# Disentangling Stellar and Airglow Emission Lines from HST-COS Spectra

Fernando Cruz Aguirre  Laboratory for Atmospheric and Space Physics
CU Boulder, Boulder, CO  Allison Youngblood  NASA Goddard Space Flight Center
Greenbelt, MD  Kevin France  Laboratory for Atmospheric and Space Physics
CU Boulder, Boulder, CO  Vincent Bourrier  Geneva Observatory
Versoix, Switzerland

###### Abstract

H I Ly$\alpha$ ($1215.67$ Å) and the O I triplet ($1302.17$, $1304.86,$ and
$1306.03$ Å) are bright far-ultraviolet (FUV) emission lines that trace the
stellar chromosphere. Observations of stellar Ly$\alpha$ and O I using the
Hubble Space Telescope’s (HST) most sensitive FUV spectrograph, the Cosmic
Origins Spectrograph (COS), are contaminated with geocoronal emission, or
airglow. This study demonstrates that airglow emission profiles as observed by
COS are sufficiently stable to create airglow templates which can be reliably
subtracted from the data, recovering the underlying stellar flux. We developed
a graphical user interface to implement the airglow subtraction on a sample of
171 main sequence F, G, K, and M-type dwarfs from the COS data archive.
Correlations between recovered stellar emission and measures of stellar
activity were investigated. Several power law relationships are presented for
predicting the stellar Ly$\alpha$ and O I emission. The apparent brightness of
the stellar emission relative to the airglow is a critical factor in the
success or failure of an airglow subtraction. We developed a predictor for the
success of an airglow subtraction using the signal-to-noise ratio (SNR) of the
nearby chromospheric emission line Si III ($1206.51$ Å). The minimum
attenuated Ly$\alpha$ flux which was successfully recovered is $1.39\times
10^{-14}$ erg cm-2 s-1, and we recommend this as a minimum flux for COS
Ly$\alpha$ recoveries.

##  1 Introduction

The hydrogen Lyman alpha (Ly$\alpha$, $\lambda=1215.67$ Å) emission line is
the dominant feature of the far ultraviolet (FUV; 912 - 1700 Å) spectrum of F,
G, K, and M dwarf stars. For M dwarfs, Ly$\alpha$ flux alone can account for
up to 75% of the total ultraviolet (UV) stellar flux (France et al., 2013).
Ly$\alpha$ and O I triplet ($\lambda=1302.17,1304.86,$ and $1306.03$ Å)
emission act as tracers for stellar chromospheric activity (Vidal-Madjar et
al., 2004; Ben-Jaffel & Ballester, 2013; Linsky et al., 2010; Ballester & Ben-
Jaffel, 2015; Bourrier et al., 2018a). The line cores of Ly$\alpha$ and the O
I triplet are formed in the transition region and chromosphere, both with a
formation temperature of $\sim$30,000K (Dere et al., 1997; Landi et al.,
2012). The wings of the line profiles originate from a range of cooler
temperatures within the chromosphere (Avrett & Loeser, 2008; Linsky et al.,
2013).

Ly$\alpha$ photons, and O I triplet photons to a lesser but non-negligible
extent, act as drivers for photochemistry in exoplanet atmospheres. This is
primarily due to the large photoabsorption cross sections across the FUV for
many molecules typically present in exoplanet atmospheres (Miguel et al.,
2015; Venot et al., 2013). FUV photochemical effects include the UV sensitive
formation of haze layers, which can obscure key indicators of atmospheric
habitability in exoplanet transmission spectra (Morley et al., 2015; Kawashima
& Ikoma, 2019), and the alteration of the abundances (and therefore the mixing
ratios) of biosignature molecules (e.g., CH4, O2, O3) (Miguel et al., 2015;
Harman et al., 2015; Rugheimer & Kaltenegger, 2018; Tian et al., 2014; Ranjan
et al., 2022).

Understanding the UV radiation environment, and in particular the dominating
Ly$\alpha$ emission, around exoplanet host stars is crucial for properly
interpreting biosignatures and habitability indicators (Peacock et al., 2019;
Youngblood et al., 2022; Teal et al., 2022). Morley et al. (2015) explores how
the photodissociation of CH4 ultimately results in the formation of haze
layers in super earth atmospheres. This study found that for low incident UV
flux, the rate of CH4 dissociation was also low. For high incident UV flux,
the carbon photochemistry is altered and produces a CO dominated atmosphere,
blocking critical chemical pathways between CH4 dissociation and haze
formation.

The spectral type of the host star is a key factor in interpreting O2 features
as a biosignature. Harman et al. (2015) found that for Earth-like exoplanets
orbiting around F and G type stars, the presence of both strong FUV and near
ultraviolet (NUV; 1700 - 4000 Å) flux from the host star resulted in little
accumulation of abiotic O2 from CO2 photolysis. Due to the decreased NUV
continuum flux from K and M type stars, the O2 dissociation rate decreases and
an abiotic buildup of O2 on Earth-like exoplanets is possible, a false
positive for life. A similar effect is also seen in the O3 abundance of Earth-
like planets (Rugheimer & Kaltenegger, 2018; Tian et al., 2014).

In addition to driving photochemistry, Ly$\alpha$ and O I are also probes of
exoplanet atmospheric escape (Vidal-Madjar et al., 2003; Allan & Vidotto,
2019; Lecavelier Des Etangs et al., 2010; Lecavelier des Etangs et al., 2012;
Ben-Jaffel & Ballester, 2013; Kulow et al., 2014; Ehrenreich et al., 2015;
Lavie et al., 2017; Bourrier et al., 2018b) and predictors of extreme
ultraviolet (EUV; 100 - 912 Å) emission (Linsky et al., 2014). Vidal-Madjar et
al. (2004) details the detection of Ly$\alpha$, O I triplet, and C II doublet
($\lambda=1334.53$ and $1335.71$ Å) transits of the exoplanet HD 209458b. The
presence of O I and C II transits at high altitudes constrains the escape
method to hydrodynamic escape (Koskinen et al., 2013a, b). The key driver of
escape in exoplanet atmospheres is stellar EUV flux; characterizing the host
star’s EUV emission is necessary for proper modeling of atmospheric escape.
There are few stars for which an EUV spectrum has been observed, with strong
attenuation from the interstellar medium (ISM) in the range $\sim$400 - 912 Å.
As shown in Linsky et al. (2014), Ly$\alpha$ can be used to predict the EUV
flux of dwarf stars.

While Ly$\alpha$ can be used to estimate the unobserved EUV flux of a star, it
too suffers from ISM absorption. For nearby stars, the line core of Ly$\alpha$
is completely attenuated when the radial velocity difference between the
stellar and ISM features are within 80 km s-1 from each other, leaving only
the wings present in FUV spectra (Youngblood et al., 2022). The severity of
the attenuation varies depending on the direction and distance to the target
star due to the nonuniform structure of the ISM. The O I triplet lines can
also be affected by ISM attenuation. Due to smaller ISM abundances, a weaker
oscillator strength, and requiring that the stellar and ISM velocities be
similar to align the absorption with the more narrow emission feature, it is
normally not as pronounced in FUV spectra.

The observed spectra from FUV instruments also display bright Ly$\alpha$ and O
I emission features originating from Earth’s exosphere and upper thermosphere;
this is known as geocoronal emission or airglow. Hydrogen and oxygen atoms
within these regions are excited by either solar photons or from collisions.
These atoms will then radiatively de-excite, releasing Ly$\alpha$ and O I
triplet photons in the process. Geocoronal Ly$\alpha$ is observed on both the
day and night sides of the planet, while geocoronal O I emission is only
strong on the day side (Meier, 1991). This different behavior is driven by the
large difference in the scale heights of both species, which is inversely
proportional to atomic weight. Both species are excited by solar UV photons on
the day side, but the density of oxygen atoms is too low in the exosphere for
collisional excitation to occur on the night side. The hydrogen density is
still large enough in the exosphere for geocoronal Ly$\alpha$ to be generated
through collisions. Typical airglow intensities of during orbital day are
20,000 Rayleighs (R) for Ly$\alpha$ and 2,000 R for the individual O I triplet
lines, whereas during orbital night typical values decrease to 2,000 R for
Ly$\alpha$ and effectively 0 R for the O I triplet lines (James et al., 2022).

The orbit of the Hubble Space Telescope (HST; $\sim$540 km) lies within the
Earth’s exosphere, which extends beyond 38 Earth radii (Kameda et al., 2017).
The lower boundary of the exosphere is defined by the altitude in which
atmospheric density is low enough such that particles become collisionless,
which varies with stellar activity. Airglow fully illuminates the slits of the
Cosmic Origins Spectrograph (COS) and the Space Telescope Imaging Spectrograph
(STIS). All spectra observed by these spectrographs become contaminated with
airglow, obscuring stellar Ly$\alpha$ and O I emission.

Figure 1: 2D detector images of COS (left) and STIS (right) observations of GJ
876, centered on the Ly$\alpha$ stellar and airglow emission features. The
stellar spectrum runs along the X axis in both images. The circular COS and
rectangular STIS apertures are fully illuminated by airglow, contaminating the
stellar spectrum. Aspect ratios of both detector images were altered for a
better visual comparison.

Due to the different designs of these spectrographs, they experience airglow
contamination differently. STIS is an imaging spectrograph, with a spatial
resolution capable of distinguishing the target spectrum from the off-target
background spectrum. Airglow can then be subtracted during standard background
removal procedures, recovering the stellar emission. The optical design of COS
prioritized the spectral resolution of faint point sources through the use of
a single optic which corrects for multiple aberrations (Green et al., 2012),
but suffers from strong vignetting and uncorrected astigmatism in the spatial
axis, so an off-target background spectrum is impossible (James et al., 2022).
The large, circular COS aperture (2.5” diameter) also results in more airglow
captured by the instrument, compared to the narrow, rectangular slits (52”
length and 0.05 - 2” width for first-order spectral imaging, 0.2 - 1” length
and 0.025 - 0.5” width for echelle spectroscopy) employed by STIS (Green et
al., 2012; Woodgate et al., 1998). The instrument design of COS results in
severe airglow contamination, without the ability to subtract the airglow from
a single exposure. Examples of COS and STIS 2D detector images of the M3.5 V
dwarf GJ 876 are shown in Figure 1, illustrating the differences in how the
two spectrographs experience airglow.

Few stars with COS spectra have had an airglow subtraction performed (Ben-
Jaffel & Ballester, 2013; Wilson et al., 2017; Bourrier et al., 2018a; dos
Santos et al., 2019; Bourrier et al., 2021), however there are more than 170
dwarf stars in the COS data archive. This paper describes the airglow
subtraction of archival F, G, K, and M dwarf star COS spectra and the
subsequent analysis of the recovered profiles. Section 2 describes the data
collection and coaddition of the stellar sample, and the creation of airglow
templates from COS observations. Section 3 details the development of a
graphical user interface (GUI) which performs the airglow subtraction for
contaminated Ly$\alpha$ and O I triplet line profiles. The integrated fluxes
obtained from recovered stellar profiles are compared to other stellar
chromospheric fluxes and activity indicators in Section 4.

##  2 COS and STIS Observations

We identified 171 stars of F, G, K, or M type from available COS G130M spectra
in the Mikulski Archive for Space Telescopes (MAST) data archive. All COS
observations analyzed in this work can be accessed through
thishttp://dx.doi.org/10.17909/0sc9-b207 (catalog DOI). There are 78 confirmed
exoplanet host stars in this sample (NASA Exoplanet Science Institute, 2020).
Characterizing the Ly$\alpha$ and O I emission of exoplanet host stars is
critical for interpreting star-planet interactions, requiring a proper airglow
subtraction of COS stellar data.

Stars with both COS and STIS observations allow for a verification of proper
airglow subtraction of the star. We identified 35 stars that have STIS G140M
or E140M spectra at comparable wavelengths which can be used for comparison
with our airglow subtracted COS spectra. These STIS observations were obtained
from MAST, and can be accessed through a
separatehttp://dx.doi.org/10.17909/nsag-sq06 (catalog DOI). There were 20 STIS
spectra observed as part of the same programs as the COS data; this assists in
minimizing the effect of stellar variability, as the COS and STIS observations
were acquired at similar times.

Settings for the COS G130M grating and detector are the Lifetime Position
(LP), the focal plane position (FP-POS, FP), and the Cenwave (in Å). The LP
refers to the location where the spectrum falls along the cross-dispersion
direction of the detector. The different LPs were created to address regions
on the detector that began to lose efficiency after prolonged photon exposure,
a phenomenon known as gain sag. As gain sag increases over time, the ability
to distinguish a real photon from a background event is no longer possible.
This manifests as a depression in the spectrum due to real photon events being
mistakenly discarded by the COS data calibration pipeline (CALCOS) (James et
al., 2022). These heavily gain sagged regions are marked with a gain sag data
quality (DQ) flag in the CALCOS-generated data files, indicating that the data
in the region may not be reliable (Soderblom et al., 2021). The first region
to experience gain sag is where bright geocoronal Ly$\alpha$ emission lands on
the detector. Over time, gain sag is seen across the detector face, and a new
LP is chosen (James et al., 2022), shifted above or below the previous LP
(Table A1 lists each LP start date/cycle). The LPs are numbered 1 through 6,
however all stellar data used in this work was taken using LPs 1-4.

The Cenwave refers to the central wavelength of the spectrum that falls on the
detector. The gratings on COS can be tilted such that different wavelength
ranges fall onto the detector. The COS detector consists of two separate
plates, referred to as Segment A (longer wavelengths) and Segment B (shorter
wavelengths), and the Cenwave number is approximately the shortest wavelength
observed on Segment A (James et al., 2022). Because the detector consists of
two separate plates, there is a gap in the spectrum. Observations of the same
target with different Cenwaves make up for these gaps. The five Cenwaves
considered in this work are 1291, 1300, 1309, 1318, and 1327. While all five
Cenwaves are available for use at LP4 (with Segment restrictions), the only
available LP4 stellar spectra in the COS data archive that were relevant to
this work were taken using Cenwave 1291 (James et al., 2022).

In addition to the Cenwave, the different FPs allow for finer adjustments of
the spectral location on the detector. There are four FP positions, numbered 1
to 4. For a given Cenwave, the four FPs offset the spectrum in the dispersion
direction by a small amount (250 px in the FUV channel, or $\sim$2.5 Å for
G130M). The nominal position is FP3. Taking multiple observations of the same
target with various FPs can increase the overall signal-to-noise ratio (SNR)
by smoothing over the fixed pattern noise of the FUV detector (James et al.,
2022).

###  2.1 Stellar Observations

The COS stellar observations addressed in this work were obtained using the
G130M grating. The STIS stellar observations used in this work were obtained
using the G140M or E140M gratings. Tables A2 and A4 contain the observing
programs of the stellar COS and STIS data, respectively.

For each star, we created a coadded COS spectrum consisting of all available
observations taken within a $\pm$2 week time frame. The spectral location of
the airglow is known to change over time with the spacecraft’s orbital motion,
however it is not expected to change significantly within this time frame. In
the case where a star has multiple possible $\pm$2 week windows, we use the
set of observations which results in the maximum usable exposure time. We
exclude certain observations within these time frames due to the effects of
gain sag (see discussion below) or because a Cenwave other than the ones
considered in this work were used. Exposures of exoplanets mid-transit were
not excluded. In the few cases where we would expect a detectable transit, the
exclusion of transit exposures from the coadded spectrum did not significantly
change the results of this work.

The coaddition process used a modified version of the COADD_X1D IDL code
developed for the coaddition of individual COS G130M x1d
files.111https://casa.colorado.edu/$∼$danforth/science/cos/coadd_x1d.pro The
airglow contaminated stellar Ly$\alpha$ and O I triplet profiles were
coaligned through a cross correlation process. Changes in the airglow profile
are minimized within the $\pm$2 week window, allowing for stable coadditions.
A weighted average was taken within each wave bin to produce the final coadded
spectrum of each star. Nearby spectral emission features were used to
determine that the cross correlation had properly aligned individual spectra.

We do not perform the cross correlation on these nearby emission features to
minimize smearing of the Ly$\alpha$ and O I profiles. We later found that
within these $\pm$2 week windows, a cross correlation on either the nearby
emission features or the airglow contaminated airglow features produce similar
spectra. Applying the procedures detailed in Section 3 on both cross
correlated spectra produced results consistent within 1$\sigma$, and we
continue with Ly$\alpha$ and O I cross correlations throughout this work.

We use the coadded G140M and E140M spectra of MUSCLES (v2.2) and Mega-MUSCLES
(v2.3) targets within our sample (France et al., 2016; Youngblood et al.,
2016; Loyd et al., 2016; Froning et al., 2019; Wilson et al., 2021). For the
remaining STIS targets, a weighted average coaddition is performed with all
available G140M or E140M exposures for a given target. As with COS data, the
exclusion of transit exposures did not result in a significant change.

For faint G140M spectra, the STIS data calibration pipeline (CALSTIS) fails to
discern the dim stellar spectral trace from the surrounding background (Loyd
et al., 2016). This is a known issue in the CALSTIS pipeline which affected 12
targets observed with the G140M grating. In these instances, spectra were
manually extracted from the 2D detector image of the exposure through the use
of the stistools python package distributed by the Space Telescope Science
Institute (STScI).222https://stistools.readthedocs.io/en/latest/ For the M
dwarf L 980-5, the stellar spectra were dim enough that a manual extraction
was impossible, as the stellar trace was not discernible from the background
by eye.

As mentioned above, gain sag can heavily affect the quality and reliability of
COS stellar spectra. Within our sample, gain sag was observed in LP3 and LP4
data. A visual inspection of the shapes of Ly$\alpha$ profiles for these stars
was conducted to determine if the datasets were of acceptable quality. All LP4
exposures observed with FP3 were discarded due to heavy gain sag.

We note that for the SNAP 14633 program data, we ignored the DQ flag relating
to detector gridwire shadows. This program only took two exposures per star,
at FP3 and FP4. The FP3 exposures had the detector gridwire shadow DQ flag
appear within the Ly$\alpha$ profile, and the COADD_X1D code will deweight the
flux in this region. With only two exposures, this directly affect the
weighted average and causes depressions in the coadded spectrum. At worst, we
expect a flux decrease up to 20% due to the detector gridwire shadows in these
regions (Ely et al., 2011).

Six stars within our sample were too bright for COS to observe with both
detector segments, and were observed only using Segment A which does not
contain Ly$\alpha$. This reduced the total number of stars for which a
Ly$\alpha$ airglow subtraction was attempted to 165, where 28 of these stars
had STIS spectra available for comparison. For observations using Cenwave
1309, the O I triplet lies within the detector gap. Stellar O I data was not
available for 19 targets observed with Cenwave 1309. The STIS G140M grating
cannot cover both Ly$\alpha$ and the O I triplet in a single exposure; all
G140M spectra used in this work cover Ly$\alpha$. STIS E140M spectra cover
both Ly$\alpha$ and the O I triplet. The total number of stars for which an O
I triplet airglow subtraction was attempted was 152, and 12 had STIS spectra
available for comparison.

###  2.2 Airglow Observations

The airglow observations used in this work were also obtained from the MAST
data
archive.333https://www.stsci.edu/hst/instrumentation/cos/calibration/airglow
We build upon the airglow template creation and subtraction techniques
developed in Ben-Jaffel & Ballester (2013), Wilson et al. (2017), and Bourrier
et al. (2018a). Both intentional and serendipitous observations were used, for
combinations of LPs 1, 2, and 3, with Cenwaves 1291, 1309, and 1327. The
serendipitous observations are only available for LP1, and show no significant
difference from intentional observations. For a given LP and Cenwave, all
available observations were shifted, scaled, and coadded together into a
single LP/Cenwave template using another modified version of the COADD_X1D
code. The shifts are obtained through the same cross correlation method used
for the stellar profiles, centered on the geocoronal emission. The individual
observations were all scaled to the same flux level, and the coadded flux was
determined as the median flux in each wave bin. The flux errors for these
templates were calculated using the Median Absolute Deviant (MAD) (Leys et
al., 2013), defined as the median of all absolute flux deviations from the
median flux. The MAD is multiplied by 1.4826 to obtain an equivalent estimator
for $\sigma$ (Leys et al., 2013). This median method was chosen over a simple
mean due to being less sensitive to flux outliers within each wave bin,
producing more stable coadded airglow templates with flux errors similar to
that of an unweighted average.

We first compared templates for Cenwaves within a given LP to each other in
order to determine if there were any differences in the airglow profiles of
different Cenwaves. Afterwards, we compared representative airglow templates
of each LP to representatives of the other LPs. For LP 1-3, airglow was not
observed for every possible LP/Cenwave combination, and there is no airglow
data available for LP4. The missing combinations are inferred from available
templates.

####  2.2.1 Cenwave Comparison

Within each LP, airglow templates were created for each available Cenwave.
These templates were then shifted in wavelength and scaled on top of one
another to examine differences in the shapes of the airglow profiles. An
example is shown in Figure 2 (see full collection in Figures A1, A2 and A3).

Figure 2: A comparison of LP3 1291 and LP3 1327 Ly$\alpha$ airglow templates
on the upper plot, and the difference between the two templates on the lower
plot. The templates are shifted such that the templates are centered on one
another, then scaled to each other. The 1327 template is broader in the line
wings. This discrepancy is seen in the difference plot, where the variations
tend to be larger than the flux subtraction error (shaded region).

For LPs 1 and 2, there were no significant differences in the different
Cenwave templates for all four airglow lines. The LP3 1327 Ly$\alpha$ template
displays enhancements in the wings of the profile when compared to that of LP3
1291, but no differences were observed between the Cenwaves for O I.
Therefore, for each O I line, one template can be used within each LP. One
general Ly$\alpha$ template can be used for LP 1 and 2, but individual
templates are needed for LP3 (See Figure 2). No airglow observations are
available for LP4 and beyond, so no comparison could be made.

####  2.2.2 Lifetime Position Comparison

After determining the representative templates for each LP, these were
compared to each other. An example is shown in Figure 3 (see full collection
in Figures A4, A5, A6 and A7). The shift and scale factors are determined in
the same way as in the previous section. These comparisons show that each O I
triplet line only needs a single airglow template across LPs 1-3 and Cenwaves
1291-1327, with the exception of Cenwave 1309 which places the triplet in the
gap between detector plates. For Ly$\alpha$, one general template can be used
for most configurations, except for LP3 1327 which requires a separate
template. We examine the location of the Sun, the Moon, and the orientation of
HST during all airglow observations, however these were unable to explain the
observed difference in the shape of the LP3 1327 profiles.

Figure 3: A comparison of LP2 and LP3 airglow templates of O I 1302 on the
upper plot, and the difference between the two templates on the lower plot.
The flux variation in the difference plot is consistent with zero.

Figure 4: The airglow templates developed and used throughout this work.
Shaded regions show the 1$\sigma$ uncertainties. The general Ly$\alpha$
template can be used for all LP and Cenwave combinations, except LP3 1327
which requires its own template. The O I triplet templates can be used for all
LP and Cenwave combinations for which the triplet is not within the gap
between detector plates. Individual airglow exposures are overlain in each
subplot as thin black curves.

Figure 5: The four general cases of the contaminated Ly$\alpha$ profiles we
observe from our sample of stars.

Template Name | Applicable LP | Applicable Cenwave
---|---|---
Ly$\alpha$ \- General | 1,2,3,4 | 1291,1300,1309,1318,1327*
Ly$\alpha$ \- LP3 1327 | 3 | 1327
O I 1302 | 1,2,3,4 | 1291,1300,1318,1327
O I 1305 | 1,2,3,4 | 1291,1300,1318,1327
O I 1306 | 1,2,3,4 | 1291,1300,1318,1327

Table 1: A summary of the five airglow templates created for airglow
subtraction, and which detector settings each template is applicable to.
**Cenwave 1327 not applicable for LP3.

No data is available for LP3 1300 - 1318, so it was unclear which Ly$\alpha$
template would be appropriate to use for stars observed using these detector
settings. Through the least squares minimization technique which will be
described in Section 3.3, we determined that the general Ly$\alpha$ template
produced a lower chi squared ($\chi^{2}$) than the LP3 1327 template when
modeling airglow contaminated LP3 1300 - 1318 spectra. This method also
indicated that the general Ly$\alpha$ template and the O I templates are
appropriate for LP4 1291 data, without significant gain sag present at
Ly$\alpha$. The airglow templates are shown in Figure 5, and Table 1
summarizes the detector settings these templates are applicable for.

##  3 Recovering Stellar Emission

Using the appropriate airglow template from Section 2.2, we perform airglow
subtractions on the stellar spectra described in Section 2.1. The templates
must be shifted and scaled onto the stellar spectrum in order to properly
subtract the airglow and recover the underlying stellar profiles. Building
upon the techniques developed in Ben-Jaffel & Ballester (2013), Wilson et al.
(2017), and Bourrier et al. (2018a), we developed airglow subtraction methods
which recover the stellar Ly$\alpha$ and O I triplet profiles. These methods
were first tested on a subset of stars for which both COS spectra and airglow-
subtracted STIS spectra were available. This allows for a way to verify that
the subtraction method is functioning as expected and is producing
satisfactory results.

###  3.1 General Cases of Airglow Contamination

We have generally categorized contaminated Ly$\alpha$ profiles into four
groups, which can be seen in Figure 5. The first category is Definite Stellar,
Strong. This refers to cases where the stellar profile is clearly visible
above the airglow profile. The second category is Definite Stellar, Weak,
where the stellar wings rise above the airglow, however their amplitude is
comparable to that of the airglow profile. For these two categories,
separation of the stellar and airglow signals is straightforward.

The third category is Questionable Stellar, Strong. This refers to a profile
in which the airglow dominates, however the inclusion of an attenuated stellar
profile produces a better fit than the airglow template alone. When the
observed profile could potentially be well fit by the airglow template alone,
stars are placed in the fourth category, Questionable Stellar, Weak.
Recovering the comparatively weak stellar signal in these cases is where the
difficulty lies.

There are three general cases for O I triplet airglow emission in contaminated
COS spectra. The first is Stellar Dominant, where the stellar emission feature
dominates. These observations were taken during orbital night, where
geocoronal O I emission is either very dim or undetectable. The second case is
Mixed Emission, a mixture of a narrow stellar emission feature and a broad
geocoronal emission feature. The stellar line noticeably peaks above the
airglow line, making airglow template placement straightforward (See Figure
7). The final case is Airglow Dominant, where the airglow dominates, and the
stellar oxygen line is difficult to separate from the noise after airglow
removal.

###  3.2 Airglow Subtraction Model

In order to determine the spectral location and amplitude of the airglow
templates, models of contaminated stellar Ly$\alpha$ and O I triplet emission
as observed by COS were fit to the data using the LMFIT package in python
(Newville et al., 2014). LMFIT is a non-linear least squares minimization and
curve fitting package that uses the Levenberg-Marquardt (LM) algorithm. This
approach allows for simultaneous fitting of stellar emission, ISM attenuation,
and contaminating airglow.

We verified the accuracy of the model by using a Markov chain Monte Carlo
(MCMC) for three stars spanning the range in Ly$\alpha$ data quality; 55 Cnc
(Definite Stellar, Strong), HD 121504 (Questionable Stellar, Strong), and K2-3
(Questionable Stellar, Weak). The stellar Ly$\alpha$ profile of K2-3 could not
be recovered through our recovery tool. We utilize the MCMC method within
LMFIT, which employs the emcee package (Newville et al., 2014; Foreman-Mackey
et al., 2013).

When comparing our model results with those of the MCMC, we find excellent
agreement between best fit parameters, Ly$\alpha$ fluxes, and parameter errors
in all three cases. The MCMC was run to convergence for 55 Cnc and HD 121504.
While the MCMC shows the potential to extract the dim stellar emission of K2-3
from the dominating airglow contamination, the computational time to run the
MCMC to convergence was prohibitively expensive, and its application would be
unfeasible for the full sample of failed recoveries. The MCMC results give us
confidence that the results of our model can provide similar results to those
of a computationally intensive MCMC in significantly less time.

####  3.2.1 Model Components

The first of the model components is the underlying stellar emission. For
Ly$\alpha$, this is represented as a Voigt profile (Wilson et al., 2017;
Bourrier et al., 2018a). A Gaussian profile was instead used for the O I
triplet’s stellar component (Redfield & Linsky, 2004; Bourrier et al., 2018a).
The free parameters for this component are the star’s radial velocity, the
Gaussian FWHM, the Lorentzian FWHM for the Voigt profile only, and the flux
amplitude of the Lorentzian/Gaussian. We bound the Gaussian FWHM for the O I
triplet profiles to 41.6 km s-1 based on the measured widths of the 55 Cnc O I
triplet. This upper bound prevents the model from trying to fit a Gaussian to
the airglow signal rather than the stellar signal.

The stellar profiles were produced using Astropy’s Gaussian1D and Voigt1D
functions. We also include a self-reversal subcomponent to the Ly$\alpha$
profile, represented as a Gaussian absorption centered on the Voigt profile,
as its exclusion can result in an overestimation of the underlying stellar
Ly$\alpha$ flux (Youngblood et al., 2022). The FWHM of this absorption
component is fixed at 47% of the Gaussian FWHM of the Voigt profile. For FGK
stars, the absorption depth is fixed at 50%. These fixed values were selected
to produce self-absorbed profiles that are qualitatively similar to solar
Ly$\alpha$ profiles across a range of typical Gaussian FWHM values that were
observed in fits to stellar profiles. For M dwarfs, we determined that a
shallower absorption depth of 35% was more appropriate based on Kapteyn’s
Star. With a radial velocity of 245 km s-1, the Ly$\alpha$ profile of
Kapteyn’s Star is shifted away from both the contaminating airglow and the ISM
absorption, allowing for a rare view at the shape of the stellar Ly$\alpha$
profile (Guinan et al., 2016; Youngblood et al., 2016, 2022).

The second model component is the ISM attenuation for Ly$\alpha$. This
component includes attenuation from both hydrogen and deuterium. While ISM
attenuation can be present in the O I lines, this feature is only seen in a
few stars within our sample and is not generally applicable. The free
parameters for the ISM model component are the hydrogen column density and the
radial velocity of the ISM. There is a known degeneracy between the column
density and the Doppler b parameter (Silva et al., 2018). Because accurate ISM
parameters are not a priority of our fits, for simplicity we fix the Doppler b
parameter to 11.5 km s-1 for Ly$\alpha$. This value is based on typical values
from local ISM observations, and the bounds for the column densities and ISM
radial velocities were also based on the range of typically observed values
(Wood et al., 2004, 2005; Redfield & Linsky, 2004).

An optical depth profile is created using these ISM parameters, where the
absorption cross section is modeled by a Voigt function (Harris, 1948). The
deuterium column density is determined as the hydrogen column density
multiplied by the $D/H$ ratio. For this work, $D/H=1.5\times 10^{-5}$ was used
(Linsky, 1998; Hébrard & Moos, 2003; Linsky et al., 2006). The optical depths
of hydrogen and deuterium are added together to produce a final Ly$\alpha$
optical depth ($\tau$), and the underlying stellar emission is multiplied by
$e^{-\tau}$ to create the ISM attenuated stellar emission.

Finally, the modeled profile is then convolved with the COS Line Spread
Function (LSF) that corresponds to the LP that the stellar data was observed
with. Because the coadded spectra can be created from observations of multiple
Cenwaves, we utilize the Cenwave 1291 LSF for the given LP. These LSFs were
obtained from
STScI.444https://www.stsci.edu/hst/instrumentation/cos/performance/spectral-
resolution

Parameter Name | Lower Bound | Upper Bound
---|---|---
Stellar
Gaussian | 0.0 | N/A (Ly$\alpha$)
FWHM (km/s) | 41.6 (O I)
Lorentzian | 0.0 (Ly$\alpha$) | N/A
FWHM (km/s) | N/A (O I)
ISM
Column Density | 17.1 (Ly$\alpha$) | 19.1 (Ly$\alpha$)
($10^{x}$ cm-2) | N/A (O I) | N/A (O I)
ISM Velocity | -50.0 (Ly$\alpha$) | 50.0 (Ly$\alpha$)
(km/s) | N/A (O I) | N/A (O I)
Airglow
Airglow | -1.5 | 1.5
Shift (Å)
Airglow | 0 | 10
Scale Factor

Table 2: Upper and lower bounds for the model parameters which are bounded.

The final model component is the airglow template, where the appropriate
template developed in Section 2.2 is added onto the convolved stellar (and ISM
attenuated, if appropriate) emission. The two parameters of this model
component are a wavelength shift and a scale factor to the template,
accounting for changes in the location and amplitude of the profile. The
airglow template is subtracted from stellar data in order to produce a
recovered profile. The error of the airglow template and the error of the COS
data are added in quadrature, producing the error of the recovered profile.
Bounded parameter limits are shown in Table 2.

###  3.3 The Stellar Emission Recovery Tool

A GUI was developed to combine the model components, simultaneously fitting
for the underlying stellar emission, the attenuating ISM, and the
contaminating airglow (Cruz Aguirre et al., 2022). We explored an alternate
model which performs a second fit after the airglow was removed,
simultaneously fitting the stellar and ISM components to the recovered profile
which reflects the errors in the airglow subtraction. We found that there were
no significant differences in the best fit parameters between the two fitting
methods. We also explored manual placement of the airglow template on the
subset of stars with both COS and STIS observations, and found that this also
did not produce a significantly different fit. All airglow subtractions
presented in this work were done by simultaneous fitting of all available
model components for each emission line.

The GUI takes in x1d COS G130M files or output ascii files produced from the
coaddition process described in Section 2.1, automatically searching the data
header for the target name, the LP, and detector Segment(s) used during the
observation. The user is prompted for this information if it cannot be
obtained from the input file. The GUI optionally takes in x1d STIS G140M or
E140M files for the purpose of making visual comparisons with STIS data. The
GUI currently does not support stellar reconstructions on STIS data.

After selecting which emission line to remove airglow from, the user must then
input the radial velocity of the star as an initial guess for the models. For
this work, nearly all radial velocities were obtained from the SIMBAD
astronomical database.555http://simbad.u-strasbg.fr/simbad/ The user must also
input an initial guess for the ISM velocity. We calculated ISM velocities
using the Local ISM (LISM) Kinematic Calculator (Redfield & Linsky,
2008).666http://lism.wesleyan.edu/LISMdynamics.html We input the Right
Ascension (RA) and Declination (Dec) of the target star into the Kinematic
Calculator, which results radial velocities of clouds in the LISM. We
calculate a weighted average of radial velocities of clouds in the line of
sight, and if there are no such clouds then we calculate the weighted average
of nearby ($<20^{\circ}$) clouds.

Four sliders are available to make adjustments to the fit. The primary two
sliders allow the user to provide initial guesses to the airglow template
shift and scale factor. The secondary two sliders allow for an overall
wavelength shift to the total fit which shifts all of the individual
components, and an overall scale factor to the best fit which scales all of
the individual components. This can serve as a guide for determining initial
guesses for the airglow parameters. The user also has direct control over the
wavelength range in which the fit is performed on, which then corresponds to
the integration region when calculating integrated fluxes. While other model
parameters cannot be accessed by the user, their initial guesses and parameter
ranges have been selected such that the model is generally stable and widely
applicable to COS stellar spectra.

Once a model is fit to the data, the user has the ability to display
individual model components along with the fit and the COS data, the best fit
parameters and 1$\sigma$ parameter errors, and fit statistics such as
$\chi^{2}$ and the Bayesian Information Criterion (BIC). The user can then
view the normalized residuals, $[(Fit-Data)/(Data$ $Error)]^{2}$, plotted
against wavelength. This serves as a useful diagnostic for locating data
points with unusually small error bars than undesirably drive the best fit,
and the user has the ability to remove these points through the use of a
residual cutoff value. The model is then run again to generate a new best fit.
If STIS G140M or E140M data is loaded, the user can compare the recovered
profile to the STIS data. An additional window becomes available to scale the
STIS data to the COS data for a visual inspection of the two profiles. The
integrated attenuated fluxes are also reported as another metric of
comparison.

When the ‘Remove Airglow’ button is pressed, the airglow component of the
current best fit is subtracted from the COS data. A result plot and a
diagnostic plot (see Figures A10 and A11, respectively) are then produced and
can be saved by the user. If the user desires, a bootstrap of this best fit
can then be run following the method described in Section 3.3.1. This process
is then repeated for all of the available airglow lines, and the final
recovered spectrum can be saved as a CSV file. A second CSV file is
automatically generated which contains all of the user inputs that led to the
saved recovered spectrum, along with best fit parameters and their errors for
the selected model.

Figure 6: The results of the Ly$\alpha$ airglow subtraction for GJ 876
produced by the airglow removal tool (see Section 3.3). The upper left plot
compares the overall fit to the COS data, the upper right plot breaks the fit
down to its constituents (SR = self reversal), the lower left plot displays
the STIS spectrum when available, and the lower right plot compares the
recovered COS spectrum to the model’s recovered spectrum, and to a scaled STIS
spectrum when available.

Figure 7: The results of the O I 1305 airglow subtraction for $\kappa^{1}$
Ceti produced by the airglow removal GUI. The descriptions of the subplots are
given in Figure 7. The Si II 1304 line is present in both COS and STIS data,
however it does not significantly affect fitting the O I 1305 line.

####  3.3.1 Residual Resampling Circular Block Bootstrap

The LMFIT fitting routine does not always report 1$\sigma$ errors for the
fitted parameters. This can happen for a number of reasons, such as a
parameter remaining stuck at an upper or lower bound, or if varying the
parameter does not influence the fit, remaining stuck at its initial guess.
Even when parameter errors are reported, these may not accurately represent
the underlying parameter distributions. The authors of LMFIT recommend using
the reported errors as initial estimates, and to conduct a more thorough
exploration of the parameter space.777https://lmfit.github.io/lmfit-
py/index.html We perform this exploration through residual resampling circular
block bootstrapping (RRCBB). The details of this technique are described in
Appendix A. The user has the option of running the bootstrap in order to
generate a 1$\sigma$ confidence interval of the LMFIT best fit parameters and
the integrated stellar flux. We utilized this bootstrapping technique for all
available emission lines for every star in our sample.

###  3.4 Validation of the Method

Using the methodology described in Section 3.3, we remove the airglow
contribution from Ly$\alpha$ and the O I triplet, recovering the stellar
profiles for the subset of stars where both COS and STIS data were available.
The recovered COS profiles were then compared to the STIS spectra, where
airglow is already removed by the CALSTIS pipeline. Examples of these
recovered spectra are shown in Figures 7 and 7.

####  3.4.1 STIS Comparison

A version of our airglow subtraction model was created to fit the stellar,
self reversal, and ISM components to STIS/G140M and STIS/E140M Ly$\alpha$
profiles. This allowed for a better comparison between the best fit parameters
of both instrument datasets. Additional STIS LSFs were obtained from STScI for
the G140M and E140M gratings for use with the modified model.

The modified Ly$\alpha$ reconstruction model was run on 21 G140M spectra and 7
E140M spectra, totaling to 28 stars. The results of these reconstructions were
then compared to those of the recovered COS profiles. A STIS/E140M comparison
is shown as an example in Table 3. Of these 28 stars, there were 18 successful
COS stellar recoveries. Of these 10 failed recoveries, four failed due to
poorly fitted ISM parameters, while the remaining six failed due to an overall
poor fit to the data (See Section 3.5 for further explanation on what can
cause a failed recovery).

We note that there can occasionally be large discrepancies between COS and
STIS integrated fluxes. This can partially be attributed to variation over a
stellar activity cycle. COS and STIS observations were not always taken at
similar times; observations taken at different points in the stellar cycle can
result in different observed fluxes. This is observed in the solar cycle,
where the Ly$\alpha$ flux at solar maximum is $\sim$1.5 - 2.0$\times$ the flux
at solar minimum (Woods et al., 2020; Vidal-Madjar et al., 2003).

We also observe discrepancies in literature values for the Ly$\alpha$ flux for
a given star. One such example is Kapteyn’s Star, with a reported literature
value of $5.32\times 10^{-13}$ erg cm-2 s-1 using G130M data in Guinan et al.
(2016), while this is reported as $(2.88^{+0.16}_{-0.08})\times 10^{-13}$ erg
cm-2 s-1 in Youngblood et al. (2022) using G140M data. We also note that our
G130M value of $(5.67^{+0.46}_{-0.12})\times 10^{-13}$ erg cm-2 s-1 is similar
to that of Guinan et al. (2016), and our G140M value of
$(2.83^{+0.36}_{-0.12})\times 10^{-13}$ erg cm-2 s-1 agrees with that of
Youngblood et al. (2022). This discrepancy may partially be due to the known
slit loss of STIS observations due to sub-optimal target centering of narrow
STIS slits (See Youngblood et al. (2016); Loyd et al. (2016)). Based primarily
on the likely range of intrinsic stellar variability, and a smaller but non-
negligible contribution from flux calibration variations, we assume in this
work that Ly$\alpha$ fluxes within a factor of two are considered in
sufficient agreement.

Parameter | COS | STIS | Literature
---|---|---|---
Radial Velocity | $21.933^{+3.55}_{-3.534}$ | $12.836^{+2.571}_{-1.871}$ | $13.164$
(km/s)
Gaussian FWHM | $113.926^{+3.036}_{-3.301}$ | $117.651^{+3.518}_{-3.624}$ | $N/A$
(km/s)
Lorentz FWHM | $14.489^{+1.504}_{-1.437}$ | $18.12^{+2.163}_{-2.149}$ | $N/A$
(km/s)
Flux Amplitude | $-10.844^{+0.086}_{-0.094}$ | $-11.067^{+0.099}_{-0.087}$ | $N/A$
(erg cm-2 s-1 Å-1)
Column Density | $18.056^{+0.065}_{-0.083}$ | $18.103^{+0.057}_{-0.059}$ | $18.2^{+0.03}_{-0.03}$
($10^{x}$ cm-2)
ISM Velocity | $-12.526^{+1.8}_{-1.196}$ | $-15.531^{+0.782}_{-1.078}$ | $-17.1^{+0.8}_{-0.7}$
(km/s)
Integrated Flux | $1.13^{+0.12}_{-0.11}\times 10^{-12}$ | $8.45^{+0.98}_{-0.88}\times 10^{-13}$ | $9.5^{+0.6}_{-0.6}\times 10^{-13}$
(erg cm-2 s-1)

Table 3: The best fit results of the COS/G130M and STIS/E140M Ly$\alpha$
profiles of GJ 832. Reported parameter errors were obtained using our
bootstrapping method. See Table A2 for literature references.

####  3.4.2 Literature Comparison

In addition to comparisons between COS and STIS Ly$\alpha$ reconstructions
using the same methods, we also compare these results with values reported in
the literature. An example is shown in Table 3 which reports literature values
for the stellar radial velocity, the ISM column density, the ISM velocity, and
the Ly$\alpha$ integrated flux as observed from Earth. We primarily focus on
literature agreement for the column density and the integrated flux, however
all parameter values are reported for completeness. Again, we adopt that
fluxes within a factor of 2 were comparable.

Of the subset of 28 stars with COS and STIS Ly$\alpha$ observations, we were
able to successfully recover the COS Ly$\alpha$ profiles of 18 stars. We find
a generally acceptable agreement between the COS and STIS integrated fluxes of
these stars when compared to values reported in the literature. We find less
agreement for the column density; this is a consequence of fixing the Doppler
b parameter to compensate for the degeneracy with the column density.
Comparisons for the column density and integrated fluxes are shown in Figure
8. In 8(b), the integrated flux of GJ 1214 (leftmost G140M point) was
consistent with a non-detection, represented by the error bar extending below
the range of the log-log plot. The Ly$\alpha$ flux of GJ 1214 was not detected
in France et al. (2013) and marginally detected in France et al. (2016),
however the reconstructed emission was poorly constrained.

(a) Column Density

(b) Integrated Flux

Figure 8: Comparisons between 18 recovered COS best fit parameters (blue
points) and 28 reconstructed STIS best fit parameters (orange points for G140M
spectra, and golden points for E140M spectra) to the literature values for (a)
ISM column density and (b) integrated Ly$\alpha$ flux. Literature sources are
found in Table A2. The dashed lines in both subplots is the 1:1 line. The
shaded region in (b) represents a factor of 2 region about the 1:1 line.

###  3.5 Limitations of the Method

####  3.5.1 Si III Diagnostics

While the stellar recovery tool is capable of extracting the underlying
stellar spectrum from COS data, it does not always do so successfully. The Si
III emission line’s SNR (flux divided by flux error) is used as a metric for
determining the likelihood of the stellar recovery tool producing a reliable
recovered Ly$\alpha$ spectrum. Si III fluxes below a 3$\sigma$ detection, but
with a measured flux statistically above zero, are plotted in Figure 9 as
triangles. We define three regions of varying success. The first region (Si
III SNR $<$ 3) sees a 30% success rate, the second (3 $\leq$ SNR $<$ 28) a 50%
success rate, and the third (SNR $\geq$ 28) a 90% success rate of recovering
stellar Ly$\alpha$ emission.

Figure 9: Ly$\alpha$ recovered flux vs Si III SNR. Points on the plot are
colored and filled in the same way as plots in Section 4. We identify three
regimes of Si III SNR in which the stellar recovery tool has a 30% success
rate (SNR $<$ 3), a 50% success rate (3 $\leq$ SNR $<$ 28), and a 90% success
rate (SNR $\geq$ 28) of recovering stellar Ly$\alpha$.

We compare the recoverable Ly$\alpha$ stellar flux to the Si III SNR (Figure
9). We find the lowest recoverable flux in the 50% success region to be
$F_{Ly\alpha}=1.39\times 10^{-14}$ erg cm-2 s-1. While the lowest successfully
recovered flux observed in the entire sample was $F_{Ly\alpha}=1.28\times
10^{-14}$ erg cm-2 s-1, this star lies within the 30% success regime. For
future observations with the COS instrument, we recommend a combination of an
estimated Si III SNR $\geq$ 3 and an estimated attenuated Ly$\alpha$ flux
$\geq$ $1.39\times 10^{-14}$ erg cm-2 s-1 for a 50% minimum likelihood of
recovering and reconstructing the underlying stellar emission from the
contaminating airglow.

####  3.5.2 Gain Sag and Future Observations

Gain sag will affect the majority of COS stellar spectra in the future, making
it increasingly difficult to retrieve faint stellar spectra. Currently there
are no airglow spectra available beyond LP3. With the implementation of LP4 in
Cycle 25, the COS2025 policy was introduced with the aim of extend the science
capabilities of the COS detector to 2025 and beyond by minimizing the ever
increasing gain sag caused by geocoronal Ly$\alpha$ (Rafelski et al., 2018).

Cenwave 1222, implemented in Cycle 19 (Roman-Duval et al., 2014), places
geocoronal (and stellar) Ly$\alpha$ within the gap between detector plates.
This Cenwave prevents further gain sag while still capturing other important
nearby FUV emission lines such as Si III and N V. Due to the COS2025 policy
discouraging unnecessary airglow exposure on the detector face, pure airglow
spectra taken at LPs 4, 5, or 6 appear to be unlikely, as these, along with
LPs 2 and 3, are currently being utilized (James et al., 2022).

It may be beneficial to implement a new Cenwave purely for Ly$\alpha$ studies
with COS. Such a Cenwave should place Ly$\alpha$ in a location on the detector
which is generally free from other major FUV features amongst the various COS
settings. The Cenwave could also be used exclusively at LP1, which is
otherwise unused. The use of a dedicated Cenwave could extend the Ly$\alpha$
science output of COS without compromising its various other science
capabilities.

##  4 Recovered Emission Profiles and Stellar Activity Indicators

Of the initial 165 Ly$\alpha$ profiles and 152 O I triplet profiles where a
recovery was possible, the stellar recovery tool successfully recovered 93
Ly$\alpha$ profiles, 91 O I 1302 profiles, 112 O I 1305 profiles, and 118 O I
1306 profiles. Section 4.1 provides a discussion on why a stellar spectrum may
not be successfully recovered/reconstructed. Figure A8 breaks down the number
of successful and failed recoveries for each emission line by spectral type.

The best fit self reversed Ly$\alpha$ and stellar O I profiles were used to
calculate integrated line fluxes and line luminosities. The integrated fluxes
and luminosities were compared to various stellar activity indicators
($R^{\prime}_{HK}$, stellar rotation period, stellar effective temperature, Si
III ($\lambda=1206.51$ Å) luminosity, and N V ($\lambda=1238.82$ and $1242.80$
Å) luminosity) to produce the largest direct study of Ly$\alpha$ emission on
nearby stars.

###  4.1 Failed Recoveries

We identify 72 unsuccessful Ly$\alpha$ profile recoveries. These failures can
be divided into two categories. Category A failures are those in which the
observed profile fits in either the Definite Stellar, Strong or Weak
morphological categories (see Section 3.1), and the GUI failed to recover the
bright stellar emission. Nearly every Category A failure was due to the
effects of gain sag being too severe even for bright targets to be properly
recovered. Other reasons for Category A failures were that the throughput
decreasing effect of detector gridwire shadows were too strong, or that the
model was unable to find a solution within the allowed parameter space.
Category B failures are those whose observed profile falls under the
Questionable Stellar, Strong or Weak categories, and the GUI was unable to
properly detect, recover, or reconstruct the dim stellar signal from the
dominating airglow contamination. The effects of gain sag are also more severe
for fainter targets, resulting in nearly every failed recovery in this
category. There were 18 Category A failures and 54 Category B failures.

A failed recovery is identified if it fails one or more criteria. For the
Ly$\alpha$ profiles, the first pass of flagging failures is by their ISM
parameters. If a star’s best fit column density or ISM velocity hits an upper
or lower limit listed in Table 2, it is flagged as a failed recovery. By this
criterion, we flag 61 recoveries as failures. Most often, the upper limit of
the column density ($10^{19.1}$ cm-2) was hit. There are column densities
reported in the literature slightly larger than our upper limit, so it is
possible that an increase in our upper limit would flag these stars as
successes, although many of these instances are also associated with gain sag
which causes additional fit complications (see Section 3.5.2).

Our second pass was based on whether the model was able to visually fit the
data or not, and that the parameter errors were not unreasonably large. The
definition of a poor visual fit is admittedly subjective, but generally these
cases are flagged when the model clearly does not track with the shape of the
data. Unreasonably large parameter errors are those such that the reported
errors are several orders of magnitude larger than the best fit parameter. We
identify 20 failures through this criterion, however we do note that only two
recoveries were flagged as a failure for this reason alone, and their
inclusion would not significantly change our results.

Our final pass was based on the ratio between the Lorentzian and Gaussian
FWHMs of the Voigt profile. We found it unfeasible to customize fit components
and parameter bounds for each star due to the size of our sample, and decided
to apply the same model to every star. As a consequence, a small number of
stellar Ly$\alpha$ profiles were not well fit by a Voigt profile. If the
$(FWHM_{L}/FWHM_{G})$ ratio is very small, the flux amplitude is driven to be
larger, which is compensated by an increase in the column density. This effect
can lead to reaching the upper limit of the column density, which we observe
for $\sim$66% of failed recoveries with small Lorentzian FWHMs. It is an
indicator that the underlying Voigt profile is not performing well in modeling
the data, and is flagged as a failed recovery. We characterize the ratio as
$Y=\sqrt{ln(2)}\times(FWHM_{L}/FWHM_{G})$, and for $Y\leq 0.01$
($FWHM_{L}\lesssim 2$ km s-1) we flag the recovery as a failure. We identified
38 fits where $Y\leq 0.01$, flagging them as failed recoveries. Of these, only
7 were flagged as a failed recovery for this reason alone.

Of the 72 failed Ly$\alpha$ recoveries, one was observed with LP1, one was
observed with LP2, 17 were observed with LP3, and 53 were observed with LP4.
The LP1 star, HD 103095, was flagged as a Category A failure due to hitting
the upper ISM velocity limit. The bootstrap samples for this star also
fluctuate between two possible solutions, one of which visibly did not fit the
data. The LP2 star, KIC 11560431 is a spectroscopically resolved binary star
system, which the GUI was not designed to handle. It is marked as a Category B
failure, as both Ly$\alpha$ profiles were dim compared to the airglow. The
reasons for the LP3 and LP4 failures are primarily driven by detector gridwire
shadows and gain sag, respectively.

Of the 17 failed LP3 Ly$\alpha$ recoveries, 14 of these were part of the SNAP
14633 observing program, in which we ignored the detector gridwire shadow DQ
flag to prevent the COADD_X1D code from deweighting FP3 exposures and
significantly altering the shape of the coadded spectrum. We observe both
Category A and B failures in the SNAP stars, indicating that the gridwire
shadow is affecting the GUI’s ability to recover even bright stellar emission.
This throughput diminishing effect was more prevalent than we anticipated, and
these flags should be ignored with caution in the future. Detector gridwire
shadow flags were also found and ignored for two non-SNAP stars, GJ 581 and
2MASSJ02543316-5108313, which both resulted in Category B failures. The final
LP3 failure was GJ 1214, another Category B failure. The stellar spectrum of
this star was dim enough that stistools was unable to locate the spectrum. A
manual extraction was also impossible, as the stellar spectrum location in the
2D detector image was unclear. The Si III fluxes of GJ 1214 also indicates
that the Ly$\alpha$ flux is either very dim or nondetectable, consistent with
previous work (e.g., France et al., 2013, 2016).

Of the 53 failed LP4 Ly$\alpha$ recoveries, 49 were targets flagged with gain
sag. We determined that the effects of gain sag were most significant in FP3
data, and our coadditions do not include these spectra. The remaining data can
still display significant gain sag effects, and this is the primary cause for
failure of LP4 data. This includes both Category A and Category B failures,
however we note that stars with bright stellar emission can result in
successful recoveries despite the present gain sag. The secondary reason for
failure is due to the stellar fluxes likely being too dim or nondetectable,
based on their observed Si III fluxes. Often, both effects are seen together
in the available LP4 data.

For a handful of targets, the stellar signal is low due to the large distances
($d_{*}\gtrsim 50$ pc) to the targets. There is a subset of failed LP4
recoveries which did not suffer from gain sag, and are $\gtrsim 80$ pc away.
These were all F type stars, with no reported $R^{\prime}_{HK}$ or $P_{rot,*}$
in the literature. We note that it may be possible for the H I column density
to exceed our upper limit of $10^{19.1}$ cm-2 along certain lines of sight at
these distances, however in general we do not expect a column density larger
than this limit. While raising this upper limit could result in a successful
recovery, the dimmer stellar emission at these distances combined with
stronger ISM attenuation works against a successful recovery. Because it is
unclear whether distance or an unusually large column density results in these
failures, the upper limit is kept at $10^{19.1}$ cm-2 based on typical values
reported in the literature.

There were 61 failed O I 1302 recoveries, 40 failed O I 1305 recoveries, and
34 failed O I 1306 recoveries. The primary reason for these failures was that
the stellar emission is too dim to be recovered, and is lost in the noise
after the airglow subtraction. Occasionally, the GUI also fails by reporting a
very small Gaussian FWHM, resulting in a narrow profile which, when convolved
with the COS LSF, can appear to fit the COS data. For O I 1302, ISM
attenuation is possible. We did not include this in our models as it is
generally not the case that the ISM velocity and the stellar velocity
coincide. It is possible that the larger number of failed O I 1302 profiles
due to dim stellar emission is related to the ISM obscuring what little
stellar signal is present.

###  4.2 $R^{\prime}_{HK}$ and Ly$\alpha$ Luminosity

The $R^{\prime}_{HK}$ index is a chromospheric activity index which measures
the strength of the narrow Ca II H ($\lambda=3968.47$ Å) and K
($\lambda=3933.66$ Å) resonance emission lines without contamination from the
surrounding broad photospheric absorption lines, allowing for comparison
between spectral types (Noyes et al., 1984). These chromospheric emission
lines have a formation temperature of $\sim$6,000K (Vernazza et al., 1981).
$R^{\prime}_{HK}$ is known to correlate well with various chromospheric and
transition region lines such as Ly$\alpha$ (Soderblom & Clements, 1987;
Youngblood et al., 2017; Melbourne et al., 2020a). We compared literature
$R^{\prime}_{HK}$ values to the reconstructed Ly$\alpha$ luminosity normalized
by the bolometric luminosity of the star (Figure 10). The bolomeric luminosity
is calculated as $L_{bol}=4\pi R_{*}^{2}\sigma_{SB}T_{eff,*}^{4}$, where
literature values were obtained for the stellar radius ($R_{*}$) and the
stellar effective temperature ($T_{eff,*}$). For the remainder of this work,
we primarily make comparisons with normalized luminosity ratios, as they allow
for a better comparison of stellar activity between spectral types (France et
al., 2018; Melbourne et al., 2020a).

Figure 10: Reconstructed Ly$\alpha$ luminosity normalized by stellar
bolometric luminosity vs $R^{\prime}_{HK}$ index. Stars are colored by
spectral type. A filled marker represents a successful recovery, while an
empty marker represents a failed recovery. Subplots are divided by spectral
type. F-type stars are grouped with G-type stars. Best fit lines are shown as
a solid line, only considering successful recoveries. The grey region about
the best fit line is the factor of 2 region (See Section 3.4.1). This
convention remain consistent for the remainder of this work. A comparison is
made to M dwarfs studied in Melbourne et al. (2020a). A best fit line and
Spearman statistics are calculated for comparison.

We fit power laws to the data using SciPy’s Orthogonal Distance Regression
(ODR) method (Virtanen et al., 2020), which considers the data uncertainties
in both variables when determining the best fit slope and intercept in log-log
space. We calculate separate power law fits to each spectral type, as their
best fit parameters differed significantly. F-type stars are grouped with
G-type stars, as there were not enough successfully recovered F-types to
justify a separate fit.

For each line of best fit in Figure 10, we report the Spearman rank
coefficient ($\rho$), a measure of the monotonic relation between the X data
and the Y data. A $\rho$ that approaches $\pm 1$ means that the quantities
approach a perfect positive or negative monotonic correlation. Below the
correlation coefficient is the value $n$, the probability that the X and Y
data do not have a monotonic correlation and the data happens to exhibit a
correlation that is at least as strong as the reported $\rho$.

Throughout the remainder of this work, several Spearman correlation
coefficients will be shown. We assign correlation strengths as follows: very
weak correlations ($0.00<|\rho|\leq 0.19$), weak correlations
($0.20\leq|\rho|\leq 0.39$), moderate correlations ($0.40\leq|\rho|\leq
0.59$), strong correlations ($0.60\leq|\rho|\leq 0.79$), and very strong
correlations ($0.80\leq|\rho|<1.00$).

We compare the M dwarfs between our sample and that of Melbourne et al.
(2020a) to check for consistency with previous studies. This is shown in the
bottom subplot of Figure 10. We omit the outlier LP247-13 from the literature
dataset, and recalculate the fit using the ODR method. We find good agreement
between the two M dwarf datasets. A summary of best fit parameters and
Spearman statistics are given in Table 4.

We find a very strong correlation between the normalized Ly$\alpha$ luminosity
ratio and the $R^{\prime}_{HK}$ Index for M dwarfs, a strong correlation is
observed for the K dwarfs, and a moderate correlation is observed for FG
dwarfs. While we observe a strong correlation for M dwarfs, we also note that
the normalized Ly$\alpha$ luminosity ratio increases slowly over a wide range
of $R^{\prime}_{HK}$ values. While $R^{\prime}_{HK}$ is a very strong
predictor of Ly$\alpha$ emission of M dwarfs, the shallow slope suggests that
the formation location of these emission features within the stellar
atmospheres of M dwarfs are not strongly coupled.

While we observe a weaker correlation for K dwarfs, we also find a steeper
slope, indicating that Ca II and H I emission in the atmospheres of K dwarfs
are more strongly coupled. The FG dwarfs in our stellar sample do not span as
wide a range of $R^{\prime}_{HK}$ values as K and M dwarfs, while also
spanning a similar range of normalized Ly$\alpha$ luminosity. This grouping of
similar stars in this parameter space makes physical interpretations
difficult. The observed correlation of the FG dwarfs is set by the four stars
with the largest $R^{\prime}_{HK}$ values in the upper subplot of Figure 10
(from right to left, HD 62850, HD 25825, HD 36767, and HD 150706), and
removing these results in a weak Spearman correlation coefficient of 0.29,
with a relatively large 1.04$\times 10^{-1}$ probability of no correlation.
The clustering of F, G, and K dwarfs is discussed in more detail in Section
4.6.

Fit Type | $\alpha$ | $\beta$ | $\rho$ | n
---|---|---|---|---
FG-Types | 2.65$\pm$0.46 | 8.04$\pm$2.27 | 0.46 | 5.22e-3
K-Types | 1.59$\pm$0.27 | 2.81$\pm$1.28 | 0.61 | 1.50e-3
M-types | 0.62$\pm$0.11 | -1.31$\pm$0.50 | 0.86 | 1.54e-5
Melbourne et al. 2020 | 0.66$\pm$0.11 | -1.04$\pm$0.50 | 0.76 | 8.22e-6

Table 4: Best fit parameters for the equation
$log_{10}(L_{Ly\alpha}/L_{bol})=\alpha$ $\times$ $log_{10}(R^{\prime}_{HK})$
\+ $\beta$, along with Spearman rank coefficients and probabilities of no
correlation. The Melbourne et al. (2020a) parameters apply only to M dwarfs.

###  4.3 Stellar Rotation Period and Ly$\alpha$ Luminosity

Fit Type | $\alpha$ | $\beta$ | $log_{10}(P_{rot,sat})$ | $\rho$ | n
---|---|---|---|---|---
FGK-types (L) | -0.66$\pm$0.20 | -4.01$\pm$0.29 | - | -0.21 | 1.56e-1
M-types (LS) | -0.67$\pm$0.04 | -3.37$\pm$0.07 | 0.63$\pm$0.08 | - | -

Table 5: Best Fit parameters for the equation
$log_{10}(L_{Ly\alpha}/L_{bol})=\alpha$ $\times$ $log_{10}(P_{rot})$ \+
$\beta$ for (L). A piecewise function is used for (LS), where the two regions
are separated by the saturation period $P_{rot,sat}$. For
$log_{10}(P_{rot})>log_{10}(P_{rot,sat})$ the same equation as (L) is used,
and for $log_{10}(P_{rot})\leq log_{10}(P_{rot,sat})$ the equation becomes
$log_{10}(L_{Ly\alpha}/L_{bol})=\alpha$ $\times$ $log_{10}(P_{rot,sat})$ \+
$\beta$. The Spearman rank coefficient and probability of no correlation is
reported for the linear fit.

The stellar rotation period ($P_{rot,*}$) is known to strongly correlate with
chromospheric activity (Noyes et al., 1984). $P_{rot,*}$ is related to
differential rotation within the star, which drives magnetic heating from the
stellar dynamo, ultimately leading to stellar emission in the chromosphere,
the transition region, and the corona (Duvall et al., 1984; Wright et al.,
2011; Linsky et al., 2013). Figure 11 shows the relations between normalized
Ly$\alpha$ luminosity and $P_{rot,*}$ for M dwarfs and FGK dwarfs separately.
We do not separate the K dwarfs as in Section 4.2 as the separate fits do not
significantly differ from each other.

As stellar rotation period decreases, chromospheric activity indicators (e.g.
Ly$\alpha$, X-ray emission) of FGKM dwarf stars reach a saturation point
(Fleming et al., 1993; Pizzolato et al., 2003). The normalized luminosity in
the saturated regime becomes independent of spectral type (e.g., Pizzolato et
al., 2003; Wright et al., 2011; Newton et al., 2017; France et al., 2018).
While the luminosity ratio in the saturated regime is the same for different
spectral types, departure from the saturated regime occurs at different
$P_{rot,*}$ (Pizzolato et al., 2003; Katsova, 2020). As stellar mass
increases, the critical rotation period which separates the saturated and
unsaturated regimes ($P_{rot,sat}$) decreases (Nizamov et al., 2017; Katsova,
2020).

There is not enough stellar diversity of FGK dwarfs in our sample (that had
reported $P_{rot,*}$ in the literature) to properly determine when these
spectral types reach the saturation point, so a power law fit was used. For
the M dwarfs, a saturated fit was possible and is shown below the FGK dwarfs.
The saturated fit was calculated using the Differential Evolution (DE)
algorithm available through SciPy (Virtanen et al., 2020).

Figure 11: Reconstructed Ly$\alpha$ luminosity normalized by stellar
bolometric luminosity vs stellar rotation period. Saturation was only seen for
M dwarfs in our sample. The Spearman statistics are relevant only to FGK
dwarfs.

We summarize the saturated and linear fits in Table 5. We find a weak
correlation (-0.21) between the normalized Ly$\alpha$ luminosity ratio and
stellar rotation period for our FGK dwarfs. This is due to most of these stars
occupying a narrow range of rotation periods in log space (1.25 $\lesssim
log_{10}(P_{rot,*})\lesssim$ 1.75), unlike the M dwarfs which span a larger
range. Further discussion on this is provided in Section 4.6.

The slopes ($\alpha$) in the unsaturated regime of the FGK and M dwarf fits
are found to be -0.66$\pm$0.20 and -0.67, respectively, indicating that the
rate at which activity from the stellar dynamo decreases is similar for FGKM
dwarfs. The offset between the two populations in the unsaturated regime (the
difference in $\beta$) indicates that the higher mass FGK stars depart from
the saturated regime at shorter rotation periods than M dwarfs, as we expect.
We see this departure for the M dwarfs at $P_{rot,sat}$=4.27$\pm$0.79 days. We
made additional DE saturated fits to M dwarfs against Si III and N V emission,
and see similar departures at 5.89$\pm$0.27 and 8.32$\pm$0.57 days,
respectively. With additional observations of M dwarfs with rotation periods
between $\sim$2 - 20 days, a more precise $P_{rot,sat}$ could be measured for
Ly$\alpha$, Si III, and N V saturation.

In Loyd et al. (2021), the value of $P_{rot,sat}$ is simultaneously fit for
several FUV surface fluxes of M dwarfs, and was found to be $\sim$7.01 days.
We convert the reconstructed Ly$\alpha$, Si III, and N V fluxes of the M
dwarfs in our sample to surface fluxes, and find saturation periods of
3.98$\pm$0.73, 6.92$\pm$0.27, and 8.91$\pm$0.62 days, respectively. For the
FGK dwarfs, we also convert the reconstructed Ly$\alpha$ fluxes to surface
fluxes and compare these with the study of Ly$\alpha$ fluxes recovered from
echelle-mode STIS data from Wood et al. (2005). For the region of overlap in
rotation period between the two data sets, we find good agreement between our
best fit results.

###  4.4 Effective Temperature and Ly$\alpha$ Luminosity

It has been shown that stellar effective temperature ($T_{eff,*}$) can be used
to roughly predict the Ly$\alpha$ flux of a star (Linsky et al., 2013). We
expect that normalized Ly$\alpha$ luminosity will also display a correlation
with $T_{eff,*}$, and is shown in Figure 12. All spectral types are considered
when calculating this power law fit. With a Spearman rank coefficient of -0.58
and a probability $1.85\times 10^{-9}$ of no correlation, the two data sets
exhibit a moderate correlation. The large spread of normalized Ly$\alpha$
luminosity at a given $T_{eff,*}$ observed in Figure 12 is due to variations
in stellar activity at a given $T_{eff,*}$ (Linsky et al., 2013). For the
equation $log_{10}(L_{Ly\alpha}/L_{bol})=\alpha$ $\times$ $T_{eff,*}$ \+
$\beta$, we find that $\alpha$=(-3.91$\pm$0.38)$\times 10^{-4}$ and
$\beta$=-2.87$\pm$0.19 are the best fit parameters.

Figure 12: Reconstructed Ly$\alpha$ luminosity normalized by stellar
bolometric luminosity vs stellar effective temperature.

###  4.5 Line Luminosities

Chromospheric and transition region emission lines such as Ly$\alpha$, Si III,
N V, and the O I triplet, are expected to strongly correlate with each other
(e.g., Landsman & Simon, 1993; Linsky et al., 2013; Youngblood et al., 2017;
Melbourne et al., 2020a). These emission features all arise from dynamo driven
magnetic heating (See Section 4.3). Si III and N V are transition region
emission lines with formation temperatures of $\sim$50,000 K and $\sim$160,000
K, respectively (Dere et al., 1997; Landi et al., 2012). Integrated fluxes of
Si III and N V were calculated from the same COS coadded spectra developed in
Section 2.1. The fluxes of the individual N V emission lines were summed
together, and all N V fluxes and luminosities hereafter represent combined
emission unless otherwise stated. For this work, we only consider 3$\sigma$
detections of Si III and N V fluxes for comparison with Ly$\alpha$ and O I,
unless otherwise stated. The nearby Si II ($\lambda=$ 1304 Å) did not
interfere when calculating O I 1305 integrated fluxes (See Figure 7 for their
spectral locations).

####  4.5.1 Si III and Ly$\alpha$ Luminosities

Figure 13: Reconstructed Ly$\alpha$ luminosity vs Si III luminosity, both
normalized by stellar bolometric luminosity. M-types are separated from FGK-
types, and a comparison is made to M-types studied in Youngblood et al.
(2017).

Figure 13 compares Si III normalized luminosity and the reconstructed
Ly$\alpha$ normalized luminosity. We separate the M dwarfs from FGK dwarfs as
the y-intercept differs. This correlation is found to be very strong in
Youngblood et al. (2017) for M dwarf surface fluxes of Si III and
reconstructed Ly$\alpha$, and we expect a similar correlation for our FGK and
M dwarfs. The power law parameters and Spearman statistics are reported in
Table 6. We find a strong correlation for M dwarfs, and a moderate correlation
for FGK dwarfs.

There is a noticeable gap in our sample ranging from $-6.5\lesssim
log_{10}(L_{SiIII}/L_{bol})\lesssim-5.8$, with few stars within it. This gap
in parameter space is attributed to an observational bias, discussed in
further detail in Section 4.6. The stars above the gap ($\gtrsim-5.8$) are the
same stars that appear in the saturated regime of Figure 11, while stars below
the gap ($\lesssim-6.5$) appear in the unsaturated regime. Five stars are
located within this gap, three G dwarfs (HD 62850, HD 150706, and HD 25825)
and two F dwarfs (HD 24636 and HD 39755). The two F dwarfs and HD 62850 did
not have reported rotation periods in the literature. The remaining two G
dwarfs are the two fastest rotating G dwarfs in Figure 11, with $\sim$6 day
rotation periods. While we do not have enough stellar diversity of rapidly
rotating F and G dwarfs to definitively say that these stars are in the
saturated regime or not, Figure 13 suggests that these F and G dwarfs are near
the saturation limit for their spectral types.

The slopes of the FGK and M fits are consistent with each other, however their
y intercepts differ at the 1$\sigma$ level, with the M dwarfs located slightly
above the FGK dwarfs. This is similar to the observed difference in intercepts
in Figure 11. It is possible that the M dwarfs are exhibiting Ly$\alpha$
saturation with Si III, similar to saturation with $P_{rot,*}$, and the
difference in intercept indicates that the spectral types depart saturation at
different $log_{10}(L_{SiIII}/L_{bol})$. Additional observations of stars
within $-6.5\lesssim log_{10}(L_{SiIII}/L_{bol})\lesssim-5.8$ are needed to
better interpret this result.

Fit Type | $\alpha$ | $\beta$ | $\rho$ | n
---|---|---|---|---
FGK-Types | 0.37$\pm$0.08 | -2.34$\pm$0.56 | 0.46 | 1.31e-4
M-types | 0.45$\pm$0.08 | -1.27$\pm$0.53 | 0.77 | 6.81e-5

Table 6: Best Fit parameters for the equation
$log_{10}(L_{Ly\alpha}/L_{bol})=\alpha$ $\times$ $log_{10}(L_{SiIII}/L_{bol})$
\+ $\beta$. The Spearman rank coefficients and probabilities of no correlation
are reported.

####  4.5.2 N V and Ly$\alpha$ Luminosities

We compare Ly$\alpha$ normalized luminosity to the combined N V normalized
luminosity, show in Figure 14. For M dwarfs, Youngblood et al. (2017) finds a
very strong correlation between surface fluxes of combined N V and
reconstructed Ly$\alpha$, and we expect to see a similar correlation for our
sample. Similar to Figure 13, a gap is present between $-6.25\lesssim
log_{10}(L_{NV}/L_{bol})\lesssim-5.95$ for the same reasons as with Si III. We
do not separate the M dwarfs as in Section 4.5.1 due to the two fits were
consistent with each other, indicating that the conditions in which these
emission features form is similar across the four spectral types. For the
equation $log_{10}(L_{Ly\alpha}/L_{bol})=\alpha$ $\times$
$log_{10}(L_{NV}/L_{bol})$ \+ $\beta$, we find the best fit parameters to be
$\alpha$=0.57$\pm$0.04 and $\beta$=-0.59$\pm$0.33. We observe a very strong
correlation with a Spearman correlation coefficient of 0.84 and a 2.37$\times
10^{-14}$ probability of no correlation.

Figure 14: Reconstructed Ly$\alpha$ luminosity vs N V luminosity, both
normalized by stellar bolometric luminosity.

####  4.5.3 OI Luminosities

Figure 15 displays the correlation between the normalized luminosities of the
recovered O I triplet and normalized luminosities of reconstructed Ly$\alpha$,
Si III, and N V, respectively. The recovered flux of individual oxygen lines
are summed together. The number of summed O I lines determines the marker
shape in Figure 15.

O I triplet emission originates in the chromosphere, the same region where the
Ly$\alpha$ emission originates. We expect to see these two to strongly
correlate. For the comparison between O I and Ly$\alpha$, only stars that saw
successful recoveries for both Ly$\alpha$ and O I were considered when
determining the correlation and the line of best fit. Si III and N V are
transition region lines, however as mentioned in Section 4.3, dynamo driven
magnetic heating gives rise to the flux in both regions of the stellar
atmosphere. We observe strong or very strong correlations between these
various chromospheric and transition region emission lines, and the best fit
lines and Spearman statistics for each luminosity comparison is summarized in
Table 7.

Fit Type | $\alpha$ | $\beta$ | $\rho$ | n
---|---|---|---|---
O I - Ly$\alpha$ | 1.30$\pm$0.14 | -0.40$\pm$0.72 | 0.71 | 2.80e-9
O I - Si III (FG) | 0.59$\pm$0.05 | -2.77$\pm$0.34 | 0.76 | 4.86e-9
O I - Si III (KM) | 0.81$\pm$0.08 | -1.00$\pm$0.59 | 0.91 | 2.03e-13
O I - N V | 0.63$\pm$0.05 | -2.08$\pm$0.40 | 0.82 | 3.18e-11

Table 7: Best Fit parameters for the equation
$log_{10}(L_{OI}/L_{bol})=\alpha$ $\times$ $log_{10}(L_{UV}/L_{bol})$ \+
$\beta$, where UV = Ly$\alpha$, Si III, or N V. Spearman rank coefficients and
probabilities of no correlation are reported.  Figure 15: Recovered O I
triplet luminosity vs reconstructed Ly$\alpha$ luminosity (top left), Si III
luminosity (right), and N V luminosity (bottom left), all normalized by
stellar bolometric luminosity. Sums of all three O I lines are represented as
circular markers, sums of two are represented as diamond markers, and a single
line is represented as an X marker. Si III is split between FG and KM dwarfs
and share X and Y axes.

We successfully recover a similar number of FGK O I profiles as we do
Ly$\alpha$ profiles, however we do not successfully recover as many M dwarf O
I profiles as with Ly$\alpha$. Due to the few recovered M dwarfs, we group
them with K dwarfs. We find no significant difference in separating FG and KM
dwarfs for the Ly$\alpha$ and N V power law fits, however we do find a
difference for Si III in both slope and intercept. As with the Ly$\alpha$
comparison between Si III and N V, we see a gap structure when comparing O I
to Si III and N V. With more observations of dwarf stars in the range
$-6.5\lesssim log_{10}(L_{SiIII}/L_{bol})\lesssim-5.8$ would allow for
determining if FG and KM dwarfs truly follow separate trend lines.

###  4.6 The Narrow Range of F, G, and K Dwarfs in the COS Data Archive

Of all four spectral types, only F dwarfs resulted in more failed Ly$\alpha$
recoveries than successful ones. The causes for failure are a mixture of the
effects of gain sag, detector gridwire shadow, and weak stellar signals due to
the large distances to these stars (See Section 4.1). Even if we were able to
recover more F dwarf profiles, very few had reported $R^{\prime}_{HK}$ and
$P_{rot,*}$ in the literature. It would be impossible to properly sample both
the saturated and unsaturated regimes for F dwarfs with the currently
available COS data alone.

The G-type stars in our sample are mostly limited to low activity stars, with
narrow ranges of $P_{rot,*}$ ($\sim$ 15 to 38 days, i.e,. the unsaturated
regime) and $log_{10}(R^{\prime}_{HK})$ ($\sim$ -5.1 to -4.7) as seen in
Figures 11 and 10, respectively. Of the G dwarfs in Figure 11, 76% were
obtained from the SNAP 14633 observing program, which observed G and K-type
exoplanet host stars in the solar neighborhood (France et al., 2018).
Exoplanet detection techniques have an observational bias for low-activity,
and often slowly rotating, stars (Vanderburg et al., 2016; France et al.,
2018).

There are four G dwarfs in our sample with more rapid ($\lesssim$ 10 day)
rotation periods, however these were observed only using Segment A to protect
the COS detector from these bright targets, and Ly$\alpha$ could not be
observed. A sample of nearby, active G dwarfs observed with COS does not
currently exist because this region of parameter space is best explored with
STIS, which can readily observe these bright targets. Outside of the solar
neighborhood, it would be possible to observe faint, active G dwarfs with COS
to begin to sample the saturated regime, however the effects of gain sag will
strongly work against successfully recovering these stellar profiles.

The K dwarfs in our sample come from a variety of observing programs. While
they do cover larger stellar activity spaces than G dwarfs, we still do not
see enough stellar diversity to properly sample the saturated regime. The K
Dwarf Advantage (GO 15955) surveys several K dwarfs that may begin to sample
the saturated regime. Literature values of $R^{\prime}_{HK}$ and $P_{rot,*}$
were unavailable for many of these stars. Severe gain sag is also prevalent in
the Ly$\alpha$ profiles, largely the result of these stars being observed
recently, when the COS detector sensitivity at airglow wavelengths have been
completely depleted.

##  5 Conclusions

Ly$\alpha$ and O I triplet fluxes serve as tracers of the stellar activity of
F, G, K, and M dwarfs. These fluxes drive photochemistry in the atmospheres of
orbiting exoplanets, altering the chemistry and abundances of key constituents
in exoplanet atmospheres. Both Ly$\alpha$ and the O I triplet can additionally
probe the atmospheric escape of exoplanets. The heavily attenuated EUV flux,
critical for atmospheric escape models, can also be estimated from Ly$\alpha$
flux.

We have shown that the airglow which contaminates COS spectra can often be
removed, revealing the underlying stellar emission. We created templates for
the Ly$\alpha$ and O I triplet geocoronal emission lines based on observations
taken with the COS instrument at LPs 1, 2, and 3. These templates were then
used to recover the spectra on a sample of 171 archival F, G, K, and M dwarf
stars. Moderate to very strong correlations were found with stellar properties
and activity indicators.

We developed an airglow subtraction and stellar recovery tool which
simultaneously fits underlying stellar emission, attenuation from the ISM, and
airglow contamination. The tool is made available through this
https://doi.org/10.5281/zenodo.7435191 (catalog DOI) (Cruz Aguirre et al.,
2022). The comparisons to STIS data and the available literature in Section
3.4 and the subsequent analysis of the results presented in Section 4
demonstrate the capability of the stellar recovery tool to recover the
underlying stellar spectrum.

We discuss the limitations of this method and develop criteria to assist
future observers aiming to study stellar Ly$\alpha$ with the COS instrument,
recommending that estimated attenuated Ly$\alpha$ flux be greater than
$1.39\times 10^{-14}$ erg cm-2 s-1. We also recommend a Si III SNR of at least
3 for a 50% successful recovery rate, and an SNR of at least 28 for a 90%
successful recovery rate. In the future, stellar Ly$\alpha$ studies may
benefit from a dedicated Cenwave at the currently unused LP1, extending the
science capabilities of COS without compromising currently used detector
regions.

The stellar recovery tool has demonstrated its ability to separate stellar and
geocoronal signals for a majority of archival dwarf stars. This tool provides
the opportunity to make the fluxes of critical photochemical drivers available
for future investigations of exoplanet host stars with the COS instrument.

## Acknowledgements

The authors thank the anonymous referees for their thorough review of and
constructive comments on this manuscript and data products.

Support for Program number AR 15635 was provided by NASA through a grant from
the Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Incorporated, under NASA contract
NAS5-26555.

This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(project Spice Dune).

This research has made use of the NASA Exoplanet Archive, which is operated by
the California Institute of Technology, under contract with the National
Aeronautics and Space Administration under the Exoplanet Exploration Program.

The authors thank the members of the Colorado Ultraviolet Spectroscopy Program
(CUSP) for helpful feedback and discussion on the stellar recovery tool
developed for this work. Author Cruz Aguirre additionally thanks P. C. Hinton,
Daniel Sega, Adriana Valverde, and Jim Green for useful discussion.

##  Appendix A Residual Resampling Circular Block Bootstrap

Bootstrapping is a technique that can be used to estimate the underlying
distribution from which a data set is sampled. This is accomplished by
generating a number of samples from the original data set. Each individual
sample is generated by resampling with replacement. For a data set consisting
of M data points, a random value is drawn from the original data set
(resampling). Each point has equal probability of being drawn, and can be
drawn multiple times when generating a bootstrap sample (replacement). Values
are drawn until the bootstrap sample has the same length as the original data
set, and the process is repeated N times, generating N bootstrap samples of
length M. Each of these bootstrap samples will have their own statistics, such
as the sample mean. By taking the 15.865th and 85.135th percentiles of the
distribution of all bootstrap sample means, a 1$\sigma$ confidence interval is
constructed.

This idea can be extended to creating a distribution of best fit parameters
from N bootstrap samples, however the simple bootstrap is not applicable in
our case. An assumption of the bootstrap is that each point in the original
data set is independent and identically distributed. This assumption is not
true for spectral data, as there is an inherent order and structure to the
data points in a spectrum. A compromise to this is the block bootstrap, where
instead of resampling individual data points, blocks of data are resampled.
Within each block, the inherent order and structure is preserved. Blocks are
constructed with a fixed length B data points, and these blocks are resampled
with replacement in the same way, each having equal probability of being drawn
and can be drawn multiple times. There are a number of techniques to assure
that each bootstrap sample has the correct length M.

We implement a circular block bootstrap technique, in which the ordered data
in the final block will loop back to the data in the beginning of the spectrum
if M/B does not result in an integer. For example, if a data set has length
M=15 and a block length B=4 is chosen, the generated blocks would consist of
the points {1,2,3,4}, {5,6,7,8}, {9,10,11,12}, and {13,14,15,1}, where it
circles back to the first data point when constructing the final block. These
blocks could be used to generate a bootstrap sample, say of data points
{5,6,7,8,13,14,15,1,5,6,7,8,1,2,3}, where the final block {1,2,3,4} had its
final point cut off in order to keep this sample at length M.

In order to generate best fit parameter distributions, we generate circular
block bootstrap samples using the residuals of the best fit subtracted from
the stellar flux. These residuals are grouped into blocks of length B, and are
then resampled with replacement to generate N bootstrap samples. These
residual bootstrap samples are then added to the best fit profile to the
spectral data, and the LMFIT model is run on this bootstrap profile. The best
fit parameters of this bootstrap sample are then saved, and this process is
repeated for all N bootstrap samples. Parameter distributions can then be
generated, and a 1$\sigma$ confidence interval is calculated.

The accuracy of the block bootstrap depends critically on the choice of block
length B (Hall et al., 1995; Bühlmann & Künsch, 1999). We utilize the
recombinator python package to estimate the optimal block length for a
circular block bootstrap.888https://github.com/InvestmentSystems/recombinator
The optimal block length is determined using the methodology described in
Politis & White (2004); Patton et al. (2009). In the case where this method
returns a block length that results in less than 5 blocks, 1000 unique samples
cannot be generated, and the block length is decreased such that 5 blocks are
created.

In practice, N=1000 bootstrap samples are generated using an estimate of the
optimal block length B as described above. We originally chose 1000 samples as
a balance between having enough bootstrap samples to properly generate the
underlying parameter distributions and to minimize the computation time
required to generate the parameter distributions. We demonstrate that 1000
samples is sufficient by running several bootstraps on a given data set, which
all produced parameter distributions which were not significantly different
from one another.

##  Appendix B Additional Figures and Tables

LP | Start Date or Start Cycle | Notes
---|---|---
LP1 | May 2009 | All Cenwaves, All Gratings
LP2 | 07-23-2012 | All Cenwaves, All Gratings
LP3 | 02-09-2015 | All Cenwaves, All Gratings
LP4 | 10-02-2017 | All Cenwaves, All Gratings
LP5 | Cycle 29 (2021) | G130M Cenwaves 1291 and Longer
LP6 | Cycle 30 (2022) | Long ($\gtrsim$1/2 Orbit) G160M
Table A1: The Lifetime Positions of the COS FUV detector. The LP is changed
every few years to combat the effects of gain sag (James et al., 2022). No LP5
or LP6 data was available for this work. Figure A1: All Cenwave comparisons
made between the available airglow templates for LP1. Shaded regions in the
difference plots show the propagated error uncertainties.  Figure A2: Same as
Figure A1 but for LP2.  Figure A3: Same as Figure A1 but for LP3.  Figure A4:
All LP comparisons made between the available airglow templates for
Ly$\alpha$. Unless otherwise noted, all templates used in these comparisons
are the Cenwave 1291 templates. Shaded regions in the difference plots show
the propagated error uncertainties.  Figure A5: Same as Figure A4 but for O I
1302.  Figure A6: Same as Figure A4 but for O I 1305.  Figure A7: Same as
Figure A4 but for O I 1306.

Figure A8: Bar charts representing the number of successful and failed
recoveries of each contaminated emission line. Filled bars represent
successful recoveries, while empty bars represent failed recoveries.

Star | Spectral | Observing | Date of | Exoplanet | Radial Vel. | ISM Vel. | $log_{10}(N_{col,HI})$ | Ly$\alpha$ Flux | $log_{10}(R^{\prime}_{HK})$ | $T_{eff}$ | $R_{*}$ | Dist. | $P_{rot,*}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---
Name | Type | Program | First Obs. | Host? | (km s-1) | (km s-1) | (erg cm-2 s-1) | (K) | (R⊙) | (pc) | (days)
16 Cyg A | G1.5 Vb(1) | GO 13861 | 2015-10-23 |  | -27.61(2) | -6.65 |  |  | $-5.12\pm 0.188157$(83,∗) | $5830.0\pm 7.0$(95) | $1.294\pm 0.024$(102) | $21.1519\pm 0.0146$(3) | $30.0\pm 6.0$(123)
01:58:56 |  |  |  |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮
WASP-80 | K7 V-M0 V(70) | GO 14767 | 2018-07-22 | Yes | 9.82(3) | -17.47 | $19.27^{+nan}_{-nan}$(76) | $7.3^{+nan}_{-nan}\times 10^{-14}$(76) |  |  |  | $49.8591\pm 0.1155$(3) |
09:53:35 |  |  |  |  |

Table A2: For each star, the spectral type, COS observing program ID, and the
observation start date are listed. If the star is a known exoplanet host, a
“Yes” will be listed in the fourth column. Columns 6 and onward list
literature values of various quantities. All ISM velocities were calculated
using the Local ISM (LISM) Kinematic Calculator (Redfield & Linsky, 2008). The
full version of this table is available online.

1 Keenan & McNeil (1989), 2 Nidever et al. (2002), 3 Gaia Collaboration
(2018), 4 Soubiran et al. (2018), 5 Torres et al. (2006), 6 Kraus et al.
(2014), 7 Riedel et al. (2017), 8 Riaz et al. (2006), 9 Endl et al. (2006), 10
Gray et al. (2003), 11 Stephenson (1986), 12 Chubak & Marcy (2011), 13 Scholz
et al. (2005), 14 Bidelman (1985), 15 Kordopatis et al. (2013), 16 Lurie et
al. (2014), 17 Newton et al. (2014), 18 Koen et al. (2010), 19 Hawley et al.
(1996), 20 von Braun et al. (2014), 21 Schneider & Shkolnik (2018), 22 Lépine
et al. (2013), 23 Fouqué et al. (2018), 24 Kirkpatrick et al. (1991), 25
Geballe et al. (2002), 26 Houk (1978), 27 Joy & Abt (1974), 28 Walker (1983),
29 Malo et al. (2014), 30 Faedi et al. (2013), 31 Gray et al. (2006), 32 Houk
& Cowley (1975), 33 Gray et al. (2001), 34 Houk & Smith-Moore (1988), 35 Houk
& Swift (1999), 36 Montes et al. (2001), 37 Ayres (2021), 38 Cannon &
Pickering (1993), 39 Wilson & Joy (1950), 40 Montes et al. (2018), 41 Cenarro
et al. (2007), 42 Gontcharov (2006), 43 Roman (1955), 44 White et al. (2007),
45 Moore & Paddock (1950), 46 France et al. (2018), 47 Houk (1982), 48
Wittrock et al. (2017), 49 Halbwachs et al. (2018), 50 Cenarro et al. (2009),
51 Valenti & Fischer (2005), 52 Vogt et al. (2000), 53 da Silva et al. (2011),
54 Deka-Szymankiewicz et al. (2018), 55 Moutou et al. (2014), 56 Dressing et
al. (2019), 57 Frasca et al. (2018), 58 Vanderspek et al. (2019), 59 Gaidos et
al. (2014), 60 Dittmann et al. (2017), 61 Alonso-Floriano et al. (2015), 62
Terrien et al. (2015), 63 Kunder et al. (2017), 64 Pesch (1968), 65 Costa et
al. (2006), 66 Burgasser et al. (2015), 67 Richey-Yowell et al. (2022), 68
Ehrenreich & Désert (2011), 69 Anderson et al. (2014), 70 Triaud et al.
(2013), 71 Youngblood et al. (2016), 72 Waalkes et al. (2019), 73 Bourrier et
al. (2018b), 74 Villarreal D’Angelo et al. (2021), 75 Melbourne et al.
(2020b), 76 King et al. (2018), 77 Bourrier et al. (2020), 78 Edelman et al.
(2019), 79 García Muñoz et al. (2020), 80 Guinan et al. (2016), 81 Wilson et
al. (2021), 82 dos Santos et al. (2021), 83 Katsova & Livshits (2011), 84
Wright et al. (2004), 85 Herrero et al. (2012), 86 Boro Saikia et al. (2018),
87 Astudillo-Defru et al. (2017), 88 Schröder et al. (2009), 89 Suárez
Mascareño et al. (2018), 90 Henry et al. (1996), 91 Murgas et al. (2013), 92
Isaacson & Fischer (2010), 93 Jenkins et al. (2011), 94 Fossati et al. (2015),
95 Tucci Maia et al. (2014), 96 Boyajian et al. (2012), 97 Kovtyukh et al.
(2003), 98 Morales et al. (2008), 99 Bailer-Jones (2011), 100 Hinkel et al.
(2017), 101 van Belle & von Braun (2009), 102 Masana et al. (2006), 103 Muñoz
Bermejo et al. (2013), 104 McDonald et al. (2012), 105 Taylor (2003), 106
Robertson et al. (2012), 107 Anglada-Escude et al. (2014), 108 Notsu et al.
(2015), 109 Malik et al. (2019), 110 Cifuentes et al. (2020), 111 Khalafinejad
et al. (2021), 112 Bazot et al. (2011), 113 Pasinetti Fracassini et al.
(2001), 114 Newton et al. (2017), 115 Kervella et al. (2019), 116 Stassun et
al. (2017), 117 Bonfanti et al. (2016), 118 Soto & Jenkins (2018), 119 Ghezzi
et al. (2010), 120 Houdebine (2010), 121 Nielsen et al. (2013), 122 Schofield
et al. (2019), 123 do Nascimento et al. (2014), 124 Petit et al. (2008), 125
Messina et al. (2010), 126 Loyd et al. (2021), 127 Hempelmann et al. (2016),
128 Donahue et al. (1996), 129 Newton et al. (2016), 130 Newton et al. (2018),
131 Mallonn et al. (2018), 132 Suárez Mascareño et al. (2015), 133 Giacobbe et
al. (2020), 134 DeWarf et al. (2010), 135 Kovacs (2018), 136 Suárez Mascareño
et al. (2016), 137 Lovis et al. (2005), 138 Olmedo et al. (2013), 139 Marmier
et al. (2013), 140 Barnes (2001), 141 Wright et al. (2011), 142 Fischer et al.
(2002), 143 Simpson et al. (2010), 144 Howard et al. (2011), 145 Pepe et al.
(2011), 146 Santos et al. (2001), 147 Santos et al. (2002), 148 Bouchy et al.
(2009), 149 Howard et al. (2009), 150 Meschiari et al. (2011), 151 Stelzer et
al. (2016), 152 Vida et al. (2017), 153 Jaehnig et al. (2019)
∗ Error estimated based on other reported errors.
† Calculated using Ly$\alpha$ reconstruction method developed in Youngblood et
al. (2016).
‡ Upper limit based on $v$ sin $i$

Star | Emission | Radial Vel. | FWHMG | FWHML | $log_{10}(F_{amp})$ | $log_{10}(N_{col,HI})$ | ISM Vel. | Airglow Shift | Airglow | Rec. Flux | Morph.
---|---|---|---|---|---|---|---|---|---|---|---
Name | Line | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (Å) | Scale Factor | (erg cm-2 s-1) | Cat.
16 Cyg A | Ly$\alpha$ | $-27.398^{+2.412}_{-4.066}$ | $138.813^{+4.702}_{-4.283}$ | $6.665^{+2.373}_{-1.185}$ | $-10.24^{+0.224}_{-0.334}$ | $18.78^{+0.07}_{-0.103}$ | $-16.858^{+4.365}_{-0.753}$ | $-0.126^{+0.004}_{-0.001}$ | $1.731^{+0.006}_{-0.006}$ | $1.93^{+0.78}_{-0.81}\times 10^{-12}$ | QS,W
O I 1306 | $-36.221^{+5.314}_{-5.191}$ | $38.161^{+6.175}_{-22.467}$ | $-$ | $-13.547^{+0.455}_{-0.079}$ | $-$ | $-$ | $0.002^{+0.007}_{-0.007}$ | $6.43^{+0.205}_{-0.152}$ | $5.01^{+0.99}_{-0.88}\times 10^{-15}$ | ME
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮
WASP-80 | O I 1302 | $6.267^{+0.745}_{-0.655}$ | $28.825^{+2.391}_{-2.558}$ | $-$ | $-14.972^{+0.03}_{-0.029}$ | $-$ | $-$ | $0.017^{+0.012}_{-0.007}$ | $0.007^{+0.0}_{-0.0}$ | $1.42^{+0.06}_{-0.06}\times 10^{-16}$ | ME
O I 1305 | $-1.136^{+0.824}_{-0.747}$ | $19.151^{+2.829}_{-2.836}$ | $-$ | $-14.884^{+0.061}_{-0.053}$ | $-$ | $-$ | $0.034^{+0.01}_{-0.007}$ | $0.006^{+0.0}_{-0.0}$ | $1.16^{+0.05}_{-0.06}\times 10^{-16}$ | ME
O I 1306 | $3.776^{+1.519}_{-1.159}$ | $31.43^{+3.954}_{-4.82}$ | $-$ | $-15.206^{+0.057}_{-0.043}$ | $-$ | $-$ | $-0.003^{+0.013}_{-0.011}$ | $0.004^{+0.001}_{-0.001}$ | $9.07^{+0.61}_{-0.68}\times 10^{-17}$ | ME

Table A3: Best fit results for all stars where the GUI successfully recovered
the stellar emission. Fit parameters are described in Section 3.2.1. All
parameter errors were calculated from the bootstrapping technique described in
Section 3.3.1. Reconstructed stellar flux for Ly$\alpha$ and recovered stellar
flux for the O I triplet are reported after best fit parameters. The final
column (Morph. Cat.) displays the morphological category of the observed
Ly$\alpha$ and O I profiles (DS,S = Definite Stellar, Strong, DS,W = Definite
Stellar, Weak, QS,S = Questionable Stellar, Strong, QS,W = Questionable
Stellar, Weak, SD = Stellar Dominant, ME = Mixed Emission, AD = Airglow
Dominant). The full version of this table is available online.

Star Name | Observing Program | First Obs. Date | Grating Used
---|---|---|---
55 Cnc | GO/DD 12681 | 3/7/2012 | G140M
eps Eri | GO 13650 | 2/1/2015 | G140M
GJ 1132 | GO 14462 | 2/13/2016 | G140M
GO 14757
GJ 1214 | GO 13650 | 8/19/2015 | G140M
GJ 163 | GO 15071 | 7/10/2019 | G140M
GJ 173 | GO 14084 | 9/22/2016 | E140M
GJ 176 | GO 13650 | 3/3/2015 | G140M
GJ 3470 | GO 14767 | 11/28/2017 | G140M
GJ 436 | GO 13650 | 6/24/2015 | G140M
GJ 581 | GO 13650 | 8/10/2015 | G140M
GJ 667C | GO 13650 | 8/10/2015 | G140M
GJ 832 | GO 13650 | 10/10/2014 | G140M
GJ 849 | GO 15071 | 6/9/2019 | G140M
GJ 876 | GO 13650 | 7/6/2015 | G140M
HAT-P-11 | GO 14625 | 10/23/2016 | G140M
GO 14767
HD 103095 | GO 9455 | 7/19/2003 | E140M
HD 129333 | GO 12566 | 3/27/2012 | E140M
HD 189733 | GO 11673 | 4/6/2010 | G140M
GO 12920
HD 192310 | GO 12475 | 11/28/2011 | E140M
HD 209458 | GO 7508 | 8/28/2001 | G140M
GO 9064
HD 39091 | GO 15699 | 7/24/2019 | G140M
HD 39587 | GO 8280 | 10/3/2000 | E140M
HD 40307 | GO 13650 | 3/16/2015 | E140M
HD 72905 | GO 12596 | 9/25/2012 | E140M
HD 85512 | GO 13650 | 3/13/2015 | E140M
HD 97658 | GO 13650 | 2/12/2015 | E140M
KAP01 CET | GO 8280 | 9/19/2000 | E140M
Kapteyn’s Star | GO 15190 | 4/3/2019 | E140M
L 980-5 | GO 15071 | 3/17/2019 | G140M
LHS 1140 | GO 14888 | 8/17/2017 | G140M
GO 15264
LP 756-18 | GO 15071 | 8/7/2019 | G140M
TRAPPIST-1 | GO 15071 | 12/9/2018 | G140M
WASP-29 | GO 14767 | 8/9/2019 | G140M
WASP-69 | GO 14767 | 6/5/2018 | G140M
WASP-80 | SNAP 13487 | 7/14/2014 | G140M
GO 14767
Table A4: Observing program, date of first observation, and grating used for
STIS observations of stars in this study. Figure A9: The GUI developed in this
work, in the process of an airglow subtraction for GSC 08056-0482. See Section
3.2 for details on the model used by the GUI and Section 3.3 for details on
using the GUI.  Figure A10: The results of the Ly$\alpha$ airglow subtraction
for GJ 667C. Plot descriptions are the same as Figure 7.  Figure A11: The
diagnostics of the Ly$\alpha$ airglow subtraction for GJ 667C produced by the
airglow removal GUI. The upper left and right plots show the original COS flux
normalized by the original COS error, in log space and linear space
respectively, for cases where one is more useful than the other. The two lower
left plots show the recovered COS - STIS residual, and this residual
normalized by the STIS error. The two lower right plots show the observed COS
- best fit residual, and this residual normalized by the observed COS error.
Both normalized plots on the bottom show the absolute value of the residuals.

Figure A12: Versions of Figures 10, 12, 13, 15 and 11 that display previously
cropped failed recoveries.

## References

  * Allan & Vidotto (2019) Allan, A., & Vidotto, A. A. 2019, MNRAS, 490, 3760, doi: 10.1093/mnras/stz2842
  * Alonso-Floriano et al. (2015) Alonso-Floriano, F. J., Morales, J. C., Caballero, J. A., et al. 2015, A&A, 577, A128, doi: 10.1051/0004-6361/201525803
  * Anderson et al. (2014) Anderson, D. R., Collier Cameron, A., Delrez, L., et al. 2014, MNRAS, 445, 1114, doi: 10.1093/mnras/stu1737
  * Anglada-Escude et al. (2014) Anglada-Escude, G., Arriagada, P., Tuomi, M., et al. 2014, MNRAS, 443, L89, doi: 10.1093/mnrasl/slu076
  * Astudillo-Defru et al. (2017) Astudillo-Defru, N., Delfosse, X., Bonfils, X., et al. 2017, A&A, 600, A13, doi: 10.1051/0004-6361/201527078
  * Avrett & Loeser (2008) Avrett, E. H., & Loeser, R. 2008, ApJS, 175, 229, doi: 10.1086/523671
  * Ayres (2021) Ayres, T. R. 2021, ApJ, 910, 71, doi: 10.3847/1538-4357/abd7a2
  * Bailer-Jones (2011) Bailer-Jones, C. A. L. 2011, MNRAS, 411, 435, doi: 10.1111/j.1365-2966.2010.17699.x
  * Ballester & Ben-Jaffel (2015) Ballester, G. E., & Ben-Jaffel, L. 2015, ApJ, 804, 116, doi: 10.1088/0004-637X/804/2/116
  * Barnes (2001) Barnes, S. A. 2001, ApJ, 561, 1095, doi: 10.1086/323373
  * Bazot et al. (2011) Bazot, M., Ireland, M. J., Huber, D., et al. 2011, A&A, 526, L4, doi: 10.1051/0004-6361/201015679
  * Ben-Jaffel & Ballester (2013) Ben-Jaffel, L., & Ballester, G. E. 2013, A&A, 553, A52, doi: 10.1051/0004-6361/201221014
  * Bidelman (1985) Bidelman, W. P. 1985, ApJS, 59, 197, doi: 10.1086/191069
  * Bonfanti et al. (2016) Bonfanti, A., Ortolani, S., & Nascimbeni, V. 2016, A&A, 585, A5, doi: 10.1051/0004-6361/201527297
  * Boro Saikia et al. (2018) Boro Saikia, S., Marvin, C. J., Jeffers, S. V., et al. 2018, A&A, 616, A108, doi: 10.1051/0004-6361/201629518
  * Bouchy et al. (2009) Bouchy, F., Mayor, M., Lovis, C., et al. 2009, A&A, 496, 527, doi: 10.1051/0004-6361:200810669
  * Bourrier et al. (2018a) Bourrier, V., Ehrenreich, D., Lecavelier des Etangs, A., et al. 2018a, A&A, 615, A117, doi: 10.1051/0004-6361/201832700
  * Bourrier et al. (2018b) Bourrier, V., Lecavelier des Etangs, A., Ehrenreich, D., et al. 2018b, A&A, 620, A147, doi: 10.1051/0004-6361/201833675
  * Bourrier et al. (2020) Bourrier, V., Wheatley, P. J., Lecavelier des Etangs, A., et al. 2020, MNRAS, 493, 559, doi: 10.1093/mnras/staa256
  * Bourrier et al. (2021) Bourrier, V., dos Santos, L. A., Sanz-Forcada, J., et al. 2021, A&A, 650, A73, doi: 10.1051/0004-6361/202140487
  * Boyajian et al. (2012) Boyajian, T. S., McAlister, H. A., van Belle, G., et al. 2012, ApJ, 746, 101, doi: 10.1088/0004-637X/746/1/101
  * Bühlmann & Künsch (1999) Bühlmann, P., & Künsch, H. R. 1999, Computational Statistics & Data Analysis, 31, 295, doi: 10.1016/s0167-9473(99)00014-6
  * Burgasser et al. (2015) Burgasser, A. J., Logsdon, S. E., Gagné, J., et al. 2015, ApJS, 220, 18, doi: 10.1088/0067-0049/220/1/18
  * Cannon & Pickering (1993) Cannon, A. J., & Pickering, E. C. 1993, VizieR Online Data Catalog, III/135A
  * Cenarro et al. (2009) Cenarro, A. J., Cardiel, N., Vazdekis, A., & Gorgas, J. 2009, MNRAS, 396, 1895, doi: 10.1111/j.1365-2966.2009.14839.x
  * Cenarro et al. (2007) Cenarro, A. J., Peletier, R. F., Sánchez-Blázquez, P., et al. 2007, MNRAS, 374, 664, doi: 10.1111/j.1365-2966.2006.11196.x
  * Chubak & Marcy (2011) Chubak, C., & Marcy, G. 2011, in American Astronomical Society Meeting Abstracts, Vol. 217, American Astronomical Society Meeting Abstracts #217, 434.12
  * Cifuentes et al. (2020) Cifuentes, C., Caballero, J. A., Cortés-Contreras, M., et al. 2020, A&A, 642, A115, doi: 10.1051/0004-6361/202038295
  * Costa et al. (2006) Costa, E., Méndez, R. A., Jao, W. C., et al. 2006, AJ, 132, 1234, doi: 10.1086/505706
  * Cruz Aguirre et al. (2022) Cruz Aguirre, F., Youngblood, A., France, K., & Bourrier, V. 2022, subtractAirglow, Zenodo, doi: 10.5281/zenodo.7435191
  * da Silva et al. (2011) da Silva, R., Milone, A. C., & Reddy, B. E. 2011, A&A, 526, A71, doi: 10.1051/0004-6361/201015907
  * Deka-Szymankiewicz et al. (2018) Deka-Szymankiewicz, B., Niedzielski, A., Adamczyk, M., et al. 2018, A&A, 615, A31, doi: 10.1051/0004-6361/201731696
  * Dere et al. (1997) Dere, K. P., Landi, E., Mason, H. E., Monsignori Fossi, B. C., & Young, P. R. 1997, A&AS, 125, 149, doi: 10.1051/aas:1997368
  * DeWarf et al. (2010) DeWarf, L. E., Datin, K. M., & Guinan, E. F. 2010, ApJ, 722, 343, doi: 10.1088/0004-637X/722/1/343
  * Dittmann et al. (2017) Dittmann, J. A., Irwin, J. M., Charbonneau, D., et al. 2017, Nature, 544, 333, doi: 10.1038/nature22055
  * do Nascimento et al. (2014) do Nascimento, J. D., J., García, R. A., Mathur, S., et al. 2014, ApJ, 790, L23, doi: 10.1088/2041-8205/790/2/L23
  * Donahue et al. (1996) Donahue, R. A., Saar, S. H., & Baliunas, S. L. 1996, ApJ, 466, 384, doi: 10.1086/177517
  * dos Santos et al. (2019) dos Santos, L. A., Ehrenreich, D., Bourrier, V., et al. 2019, A&A, 629, A47, doi: 10.1051/0004-6361/201935663
  * dos Santos et al. (2021) dos Santos, L. A., Bourrier, V., Ehrenreich, D., et al. 2021, A&A, 649, A40, doi: 10.1051/0004-6361/202140491
  * Dressing et al. (2019) Dressing, C. D., Hardegree-Ullman, K., Schlieder, J. E., et al. 2019, AJ, 158, 87, doi: 10.3847/1538-3881/ab2895
  * Duvall et al. (1984) Duvall, T. L., J., Dziembowski, W. A., Goode, P. R., et al. 1984, Nature, 310, 22, doi: 10.1038/310022a0
  * Edelman et al. (2019) Edelman, E., Redfield, S., Linsky, J. L., Wood, B. E., & Müller, H. 2019, ApJ, 880, 117, doi: 10.3847/1538-4357/ab1f6d
  * Ehrenreich & Désert (2011) Ehrenreich, D., & Désert, J. M. 2011, A&A, 529, A136, doi: 10.1051/0004-6361/201016356
  * Ehrenreich et al. (2015) Ehrenreich, D., Bourrier, V., Wheatley, P. J., et al. 2015, Nature, 522, 459, doi: 10.1038/nature14501
  * Ely et al. (2011) Ely, J., Massa, D., Ake, T., et al. 2011, COS FUV Gridwire Flat Field Template, Instrument Science Report COS 2011-03, 20 pages
  * Endl et al. (2006) Endl, M., Cochran, W. D., Kürster, M., et al. 2006, ApJ, 649, 436, doi: 10.1086/506465
  * Faedi et al. (2013) Faedi, F., Staley, T., Gómez Maqueo Chew, Y., et al. 2013, MNRAS, 433, 2097, doi: 10.1093/mnras/stt885
  * Fischer et al. (2002) Fischer, D. A., Marcy, G. W., Butler, R. P., et al. 2002, PASP, 114, 529, doi: 10.1086/341677
  * Fleming et al. (1993) Fleming, T. A., Giampapa, M. S., Schmitt, J. H. M. M., & Bookbinder, J. A. 1993, ApJ, 410, 387, doi: 10.1086/172755
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306, doi: 10.1086/670067
  * Fossati et al. (2015) Fossati, L., Ingrassia, S., & Lanza, A. F. 2015, ApJ, 812, L35, doi: 10.1088/2041-8205/812/2/L35
  * Fouqué et al. (2018) Fouqué, P., Moutou, C., Malo, L., et al. 2018, MNRAS, 475, 1960, doi: 10.1093/mnras/stx3246
  * France et al. (2018) France, K., Arulanantham, N., Fossati, L., et al. 2018, ApJS, 239, 16, doi: 10.3847/1538-4365/aae1a3
  * France et al. (2013) France, K., Froning, C. S., Linsky, J. L., et al. 2013, ApJ, 763, 149, doi: 10.1088/0004-637X/763/2/149
  * France et al. (2016) France, K., Loyd, R. O. P., Youngblood, A., et al. 2016, ApJ, 820, 89, doi: 10.3847/0004-637X/820/2/89
  * Frasca et al. (2018) Frasca, A., Guillout, P., Klutsch, A., et al. 2018, A&A, 612, A96, doi: 10.1051/0004-6361/201732028
  * Froning et al. (2019) Froning, C. S., Kowalski, A., France, K., et al. 2019, ApJ, 871, L26, doi: 10.3847/2041-8213/aaffcd
  * Gaia Collaboration (2018) Gaia Collaboration. 2018, VizieR Online Data Catalog, I/345
  * Gaidos et al. (2014) Gaidos, E., Mann, A. W., Lépine, S., et al. 2014, MNRAS, 443, 2561, doi: 10.1093/mnras/stu1313
  * García Muñoz et al. (2020) García Muñoz, A., Youngblood, A., Fossati, L., et al. 2020, ApJ, 888, L21, doi: 10.3847/2041-8213/ab61ff
  * Geballe et al. (2002) Geballe, T. R., Knapp, G. R., Leggett, S. K., et al. 2002, ApJ, 564, 466, doi: 10.1086/324078
  * Ghezzi et al. (2010) Ghezzi, L., Cunha, K., Smith, V. V., et al. 2010, ApJ, 720, 1290, doi: 10.1088/0004-637X/720/2/1290
  * Giacobbe et al. (2020) Giacobbe, P., Benedetto, M., Damasso, M., et al. 2020, MNRAS, 491, 5216, doi: 10.1093/mnras/stz3364
  * Gontcharov (2006) Gontcharov, G. A. 2006, Astronomy Letters, 32, 759, doi: 10.1134/S1063773706110065
  * Gray et al. (2006) Gray, R. O., Corbally, C. J., Garrison, R. F., et al. 2006, AJ, 132, 161, doi: 10.1086/504637
  * Gray et al. (2003) Gray, R. O., Corbally, C. J., Garrison, R. F., McFadden, M. T., & Robinson, P. E. 2003, AJ, 126, 2048, doi: 10.1086/378365
  * Gray et al. (2001) Gray, R. O., Napier, M. G., & Winkler, L. I. 2001, AJ, 121, 2148, doi: 10.1086/319956
  * Green et al. (2012) Green, J. C., Froning, C. S., Osterman, S., et al. 2012, ApJ, 744, 60, doi: 10.1088/0004-637X/744/1/60
  * Guinan et al. (2016) Guinan, E. F., Engle, S. G., & Durbin, A. 2016, ApJ, 821, 81, doi: 10.3847/0004-637X/821/2/81
  * Halbwachs et al. (2018) Halbwachs, J. L., Mayor, M., & Udry, S. 2018, A&A, 619, A81, doi: 10.1051/0004-6361/201833377
  * Hall et al. (1995) Hall, P., Horowitz, J. L., & Jing, B.-Y. 1995, Biometrika, 82, 561.  http://www.jstor.org/stable/2337534
  * Harman et al. (2015) Harman, C. E., Schwieterman, E. W., Schottelkotte, J. C., & Kasting, J. F. 2015, ApJ, 812, 137, doi: 10.1088/0004-637X/812/2/137
  * Harris (1948) Harris, Daniel L., I. 1948, ApJ, 108, 112, doi: 10.1086/145047
  * Hawley et al. (1996) Hawley, S. L., Gizis, J. E., & Reid, I. N. 1996, AJ, 112, 2799, doi: 10.1086/118222
  * Hébrard & Moos (2003) Hébrard, G., & Moos, H. W. 2003, ApJ, 599, 297, doi: 10.1086/379162
  * Hempelmann et al. (2016) Hempelmann, A., Mittag, M., Gonzalez-Perez, J. N., et al. 2016, A&A, 586, A14, doi: 10.1051/0004-6361/201526972
  * Henry et al. (1996) Henry, T. J., Soderblom, D. R., Donahue, R. A., & Baliunas, S. L. 1996, AJ, 111, 439, doi: 10.1086/117796
  * Herrero et al. (2012) Herrero, E., Ribas, I., Jordi, C., Guinan, E. F., & Engle, S. G. 2012, A&A, 537, A147, doi: 10.1051/0004-6361/201117809
  * Hinkel et al. (2017) Hinkel, N. R., Mamajek, E. E., Turnbull, M. C., et al. 2017, ApJ, 848, 34, doi: 10.3847/1538-4357/aa8b0f
  * Houdebine (2010) Houdebine, E. R. 2010, MNRAS, 407, 1657, doi: 10.1111/j.1365-2966.2010.16827.x
  * Houk (1978) Houk, N. 1978, Michigan catalogue of two-dimensional spectral types for the HD stars
  * Houk (1982) —. 1982, Michigan Catalogue of Two-dimensional Spectral Types for the HD stars. Volume_3. Declinations -40_f0 to -26_f0.
  * Houk & Cowley (1975) Houk, N., & Cowley, A. P. 1975, University of Michigan Catalogue of two-dimensional spectral types for the HD stars. Volume I. Declinations -90_ to -53_f0.
  * Houk & Smith-Moore (1988) Houk, N., & Smith-Moore, M. 1988, Michigan Catalogue of Two-dimensional Spectral Types for the HD Stars. Volume 4, Declinations -26°.0 to -12°.0., Vol. 4
  * Houk & Swift (1999) Houk, N., & Swift, C. 1999, Michigan Spectral Survey, 5, 0
  * Howard et al. (2009) Howard, A. W., Johnson, J. A., Marcy, G. W., et al. 2009, ApJ, 696, 75, doi: 10.1088/0004-637X/696/1/75
  * Howard et al. (2011) —. 2011, ApJ, 726, 73, doi: 10.1088/0004-637X/726/2/73
  * Isaacson & Fischer (2010) Isaacson, H., & Fischer, D. 2010, ApJ, 725, 875, doi: 10.1088/0004-637X/725/1/875
  * Jaehnig et al. (2019) Jaehnig, K., Somers, G., & Stassun, K. G. 2019, ApJ, 879, 39, doi: 10.3847/1538-4357/ab21cf
  * James et al. (2022) James, B. L., et al. 2022, in COS Instrument Handbook v. 14.0, Vol. 14, 14
  * Jenkins et al. (2011) Jenkins, J. S., Murgas, F., Rojo, P., et al. 2011, A&A, 531, A8, doi: 10.1051/0004-6361/201016333
  * Joy & Abt (1974) Joy, A. H., & Abt, H. A. 1974, ApJS, 28, 1, doi: 10.1086/190307
  * Kameda et al. (2017) Kameda, S., Ikezawa, S., Sato, M., et al. 2017, Geophys. Res. Lett., 44, 11,706, doi: 10.1002/2017GL075915
  * Katsova (2020) Katsova, M. M. 2020, Journal of Atmospheric and Solar-Terrestrial Physics, 211, 105456, doi: 10.1016/j.jastp.2020.105456
  * Katsova & Livshits (2011) Katsova, M. M., & Livshits, M. A. 2011, Astronomy Reports, 55, 1123, doi: 10.1134/S1063772911120055
  * Kawashima & Ikoma (2019) Kawashima, Y., & Ikoma, M. 2019, ApJ, 877, 109, doi: 10.3847/1538-4357/ab1b1d
  * Keenan & McNeil (1989) Keenan, P. C., & McNeil, R. C. 1989, ApJS, 71, 245, doi: 10.1086/191373
  * Kervella et al. (2019) Kervella, P., Arenou, F., Mignard, F., & Thévenin, F. 2019, A&A, 623, A72, doi: 10.1051/0004-6361/201834371
  * Khalafinejad et al. (2021) Khalafinejad, S., Molaverdikhani, K., Blecic, J., et al. 2021, A&A, 656, A142, doi: 10.1051/0004-6361/202141191
  * King et al. (2018) King, G. W., Wheatley, P. J., Salz, M., et al. 2018, MNRAS, 478, 1193, doi: 10.1093/mnras/sty1110
  * Kirkpatrick et al. (1991) Kirkpatrick, J. D., Henry, T. J., & McCarthy, Donald W., J. 1991, ApJS, 77, 417, doi: 10.1086/191611
  * Koen et al. (2010) Koen, C., Kilkenny, D., van Wyk, F., & Marang, F. 2010, MNRAS, 403, 1949, doi: 10.1111/j.1365-2966.2009.16182.x
  * Kordopatis et al. (2013) Kordopatis, G., Gilmore, G., Steinmetz, M., et al. 2013, AJ, 146, 134, doi: 10.1088/0004-6256/146/5/134
  * Koskinen et al. (2013a) Koskinen, T. T., Harris, M. J., Yelle, R. V., & Lavvas, P. 2013a, Icarus, 226, 1678, doi: 10.1016/j.icarus.2012.09.027
  * Koskinen et al. (2013b) Koskinen, T. T., Yelle, R. V., Harris, M. J., & Lavvas, P. 2013b, Icarus, 226, 1695, doi: 10.1016/j.icarus.2012.09.026
  * Kovacs (2018) Kovacs, G. 2018, A&A, 612, L2, doi: 10.1051/0004-6361/201731355
  * Kovtyukh et al. (2003) Kovtyukh, V. V., Soubiran, C., Belik, S. I., & Gorlova, N. I. 2003, A&A, 411, 559, doi: 10.1051/0004-6361:20031378
  * Kraus et al. (2014) Kraus, A. L., Shkolnik, E. L., Allers, K. N., & Liu, M. C. 2014, AJ, 147, 146, doi: 10.1088/0004-6256/147/6/146
  * Kulow et al. (2014) Kulow, J. R., France, K., Linsky, J., & Loyd, R. O. P. 2014, ApJ, 786, 132, doi: 10.1088/0004-637X/786/2/132
  * Kunder et al. (2017) Kunder, A., Kordopatis, G., Steinmetz, M., et al. 2017, AJ, 153, 75, doi: 10.3847/1538-3881/153/2/75
  * Landi et al. (2012) Landi, E., Del Zanna, G., Young, P. R., Dere, K. P., & Mason, H. E. 2012, ApJ, 744, 99, doi: 10.1088/0004-637X/744/2/99
  * Landsman & Simon (1993) Landsman, W., & Simon, T. 1993, ApJ, 408, 305, doi: 10.1086/172589
  * Lavie et al. (2017) Lavie, B., Ehrenreich, D., Bourrier, V., et al. 2017, A&A, 605, L7, doi: 10.1051/0004-6361/201731340
  * Lecavelier Des Etangs et al. (2010) Lecavelier Des Etangs, A., Ehrenreich, D., Vidal-Madjar, A., et al. 2010, A&A, 514, A72, doi: 10.1051/0004-6361/200913347
  * Lecavelier des Etangs et al. (2012) Lecavelier des Etangs, A., Bourrier, V., Wheatley, P. J., et al. 2012, A&A, 543, L4, doi: 10.1051/0004-6361/201219363
  * Lépine et al. (2013) Lépine, S., Hilton, E. J., Mann, A. W., et al. 2013, AJ, 145, 102, doi: 10.1088/0004-6256/145/4/102
  * Leys et al. (2013) Leys, C., Ley, C., Klein, O., Bernard, P., & Licata, L. 2013, Journal of Experimental Social Psychology, 49, 764, doi: 10.1016/j.jesp.2013.03.013
  * Linsky (1998) Linsky, J. L. 1998, Space Sci. Rev., 84, 285
  * Linsky et al. (2014) Linsky, J. L., Fontenla, J., & France, K. 2014, ApJ, 780, 61, doi: 10.1088/0004-637X/780/1/61
  * Linsky et al. (2013) Linsky, J. L., France, K., & Ayres, T. 2013, ApJ, 766, 69, doi: 10.1088/0004-637X/766/2/69
  * Linsky et al. (2010) Linsky, J. L., Yang, H., France, K., et al. 2010, ApJ, 717, 1291, doi: 10.1088/0004-637X/717/2/1291
  * Linsky et al. (2006) Linsky, J. L., Draine, B. T., Moos, H. W., et al. 2006, ApJ, 647, 1106, doi: 10.1086/505556
  * Lovis et al. (2005) Lovis, C., Mayor, M., Bouchy, F., et al. 2005, A&A, 437, 1121, doi: 10.1051/0004-6361:20052864
  * Loyd et al. (2016) Loyd, R. O. P., France, K., Youngblood, A., et al. 2016, ApJ, 824, 102, doi: 10.3847/0004-637X/824/2/102
  * Loyd et al. (2021) Loyd, R. O. P., Shkolnik, E. L., Schneider, A. C., et al. 2021, ApJ, 907, 91, doi: 10.3847/1538-4357/abd0f0
  * Lurie et al. (2014) Lurie, J. C., Henry, T. J., Jao, W.-C., et al. 2014, AJ, 148, 91, doi: 10.1088/0004-6256/148/5/91
  * Malik et al. (2019) Malik, M., Kempton, E. M. R., Koll, D. D. B., et al. 2019, ApJ, 886, 142, doi: 10.3847/1538-4357/ab4a05
  * Mallonn et al. (2018) Mallonn, M., Herrero, E., Juvan, I. G., et al. 2018, A&A, 614, A35, doi: 10.1051/0004-6361/201732300
  * Malo et al. (2014) Malo, L., Artigau, É., Doyon, R., et al. 2014, ApJ, 788, 81, doi: 10.1088/0004-637X/788/1/81
  * Marmier et al. (2013) Marmier, M., Ségransan, D., Udry, S., et al. 2013, A&A, 551, A90, doi: 10.1051/0004-6361/201219639
  * Masana et al. (2006) Masana, E., Jordi, C., & Ribas, I. 2006, A&A, 450, 735, doi: 10.1051/0004-6361:20054021
  * McDonald et al. (2012) McDonald, I., Zijlstra, A. A., & Boyer, M. L. 2012, MNRAS, 427, 343, doi: 10.1111/j.1365-2966.2012.21873.x
  * Meier (1991) Meier, R. R. 1991, Space Sci. Rev., 58, 1, doi: 10.1007/BF01206000
  * Melbourne et al. (2020a) Melbourne, K., Youngblood, A., France, K., et al. 2020a, arXiv e-prints, arXiv:2009.07869.  https://arxiv.org/abs/2009.07869
  * Melbourne et al. (2020b) —. 2020b, AJ, 160, 269, doi: 10.3847/1538-3881/abbf5c
  * Meschiari et al. (2011) Meschiari, S., Laughlin, G., Vogt, S. S., et al. 2011, ApJ, 727, 117, doi: 10.1088/0004-637X/727/2/117
  * Messina et al. (2010) Messina, S., Desidera, S., Turatto, M., Lanzafame, A. C., & Guinan, E. F. 2010, A&A, 520, A15, doi: 10.1051/0004-6361/200913644
  * Miguel et al. (2015) Miguel, Y., Kaltenegger, L., Linsky, J. L., & Rugheimer, S. 2015, MNRAS, 446, 345, doi: 10.1093/mnras/stu2107
  * Montes et al. (2001) Montes, D., López-Santiago, J., Gálvez, M. C., et al. 2001, MNRAS, 328, 45, doi: 10.1046/j.1365-8711.2001.04781.x
  * Montes et al. (2018) Montes, D., González-Peinado, R., Tabernero, H. M., et al. 2018, MNRAS, 479, 1332, doi: 10.1093/mnras/sty1295
  * Moore & Paddock (1950) Moore, J. H., & Paddock, G. F. 1950, ApJ, 112, 48, doi: 10.1086/145318
  * Morales et al. (2008) Morales, J. C., Ribas, I., & Jordi, C. 2008, A&A, 478, 507, doi: 10.1051/0004-6361:20078324
  * Morley et al. (2015) Morley, C. V., Fortney, J. J., Marley, M. S., et al. 2015, ApJ, 815, 110, doi: 10.1088/0004-637X/815/2/110
  * Moutou et al. (2014) Moutou, C., Hébrard, G., Bouchy, F., et al. 2014, A&A, 563, A22, doi: 10.1051/0004-6361/201322067
  * Muñoz Bermejo et al. (2013) Muñoz Bermejo, J., Asensio Ramos, A., & Allende Prieto, C. 2013, A&A, 553, A95, doi: 10.1051/0004-6361/201220961
  * Murgas et al. (2013) Murgas, F., Jenkins, J. S., Rojo, P., Jones, H. R. A., & Pinfield, D. J. 2013, A&A, 552, A27, doi: 10.1051/0004-6361/201219483
  * NASA Exoplanet Science Institute (2020) NASA Exoplanet Science Institute. 2020, Planetary Systems Table, IPAC, doi: 10.26133/NEA12
  * Newton et al. (2014) Newton, E. R., Charbonneau, D., Irwin, J., et al. 2014, AJ, 147, 20, doi: 10.1088/0004-6256/147/1/20
  * Newton et al. (2017) Newton, E. R., Irwin, J., Charbonneau, D., et al. 2017, ApJ, 834, 85, doi: 10.3847/1538-4357/834/1/85
  * Newton et al. (2016) —. 2016, ApJ, 821, 93, doi: 10.3847/0004-637X/821/2/93
  * Newton et al. (2018) Newton, E. R., Mondrik, N., Irwin, J., Winters, J. G., & Charbonneau, D. 2018, AJ, 156, 217, doi: 10.3847/1538-3881/aad73b
  * Newville et al. (2014) Newville, M., Stensitzki, T., Allen, D. B., & Ingargiola, A. 2014, LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python, Zenodo, doi: 10.5281/ZENODO.11813
  * Nidever et al. (2002) Nidever, D. L., Marcy, G. W., Butler, R. P., Fischer, D. A., & Vogt, S. S. 2002, ApJS, 141, 503, doi: 10.1086/340570
  * Nielsen et al. (2013) Nielsen, M. B., Gizon, L., Schunker, H., & Karoff, C. 2013, A&A, 557, L10, doi: 10.1051/0004-6361/201321912
  * Nizamov et al. (2017) Nizamov, B. A., Katsova, M. M., & Livshits, M. A. 2017, Astronomy Letters, 43, 202, doi: 10.1134/S1063773717020049
  * Notsu et al. (2015) Notsu, Y., Honda, S., Maehara, H., et al. 2015, PASJ, 67, 32, doi: 10.1093/pasj/psv001
  * Noyes et al. (1984) Noyes, R. W., Hartmann, L. W., Baliunas, S. L., Duncan, D. K., & Vaughan, A. H. 1984, ApJ, 279, 763, doi: 10.1086/161945
  * Olmedo et al. (2013) Olmedo, M., Chávez, M., Bertone, E., & De la Luz, V. 2013, PASP, 125, 1436, doi: 10.1086/674332
  * Pasinetti Fracassini et al. (2001) Pasinetti Fracassini, L. E., Pastori, L., Covino, S., & Pozzi, A. 2001, A&A, 367, 521, doi: 10.1051/0004-6361:20000451
  * Patton et al. (2009) Patton, A., Politis, D. N., & White, H. 2009, Econometric Reviews, 28, 372, doi: 10.1080/07474930802459016
  * Peacock et al. (2019) Peacock, S., Barman, T., Shkolnik, E. L., et al. 2019, ApJ, 886, 77, doi: 10.3847/1538-4357/ab4f6f
  * Pepe et al. (2011) Pepe, F., Lovis, C., Ségransan, D., et al. 2011, A&A, 534, A58, doi: 10.1051/0004-6361/201117055
  * Pesch (1968) Pesch, P. 1968, ApJ, 151, 605, doi: 10.1086/149460
  * Petit et al. (2008) Petit, P., Dintrans, B., Solanki, S. K., et al. 2008, MNRAS, 388, 80, doi: 10.1111/j.1365-2966.2008.13411.x
  * Pizzolato et al. (2003) Pizzolato, N., Maggio, A., Micela, G., Sciortino, S., & Ventura, P. 2003, A&A, 397, 147, doi: 10.1051/0004-6361:20021560
  * Politis & White (2004) Politis, D. N., & White, H. 2004, Econometric Reviews, 23, 53, doi: 10.1081/etc-120028836
  * Rafelski et al. (2018) Rafelski, M., De Rosa, G., Fischer, W. J., et al. 2018, in American Astronomical Society Meeting Abstracts, Vol. 231, American Astronomical Society Meeting Abstracts #231, 150.38
  * Ranjan et al. (2022) Ranjan, S., Seager, S., Zhan, Z., et al. 2022, ApJ, 930, 131, doi: 10.3847/1538-4357/ac5749
  * Redfield & Linsky (2004) Redfield, S., & Linsky, J. L. 2004, ApJ, 602, 776, doi: 10.1086/381083
  * Redfield & Linsky (2008) —. 2008, ApJ, 673, 283, doi: 10.1086/524002
  * Riaz et al. (2006) Riaz, B., Gizis, J. E., & Harvin, J. 2006, AJ, 132, 866, doi: 10.1086/505632
  * Richey-Yowell et al. (2022) Richey-Yowell, T., Shkolnik, E. L., Loyd, R. O. P., et al. 2022, ApJ, 929, 169, doi: 10.3847/1538-4357/ac5f48
  * Riedel et al. (2017) Riedel, A. R., Alam, M. K., Rice, E. L., Cruz, K. L., & Henry, T. J. 2017, ApJ, 840, 87, doi: 10.3847/1538-4357/840/2/87
  * Robertson et al. (2012) Robertson, P., Endl, M., Cochran, W. D., et al. 2012, ApJ, 749, 39, doi: 10.1088/0004-637X/749/1/39
  * Roman (1955) Roman, N. G. 1955, ApJS, 2, 195, doi: 10.1086/190021
  * Roman-Duval et al. (2014) Roman-Duval, J., Ely, J., Oliveira, C., et al. 2014, Summary of the Cycle 19 COS Calibration Program, Instrument Science Report COS 2014-01, 31 pages
  * Rugheimer & Kaltenegger (2018) Rugheimer, S., & Kaltenegger, L. 2018, ApJ, 854, 19, doi: 10.3847/1538-4357/aaa47a
  * Santos et al. (2001) Santos, N. C., Mayor, M., Naef, D., et al. 2001, A&A, 379, 999, doi: 10.1051/0004-6361:20011366
  * Santos et al. (2002) —. 2002, A&A, 392, 215, doi: 10.1051/0004-6361:20020876
  * Schneider & Shkolnik (2018) Schneider, A. C., & Shkolnik, E. L. 2018, AJ, 155, 122, doi: 10.3847/1538-3881/aaaa24
  * Schofield et al. (2019) Schofield, M., Chaplin, W. J., Huber, D., et al. 2019, ApJS, 241, 12, doi: 10.3847/1538-4365/ab04f5
  * Scholz et al. (2005) Scholz, R. D., Meusinger, H., & Jahreiß, H. 2005, A&A, 442, 211, doi: 10.1051/0004-6361:20053004
  * Schröder et al. (2009) Schröder, C., Reiners, A., & Schmitt, J. H. M. M. 2009, A&A, 493, 1099, doi: 10.1051/0004-6361:200810377
  * Silva et al. (2018) Silva, M., Humphrey, A., Lagos, P., et al. 2018, MNRAS, 474, 3649, doi: 10.1093/mnras/stx3019
  * Simpson et al. (2010) Simpson, E. K., Baliunas, S. L., Henry, G. W., & Watson, C. A. 2010, MNRAS, 408, 1666, doi: 10.1111/j.1365-2966.2010.17230.x
  * Soderblom & Clements (1987) Soderblom, D. R., & Clements, S. D. 1987, AJ, 93, 920, doi: 10.1086/114378
  * Soderblom et al. (2021) Soderblom, D. R., et al. 2021, in COS Data Handbook v. 5.0, Vol. 5, 5
  * Soto & Jenkins (2018) Soto, M. G., & Jenkins, J. S. 2018, A&A, 615, A76, doi: 10.1051/0004-6361/201731533
  * Soubiran et al. (2018) Soubiran, C., Jasniewicz, G., Chemin, L., et al. 2018, A&A, 616, A7, doi: 10.1051/0004-6361/201832795
  * Stassun et al. (2017) Stassun, K. G., Collins, K. A., & Gaudi, B. S. 2017, AJ, 153, 136, doi: 10.3847/1538-3881/aa5df3