$ | 10.2${}^{+0.2}_{-0.2}$ | 0.049${}^{+0.008}_{-0.012}$ | 0.0002${}^{+0.0019}_{-0.0002}$
RU Lup | 2.3 | 59805.10 | 8.5${}^{+0.2}_{-0.2}$ | 0.09${}^{+0.59}_{-0.07}$ | 13.3${}^{+0.2}_{-0.3}$ | 0.09${}^{+0.01}_{-0.01}$ | 0.0002${}^{+0.0014}_{-0.0001}$
RU Lup | 2.4 | 59805.90 | 5.7${}^{+0.1}_{-0.1}$ | 0.11${}^{+0.82}_{-0.09}$ | 8.9${}^{+0.2}_{-0.2}$ | 0.066${}^{+0.009}_{-0.009}$ | 0.0002${}^{+0.0013}_{-0.0001}$
RU Lup | 2.5 | 59806.69 | 3.6${}^{+0.2}_{-0.1}$ | 0.3${}^{+2.9}_{-0.3}$ | 5.9${}^{+0.2}_{-0.2}$ | 0.014${}^{+0.009}_{-0.012}$ | 0.0004${}^{+0.0022}_{-0.0004}$
RU Lup | 2.6 | 59807.62 | 3.5${}^{+0.2}_{-0.2}$ | 0.2${}^{+1.4}_{-0.2}$ | 5.6${}^{+0.2}_{-0.2}$ | 0.025${}^{+0.009}_{-0.018}$ | 0.0003${}^{+0.0032}_{-0.0003}$
RU Lup | 2.7 | 59808.55 | 4.8${}^{+0.1}_{-0.1}$ | 0.1${}^{+0.6}_{-0.08}$ | 7.3${}^{+0.2}_{-0.2}$ | 0.069${}^{+0.009}_{-0.009}$ | 0.0001${}^{+0.0011}_{-0.0001}$
RU Lup | 2.8 | 59809.54 | 4.8${}^{+0.1}_{-0.1}$ | 0.1${}^{+0.57}_{-0.08}$ | 7.3${}^{+0.2}_{-0.2}$ | 0.064${}^{+0.007}_{-0.008}$ | 0.0001${}^{+0.001}_{-0.0001}$
RU Lup | 2.9 | 59810.40 | 4.3${}^{+0.1}_{-0.1}$ | 0.06${}^{+0.25}_{-0.04}$ | 6.9${}^{+0.1}_{-0.1}$ | 0.026${}^{+0.006}_{-0.007}$ | 0.0002${}^{+0.0012}_{-0.0001}$
RU Lup | 2.10 | 59811.39 | 8.7${}^{+0.2}_{-0.2}$ | 0.06${}^{+0.3}_{-0.05}$ | 14.0${}^{+0.2}_{-0.3}$ | 0.06${}^{+0.01}_{-0.01}$ | 0.0002${}^{+0.0011}_{-0.0001}$
RU Lup | 2.11 | 59814.43a | 11.4${}^{+1.1}_{-0.6}$ | 1.6${}^{+16.3}_{-1.6}$ | 18.0${}^{+0.6}_{-0.6}$ | 0.09${}^{+0.03}_{-0.09}$ | 0.002${}^{+0.017}_{-0.002}$
RU Lup | 2.12 | 59815.43a | 12.2${}^{+1.2}_{-0.6}$ | 1.8${}^{+19.0}_{-1.8}$ | 19.4${}^{+0.6}_{-0.7}$ | 0.09${}^{+0.03}_{-0.08}$ | 0.001${}^{+0.016}_{-0.001}$

aafootnotetext: No contemporaneous photometry

Table 5: Shock model results for BP Tau and GM Aur.

Object | Visit | Date | $\dot{M}$ | $f_{Low}$ | $f_{Medium}$ | $f_{High}$ | $f_{Very\ High}$
---|---|---|---|---|---|---|---
|  | [MJD] | [10-8 M⊙ yr-1 ] | [%] | [%] | [%] | [%]
BP Tau | 1.1 | 59446.84 | 1.86${}^{+0.09}_{-0.08}$ | 1.5${}^{+1.5}_{-1.1}$ | 1.55${}^{+0.08}_{-0.1}$ | 0.0009${}^{+0.0043}_{-0.0007}$ | 0.066${}^{+0.001}_{-0.001}$
BP Tau | 1.2 | 59448.82a | 2.1${}^{+0.2}_{-0.2}$ | 27.8${}^{+3.3}_{-3.2}$ | 0.9${}^{+0.1}_{-0.1}$ | 0.001${}^{+0.006}_{-0.001}$ | 0.0153${}^{+0.0006}_{-0.0011}$
BP Tau | 1.3 | 59450.81a | 3.1${}^{+0.1}_{-0.2}$ | 37.8${}^{+1.6}_{-3.2}$ | 0.88${}^{+0.12}_{-0.09}$ | 0.0011${}^{+0.0062}_{-0.0008}$ | 0.054${}^{+0.001}_{-0.001}$
BP Tau | 1.4 | 59452.93 | 1.19${}^{+0.09}_{-0.07}$ | 1.1${}^{+1.6}_{-1.0}$ | 1.16${}^{+0.07}_{-0.08}$ | 0.0008${}^{+0.0038}_{-0.0006}$ | 0.0365${}^{+0.0009}_{-0.001}$
BP Tau | 1.5 | 59454.85a | 2.7${}^{+0.2}_{-0.2}$ | 33.8${}^{+3.9}_{-4.4}$ | 0.9${}^{+0.2}_{-0.2}$ | 0.001${}^{+0.01}_{-0.001}$ | 0.034${}^{+0.001}_{-0.002}$
BP Tau | 1.6 | 59457.43 | 1.2${}^{+0.1}_{-0.1}$ | 3.5${}^{+1.0}_{-1.0}$ | 1.59${}^{+0.07}_{-0.15}$ | 0.004${}^{+0.022}_{-0.003}$ | 0.0174${}^{+0.0008}_{-0.0039}$
BP Tau | 1.7 | 59458.95 | 1.26${}^{+0.05}_{-0.06}$ | 0.04${}^{+0.12}_{-0.03}$ | 1.24${}^{+0.07}_{-0.05}$ | 0.126${}^{+0.004}_{-0.01}$ | 0.0002${}^{+0.002}_{-0.0002}$
BP Tau | 1.8 | 59460.87 | 1.3${}^{+0.3}_{-0.2}$ | 0.07${}^{+0.29}_{-0.05}$ | 1.6${}^{+0.2}_{-0.3}$ | 0.03${}^{+0.05}_{-0.02}$ | 0.025${}^{+0.005}_{-0.008}$
BP Tau | 1.9 | 59462.92 | 1.31${}^{+0.05}_{-0.04}$ | 0.11${}^{+0.51}_{-0.09}$ | 1.05${}^{+0.05}_{-0.07}$ | 0.001${}^{+0.007}_{-0.001}$ | 0.051${}^{+0.001}_{-0.002}$
BP Tau | 1.10 | 59464.97 | 1.2${}^{+0.3}_{-0.2}$ | 0.04${}^{+0.12}_{-0.03}$ | 1.3${}^{+0.2}_{-0.3}$ | 0.04${}^{+0.04}_{-0.03}$ | 0.019${}^{+0.005}_{-0.008}$
BP Tau | 1.11 | 59467.09 | 1.1${}^{+0.2}_{-0.2}$ | 0.04${}^{+0.1}_{-0.03}$ | 0.9${}^{+0.2}_{-0.1}$ | 0.12${}^{+0.02}_{-0.03}$ | 0.004${}^{+0.006}_{-0.004}$
BP Tau | 1.12 | 59469.14 | 0.91${}^{+0.06}_{-0.06}$ | 2.8${}^{+0.9}_{-0.9}$ | 1.16${}^{+0.05}_{-0.06}$ | 0.0011${}^{+0.0056}_{-0.0009}$ | 0.0123${}^{+0.0004}_{-0.001}$
BP Tau | 2.1 | 59926.16 | 1.3${}^{+0.3}_{-0.3}$ | 7.5${}^{+1.2}_{-1.2}$ | 1.4${}^{+0.2}_{-0.3}$ | 0.03${}^{+0.05}_{-0.03}$ | 0.009${}^{+0.005}_{-0.009}$
BP Tau | 2.2 | 59928.47 | 1.4${}^{+0.3}_{-0.3}$ | 6.2${}^{+1.2}_{-1.3}$ | 1.1${}^{+0.3}_{-0.2}$ | 0.09${}^{+0.03}_{-0.04}$ | 0.006${}^{+0.008}_{-0.006}$
BP Tau | 2.3 | 59930.06 | 1.11${}^{+0.06}_{-0.06}$ | 9.5${}^{+1.0}_{-0.9}$ | 0.83${}^{+0.06}_{-0.05}$ | 0.044${}^{+0.002}_{-0.005}$ | 0.0001${}^{+0.0009}_{-0.0001}$
BP Tau | 2.4 | 59932.57 | 1.12${}^{+0.04}_{-0.04}$ | 0.04${}^{+0.12}_{-0.03}$ | 0.9${}^{+0.06}_{-0.05}$ | 0.132${}^{+0.004}_{-0.007}$ | 0.0002${}^{+0.0012}_{-0.0001}$
BP Tau | 2.5 | 59936.54a | 1.7${}^{+0.3}_{-0.3}$ | 5.0${}^{+4.4}_{-4.3}$ | 1.1${}^{+0.3}_{-0.2}$ | 0.164${}^{+0.009}_{-0.05}$ | 0.001${}^{+0.009}_{-0.001}$
BP Tau | 2.6 | 59938.52 | 1.4${}^{+0.2}_{-0.2}$ | 12.0${}^{+1.3}_{-1.4}$ | 1.2${}^{+0.2}_{-0.2}$ | 0.03${}^{+0.02}_{-0.03}$ | 0.004${}^{+0.005}_{-0.004}$
BP Tau | 2.7 | 59940.70 | 0.9${}^{+0.1}_{-0.2}$ | 0.2${}^{+0.7}_{-0.2}$ | 1.0${}^{+0.2}_{-0.1}$ | 0.07${}^{+0.01}_{-0.03}$ | 0.003${}^{+0.005}_{-0.003}$
BP Tau | 2.8 | 59942.55 | 1.44${}^{+0.09}_{-0.08}$ | 8.0${}^{+1.4}_{-1.3}$ | 1.53${}^{+0.07}_{-0.09}$ | 0.001${}^{+0.009}_{-0.001}$ | 0.0174${}^{+0.0006}_{-0.0015}$
BP Tau | 2.9 | 59944.67 | 1.6${}^{+0.3}_{-0.3}$ | 0.11${}^{+0.58}_{-0.09}$ | 1.6${}^{+0.2}_{-0.3}$ | 0.12${}^{+0.04}_{-0.04}$ | 0.015${}^{+0.007}_{-0.008}$
BP Tau | 2.10 | 59946.58 | 1.57${}^{+0.1}_{-0.09}$ | 16.4${}^{+1.3}_{-1.3}$ | 1.07${}^{+0.07}_{-0.1}$ | 0.002${}^{+0.013}_{-0.002}$ | 0.0138${}^{+0.0007}_{-0.0023}$
BP Tau | 2.11 | 59948.63 | 1.4${}^{+0.3}_{-0.3}$ | 7.1${}^{+1.5}_{-1.5}$ | 1.1${}^{+0.3}_{-0.3}$ | 0.07${}^{+0.05}_{-0.04}$ | 0.01${}^{+0.008}_{-0.008}$
BP Tau | 2.12 | 59950.48 | 1.6${}^{+0.4}_{-0.5}$ | 5.7${}^{+1.6}_{-2.1}$ | 1.5${}^{+0.6}_{-0.2}$ | 0.11${}^{+0.02}_{-0.09}$ | 0.004${}^{+0.016}_{-0.004}$
GM Aur | 1.1 | 59500.52 | 0.49${}^{+0.04}_{-0.04}$ | 7.2${}^{+0.9}_{-0.9}$ | 0.59${}^{+0.04}_{-0.04}$ | 0.0007${}^{+0.0025}_{-0.0005}$ | 0.0008${}^{+0.0003}_{-0.0005}$
GM Aur | 1.2 | 59502.30 | 0.86${}^{+0.05}_{-0.05}$ | 7.2${}^{+1.1}_{-1.1}$ | 1.14${}^{+0.05}_{-0.06}$ | 0.0007${}^{+0.0031}_{-0.0005}$ | 0.0152${}^{+0.0004}_{-0.0007}$
GM Aur | 1.3 | 59503.69 | 0.58${}^{+0.03}_{-0.03}$ | 9.5${}^{+0.8}_{-0.8}$ | 0.46${}^{+0.03}_{-0.04}$ | 0.0006${}^{+0.0022}_{-0.0004}$ | 0.0049${}^{+0.0003}_{-0.0004}$
GM Aur | 1.4 | 59504.88 | 0.43${}^{+0.03}_{-0.03}$ | 5.1${}^{+0.7}_{-0.7}$ | 0.58${}^{+0.03}_{-0.03}$ | 0.0005${}^{+0.0014}_{-0.0003}$ | 0.0026${}^{+0.0002}_{-0.0003}$
GM Aur | 1.5 | 59506.67 | 0.58${}^{+0.04}_{-0.04}$ | 3.6${}^{+0.8}_{-0.8}$ | 1.11${}^{+0.04}_{-0.05}$ | 0.0007${}^{+0.0036}_{-0.0006}$ | 0.003${}^{+0.0003}_{-0.0006}$
GM Aur | 1.6 | 59507.93 | 1.04${}^{+0.03}_{-0.02}$ | 0.1${}^{+0.6}_{-0.1}$ | 2.38${}^{+0.04}_{-0.05}$ | 0.0007${}^{+0.0034}_{-0.0006}$ | 0.0132${}^{+0.0005}_{-0.0007}$
GM Aur | 1.7 | 59509.65 | 2.15${}^{+0.08}_{-0.08}$ | 28.6${}^{+1.8}_{-1.8}$ | 1.7${}^{+0.1}_{-0.1}$ | 0.0008${}^{+0.0043}_{-0.0006}$ | 0.04${}^{+0.001}_{-0.001}$
GM Aur | 1.8 | 59554.32 | 0.26${}^{+0.03}_{-0.02}$ | 0.07${}^{+0.27}_{-0.05}$ | 0.61${}^{+0.03}_{-0.04}$ | 0.004${}^{+0.007}_{-0.004}$ | 0.0013${}^{+0.0007}_{-0.0013}$
GM Aur | 1.9 | 59557.17 | 0.96${}^{+0.06}_{-0.06}$ | 9.8${}^{+1.3}_{-1.3}$ | 1.21${}^{+0.06}_{-0.07}$ | 0.0009${}^{+0.0054}_{-0.0007}$ | 0.013${}^{+0.0006}_{-0.001}$
GM Aur | 1.10 | 59558.69 | 0.39${}^{+0.03}_{-0.02}$ | 0.2${}^{+0.7}_{-0.1}$ | 0.92${}^{+0.03}_{-0.04}$ | 0.0006${}^{+0.0023}_{-0.0005}$ | 0.0037${}^{+0.0003}_{-0.0005}$
GM Aur | 1.11 | 59560.21 | 0.32${}^{+0.02}_{-0.01}$ | 0.1${}^{+0.37}_{-0.08}$ | 0.68${}^{+0.02}_{-0.03}$ | 0.0007${}^{+0.0031}_{-0.0006}$ | 0.006${}^{+0.0003}_{-0.0006}$
GM Aur | 2.1 | 59909.89 | 0.51${}^{+0.04}_{-0.04}$ | 9.5${}^{+1.0}_{-1.1}$ | 0.4${}^{+0.04}_{-0.04}$ | 0.0007${}^{+0.0029}_{-0.0005}$ | 0.001${}^{+0.0003}_{-0.0005}$
GM Aur | 2.2 | 59911.41 | 0.55${}^{+0.05}_{-0.04}$ | 8.0${}^{+1.1}_{-1.1}$ | 0.62${}^{+0.05}_{-0.05}$ | 0.0006${}^{+0.0019}_{-0.0004}$ | 0.0026${}^{+0.0003}_{-0.0004}$
GM Aur | 2.3 | 59912.80 | 1.07${}^{+0.05}_{-0.06}$ | 7.5${}^{+1.2}_{-1.3}$ | 1.25${}^{+0.07}_{-0.07}$ | 0.0007${}^{+0.0031}_{-0.0005}$ | 0.0293${}^{+0.0007}_{-0.0008}$
GM Aur | 2.4 | 59914.39 | 0.57${}^{+0.05}_{-0.05}$ | 7.3${}^{+1.1}_{-1.1}$ | 0.73${}^{+0.05}_{-0.05}$ | 0.0006${}^{+0.0025}_{-0.0005}$ | 0.0027${}^{+0.0003}_{-0.0005}$
GM Aur | 2.5 | 59915.78 | 0.69${}^{+0.06}_{-0.06}$ | 8.4${}^{+1.4}_{-1.3}$ | 0.83${}^{+0.06}_{-0.07}$ | 0.0006${}^{+0.0029}_{-0.0005}$ | 0.0064${}^{+0.0004}_{-0.0006}$
GM Aur | 2.6 | 59917.30 | 0.71${}^{+0.05}_{-0.05}$ | 6.0${}^{+1.3}_{-1.3}$ | 1.19${}^{+0.06}_{-0.06}$ | 0.0007${}^{+0.0034}_{-0.0006}$ | 0.0044${}^{+0.0004}_{-0.0006}$
GM Aur | 2.7 | 59919.29 | 0.69${}^{+0.03}_{-0.03}$ | 5.2${}^{+0.8}_{-0.8}$ | 1.1${}^{+0.04}_{-0.04}$ | 0.0005${}^{+0.0018}_{-0.0004}$ | 0.008${}^{+0.0003}_{-0.0004}$
GM Aur | 2.8 | 59920.34 | 0.6${}^{+0.03}_{-0.03}$ | 8.6${}^{+0.8}_{-0.8}$ | 0.67${}^{+0.03}_{-0.03}$ | 0.0004${}^{+0.0013}_{-0.0003}$ | 0.003${}^{+0.0002}_{-0.0003}$
GM Aur | 2.9 | 59922.33 | 0.69${}^{+0.05}_{-0.05}$ | 12.7${}^{+1.1}_{-1.2}$ | 0.5${}^{+0.05}_{-0.05}$ | 0.0005${}^{+0.0015}_{-0.0003}$ | 0.0031${}^{+0.0003}_{-0.0003}$
GM Aur | 2.10 | 59923.52 | 0.67${}^{+0.04}_{-0.04}$ | 5.8${}^{+0.9}_{-0.9}$ | 1.12${}^{+0.04}_{-0.04}$ | 0.0005${}^{+0.0017}_{-0.0004}$ | 0.0036${}^{+0.0003}_{-0.0003}$
GM Aur | 2.11 | 59925.17 | 0.62${}^{+0.04}_{-0.04}$ | 3.3${}^{+1.0}_{-1.0}$ | 1.17${}^{+0.04}_{-0.05}$ | 0.0006${}^{+0.0024}_{-0.0004}$ | 0.0059${}^{+0.0003}_{-0.0004}$

aafootnotetext: No contemporaneous photometry

Figure 7: Shock model fits for TW Hya, Epoch 1. Black, red, and dotted blue
lines are the data, total model, and scaled WTTS template (F${}_{Phot,\
Obs}$), respectively. Black circles are contemporaneous photometry points.
Cyan, green, pink, and orange lines are the low, medium, high, and very high
density accretion columns. In some cases the contribution from an individual
column is low and does not appear in the plot. Filled grey regions are masked
in the fitting due to the presence of bright emission lines. Figure 8: Same as
Figure 7, but for TW Hya, Epoch 2. Figure 9: Same as Figure 7, but for RU Lup,
Epoch 1. Figure 10: Same as Figure 7, but for RU Lup, Epoch 2. Figure 11: Same
as Figure 7, but for BP Tau, Epoch 1. Figure 12: Same as Figure 7, but for BP
Tau, Epoch 2. Figure 13: Same as Figure 7, but for GM Aur, Epoch 1. Figure 14:
Same as Figure 7, but for GM Aur, Epoch 2.

##  Appendix D UV Luminosities

In Tables 6–9 are the UV feature luminosities, including 11 FUV-NUV lines,
FUV/NUV continua, and the H2 Bump. Table 10 gives the log-log linear fit and
Spearman correlation coefficients between Lacc and LUV for each UV feature.

Table 6: UV line, FUV/NUV continuum, and H2 bump luminosities for TW Hya in units of 1029 erg s-1. Object | Visit | Si III | Si IV | C I | C IV | He II | O III] | Si II | Si III] | C III] | Al III] | Mg II | FUV | NUV | Bump
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
TW Hya | 1.1 | 3.2$\pm$0.1 | 4.3$\pm$0.1 | 2.4$\pm$0.1 | 37.6$\pm$0.3 | 21.6$\pm$0.3 | 0.3$\pm$0.1 | 1.3$\pm$0.4 | 0.8$\pm$0.3 | 1.0$\pm$0.3 | 2.4$\pm$0.3 | 83.8$\pm$1.5 | 40.9$\pm$0.1 | 83.1$\pm$0.2 | 3.5$\pm$0.4
TW Hya | 1.2 | 3.7$\pm$0.1 | 5.3$\pm$0.1 | 2.8$\pm$0.1 | 47.9$\pm$0.3 | 24.4$\pm$0.3 | 0.5$\pm$0.1 | 1.4$\pm$0.4 | 1.2$\pm$0.3 | 2.0$\pm$0.4 | 2.8$\pm$0.6 | 117.0$\pm$1.8 | 73.3$\pm$0.2 | 165.0$\pm$0.4 | 4.3$\pm$0.4
TW Hya | 1.3 | 3.1$\pm$0.1 | 6.4$\pm$0.1 | 3.2$\pm$0.1 | 93.7$\pm$0.4 | 32.8$\pm$0.4 | 0.9$\pm$0.1 | 2.4$\pm$0.6 | 1.2$\pm$0.5 | 1.6$\pm$0.5 | 1.3$\pm$0.6 | 109.0$\pm$1.7 | 115.0$\pm$0.3 | 261.0$\pm$0.6 | 6.7$\pm$0.7
TW Hya | 1.4 | 3.0$\pm$0.1 | 5.2$\pm$0.1 | 2.7$\pm$0.1 | 64.6$\pm$0.3 | 27.4$\pm$0.3 | 0.7$\pm$0.1 | 3.1$\pm$0.6 | 1.4$\pm$0.6 | 0.3$\pm$0.5 | 1.7$\pm$0.8 | 141.0$\pm$2.3 | 128.0$\pm$0.3 | 268.0$\pm$0.7 | 5.4$\pm$0.6
TW Hya | 1.5 | 3.3$\pm$0.1 | 6.1$\pm$0.1 | 3.0$\pm$0.1 | 57.1$\pm$0.4 | 27.2$\pm$0.3 | 0.5$\pm$0.1 | 1.4$\pm$0.4 | 1.7$\pm$0.4 | 1.7$\pm$0.4 | 2.2$\pm$0.5 | 104.0$\pm$1.5 | 63.8$\pm$0.2 | 135.0$\pm$0.3 | 4.3$\pm$0.4
TW Hya | 1.6 | 4.0$\pm$0.1 | 6.3$\pm$0.1 | 3.0$\pm$0.1 | 96.0$\pm$0.4 | 39.4$\pm$0.3 | 0.8$\pm$0.1 | 0.3$\pm$0.5 | 1.0$\pm$0.6 | 2.1$\pm$0.5 | 1.5$\pm$0.8 | 110.0$\pm$2.1 | 158.0$\pm$0.4 | 343.0$\pm$0.8 | 7.9$\pm$0.8
TW Hya | 1.7 | 4.2$\pm$0.1 | 5.6$\pm$0.1 | 3.2$\pm$0.1 | 69.5$\pm$0.4 | 35.5$\pm$0.4 | 0.4$\pm$0.1 | 1.7$\pm$0.4 | 0.2$\pm$0.3 | 1.5$\pm$0.4 | 1.7$\pm$0.6 | 68.5$\pm$1.4 | 79.1$\pm$0.2 | 169.0$\pm$0.4 | 5.2$\pm$0.5
TW Hya | 1.8 | 4.3$\pm$0.1 | 7.3$\pm$0.1 | 3.7$\pm$0.1 | 131.0$\pm$0.5 | 49.0$\pm$0.4 | 1.0$\pm$0.1 | 2.4$\pm$0.7 | 1.8$\pm$0.5 | 1.7$\pm$0.6 | 2.4$\pm$0.7 | 123.0$\pm$1.7 | 176.0$\pm$0.4 | 407.0$\pm$1.1 | 7.4$\pm$0.8
TW Hya | 1.9 | 4.5$\pm$0.1 | 6.4$\pm$0.1 | 3.6$\pm$0.1 | 74.6$\pm$0.4 | 31.7$\pm$0.3 | 0.6$\pm$0.1 | 1.6$\pm$0.3 | 0.9$\pm$0.3 | 1.7$\pm$0.3 | 1.9$\pm$0.5 | 89.6$\pm$1.1 | 66.9$\pm$0.2 | 131.0$\pm$0.3 | 5.7$\pm$0.6
TW Hya | 1.10 | 4.0$\pm$0.1 | 5.6$\pm$0.1 | 3.2$\pm$0.1 | 43.7$\pm$0.2 | 18.9$\pm$0.3 | 0.6$\pm$0.1 | 1.0$\pm$0.4 | 0.4$\pm$0.3 | 2.3$\pm$0.4 | 0.7$\pm$0.5 | 100.0$\pm$1.6 | 49.0$\pm$0.1 | 106.0$\pm$0.3 | 5.2$\pm$0.5
TW Hya | 1.11 | 3.6$\pm$0.1 | 5.1$\pm$0.1 | 2.8$\pm$0.1 | 33.5$\pm$0.2 | 20.3$\pm$0.3 | 0.3$\pm$0.1 | 0.8$\pm$0.3 | 0.4$\pm$0.2 | 1.1$\pm$0.3 | 1.1$\pm$0.3 | 57.3$\pm$1.1 | 42.7$\pm$0.1 | 70.5$\pm$0.2 | 4.6$\pm$0.5
TW Hya | 2.1 | 3.9$\pm$0.1 | 5.2$\pm$0.1 | 3.3$\pm$0.1 | 58.8$\pm$0.4 | 29.3$\pm$0.4 | 0.3$\pm$0.1 | 0.4$\pm$0.3 | -0.0$\pm$0.3 | 0.8$\pm$0.3 | 1.3$\pm$0.5 | 65.7$\pm$1.3 | 59.1$\pm$0.2 | 109.0$\pm$0.3 | 5.8$\pm$0.6
TW Hya | 2.2 | 4.1$\pm$0.1 | 5.6$\pm$0.1 | 3.2$\pm$0.1 | 81.2$\pm$0.5 | 36.7$\pm$0.5 | 0.7$\pm$0.2 | 0.1$\pm$0.8 | 0.6$\pm$0.7 | 1.1$\pm$0.8 | -0.0$\pm$0.7 | 49.1$\pm$1.5 | 301.0$\pm$0.7 | 385.0$\pm$1.0 | 6.6$\pm$0.7
TW Hya | 2.3 | 3.5$\pm$0.1 | 5.0$\pm$0.1 | 3.1$\pm$0.1 | 65.4$\pm$0.4 | 31.1$\pm$0.5 | 0.4$\pm$0.1 | 1.5$\pm$0.4 | 0.9$\pm$0.3 | 1.2$\pm$0.4 | 1.2$\pm$0.5 | 56.7$\pm$1.2 | 75.5$\pm$0.2 | 159.0$\pm$0.4 | 5.3$\pm$0.5
TW Hya | 2.4 | 3.5$\pm$0.1 | 6.2$\pm$0.1 | 3.3$\pm$0.1 | 134.0$\pm$0.5 | 47.0$\pm$0.4 | 0.7$\pm$0.1 | 0.9$\pm$0.4 | 1.1$\pm$0.5 | 2.2$\pm$0.5 | 3.7$\pm$0.7 | 86.4$\pm$1.5 | 126.0$\pm$0.3 | 283.0$\pm$0.7 | 7.7$\pm$0.8
TW Hya | 2.5 | 4.0$\pm$0.1 | 6.5$\pm$0.1 | 3.6$\pm$0.1 | 102.0$\pm$0.5 | 49.5$\pm$0.6 | 0.8$\pm$0.1 | 1.3$\pm$0.6 | 1.1$\pm$0.5 | 0.8$\pm$0.5 | 0.9$\pm$0.5 | 57.8$\pm$1.8 | 145.0$\pm$0.4 | 274.0$\pm$0.7 | 7.3$\pm$0.7
TW Hya | 2.6 | 3.3$\pm$0.1 | 5.2$\pm$0.1 | 3.3$\pm$0.1 | 108.0$\pm$0.6 | 51.2$\pm$0.6 | 0.8$\pm$0.2 | 1.7$\pm$0.7 | 0.9$\pm$0.7 | 2.3$\pm$0.7 | 0.4$\pm$0.8 | 84.4$\pm$1.9 | 253.0$\pm$0.6 | 453.0$\pm$1.1 | 5.3$\pm$0.6
TW Hya | 2.7 | 3.8$\pm$0.1 | 5.6$\pm$0.1 | 3.2$\pm$0.1 | 90.2$\pm$0.5 | 41.8$\pm$0.5 | 0.7$\pm$0.1 | 2.3$\pm$0.5 | 0.7$\pm$0.5 | 1.6$\pm$0.6 | 3.0$\pm$0.7 | 82.1$\pm$1.8 | 157.0$\pm$0.4 | 311.0$\pm$0.7 | 5.4$\pm$0.6
TW Hya | 2.8 | 3.9$\pm$0.1 | 6.5$\pm$0.1 | 3.7$\pm$0.1 | 100.0$\pm$0.5 | 45.5$\pm$0.6 | 0.9$\pm$0.2 | 0.7$\pm$0.8 | 1.1$\pm$0.6 | 1.2$\pm$0.7 | -0.0$\pm$0.8 | 66.2$\pm$1.9 | 319.0$\pm$0.8 | 448.0$\pm$1.2 | 6.8$\pm$0.7
TW Hya | 2.9 | 3.6$\pm$0.1 | 5.6$\pm$0.1 | 3.4$\pm$0.1 | 68.6$\pm$0.5 | 34.5$\pm$0.5 | 0.5$\pm$0.1 | 0.9$\pm$0.4 | 0.9$\pm$0.4 | 0.7$\pm$0.4 | 2.0$\pm$0.5 | 65.6$\pm$1.4 | 94.0$\pm$0.2 | 186.0$\pm$0.5 | 6.3$\pm$0.6
TW Hya | 2.10 | 4.1$\pm$0.1 | 6.6$\pm$0.1 | 3.5$\pm$0.1 | 78.5$\pm$0.4 | 39.8$\pm$0.5 | 0.2$\pm$0.2 | 0.4$\pm$0.7 | 2.4$\pm$0.8 | 1.4$\pm$0.8 | -1.6$\pm$0.8 | 111.0$\pm$1.7 | 317.0$\pm$0.8 | 346.0$\pm$0.9 | 9.4$\pm$1.0

Table 7: Same as Table 6, but for RU Lup Object | Visit | Si III | Si IV | C I | C IV | He II | O III | Si II | Si III] | C III] | Al III] | Mg II | FUV | NUV | Bump
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
RU Lup | 1.1 | 0.7$\pm$0.0 | 7.8$\pm$0.1 | 0.5$\pm$0.0 | 12.7$\pm$0.2 | 1.6$\pm$0.1 | 1.1$\pm$0.1 | 3.5$\pm$0.6 | 18.1$\pm$0.8 | 0.8$\pm$0.4 | 30.7$\pm$1.2 | 338.0$\pm$2.6 | 523.0$\pm$1.5 | 4670.0$\pm$12.8 | 3.1$\pm$0.6
RU Lup | 1.2 | 0.6$\pm$0.0 | 8.1$\pm$0.1 | 0.5$\pm$0.0 | 14.9$\pm$0.2 | 1.8$\pm$0.1 | 1.3$\pm$0.1 | 2.7$\pm$0.5 | 12.8$\pm$0.8 | 0.5$\pm$0.5 | 23.3$\pm$0.9 | 289.0$\pm$2.8 | 501.0$\pm$1.4 | 3890.0$\pm$10.1 | 4.6$\pm$1.0
RU Lup | 1.3 | 0.6$\pm$0.0 | 8.9$\pm$0.1 | 0.5$\pm$0.0 | 16.5$\pm$0.2 | 2.3$\pm$0.2 | 1.3$\pm$0.1 | 8.6$\pm$0.8 | 17.5$\pm$1.0 | 1.9$\pm$0.5 | 24.6$\pm$1.2 | 314.0$\pm$2.5 | 521.0$\pm$1.4 | 4250.0$\pm$11.1 | 7.0$\pm$1.4
RU Lup | 1.4 | 0.7$\pm$0.0 | 8.8$\pm$0.1 | 0.5$\pm$0.0 | 17.3$\pm$0.2 | 2.0$\pm$0.1 | 1.2$\pm$0.1 | 6.7$\pm$0.7 | 16.7$\pm$0.9 | 0.9$\pm$0.4 | 29.2$\pm$1.1 | 322.0$\pm$2.7 | 467.0$\pm$1.3 | 3880.0$\pm$9.3 | 12.3$\pm$2.5
RU Lup | 1.5 | 0.6$\pm$0.0 | 10.6$\pm$0.1 | 0.5$\pm$0.0 | 20.5$\pm$0.2 | 2.3$\pm$0.1 | 1.5$\pm$0.1 | 8.8$\pm$0.6 | 20.0$\pm$1.0 | 2.0$\pm$0.5 | 26.9$\pm$1.1 | 319.0$\pm$3.1 | 582.0$\pm$1.6 | 4900.0$\pm$12.0 | 6.3$\pm$1.3
RU Lup | 1.6 | 0.6$\pm$0.0 | 7.2$\pm$0.1 | 0.5$\pm$0.0 | 12.9$\pm$0.2 | 1.7$\pm$0.1 | 1.3$\pm$0.1 | 6.5$\pm$0.6 | 15.7$\pm$0.8 | 0.6$\pm$0.4 | 33.6$\pm$1.3 | 295.0$\pm$2.6 | 529.0$\pm$1.5 | 4760.0$\pm$12.1 | 15.0$\pm$3.0
RU Lup | 1.7 | 0.7$\pm$0.0 | 6.6$\pm$0.1 | 0.4$\pm$0.0 | 11.9$\pm$0.2 | 1.6$\pm$0.1 | 1.2$\pm$0.1 | 4.8$\pm$0.6 | 13.0$\pm$0.9 | 1.7$\pm$0.4 | 29.1$\pm$1.1 | 308.0$\pm$2.7 | 435.0$\pm$1.3 | 4290.0$\pm$10.9 | 1.4$\pm$0.3
RU Lup | 1.8 | 0.5$\pm$0.0 | 7.0$\pm$0.1 | 0.5$\pm$0.0 | 12.9$\pm$0.2 | 1.6$\pm$0.1 | 1.4$\pm$0.1 | 2.2$\pm$0.5 | 17.0$\pm$0.9 | 0.7$\pm$0.5 | 37.8$\pm$1.4 | 359.0$\pm$3.2 | 558.0$\pm$1.7 | 5360.0$\pm$13.5 | 3.5$\pm$0.7
RU Lup | 1.9 | 0.6$\pm$0.0 | 7.6$\pm$0.1 | 0.5$\pm$0.0 | 14.0$\pm$0.2 | 1.5$\pm$0.1 | 1.2$\pm$0.1 | 6.0$\pm$0.6 | 17.2$\pm$0.9 | 1.3$\pm$0.5 | 29.4$\pm$1.2 | 297.0$\pm$3.1 | 545.0$\pm$1.5 | 5330.0$\pm$13.8 | 10.3$\pm$2.1
RU Lup | 1.10 | 0.5$\pm$0.0 | 9.5$\pm$0.1 | 0.5$\pm$0.0 | 19.0$\pm$0.2 | 2.0$\pm$0.1 | 1.5$\pm$0.1 | 3.0$\pm$0.6 | 19.7$\pm$0.9 | 2.6$\pm$0.5 | 24.4$\pm$1.2 | 430.0$\pm$3.5 | 574.0$\pm$1.6 | 5320.0$\pm$13.4 | 4.8$\pm$1.0
RU Lup | 2.1 | 0.8$\pm$0.0 | 8.0$\pm$0.1 | 0.5$\pm$0.0 | 22.4$\pm$0.3 | 3.2$\pm$0.1 | 1.6$\pm$0.1 | 5.0$\pm$0.6 | 13.9$\pm$0.7 | 1.5$\pm$0.4 | 20.7$\pm$0.9 | 263.0$\pm$2.1 | 492.0$\pm$1.3 | 3440.0$\pm$8.9 | 11.3$\pm$2.3
RU Lup | 2.2 | 0.7$\pm$0.0 | 5.1$\pm$0.1 | 0.4$\pm$0.0 | 13.3$\pm$0.2 | 2.7$\pm$0.1 | 0.8$\pm$0.1 | 5.5$\pm$0.6 | 9.6$\pm$0.6 | 2.5$\pm$0.4 | 16.9$\pm$0.8 | 257.0$\pm$2.7 | 284.0$\pm$0.7 | 2180.0$\pm$5.5 | 9.1$\pm$1.8
RU Lup | 2.3 | 0.5$\pm$0.0 | 5.3$\pm$0.1 | 0.4$\pm$0.0 | 13.6$\pm$0.2 | 2.4$\pm$0.1 | 0.9$\pm$0.1 | 4.6$\pm$0.6 | 10.7$\pm$0.6 | 1.4$\pm$0.4 | 17.3$\pm$1.0 | 326.0$\pm$2.5 | 372.0$\pm$1.0 | 2940.0$\pm$7.5 | 7.5$\pm$1.5
RU Lup | 2.4 | 0.6$\pm$0.0 | 5.6$\pm$0.1 | 0.5$\pm$0.0 | 15.8$\pm$0.2 | 3.0$\pm$0.1 | 1.2$\pm$0.1 | 2.5$\pm$0.4 | 9.3$\pm$0.7 | 1.6$\pm$0.3 | 15.0$\pm$0.8 | 262.0$\pm$2.4 | 272.0$\pm$0.7 | 1930.0$\pm$4.8 | 6.3$\pm$1.3
RU Lup | 2.5 | 0.7$\pm$0.0 | 4.2$\pm$0.1 | 0.5$\pm$0.0 | 12.2$\pm$0.2 | 2.8$\pm$0.1 | 0.8$\pm$0.1 | 3.7$\pm$0.4 | 6.2$\pm$0.4 | 1.7$\pm$0.3 | 10.1$\pm$0.7 | 242.0$\pm$2.4 | 186.0$\pm$0.5 | 1180.0$\pm$3.0 | 5.0$\pm$1.0
RU Lup | 2.6 | 0.7$\pm$0.0 | 3.5$\pm$0.1 | 0.5$\pm$0.0 | 10.4$\pm$0.1 | 2.2$\pm$0.1 | 0.7$\pm$0.1 | 3.2$\pm$0.4 | 6.0$\pm$0.4 | 1.9$\pm$0.3 | 11.5$\pm$0.5 | 229.0$\pm$2.4 | 186.0$\pm$0.5 | 1220.0$\pm$3.0 | 10.6$\pm$2.1
RU Lup | 2.7 | 0.7$\pm$0.0 | 4.1$\pm$0.1 | 0.5$\pm$0.0 | 12.6$\pm$0.2 | 2.3$\pm$0.1 | 0.7$\pm$0.1 | 4.9$\pm$0.5 | 7.7$\pm$0.6 | 2.6$\pm$0.4 | 16.4$\pm$0.6 | 233.0$\pm$2.8 | 230.0$\pm$0.6 | 1620.0$\pm$4.1 | 6.3$\pm$1.3
RU Lup | 2.8 | 0.6$\pm$0.0 | 3.6$\pm$0.1 | 0.4$\pm$0.0 | 11.2$\pm$0.2 | 2.4$\pm$0.1 | 0.9$\pm$0.1 | 4.4$\pm$0.5 | 5.5$\pm$0.6 | 2.4$\pm$0.3 | 15.4$\pm$0.9 | 193.0$\pm$2.1 | 243.0$\pm$0.6 | 1680.0$\pm$4.4 | 8.9$\pm$1.8
RU Lup | 2.9 | 0.8$\pm$0.0 | 3.7$\pm$0.1 | 0.5$\pm$0.0 | 12.2$\pm$0.2 | 2.4$\pm$0.1 | 0.9$\pm$0.1 | 3.9$\pm$0.4 | 6.6$\pm$0.5 | 1.8$\pm$0.3 | 10.2$\pm$0.6 | 191.0$\pm$2.2 | 202.0$\pm$0.5 | 1480.0$\pm$3.8 | 12.6$\pm$2.5
RU Lup | 2.10 | 0.6$\pm$0.0 | 3.1$\pm$0.1 | 0.4$\pm$0.0 | 8.8$\pm$0.1 | 1.9$\pm$0.1 | 0.7$\pm$0.1 | 1.2$\pm$0.5 | 6.6$\pm$0.7 | 2.6$\pm$0.5 | 14.9$\pm$0.9 | 213.0$\pm$2.7 | 330.0$\pm$0.9 | 3110.0$\pm$7.9 | 6.7$\pm$1.3
RU Lup | 2.11 | 0.5$\pm$0.0 | 6.3$\pm$0.1 | 0.5$\pm$0.0 | 15.8$\pm$0.2 | 2.2$\pm$0.1 | 1.5$\pm$0.1 | 1.4$\pm$0.5 | 16.5$\pm$0.8 | 1.9$\pm$0.5 | 21.1$\pm$1.1 | 242.0$\pm$2.6 | 496.0$\pm$1.4 | 3810.0$\pm$9.6 | 3.8$\pm$0.8
RU Lup | 2.12 | 0.7$\pm$0.0 | 7.5$\pm$0.1 | 0.5$\pm$0.0 | 16.8$\pm$0.2 | 2.2$\pm$0.1 | 1.5$\pm$0.1 | 4.9$\pm$0.7 | 15.5$\pm$0.8 | 1.4$\pm$0.5 | 22.4$\pm$1.0 | 252.0$\pm$2.8 | 528.0$\pm$1.5 | 4170.0$\pm$10.8 | 7.2$\pm$1.5

Table 8: Same as Table 6, but for BP Tau Object | Visit | Si III | Si IV | C I | C IV | He II | O III | Si II | Si III] | C III] | Al III] | Mg II | FUV | NUV | Bump
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
BP Tau | 1.1 | 0.2$\pm$0.0 | 1.0$\pm$0.1 | 0.3$\pm$0.1 | 8.1$\pm$0.2 | 4.7$\pm$0.3 | 0.6$\pm$0.1 | 1.2$\pm$0.2 | 2.0$\pm$0.2 | 0.2$\pm$0.2 | 0.9$\pm$0.2 | 75.2$\pm$0.5 | 386.0$\pm$0.9 | 543.0$\pm$1.3 | 69.5$\pm$7.0
BP Tau | 1.2 | 0.1$\pm$0.0 | 1.1$\pm$0.1 | 0.2$\pm$0.0 | 10.4$\pm$0.2 | 5.2$\pm$0.3 | 0.3$\pm$0.1 | 2.5$\pm$0.1 | 1.9$\pm$0.2 | 0.8$\pm$0.1 | 1.3$\pm$0.1 | 80.9$\pm$0.6 | 133.0$\pm$0.3 | 344.0$\pm$0.9 | 24.8$\pm$2.5
BP Tau | 1.3 | 0.3$\pm$0.1 | 1.4$\pm$0.1 | 0.2$\pm$0.1 | 14.6$\pm$0.2 | 6.2$\pm$0.2 | 0.8$\pm$0.1 | 2.1$\pm$0.2 | 2.4$\pm$0.2 | 0.4$\pm$0.2 | 0.5$\pm$0.2 | 66.6$\pm$0.5 | 347.0$\pm$0.8 | 575.0$\pm$1.4 | 34.5$\pm$3.5
BP Tau | 1.4 | 0.3$\pm$0.0 | 0.6$\pm$0.0 | 0.2$\pm$0.0 | 6.4$\pm$0.2 | 4.0$\pm$0.2 | 0.3$\pm$0.1 | 0.9$\pm$0.2 | 1.8$\pm$0.2 | -0.0$\pm$0.1 | 0.3$\pm$0.2 | 42.3$\pm$0.4 | 199.0$\pm$0.5 | 340.0$\pm$0.8 | 48.2$\pm$4.9
BP Tau | 1.5 | 0.1$\pm$0.0 | 1.6$\pm$0.1 | 0.2$\pm$0.0 | 14.3$\pm$0.2 | 3.4$\pm$0.2 | 0.6$\pm$0.1 | 2.0$\pm$0.2 | 3.5$\pm$0.2 | 0.8$\pm$0.1 | 1.3$\pm$0.2 | 84.5$\pm$0.7 | 242.0$\pm$0.6 | 471.0$\pm$1.2 | 35.3$\pm$3.6
BP Tau | 1.6 | 0.2$\pm$0.0 | 0.8$\pm$0.0 | 0.2$\pm$0.0 | 8.5$\pm$0.2 | 4.1$\pm$0.2 | 0.4$\pm$0.1 | 1.4$\pm$0.1 | 1.5$\pm$0.2 | 0.9$\pm$0.1 | 1.0$\pm$0.1 | 65.6$\pm$0.6 | 115.0$\pm$0.3 | 327.0$\pm$0.8 | 5.2$\pm$0.6
BP Tau | 1.7 | 0.1$\pm$0.0 | 1.1$\pm$0.1 | 0.2$\pm$0.0 | 10.5$\pm$0.2 | 4.9$\pm$0.2 | 0.6$\pm$0.1 | 2.2$\pm$0.1 | 1.2$\pm$0.1 | 0.5$\pm$0.1 | 0.8$\pm$0.1 | 59.1$\pm$0.5 | 160.0$\pm$0.4 | 394.0$\pm$1.0 | 28.8$\pm$3.0
BP Tau | 1.8 | 0.2$\pm$0.0 | 0.9$\pm$0.1 | 0.2$\pm$0.0 | 8.4$\pm$0.2 | 4.5$\pm$0.2 | 0.9$\pm$0.1 | 1.6$\pm$0.1 | 1.2$\pm$0.2 | 0.1$\pm$0.1 | 0.9$\pm$0.2 | 71.9$\pm$0.5 | 178.0$\pm$0.4 | 381.0$\pm$1.0 | 38.7$\pm$3.9
BP Tau | 1.9 | 0.2$\pm$0.0 | 0.7$\pm$0.1 | 0.2$\pm$0.0 | 8.1$\pm$0.2 | 4.7$\pm$0.2 | 0.6$\pm$0.1 | 1.9$\pm$0.2 | 1.9$\pm$0.2 | 0.2$\pm$0.1 | 0.9$\pm$0.2 | 58.1$\pm$0.5 | 301.0$\pm$0.7 | 399.0$\pm$1.0 | 77.4$\pm$7.8
BP Tau | 1.10 | 0.2$\pm$0.0 | 0.6$\pm$0.0 | 0.2$\pm$0.0 | 7.5$\pm$0.2 | 4.2$\pm$0.2 | 0.4$\pm$0.1 | 0.5$\pm$0.1 | 1.1$\pm$0.2 | 0.4$\pm$0.1 | 0.4$\pm$0.2 | 49.7$\pm$0.5 | 158.0$\pm$0.4 | 356.0$\pm$0.9 | 11.8$\pm$1.2
BP Tau | 1.11 | 0.3$\pm$0.0 | 0.9$\pm$0.1 | 0.2$\pm$0.0 | 8.6$\pm$0.2 | 5.3$\pm$0.2 | 0.6$\pm$0.1 | 1.6$\pm$0.1 | 1.6$\pm$0.2 | 0.4$\pm$0.1 | 1.1$\pm$0.2 | 52.0$\pm$0.5 | 154.0$\pm$0.4 | 356.0$\pm$0.9 | 13.6$\pm$1.4
BP Tau | 1.12 | 0.3$\pm$0.0 | 0.6$\pm$0.0 | 0.2$\pm$0.0 | 6.2$\pm$0.2 | 3.6$\pm$0.2 | 0.2$\pm$0.1 | 1.3$\pm$0.1 | 1.0$\pm$0.1 | 0.4$\pm$0.1 | 0.7$\pm$0.1 | 44.9$\pm$0.4 | 84.8$\pm$0.2 | 241.0$\pm$0.6 | 30.2$\pm$3.1
BP Tau | 2.1 | 0.1$\pm$0.0 | 1.0$\pm$0.0 | 0.1$\pm$0.0 | 6.9$\pm$0.1 | 4.9$\pm$0.2 | 0.4$\pm$0.1 | 0.7$\pm$0.2 | 1.6$\pm$0.3 | 0.6$\pm$0.2 | 1.7$\pm$0.3 | 72.6$\pm$0.8 | 112.0$\pm$0.3 | 313.0$\pm$0.8 | 5.0$\pm$0.6
BP Tau | 2.2 | 0.2$\pm$0.0 | 1.1$\pm$0.1 | 0.2$\pm$0.0 | 7.2$\pm$0.2 | 4.3$\pm$0.2 | 0.5$\pm$0.1 | 1.4$\pm$0.2 | 1.5$\pm$0.2 | 0.7$\pm$0.2 | 0.9$\pm$0.3 | 54.5$\pm$0.7 | 140.0$\pm$0.3 | 355.0$\pm$0.9 | 15.6$\pm$1.6
BP Tau | 2.3 | 0.2$\pm$0.0 | 0.9$\pm$0.0 | 0.1$\pm$0.0 | 6.2$\pm$0.1 | 3.7$\pm$0.2 | 0.3$\pm$0.1 | 0.6$\pm$0.2 | 0.7$\pm$0.2 | 0.5$\pm$0.2 | 1.2$\pm$0.2 | 57.3$\pm$0.8 | 71.2$\pm$0.2 | 240.0$\pm$0.6 | 4.3$\pm$0.5
BP Tau | 2.4 | 0.3$\pm$0.0 | 2.3$\pm$0.1 | 0.2$\pm$0.0 | 16.0$\pm$0.3 | 7.6$\pm$0.2 | 0.5$\pm$0.1 | 0.4$\pm$0.2 | 0.9$\pm$0.2 | 0.7$\pm$0.2 | 1.0$\pm$0.2 | 35.2$\pm$0.6 | 155.0$\pm$0.4 | 359.0$\pm$0.9 | 14.4$\pm$1.5
BP Tau | 2.5 | 0.1$\pm$0.0 | 0.9$\pm$0.1 | 0.1$\pm$0.0 | 7.6$\pm$0.1 | 6.4$\pm$0.2 | 0.4$\pm$0.1 | 1.4$\pm$0.3 | 0.7$\pm$0.3 | -0.4$\pm$0.3 | 0.4$\pm$0.2 | 55.0$\pm$0.9 | 192.0$\pm$0.4 | 300.0$\pm$0.9 | 15.4$\pm$1.6
BP Tau | 2.6 | 0.1$\pm$0.0 | 1.0$\pm$0.0 | 0.1$\pm$0.0 | 7.6$\pm$0.2 | 6.2$\pm$0.2 | 0.3$\pm$0.1 | 1.2$\pm$0.2 | 0.7$\pm$0.2 | 0.3$\pm$0.1 | 1.2$\pm$0.2 | 42.8$\pm$0.7 | 81.1$\pm$0.2 | 303.0$\pm$0.7 | 5.9$\pm$0.7
BP Tau | 2.7 | 0.1$\pm$0.0 | 0.7$\pm$0.0 | 0.1$\pm$0.0 | 5.5$\pm$0.1 | 4.5$\pm$0.2 | 0.2$\pm$0.1 | 0.9$\pm$0.2 | 0.6$\pm$0.3 | -0.3$\pm$0.2 | 1.1$\pm$0.2 | 36.5$\pm$0.6 | 94.1$\pm$0.2 | 264.0$\pm$0.7 | 7.0$\pm$0.7
BP Tau | 2.8 | 0.1$\pm$0.0 | 0.6$\pm$0.0 | 0.1$\pm$0.0 | 5.9$\pm$0.1 | 4.7$\pm$0.2 | 0.3$\pm$0.1 | 0.3$\pm$0.2 | 0.4$\pm$0.2 | -0.3$\pm$0.2 | 1.0$\pm$0.2 | 43.5$\pm$0.7 | 117.0$\pm$0.3 | 343.0$\pm$0.9 | 20.5$\pm$2.1
BP Tau | 2.9 | 0.1$\pm$0.0 | 1.2$\pm$0.1 | 0.2$\pm$0.0 | 9.1$\pm$0.2 | 7.3$\pm$0.2 | 0.4$\pm$0.1 | 0.8$\pm$0.3 | 1.2$\pm$0.3 | 0.2$\pm$0.3 | 1.1$\pm$0.3 | 58.1$\pm$0.8 | 217.0$\pm$0.5 | 491.0$\pm$1.2 | 26.4$\pm$2.7
BP Tau | 2.10 | 0.2$\pm$0.0 | 1.1$\pm$0.0 | 0.1$\pm$0.0 | 7.5$\pm$0.1 | 4.8$\pm$0.2 | 0.3$\pm$0.1 | 1.3$\pm$0.2 | 0.5$\pm$0.2 | 0.2$\pm$0.2 | 1.1$\pm$0.2 | 52.2$\pm$0.9 | 101.0$\pm$0.2 | 299.0$\pm$0.7 | 17.8$\pm$1.8
BP Tau | 2.11 | 0.2$\pm$0.0 | 1.1$\pm$0.0 | 0.2$\pm$0.0 | 7.3$\pm$0.1 | 5.2$\pm$0.2 | 0.6$\pm$0.1 | 0.7$\pm$0.2 | 0.6$\pm$0.2 | 0.4$\pm$0.2 | 1.2$\pm$0.2 | 50.1$\pm$0.8 | 148.0$\pm$0.4 | 357.0$\pm$0.9 | 21.2$\pm$2.2
BP Tau | 2.12 | 0.2$\pm$0.0 | 1.1$\pm$0.0 | 0.1$\pm$0.0 | 8.4$\pm$0.1 | 5.2$\pm$0.2 | 0.4$\pm$0.1 | 1.5$\pm$0.3 | 1.3$\pm$0.3 | 0.1$\pm$0.2 | 1.6$\pm$0.3 | 81.4$\pm$0.9 | 157.0$\pm$0.4 | 437.0$\pm$1.1 | 8.2$\pm$0.8

Table 9: Same as Table 6, but for GM Aur Object | Visit | Si III | Si IV | C I | C IV | He II | O III | Si II | Si III] | C III] | Al III] | Mg II | FUV | NUV | Bump
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
GM Aur | 1.1 | 0.4$\pm$0.0 | 0.4$\pm$0.0 | 0.3$\pm$0.0 | 5.3$\pm$0.1 | 1.9$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.1 | 0.1$\pm$0.1 | 0.0$\pm$0.1 | 0.6$\pm$0.1 | 24.0$\pm$0.3 | 52.7$\pm$0.1 | 161.0$\pm$0.4 | 22.4$\pm$2.3
GM Aur | 1.2 | 0.4$\pm$0.0 | 0.5$\pm$0.0 | 0.3$\pm$0.0 | 6.3$\pm$0.1 | 2.7$\pm$0.2 | 0.2$\pm$0.1 | 0.0$\pm$0.1 | 0.2$\pm$0.1 | 0.4$\pm$0.1 | 0.1$\pm$0.1 | 23.5$\pm$0.4 | 150.0$\pm$0.4 | 343.0$\pm$0.9 | 11.7$\pm$1.3
GM Aur | 1.3 | 0.5$\pm$0.0 | 0.4$\pm$0.0 | 0.3$\pm$0.0 | 4.4$\pm$0.1 | 1.8$\pm$0.1 | 0.1$\pm$0.1 | 0.3$\pm$0.1 | 0.1$\pm$0.1 | 0.1$\pm$0.1 | 0.3$\pm$0.1 | 20.0$\pm$0.3 | 76.9$\pm$0.2 | 179.0$\pm$0.4 | 32.2$\pm$3.3
GM Aur | 1.4 | 0.4$\pm$0.0 | 0.4$\pm$0.0 | 0.3$\pm$0.0 | 3.1$\pm$0.1 | 1.3$\pm$0.2 | 0.0$\pm$0.1 | 0.2$\pm$0.1 | 0.0$\pm$0.1 | 0.1$\pm$0.1 | 0.6$\pm$0.1 | 23.9$\pm$0.3 | 46.2$\pm$0.1 | 157.0$\pm$0.4 | 23.5$\pm$2.4
GM Aur | 1.5 | 0.4$\pm$0.0 | 0.5$\pm$0.0 | 0.3$\pm$0.0 | 6.3$\pm$0.1 | 2.0$\pm$0.1 | 0.0$\pm$0.1 | 0.3$\pm$0.1 | 0.2$\pm$0.1 | 0.1$\pm$0.1 | 0.5$\pm$0.1 | 26.3$\pm$0.3 | 67.2$\pm$0.2 | 236.0$\pm$0.6 | 22.7$\pm$2.4
GM Aur | 1.6 | 0.4$\pm$0.0 | 0.6$\pm$0.0 | 0.3$\pm$0.0 | 11.8$\pm$0.2 | 3.1$\pm$0.1 | 0.0$\pm$0.1 | 0.6$\pm$0.1 | 0.3$\pm$0.1 | 0.1$\pm$0.1 | 0.6$\pm$0.1 | 41.5$\pm$0.4 | 157.0$\pm$0.4 | 487.0$\pm$1.2 | 37.2$\pm$3.8
GM Aur | 1.7 | 0.3$\pm$0.0 | 0.8$\pm$0.0 | 0.4$\pm$0.0 | 12.4$\pm$0.2 | 3.3$\pm$0.2 | 0.7$\pm$0.1 | 0.4$\pm$0.1 | 0.7$\pm$0.1 | 0.2$\pm$0.1 | 0.0$\pm$0.2 | 39.3$\pm$0.4 | 393.0$\pm$0.9 | 737.0$\pm$1.9 | 58.9$\pm$6.1
GM Aur | 1.8 | 0.4$\pm$0.0 | 0.4$\pm$0.0 | 0.3$\pm$0.0 | 4.0$\pm$0.1 | 1.7$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.1 | 0.1$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.2 | 14.4$\pm$0.5 | 44.8$\pm$0.1 | 132.0$\pm$0.3 | 26.5$\pm$2.7
GM Aur | 1.9 | 0.4$\pm$0.0 | 0.5$\pm$0.0 | 0.3$\pm$0.0 | 7.3$\pm$0.2 | 2.7$\pm$0.1 | 0.1$\pm$0.1 | 0.1$\pm$0.2 | 0.3$\pm$0.1 | 0.2$\pm$0.2 | 0.1$\pm$0.3 | 19.0$\pm$0.6 | 148.0$\pm$0.4 | 360.0$\pm$0.9 | 47.0$\pm$4.8
GM Aur | 1.10 | 0.3$\pm$0.0 | 0.4$\pm$0.0 | 0.3$\pm$0.0 | 5.2$\pm$0.1 | 1.8$\pm$0.1 | 0.1$\pm$0.1 | 0.6$\pm$0.2 | 0.0$\pm$0.1 | 0.1$\pm$0.1 | 0.6$\pm$0.2 | 17.7$\pm$0.5 | 60.0$\pm$0.1 | 191.0$\pm$0.5 | 35.6$\pm$3.6
GM Aur | 1.11 | 0.3$\pm$0.0 | 0.3$\pm$0.0 | 0.2$\pm$0.0 | 2.6$\pm$0.1 | 1.0$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.2 | 0.3$\pm$0.1 | 0.3$\pm$0.1 | 0.2$\pm$0.2 | 13.9$\pm$0.5 | 59.1$\pm$0.1 | 156.0$\pm$0.4 | 28.8$\pm$2.9
GM Aur | 2.1 | 0.3$\pm$0.0 | 0.3$\pm$0.0 | 0.2$\pm$0.0 | 4.8$\pm$0.1 | 2.0$\pm$0.1 | 0.2$\pm$0.1 | 0.1$\pm$0.1 | 0.1$\pm$0.1 | 0.1$\pm$0.1 | 0.1$\pm$0.1 | 19.0$\pm$0.2 | 46.2$\pm$0.1 | 149.0$\pm$0.4 | 30.5$\pm$3.1
GM Aur | 2.2 | 0.4$\pm$0.0 | 0.3$\pm$0.0 | 0.3$\pm$0.0 | 5.0$\pm$0.1 | 2.3$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.1 | 0.1$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.1 | 19.5$\pm$0.3 | 59.0$\pm$0.1 | 187.0$\pm$0.5 | 30.3$\pm$3.1
GM Aur | 2.3 | 0.4$\pm$0.0 | 0.5$\pm$0.0 | 0.2$\pm$0.0 | 5.9$\pm$0.2 | 2.3$\pm$0.2 | 0.2$\pm$0.1 | 0.4$\pm$0.2 | 0.6$\pm$0.1 | 0.1$\pm$0.1 | -0.1$\pm$0.1 | 24.5$\pm$0.4 | 280.0$\pm$0.7 | 449.0$\pm$1.2 | 29.2$\pm$3.0
GM Aur | 2.4 | 0.3$\pm$0.0 | 0.4$\pm$0.0 | 0.2$\pm$0.0 | 5.9$\pm$0.2 | 1.9$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.1 | 0.2$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.1 | 19.5$\pm$0.3 | 60.0$\pm$0.1 | 201.0$\pm$0.5 | 31.1$\pm$3.2
GM Aur | 2.5 | 0.3$\pm$0.0 | 0.4$\pm$0.0 | 0.2$\pm$0.0 | 5.0$\pm$0.1 | 1.7$\pm$0.2 | 0.2$\pm$0.1 | 0.3$\pm$0.1 | 0.1$\pm$0.1 | 0.0$\pm$0.1 | -0.0$\pm$0.1 | 22.2$\pm$0.4 | 83.2$\pm$0.2 | 246.0$\pm$0.7 | 31.1$\pm$3.2
GM Aur | 2.6 | 0.3$\pm$0.0 | 0.4$\pm$0.0 | 0.2$\pm$0.0 | 6.2$\pm$0.1 | 2.2$\pm$0.2 | 0.2$\pm$0.1 | 0.2$\pm$0.1 | -0.0$\pm$0.1 | 0.1$\pm$0.1 | 0.4$\pm$0.1 | 29.4$\pm$0.4 | 75.9$\pm$0.2 | 288.0$\pm$0.7 | 20.0$\pm$2.1
GM Aur | 2.7 | 0.3$\pm$0.0 | 0.4$\pm$0.0 | 0.2$\pm$0.0 | 5.1$\pm$0.1 | 2.3$\pm$0.2 | 0.3$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.1 | 0.2$\pm$0.1 | 0.3$\pm$0.1 | 22.4$\pm$0.3 | 100.0$\pm$0.2 | 280.0$\pm$0.7 | 24.6$\pm$2.6
GM Aur | 2.8 | 0.3$\pm$0.0 | 0.3$\pm$0.0 | 0.2$\pm$0.0 | 5.0$\pm$0.1 | 1.6$\pm$0.1 | 0.1$\pm$0.1 | 0.3$\pm$0.1 | 0.1$\pm$0.1 | 0.3$\pm$0.1 | 0.1$\pm$0.1 | 17.8$\pm$0.3 | 64.8$\pm$0.2 | 194.0$\pm$0.5 | 36.3$\pm$3.7
GM Aur | 2.9 | 0.3$\pm$0.0 | 0.4$\pm$0.0 | 0.2$\pm$0.0 | 6.1$\pm$0.1 | 2.3$\pm$0.1 | 0.1$\pm$0.1 | 0.1$\pm$0.1 | 0.4$\pm$0.1 | 0.1$\pm$0.1 | 0.0$\pm$0.1 | 20.9$\pm$0.3 | 71.8$\pm$0.2 | 205.0$\pm$0.5 | 18.3$\pm$1.9
GM Aur | 2.10 | 0.4$\pm$0.0 | 0.4$\pm$0.0 | 0.2$\pm$0.0 | 6.0$\pm$0.1 | 3.4$\pm$0.2 | 0.2$\pm$0.1 | 0.2$\pm$0.1 | 0.0$\pm$0.1 | 0.1$\pm$0.1 | 0.2$\pm$0.1 | 23.9$\pm$0.4 | 62.6$\pm$0.2 | 258.0$\pm$0.7 | 14.6$\pm$1.5
GM Aur | 2.11 | 0.3$\pm$0.0 | 0.3$\pm$0.0 | 0.2$\pm$0.0 | 4.5$\pm$0.1 | 2.0$\pm$0.1 | 0.1$\pm$0.1 | 0.3$\pm$0.1 | 0.2$\pm$0.1 | 0.2$\pm$0.1 | 0.1$\pm$0.1 | 22.5$\pm$0.3 | 84.6$\pm$0.2 | 262.0$\pm$0.6 | 15.3$\pm$1.6
Table 10: Lacc–LUV Log-log Linear Fit Coefficients

Line | Coefficient | TW Hya | RU Lup | BP Tau | GM Aur | Global
---|---|---|---|---|---|---
Mg II | $m$ | 0.20${}^{0.10}_{0.10}$ | 1.85${}^{0.08}_{0.07}$ | 0.76${}^{0.10}_{0.10}$ | 1.25${}^{0.07}_{0.07}$ | 0.78${}^{0.01}_{0.01}$
Mg II | $b$ | -0.75${}^{0.27}_{0.26}$ | 3.88${}^{0.16}_{0.16}$ | 1.31${}^{0.29}_{0.30}$ | 3.08${}^{0.24}_{0.22}$ | 1.33${}^{0.02}_{0.02}$
Mg II | $r$ | 0.10${}^{0.05}_{0.05}$ | 0.73${}^{0.02}_{0.02}$ | 0.59${}^{0.07}_{0.07}$ | 0.75${}^{0.03}_{0.03}$ | 0.66${}^{0.01}_{0.01}$
Mg II | $p$ | 0.68${}^{0.15}_{0.14}$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.01}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$
Al III] | $m$ | 0.02${}^{0.15}_{0.10}$ | 1.14${}^{0.08}_{0.08}$ | 0.02${}^{0.10}_{0.10}$ | -0.05${}^{0.08}_{0.05}$ | 0.30${}^{0.07}_{0.07}$
Al III] | $b$ | -1.23${}^{0.64}_{0.46}$ | 3.63${}^{0.26}_{0.25}$ | -0.78${}^{0.47}_{0.45}$ | -1.22${}^{0.43}_{0.27}$ | 0.51${}^{0.27}_{0.27}$
Al III] | $r$ | 0.04${}^{0.29}_{0.25}$ | 0.87${}^{0.03}_{0.03}$ | 0.04${}^{0.20}_{0.21}$ | -0.24${}^{0.41}_{0.26}$ | 0.55${}^{0.06}_{0.07}$
Al III] | $p$ | 0.44${}^{0.36}_{0.30}$ |  $<$0.01${}^{0.00}_{0.00}$ | 0.51${}^{0.34}_{0.32}$ | 0.20${}^{0.49}_{0.17}$ |  $<$0.01${}^{0.00}_{0.00}$
C III] | $m$ | 0.03${}^{0.09}_{0.07}$ | -0.10${}^{0.07}_{0.08}$ | 2.5e-3${}^{0.03}_{0.03}$ | 0.01${}^{0.05}_{0.04}$ | 0.08${}^{0.04}_{0.03}$
C III] | $b$ | -1.16${}^{0.40}_{0.33}$ | -0.52${}^{0.32}_{0.34}$ | -0.83${}^{0.16}_{0.14}$ | -0.90${}^{0.25}_{0.23}$ | -0.37${}^{0.20}_{0.17}$
C III] | $r$ | 0.06${}^{0.15}_{0.15}$ | -0.21${}^{0.16}_{0.14}$ | 0.01${}^{0.16}_{0.16}$ | 0.06${}^{0.20}_{0.21}$ | 0.15${}^{0.07}_{0.06}$
C III] | $p$ | 0.63${}^{0.24}_{0.33}$ | 0.35${}^{0.38}_{0.23}$ | 0.64${}^{0.26}_{0.27}$ | 0.51${}^{0.34}_{0.33}$ | 0.16${}^{0.24}_{0.12}$
Si III] | $m$ | 0.07${}^{0.11}_{0.09}$ | 0.98${}^{0.10}_{0.09}$ | 0.12${}^{0.07}_{0.05}$ | 0.05${}^{0.05}_{0.04}$ | 0.33${}^{0.06}_{0.06}$
Si III] | $b$ | -0.95${}^{0.48}_{0.42}$ | 3.36${}^{0.33}_{0.30}$ | -0.32${}^{0.32}_{0.24}$ | -0.70${}^{0.27}_{0.22}$ | 0.70${}^{0.26}_{0.25}$
Si III] | $r$ | 0.15${}^{0.21}_{0.21}$ | 0.88${}^{0.03}_{0.04}$ | 0.29${}^{0.13}_{0.12}$ | 0.25${}^{0.19}_{0.20}$ | 0.61${}^{0.05}_{0.06}$
Si III] | $p$ | 0.44${}^{0.37}_{0.34}$ |  $<$0.01${}^{0.00}_{0.00}$ | 0.16${}^{0.27}_{0.13}$ | 0.27${}^{0.45}_{0.22}$ |  $<$0.01${}^{0.00}_{0.00}$
Si II | $m$ | -0.02${}^{0.09}_{0.06}$ | 0.09${}^{0.12}_{0.09}$ | 0.12${}^{0.07}_{0.05}$ | 0.01${}^{0.06}_{0.04}$ | 0.24${}^{0.07}_{0.06}$
Si II | $b$ | -1.34${}^{0.40}_{0.28}$ | 0.28${}^{0.47}_{0.37}$ | -0.28${}^{0.29}_{0.25}$ | -0.92${}^{0.33}_{0.23}$ | 0.30${}^{0.32}_{0.26}$
Si II | $r$ | -0.05${}^{0.24}_{0.20}$ | 0.12${}^{0.11}_{0.12}$ | 0.30${}^{0.11}_{0.11}$ | 0.03${}^{0.24}_{0.19}$ | 0.38${}^{0.06}_{0.06}$
Si II | $p$ | 0.50${}^{0.35}_{0.32}$ | 0.59${}^{0.27}_{0.29}$ | 0.16${}^{0.23}_{0.11}$ | 0.53${}^{0.33}_{0.35}$ |  $<$0.01${}^{0.00}_{0.00}$
O III] | $m$ | 0.30${}^{0.25}_{0.26}$ | 0.97${}^{0.20}_{0.17}$ | 0.10${}^{0.08}_{0.09}$ | 0.03${}^{0.04}_{0.03}$ | 0.24${}^{0.08}_{0.07}$
O III] | $b$ | 0.17${}^{1.21}_{1.24}$ | 4.32${}^{0.94}_{0.77}$ | -0.37${}^{0.40}_{0.45}$ | -0.81${}^{0.21}_{0.18}$ | 0.41${}^{0.37}_{0.33}$
O III] | $r$ | 0.37${}^{0.22}_{0.29}$ | 0.65${}^{0.09}_{0.11}$ | 0.22${}^{0.18}_{0.21}$ | 0.15${}^{0.17}_{0.17}$ | 0.33${}^{0.06}_{0.06}$
O III] | $p$ | 0.10${}^{0.61}_{0.09}$ |  $<$0.01${}^{0.01}_{0.00}$ | 0.29${}^{0.48}_{0.24}$ | 0.47${}^{0.35}_{0.32}$ |  $<$0.01${}^{0.01}_{0.00}$
He II | $m$ | 1.76${}^{0.10}_{0.09}$ | -0.98${}^{0.20}_{0.21}$ | 0.24${}^{0.17}_{0.15}$ | 0.90${}^{0.15}_{0.14}$ | -0.54${}^{0.02}_{0.01}$
He II | $b$ | 4.11${}^{0.31}_{0.28}$ | -4.24${}^{0.87}_{0.92}$ | 0.09${}^{0.67}_{0.60}$ | 2.87${}^{0.64}_{0.61}$ | -2.90${}^{0.06}_{0.05}$
He II | $r$ | 0.85${}^{0.02}_{0.03}$ | -0.49${}^{0.10}_{0.08}$ | 0.18${}^{0.11}_{0.11}$ | 0.67${}^{0.06}_{0.07}$ | -0.56${}^{0.01}_{0.01}$
He II | $p$ |  $<$0.01${}^{0.00}_{0.00}$ | 0.02${}^{0.05}_{0.02}$ | 0.41${}^{0.33}_{0.24}$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$
C IV | $m$ | 1.40${}^{0.08}_{0.07}$ | 1.16${}^{0.07}_{0.08}$ | 0.62${}^{0.07}_{0.07}$ | 1.03${}^{0.05}_{0.05}$ | -0.21${}^{0.01}_{0.01}$
C IV | $b$ | 2.53${}^{0.20}_{0.19}$ | 3.89${}^{0.25}_{0.28}$ | 1.41${}^{0.25}_{0.24}$ | 3.00${}^{0.20}_{0.20}$ | -1.52${}^{0.03}_{0.03}$
C IV | $r$ | 0.86${}^{0.02}_{0.02}$ | 0.51${}^{0.03}_{0.03}$ | 0.55${}^{0.05}_{0.05}$ | 0.81${}^{0.03}_{0.03}$ | -0.20${}^{0.01}_{0.01}$
C IV | $p$ |  $<$0.01${}^{0.00}_{0.00}$ | 0.02${}^{0.01}_{0.01}$ |  $<$0.01${}^{0.01}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$ | 0.07${}^{0.01}_{0.01}$
C I | $m$ | 2.52${}^{0.55}_{0.51}$ | 0.24${}^{0.56}_{0.52}$ | 0.09${}^{0.11}_{0.13}$ | 0.35${}^{0.23}_{0.21}$ | -0.27${}^{0.02}_{0.02}$
C I | $b$ | 9.02${}^{2.21}_{2.10}$ | 1.11${}^{2.74}_{2.57}$ | -0.34${}^{0.60}_{0.68}$ | 0.84${}^{1.21}_{1.08}$ | -2.14${}^{0.11}_{0.11}$
C I | $r$ | 0.50${}^{0.09}_{0.10}$ | 0.08${}^{0.19}_{0.18}$ | 0.16${}^{0.20}_{0.21}$ | 0.25${}^{0.15}_{0.16}$ | -0.29${}^{0.02}_{0.02}$
C I | $p$ | 0.02${}^{0.05}_{0.02}$ | 0.53${}^{0.34}_{0.34}$ | 0.39${}^{0.39}_{0.31}$ | 0.26${}^{0.39}_{0.19}$ |  $<$0.01${}^{0.00}_{0.00}$
Si IV | $m$ | 2.73${}^{0.38}_{0.35}$ | 1.18${}^{0.05}_{0.04}$ | 0.39${}^{0.08}_{0.08}$ | 0.99${}^{0.22}_{0.19}$ | 0.30${}^{0.01}_{0.01}$
Si IV | $b$ | 9.16${}^{1.45}_{1.32}$ | 4.39${}^{0.17}_{0.16}$ | 0.93${}^{0.38}_{0.35}$ | 3.95${}^{1.08}_{0.95}$ | 0.52${}^{0.04}_{0.03}$
Si IV | $r$ | 0.57${}^{0.06}_{0.07}$ | 0.84${}^{0.01}_{0.02}$ | 0.43${}^{0.07}_{0.09}$ | 0.61${}^{0.09}_{0.11}$ | 0.33${}^{0.01}_{0.01}$
Si IV | $p$ |  $<$0.01${}^{0.01}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$ | 0.04${}^{0.07}_{0.03}$ |  $<$0.01${}^{0.01}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$
Si III | $m$ | 0.88${}^{0.48}_{0.47}$ | -0.79${}^{0.43}_{0.39}$ | -0.06${}^{0.10}_{0.09}$ | -0.13${}^{0.43}_{0.35}$ | -0.26${}^{0.02}_{0.02}$
Si III | $b$ | 2.23${}^{1.93}_{1.87}$ | -3.88${}^{2.07}_{1.88}$ | -1.18${}^{0.54}_{0.48}$ | -1.62${}^{2.20}_{1.79}$ | -2.06${}^{0.10}_{0.11}$
Si III | $r$ | 0.17${}^{0.09}_{0.09}$ | -0.27${}^{0.14}_{0.13}$ | -0.12${}^{0.20}_{0.18}$ | -0.08${}^{0.24}_{0.21}$ | -0.28${}^{0.02}_{0.02}$
Si III | $p$ | 0.45${}^{0.28}_{0.20}$ | 0.23${}^{0.34}_{0.16}$ | 0.43${}^{0.37}_{0.29}$ | 0.46${}^{0.37}_{0.31}$ |  $<$0.01${}^{0.00}_{0.00}$
FUV | $m$ | 0.88${}^{0.04}_{0.04}$ | 1.26${}^{0.02}_{0.02}$ | 0.40${}^{0.04}_{0.04}$ | 0.68${}^{0.02}_{0.02}$ | 1.23${}^{0.01}_{0.01}$
FUV | $b$ | 0.95${}^{0.09}_{0.08}$ | 2.44${}^{0.04}_{0.05}$ | 0.10${}^{0.09}_{0.10}$ | 0.86${}^{0.05}_{0.05}$ | 2.15${}^{0.02}_{0.02}$
FUV | $r$ | 0.92${}^{0.01}_{0.01}$ | 0.98${}^{2.7e-3}_{2.9e-3}$ | 0.55${}^{0.04}_{0.05}$ | 0.88${}^{0.01}_{0.02}$ | 0.85${}^{3.3e-3}_{3.3e-3}$
FUV | $p$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.01}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$
NUV | $m$ | 1.05${}^{0.04}_{0.04}$ | 1.01${}^{0.02}_{0.02}$ | 0.94${}^{0.08}_{0.09}$ | 0.95${}^{0.03}_{0.03}$ | 0.92${}^{0.01}_{0.01}$
NUV | $b$ | 1.10${}^{0.09}_{0.09}$ | 1.02${}^{0.02}_{0.02}$ | 1.06${}^{0.17}_{0.18}$ | 1.13${}^{0.06}_{0.06}$ | 0.94${}^{0.01}_{0.01}$
NUV | $r$ | 0.96${}^{0.01}_{0.01}$ | 0.99${}^{1.9e-3}_{2.5e-3}$ | 0.66${}^{0.05}_{0.05}$ | 0.92${}^{0.01}_{0.01}$ | 0.96${}^{2.1e-3}_{2.3e-3}$
NUV | $p$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$ |  $<$0.01${}^{0.00}_{0.00}$
H2 Bump | $m$ | 0.99${}^{0.26}_{0.26}$ | -0.14${}^{0.10}_{0.10}$ | 0.12${}^{0.03}_{0.03}$ | 0.22${}^{0.12}_{0.12}$ | -0.13${}^{0.05}_{0.05}$
H2 Bump | $b$ | 2.50${}^{0.99}_{0.99}$ | -0.63${}^{0.37}_{0.39}$ | -0.46${}^{0.11}_{0.10}$ | -0.28${}^{0.38}_{0.38}$ | -1.26${}^{0.19}_{0.19}$
H2 Bump | $r$ | 0.54${}^{0.13}_{0.14}$ | -0.20${}^{0.13}_{0.14}$ | 0.31${}^{0.08}_{0.08}$ | 0.22${}^{0.11}_{0.12}$ | -0.11${}^{0.05}_{0.04}$
H2 Bump | $p$ | 0.01${}^{0.06}_{0.01}$ | 0.37${}^{0.36}_{0.25}$ | 0.14${}^{0.15}_{0.08}$ | 0.32${}^{0.33}_{0.19}$ | 0.30${}^{0.24}_{0.16}$

Note. — Fit takes the form of $log_{10}(L_{acc}/L_{\odot})=m\cdot
log_{10}(L_{UV}/L_{\odot})+b$. $r$ is the Pearson correlation coefficient and
$p$ is the p-value of the null hypothesis. See Figure 3.