# The Strength and Variability of the Helium 10830 Å Triplet in Young Stars,
with Implications for Exosphere Detection

Daniel M. Krolikowski Department of Astronomy, University of Texas at Austin,
2515 Speedway, Stop C1400, Austin, TX 78751, USA  Steward Observatory, The
University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721, USA  Adam L. Kraus
Benjamin M. Tofflemire Caroline V. Morley Department of Astronomy, University
of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78751, USA  Andrew
W. Mann Department of Physics and Astronomy, The University of North Carolina
at Chapel Hill, Chapel Hill, NC 27599, USA  Andrew Vanderburg Department of
Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA

(Received June 3, 2022; Revised October 17, 2023; Accepted November 7, 2023)

###### Abstract

Young exoplanets trace planetary evolution, particularly the atmospheric mass
loss that is most dynamic in youth. However, the high activity level of young
stars can mask or mimic the spectroscopic signals of atmospheric mass loss.
This includes the activity-sensitive He 10830 Å triplet, which is an
increasingly important exospheric probe. To characterize the He-10830 triplet
at young ages, we present time-series NIR spectra for young transiting planet
hosts taken with the Habitable-zone Planet Finder. The He-10830 absorption
strength is similar across our sample, except at the fastest and slowest
rotation, indicating that young chromospheres are dense and populate
metastable helium via collisions. Photoionization and recombination by coronal
radiation only dominates metastable helium population at the active and
inactive extremes. Volatile stellar activity, such as flares and changing
surface features, drives variability in the He-10830 triplet. Variability is
largest at the youngest ages before decreasing to $\lesssim 5-10$ mÅ (or 3%)
at ages above 300 Myr, with 6 of 8 stars in this age range agreeing with no
intrinsic variability. He-10830 triplet variability is smallest and age-
independent at the shortest timescales. Intrinsic stellar variability should
not preclude detection of young exospheres, except at the youngest ages. We
recommend out-of-transit comparison observations taken directly surrounding
transit and observation of multiple transits to minimize activity’s effect.
Regardless, caution is necessary when interpreting transit observations in the
context of stellar activity, as many scenarios can lead to enhanced stellar
variability even on timescales of an hour.

stellar activity (1580), atomic spectroscopy (2099), stellar chromospheres
(230), exoplanet atmospheres (487)

††journal: AJ††software: Astropy (Astropy Collaboration et al., 2013, 2018),
barycorrpy (Kanodia & Wright, 2018), ipython (Perez & Granger, 2007), jupyter
(Kluyver et al., 2016), matplotlib (Hunter, 2007), NumPy (van der Walt et al.,
2011), pandas (Reback et al., 2020), SciPy (Virtanen et al., 2020), TelFit
(Gullikson et al., 2014)

##  1 Introduction

Planetary evolution within the first billion years, when stellar activity and
planetary orbits are most dynamic, establishes a planet’s ultimate atmospheric
properties and habitability potential. A planet’s birth location in the disk
determines the initial mass and composition of atmosphere that can be accreted
(Öberg et al., 2011; Ikoma & Hori, 2012), and its final orbital configuration
after any migration sets the planet’s radiative environment and atmospheric
retention (Owen & Wu, 2013; Shields et al., 2016). A majority of super-Earth
to sub-Neptune sized planets form with a massive H/He envelope that precludes
habitability (Wolfgang & Lopez, 2015; Owen & Mohanty, 2016). Losing this
massive, gaseous envelope is necessary to produce habitable conditions, such
as a favorable surface environment and the creation of a secondary atmosphere
(Pierrehumbert & Gaidos, 2011; Lammer et al., 2014).

High-energy irradiation can sculpt a massive H/He envelope (Lammer et al.,
2003; Kubyshkina et al., 2018), leading to photoevaporative mass loss that
will alter the atmosphere’s size and composition. This mass loss carves the
gap in planet occurrence at a radius of $\sim 1.7R_{\oplus}$, separating
smaller rocky super-Earths from larger sub-Neptunes with gaseous envelopes
(Fulton et al., 2017). Photoevaporation is the leading theory for the cause of
this atmospheric evolution (Owen & Wu, 2013; Lopez & Fortney, 2013; Jin et
al., 2014), but mass loss could also be driven by heat from the contracting
core or impacts (Liu et al., 2015; Ginzburg et al., 2018). The exact mechanism
sculpting the atmosphere and the timescale over which it acts are crucial
inputs for models predicting the habitability of exoplanets (Johnstone et al.,
2015; Owen & Mohanty, 2016).

One way to distinguish different atmospheric evolutionary pathways is to
directly detect ongoing mass loss, and correlate the mass-loss rate with
system characteristics, such as the host star’s spectrum and planet’s orbit.
Exoplanet transit spectroscopy can detect excess absorption from gas in the
evaporating atmosphere, also known as an exosphere. The first exosphere
detections were of escaping hydrogen gas using the Lyman-$\alpha$ spectral
line (e.g. Vidal-Madjar et al., 2003; Lecavelier Des Etangs et al., 2010;
Ehrenreich et al., 2012; Bourrier et al., 2018). Unfortunately, there are
difficulties in observing Lyman-$\alpha$ exospheres because the line is
heavily absorbed by the interstellar medium, is contaminated by geocoronal
emission, and requires expensive space-based observations (Neff et al., 1986;
Dring et al., 1997; Ehrenreich et al., 2011). Therefore, Lyman-$\alpha$
exospheres are only detectable around the very nearest planets.

Fortunately, there is an increasingly popular probe of atmospheric mass loss
that is free of Lyman-$\alpha$’s complications: the helium 10830 Å triplet
feature (Seager & Sasselov, 2000; Oklopčić & Hirata, 2018), which has been
used to detect many exospheres over the last five years (e.g. Spake et al.,
2018; Allart et al., 2018; Salz et al., 2018; Ninan et al., 2020; Czesla et
al., 2022; Orell-Miquel et al., 2022). This feature is formed from the
transition between the two lowest energy He i triplet states (23S to 23P).
Importantly, the 23S state is radiatively decoupled from the ground state and
thus metastable; a He atom will remain in this state long enough to absorb
incoming photons and make the He 10830 Å transition. Ground-based high
resolution NIR spectrographs can access this line, enabling survey
observations to map atmospheric mass loss across system demographics.

It is crucial to find young exospheres to reveal the mechanisms driving
atmospheric mass loss, because the most significant mass loss is expected
within the first Gyr when the stellar high-energy radiative output is highest
(Micela et al., 1985; Preibisch & Feigelson, 2005; Jackson et al., 2012).
While a subset of the known young transiting planets have been targeted in the
search for helium exospheres (Hirano et al., 2020; Gaidos et al., 2020a, b,
2021; Vissapragada et al., 2021; Gaidos et al., 2022; Zhang et al., 2022c),
only one robust detection has been made (HD 73583 b; Zhang et al., 2022b).
This is not surprising, as young stars have high levels of magnetic activity
that introduce chromatic, temporally coherent noise across the stellar
spectrum (Desort et al., 2007; Reiners, 2012) that can mask or mimic a
planetary signal in transmission spectra (Rackham et al., 2018; Boldt et al.,
2020). The stellar He-10830 triplet is chromospheric, and thus is sensitive to
stellar activity. This can lead to confusion between a stellar or planetary
nature for changes in the He-10830 triplet absorption. The stellar He-10830
triplet of FGKM dwarfs is intrinsically variable (Zirin, 1975, 1976; Sanz-
Forcada & Dupree, 2008; Fuhrmeister et al., 2020), but the connection between
this variability and activity is unexplored, particularly at young ages. This
complicates the interpretation of changes in the He-10830 triplet absorption
strength for transit spectra of young planets.

In the stellar chromosphere, there are two main pathways to populate the
metastable state: photoionization and recombination (PR), and collisional
excitation (CE). In the PR mechanism, a He atom is photoionized (by photons
with $\lambda\leq 504$ Å) and then recombines to populate the metastable
state. This process is driven by high energy coronal radiation incident upon
He atoms in the upper chromosphere (Goldberg, 1939; Zirin, 1975). The
metastable state can be directly populated through CE from the ground state
(Hartmann et al., 1979; Wolff & Heasley, 1984), although this requires a dense
enough chromosphere for collisions to dominate over the PR mechanism (Sanz-
Forcada & Dupree, 2008). In exospheres, the PR mechanism driven by high energy
instellation would form the feature because the exosphere density is too low
for CE. An exosphere’s He-10830 triplet signal is thus dependent on its host
star’s high energy output, particularly the intensity and shape of the stellar
UV spectrum (Oklopčić & Hirata, 2018; Oklopčić, 2019; Poppenhaeger, 2022).

Once He atoms populate the metastable state, they can absorb photospheric NIR
continuum to excite into the 23P state and produce the He-10830 triplet
absorption feature. Due to splitting of the 23P state, the feature consists of
three lines: two blended lines (rest vacuum wavelengths of 10833.217 Å and
10833.306 Å), and a weaker resolved component with a rest vacuum wavelength of
10832.057 Å (Martin, 1960). The feature forms higher in the chromosphere than
other traditional spectral chromospheric activity indicators (e.g. Ca ii H and
K, H-$\alpha$; Dupree et al., 1992; Avrett, 1998), and its formation depends
on the structure of the chromosphere, transition region, and corona (Avrett et
al., 1994; Andretta & Jones, 1997).

He-10830 triplet absorption on the Sun is stronger in active regions with
higher X-ray emission (Andretta & Jones, 1997; Mauas et al., 2005; Andretta et
al., 2017) and He-10830 triplet equivalent width correlates with X-ray
luminosity for inactive FGK dwarfs (Zarro & Zirin, 1986), both implying that
the PR mechanism is dominant for inactive solar-type stars. This relation does
not hold for active FGK dwarfs because their chromospheres are dense enough
for CE to dominate (Sanz-Forcada & Dupree, 2008). There is no detectable
absorption for SpT $\geq$ M5, due to emission fill-in and reduced line
excitation from the PR mechanism (Fuhrmeister et al., 2019).

Volatility of the stellar activity level, from secular changes in the magnetic
field and short-term evolution of active events (e.g. surface features, winds,
mass loss, or flaring), can cause variability in the He-10830 triplet. This
has been observed in FGK dwarfs and giants (although with sparse, telluric-
contaminated observations; Zirin, 1976; Obrien & Lambert, 1986; Katsova &
Shcherbakov, 1998), and more recently in M-dwarfs (with CARMENES; Fuhrmeister
et al., 2020). However, the amplitude and timescale of variability remains
uncharacterized for young stars with high activity levels.

To better understand the He-10830 triplet in young stars, and the potential
for a stellar signal to mask or mimic an exosphere, its absorption strength
and variability must be characterized spanning a range of stellar parameters.
We have gathered a data set that is well suited for this task: time series NIR
spectroscopy of young transiting planet hosts from the Habitable-zone Planet
Finder. With these data, we study the He-10830 triplet across age, spectral
type, and activity level to explore the effect of stellar activity on the
He-10830 triplet and assess the feasibility of detecting young helium
exospheres.

Table 1: HPF young transiting planet host star sample Object | RA | Dec | $J$ | Membership | AgeaaWe adopt the same age for Hyades and Praesepe, 700 Myr, which is roughly the average of previous age determinations (Brandt & Huang, 2015; Martín et al., 2018; Gossage et al., 2018). The age for V1298 Tau comes from Johnson et al. (2022), and all other ages are from the planet discovery papers. | $T_{\rm eff}$ | $P_{\rm rot}$ |  $N_{\rm ep}$bbNumber of in-hand and usable visits for each target through 10/18/2021. | Plot MarkerccMarker and color used for each object’s plotted point in Figures 6, 7, 8, 9, 11 | RefddPlanet discovery references: (1) Mann et al. (2016), (2) David et al. (2016), (3) Gaidos et al. (2017), (4) Mann et al. (2017), (5) Mann et al. (2018), (6) Ciardi et al. (2018), (7) Livingston et al. (2018), (8) Vanderburg et al. (2018), (9) Rizzuto et al. (2018), (10) David et al. (2018), (11) David et al. (2019b), (12) David et al. (2019a), (13) Mann et al. (2020), (14) Newton et al. (2022)
---|---|---|---|---|---|---|---|---|---|---
| h m s | d m s | mag |  | Myr | K | d |  |  |
Objects included in helium analysis
V1298 Tau | 04 05 19.6 | +20 09 25.6 | 8.7 | Taurus | $28$ | 4970 | 2.851 | 42 | $\blacksquare$ | 11,12
K2-284 | 05 16 33.8 | +20 15 18.4 | 10.9 | Field | $120$ | 4140 | 8.88 | 13 | $\blacksquare$ | 10
TOI 2048 | 15 51 41.8 | +52 18 22.7 | 9.9 | Group X | $300$ | 5185 | 7.97 | 13 | $\bullet$ | 14
HD 63433 | 07 49 55.1 | +27 21 47.5 | 5.6 | Ursa Major | $414$ | 5640 | 6.45 | 13 | $\bullet$ | 13
HD 283869 | 04 47 41.8 | +26 09 00.8 | 8.4 | Hyades | $700$ | 4655 | 37 | 15 | $\blacksquare$ | 8
K2-136 | 04 29 38.9 | +22 52 57.8 | 9.1 | Hyades | $700$ | 4499 | 15 | 36 | $\blacksquare$ | 5,6,7
K2-100 | 08 38 24.30 | +20 06 21.83 | 9.5 | Praesepe | $700$ | 6120 | 4.3 | 29 | $\blacksquare$ | 4
K2-101 | 08 41 22.58 | +18 56 01.95 | 11.2 | Praesepe | $700$ | 4819 | 10.6 | 3 | $\bullet$ | 4
K2-102 | 08 40 13.45 | +19 46 43.71 | 11.3 | Praesepe | $700$ | 4695 | 11.5 | 5 | $\bullet$ | 4
K2-77 | 03 40 54.8 | +12 34 21.4 | 10.4 | Field | 850 | 4970 | 19.8 | 13 | $\bullet$ | 3
Objects not included in helium analysis
K2-25 | 04 13 05.6 | +15 14 52.0 | 11.3 | Hyades | $700$ | 3207 | 1.88 | 31 | – | 1,2
K2-103 | 08 41 38.49 | +17 38 24.08 | 12.3 | Praesepe | $700$ | 3880 | 14.6 | 4 | – | 4
K2-104 | 08 38 32.84 | +19 46 25.59 | 12.9 | Praesepe | $700$ | 3660 | 9.3 | 4 | – | 4
K2-264 | 08 45 26.05 | +19 41 54.46 | 13.1 | Praesepe | $700$ | 3580 | 22.8 | 6 | – | 9
EPIC 211901114 | 08 41 35.69 | +18 44 34.98 | 13.2 | Praesepe | $700$ | 3440 | 8.6 | 3 | – | 4
K2-95 | 08 37 27.06 | +18 58 36.02 | 13.3 | Praesepe | $700$ | 3410 | 23.9 | 4 | – | 4

##  2 Description of stellar sample and HPF observations

We present observations of 10 young ($\tau<1$ Gyr) transiting planet hosts,
comprising all such known systems as of July 2020 that are observable with the
HET at McDonald Observatory ($-10\arcdeg<\delta<72\arcdeg$). We obtained these
observations for a survey to search for outer giant planets in these systems,
which will be described in a forthcoming paper. These 10 stars are a subset of
a larger 16 target sample used in the RV planet search survey. The 6 stars
that are excluded are faint enough that it is difficult to measure precise and
reliable spectral line equivalent widths. This removes all M-dwarfs from our
sample, so our study here concerns only FGK dwarfs. The stars in this paper’s
sample span: $\sim 25$ Myr to 1 Gyr in age, late-F to late-K in spectral type,
and 1.88 days to 37 days in rotation period. Information for the full sample
is listed in Table 1, including the targets that are excluded in this
analysis.

We obtained NIR spectra with the Habitable-zone Planet Finder (HPF; Mahadevan
et al., 2012, 2014) on the 10-m Hobby-Eberly Telescope at McDonald
Observatory. HPF is a high-resolution ($R\sim 55000$), fiber-fed, stabilized
NIR spectrograph covering $z,Y,J$ bands from $8100-12700$ Å (Hearty et al.,
2014; Stefansson et al., 2016). HPF has a laser frequency comb (LFC) to
achieve extremely high quality wavelength calibration, exhibiting $\sim 20$ cm
s-1 calibration precision and $\sim 1.5$ m s-1 on sky precision for Barnard’s
Star (Metcalf et al., 2019). HPF has three fibers: a science, sky, and
calibration fiber. The sky fiber provides simultaneous observations of nearby
sky to subtract sky background (e.g. Moon contamination or airglow), and the
calibration fiber can observe the LFC to provide an instantaneous wavelength
solution.

Our observational set up is designed for a precision RV planet search. For
targets brighter than $J=10$ we use an exposure time of 5 minutes, which is
the maximum allowed exposure time while simultaneously observing the LFC to
avoid LFC saturation. This strategy optimizes target S/N with a precise,
instantaneous wavelength calibration. The sole exception is for HD 63433,
which is bright enough to reach high S/N in only 3 minutes. The 5 minute
exposure scheme was used for targets fainter than $J=10$ in the first year of
observations. From August 2019 onward, we use an exposure time of 10 minutes
to reach higher S/N for these fainter objects. We bracket these 10 minute
exposures with LFC-only observations to improve the wavelength calibration.
This method can correct for HPF drift and provides similarly precise
wavelength calibration as LFC-simultaneous observations (Stefansson et al.,
2020).

These observations are made using HET’s flexible queue-mode scheduling
(Shetrone et al., 2007), which allows for observations to be spread throughout
the trimester to cover baselines of days to months. Each observation (which we
call a “visit”) is composed of three sequential exposures to increase signal
and average over high-frequency, oscillation-driven stellar RV variation. The
sole planned exception to this is an observation of V1298 Tau that attempted
to measure Planet b’s transit on UT 2019/10/24, during which we obtained 11
sequential exposures. However, based on an updated prediction for the time of
planet b’s transits from TESS data (Feinstein et al., 2022), this visit did
not occur during transit. Occasionally, there were other unplanned exceptions
to our three-exposure-per-visit strategy, such as when additional exposures
were taken due to poor S/N from passing clouds.

The raw 2D images were reduced to 1D spectra using the HPF team’s custom
pipeline following the procedures of Ninan et al. (2018), Kaplan et al. (2019)
and Metcalf et al. (2019). We correct the derived wavelength solution for
barycentric motion using barycentric velocities calculated at each exposure
time using barycorrpy (Kanodia & Wright, 2018), which is a Python
implementation of the formalism from Wright & Eastman (2014).

We began observations in November of 2018, and the program is still ongoing.
All targets have time series spanning at least 9 months, with roughly half of
the targets having observations spanning the entire two and a half year
program. This unique data set – namely time series, high resolution NIR
spectra of young planet hosts – enables us to study the strength and intrinsic
variability of the stellar He-10830 triplet at young ages.

##  3 measuring spectral line equivalent widths

To study the behavior of the He-10830 triplet at young ages, we measure the
feature’s equivalent width (EW) from the HPF spectral time series for each
star. For this analysis, we must first correct the spectra for telluric
contamination before measuring the EWs. We describe our procedures for both of
these steps in this section.

###  3.1 Correcting telluric contamination

The region of interest around the He-10830 triplet contains significant
telluric contamination, including sky emission and water absorption. These
telluric features can significantly affect the measurement precision of the
He-10830 triplet’s EW and line profile shape, the latter of which is needed to
detect velocity structure and study planetary outflow dynamics. There are
drawbacks to both empirical and theoretical telluric modeling, and adequately
removing the contamination is a difficult task.

One way to avoid telluric contamination is to observe targets when the strong
features do not directly overlap the He-10830 triplet, due to the Doppler
shift of the stellar spectral lines from relative motion between the target
and the Earth. However, this strategy cannot be used for all targets because
it is possible that the barycentric motion of a given object during its peak
observability places the telluric features within the He-10830 triplet region.
This can be an even more pressing issue for the time-sensitive constraints of
transit observations.

This is particularly a problem for the nearby young clusters and associations
hosting a majority of the known young transiting planets. We calculated the
wavelength of the strong sky emission line near the He-10830 triplet in the
rest-frame of a variety of these young stellar associations (Hyades, Praesepe,
Pleiades, Taurus, Ursa Major, and Group X) across the year for observations
taken at McDonald Observatory. On average, the emission line is 1 Å from the
strong, red component of the He-10830 triplet, ranging from 2.7 Å to directly
overlapping the He line. The young clusters along the ecliptic that were
accessible by K2 feature the worst contamination. This highlights the
importance of TESS’s all-sky search which includes many other young stellar
associations (including Ursa Major and Group X). It is therefore crucial to
adequately correct for this telluric contamination. Below, we describe our
methods for removing sky emission lines (Section 3.1.1) and water absorption
features (Section 3.1.2).

Figure 1: The spectral region around the He-10830 triplet for the A2 star HR
5162. We show an A-star to highlight the emission line over-subtraction as it
is devoid of stellar absorption lines. The cyan spectrum is the science fiber
flux prior to sky subtraction, which shows the sky emission lines, and the
pink spectrum is the sky-subtracted spectrum following naive subtraction. For
the strongest sky line, the over-subtraction is roughly 10% of the nearby
continuum, which is significantly larger than the measurement error. The red
spectrum shows the sky-subtracted spectrum using the scale factor $\beta$
determined from the sky emission line at 10289.5 Å. The scaling removes the
over-subtraction, and the resultant spectrum agrees with the nearby continuum
within errors. Both subtraction methods are adequate and agree for the nearby
weak emission doublet.

####  3.1.1 Subtraction of sky emission lines

There are three sky emission lines in the He-10830 triplet spectral region:
one strong line (which is actually an unresolved doublet) with a rest vacuum
wavelength of 10834.2895 Å, and a weaker resolved doublet at 10832.103 Å and
10832.412 Å (Oliva et al., 2015). In principle, the presence of sky emission
lines should not be an issue because HPF has a dedicated fiber to
simultaneously observe blank sky during every visit. The spectrum observed by
this fiber, $f_{\rm sky}$, could then be subtracted from the science fiber
spectrum, $f_{\rm sci}$, to produce a telluric emission free spectrum, $f_{\rm
skysub}$. However, this naive sky subtraction often results in an over-
subtraction of the emission lines in HPF data, introducing residual absorption
artifacts in the resultant spectrum. Figure 1 shows the result of a naive sky
subtraction with HPF data of the A-star HR 5162. It is difficult to assess the
amount of over-subtraction in stars of later type due to the multiple stellar
lines near the He-10830 triplet, but the lack of stellar features in the
A-star spectrum highlights the over-subtraction.

The degree to which the emission lines are over-subtracted depends on the
relative flux from the target and the sky, which is demonstrated by the lack
of over-subtraction for the weak emission doublet in Figure 1. The over-
subtraction residual approaches the measurement uncertainty, and eventually
disappears, as the ratio of the target flux to the peak of the sky emission
line increases. This means that the brightest targets will have no significant
over-subtraction. Therefore, over-subtraction is a greater issue for bright
sky emission lines and “faint” targets. This applies to many of our
observations: the emission line at 10834.2895 Å is bright enough, and many of
our young transiting planet host sample are faint enough, for the over-
subtraction to be significant.

A better method for sky subtraction would involve scaling the sky fiber flux
to account for the difference between the science and sky fiber fluxes (such
as from throughput differences). Most simply, we can do this by multiplying
the entire sky spectrum by a scalar value, which we call $\beta$. The equation
describing the sky subtraction is then:

$f_{\rm skysub}=f_{\rm sci}-\beta f_{\rm sky}$ (1)

To determine $\beta$ for each observation, we could fit the spectrum around
the sky emission line and find the $\beta$ value that results in a spectrum
closest to the nearby continuum. However, we cannot use the region around the
He-10830 triplet to determine $\beta$ because there is no clear continuum due
to the presence of multiple stellar and telluric absorption features.

Figure 2: Comparison of the amplitudes for the strong sky emission line near
the He-10830 triplet ($\lambda=10834.3$ Å) and the calibration sky emission
line ($\lambda=10289.5$ Å) used to determine the sky subtraction scale factor
$\beta$. The amplitudes of the emission lines are well-correlated, and their
relationship is linear over an order of magnitude in amplitude.

We instead use a different strong sky emission line that is isolated from
other spectral features to measure $\beta$. We assume that the OH sky emission
lines all behave similarly because their strength should largely be a product
of sky conditions, although there may be slight differences depending on the
physics of the transitions. We searched the full HPF spectral range for a sky
emission line of similar strength to the line at 10834 Å to use as a
calibrator line. While there are many strong sky lines throughout the HPF
bandpass, a vast majority of them reside in regions with many stellar and
telluric absorption features. We were able to identify one high quality
candidate calibration sky emission line without any nearby absorption
features: an unresolved doublet with a rest vacuum wavelength of 10289.455 Å.
Figure 2 shows a comparison of the two sky emission line amplitudes using the
sky fiber spectra from our observations of K2-136. The amplitudes are well-
correlated with minimal scatter, and we conclude that this sky emission line
is an adequate calibrator with which to determine $\beta$.

To calculate $\beta$, we find the scale factor needed to match the calibration
line flux in the sky fiber spectrum to that of the science fiber spectrum
(thus accounting for underlying continuum flux). We perform a minimization to
find the best fit $\beta$ value, represented as:

$\min_{\beta}~{}{\rm stdev}\left(\frac{f_{\rm sci}-\beta f_{\rm sky}}{f_{\rm
cont}}\right)$ (2)

We perform the minimization over a 2.5 Å region around the calibration line
between 10288.105 Å and 10290.605 Å. The sky fiber spectrum is scaled and
subtracted from the science fiber spectrum, producing a sky-subtracted
residual spectrum. This residual spectrum is fit with a line to obtain a rough
estimate of the continuum level in the region, $f_{\rm cont}$. The best fit
$\beta$ value is the scale factor such that the standard deviation of the
continuum-normalized, scaled sky-subtracted spectrum is minimized. We use the
adopted $\beta$ value to scale the entire sky spectrum and subtract it from
the science fiber spectrum to produce the sky-free spectrum as described in
Equation 1.

Figure 1 shows the scaled sky subtraction of the A-star HR 5162 in the
He-10830 triplet region. The scaling factor works well, and the sky-free
spectrum at the location of the strong sky emission line agrees with the
nearby continuum value within measurement uncertainty. This demonstrates that
the $\beta$ value determined using the calibrator can be applied to the rest
of the sky spectrum, and we perform this corrected sky subtraction method for
nearly all data presented in this paper. The only exception is for the target
HD 63433, which is bright enough for over-subtraction to not be a significant
issue. Thus, we naively subtract the sky emission for all spectra of HD 63433.

Figure 3: Telluric absorption model fitting for the A-star HR 3711. The black
spectrum shows the sky-subtracted, continuum-normalized data, the red spectrum
is the best-fit telluric model, and the pink spectrum is the telluric-
corrected spectrum. Left Panel: The region in spectral order 20 used to find
the best-fit model. There are slight residuals likely due to continuum
division or theoretical model imperfections. Right panel: The He-10830 triplet
spectral region. The two strong water lines are well-corrected. The resulting
residuals across the range shown is 0.4%, which is very close to the typical
measurement uncertainty of 0.3%.

####  3.1.2 Telluric absorption correction

There are also two water absorption features in the He-10830 triplet region
that can affect EW measurement: a strong line with a rest vacuum wavelength of
10835.08 Å that can often overlap the He-10830 triplet and a weaker line with
a rest vacuum wavelength of 10836.95 Å. Telluric standard observations are not
taken regularly with HPF as the overhead for these observations is impractical
for typical programs. Without observed standards, we can not empirically
correct for telluric absorption features in our data. Masking the spectra near
strong telluric absorption features would exclude important spectral
information, especially because the strong water line often directly overlaps
the He-10830 triplet profile.

Given these analysis constraints, we decided to generate theoretical telluric
absorption models that are custom fit for each individual observation. We use
the TelFit python package (Gullikson, 2014), which can generate telluric
absorption models and iteratively fit data for the best parameter values. We
only fit for the humidity value because the humidity provided in the
observation header is often not close to producing a well-fitting model, and
humidity has the largest effect on the telluric model itself. We fix the
temperature and pressure values to those recorded in the observation headers.
During the fitting process, we fix the spectral resolution to the instrument
resolution of 55000.

Using 43 A-star observations from a telluric standard library that has been
slowly built since HPF’s commissioning, we ran telluric fits on all spectral
orders except for those with very strong telluric absorption bands to assess
the fit quality across wavelength. We find a wavelength dependence in the best
fit humidity value, where the 6 orders blueward of 1 µm produce a consistently
lower humidity value than the 5 orders redward of 1 µm. This is perhaps due to
systematic differences in the molecular transition database across wavelength,
and is unlikely to be due to the varying presence of stellar spectral features
which are largely absent in A-star spectra. We find that the spectral order
containing the He-10830 triplet provides humidity values with large scatter
relative to the mean humidity value across all orders, indicating that it is
not reliable for the fitting process. The typical value found in the He-10830
triplet’s order is similar to the subsequent redder order, though, so we use
that order for all telluric model fits moving forward.

For the final telluric absorption model fitting, we use a 20 Å wide region in
spectral order 20 covering $11075-11095$ Å. We use this small region because
it has many non-saturated water lines that are separated enough to avoid
issues from blending, while having little stellar contamination. By operating
on a small spectral segment, we also avoid additional error introduced from
the continuum and blaze correction on a full spectral order. With the best fit
telluric model parameters from order 20, we then generate a telluric model for
the entire HPF bandpass. Figure 3 shows an example of the telluric absorption
model fit for the A-star HR 3711. Two spectral regions are shown: the region
in spectral order 20 where the fit is performed, and the He-10830 triplet
region in spectral order 19. The two water lines in the He-10830 triplet
region are well-corrected using the model, leaving us confident in our
procedure for removing telluric absorption.

###  3.2 Measuring the equivalent width of spectral lines in the He-10830
triplet region

With telluric contamination removed, we can precisely measure the EW of the
He-10830 triplet. The spectral region around the He-10830 triplet has other
stellar spectral lines which complicates the measurement of the isolated
He-10830 triplet EW. The nearby stellar and telluric features also make it
more difficult to define the continuum level directly adjacent to the He-10830
triplet. We therefore fit the entire spectral region from 10822 Å to 10845 Å,
including all stellar spectral lines, to provide the best leverage for fitting
the continuum level and measuring EWs. This also results in EWs for a handful
of other presumably inactive lines that provide useful comparison to the
active He-10830 triplet.

Table 2: Spectral lines in the fit region Element |  $\lambda$aaVacuum line center wavelength taken from the NIST atomic spectral line database (Kramida et al., 2021). | Line Profile
---|---|---
| (${\rm\AA}$) |
Cs iibbThis line may be blended with a nearby Cr i line. | 10824.6926 | Gaussian
Si i | 10830.054 | Lorentzian
He i | 10832.057 | Gaussian
He i | 10833.2615ccThe average wavelength of the two blended red components of the helium triplet. | Gaussian
Ti i | 10836.38 | Gaussian
Na i | 10837.8435ddThe average wavelength of two close Na i transitions. | Gaussian
Ca i | 10841.95 | Gaussian

In addition to the two resolved components of the He-10830 triplet, there are
5 other prominent stellar spectral lines in this wavelength range, although
their strength varies across the range of effective temperatures covered in
our sample. All of the stellar spectral lines included in fits of this region
are listed in Table 2. The nearby strong silicon line is the closest spectral
feature to the He-10830 triplet in wavelength, which it overlaps with its
broad wings. The other lines do not directly contaminate the He-10830 triplet,
and are relatively weak and narrow.

Our spectral model has three components: 1) the combined profiles of the 7
spectral lines listed in Table 2, 2) the telluric model that is separately fit
for each individual exposure (as described in Section 3.1.2), and 3) a 2nd
order polynomial continuum. We model the silicon line profile with a
Lorentzian due to its wide wings, and the other 6 line profiles with
Gaussians. In our data processing pipeline, we use an iterative b-spline to
fit the continuum level of the entire He-10830 triplet spectral order. For
this subset of the spectral order, we initialize the continuum parameters by
fitting a polynomial to the b-spline continuum only for the 23 Å region we
study here. The full model is described as:

$f(\lambda)_{\rm model}=C(\lambda)~{}f(\lambda)_{\rm
tell}~{}\sum_{i=1}^{N_{\rm lines}}{p(\lambda,A_{i},\mu_{i},s_{i})}$ (3)

$C(\lambda)=c_{0}+c_{1}\lambda+c_{2}\lambda^{2}$ (4)

where $C(\lambda)$ is the continuum polynomial, $f(\lambda)_{\rm tell}$ is the
telluric absorption model described in Section 3.1.2, and the summation
represents the combined spectral line profiles. In the summation, $N_{\rm
lines}$ is the number of spectral lines included in the fit, $p$ is the
profile used to describe each particular spectral line listed in Table 2, $A$
is the amplitude of the line profile, $\mu$ is the wavelength of the spectral
line, and $s$ is the scale factor of the line profile. The scale factor is
given by the standard deviation of a Gaussian profile and the scale parameter
of a Lorentzian profile. In all, the free parameters in our model are the
three continuum polynomial coefficients ($c_{0},c_{1},c_{2}$) and the three
parameters describing each spectral line included in the model
($A_{i},\mu_{i},s_{i}$). We explicitly remind readers that the telluric
absorption model is fit independently prior to the procedure described here.

We modify the model described in Equation 3 for two stars in our sample:
K2-100 and V1298 Tau. Both of these stars are rapid rotators, and a stellar
rotational broadening profile is not a Gaussian or a Lorentzian. Thus, we
rotationally broaden the model using literature measurements of their $v\sin
i$. For K2-100, we exclude the Cs and Ti spectral lines because they are too
weak at the star’s effective temperature to be detectable given the rotational
broadening. For V1298 Tau, we exclude the Ti line and the blue component of
the He-10830 triplet, which are completely blended with nearby lines. We also
modify the continuum for V1298 Tau to be a line, because it is so rapidly
rotating that a 2nd order polynomial overfits the blended helium and silicon
absorption.

We fit the observed flux after scaled sky subtraction, $f_{\rm skysub}$
(Equation 1), with the model described in Equation 3 using the least squares
optimization implemented in curve_fit from the scipy package (Virtanen et al.,
2020). We use the implementation of the Gaussian and Lorentzian profiles from
astropy (Astropy Collaboration et al., 2013, 2018). We include uncertainties
on the observed flux which are calculated by adding in quadrature the errors
on the science and sky fiber spectra. Figure 4 shows an example fit of an
observation of K2-136. The resultant model captures the continuum level and
shape, and adequately fits the individual spectral line profiles.

Figure 4: An example result for the spectral fitting of the He-10830 triplet
region on an observation of K2-136. The brown spectrum is the telluric-
corrected data, the red line is the best fit spectral model, and the teal line
is the continuum polynomial. The telluric absorption model has been removed
from the data and spectral model to highlight the stellar lines. The bottom
panel shows the residuals from subtracting the model from the data. The
standard deviation of the residuals is 0.8 e-/s, which corresponds to a
percent error on the flux of 1.4%. This is slightly larger than the typical
measurement error of 0.5 e-/s (0.9%). The continuum level and stellar line
profiles are well-matched by the model.

We compute EWs for all spectral lines included in each particular star’s fits
by numerically integrating the observed spectra. We first divide the sky-
subtracted spectrum by the best fit model, and fit this residual spectrum with
a 2nd order polynomial to remove any remaining continuum shape that may bias
the numerical EWs. To assess the quality of the spectral fit and secondary
continuum correction, we measure the EW of both the corrected and uncorrected
residual spectra, which should be 0. The median residual spectrum EW across
all observations is $9.2\pm 17.9$ mÅ without the secondary continuum
correction, and $-0.23\pm 0.76$ mÅ following the correction. The EW for the
corrected residual spectrum is much closer to 0 and has significantly less
variation across observations, showing that our secondary continuum correction
is necessary to capture remaining continuum deviations that could affect the
numerical EW integration.

For each individual element, we generate a model that includes all spectral
lines _except for that element’s feature_ ; for helium this includes the two
Gaussian lines for each resolved component of the triplet (except for V1298
Tau which only fits one helium component). We then compute the residual
spectrum using this modified model, which will leave only that element’s
feature in the data, and numerically integrate to compute the EW. We perform
sampling, using draws from the spectral model fit parameters and covariance
matrix to calculate 1000 residual spectra for each element. We adopt the
median and the median absolute deviation (scaled by 1.4826 to be statistically
equivalent to the Gaussian standard deviation) of the EW samples as the value
and uncertainty.

By direct numerical integration of the data, the EWs will not be affected by
potential mismatch between the actual and modeled line profiles. This also
accounts for any asymmetries in the spectral lines included in our fit, such
as for the inherent asymmetry of the redder component of the He-10830 triplet.
As a comparison check, we also computed the EWs analytically from the fit
parameters for each spectral line profile. The numerical and analytical values
agree within uncertainties. Given the advantages that the numerical EW
calculation has with using the data’s line profile, we are confident in
adopting the numerical EWs for this paper.

Figure 5: The measurement error of each spectral line for all targets as a
function of the median spectrum signal-to-noise in the He-10830 triplet order.
The 3-pronged smaller markers are measurements for K2-100 and V1298 Tau, which
feature larger error than the rest due to their rapid rotation. The inverse
relationship expected is shown, and the uncertainty plateaus at $\lesssim 5$
mÅ for the He-10830 triplet above S/N $\sim 300$.

Figure 5 shows the EW measurement uncertainty of each spectral line as a
function of the median signal-to-noise in the He-10830 triplet spectral order
for all targets. The uncertainty decreases with increasing signal-to-noise, as
expected. The typical uncertainties are larger for helium and silicon compared
to the other lines, at least partially due to the fact that they have
significantly larger EWs. The two features are also broader, and the silicon
line in particular features strong absorption wings. Regardless, the EW
uncertainty is in general precise enough to adequately measure the variability
of our time series data, and it plateaus at $\sim 5$ mÅ for the highest
quality spectra. Given the typical He EW value ($\sim 325$ mÅ), a single-epoch
measurement error of $5$ mÅ produces a 1.5 % error in the EW value.

For the rest of the paper, we denote the He-10830 triplet EW as EW[He]; for
the objects with both resolved components fit, this value is the sum of the
individual component EWs. Table 3 shows all EW[He] measurements, and provides
an explanation for observations without a calculated EW[He] (from low spectral
S/N or a failed spectral fit).

Table 3: Helium 10830 Å Triplet EW Measurements

Date (JD) | EW[He] | $\sigma_{\rm EW[He]}$ | FlagaaFlag denoting the reason for missing EW measurement: (1) Low spectrum S/N, (2) failed spectral fit, (3) bad spectral fit.
---|---|---|---
| mÅ | mÅ |
K2-136
2458425.972 | 315.26 | 10.43 | -
2458425.976 | 307.7 | 12.42 | -
2458425.98 | 326.86 | 12.29 | -
V1298 Tau
2458548.609 | 409.43 | 10.77 | -
2458548.613 | - | - | 1
2458548.618 | 456.2 | 36.62 | -

††footnotetext: Small sample of EW measurements shown, all measurements are in
the machine readable table file.

##  4 Time series properties of the He triplet

The line profile of the He-10830 triplet probes the conditions in the stellar
atmosphere from which the line arises. Different line formation pathways (e.g.
the photoionization-recombination mechanism or collisional excitation) will
set the dependence of absorption strength on various stellar properties and is
indicative of the stellar activity level (Zarro & Zirin, 1986; Sanz-Forcada &
Dupree, 2008). Evolution in the stellar activity can cause variability in the
line strength, and the amplitude and timescale of variation can indicate the
types of active features that affect the He-10830 triplet (Zirin, 1976;
Fuhrmeister et al., 2020). With our sample, we have a unique window into the
He-10830 triplet in young active stars spanning age and spectral type.

###  4.1 He-10830 triplet absorption strength

Figure 6: EW[He] (top panel) and the Ca i 10842 Å line (bottom panel) as a
function of effective temperature. Our sample is plotted as large colored
circles and squares, and values are taken as the median of the time series
measurements. The uncertainties are often smaller than the points. In the top
panel, the black x’s and red +’s show literature He-10830 triplet EWs for
field inactive (Zarro & Zirin, 1986) and active (Sanz-Forcada & Dupree, 2008)
dwarfs respectively. Our young stars have EW[He] above the inactive dwarfs,
confirming that active stars feature enhanced He-10830 triplet absorption. The
dashed line and gray shaded region show a linear fit and 3$\sigma$-range for
the EW-$T_{\rm eff}$ relation. The EW[He] outliers (V1298 Tau and HD 283869)
are excluded from the helium-$T_{\rm eff}$ fit. The chromospheric He-10830
triplet has no $T_{\rm eff}$ dependence, unlike the photospheric Ca i 10842 Å
line, highlighting the difference in line formation. The different
combinations of marker shape and color for our sample correspond to particular
stars as designated in Table 1. This plotting scheme is also used in Figures
7, 8, 9, 11.

The top panel of Figure 6 shows the median EW[He] as a function of $T_{\rm
eff}$ for each star in our sample, along with literature values of inactive
and active dwarfs. Relative to stars of the same effective temperature, the
young stars in our sample show EW[He] that is enhanced over inactive dwarf
stars (Zarro & Zirin, 1986) and comparable to active dwarf stars (Sanz-Forcada
& Dupree, 2008). The correlation between EW[He] and $T_{\rm eff}$ is
consistent with a flat slope. This agrees with previous literature studies, in
which no dependence on $T_{\rm eff}$ has been found for either inactive or
active dwarf stars within this temperature range. From the lack of temperature
dependence in our sample, we conclude that the stellar atmospheric conditions
that lead to the formation of the He-10830 triplet are roughly the same for
late-F to late-K dwarfs with $\tau\leq 1$ Gyr. Table 4 shows the EW[He] median
value and variability metrics for our sample described in the following
subsections.

Table 4: Overview of Helium EW Measurements

Object | med[EWHe] | MAD[EWHe]aaEW[He] time series variability, calculated as described in Section 4.2. | MADintr[EWHe]bbThe estimated intrinsic EW[He] variability, calculated as described in Section 4.2. K2-101, K2-102, and K2-77 measurements are 90th percentile upper limits. |  $\sigma_{D,\rm rel,red}$c,$\bigstar$c,$\bigstar$footnotemark:  |  $\sigma_{D,\rm rel}$d,$\bigstar$d,$\bigstar$footnotemark:
---|---|---|---|---|---
| mÅ | mÅ | mÅ | % | %
V1298 Tau | $447.6\pm 5.8$ | $62.5_{-7.7}^{+8.2}$ | $61.5_{-7.8}^{+8.4}$ | $-$ | $3.93_{-0.5}^{+0.54}$
K2-284 | $315.8\pm 4.7$ | $27.9_{-6.4}^{+11.2}$ | $23.5_{-10.0}^{+12.0}$ | $2.76_{-1.47}^{+1.02}$ | $3.11_{-1.32}^{+1.58}$
TOI 2048 | $316.2\pm 2.1$ | $13.5_{-3.1}^{+3.9}$ | $4.3_{-4.3}^{+8.2}$ | $<1.53$ | $0.52_{-0.52}^{+1.02}$
HD 63433 | $315.5\pm 1.4$ | $8.0_{-1.9}^{+1.2}$ | $7.1_{-2.2}^{+1.4}$ | $0.79_{-0.31}^{+0.21}$ | $0.80_{-0.25}^{+0.15}$
HD 283869 | $191.3\pm 2.0$ | $12.5_{-2.7}^{+4.1}$ | $8.0_{-8.0}^{+5.6}$ | $0.68_{-0.68}^{+0.80}$ | $0.93_{-0.93}^{+0.66}$
K2-136 | $302.2\pm 1.3$ | $13.4_{-1.8}^{+2.1}$ | $8.6_{-4.0}^{+3.2}$ | $1.33_{-0.50}^{+0.40}$ | $1.14_{-0.52}^{+0.42}$
K2-100 | $349.6\pm 2.4$ | $21.0_{-3.7}^{+5.0}$ | $6.6_{-6.6}^{+10.8}$ | $<2.75$ | $0.62_{-0.62}^{+1.01}$
K2-101 | $323.1\pm 3.3$ | $8.7_{-6.6}^{+9.2}$ | $<20.0$ | $1.55_{-1.55}^{+4.86}$ | $<2.54$
K2-102 | $303.3\pm 4.2$ | $13.9_{-3.1}^{+10.8}$ | $<18.7$ | $<3.85$ | $<2.42$
K2-77 | $309.0\pm 2.6$ | $14.2_{-3.1}^{+3.8}$ | $<13.1$ | $<1.69$ | $<1.60$

††footnotetext: $\bigstar$ Important note for interpretation: The intrinsic
relative absorption depth variability, $\sigma_{D,\rm rel}$, represents the
1$\sigma$ amplitude of the intrinsic stellar He-10830 triplet variability.
Thus it should not be directly used as a detection limit for exospheres. We
suggest adopting 1.7-times this value as an estimated one-sided 95th
percentile detection limit.

ccfootnotetext: The intrinsic relative absorption depth variability of the
He-10830 triplet’s red component, as described in Section 5.1. V1298 Tau does
not have a value because the feature is rotationally unresolved.

ddfootnotetext: The intrinsic relative absorption depth variability of the
full He-10830 triplet, as described in Section 5.1. In Figure 16 we compare
these values with literature helium exosphere measurements listed in Table 5.

The EW values of the nearby Ca i 10842 Å line are shown in the bottom panel of
Figure 6. There is a strong decrease in strength with increasing $T_{\rm
eff}$, and a turnover at cooler temperatures. This highlights the difference
in the line formation pathways between the chromospheric He-10830 triplet and
the largely photospheric Ca i 10842 Å line. The Ca i 10842 Å EW-$T_{\rm eff}$
trend we find follows predictions from the photospheric PHOENIX spectral
models (Husser et al., 2013).

Figure 7: EW[He] as a function of stellar rotation period for our sample. The
error bars are the median absolute deviation in EW[He] to show the amplitude
of variability as compared to the EW[He] value (note this is not the
uncertainty on the median EW[He]). He-10830 triplet absorption shows a clear
morphology with the stellar rotation period: more absorption at shorter
rotation periods, leading to a plateau below $P_{\rm rot}\sim 20$ d, before
decreasing at the longest rotation period. This is indicative of the He-10830
feature’s nature as an activity sensitive line: stars with shorter rotation
periods have more intense high-energy coronal radiation and denser
chromospheres, both of which help to form the stellar He-10830 feature.

However, there are two outliers in the EW[He]-$T_{\rm eff}$ plane amongst our
sample. This is likely explained by the stellar activity level, which can
affect the population of metastable helium and therefore the absorption
strength. One of the outliers is V1298 Tau, which is by far the youngest star
in our sample ($\tau\sim 25$ Myr). The other is HD 283869, which is a
peculiarly inactive Hyades member (Vanderburg et al., 2018). As a proxy for
activity level, we plot EW[He] as a function of stellar rotation period in
Figure 7. There is a clear variation in the absorption strength with respect
to the rotation period: it is very strong at the fastest rotation, decreases
through $\sim 5$ days, plateaus between $5$ and $\sim 20$ days, and then has a
significant decrease in strength by $\sim 35$ days. We note for comparison
that the photospheric Ca i 10842 Å line does not show a rotation period
dependence after removing the line’s $T_{\rm eff}$ dependence.

It is unsurprising that V1298 Tau would have the strongest He-10830 absorption
strength in our sample because it is the most active due to its youth and
rapid rotation. V1298 Tau is known to flare (David et al., 2019b, a;
Vissapragada et al., 2021; Feinstein et al., 2022), has a photometric
variability amplitude indicative of a large spot filling fraction (David et
al., 2019b), and potential spectroscopic indications of spots surrounded by
facular regions (Feinstein et al., 2021). All of these can enhance absorption
in the He-10830 triplet, as well as lead to greater variability in its
absorption strength (see Section 4.2).

K2-100 has the second highest EW[He] in our sample, which is unsurprising as
it is also the second fastest rotator. This enhanced absorption strength is
despite its older age, and may indicate that the structure of rapidly rotating
stars introduces departures from models of chromospheres based on the Sun
(e.g. Andretta & Giampapa, 1995).

HD 283869 has a long rotation period (nearly double that of the next slowest
rotator in our sample), and weaker activity than other Hyades members (from Ca
ii HK and H-$\alpha$; Vanderburg et al., 2018). Given the strong dependence of
the He-10830 absorption strength on activity, it follows that our data would
show weak absorption relative to more rapidly rotating stars. HD 283869 still
resides at the upper envelope of the inactive dwarf He-10830 absorption
sequence, so it may represent a transition between the active and inactive
populations. Unfortunately, we do not observe stars with rotation periods
between 20 and 35 days, which would help to clarify the nature of the
weakening absorption (e.g. a gradual decline or a sharp discontinuity).
Despite its lower EW[He] and slower rotation, HD 283869 is the same mass as
fellow Hyades member K2-136. Surface gravity cannot explain the difference in
absorption strength for this case.

While our sample does not cover a large range in $T_{\rm eff}$ or age, the
stellar high-energy spectral distributions should still be changing across our
targets. Differences in high-energy radiative output (such as in X-rays) would
change the metastable helium population level if the PR mechanism dominates,
in turn changing the He-10830 triplet absorption strength. Not all of our
sample stars have literature X-ray observations, but given their rotation
periods and masses they almost all likely rotate slower than the saturated
X-ray luminosity regime (Pizzolato et al., 2003; Douglas et al., 2014; Núñez
et al., 2015). This means that the stellar X-ray luminosities should be
decreasing with increasing rotation period in our sample. Our results showing
a lack of dependence on $T_{\rm eff}$ or rotation period (within 5 to 20 days)
reinforces the conclusion from Sanz-Forcada & Dupree (2008) that CE is more
important than the PR mechanism in driving the population of metastable helium
for active stars. This is likely due to active stars having hotter and denser
chromospheres. In the EW[He]-$P_{\rm rot}$ plateau, CE dominates any decrease
in PR excitation from decreasing high-energy coronal radiation, leading to no
change in the EW.

Interestingly, V1298 Tau has a median EW[He] larger than the maximum predicted
by models with active region filling factors of unity from Andretta & Giampapa
(1995), even including some epochs with values greater than 50% higher. In
these models, the resulting predicted EW[He] is set by the density and
temperature structure of the chromosphere. EW[He] increases as activity
increases, which is parameterized with the chromospheric density. Once the
density is high enough, collisional de-excitation controls the metastable
helium population and drives the line into emission, leading to a turnover in
EW[He] (Andretta et al., 2017).

It is possible that V1298 Tau’s youth, even relative to the other stars in our
sample, alters chromospheric conditions to further heighten the He-10830
triplet absorption strength. For example, there are activity-driven phenomena
not considered in these models, such as a constant level of flaring or
eruption, that could be unique to particularly young stars. These conditions
would alter the metastable helium population, and thus the models of EW[He].
It is also important to point out that V1298 Tau has a lower $T_{\rm eff}$
than the models, which Andretta & Giampapa (1995) explicitly state may be an
issue for K-type stars.

Also, V1298 Tau has a lower surface gravity due to its youth that may lead to
a larger chromospheric scale height with reduced density. This may seem
counter to our earlier argument that young stars have higher EW[He] because of
denser chromospheres. However, we posit that V1298 Tau has an extended, more
rarefied upper chromosphere near the transition region above denser
chromospheric layers. This can be illustrated with the VAL C model in Figure 4
of Andretta et al. (2017), where a decrease in the upper region density
corresponds to an increase in the predicted maximum EW[He]. In this case, the
column density of metastable helium increases to produce a larger EW[He]
before reaching the volume density that initiates collisional control of the
population. With this lower density, coronal EUV radiation would also be able
to penetrate deeper into the chromosphere to raise the contribution of the PR
mechanism to population metastable helium. A combination of density and
radiation conditions in the chromosphere would thus lead to elevated EW[He] in
stars of V1298 Tau’s age.

Regardless of the speculated cause, our results imply that the chromospheres
of young and active stars diverge from models used for main sequence solar-
type stars. In the case of the youngest and most active stars, like V1298 Tau,
conditions likely significantly diverge from previous literature models.
Between an altered, denser chromospheric structure, rapid rotation, and more
intense high energy radiative environment, the He-10830 triplet’s absorption
is much greater for active stars than inactive stars.

###  4.2 Amplitude of variability in the He-10830 triplet’s absorption
strength

Figure 8: Long-term time-averaged EW[He] variability as a function of age. The
dashed lines show power law fits to the data, with the shaded regions denoting
the 1-$\sigma$ (darker gray) and 3-$\sigma$ (lighter gray) intervals. The
plotted ages for the Hyades and Praesepe members are artificially spread to
avoid overlapping points. Top panel: The variability shown is the median
absolute deviation of the EW[He] time series, scaled by 1.4826 to be
statistically equivalent to the Gaussian standard deviation. Using the MAD
accounts for outliers from low spectral S/N or poor spectral fitting. The
error bars are generated from bootstrap sampling of the data (see text for
further explanation). The variability decreases with age, plateauing above 300
Myr at $10-15$ mÅ. The variability increases significantly at younger ages,
but the relation is ill-defined due to only having two targets with $\tau\leq
120$ Myr. Bottom panel: The plotted MAD is an estimate of the intrinsic
variability in EW[He], quantifying variability that cannot be accounted for
with measurement error (see text for further explanation). Only upper limits
are measured for 3 targets, for which the 90% upper limits are denoted by the
triangle marker. The variability-age relation persists, showing that the
relation is intrinsic to the stars. The objects at the oldest ages are in
agreement with intrinsic variability between $5-10$ mÅ, with 6 of the 8 older
targets in agreement with no intrinsic variability due to the magnitude of
their EW[He] measurement uncertainties. Figure 9: Intrinsic variability of
EW[He] as a function of stellar rotation period, following the calculation
described in the text and also shown in Figure 8. There is no relation between
the variability and rotation period, which we use as a proxy for activity
level. This is unlike for the EW itself, which correlates with the rotation
period. The two objects with high variability (V1298 Tau and K2-284) are
younger than the rest of the sample.

Figure 8 shows that the stars in our sample span a wide range of EW[He]
variability, with very high variability in youth that decreases expeditiously
towards older ages. We quantify the variability using the median absolute
deviation (MAD), scaled by 1.4826 to be statistically equivalent to the
Gaussian standard deviation. There is variability in the EW[He] value both
with (top panel) and without (bottom panel) accounting for measurement
uncertainty, which will inflate the measured MAD, indicating that at least
some changes in the He-10830 triplet absorption strength are intrinsic to the
stars.

In the top panel of Figure 8 we show the MAD of the EW[He] time series for
each star. To measure the uncertainty of our measurement of the MAD, we
perform bootstrap sampling of each target’s EW[He] time series. For a target
with $N$ measurements, we generate a simulated time series by sampling $N$
EW[He] values with replacement and calculate its MAD. We repeat this process
500000 times, and adopt the median and 16th-84th percentile ranges as the
value and uncertainty in the MAD, respectively. The relationship between
EW[He] and age is well described by a power law, which we fit to our data and
show in the figure. The variability is highest at the youngest ages ($\sim 25$
Myr), roughly halves by $\sim 100$ Myr, before plateauing at ages older than
$\tau\sim 300$ Myr.

However, some of this measured variability is introduced by the uncertainty of
our EW[He] measurements. To estimate the true intrinsic variability of the
He-10830 triplet absorption strength, we compute a MAD quantity with the
measurement uncertainty deconvolved and show it in the bottom panel of Figure
8. For each target, we first generate a simulated time series with no
intrinsic variability by sampling for each data point from a Gaussian
distribution with a mean of 0 and a standard deviation of the individual
measurement uncertainty. The MAD of this time series, which we call MADmeas,
encapsulates just the measurement uncertainty. We then sample one of the
500000 bootstrapped time series MAD values described in the previous paragraph
to represent the combined intrinsic and measurement variability, called
MADfull. The intrinsic variability is then estimated as:

${\rm MAD}_{\rm intr}=\sqrt{{\rm MAD}_{\rm full}^{2}-{\rm MAD}_{\rm
meas}^{2}}$ (5)

We repeat this 500000 times to build a distribution of intrinsic variability
estimates. If the measurement-only variability is larger than the combined
variability, we set the MADintr to 0, as such a time series agrees with no
intrinsic variability. We adopt the median and 16th-84th percentiles of the
MADintr distribution as the value and uncertainty. If the median value for a
target is 0, we adopt the 90th percentile as an upper limit on the intrinsic
variability.

A power law also describes the relationship between intrinsic EW[He]
variability and age, with a plateau below 10 mÅ at ages above 300 Myr and
increasing variability below 120 Myr. Of the 8 stars in the older age range, 6
of them have intrinsic variability estimates that agree with 0, so the plateau
above 300 Myr may agree with no intrinsic variability. The 3-$\sigma$ range of
the fit encompasses the scenario where there is no intrinsic variability at
older ages with a sharp, immediate increase at the youngest ages. This is not
the preferred fit, though, and 2 of the older stars in our sample do have
resolved intrinsic variability (K2-136 and HD 63433).

We make particular note of HD 63433, which is by far the brightest star in our
sample, leading to the highest typical spectral S/N and therefore the lowest
typical measurement error on EW[He]. HD 63433 may therefore be the exemplar of
intrinsic EW[He] variability in this age range, disputing the lack of
intrinsic variability from our upper limit measurements but confirming that
the level of variability is relatively low. The 1-$\sigma$ range of intrinsic
EW[He] variability measurement for HD 63433 is 4.9 to 8.4 mÅ, which
corresponds to 1.5 to 2.7% when normalized by its median EW[He] value. For our
highest quality spectra we can measure the intrinsic variability to a
precision of roughly 0.5%.

We tentatively suggest that this roughly 2% intrinsic long-term average EW[He]
variability is likely representative of the typical variability in the 300 Myr
to 1 Gyr age range, although the multiple measurements that agree with 0 show
that some targets may have no intrinsic variability and that more monitoring
at higher S/N is necessary to resolve the intrinsic variability.

We do want to address the stars that agree with no intrinsic variability, and
why it may or may not be indicative of an actual lack of variability. Of the 8
stars in this older age range, 6 of them have intrinsic variability estimates
that agree with 0. We only determine upper limits for 3 of the stars, meaning
that any intrinsic variability is below the contribution of measurement error.
Two of the three stars with upper limits, K2-101 and K2-102, are relatively
faint with the fewest number of observations in our sample, which would lead
to larger measurement uncertainty. The other star with an upper limit, K2-77,
is also on the faint end of our sample in addition to being the oldest, so it
may be indicative of a true lack of intrinsic variability. For 3 other stars
(K2-100, HD 283869, and TOI 2048), we resolve an intrinsic variability
measurement that agrees with 0 within 1-$\sigma$. K2-100 is not surprising, as
its broad lines from rapid rotation lead to larger EW[He] measurement
uncertainty than is typical. HD 283869 is by far the least active star in our
sample, so it agreeing with no intrinsic variability is expected. TOI 2048 is
slightly more surprising, although it has the shortest survey baseline with
half of its observations taken within a single month which may lead to less
variability being captured.

The variability we find at $\tau\gtrsim 300$ Myr is comparable to the field
M-dwarfs studied by Fuhrmeister et al. (2020). The median variability across
their sample is $\sim 12$ mÅ (also quantified with MAD), which is similar to
the plateau in variability at older ages in our sample (top panel of Figure
8). While the strength of He-10830 absorption decreases through the M-dwarf
regime, this result shows that above ages of $300$ Myr, the activity-induced
variability does not have a significant spectral type dependence through SpT
$\sim$ M3. The young V1298 Tau and K2-284 do have larger variability
amplitudes than the early M-dwarfs. K2-284 has variability comparable to the
late M-dwarfs and V1298 Tau has variability larger than all but a few of the
M-dwarfs in the CARMENES sample. Activity-induced variability is significant
at young ages and low effective temperatures, being the most significant at
the youngest ages regardless of SpT.

While variability increases significantly at younger ages, there is no
correlation between variability and rotation period. This stands in contrast
to the dependence of EW[He] on rotation period (see Figure 7). Figure 9 shows
the intrinsic variability of EW[He] as a function of stellar rotation period,
where stars with ages above 300 Myr either have comparable scatter to the most
slowly rotating stars or only upper limits for the intrinsic variability.
Rotation is a direct proxy for activity level, so we conclude that there must
be a non-rotation activity effect that drives variability in the helium
absorption strength. The two outliers in Figure 9 are both young, so age may
be a factor. V1298 Tau is the most significant outlier, while being the
youngest and most rapidly rotating star in our sample. Its helium variability
may therefore be driven primarily by its rotation. While the other outlier,
K2-284, is also young, it has a typical rotation period for our sample but a
later spectral type (late-K to M0, rather than mid-K or earlier; David et al.,
2018; Dressing et al., 2019). It may be more active than earlier-type stars at
the same rotation period, resulting in greater helium variability.

This lack of clear relation between helium variability and rotation implies
that there is a combination of effects on the stellar activity level that
drive changes in the helium absorption strength, such as from age, rotation,
and stellar structure (spectral type). We conclude that the EW[He] variability
is set by activity evolution. Examples of this would be from acute changes in
the He-10830 absorption strength (e.g. from flares; Vissapragada et al.,
2021), short-term variability from rotational modulation of active regions
(e.g. spots and plage, as on the sun; e.g. Brajša et al., 1996), and long term
activity cycles (as seen for solar-type stars in other chromospheric lines
such as Ca ii H and K; e.g. Baliunas et al., 1995; Boro Saikia et al., 2022).
Further work studying the relationship between activity and rotation period at
older ages, such as by studying fast rotating tidally locked binaries, would
help disentangle the complicated connection between activity level and the
stellar dynamo.

We show that the long-term time-averaged variability in EW[He] is stable and
relatively low for stars with $\tau\gtrsim 300$ Myr, and cannot rule out the
absence of intrinsic variability for most of our targets in that age range.
This means that even observations separated by months to years might have a
comparable EW[He] baseline, although there are physical mechanisms that may
drive variability on shorter timescales; the relative timing of observations
and variability will be a crucial constraint on exosphere detectability. Stars
older than 300 Myr seem to behave like field stars, but we find high-amplitude
statistically significant intrinsic variability for stars with $\tau\lesssim
120$ Myr. Observations of stars with ages between $50-300$ Myr are needed to
fully map the EW[He] variability-age dependence. Such measurements will become
available as NIR RV surveys of young stars continue (e.g. Tran et al., 2021).

###  4.3 Timescale of variability in the He-10830 triplet

Figure 10: The “EW difference power spectrum” of the He-10830 triplet time
series for our targets. We compute the pairwise difference in the EW[He] for
each observation of a particular target as a function of the time separating
the observations. We stack the “EW difference power spectra” for all targets
besides V1298 Tau, as they are older and have lower long-term average
variability. The small background points show all pairwise differences. We
generate 10000 “EW difference power spectra” accounting for measurement
uncertainty on individual EW[He], and the large foreground points show the
median of these “EW difference power spectra” samples baseline-binned to
reflect the typical variability at each timescale. The x-axis error bars show
the timescale bin extents, and the y-axis error bars show the 16th-84th
percentile error on the median “EW difference power spectrum”. The variability
is smallest at the shortest timescales, increases after only a few hours, and
plateaus out to separations of years.

Our above analysis of the He-10830 triplet absorption variability represents
the time-averaged variability over the full observation baseline of our
targets, spanning minutes through years. While this provides insight into the
typical variability amplitude of the He-10830 triplet, it does not reveal the
timescale over which this variability occurs. As exosphere observations are
inherently temporal, the timescale of variability is crucial to assess the
feasibility of young exosphere detection. Most exosphere detection programs
include out-of-transit observations on the same night as the transit, which
would be affected by stellar variability on timescales of hours. Our long-term
variability analysis shows the limits of comparing observations over full
observing seasons (weeks to months to years). We must investigate the
timescale of variability in EW[He] to assess out-of-transit observation
comparison at shorter time baselines.

To quantify the He-10830 triplet variability as a function of the time
baseline between observations we compute an “EW difference power spectrum”.
For each target, we calculate the difference in the EW[He] for each pair of
observations as a function of the time separation of the observations, and we
show the result in Figure 10. The “EW difference power spectra” for all
targets besides V1298 Tau are stacked to increase precision, because they have
roughly the same amount of long-term average variability and because these
“older” stars appear to act similarly. V1298 Tau is plotted separately to
highlight the increased variability at the youngest ages. To account for
measurement uncertainty, we generate 10000 mock time series for each object
using the EW[He] values and errors and compute the 10000 corresponding “EW
difference power spectra”. The large points plotted in Figure 10 are the
median of the 10000 sample “EW difference power spectra”, and the error bars
are the 16th and 84th percentile values to represent the error on the median
difference. The x-axis error bars show the timescale bin extents.

At the shortest timescales ($\Delta t\lesssim 1$ hr), the variability is lower
than for longer time baselines, and the same for both the “older” objects and
V1298 Tau. While variability may still be a significant issue depending on the
exosphere parameters, it is smallest on the shortest timescales regardless of
age and may be most affected by acute changes in He-10830 triplet absorption
(e.g. flaring). For the “older” objects, the variability increases slightly
beyond $\Delta t\sim 5$ hr, and is then relatively stable at longer
timescales. The variability for V1298 Tau follows a similar morphology, but
has a much larger amplitude, even on the same night, which is expected given
its larger long-term variability and the increased volatility in activity at
young ages.

The typical EW variability increases significantly even after just a few
hours, represented by the second binned data point at 5 hours in Figure 10.
The only two targets with observations covering this baseline are V1298 Tau
and K2-100, both of which have relatively short rotation periods. It is
important to note that there were only two nights for which K2-100 was
observed on both tracks available for the HET (as opposed to 7 nights for
V1298 Tau), so the second binned data point for the older objects must be
interpreted with caution. It is possible that the heightened variability on
this timescale is from active regions of varying He-10830 absorption strength
beginning to rotate in and out of view. This may also be capturing acute
changes in the He-10830 absorption strength due to flaring (particularly for
V1298 Tau). This timescale of increased variability might be due to the
lifetime of the helium metastable state, which is 2.2 hours (Drake, 1971). The
changing He-10830 absorption strength on this relatively short timescale of
$\Delta t\sim 5$ hr may represent de- and re-population of the helium
metastable state between observations. Above timescales of $\Delta t\sim 5$
hr, the EW difference plateau represents variability in the He-10830
absorption strength (e.g. from active regions, flares, stochastic activity)
that is averaged out over multiple epochs.

####  4.3.1 Short timescales: intra-night variability

Figure 11: Intra-visit variability of EW[He] as a function of age, to
demonstrate variability within a 30 minute baseline. The plotted ages for the
Hyades and Praesepe members are artificially spread for clarity. The markers
show the median EW[He] difference for pairs of observations within the same
visit for each object. The lines bracketed by triangles are not error bars.
They show the 90th percentile range of intra-visit variability measurements
that would be found if we assume no intrinsic variability, only measurement
error. The measured intra-visit variability is in agreement with no intrinsic
variability for 8 of the 10 objects, and just in slight disagreement for the
other 2. At these shortest timescales, the variability measurement is
independent of age and can be explained solely by measurement error without
any intrinsic EW[He] variability. This gives confidence that detecting even
the youngest exospheres is possible with comparison observations directly
surrounding transit.

We can also assess variability on the shortest timescales by inspecting
measurements taken on the same night. An observation of a target, which we
call a visit, is composed of multiple consecutive exposures (normally 3). This
provides multiple spectra separated by $5-10$ minutes. Figure 11 shows the
intra-visit EW[He] variability, representing timescales of $\lesssim 30$
minutes, as a function of age. We quantify the intra-visit variability by
computing the absolute EW difference between each pair of observations in a
single visit, and then present the median pairwise difference for each target.
This is directly comparable to exosphere detections which are presented as
measurements of excess absorption depth, which are essentially differences in
EW.

Compared to the long-term time-averaged variability (Figure 8), the intra-
visit variability has no dependence on age, and has similar or smaller
amplitude to the MAD of the EW[He] time series. These conclusions are in
agreement with those drawn from the “EW difference power spectra” about
variability on the shortest timescales (Figure 10, Section 4.3).

The intra-visit variability measurements represent both measurement error and
the intrinsic variability of He-10830 absorption strength. To determine the
significance of the measured variability, we estimate the intra-visit
variability produced solely by the measurement uncertainty. For each target,
we generate 5000 EW[He] time series wherein the EW[He] value is assumed to be
constant within a visit and the individual measurements are sampled using the
measurement uncertainty. We then calculate the intra-visit variability for
each simulated time series following the procedure described previously. The
vertical lines bracketed by triangle markers plotted in Figure 11 show the
smallest range of intra-visit variability values that include 90 percent of
the simulations, denoting the range of values consistent with no intrinsic
variability.

Of the 10 objects in our sample, 8 have measured values for their intra-visit
variability that agree with no intrinsic intra-visit variability. The other 2
objects (HD 63433 and K2-136) just barely do not agree. This result agrees
with all objects having no intrinsic intra-visit variability. This is
promising for the detection of young exospheres if out-of-transit observations
are taken directly surrounding transit. The intra-visit variability
measurements of the stars with $\tau\gtrsim 300$ Myr are comparable in
amplitude to their long-term time-averaged variabilities, when not
deconvolving the measurement uncertainty. However, while some objects in this
age range have measurable statistically significant intrinsic long-term time-
averaged variability, all objects have intra-visit variability in agreement
with only being caused by measurement quality. This reinforces the conclusion
that variability on such a short timescale should be negligible, and the
notion that higher S/N from stacked spectra taken across the transit will
increase the reliability of exosphere observations.

However, there still could be increased variability on short timescales. The
He-10830 triplet strength increases from flares (Fuhrmeister et al., 2020),
which act on timescales of minutes to hours. Vissapragada et al. (2021) even
found a linear increase in the He-10830 triplet strength of V1298 Tau in the
decay phase of a flare, potentially indicating the line’s temporal response.
The observation was during a transit of V1298 Tau c, though, so the increase
could have been due to either the flare or an exosphere. Other acute active
phenomena could change the He-10830 triplet strength, such as spot/plage
rotation, chromospheric network variability, winds, and mass loss. While
variability is small on timescales that cover out-of-transit observations
directly surrounding transit, even agreeing with no intrinsic variability on
timescales within 30 minutes, care must still be taken when interpreting
He-10830 triplet transit observations in the context of stellar activity.

####  4.3.2 Intermediate timescales: intensive observing campaigns

We further investigate variability in the He-10830 absorption strength at
intermediate timescales using the intensive campaigns that were taken for
three targets in our sample: V1298 Tau, K2-136, and K2-100. These intensive
campaigns include regular observations over a months-long span, with
individual visits often only separated by a day. The high cadence of these
data is useful to search for periodicity, unlike the sparse, years-long time
series for most targets in our sample. More frequent observations are also
more likely to catch acute changes in the He-10830 absorption such as from
flares. We computed periodograms for each intensive time series to search for
periodicity, and discuss these observations below.

V1298 Tau: With the highest EW[He] variability in our sample, V1298 Tau
provides an important opportunity to study significant absorption strength
changes at high cadence. V1298 Tau is a unique system: it is a very young
($\tau\sim 25$ Myr) early K-dwarf, hosts 4 known transiting planets (David et
al., 2019b, a), is a promising candidate for follow-up atmospheric
characterization of young planets, and is a useful probe of star and planet
formation as a member of the older distributed stellar groups around Taurus
(Krolikowski et al., 2021). The intensive campaign for V1298 Tau comprises 30
visits (98 spectra) spanning 45 days, with a median visit separation of 1 day.
There was a brief break in observations for 12 days in the middle of the
campaign. This intensive campaign was taken in October-November of 2019 with
the goal of measuring the mass of V1298 Tau b, which will be presented in a
future paper. Figure 12 shows the intensive EW[He] time series of V1298 Tau,
which features significant structure. The EW[He] varies by almost $300$ mÅ in
the first week and a half of the intensive campaign, before settling down to
vary by $\sim 100$ mÅ around a stable value, and then dropping further in the
last few days. There is also an observation with greatly elevated EW[He] at JD
$\sim 2458786$ that may be indicative of a flare.

There is no significant periodicity across the entire time series, which may
indicate that the variability in the He-10830 absorption strength comes from
equal spatial distribution of active regions across the surface, such as
extreme spot coverage and the chromospheric network. However, there is
significant periodicity near the stellar rotation period within the first week
and a half of the campaign when the absorption varies wildly. The periodogram
of the first week and a half of data is shown in the top panel of Figure 13.
The bottom panel of Figure 13 shows the intensive campaign phased to the
period of peak periodogram power, and the data from the first week and a half
is coherent unlike the rest of the time series.

This contradicts the conclusion from the entire intensive data set that
variability is essentially smeared out across the stellar rotation. We posit
that the large amplitude variation at the stellar rotation period may be from
an extreme flaring or mass loss event that created a large but spatially
concentrated bright spot on the stellar chromosphere, which would then show
enhanced He-10830 absorption when it rotates into view. This highlights the
volatility in EW[He] at such high activity levels, and warrants even further
caution for planning time sensitive transit observations.

Figure 12: The EW[He] time series for the V1298 Tau intensive campaign. In the
first week and a half of the campaign there is extreme variability in the EW
value, which then steadies at a slightly lower value for the remaining time
series coverage. Figure 13: Periodicity analysis of the V1298 Tau intensive
campaign. Top Panel: The periodogram of the first week and a half of data from
the intensive campaign, which features extreme variability. The peak of the
periodogram ($P=3.02$ d) is very close to the rotation period of the star
($P=2.9$ d), and has power well above the 1% false alarm probability level.
Bottom panel: The intensive campaign phased to the periodogram peak’s period,
shown for the first week and a half separately from the rest of the intensive
time series data. The coherence at the start of the campaign is stark, while
there is no apparent rotational modulation for the data from the remainder of
the campaign.

K2-136: K2-136 is a K5.5-dwarf Hyades member that hosts 3 transiting planets
(Mann et al., 2018; Ciardi et al., 2018; Livingston et al., 2018), and is
representative of the older targets in our sample that have He-10830
variability in line with the field. It has a rotation period on the slower end
of our sample’s range (15 days), with 7 of the 10 stars having faster
rotation. The intensive campaign for K2-136 comprises 22 visits (68 spectra)
spanning 80 days, with a median visit separation of 2 days. There was a brief
break in observations for 20 days in the middle of the campaign. This
intensive campaign was observed soon after HPF’s commissioning, and has been
used as a standard reference by our team in analyzing HPF data. The top panel
of Figure 14 shows the intensive EW[He] time series of K2-136, which is fairly
flat over the course of the observations. We generate mock time series
assuming constant EW using each observation’s measurement error to determine
if the data variability is consistent with zero. The scatter for the data is
$\sigma=11.3$ mÅ, which agrees with the simulated scatter assuming no
intrinsic variability of $\sigma=10.3\pm 1.0$ mÅ. It is unsurprising that an
older, less active star would show less structure in the high cadence EW[He]
measurements. The intensive campaign has periodicity near the stellar rotation
period, shown by the periodogram in the bottom panel of Figure 14, but it has
power just barely above the 1% false alarm probability level. This potential
rotational modulation is inconclusive, and we do not show the phased time
series because it does not show clear modulation. The average EW during the
intensive campaign is lower than for the rest of the sparse time series, which
may be indicative of longer term (months to years-long) activity cycles
manifesting in the EW[He] of K2-136.

Figure 14: Top Panel: The EW[He] time series for the K2-136 intensive
campaign. The data is fairly flat, and most of the variability shown is within
the individual EW measurement uncertainties. Bottom panel: The periodogram for
the full intensive campaign of K2-136, which shows a peak that is significant
just above the 1% false alarm probability level. The period of the peak
($P=14$ d) is close to the stellar rotation period ($P=15$ d). Given the power
of the peak, the periodicity found here is taken to be inconclusive.

K2-100: K2-100 is an F6-dwarf Praesepe member that hosts a transiting planet
(Mann et al., 2017), and features the fastest rotation period in our sample
besides the much younger V1298 Tau. However, it has He-10830 absorption
strength and variability comparable to the rest of the “older” targets in our
sample. The intensive campaign for K2-100 comprises 24 visits (72 spectra)
spanning 80 days, with a median visit separation of 1 day. There are two brief
16-day breaks in the observations in the middle of the campaign. This
intensive campaign was taken to measure the mass of K2-100b, which will be
presented in a future paper. Figure 15 shows the intensive EW[He] time series
of K2-100, which is fairly flat over the course of the observations, similarly
to K2-136. We again generate mock time series assuming constant EW using each
observation’s measurement error to determine if the data variability is
consistent with zero. We exclude from this calculation three data points with
measurement errors in excess of 100 mÅ. The scatter for the data is
$\sigma=23.9$ mÅ, which agrees with the simulated scatter assuming no
intrinsic variability of $\sigma=26.0\pm 4.6$ mÅ. Interestingly, there are no
significant periodicities found for this data set. We may have expected
rotational modulation due to its faster rotation period than K2-136, but this
may be indicative of rotationally-smeared He-10830 absorption from the general
chromospheric network or spatially distributed surface active regions.

Figure 15: The EW[He] time series for the K2-100 intensive campaign. The data
is fairly flat, and most of the variability shown is within the individual EW
measurement uncertainties.

For completeness, we compute the periodogram power spectra of all targets’
full time series and see no significant periodicity, which is not surprising
given their sparse cadence. In all, we only see any amount of rotational
modulation in two targets: V1298 Tau with significant modulation over just one
week and a half of the observations, and K2-136 with a periodigram power that
is barely significant. While the He-10830 absorption strength variability
seems to be dependent on the stellar age, and thus activity level and
volatility, there is no significant relation between the He-10830 variability
and stellar rotation. This may indicate that He-10830 line formation is not
solely tied to spot or plage features, which are typically visualized as
producing rotationally modulated stellar activity signals. Instead, He-10830
may be formed in active regions as well as from flares or other stochastic
events in the broader chromospheric network, which essentially smears the
He-10830 absorption changes across the stellar surface.

##  5 Implications for the detection of young exospheres

With the intrinsic stellar variability of the He-10830 triplet at young ages
quantified, we can contemplate the possible effects of stellar activity on
observations to find and characterize young helium exospheres. The stellar
He-10830 triplet is demonstrably sensitive to activity, and intrinsic
absorption changes could masquerade as an exosphere signal. The amplitude of
the planetary He-10830 triplet absorption signal is set by the exosphere’s
metastable helium population and the atmospheric mass loss rate, both of which
depend on the activity-sensitive high-energy radiative output of the host star
(Oklopčić, 2019; Poppenhaeger, 2022). In this section, we discuss the
feasibility of detecting young helium exospheres in the presence of stellar
variability, and explore scenarios in which activity may affect exosphere
observations.

###  5.1 Relating equivalent width variability to line depth variability

To assess the degree to which changes in the stellar He-10830 triplet may be
confused with an exosphere’s signal, we want to compare our sample’s intrinsic
He-10830 triplet absorption strength variability to measured helium exosphere
depths. However, we cannot directly compare our intrinsic EW[He] variability
measurements to exosphere depths. Exosphere detections are most commonly
presented as the peak in-transit excess absorption relative to an out-of-
transit reference spectrum at the center of the He-10830 triplet (typically
the redder of the two resolved components). This would be equivalent to the
variability in the flux at the line center rather than variability in the
integrated line strength; our intrinsic EW[He] variability measures the
latter.

For more accurate comparison we must convert the EW[He] variability to an
equivalent relative absorption depth variability, which we call $\sigma_{D,\rm
rel}$. This quantity also represents the excess absorption typically presented
as an exosphere measurement. Let us consider a hypothetical spectral line with
depth $D$ as a fraction of the continuum level. If there is a change in the
depth of the line, called $\Delta D$, then the relative absorption depth
variability can be calculated as:

$\sigma_{D,\rm rel}=\frac{\Delta D}{1-D}$ (6)

If we assume that only the line depth is changing (i.e. the line profile is
the same), then any change in the equivalent width is proportional to the
change in the line depth. We denote this as $\sigma_{\rm EW,rel}$, which is
the relative change in the EW value:

$\sigma_{\rm EW,rel}=\frac{\Delta\rm EW}{\rm EW}=\frac{\Delta D}{D}$ (7)

We can measure $\sigma_{\rm EW,rel}$ by normalizing our measured intrinsic
EW[He] variability by a target’s typical EW[He] value. By combining Equations
6 and 7, we can express the relative absorption depth variability (or excess
absorption) in terms of the relative EW variability:

$\sigma_{D,\rm rel}=\frac{D}{1-D}\sigma_{\rm EW,rel}$ (8)

With these equations, we can convert the measured intrinsic EW[He]
variabilities for each target (given under column MADintr[EWHe] in Table 4 and
described in Section 4.2) into relative absorption depth variabilities that
are directly comparable to exosphere measurements.

We normalize the intrinsic EW[He] variability by the typical He-10830 triplet
absorption depth provided by the spectral fits from Section 3.2. The EW[He] we
measure is of the full He-10830 triplet feature, which has two resolved
components for 9 targets in our sample (the feature is unresolved for V1298
Tau due to its rapid rotation). For these 9 targets we use an “equivalent
single line” depth for the value $D$ in Equation 8 by computing the depth
required for an absorption line to have the same EW as the full feature EW.
The width of the “equivalent single line” is taken from the quadrature added
variances of the individual He-10830 triplet components (using the median of
the best fit values of the time series spectral fits). For V1298 Tau we use
the depth of the unresolved line from the spectral fit.

We then substitute this intrinsic relative EW[He] variability into Equation 8.
The resulting intrinsic relative absorption depth variabilities are listed in
Table 4 as $\sigma_{D,\rm rel}$. Since we measure the intrinsic EW[He]
variability using bootstrap sampling, we can calculate a distribution of
intrinsic relative absorption depth variabilities for each target and estimate
the uncertainty in expected variability. It is this distribution that is
converted using Equation 8. The $\sigma_{D,\rm rel}$ values and uncertainties
in Table 4 are the median and 16th-84th percentile confidence interval of each
target’s bootstrap distribution, representing the typical $1\sigma$ amplitude
of the stellar variability signal and the uncertainty in our measurement of
it.

We also calculate a combined $\sigma_{D,\rm rel}$ value for the intermediate-
aged stars in our sample (300 Myr to 1 Gyr) to best represent the variability
at these ages by combining each target’s individual $\sigma_{D,\rm rel}$
bootstrap distributions. These 8 targets all have similar EW[He] values and
scatters which justifies the simple joining of their variability
distributions. This combined distribution gives a $\sigma_{D,\rm rel}$ value
of $0.65_{-0.65}^{+0.82}$, which agrees with a value of 0. This highlights
that we cannot rule out the absence of intrinsic variability at these ages
with our observations.

It is important to note that exosphere measurements typically only use the
redder of the two resolved He-10830 triplet components. However, the triplet
is unresolved for rapidly rotating stars such as V1298 Tau, which is why our
EW[He] measurements use the full He-10830 triplet feature. To resolve this
discrepancy, we recalculate $\sigma_{D,\rm rel}$ using only the red He-10830
triplet component for the 9 targets with a resolved feature. The EW
calculation procedure from Section 3.2 outputs the EW for the individual
He-10830 triplet components. We then follow the steps in Section 4.2 to
compute the red component’s intrinsic variability, and substitute the red
component’s EW and variability into the steps listed previously in this
section to calculate $\sigma_{D,\rm rel}$ in just the red component. For the
depth value $D$ we use the best fit depth of the red component from Section
3.2’s spectral fits. The values for the red component are listed in Table 4
under the column labeled $\sigma_{D,\rm rel,red}$.

The $\sigma_{D,\rm rel}$ and $\sigma_{D,\rm rel,red}$ values agree within
1$\sigma$ for the 9 targets with resolved features. Thus, the relative
intrinsic variability is not significantly different when considering the full
feature or a subset of it. Any results concerning the He-10830 triplet should
not be affected by the choice of which component(s) to measure. This is also
encouraging for the ability to look for velocity-shifted signals with high-
precision data. We note that $\sigma_{D,\rm rel,red}$ is typically lower
precision and less constraining than $\sigma_{D,\rm rel}$. Using the full
feature is ideal for variability measurements because it contains the most
spectral information.

For the rest of the discussion we use the intrinsic relative absorption depth
variabilities calculated with the full He-10830 triplet feature
($\sigma_{D,\rm rel}$ in Table 4). We make this decision because V1298 Tau has
an unresolved feature and is crucial to our analysis as the youngest star in
the sample. This also keeps consistent our use of the full EW[He] across the
paper. The agreement between the values calculated with the full feature and
only the red component further justifies this decision.

###  5.2 Comparisons with known helium exospheres

Figure 16: Literature helium exosphere detections (circles) and upper limits
(triangles) compared to our measurements of the 1$\sigma$ intrinsic stellar
variability level (see Section 5.1 for a description of the calculation). To
show the age dependence, we plot the variability of V1298 Tau, K2-284, and HD
63433 as separate horizontal lines. The error bars at the left end of the plot
show the 16th-84th percentile confidence interval on our measurement of the
1$\sigma$ intrinsic stellar variability. The gray hatched region shows the
16th-84th percentile confidence interval on the variability measured with the
combined $>300$ Myr sample, which agrees with no intrinsic variability. All
but a few exosphere detections are smaller than variability at the youngest
ages, but by 400 Myr all exosphere detections are comparable to or larger than
the intrinsic stellar variability. Stellar variability should not preclude
detection at these intermediate ages. The literature data is presented in
Table 5.

Figure 16 shows helium exosphere detections and upper limits from the
literature as percentage excess absorption depths, plotted alongside some of
our measurements of the intrinsic relative absorption depth variability
($\sigma_{D,\rm rel}$) for our sample plotted as horizontal lines. The
$\sigma_{D,\rm rel}$ quantity represents a 1$\sigma$ variability amplitude and
thus it is not directly comparable to a detection limit, although it could be
scaled to serve as one if an assumption is made for the underlying depth
variability distribution.

We have separately plotted 4 different $\sigma_{D,\rm rel}$ values from our
sample to visualize the age dependence. We show the $\sigma_{D,\rm rel}$ value
(solid line) and its 16th-84th percentile confidence interval (error bar at
plot’s left side) for V1298 Tau to represent the youngest and most active
stars, HD 63433 to represent ages when variability approaches the field’s, and
K2-284 to represent ages between these two extremes. To compare to the upper
limit on intrinsic variability calculated for stars older than 300 Myr, we
show the 16th-84th percentile confidence interval of the combined intermediate
age $\sigma_{D,\rm rel}$ as the gray hatched region. Note that this range
agrees with 0, meaning no intrinsic variability to prevent exosphere
detection.

A vast majority of all currently detected helium exospheres have depths
significantly smaller than the intrinsic variability measured for stars with
$\tau\lesssim 120$ Myr (V1298 Tau and K2-284). There are however a handful of
extreme detections, with depths $\gtrsim 4\%$, that are comparable in
amplitude to or even larger than the variability at these youngest ages. From
this, we conclude that comparing spectra from across observing seasons (even
separated by days) is inadequate for detecting helium exospheres at ages below
$\sim 120$ Myr, although large transit absorption signals like WASP-107 b’s
can likely be ruled out (Allart et al., 2019; Kirk et al., 2020; Spake et al.,
2021). Directly contemporaneous out-of-transit comparison observations and the
use of multiple transit detections are likely needed for significant
detections of the youngest exospheres.

We show HD 63433 separately from the rest of the sample at ages older than 300
Myr because it is the most precise variability measurement that we make. All
exosphere detections are either larger than or in agreement with the 16th-84th
percentile confidence interval of HD 63433’s variability, and only the most
precise upper limits are smaller. This is promising for the detection of
helium exospheres at intermediate ages and agrees with our conclusion that
stars of this age exhibit similar He-10830 triplet behavior as the field. HD
63433 may not be representative of all stars in this age range, so we also
show the 16th-84th percentile confidence interval of the intrinsic variability
for the ensemble of stars older than 300 Myr. While the top of this interval
is larger than a majority of the known helium exosphere depths, the
measurement from this stellar ensemble agrees with a total lack of intrinsic
stellar variability that would ensure the detectability of all helium
exospheres (barring significant instrumental or measurement errors).

It is very important to note that the $\sigma_{D,\rm rel}$ values we calculate
are essentially a 1$\sigma$ amplitude for the intrinsic relative depth
variability. This quantity does not directly provide an exosphere detection
limit because a statistically significant measurement typically requires
precision $>1\sigma$. This is complicated by the fact that while an exosphere
may or may not be present, a transit is not a random event. It is difficult to
determine a detection limit from these values, so the comparison with
literature exospheres is meant to be illustrative. One suggestion is to adopt
$1.7\sigma_{D,\rm rel}$ as a limit, which represents an estimated one-sided
95th percentile limit on the relative depth change, if the variability follows
a Gaussian distribution.

There are caveats to discuss that both positively and negatively impact the
potential detection of young helium exospheres. We so far discuss the long-
term, time-averaged variability, which represents the typical difference in EW
from the median value averaged across long observation baselines. Crucially,
we show in Section 4.3 that EW[He] variability on the shortest timescales
($\Delta t\lesssim 30$ min) is statistically consistent with no intrinsic
variability across age. Out-of-transit observations directly surrounding
transit should further decrease the prospect of activity-driven confusion in
interpreting results. There are also reasons why young exosphere signals may
be larger than their older counterparts. Young stars have greater high-energy
radiative output, which should increase both the exosphere’s metastable helium
population (leading to more He-10830 triplet absorption; Oklopčić, 2019;
Poppenhaeger, 2022) and atmospheric mass loss rate (Lopez et al., 2012; Lopez
& Fortney, 2013; Owen & Wu, 2017).

However, many transits are comparable in duration to or longer than the
timescale of increased variability. If the intrinsic stellar feature is
changing over the duration of a transit, the out-of-transit reference spectra
may not be truthful representations of the base stellar absorption, and any
exosphere interpretation will be affected. There may also be spurious signals
on these short timescales caused by observations with inopportune timing, such
as from a coincident activity event (e.g. flares). We discuss such scenarios
further in Section 5.3 below. We also note that our assumption of a stable
line profile to generate Equation 8 is not wholly accurate, so the comparison
made in Figure 16 is not exact.

Overall, detecting “intermediate-aged” helium exospheres ($\tau\gtrsim 300$
Myr) is not necessarily precluded by stellar activity, even with observations
spanning an observing season. However, potential confusion is minimized with
well-timed out-of-transit reference observations and by confirming the
exosphere absorption in multiple transits. Stellar variability likely would
preclude detection at the youngest ages ($\tau\lesssim 100$ Myr) without
carefully planned observations and significant exosphere absorption.

###  5.3 Scenarios where activity may still affect exosphere observations

There are still situations in which stellar activity-driven variability in the
He-10830 triplet could complicate exosphere detection. In particular, we are
concerned with scenarios where the timescales of stellar variability and
exosphere observations overlap. While our measurement of EW[He] scatter at the
very shortest timescales is consistent with no intrinsic variability, it is
important to note that there are still situations that may lead to actual
intrinsic variability in EW[He] on these timescales. Below, we discuss four
scenarios that may affect the detection of young exospheres, although this
list is hardly exhaustive and meant to be emblematic of potential issues with
the He-10830 triplet.

1) Flares: Stellar He-10830 triplet absorption is enhanced by flares (Andretta
et al., 2008; Sanz-Forcada & Dupree, 2008; Kobanov et al., 2018). If a flare
occurs near transit, there may be an increase in the He-10830 triplet
absorption strength that could be interpreted as an exosphere, despite being
stellar in nature. This would be most likely for very young stars that feature
the greatest flare rates. In our sample this includes V1298 Tau, for which
Vissapragada et al. (2021) observed a flare during the transit of one of its
planets, and could not distinguish between the flare or an exosphere as the
cause for increased absorption. Flares could also increase the atmospheric
mass loss rate (Wang & Dai, 2021), leading to an increase in the exosphere
He-10830 triplet absorption lagged from the flare by a few hours. In that
case, enhanced absorption would be a result of both the star and the
exosphere. It may be possible to disentangle these signals given the lifetime
of each, but the temporal response of the stellar He-10830 triplet feature to
a flare is unknown.

2) Lack of rotational coherence: We find nearly no significant signals at the
stellar rotation period in our data, implying that changes in the He-10830
triplet absorption are not rotationally coherent (particularly for longer than
a few rotations). This could be detrimental to exosphere detection, as the
activity-induced variability could not be modeled at the known rotation period
and subtracted. This also means that the He-10830 triplet could not be Doppler
mapped to identify distinct causative active regions. Other traditional
spectral activity indicators that do correlate with rotation may not track
changes in the He-10830 triplet, and thus could not be used in models of
activity’s effect on the He-10830 triplet.

3) Longer baseline out-of-transit comparison: Out-of-transit comparison
spectra may simply need to be taken further separated from mid-transit than
the $\sim 5$ hr timescale of increased intrinsic stellar He-10830 absorption
variability. One reason could be a transit that is on the order of or longer
than this timescale. The median transit duration of the known young transiting
planets is 3.2 hr and the longest duration is 7.5 hr. Extended out-of-transit
baseline could be long enough from parts of the transit when stellar
variability may introduce changes in the He-10830 absorption strength.
Depending on the transit timing, object visibility, and observing conditions,
it might be necessary to obtain out-of-transit comparison spectra on a
different night, which is more susceptible to activity contamination. This
also would affect comparing absorption depth changes across multiple transits.

4) Exosphere structure: An extended exosphere may affect its own detection,
particularly for a tail-like structure that effectively increases the helium
transit duration compared to the white-light transit. Tails created by
atmospheric mass loss have long been predicted (Schneider et al., 1998), and
have now been observed in helium gas for multiple planets (Nortmann et al.,
2018; Alonso-Floriano et al., 2019; Spake et al., 2021). Bow shocks and up-
orbit accretion flows could also produce a “leading tail” (Matsakos et al.,
2015), which has been observed for one helium exosphere (Czesla et al., 2022).
By lengthening the transit, these extended exospheres increase the likelihood
of activity-induced variability occurring during transit observations, as
explained in point 3 above. Such a scenario would complicate the definition of
“out-of-transit” observations, and necessitate more baseline observations
further from transit. One can imagine an extreme situation of a compact multi-
planet system where tails from multiple planets could lead to overlapping
extended transits (e.g. TRAPPIST-1, although no helium exosphere was detected
for 3 of its planets; Krishnamurthy et al., 2021). This would result in a
“constant” presence of helium exosphere material in the system. While this
situation is not necessarily common, such multi-planet systems (like V1298
Tau) are being observed, so it is plausible enough to encourage care when
considering the timing of transit observations.

###  5.4 Companion observations for planning campaigns and mitigating He
variability

A reconnaissance NIR spectrum to measure the EW[He] of planet hosts would help
to prioritize targets for exosphere observing campaigns. High EW[He] itself,
which is enhanced by stellar activity, could indicate a higher likelihood of a
detectable helium exosphere. Activity is accompanied by greater stellar high-
energy radiative output, which would excite more metastable helium in the
exosphere to produce a deeper planetary absorption signal. EW[He] is less
informative for active stars with $\tau\gtrsim 300$ Myr, though, because the
absorption strength saturates at intermediate ages. The EW[He] reconnaissance
may be more useful for older, less active stars where the PR mechanism (and
thus coronal radiation) will dominate the metastable helium excitation. It is
important to note that activity in the youngest stars also indicates increased
stellar variability, which would impede exosphere observations. Regardless,
stronger He-10830 absorption of a host star may be useful as an indicator for
the likelihood of a detectable helium exosphere.

There are also companion observations that could help to mitigate
contamination of exosphere observations from stellar activity-driven
variability. Extended out-of-transit monitoring would establish a more
reliable baseline stellar He-10830 absorption strength, and could be used to
identify the timescale and amplitude of intrinsic stellar variability. Long-
term monitoring could also be used to distinguish between periods of increased
and decreased variability for planning observations (as we see in Section
4.3.2). Ideally, one would observe consecutive transits with baseline
observations taken before the first transit through after the last transit.
This would provide a long baseline for comparison, as well as multiple
transits to increase the reliability of any detection. Simultaneous photometry
could be used to monitor for strong flares that may affect the stellar
absorption near transit (leading to intrinsic short-timescale variability), as
was done for an observation of V1298 Tau by Vissapragada et al. (2021).

Beyond this, further studies of the stellar He-10830 triplet are needed to
connect the feature to established activity proxies that may help de-trend the
intrinsic stellar variability in the line. A larger sample of stars at younger
ages (particularly between 50 and 300 Myr) would further establish the
behavior of the He-10830 triplet in youth and the feasibility of exosphere
detections.

##  6 Conclusions and future work

Young planets hold unique potential to better our understanding of the
formation and evolution of exoplanet atmospheres. Since its mission began,
TESS has followed K2 in discovering young planetary systems around bright
stars that are well-suited for atmospheric characterization. Critically, some
of these systems have been found in new stellar associations with ages between
100 and 400 Myr (e.g. Newton et al., 2021; Tofflemire et al., 2021; Hedges et
al., 2021; Dong et al., 2022; Newton et al., 2022). With the continued use of
precision NIR spectrographs, the He-10830 triplet will persist as a crucial
probe of the mass loss from these young planets. These follow-up observations
will require knowledge of the intrinsic stellar variability of the He-10830
triplet because the host stars have high activity levels.

In this paper, we present an initial study of the He-10830 triplet in youth
using unique NIR spectroscopic data from HPF for a subset of the known young
transiting planet hosts. We measured the He-10830 triplet absorption strength
and variability of our sample to characterize the feature’s relationship with
stellar activity, and discussed implications for exosphere detections. To
summarize our results:

  1. 1.

We developed a self-calibration technique to subtract strong telluric sky
emission lines from HPF spectra, which are not adequately subtracted using
just the sky fiber spectra. This is important as there is a very strong sky
line that can overlap the He-10830 triplet, making it harder to measure the
feature’s absorption strength.

  2. 2.

We find that the EW[He] is enhanced for young stars relative to inactive
dwarfs. There is no effective temperature dependence, but there is a relation
with stellar rotation period: there is stronger absorption at shorter rotation
periods. While all of our stars are young, activity levels are higher at the
youngest ages and most rapid rotation. Despite a likely significant difference
in the high-energy radiative output across our sample, we find a plateau in
EW[He] from $P_{\rm rot}\sim 5-20$ days. We conclude that in young and active
chromospheres, metastable helium is populated primarily through collisional
excitation, and that contributions from the PR mechanism only dominates at the
high and low relative activity regimes.

  3. 3.

The intrinsic stellar variability in EW[He] is large at young ages
($\tau\lesssim 100$ Myr), and decreases to a plateau comparable to the
expected field variability at $\tau\gtrsim 300$ Myr that is in agreement with
a lack of intrinsic variability. While the intrinsic variability of the 400
Myr HD 63433 is measurable at $\sim 2$% to a precision of $\sim 0.5$%, the
measurements for 6 of the other 7 “older” stars lack EW[He] precision to rule
out no intrinsic variability. This variability is caused by volatility and
evolution of the stellar activity level, such as by flares or changing surface
heterogeneities, which is most common at the youngest ages.

  4. 4.

The stellar EW[He] variability is smallest on the shortest timescales (within
30 min), and is consistent with no intrinsic variability on this timescale
considering all data. This gives us confidence in the ability to detect young
exospheres with immediate out-of-transit comparison observations. However, the
variability increases within just 5 hours for the youngest star in our sample
(V1298 Tau) and within a day for the rest of the sample, perhaps from the
coherence of flare-induced absorption changes. Comparing spectra of young
stars from night-to-night may introduce stellar variability that can mask or
masquerade as an exosphere signal. The convolution of stellar and planetary
signals must be considered when longer baseline out-of-transit observations
are taken, particularly if the exosphere has extended structure, such as a
tail.

  5. 5.

We find little evidence for periodicity with the stellar rotation in EW[He]
implying that the chromospheric regions in which the line forms are not
rotationally localized. We do, however, see stellar rotation periodicity
within the first week and a half of a month-long intensive campaign of V1298
Tau, featuring extreme absorption strength changes. The He-10830 triplet is
most variable and complicated at the youngest ages, and may have rotational
modulation during extreme flaring events or in the presence of large,
persistent high contrast surface heterogeneities.

  6. 6.

Youth does not necessarily preclude the detection of helium exospheres, except
at the youngest ages. The intrinsic variability at ages above 300 Myr is
smaller than or comparable to all current helium exosphere detections, but for
ages below 120 Myr the intrinsic variability is larger than all but the most
extreme helium exosphere detections. Variability also further decreases at the
shortest timescales, improving detectability. However, there may still be
confusion between enhanced absorption from exospheres and stellar active
regions or flares. Care must be taken when searching for exosphere signals
when observations are separated by longer than a few hours, as is often the
case for a transit, because variability can be significant on timescales
greater than a day. Continuous spectroscopic and photometric monitoring around
transit would help to mitigate the deleterious effect of stellar activity.

Our understanding of the He-10830 triplet of young and active stars is still
incomplete. More targets must be observed and uniformly analyzed to cover our
sample’s gaps in age, spectral type, rotation period, and activity level.
Mapping EW[He] at more densely sampled stellar parameters, particularly
rotation period, would further elucidate the origin of the line in young
chromospheres. Only two of our targets are young enough to feature enhanced
He-10830 triplet variability. More young targets ($\tau\lesssim 300$ Myr) are
needed to robustly assess the feasibility of detecting young exospheres and
determine variability timescales that help to best plan observing campaigns.
Additionally, intensive campaigns of a select few highly active stars could be
used to search for activity cycles and rotational coherence in EW[He].

Other observations that are contemporaneous with NIR spectroscopy would
complement the conclusions we draw about the He-10830 triplet in youth.
Photometric monitoring could assist in connecting He-10830 triplet variability
to spot modulation and evolution, and search for rotational or long-term
cyclic modulation in the He-10830 triplet. X-ray or UV observations would
provide instantaneous measurements of the high-energy coronal radiation that
may drive the excitation of the helium metastable state, and definitively
distinguish contributions from the PR and CE mechanisms. Visible spectroscopy
would provide measurements of established chromospheric activity indicators
(such as Ca ii H and K, and H-$\alpha$), mapping lines that are formed at
varying chromospheric heights and tying helium variability to well-studied
probes of activity.

NIR precision RV measurements are still relatively new, and there are no well-
established activity indicators in the NIR bandpass that are analogous to Ca
ii H and K in the visible. The lack of rotational coherence in our
observations of the He-10830 triplet calls into question whether or not it
would work well as an activity indicator to de-trend RV jitter. It may provide
information about second-order activity effects on the stellar spectral line
profile, but may not be able to act alone as a NIR activity indicator for
precision RV studies. An in-depth analysis connecting EW[He] to RVs for our
sample is beyond the scope of this paper, but will be featured in a future
work.

Time series studies of young exoplanet hosts provide crucial data for
understanding young stellar structure, planet formation and evolution, and the
effects of stellar activity on exoplanet observations. In particular, the
recent developments in NIR precision spectroscopy have opened an entirely new
window into studies of stars and exoplanets, but the results of these ongoing
programs are nascent (Reiners et al., 2018; Donati et al., 2020; Tran et al.,
2021). With advancements in panchromatic observing capabilities, it is ever
more pressing to expand the frontiers of stellar astrophysics to best
understand the manifestation of stellar activity in extreme precision
exoplanet observations.

We thank the anonymous referee for a thorough review that improved the
manuscript and strengthened our conclusions. We thank Michael Gully-Santiago,
Antonija Oklopčić, Aaron Rizzuto, Quang Tran, and Chad Bender for useful
discussions regarding the He 10830 Å triplet feature, telluric correction,
best practices for using HPF data, and clarity of the writing. We thank the
HPF team for providing the high-quality data products necessary for the work
presented in the manuscript. We are also very grateful for the resident
astronomers and telescope operators at the HET, particularly Steven
Janowiecki, for help in planning HPF observations and using our time
allocation to its maximum potential. These results are based on observations
obtained with the Habitable-zone Planet Finder Spectrograph on the HET. 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 would like to acknowledge that the HET is built on
Indigenous land. Moreover, we would like to acknowledge and pay our respects
to the Carrizo & Comecrudo, Coahuiltecan, Caddo, Tonkawa, Comanche, Lipan
Apache, Alabama-Coushatta, Kickapoo, Tigua Pueblo, and all the American Indian
and Indigenous Peoples and communities who have been or have become a part of
these lands and territories in Texas, here on Turtle Island. This research has
made use of the SIMBAD database, operated at CDS, Strasbourg, France, and
NASA’s Astrophysics Data System Bibliographic Services. HET (HPF)

##  Appendix A Literature helium exosphere observations

In Table 5 we show the literature helium exosphere observation data points
plotted in Figure 16. These data come from studies using high resolution
spectroscopy, and include detections and upper limits. If there are multiple
published observations for a planet, whether detections or upper limits, we
include all of them in the table and the corresponding figure.

Table 5: Literature helium exosphere observations

Planet | Excess Absorption % | Instrument | Limit?aaMarked as “UL” if the measurement is an upper limit on the excess absorption. | Reference
---|---|---|---|---
HD 189733 b | 0.88 | CARMENES |  | Salz et al. (2018)
HD 189733 b | 1.04 | CARMENES |  | Nortmann et al. (2018)
HD 189733 b | 0.75 | GIANO-B |  | Guilluy et al. (2020)
HAT-P-11 b | 1.08 | CARMENES |  | Allart et al. (2018)
WASP-69 b | 3.6 | CARMENES |  | Nortmann et al. (2018)
HD 209458 b | 0.91 | CARMENES |  | Alonso-Floriano et al. (2019)
WASP-107 b | 5.54 | CARMENES |  | Allart et al. (2019)
WASP-107 b | 7.3 | NIRSPEC |  | Kirk et al. (2020)
WASP-107 b | 6.7 | NIRSPEC |  | Spake et al. (2021)
GJ 3470 b | 1.5 | CARMENES |  | Palle et al. (2020)
HAT-P-32 b | 5.3 | CARMENES |  | Czesla et al. (2022)
HD 73583 b | 0.68 | NIRSPEC |  | Zhang et al. (2022b)
GJ 1214 b | 2.1 | CARMENES |  | Orell-Miquel et al. (2022)
GJ 1214 b | 0.13 | NIRSPEC | UL | Kasper et al. (2020)
GJ 1214 b | 1.22 | NIRSPEC | UL | Spake et al. (2022)
WASP-52 b | 3.44 | NIRSPEC |  | Kirk et al. (2022)
WASP-177 b | 1.28 | NIRSPEC |  | Kirk et al. (2022)
TOI 1430.01 | 0.64 | NIRSPEC |  | Zhang et al. (2022a)
TOI 1683.01 | 0.84 | NIRSPEC |  | Zhang et al. (2022a)
TOI 2076 b | 1.01 | NIRSPEC |  | Zhang et al. (2022a)
TOI 2076 b | 1 | IRD | UL | Gaidos et al. (2023)
GJ 436 b | 0.41 | CARMENES | UL | Nortmann et al. (2018)
KELT-9 b | 0.33 | CARMENES | UL | Nortmann et al. (2018)
K2-100 b | 1.6 | IRD | UL | Gaidos et al. (2020a)
WASP-127 b | 0.87 | Gemini/Phoenix | UL | dos Santos et al. (2020)
AU Mic b | 3.5 | IRD | UL | Hirano et al. (2020)
TOI 1728 b | 1.1 | HPF | UL | Kanodia et al. (2020)
GJ 9827 b | 0.067 | NIRSPEC | UL | Kasper et al. (2020)
HD 97658 b | 0.21 | NIRSPEC | UL | Kasper et al. (2020)
55 Cnc e | 0.02 | NIRSPEC | UL | Zhang et al. (2021)
TRAPPIST-1 b | 0.06 | IRD | UL | Krishnamurthy et al. (2021)
TRAPPIST-1 e | 0.07 | IRD | UL | Krishnamurthy et al. (2021)
TRAPPIST-1 f | 0.03 | IRD | UL | Krishnamurthy et al. (2021)
WASP-76 b | 0.9 | CARMENES | UL | Casasayas-Barris et al. (2021)
K2-136 c | 8.3 | IRD | UL | Gaidos et al. (2021)
WASP-80 b | 0.7 | GIANO-B | UL | Fossati et al. (2022)
HD 63433 b | 0.5 | NIRSPEC | UL | Zhang et al. (2022c)
HD 63433 c | 0.5 | NIRSPEC | UL | Zhang et al. (2022c)
TOI 3757 b | 6.9 | HPF | UL | Kanodia et al. (2022)
TOI 1807 b | 2.4 | IRD | UL | Gaidos et al. (2023)

††footnotetext: The exosphere measurements are mostly ordered by publication
date, and separated by detection vs. upper limit. The exceptions are when
there are multiple measurements for a single planet; in that case, all
measurements are grouped together (regardless of date or distinction between
detection and upper limit). Only high resolution spectroscopic observations
are included.

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