# THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT STARS111 Based on
observations obtained with the Hobby-Eberly Telescope, which is a joint
project of the University of Texas at Austin, the Pennsylvania State
University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen.

Christopher Sneden Department of Astronomy and McDonald Observatory, The
University of Texas, Austin, TX 78712, USA  Melike Afşar Department of
Astronomy and Space Sciences, Ege University, 35100 Bornova, İzmir, Turkey
Department of Astronomy and McDonald Observatory, The University of Texas,
Austin, TX 78712, USA  Zeynep Bozkurt Department of Astronomy and Space
Sciences, Ege University, 35100 Bornova, İzmir, Turkey  Monika Adamów Center
for AstroPhysical Surveys, National Center for Supercomputing Applications,
Urbana, IL 61801, USA  Anohita Mallick Indian Institute of Astrophysics,
Bangalore – 560034, India  Bacham E. Reddy Indian Institute of Astrophysics,
Bangalore – 560034, India  Steven Janowiecki Hobby Eberly Telescope, The
University of Texas, Austin, TX 78712, USA  Suvrath Mahadevan Department of
Astronomy & Astrophysics, The Pennsylvania State University, University Park,
PA 16803, USA  Center for Exoplanets and Habitable Worlds, The Pennsylvania
State University, University Park, PA 16803, USA  Brendan P. Bowler Department
of Astronomy and McDonald Observatory, The University of Texas, Austin, TX
78712, USA  Keith Hawkins Department of Astronomy and McDonald Observatory,
The University of Texas, Austin, TX 78712, USA  Karin Lind  Department of
Astronomy, Stockholm University, AlbaNova University Centre, SE-106 91
Stockholm, Sweden  Andrea K. Dupree Center for Astrophysics/Harvard &
Smithsonian, Cambridge, MA 02138-1516, USA  Joe P. Ninan Department of
Astronomy & Astrophysics, The Pennsylvania State University, University Park,
PA 16803, USA  Center for Exoplanets and Habitable Worlds, The Pennsylvania
State University, University Park, PA 16803, USA  Neel Nagarajan Department of
Astronomy and McDonald Observatory, The University of Texas, Austin, TX 78712,
USA  Gamze Böcek Topcu  Department of Astronomy and Space Sciences, Ege
University, 35100 Bornova, İzmir, Turkey  Cynthia S. Froning Department of
Astronomy and McDonald Observatory, The University of Texas, Austin, TX 78712,
USA  Chad F. Bender Steward Observatory, University of Arizona, Tucson, AZ
85721, USA  Ryan Terrien Department of Physics and Astronomy, Carleton
College, Northfield, MN 55057, USA  Lawrence W. Ramsey Department of Astronomy
& Astrophysics, The Pennsylvania State University, University Park, PA 16803,
USA  Center for Exoplanets and Habitable Worlds, The Pennsylvania State
University, University Park, PA 16803, USA  Gregory N. Mace Department of
Astronomy and McDonald Observatory, The University of Texas, Austin, TX 78712,
USA

###### Abstract

We have gathered near-infrared $zyJ$-band high resolution spectra of nearly
300 field red giant stars with known lithium abundances in order to survey
their He i $\lambda$10830 absorption strengths. This transition is an
indicator of chromospheric activity and/or mass loss in red giants. The
majority of stars in our sample reside in the red clump or red horizontal
branch based on their $V-J,M_{V}$ color-magnitude diagram and their Gaia
$T_{\rm eff}$, log(g) values. Most of our target stars are Li-poor in the
sense of having normally low Li abundances, defined here as log $\epsilon$(Li)
$<$ 1.25. Over 90% of these Li-poor stars have weak $\lambda$10830 features.
But more than half of the 83 Li-rich stars (log $\epsilon$(Li) $>$ 1.25) have
strong $\lambda$10830 absorptions. These large $\lambda$10830 lines signal
excess chromospheric activity in Li-rich stars; there is almost no indication
of significant mass loss. The Li-rich giants also may have a higher binary
fraction than do Li-poor stars, based on their astrometric data. It appears
likely that both residence on the horizontal branch and present or past binary
interaction play roles in the significant Li-He connection established in this
survey.

††software: linemake (https://github.com/vmplacco/linemake), MOOG (Sneden
1973), IRAF (Tody 1986, Tody 1993), SPECTRE (Fitzpatrick & Sneden 1987),
Goldilocks (https://github.com/grzeimann/Goldilocks_Documentation)

##  1 INTRODUCTION

Lithium is easily destroyed in stellar interiors as part of the proton-proton
fusion cycles. At modest fusion temperatures, T $\geq$ 2.5$\times$106 K, the
reaction 7Li($p,\alpha$)$\rightarrow$4He efficiently cleans out lithium in
interior regions. Then basic stellar evolution computations (e.g., Iben 1967)
predict that for metal-rich stars the deepening convective envelopes during
subgiant and first-ascent red giant evolution will dilute the initial surface
Li abundances by factors approaching $\sim$60\. In this way the stellar age-
zero Li contents (log $\epsilon$(Li) $\simeq$ 3.3)222 We adopt the standard
spectroscopic notation (Wallerstein & Helfer, 1959) that for elements A and B,
[A/B] $\equiv$ log10(NA/NB)⋆ $-$ log10(NA/NB)⊙. We use the definition log
$\epsilon$(A) $\equiv$ log10(NA/NH) + 12.0, and equate metallicity with the
stellar [Fe/H] value. that are observed in warm main sequence stars (Randich
et al. 2020, Romano et al. 2021) and in the primordial solar system (Lodders
2021) will be substantially diminished, leaving normal red giants with log
$\epsilon$(Li) $\sim$ 1.5. But few evolved stars have that much surface Li.
Decades ago surveys of Li in red giants (e.g., Wallerstein & Conti 1969,
Lambert et al. 1980, Brown et al. 1989) established that nearly all red giants
have log $\epsilon$(Li) $<$ 1.0, and abundance upper limits are common. This
is consistent with the small Li abundances in cool main-sequence stars (dating
back to Wallerstein & Conti 1969 and Boesgaard & Tripicco 1986, 1987), those
with $T_{\rm eff}$ $<$ 6500 K. Slow circulation currents during long main
sequence lifetimes deplete the surface Li abundances before stars evolve to
become giants. The very low Li content of normal red giant stars is no
mystery.

However, about 1% of red giants have unexpectedly strong Li i 6707 Å
absorption lines, often leading to Li abundances that are much greater than
the maximum values in main-sequence stars. The first serendipitous discovery
of a Li-rich giant (Wallerstein & Sneden, 1982) has been followed by many
other detections; now more than 100 relatively bright Li-rich evolved stars
have been cataloged. The origin of this phenomenon is not clear. The best
“interior” hypothesis is the so-called beryllium transport mechanism (Cameron
& Fowler, 1971), in which the reactions 3He($\alpha,\gamma$)7Be(e-,$\nu$)7Li
create Li, which then must be quickly convected to the surface before it can
decay by capturing a proton as described above. The most prominent “exterior”
hypothesis invokes terrestrial or hot Jupiter planet engulfment by stars
(Alexander, 1967) as they bloat themselves at post-main-sequence life stages.

The observational clues are mixed, but recent evidence appears to favor the
interior production and mixing explanation. The Adamów et al. (2014)
spectroscopic red giant survey found that their four most Li-rich giants (log
$\epsilon$(Li) $>$ 1.5) either have low-mass companions or significant radial
velocity variations, suggesting that companions play roles in the Li-
enrichment processes. But Singh et al. (2019b) used asteroseismic and
spectroscopic analyses of more than 10,000 giants to show that nearly all of
the very Li-rich giants in their survey are in the He-core burning red clump
(RC) stage. Casey et al. (2019) combined these ideas to suggest that tidal
interactions between (primarily) He-core-burning RC giants and binary
companions can induce internal mixing to bring newly-created Li to the stellar
surfaces for brief ($\sim$106 yr) episodes. Singh et al. (2021) have now shown
that very high Li abundances are associated with “young” He-core-burning
giants that have just recently arrived on the clump following the RGB-tip He-
flash. Finally, Deepak et al. (2020) argue that the lack of correlation of red
giant Li abundances with rotational velocity means that mergers and tidal
interactions are unassociated with Li enhancements. However, the large survey
by Mallick et al. (2022) for IR excess among RC stars shows that Li-rich
giants with IR excess are more likely to be fast rotators compared to Li-
normal giants.

Figure 1:  Top panel: He I 10830 Å spectra of three red horizontal branch
stars (Sneden et al., 2021). Bottom panel: the Li I 6707 Å resonance feature
in these stars (Afşar et al. 2018, Bozkurt et al. in preparation).

Recently Sneden et al. (2021) used The Habitable Zone Planet Finder (hereafter
HPF) on the Hobby-Eberly Telescope (HET) to conduct a $zyJ$ high resolution
spectroscopic investigation of some red horizontal branch (RHB), or secondary
RC field giants. That study discovered a strong He i 10830 Å line in the Li-
rich RHB star HIP 99789. We illustrate the Li and He spectral features in HIP
99789 and two other RHB’s in Figure 1. The lower excitation energy of the He i
10830 Å transition is 19.8 eV; thus this line cannot be formed in the cool
photospheric layers that yield Li i resonance line absorption. Strong
$\lambda$10830 transitions in cool giant stars signal either excess
chromospheric activity or outer atmospheric wind outflow. The notion that He i
absorption might be a new clue to the Li-rich giant phenomenon has led us to a
survey of He i transitions in Li-rich and Li-poor red giants that we report in
this paper.

In this survey the first goal was to discover the fraction of Li-rich giants
that have large $\lambda$10830 features. Then we looked for correlations
between He i absorption and other stellar parameters to help clarify the roles
of Galactic population, rotation, chromospheric activity, and
stellar/planetary companions on the appearance of strong He i absorption
and/or excess Li in giant stars. In §2 we describe the stellar sample, and in
§3 we outline the observations and spectroscopic reduction steps. §4 presents
the process we used to isolate the $\lambda$10830 chromospheric lines from the
photospheric spectra, to measure their equivalent widths, and to estimate
stellar line broadening. We give the basic results in §5, using Li-He
correlations to define empirical regions of Li abundance and He absorption
line strength, and suggest that in all but one case the He lines indicate
chromospheric activity rather than mass loss. Correlations of He strengths
with space and possible binary motions are presented in §6, and we summarize
our work in §7.

##  2 THE STELLAR SAMPLE

Lithium abundances in evolved stars range over at least five orders of
magnitude, but almost all red giants have log $\epsilon$(Li) $<$ 1.5.
Therefore we initially adopted log $\epsilon$(Li) = 1.5 as the upper limit for
evolved stars that have suffered the Li destruction, envelope mixing, and
surface dilution expected during ordinary stellar evolution. For simplicity in
this paper we label all such normal Li-depleted red giants as “Li-poor” stars.
Evolved red giants with Li abundances above this limit are given the blanket
label “Li-rich”. This empirical definition will be reconsidered in §5.

Li-rich giant stars have been reported in individual spectroscopic studies
(e.g., Luck 1982, Wallerstein & Sneden 1982, Balachandran et al. 2000), and in
large-sample Li discovery surveys (e.g., Brown et al. 1989, Kumar et al. 2011,
Adamów et al. 2014, Casey et al. 2019, Deepak & Reddy 2019). We searched the
growing literature on this phenomenon and developed a target list based on the
following criteria.

  1. 1.

Confirmed evolved-star status. In general this included stars that are cool
($T_{\rm eff}$ $\lesssim$ 5500 K, or $B-V$ $\gtrsim$ 0.8) and well off the
main sequence (log(g) $<$ 3.5, or $M_{V}$ $<$ $+$1.0).

  2. 2.

Sky location in the HET-accessible domain, which is set by its declination
limits: $-$10∘ $\lesssim$ $\delta$ $\lesssim$ $+$71∘.

  3. 3.

Target brightness reasonable for HPF. The apparent magnitude bright limit is
$J$ $>$ 3.0 mag, driven by the need to avoid HPF detector saturation. The
practical faint limit is $J$ $\sim$ 13.0, to achieve signal-to-noise $S/N$ $>$
30 in several hours total observing time.333 For a more complete discussion of
HPF integration times see https://psuastro.github.io/HPF/Exposure-Times/

For Li-poor stars we primarily used two large high resolution optical
spectroscopic surveys of field red giants. Adamów et al. (2014) determined Li
abundances for 348 stars as part of the Penn State-Toruń Centre for Astronomy
Planet Search program; see also atmospheric parameter and overall chemical
abundance studies by Zieliński et al. (2012) and Niedzielski et al. (2016).
These G-K giants lie in the atmospheric parameter range 4000 K $\lesssim$
$T_{\rm eff}$ $\lesssim$ 5100 K, $-$3.0 $\lesssim$ $M_{V}$ $\lesssim$ 3.0.

We also observed some red horizontal branch stars, alternatively called the
secondary red clump (Girardi et al., 1998), from the Afşar et al. (2018)
340-star survey. Li abundances for these stars will be published by Bozkurt et
al. (in preparation). These two large samples have Li abundances derived in a
uniform manner, which is important for those stars with very weak Li i
$\lambda$6707 features.

When early observations revealed that Li-rich stars can also be rapidly-
rotating red giants ($V$sin($i$) $\gtrsim$ 7 km s-1), we also added some extra
targets with substantial rotation from several literature sources: Bizyaev et
al. (2010), Carlberg et al. (2012), Costa et al. (2015). These papers provided
some bright stars for relatively easy HPF spectrum acquisition, but do not
constitute a comprehensive list of rapidly rotating G-K giants.

In Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT STARS111 Based on
observations obtained with the Hobby-Eberly Telescope, which is a joint
project of the University of Texas at Austin, the Pennsylvania State
University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen. we list basic data for the program stars, and the most
important measured quantities in this study. The original Li abundance papers
used a variety of names for these stars. But almost all of our survey red
giants have identifications in the Tycho-2 catalog (Høg et al., 2000)444
https://www.cosmos.esa.int/web/hipparcos/tycho-2. We adopt these “TYC”
designations throughout this paper when possible. However, many discovery
papers on Li-rich red giants have focused on relatively bright stars, and have
identified them with more traditional names from the HD or BD catalogs.
Therefore we also include in Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH
RED GIANT STARS111 Based on observations obtained with the Hobby-Eberly
Telescope, which is a joint project of the University of Texas at Austin, the
Pennsylvania State University, Ludwig-Maximilians-Universität München, and
Georg-August-Universität Göttingen. the HD numbers when available, else BD
numbers when possible. There are 278 program stars entered in Table THE ACTIVE
CHROMOSPHERES OF LITHIUM-RICH RED GIANT STARS111 Based on observations
obtained with the Hobby-Eberly Telescope, which is a joint project of the
University of Texas at Austin, the Pennsylvania State University, Ludwig-
Maximilians-Universität München, and Georg-August-Universität Göttingen.. Of
this total, 76 stars are Li-rich according to the tentative definition
discussed above, 187 stars are Li-poor, and 15 stars have no Li abundance.

Some of the program stars have more than one published Li abundance. Our work
with the He i $\lambda$10830 transition does not require detailed assessment
of literature Li values, so for this paper we have cited a single Li reference
in Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT STARS111 Based on
observations obtained with the Hobby-Eberly Telescope, which is a joint
project of the University of Texas at Austin, the Pennsylvania State
University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen. for each star. We have not undertaken any
renormalization of the abundances, and quote log $\epsilon$(Li) to just one
significant digit in the table.

Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT STARS111 Based on
observations obtained with the Hobby-Eberly Telescope, which is a joint
project of the University of Texas at Austin, the Pennsylvania State
University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen. also contains two additional sets of stars that are
special-purpose targets. The first group are red giant members of NGC 7789.
This is an open cluster with intermediate-age ($t$ $\sim$ 1.7 Gyr; WEBDA,
Mermilliod 1995)555 https://webda.physics.muni.cz/navigation.html and solar
metallicity, e.g., Overbeek et al. (2015), Donor et al. (2018), Carrera et al.
(2019), Casamiquela et al. (2019). Pilachowski (1986) discovered that NGC 7789
hosts one and possibly two Li-rich giants, which made this cluster an
attractive target for our $\lambda$10830 survey. We obtained spectra for 10 of
Pilachowski’s red giants, and we tabulate here our $\lambda$10830 measurements
for them, identifying them by cluster and star name. However, we defer
discussion of these data to a more general study that contains new optical
high-resolution spectra for this cluster (Nagarajan et al., in preparation).

The second special target group are Kepler satellite field giants drawn from
those studied by Takeda & Tajitsu (2017); Singh et al. (2019b, 2021). These
are identified in Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT
STARS111 Based on observations obtained with the Hobby-Eberly Telescope, which
is a joint project of the University of Texas at Austin, the Pennsylvania
State University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen. by their Kepler Input Catalog (KIC) numbers. The Kepler
field giants have detailed evolutionary state information obtained through
asteroseismology. We have observed 13 of these stars, but our selection was
heavily biased toward those with known very high Li abundances. We are now
gathering $\lambda$10830 observations for a much larger Kepler giant sample.
Therefore we have chosen to report here the He measurements already done, but
will defer discussion of them until the larger set of spectra is gathered
(Mallick et al., in preparation).

##  3 OBSERVATIONS AND REDUCTIONS

We gathered HET/HPF high$-$resolution $zyJ$ (8100$-$12750 Å) spectra of the
program stars for about a year beginning in April 2021. HPF was designed to
aid in the search for low-mass companions to M-dwarf stars, and it has unique
design features that deliver extremely high-precision radial velocities (down
to $\sim$1-2 m s-1). This instrument has been described in detail by Mahadevan
et al. (2012, 2014).666 see https://hpf.psu.edu/ for additional instrument
information. HPF was configured for our program to deliver spectral resolving
power $R$ $\equiv$ $\lambda/\Delta\lambda$ $\sim$ 55,000.

In the $zyJ$ spectral region, telluric molecular blockage ranges from near
zero to almost a complete blanket, varying significantly with wavelength. The
dominant telluric contaminators are H2O bands, and their spectrum blockage can
change substantially on timescales of hours to nights. Regular observations
are obtained of rapidly-rotating hot stars that can be used to cancel the
telluric features in the program stars. The HET’s fixed altitude is an asset
here: all stars have identical air masses, thus it is not necessary to gather
hot-star spectra to accompany each target spectrum. Divisor-star spectra
adequate for our needs are normally gathered 1-2 times during nights with
stable atmospheric conditions.

Figure 2:  An example of telluric absorption line cancellation near the
$\lambda$10830 transition. For this figure a program star with very high S/N
but weak He i absorption depth was chosen. The top panel contains the
stellar+telluric spectrum, and the middle panel has the spectrum of a warm
(essentially featureless) star. The division of these two spectra produces the
purely stellar program star spectrum in the bottom panel.

HPF observations of target and telluric divisor stars were initially reduced
with the HPF pipeline code $Goldilocks$.777
https://github.com/grzeimann/Goldilocks_Documentation This facility, run
automatically within a day of data acquisition, processes raw HPF data frames
into useful spectra by removing bias noise, correcting for instrumental
nonlinearity, masking significant anomalous radiation events, calculating the
slope/flux and variance image using the algorithms from the $pyhxrg$ module in
the tool $HxRGproc$ (Ninan et al., 2018), and performing optimal extraction of
the 28 spectral orders. HPF’s wavelength scale in spectra reduced with
$Goldilocks$ is extremely stable and accurate to levels far beyond that needed
for our analyses of the program star spectra. For each stellar source, the
$Goldilocks$ spectral files have several extensions, including ones for the
target, the local night sky emission, noise, and wavelength calibrations.

The rest of the reductions were performed with the IRAF888
http://iraf.noao.edu/ (Tody, 1986, 1993) facility. We used the disptrans task
to shift the $Goldilocks$ vacuum wavelengths to air wavelengths. Sky
subtraction and mating of target fluxes and wavelengths produced standard
echelle FITS spectra. We then performed continuum normalization of the target
spectra and hot star spectra via the continuum task and used the telluric task
interactively to divide out this contamination from the target spectrum.
Figure 2 illustrates the large number of telluric features in the HPF spectral
order containing $\lambda$10830, and the necessity of iterative division
operations to produce optimal elimination of the tellurics. A final continuum
normalization was followed by merging into a single continuous spectrum with
the scombine task.

To correct observed stellar velocities to a rest wavelength scale accurate
enough for our purposes, we first determined the velocity shifts using IRAF
$splot$ to measure the observed wavelengths of several strong atomic lines in
the spectral order containing the He i $\lambda$10830 feature. Their average
displacement from rest in velocity units provided a shift to stellar rest
velocity accurate to $\sim\pm$0.1 km s-1.

In Figure 3 we display spectra of some typical program stars in the HPF order
that contains the He i $\lambda$10830 feature. The left-hand panel shows
essentially the entire order, covering the spectral range $\sim$10820$-$10960
Å. Star TYC 3590-03350-1 is at the low-temperature end, and TYC 0188-00998-1
is at the high-temperature end of our sample. Star TYC 1158-00345-1 has one of
the larger Li abundances, log $\epsilon$(Li) = 3.1 (Kumar et al. 2011 and
references therein). TYC 4977-01458-1 and TYC-0188-00998-1 have high
rotational velocities, and they have strong He i absorption lines, common
among our program stars. The right-hand panel shows just a small wavelength
interval centered on the $\lambda$10830 line.

Figure 3:  Reduced and telluric-corrected spectra of seven program stars in
the HPF spectral order that contains He i 10830.3 Å. The left-hand panel shows
the entire HPF order that contains the $\lambda$10830 line. The right-hand
panel zooms in to a 10 Å interval centered on the $\lambda$10830 feature. The
wavelength of the strongest two components of the He i triplet is shown with a
dotted line.

##  4 HE I $\lambda$10830 ANALYSIS

Red giants present rich absorption-line spectra in the $zyJ$ spectral domain.
But the present purpose is to investigate just the He i $\lambda$10830
transition. This line in absorption connects the energy states $1s2s^{3}S$
(19.82 eV) and $1s2p^{3}P^{o}$ (20.96 eV), as illustrated in Figure 3 of
Preston et al. (2022). Neither the lower nor the upper state has a permitted
transition to the $1s^{2}$ ${}^{2}S$ ground state. It is a hyperfine-split
triplet, with components at 10829.09, 10830.25, and 10830.34 Å, with
transition probabilities $-$0.745, $-$0.268, and $-$0.046 respectively in the
NIST database (Kramida et al., 2019; Kramida, 2019).999 National Institute of
Standards and Technology Atomic Spectra Database:
https://www.nist.gov/pml/atomic-spectra-database

Appearance of the very high-excitation He i $\lambda$10830 line in cool red
giants essentially signals chromospheric activity that is detached from the
formation of the photospheric spectrum. Its line profile can be very broad, in
some cases covering several Ångstroms. In this small region there are several
photospheric absorption lines, including the very strong Si i 10827.1 Å
transition and other weak-but-detectable ones: Ti i 10827.9 Å, Ca i 10829.3 Å,
and a couple of significant CN lines. In particular the Ca i line can
significantly contaminate the He i transition. We wanted to make accurate
estimates of the equivalent width ($EW$) of only the $\lambda$10830 He i
feature, and so we created synthetic spectra to match and then cancel the
surrounding photospheric atomic and molecular transitions.

###  4.1 Line List for Synthetic Spectra

To generate line lists for the synthetic spectra, we used the $linemake$
facility (Placco et al., 2021)101010 https://github.com/vmplacco/linemake,
which begins with the Kurucz (2011, 2018)111111
http://kurucz.harvard.edu/linelists.html line compendium, and substitutes or
adds line transition data generated in recent laboratory studies mainly by the
Wisconsin-Madison atomic physics group (Den Hartog et al. 2021 and references
therein) and by the Old Dominion University molecular physics group (e.g.,
Brooke et al. 2016 and references therein). Unfortunately there have been few
laboratory atomic studies of transitions in the past couple of decades for the
lines of interest near 10830 Å. Therefore we adopted the transition
probabilities available in the NIST database for lines of the most prominent
species in this spectral region: Na i, Mg i, Al i, Ca i, Fe i, and Sr ii.

We tested this line list by generating synthetic spectra of the red giant
standard star Arcturus. The observed spectrum was from Hinkle & Wallace
(2005). We adopted the model atmosphere parameters derived by Ramírez &
Allende Prieto (2011): $T_{\rm eff}$ = 4286 K, log(g) = 1.66, [Fe/H] =
$-$0.52, $V_{mic}$ = 1.74 km s-1, as well as the elemental abundance ratios
given in that paper. We produced an interpolated model with these values from
the Kurucz (2011, 2018) grid121212 http://kurucz.harvard.edu/grids.html using
software developed by Andy McWilliam and Inese Ivans (private communication).
The synthetic spectra for Arcturus and all other stars in this paper were
generated using the current version of the LTE synthetic spectrum code MOOG
Sneden (1973)131313 Available at http://www.as.utexas.edu/ chris/moog.html.

Iterative comparison of observed and synthetic Arcturus spectra led to
adjustments in the transition probabilities and wavelengths of some
transitions in the line list. In making these changes we did not alter any
atomic or molecular line data that were from NIST or recent laboratory
analyses. Finally, to verify the reasonableness of the final line list we also
checked its applicability to the spectra of the Sun and a couple of program
stars. This procedure yielded an atomic/molecular line list for our task of
adequately matching synthetic and observed photospheric spectra of our red
giant stars, but should not be confused with a list that would be appropriate
for detailed abundance analyses.

###  4.2 Estimated Model Photospheres

Nearly all of our program stars are Galactic disk red giants, having
metallicities almost entirely in the domain [Fe/H] $\gtrsim$ $-$0.5. With the
goal limited to adequate removal of the photospheric spectrum near the He i
$\lambda$10830 feature, we adopted effective temperatures $T_{\rm eff}$ from
photometry and surface gravities log(g) representative of first-ascent, RC,
and RHB giants at the chosen $T_{\rm eff}$ values.

We first constructed a set of model stellar photospheres. The desired
parameter domain can be seen both in a color-magnitude diagram (CMD) and a
$T_{\rm eff}$$-$log(g) HR diagram of our targets. From the magnitudes and
parallaxes in Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT
STARS111 Based on observations obtained with the Hobby-Eberly Telescope, which
is a joint project of the University of Texas at Austin, the Pennsylvania
State University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen., and ignoring possible interstellar reddening
corrections141414 Most of our stars are bright and have distances $<$1 kpc, so
the reddening should usually be small. Moreover, we lack the information to
assess reddening corrections accurately for most of our targets. , we
constructed the CMD shown in the top panel of Figure 4. Added to this figure
is a shaded area that approximately outlines the red horizontal branch CMD
area identified empirically by Kaempf et al. (2005) in $M_{V}$ versus $B-V$
coordinates. In this figure panel the majority of our stars have CMD locations
consistent with RC/RHB membership, and there is no apparent segregation
between Li-rich and Li-poor stars. On average they occupy the same
evolutionary states.

In the bottom panel of Figure 4 we plot $T_{\rm eff}$ and log(g) values of the
program stars estimated from $Gaia$ EDR3 (Gaia Collaboration et al., 2021)
photometry. Here the shaded area represents the RC/RHB $T_{\rm eff}$ domain
used by Afşar et al. (2018). There are fewer data points in this Figure 4
panel than in the top one simply because many program stars do not have $Gaia$
Tphot and log(g)phot values. But inspection of both upper and lower panels
suggests the same conclusion: most stars reside in the RC/RHB region, and on
average the locations of Li-poor and Li-rich stars are the same.

Figure 4:  Top panel: a color-magnitude diagram (CMD) for the targets. The
plot boundaries have been set to show only the CMD area containing the first-
ascent red giants, the RC, and the RHB. The main sequence, most of the
subgiant branch, and the luminous giants and supergiants are outside of this
CM area. Different colors and symbols denote Li-rich and Li-poor stars, and a
freehand shaded region represents the He-fusing RC/RHB domain. Bottom panel:
an HR diagram based on $Gaia$ photometric quantities. Colors and symbols are
the same as in the top panel.

We extracted model atmospheres from the ATLAS grid (Kurucz, 2011, 2018). The
model effective temperatures were computed in steps of 100 K in the range 4000
$\leq$ $T_{\rm eff}$ $\leq$ 5600 K. The model gravities were estimated from
recent empirical temperature-gravity correlations for metal-rich giant stars:
Figure 8 of Afşar et al. (2018), and Figure 3 of Casey et al. (2019). At the
high temperature end nearly all stars are on the core helium-burning
horizontal branch, so we adopted a uniform log(g) = 3.0 in the range
5300$-$5600 K. For cooler temperatures the adopted gravities were decreased
steadily, ending with log(g) = 1.3 at $T_{\rm eff}$ = 4000 K. Model
metallicities were assumed to be solar, [M/H] = 0.0, and microturbulent
velocities were assumed to be $V_{mic}$ = 2.0 km s-1; neither of these model
parameter choices were critical for our desired photospheric spectrum
computations.

Whenever possible, we used observed $V-J$ colors and the color-$T_{\rm eff}$
relations of Ramírez & Meléndez (2005) to select appropriate $T_{\rm eff}$
values for each star, adopting a model atmosphere with the parameters as
described above. When $J$ magnitudes were not available we used $B-V$ colors,
and in a handful of cases we adopted models near those derived in individual
papers, or simply guessed at a starting model parameter set. In this procedure
we ignored possible interstellar reddening because our stars are mostly near
enough to not suffer large amounts of extinction, as noted above. We re-
emphasize that we used the modeling only to reasonably match the photospheric
spectrum transitions. Our procedures were entirely inadequate for detailed
photospheric analyses, and so we do not publish the model parameters adopted
here.

###  4.3 Observed/Synthetic Spectrum Matches

Figure 5:  Examples of photospheric spectrum cancellation. For each star the
top panel shows an observed spectrum (black points) and the best-fit model
photospheric spectrum (line), and the bottom panel shows the result of the
observed/computed division.

We computed synthetic spectra of the stars in the 10820$-$10960 Å region (the
complete HPF spectral order containing $\lambda$10830), using the line list
described in §4.1 and model atmospheres in §4.2. The computed synthetic
spectra were compared interactively with the observed spectra. The syntheses
included combined thermal, microturbulent, and collisional damping line
broadening effects, while the observed lines included these and additional
broadening due to instrumental, macroturbulent, and in some instances
rotational effects. These extra broadening contributions were accounted for in
most cases by Gaussian smoothing functions with empirically-determined
broadening values that minimized the differences between observed and
synthetic spectra. From iterative spectrum matches we were able to determine
Gaussian full-width-half-maxima values to precisions of $\sim\pm$0.02 Å. For
some stars the smoothing functions combined Gaussian and rotational factors.
In §4.5 we discuss spectrum line broadening in more detail.

We then performed a rough abundance determination in order to best match
synthetic and observed spectra near 10830 Å. We began with setting the N
abundance, because the CN (0$-$0) Q-branch bandhead culminating at 10925 Å and
the (0$-$0) R-branch bandhead at 10870 Å often dominate those spectral regions
(see Figure 3), and weaker CN lines occur in the whole spectral order. Then we
altered the Fe, Si, and Ca abundances to minimize the differences between the
synthetic and observed atomic lines. Although Na i, Ti i, and Sr ii have
significant absorption lines in this spectral order, none of them are close
enough to the He i $\lambda$10830 transition to matter for our work.

The final step was to divide stellar and synthetic photospheric spectra to
yield an essentially pure chromospheric spectrum of the He i line. In Figure 5
we show examples of the He i isolation and measurement process for a typical
program star with a modest He i line, and for a rapid rotator with a much
stronger line. For the left-hand panels, TYC 3011-00547-1 was chosen to
illustrate typical $S/N$ conditions and the limits to our ability to
completely extinguish the photospheric spectra. In the right-hand panels we
show the same observed, synthetic, and resultant spectra for the rapidly-
rotating star TYC 0455-02910-1. Contamination by neighboring photospheric
features is the dominant uncertainty source here. But the $\lambda$10830 line
clearly is strong in the divided spectrum.

###  4.4 Equivalent Widths

We measured $EW$s of the $\lambda$10830 lines using the specialized spectrum
analysis code SPECTRE (Fitzpatrick & Sneden, 1987)151515 Available at
http://www.as.utexas.edu/$\sim$chris/spectre.html. The He i transition is
usually very broad, with extended wings sometimes covering more than 2 Å. Its
line profile often has small distortions due to incomplete cancellation of
telluric and photospheric contaminating features. Therefore we measured
$EW_{\rm He}$ via direct Simpson’s Rule161616 e.g., see
https://math24.net/simpsons-rule.html integrations. The $EW_{\rm He}$ values
are listed in Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT
STARS111 Based on observations obtained with the Hobby-Eberly Telescope, which
is a joint project of the University of Texas at Austin, the Pennsylvania
State University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen..

He i absorption always is present in our stellar sample, albeit very weak and
hard to measure in a few stars. There is a very large star-to-star
$\lambda$10830 equivalent width range, $EW_{\rm He}$ $\simeq$ 20$-$1300 mÅ.
Therefore for the remainder of this paper we will quote reduced widths for the
10830 Å lines:

${\rm log(}RW_{\rm He})\equiv\ log_{10}(EW_{\rm He}/\lambda)=log_{10}(EW_{\rm
He}/10830)$ (1)

where $EW_{\rm He}$ is in units of Å. The log($RW_{\rm He}$) range in our
stars is $\simeq$ $-$5.7 to $-$3.6.

For TYC 3011-00547-1 (Figure 5 left panels) we measured log($RW_{\rm He}$) =
$-$4.94 $\pm$ 0.04 ($EW$ = 125 $\pm$ 13 mÅ), with the large uncertainty value
based mostly on continuum placement, which directly impacts the wavelength
extent of the He i line wings. For TYC 0455-02910-1 (Figure 5 right panels) we
found log($RW_{\rm He}$) = $-$4.50 $\pm$ 0.03 ($EW$ = 345 $\pm$ 15 mÅ). Our
measurements of $\lambda$10830 in the full sample yielded an estimated general
log($RW_{\rm He}$) uncertainty of $\pm$0.04 dex, which we will adopt hereafter
in this paper.

###  4.5 Line Broadening

Figure 6:  Empirical broadening estimates compared to He i $\lambda$10830
reduced widths for stars that have relatively narrow line profiles. Point,
line, and color types are identified in the figure. The ordinate of the plot
is restricted to 0$-$12 km s-1 in order to see individual points clearly. This
means that stars with $V$sin($i$) $\gtrsim$ 12 km s-1 are not shown here. The
point with error bars in the lower right-hand corner represents the typical
uncertainties of the measurements, as explained in the text. The $FWHM$ values
were estimated to the nearest 0.01 Å ($\simeq$0.3 km s-1), as can be seen in
their “quantized” values.

As described in §4.3, for spectra without detectable rotational line
broadening we used comparisons of observed and synthetic spectra to estimate
full widths at half-maximum ($FWHM$) values for the Gaussian smoothing
functions that account for instrumental and macroturbulent broadening. In
Figure 6 we correlate these $FWHM$ estimates with He i reduced widths. The
ordinate of this figure covers only the line breadth range 5 $<$ $FWHM$ $<$ 12
km s-1, allowing one to see that our $FWHM$ estimates were quantized. That is,
in the synthesis/observation comparison the $FWHM$ values were changed in
steps of 0.01 Å, which translates to the spacing of $\simeq$0.28 km s-1 that
can be seen in Figure 6. For stars with quiet chromospheres, log($RW_{\rm
He}$) $\lesssim$ $-$4.8, the observed photospheric-line widths appear to be
constant to within our measurement uncertainties. Neglecting the few aberrant
points with $FWHM$ $\gtrsim$ 9 km s-1, the mean value is $<$FWHM$>$ = 0.28 Å
($\sigma$ = 0.03 Å), or 7.7 km s-1 ($\sigma$ = 0.5 km s-1). The median value
is slightly lower: 7.5 km s-1, which is indicated by the dotted red line in
Figure 6.

The instrumental resolving power $R$ = 55,000 contributes 5.5 km s-1 to the
FWHM. We cannot determine directly a macroturbulent velocity, but the
comparison between observed and instrumental $FWHM$ values suggests that Vmac
$\simeq$ 2.2 km s-1, a number that is nearly identical to our assumed
$V_{mic}$ = 2.0 km s-1. If Vmac $\sim$ $V_{mic}$, then the empirically
measured Gaussian smoothing values for stars with weak $\lambda$10830 lines
appear to successfully account for realistic line broadening in our red
giants. We adopt 0.5 km s-1 as a reasonable estimate of the $FWHM$
uncertainties derived from our simple estimates.

In Figure 6 some stars are identified as rapidly rotating, meaning that our
synthetic-observed spectrum matches were improved by applying a combination of
rotational and Gaussian smoothing to the calculated syntheses. Our rotational
line broadening estimates were entirely empirical, based on standard
relations171717 e.g., http://www.astro.uvic.ca/$\sim$tatum/stellatm/atm6.pdf,
with an assumed limb darkening coefficient $u$ = 0.5 (see Figure 17.6 in Gray
2008). We found through repeated trials on many program star spectra that
rotation could only be detected with confidence at smoothing widths $\gtrsim$
10 km s-1. In the cases for which rotation could be detected, we set the
Gaussian components (accounting for all broadening sources except rotation) to
have $FWHM$ values of 0.25 km s-1. The rest of the broadening was assumed to
be caused by rotation. In Figure 6 the widths plotted for these stars are the
rotational $V$sin($i$) values only.

There were some stars with derived $FWHM$ $\gtrsim$ 10 km s-1 for which we
could not detect rotational broadening with certainty. In these cases we have
reported the Gaussian-only broadening. It is likely that in some cases such
stars have rotational signatures that will be revealed with more rigorous
analyses of spectra covering a much larger wavelength range than that studied
here. The Gaussian or rotational broadening values for all stars are listed in
Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT STARS111 Based on
observations obtained with the Hobby-Eberly Telescope, which is a joint
project of the University of Texas at Austin, the Pennsylvania State
University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen..

Figure 7:  Empirical broadening estimates compared to He i $\lambda$10830
reduced widths for the whole sample. Point types and colors are as in Figure
6, except that a filled circle is used to call attention of TYC 3797-01268-1,
a program star with large infrared color excesses. This object will be
discussed in §5.3.  Figure 8:  Comparison of $V$sin($i$) estimates in this
work versus values published in various literature sources. The red dashed
line indicates agreement between the two data sets. The thick blue $\times$
symbol marks TYC-3797-01268-1, noted earlier in Figure 7.

In Figure 7 we plot log($RW_{\rm He}$) versus $FWHM$ for all of the program
stars. Red giants with large $\lambda$10830 absorption features can have sharp
line profiles ($FWHM$ $<$ 10 km s-1) or can have obvious rotationally
broadened spectra. But nearly all of our rapidly rotating program stars have
very strong He i absorption features (log($RW_{\rm He}$) $\gtrsim$ $-$4.7).
There are only two exceptions in our sample.

We have searched the literature for published $V$sin($i$) measurements of our
stars. Various papers have used heterogeneous methods to derive $V$sin($i$)
from spectroscopic data sets with a variety of attributes. In Table 2 we list
these literature values and their sources. Figure 8 shows a comparison of our
rotational velocity estimates with the published ones, and from the statistics
quoted in the figure legend, it is clear that they are in good agreement. Note
the small systematic offset at the low $V$sin($i$) end of the correlation.
This indicates that translation of our measured line widths into $V$sin($i$)
values is probably too simplistic for the complex combination of instrumental,
thermal, microturbulent, macroturbulent, and rotational line components at
small rotational velocities.

##  5 LI AND HE IN LI-POOR AND LI-RICH STARS

Figure 9:  log($RW_{\rm He}$) values plotted versus lithium abundances log
$\epsilon$(Li). The horizontal shaded region serves to roughly divide Li-rich
from Li-poor stars, and the vertical shaded region separates the weak and
strong $\lambda$10830 absorption strengths. The location of these lines is
discussed in the text. As in Figures 6 and 7, black $\times$ symbols represent
stars with Gaussian measured line profiles, blue open circles are stars with
rotational line profiles, and a blue filled circle denotes TYC 3797-01268-1
(see §5.3).  Figure 10:  Histograms representing the distribution of
log($RW_{He}$) values Li-poor (upper panel) and Li-rich (lower panel) stars.
The vertical shaded region, drawn at log($RW_{He}$) = $-$4.85 as in Figure 9,
separates the weak and strong $\lambda$10830 absorption strengths.

Our basic result is that strong He i $\lambda$10830 absorption is rare in Li-
poor stars but very common in Li-rich ones. This conclusion is clear in Figure
9, where we compare Li abundances and log($RW_{\rm He}$) values, and in Figure
10, where histograms of log($RW_{\rm He}$) are shown for the Li-poor and Li-
rich groups. The horizontal shaded area centered at log $\epsilon$(Li) = 1.25
divides Li-poor and Li-rich abundance regimes, and the vertical band at
log($RW_{\rm He}$) = $-$4.85 divides weak and strong He i absorptions. These
lines create four apparent quadrants of different Li abundances and He
strengths, as labeled in the figure. These group separations were determined
empirically, and they merit further discussion.

In this exercise one should keep in mind that our stellar sample is not
statistically robust. First and foremost, all of our Li abundances are
literature values, which guarantees their heterogeneity. We have made no
attempt to put them on a common abundance system with consistent atmospheric
parameters. This is of no consequence for stars with very large Li abundances.
However for stars with lesser abundance values, 1.0 $\lesssim$ log
$\epsilon$(Li) $\lesssim$ 1.5, assignments into Li-rich or Li-poor categories
should be viewed with caution. Secondly, our Li-rich stars were chosen through
a literature search for reports of such stars. Some of the papers considered
the relative frequency of Li-rich stars, and others concentrated mostly on the
properties of individual Li-rich objects. Our Li-rich stars have irregular
literature histories.

###  5.1 Li-poor Stars with Weak He i $\lambda$10830 Absorptions

For the Li-poor stars we used mostly candidates from the surveys of Adamów et
al. (2014) and Afşar et al. (2018), neither of which were biased in any way on
Li abundances. The Adamów et al. sample was the set of red giants of the Penn
State-Toruń Planet Search (PTPS) program (Deka-Szymankiewicz et al. 2018 and
references therein). Their Li abundances were derived in that paper and thus
took no part in sample selection. The Afşar et al. target list was formed from
CMD searches for stars that appeared to be in the He-burning red horizontal-
branch domain, ignoring possible Li abundance information. The Li abundances
for these stars in Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT
STARS111 Based on observations obtained with the Hobby-Eberly Telescope, which
is a joint project of the University of Texas at Austin, the Pennsylvania
State University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen. will be presented by Bozkurt et al. (in preparation).
In general, our Li-poor stars have an abundance spread that is typical for
normal red giants.

The observed distribution of log($RW_{\rm He}$) among Li-poor stars in the
lower left quadrant of Figure 9 shows a sharp drop in number near log($RW_{\rm
He}$) $\simeq$ $-$4.85, with an uncertainty of about $\pm$0.05 by visual
inspection. We have 187 Li-poor stars as defined earlier (log $\epsilon$(Li)
$<$ 1.5). Of these, 168 stars have log($RW_{\rm He}$) $<$ $-$4.85, or 90%,
while only 18 (10%) have stronger $\lambda$10830 He i absorptions. Small
alterations of the Li abundance and He line strength dividing lines would do
quantitatively little to this result. The vast majority of red giants have
small Li abundances and weak He i $\lambda$10830 transitions. For the rest of
this paper we adopt log($RW_{\rm He}$) = $-$4.85 as the estimated break point
between stars with weak and strong $\lambda$10830 transitions.

With this He i estimated strength boundary we revisit the CMD of Figure 4, and
in Figure 11 we show the MV versus V-J diagram with points separated at
log($RW_{\rm He}$) = $-$4.85. Comparison of this figure to the top panel of
Figure 4 reveals general similarity. The majority of both He-weak and He-
strong stars reside in the clump/RHB domain, and there is no obvious
separation between the CMD distributions of the two He groups. Strong He i
absorption features, like large Li abundances, appear most frequently in red
giant clump and red horizontal branch stars.

Investigation of He absorption in red giants began with the moderate
resolution ($R$ $\sim$ 14,000) image-tube survey by Zirin (1982) of 455 stars
of interest identified from Ca ii K-line measurements, and X-ray, and
variability studies. O’Brien & Lambert (1986) provided the pioneering high-
resolution ($R$ $\simeq$ 54,000), high signal-to-noise (typically
$\gtrsim$100) survey of $\lambda$10830 for G-K-M giants and supergiants. Many
of their targets were either luminous giants and supergiants (luminosity
classes I-II) or very cool ones (temperature class M). Such stars often have
large and variable He i $\lambda$10830 profiles, usually dissimilar to those
in the G-K giants of interest here. However, O’Brien & Lambert identified a
class of less luminous K giants, which they labeled “$\beta$ Gem type”, that
have relatively modest $\lambda$10830 absorptions which do not appear to vary
much with time. With ($V-J$) and $M_{V}$ values constructed from SIMBAD
(Wenger et al., 2000) data, we identified about 25 of their stars lying within
the boundaries of Figure 4. A direct comparison of their $EW$ values with our
measurements is not possible because their sample has only very bright stars
($J$ $<$ 3.0) that cannot be observed with HET/HPF. However, we estimated a
median log($RW_{\rm He}$) $\sim$ $-$4.95 for their less luminous K giants,
less than our estimated upper limit for weak $\lambda$10830 lines. The median
for our Li-poor stars, log($RW_{\rm He}$) $\sim$ $-$5.10, is somewhat smaller
than that from O’Brien & Lambert (1986), but with different instruments,
different log($RW_{\rm He}$) measurement techniques, and lack of stars in
common this small issue will not be pursued further.

###  5.2 The Li-poor/Li-rich Split

Papers discussing Li abundances in red giants usually adopt log $\epsilon$(Li)
= 1.5 as the minimum abundance for a star to be considered as Li-rich, and we
have followed this practice earlier in the paper. This value goes back to the
Iben (1967) stellar evolutionary computations, leading to “a standard first
dredge-up dilution factor of $\sim$60, for a star with an initial cosmic
abundance of 3.3 dex”. (Charbonnel et al., 2020). However, today we recognize
that the actual distribution of Li in evolved stars is the result of a complex
set of processes involving stars of different masses beginning with a variety
of initial conditions, followed by Li destruction mechanisms throughout the
main sequence and subgiant evolutionary phases. Several recent papers consider
this point, including Aguilera-Gómez et al. (2016), Casey et al. (2019),
Charbonnel et al., Kumar & Reddy (2020), and Martell et al. (2021). It is
evident from these studies that Li enhancement is mostly associated with RC
giants in the He-core burning phase. Singh et al. (2021) proposed a re-
classification of RC giants based on Li abundances and asteroseismic
properties into three categories: Li-normal (log $\epsilon$(Li) $<$ 1.0), Li-
rich (1.0 $<$ log $\epsilon$(Li) $<$ 3.2), and super-Li-rich (log
$\epsilon$(Li) $>$ 3.2). Thus the “traditional” Li-rich marker, log
$\epsilon$(Li) = 1.5$-$1.8 depending on mass, is now recognized as convenient
upper limit for giants ascending the RGB for the first time but too simplistic
in describing the Li abundance history of real stars. The only reported Li-
rich first-ascent RGB giant that has been classified using asteroseismic data
is KIC 9821622 (Jofré et al., 2015). Singh et al. (2020) have re-analyzed this
star and derived a lower Li abundance, substantially smaller than the
suggested super-Li-rich category. As of today we do not know of any giant with
log $\epsilon$(Li) $>$ 1.8 that is classified as a giant ascending the RGB
with a He-inert core based on astroseismic analysis; certainly no super Li-
rich RGB giant has been found (Singh et al., 2019b).

Our assessment of the Li-poor/Li-rich division comes simply from inspection of
the distribution of points in Figure 9. The most obvious separation of stars
in Li abundance occurs near log $\epsilon$(Li) $\simeq$ 1.0, with Li-poor
stars aggregating at small log($RW_{\rm He}$) values while Li-rich stars have
much larger star-to-star log($RW_{\rm He}$) scatter. Therefore, we have chosen
to set the Li-rich/Li-poor split at log $\epsilon$(Li) = 1.25, with an
uncertainty of at least 0.1 dex. We emphasize again that this line is a
convenient demarcation between the two Li stellar groups, and it should not be
considered a well-determined rigid boundary.

Figure 11:  Another CMD for the targets. This plot contains the same data that
are displayed in the top panel of Figure 4, but here the stars are divided
into He-weak and He-strong groups, as indicated in the figure legend.

###  5.3 The Li-rich Red Giants

Our sample has 84 stars with log $\epsilon$(Li) $>$ 1.25. Of these, 46 have
log($RW_{\rm He}$) $>$ $-$4.85 (55%). This high fraction of Li-rich stars with
strong $\lambda$10830 absorptions can be easily seen in Figure 9 and in the
bottom panel of Figure 10. Small adjustments of the Li abundance and/or He i
line strength divisions do not disturb the basic positive Li/He connection in
Li-rich stars.

Almost all of the strongest $\lambda$10830 features are detected in rapidly-
rotating stars. Nine of the 10 stars with log($RW_{\rm He}$) $>$ $-$4.2 ($EW$
$>$ 680 mÅ) have rotational metal line profiles. But many Li-rich stars with
$-$4.85 $<$ log($RW_{\rm He}$) $<$ $-$4.20 exhibit no excess line broadening.
Therefore, in line with conclusions of literature Li abundance studies, it is
clear that rapid rotation is not a requirement for either Li abundance excess
or for strong He i absorption. It is more certain that rotation is linked with
strong He i lines. Our sample has 28 stars with detectable rotational line
profiles, and only two of them have weak $\lambda$10830 absorptions,
log($RW_{\rm He}$) $<$ $-$4.85 (Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH
RED GIANT STARS111 Based on observations obtained with the Hobby-Eberly
Telescope, which is a joint project of the University of Texas at Austin, the
Pennsylvania State University, Ludwig-Maximilians-Universität München, and
Georg-August-Universität Göttingen.).

Large rotation and strong $\lambda$10830 absorption do not guarantee large Li:
three such stars in Figure 9 have log $\epsilon$(Li) $\lesssim$ 0.0. But Li
enhancement among giants is a transient phenomenon; very large Li abundances
decline with time, as shown by Singh et al. (2021). The consequence of this is
that there may be some Li-poor giants that still have strong He i
$\lambda$10830 transitions and high rotation rates.

The $\lambda$10830 triplet has become a powerful diagnostic of physical
conditions and dynamics in many stellar and exoplanetary objects. As discussed
in §4 the lower energy level of the transition lies at 19.8 eV and is
metastable. This mandates that reasonably high chromospheric temperatures are
required to produce the line; it cannot be a photospheric transition. Direct
evidence from the Sun demonstrated that the transition could be produced as a
result of photoionization by radiation occurring shorter than 504 Å, followed
by recombination into the lower metastable level of the transition. The
relationship between X-ray radiation and the strength of the helium line in
the solar case (Harvey et al. 1975, Cranmer 2009) inspired early studies of
the transition in cool stars (Zarro & Zirin 1986, O’Brien & Lambert 1986).
These authors found a strong correlation between the $EW$ of the
$\lambda$10830 line and the value of LX/Lbol for cool dwarfs and for G and K
giant stars. Sparse data exist for G and K supergiants, but a correlation
appears likely.

A direct measure of the photoionizing flux in dwarfs and giants suggested that
the photoionization and recombination process dominates in giant stars.
However, active dwarfs and subgiants appear not to exhibit a correlation
between the photoionizing flux and helium line strength, presumably due to
their higher chromospheric densities (Sanz-Forcada & Dupree, 2008).

Another feature of the $\lambda$10830 transition derives from its metastable
nature which makes the line profile a tracer of a stellar wind flow. Dupree et
al. (1996) detected blue-wing asymmetries of this transition, leading to the
inference of radial outflows from the Sun. This feature has also been seen in
luminous stars (O’Brien & Lambert 1986, O’Brien & Lambert 1986) including
metal-poor field giants (Dupree et al. 1992, 1996). However, stellar winds are
unlikely to be major contributors to the He i line formation in almost all of
our stars. In Figure 12 we show a mean line profile for the 40 stars with
strongest $\lambda$10830 absorptions (log($RW_{\rm He}$) $>$ $-$4.85) that
either are without detectable rotation or are not rotating rapidly
($V$sin($i$) $<$ 10 km s-1). The co-added spectra are those have already
undergone photospheric spectrum cancellation (§4.3, §4.4). Inspection of the
mean profile reveals the presence of the weakest of the $\lambda$10830 triplet
members at 10829.09 Å, but otherwise it appears to have symmetric blue and red
wings centered on the lab wavelength of the two main triplet members. There is
no evidence for the blue asymmetries that are seen in some luminous stars of
the above-cited papers.

Figure 12:  A small section of spectra showing details of the He line
profiles. The solid black line represents the mean line profile of the
strongest He i $\lambda$10830 transitions for program stars without
significant rotational broadening. The $\lambda$10830 line is a triplet, whose
components are marked with vertical red lines. The feature at 10827 Å is a
residual of imperfect cancellation of the very strong photospheric Si I line,
and should be ignored. The dotted blue line shows our single observation of
TYC 3797-01288-1. In the figure legend we quote our derived $V$sin($i$) value.
See the text for discussion of this unusual star.

###  5.4 He i $\lambda$10830 in the Unusual Li-rich Star TYC 3797-01268-1

TYC 3797-01268-1 (HD 233517) has unique properties among our program stars.
Fekel et al. (1996) first reported on the high lithium and rotation of this
star. In Tables THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT STARS111
Based on observations obtained with the Hobby-Eberly Telescope, which is a
joint project of the University of Texas at Austin, the Pennsylvania State
University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen. and 2 we quote the Balachandran et al. (2000) values of
log $\epsilon$(Li) = 4.2 and $V$sin($i$) = 17.6 km s-1. Jorissen et al. (2020)
used radial velocity and astrometric data to make a convincing case for a
binary companion to TYC 3797-01268-1.

Our He i $\lambda$10830 line spectrum for this star is very strong:
log($RW_{\rm He}$) = $-$4.10 ($EW$ = 867 mÅ). But the line profile is very
unusual for our program stars. In Figure 12 we display the TYC 3797-01268-1
spectrum, and its contrast to the 40-star mean of other strong $\lambda$10830
lines is striking. The blue-wing asymmetry discussed in §5.3 is a prominent
spectral feature of this star. To signal this star’s uniqueness we already
have labeled its position in Figures 7, 8, and 9.

Giants with very high lithium abundances and fast rotation can be understood
if the Li enhancements have been caused by external events such as mergers
with massive planets, brown dwarfs or compact objects like white dwarfs. An
expectation for the merger scenario for Li-rich giants is the presence of dust
as a result of mass loss, and hence the infrared excess (Denissenkov & Herwig,
2004; Carlberg et al., 2010; Zhang & Jeffery, 2013). However, IR excess among
giants is extremely rare as shown by various surveys, e.g., Zuckerman et al.
(1995); Bharat Kumar et al. (2015); Mallick et al. (2022). We searched for IR
excess among our program stars by using Wide-field Infrared Survey Explorer
(WISE; Wright et al. 2010) colors, as detailed in Mallick et al. (2022). Of
the 278 giants in our study 262 stars have flux measurements in all four WISE
bands (3.3 $\mu$, 4.6 $\mu$, 11.6 $\mu$, 22.1 $\mu$m). Figure 13 displays a
WISE color-diagram for red giants in general and for our program stars. This
plot is similar to the upper panels of Figure 4 in Mallick et al.. In
particular, the rectangular box is the theoretical “zero IR excess box”
computed by them based on the effective temperatures of stars in the red
giant/clump temperature domain. Observed colors with larger values of w4-w3 or
w3-w2 than the box limits are presumed to be affected by circumstellar disk
material.

Inspection of Figure 13 reveals IR excess only in TYC 3797-01268-1. This is in
agreement with the Mallick et al. conclusion that Li-rich giants with IR
excess are more likely to be fast rotators. Unfortunately, none of their
giants are in our current program because their analysis is based on the GALAH
spectroscopic survey in the southern hemisphere, largely inaccessible to
HET/HPF observations. To explore this idea more completely, it will be
necessary to analyze more rapid rotators among Li-rich giants that have strong
$\lambda$10830 transitions and IR excess. Our stellar sample, constructed with
primary attention to Li abundance, does not fairly represent the rapid-
rotation red giant sub-population. A better survey based on a large
$V$sin($i$) range is appropriate for a future study.

We also constructed flux curves for TYC 3797-01268-1 using broad-band colors
from optical to far infrared wavelengths (0.4$-$100 $\mu$m) using the spectral
energy distribution software package VOSA (Bayo et al., 2008; Rodrigo et al.,
2020)181818 Available at http://svo.cab.inta-csic.es. Comparison of the
observed flux curves to theoretical ones confirms that $IR$ excesses become
apparent at wavelengths beyond $\sim$5 $\mu$m in this star, a clean signature
of a very dusty red giant.

Figure 13:  A far-IR color-color plot from WISE. The long rectangular box
defines the limits of these colors for red giant stars without infrared
excesses, as computed by Mallick et al. (2022). Special attention is called
TYC 3797-01268-1 with a dark green $\times$ symbol. See §5.4 for discussion of
this star.

Finally, we also examined individual $\lambda$10830 profiles in our sample of
rapidly rotating stars. These profile shapes sometimes are uncertain due to
significant contamination by neighboring photospheric features, as seen in the
right panel of Figure 5. However, almost all of these He i profiles appear to
be reasonably symmetric and centered at 10830.3 Å. The single case of a
significant blue-shifted line profile is TYC 3797-01268-1.

##  6 STELLAR MOTIONS

###  6.1 Space Velocities

Figure 14:  Top panel: U-V velocity plane for Li-rich stars (orange ‘x’s) and
Li-poor stars (gray ‘x’s). Bottom Panel: Toomre Diagram for Li-rich stars and
Li-poor stars. In the Toomre diagram panel, we subtract 239 km s-1 to place
the velocities in the local standard of rest. For reference, the dashed lines
represent a constant total velocity of 70 and 180 km s-1, respectively. No
significant kinematic difference is detected between the Li-rich and Li-poor
populations.

In order to determine whether Li-rich and Li-poor stars belong to different
kinematic structures, we obtain 3 dimensional (3-D) Cartesian velocities from
Marchetti (2021). For reference, we define a 3-D Cartesian velocity (U, V, W)
and position (X, Y, Z) vector for each star whereby U is positive in the
direction pointing toward the GC, V is positive along the direction of the
disk rotation, and W is positive when pointing towards the North Galactic
pole. In this convention, we assume that the Sun’s location is (X, Y, Z) =
(8.20, 0.00, 0.025) kpc and (U, V, W) = (14.0, 250.24, 7.25) km s-1 relative
to the Galactic center (e.g., Schönrich, 2012). The spatial positions and
velocities for the stars in this study are computed using astrometric
information from the early191919 We note here that while the full third data
release of Gaia was released in June 2022, the astrometric information was not
updated between the early data release 3 and the full data release 3. data
release 3 from the Gaia spacecraft (e.g., parallax, proper motion, and sky
positions Gaia Collaboration et al., 2021). The radial velocities are also
sourced from Gaia EDR3 (Katz et al., 2019). The astrometric and radial
velocity information are then used to derive full 3-D positions and velocities
using the method outlined in section 2 of Marchetti (2021). With the 3-D
velocities for each star, we computed the probability that the star belonged
to the thin disk, thick disk, or halo population using the method outline in
section 2.4 of Ramírez et al. (2013).

In Figure 14, we show the U-V kinematic plane (top panel) and the Toomre
Diagram (bottom panel) for the Li-rich stars (orange ‘x’s) and Li-poor/normal
stars (gray ‘x’s). From these plots we find that the Li-rich stars and Li-poor
(normal) stars are mostly part of the kinematic thin disk and the two samples
do not seem significantly different. To quantify this further, we also compute
the fractions of Li-rich and Li-poor stars that are parts of the kinematic
thick and thin disks using the probabilities defined above. We find that more
than 80% of the Li-rich stars have a 70% or higher chance of belonging to the
kinematic thin disk. Similarly, $\sim$90% of the Li-normal/poor stars have a
70% or higher chance of belonging to the kinematic thin disk. From this
probabilistic kinematic analysis, as well as Figure 14, we can conclude that
the sample of Li-rich and Li-poor stars are almost entirely consistent (at the
80-90% level) of thin disk giant stars. We performed a 2-sample
Kolmogorov–Smirnov test, finding a p-value of 0.43, on the total velocity
distribution for the Li-rich and Li-poor stars. This test allows us to assess
the probability that the Li-rich and Li-poor stars are drawn from the same
underlying kinematic distribution. The results of this test indicate that
there is not sufficient evidence that the Li-rich and Li-normal stars are
drawn from different underling kinematic populations. We also find that
$\sim$90% of the He strong (log($RW_{\rm He}$) $>$ $-$4.85), have a 70% or
higher chance of belonging to the kinematic thin disk.

###  6.2 Astrometric Accelerations with $Hipparcos$ and $Gaia$

Figure 15:  Correlations of log($RW_{\rm He}$) with the $Gaia$ Renormalized
Unit Weight Error (RUWE; top panel) and $Hipparcos$-$Gaia$ Catalog of
Accelerations (HGCA; bottom panel). The symbols are the same as in Figure 9
and noted in the figure legend. The red line in each panel indicates the
minimum value of each of these excess astrometric motion indicators that might
suggest the presence of binary motion. See text for more details.  Figure 16:
Constraints on the frequency of binary companions for stars in our sample with
$Gaia$ RUWE measurements (top) and those with HGCA accelerations (bottom). In
both cases, stars with strong helium absorption have a higher companion
occurrence rate at the 2.3-$\sigma$ level for the RUWE sub-sample and at the
2.0-$\sigma$ level for the HGCA sub-sample.

In the Adamów et al. (2014) spectroscopic survey, Li was detected in 82
giants, with 11 of them being Li-rich ($A$(Li)$>$1.4). Among these, four
showed evidence of stellar or substellar companions based on radial velocity
variations. They speculated that excess lithium and binarity may be related,
although the underlying basis and statistical validation of any such
connection is not yet established. More recently, Gonçalves et al. (2020) and
Jorissen et al. (2020) have conducted radial velocity surveys of individual
Li-rich stars, with mixed conclusions. Jorissen et al. found no excess binary
frequency among their 11 Li-rich giants compared to Li-poor samples. Gonçalves
et al. (2020) studied 18 Li-rich stars and detected radial velocity variations
in some of them, but suggest that further velocity monitoring work is needed
before reaching final conclusions on binarity statistics. Systematic radial
velocity campaigns to increase sample sizes would be welcome.

To help assess the binary frequency in our Li-rich stars, we have cross-
matched the 278 stars in our program with $Gaia$ EDR3 (Gaia Collaboration et
al., 2021) and the $Hipparcos$-$Gaia$ Catalog of Accelerations (HGCA; Brandt
2018; Brandt 2021). $Gaia$’s Renormalized Unit Weight Error (RUWE) value
provides information about the goodness-of-fit of the nominal five-parameter
astrometric solution. Values near 1.0 are expected for a typical good fit,
whereas values larger than $\approx$1.4 have been shown to indicate the
presence of a stellar companion (Stassun & Torres, 2021). HGCA makes use of
recalibrated proper motions from $Hipparcos$ and $Gaia$ as well as the mean
scaled positional difference between the two epochs to measure long-term
accelerations (changes in proper motion) over this time period. The most
precise acceleration measurement that we make use of in this study is between
$Gaia$ and the $Hipparcos$-$Gaia$ scaled positional difference. The 34-month
baseline sampled in $Gaia$’s EDR3 release is most sensitive to companions at
separations of a few AU, whereas the $\approx$25-year baseline of the HGCA
catalog can reveal companions at typical separations of a few to tens of AU
(e.g., Brandt et al. 2019, Bowler et al. 2021, Franson et al. 2022). In this
way these two methods complement each other to probe stellar and substellar
masses at moderate to wide separations.202020 TYC 3797-01268-1 has $Gaia$ RUWE
= 2.81, consistent with its binary status as discussed by Jorissen et al.
(2020), but it does not have an HGCA measurement.

Figure 15 shows the $Gaia$ RUWE values and the SNR values of the HGCA
acceleration measurements as a function of He i $\lambda$10830 Å reduced
widths. Altogether 275 stars have $Gaia$ RUWE measurements. Among these, 207
stars have weak helium absorption (log($RW_{\rm He}$) $<$ $-$4.85), 24 of
which have elevated RUWE values above 1.4. This implies a binary occurrence
rate of at least 11.9${}^{+2.4}_{-2.2}$% using a binomial likelihood function.
68 stars have strong helium absorption (log($RW_{\rm He}$) $>$ $-$4.85); 17 of
these have elevated RUWE values, indicating a 25.5${}^{+5.5}_{-5.0}$% binary
occurrence rate. Similarly, 99 bright stars from our program are in the HGCA
catalog. For the 68 helium-weak sub-sample of stars, 11
(16.8${}^{4.8}_{4.2}$%) have SNR values above 3 and therefore are likely to
have long-term astrometric accelerators (and hence companions). For the
helium-strong sample, 11 stars (36.1${}^{+8.9}_{-8.1}$%) have SNR values above
3. These binomial posterior probability distributions for the companion
frequencies are shown in Figure 16.

In both cases $-$ stars with RUWE values and those with HGCA measurements $-$
the binary occurrence rate is higher for stars with strong helium absorption
compared to stars with weak helium. For the RUWE sub-sample, the significance
of the difference is at the $\approx$2.3-$\sigma$ level. For the HGCA sub-
sample, the difference is at the $\approx$2.0-$\sigma$ level. This suggests
that there is likely (although not definitively) a relationship between the
strength of the 10830 Å helium line and stellar multiplicity. Depending on the
companion mass, separation, and eccentricity, it is possible that tidal
interactions could impact the stellar chromosphere near periastron.
Alternatively, if enhanced helium is related to the engulfment of planets, the
presence of an outer stellar or substellar companion could indicate that the
inner object underwent high-eccentricity tidal migration in the same way that
hot Jupiters can form around main sequence stars (Fabrycky & Tremaine 2007;
Dawson & Johnson 2018). In this scenario, Kozai-Lidov oscillations with an
outer inclined companion can pump the eccentricity of the inner object until
the tidal influence of the host star dampens, circularizes, and decays the
planet’s orbit. These hypotheses can be tested with a suite of follow-up
observations including rotation period measurements of the strong helium
stars, radial velocity monitoring, and high-contrast imaging. $Gaia$’s final
data release will provide additional clues about the nature of companions in
these systems.

###  6.3 The motions of Li-poor, He-strong Giants

90% of Li-poor program stars exhibit weak He i $\lambda$10830 features. Here
we briefly comment on the 10% of Li-poor stars that have strong $\lambda$10830
lines. There are 16 stars in this category. Six of them have astrometric
indicators suggestive of the presence of companion objects. All of these stars
have $Gaia$ RUWE $>$ 1.4 or HGCA $>$ 3, and four of them have HGCA $>$ 3\. Two
additional stars, TYC 3304-00101-1 and TYC 3667-01280-1, are known to host
giant planets (Niedzielski et al. 2007, Niedzielski et al. 2016). And star TYC
3318-00020-1 is a rapid rotator ($V$sin($i$) = 17 km s-1). Thus 9 out of 16
Li-poor stars with strong He i lines are known or suspected to have active
chromospheres that may be due to present or past binary interactions.

The other seven stars in this group have no known observational anomalies. It
is worth noting that none of these stars has a substantial literature history;
their only high-resolution spectroscopic studies appear to be from Adamów et
al. (2014) or Afsar et al. (2018). They are worth further study, but we
conclude here that the few red giants that are Li-poor but have strong
$\lambda$10830 lines often can be understood as resulting from binary
interactions.

##  7 CONCLUSIONS

This paper has explored the relationship between Li abundances and absorption
strengths of He i $\lambda$10830 in red giant stars. Our survey considers only
observational aspects of the Li-He linkage, from which a few general
conclusions may be drawn:

  * •

90% of Li-poor stars, defined for this paper as those with log $\epsilon$(Li)
$<$ 1.25, have weak $\lambda$10830 transitions, log($RW_{\rm He}$) $<$
$-$4.85. In contrast, $\simeq$55% of Li-rich stars have strong $\lambda$10830
absorptions.

  * •

The vast majority of He-strong stars reside on the He-burning RC and RHB.

  * •

Both Li-rich and He-strong stars are heavily concentrated in the Galactic thin
disk based on kinematics.

  * •

Many of the Li-rich and He-strong stars are also rapid rotators, or have
suspected binary companions.

  * •

About half of the Li-poor, He-strong stars also have evidence for binarity or
rapid rotation.

  * •

From these observational indicators we suggest, in agreement with previous
studies, that red giants are most likely to exhibit both high Li abundances
and strong He i $\lambda$10830 absorption lines if they are He core-burning
RC/RHB stars, and have current and/or past binary companions.

Several followup studies are underway to clarify the evolutionary histories of
red giants with strong $\lambda$10830 absorption lines. The most immediate one
is a large-sample survey of Kepler-field red giants. The asteroseismic
parameters known for these stars will identify the role of horizontal-branch
“age” or time since the helium flash on the Li-He surface combination. In
Table THE ACTIVE CHROMOSPHERES OF LITHIUM-RICH RED GIANT STARS111 Based on
observations obtained with the Hobby-Eberly Telescope, which is a joint
project of the University of Texas at Austin, the Pennsylvania State
University, Ludwig-Maximilians-Universität München, and Georg-August-
Universität Göttingen. we include 13 Kepler giants observed in 2021, but our
sample has now grown to 55 stars. Mallick et al. (in preparation) will report
the He i $\lambda$10830 data for this larger sample of Kepler giants with
known Li abundances, and discuss the evolutionary implications of these stars.

We are undertaking a field star survey based only on red giant rotation to
estimate the importance of red giant envelope angular momentum in creating the
large $\lambda$10830 lines seen in many of our program stars. It will also be
worthwhile in the future to investigate $\lambda$10830 strengths and Li
abundances in binary-suspect giants, those with high values of RUWE and/or
HGCA (Figure 15). Finally it would be good to conduct a southern-hemisphere
extension to the present survey, which has been limited to $\delta$ $>$
$-$10∘. That study could be undertaken with a southern-hemisphere high-
resolution 1$\mu$m instrument, such as WINERED (Ikeda et al., 2022),
VLT/CRIRES (Kaeufl et al., 2004; Dorn et al., 2014), or PHOENIX (Hinkle et
al., 2003).

We thank Claudia Aguilere-Gómez, Bengt Gustafsson, Noriyuki Matsunaga, George
Preston, and our referee for helpful comments on this work. These results are
based on observations obtained with the Habitable-zone Planet Finder
Spectrograph on the Hobby-Eberly Telescope. We thank the Telescope Operators
at the HET for the skillful execution of our observations with HPF. The Hobby-
Eberly Telescope is a joint project of the University of Texas at Austin, the
Pennsylvania State University, Ludwig-Maximilians-Universität München, and
Georg-August Universität Gottingen. The HET is named in honor of its principal
benefactors, William P. Hobby and Robert E. Eberly. The HET collaboration
acknowledges the support and resources from the Texas Advanced Computing
Center. We are happy to acknowledge support from NSF grant AST-1616040 (CS),
and Technological Research Council of Turkey (TÜBİTAK), project No. 112T929
(MA). HET (HPF)

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Table 1: Program Star Data

Star | HD or BD | VaaMagnitudes and colors are taken from SIMBAD (Wenger et al., 2000) | B-VaaMagnitudes and colors are taken from SIMBAD (Wenger et al., 2000) | V-JaaMagnitudes and colors are taken from SIMBAD (Wenger et al., 2000) | pbbParallaxes are from $Gaia$ EDR3 (Gaia Collaboration et al., 2021) | log $\epsilon$(Li) | Source | $EW_{\rm He}$ | broadeningccIf the value is $<$1 km s-1 then the synthetic spectrum broadening function is a Gaussian with the listed FWHM. If it is $>$1 km s-1 then the estimated rotational $V$sin($i$) is listed. See the text for further comments.
---|---|---|---|---|---|---|---|---|---
|  |  |  |  | mas |  |  | mÅ | km s-1
TYC 0014-00882-1 | BD+04 112 | 9.89 | 1.21 | 2.17 | 0.819 |  $-$0.2 | 2 | 115 | 0.25
TYC 0036-01321-1 | HD 12203 | 6.76 | 1.02 | 1.73 | 5.999 | 2.0 | 4 | 80 | 0.27
TYC 0037-00427-1 | HD 12513 | 7.55 | 0.94 | 1.58 | 4.150 |  $-$1.1 | 1 | 50 | 0.28
TYC 0074-01190-1 | HD 26573 | 6.57 | 0.91 | 1.60 | 8.728 | 1.4 | 1 | 551 | 0.32
TYC 0096-00109-1 | BD+06 750 | 9.85 | 1.03 | 1.83 | 2.032 | 0.3 | 2 | 303 | 0.29
TYC 0096-00163-1 |  $\cdots$ | 10.43 | 1.08 | 1.94 | 1.699 | 0.8 | 2 | 100 | 0.27
TYC 0096-00301-1 |  $\cdots$ | 9.89 | 1.14 | 2.05 | 1.647 |  $-$0.2 | 2 | 85 | 0.25
TYC 0096-00378-1 |  $\cdots$ | 10.36 | 0.92 | 2.03 | 1.410 | 0.3 | 2 | 72 | 0.28
TYC 0096-00659-1 | HD 30897 | 8.26 | 1.28 | 2.02 | 3.666 | 1.0 | 2 | 125 | 0.24
TYC 0096-00708-1 |  $\cdots$ | 10.24 | 1.02 | 1.89 | 1.470 | 0.3 | 2 | 70 | 0.28

(This table is available in its entirety in machine-readable form.)

References. — 1 Bozkurt et al. to be surmitted, (2) Adamów et al. (2014), (3)
Mott et al. (2017), (4) Kumar et al. (2011), (5) Brown et al. (1989), (6)
Wallerstein & Sneden (1982), (7) Adamów et al. (2014), (8) Balachandran et al.
(2000), (9) Hanni (1984), (10) Deepak & Reddy (2019), (11) Adamów et al.
(2018), (12) Luck (1982), (13) Singh et al. (2019b), (14) Zhou et al. (2018),
(15) Reddy & Lambert (2016), (16) de Laverny et al. (2003), (17) Yan et al.
(2018), (18) Singh et al. (2019a), (19) Singh et al. (2021), (20) Bizyaev et
al. (2010), (21) Carlberg et al. (2012), (22) Costa et al. (2015), (23) Yan et
al. (2021), (24) Nagarajan et al. to be submitted

Table 2: Rotation Rates: This Study and Literature Star |  $V$sin($i$)aathis study |  $V$sin($i$)bbliterature | Source
---|---|---|---
| km s-1 | km s-1 |
TYC 0347-00762-1 | 18.0 | 15.3 | Bizyaev et al. (2010)
TYC 0429-02097-1 | 12.0 | 11.3 | Yan et al. (2018)
TYC 0455-02910-1 | 50.0 | 58 | Lyubimkov et al. (2012)
TYC 0575-00918-1 | 35.0 | 42 | Kriskovics et al. (2014)
TYC 1005-00073-1 | 80.0 | 84.1 | Massarotti et al. (2008)
TYC 1395-02327-1 | 90.0 | 90 | Uesugi & Fukuda (1970)
TYC 2120-00320-1 | 32.0 | 28.7 | Takeda & Tajitsu (2017)
TYC 2527-02031-1 | 7.8 | 6.1 | Rebull et al. (2015)
TYC 2724-02354-1 | 140.0 | 139.7 | Massarotti et al. (2008)
TYC 3134-00265-1 | 12.0 | 13.09 | Ceillier et al. (2017)
TYC 3282-02270-1 | 9.0 | 7.2 | Gonçalves et al. (2020)
TYC 3318-00020-1 | 17.0 | 16.3 | Adamów et al. (2014)
TYC 3340-01195-1 | 9.5 | 8.4 | Rebull et al. (2015)
TYC 3590-03350-1 | 8.5 | 6.4 | De Medeiros et al. (2002)
TYC 3676-02387-1 | 11.0 | 11.8 | Adamów et al. (2014)
TYC 3797-01268-1 | 19.0 | 17.6 | Balachandran et al. (2000)
TYC 4222-01254-1 | 30.0 | 22.1 | Guillout et al. (2009)
TYC 4977-01458-1 | 17.0 | 15.5 | Massarotti et al. (2008)