# Non-Detections of Helium in the Young Sub-Jovian Planets K2-100b, HD 63433b,
& V1298 Tau c

Munazza K. Alam These authors contributed equally to this work.  Space
Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
Carnegie Earth & Planets Laboratory, 5241 Broad Branch Road NW, Washington, DC
20015, USA  James Kirk These authors contributed equally to this work.
Department of Physics, Imperial College London, Prince Consort Road, London,
SW7 2AZ, UK  Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  Leonardo A. Dos Santos Space Telescope
Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA  Patrick
McCreery William H. Miller III Department of Physics and Astronomy, Johns
Hopkins University, Baltimore, MD 21218, USA  Andrew P. Allan Leiden
Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands
James E. Owen Department of Physics, Imperial College London, Prince Consort
Road, London, SW7 2AZ, UK  Aline A. Vidotto Leiden Observatory, Leiden
University, P.O. Box 9513, 2300 RA Leiden, The Netherlands  Romain Allart
Département de Physique, Institut Trottier de Recherche sur les Exoplanètes,
Université de Montréal, Montréal, Québec, H3T 1J4, Canada ††thanks: Trottier
Postdoctoral Fellow Vincent Bourrier Observatoire Astronomique de l’Université
de Genève, Chemin Pegasi 51b, CH-1290 Versoix, Switzerland  Néstor Espinoza
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA  George W. King Department of Astronomy, University of Michigan, Ann
Arbor, MI 48109, USA  Mercedes López-Morales Center for Astrophysics $|$
Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Julia V.
Seidel European Southern Observatory, Alonso de Córdova 3107, Vitacura, Región
Metropolitana, Chile

###### Abstract

We search for excess in-transit absorption of neutral helium at 1.083 $\mu$m
in the atmospheres of the young ($<$800 Myr) sub-Jovian (0.2–0.5 $\rm R_{J}$)
planets HD 63433b, K2-100b, and V1298 Tau c using high-resolution
(R$\sim$25,000) transit observations taken with Keck II/NIRSPEC. Our
observations do not show evidence of helium absorption for any of the planets
in our sample. We calculate $3\sigma$ upper limits on the planets’ excess
helium absorption of $<$0.47% for HD 63433b, $<$0.56% for K2-100b and $<$1.13%
for V1298 Tau c. In terms of equivalent width, we constrain these to $<$2.52,
$<$4.44 and $<$8.49 mÅ for HD 63433b, K2-100b and V1298 Tau c, respectively.
We fit our transmission spectra with one-dimensional Parker wind models to
determine upper limits on the planets’ mass-loss rates of $<$7.9$\times
10^{10}$, $<$1.25$\times 10^{11}$ and $<$7.9$\times 10^{11}$ g s-1. Our non-
detections align with expectations from one-dimensional hydrodynamic escape
models, magnetic fields, and stellar wind confinement. The upper limits we
measure for these planets are consistent with predicted trends in system age
and He equivalent width from 1D hydrodynamic models.

Exoplanet atmospheres (487) — Extrasolar gaseous planets (2172) — Infrared
astronomy (786)

##  1 Introduction

Short-period planets intermediate in size between Earth and Neptune (1–4
$R_{\oplus}$), are abundant in the galaxy (e.g., Batalha et al. 2013; Dressing
& Charbonneau 2015; Morton et al. 2016), but their formation and evolutionary
histories are currently unknown. While those larger than $\rm 1.6\,R_{\oplus}$
likely possess large H/He envelopes comprising $\sim$1% of their total mass,
planets below this threshold have densities consistent with rocky compositions
(e.g., Rogers 2015). The observed distribution of transiting planetary radii
from Kepler further reveals a dearth of exoplanets with radii between 1.5–2.0
$\rm R_{\oplus}$ (Fulton et al., 2017). While planet formation and core-
powered evolution models can partly explain these results (e.g., Ginzburg et
al. 2018; Loyd et al. 2018), photoevaporation – the escape of planetary
atmospheres caused by high-energy irradiation from their host stars – may play
an important role in sculpting these observed trends (e.g., Lopez & Fortney
2014; Owen & Wu 2017).

Intermediate-sized planets are the best targets for probing atmospheric escape
that changes the bulk characteristics of exoplanets. Jupiter-sized planets are
too massive to lose a significant part of their primordial atmospheres during
their evolution (e.g., Lecavelier Des Etangs 2007), whereas small Earth-sized
planets lose their volatile-rich atmospheres too quickly (e.g., Owen & Wu
2017) and are not accessible with currently-available instruments (e.g.,
Bourrier et al. 2017; Waalkes et al. 2019). Some of the most extreme cases of
ongoing atmospheric escape and evolution have been observed for planets with
sizes similar to Neptune: GJ 436b (Ehrenreich et al., 2015), GJ 3470b
(Bourrier et al., 2018), HAT-P-11b (Allart et al., 2018; Mansfield et al.,
2018; Ben-Jaffel et al., 2022), and tentatively K2-18b (Dos Santos et al.,
2020). Signatures of atmospheric escape imprint large ($\sim$0.1–5% for He;
$\gtrsim$10% for H) signals on transit spectra that are readily detectable
with current instruments.

The majority of observations of atmospheric escape and extended atmospheres
prior to 2018 were obtained with Lyman-$\alpha$ transmission spectroscopy
using Hubble (e.g., Vidal-Madjar et al. 2003; Lecavelier Des Etangs et al.
2010; Ehrenreich et al. 2015; Bourrier et al. 2018; Dos Santos et al. 2020).
The stellar Lyman-$\alpha$ emission line is efficiently absorbed by the
interstellar medium (ISM), limiting the detection of atmospheric escape to
nearby ($\lesssim$ 60 pc) targets. Spake et al. (2018), however, demonstrated
that the metastable He triplet at 1.083 $\mu$m – which is devoid of ISM
absorption – is a viable probe for atmospheric escape (Seager & Sasselov 2000;
Oklopčić & Hirata 2018). Several studies have since demonstrated the
feasibility of ground-based transmission spectroscopy to study atmospheric
escape via the 1.083 $\mu$m He triplet (e.g., Allart et al. 2018; Nortmann et
al. 2018; Alonso-Floriano et al. 2019; Kirk et al. 2020; Zhang et al. 2021).
Kirk et al. (2020) showed for the first time the capability of Keck II/NIRSPEC
to achieve high-precision, high-confidence (30$\sigma$) detections of excess
He absorption.

Photoevaporation models predict that planets lose a significant amount of
their primordial H/He atmospheres at early ages ($\tau$ $<$ 100-500 Myr) when
high-energy irradiation from the host star is the strongest (e.g., Jackson et
al. 2012; Owen & Wu 2013). Detecting and measuring the atmospheric escape
rates from young planets can allow us to place more direct observational
constraints on planetary evolution models at early ages. These young targets
are further favorable for helium observations because the intense stellar
X-ray and extreme ultraviolet (XUV) irradiation levels in the first 100 Myr of
a planet’s lifetime lead to a metastable He line that is more likely to be
populated (Oklopčić, 2019; Allan et al., 2024). Young transiting planets
thereby represent an unprecedented opportunity to probe atmospheric escape and
evolution in small, irradiated planets.

In this work, we present high-resolution spectroscopic observations of He i at
1.083 $\mu$m using Keck II/NIRSPEC in the young ($<$800 Myr) sub-Jovian
(0.2–0.5 $\rm R_{J}$) planets K2-100b (Livingston et al., 2018), HD 63433b
(Mann et al., 2020), and V1298 Tau c (David et al., 2019) to measure the
persistence and amplitude of the helium feature in young planets. The system
and orbital properties of our sample are included in Table 1. While
photoevaporation is predicted to be most significant at the earliest ages
($<$500 Myr; Lopez et al. 2012; Owen & Wu 2013), there are few observational
tests of this theory and a lack of planets sampling the upper limit of this
theoretical age limit. Therefore, our sample spans ages where photoevaporation
should be dominant (23 Myr) up to ages older than we would expect
photoevaporation to be dominant (750 Myr), enabling important tests of this
theory.

The paper is structured as follows. §2 details the observations and data
reduction procedures, and §3 describes our time-series analysis to obtain the
helium transmission spectra for the planets in our sample. We interpret our
observations considering the effects of magnetic fields, stellar winds, and 1D
hydrodynamic escape models in §4. In §5, we contextualize our results in light
of previous observations of these targets as well as other helium observations
for both young and older exoplanets. We summarize our conclusions in §6.

Table 1: System Parameters for HD 63433b, V1298 Tau c, & K2-100 b. Integrated fluxes received by each planet over the X-ray [0.517-12.4 nm], hard-EUV [10-36 nm], soft-EUV [36-92 nm] and mid-UV [91.2-320 nm] bands from the Allan et al. (2024) model. Stellar, planetary, and system parameters are taken from (a) Mann et al. (2020), (b) Capistrant et al. (2024), (c) Jones et al. (2015), (d) Gaia DR2, (e) Barragán et al. (2019), (f) Brandt & Huang (2015), (g) David et al. (2019), (h) Gaidos et al. (2022), (i) derived from mass-radius relation (Chen & Kipping, 2017), (j) Stassun et al. (2019).  | HD 63433b | V1298 Tau c | K2-100 b
---|---|---|---
Stellar Parameters
Mass, $M_{\star}$ [$\rm M_{\odot}$] | 0.99$\pm$0.03aafootnotemark:  | 1.10$\pm$0.05ggfootnotemark:  | 1.15$\pm$0.05eefootnotemark:
Radius, $R_{\star}$ [$\rm R_{\odot}$] | 0.91$\pm$0.03aafootnotemark:  | 1.34$\pm$0.05ggfootnotemark:  | 1.24$\pm$0.05eefootnotemark:
Effective temperature, $T_{\mathrm{eff}}$ [K] | 5640$\pm$74aafootnotemark:  |  $4962^{+88}_{-45}$ddfootnotemark:  | 5945$\pm$110eefootnotemark:
Metallicity, [Fe/H] | 0.03$\pm$0.05bbfootnotemark:  | 0.139$\pm$0.03jjfootnotemark:  | 0.22$\pm$0.09eefootnotemark:
Surface gravity, log(g) [cgs] | 4.52$\pm$0.05bbfootnotemark:  | 4.25$\pm$0.03ggfootnotemark:  | 4.33$\pm$0.10eefootnotemark:
Age [Myr] | 414$\pm$23ccfootnotemark:  | 23$\pm$4ggfootnotemark:  | 750$\pm$5fffootnotemark:
$F_{\rm X-ray}$ [erg/s/cm2] | 5.39$\times$103 | 1.84$\times$105 | 1.98$\times$104
$F_{\rm hEUV}$ [erg/s/cm2] | 4.64$\times$103 | 3.75$\times$104 | 1.70$\times$104
$F_{\rm sEUV}$ [erg/s/cm2] | 6.75$\times$103 | 1.73$\times$104 | 4.60$\times$104
$F_{\rm mid-UV}$ [erg/s/cm2] | 5.33$\times$106 | 1.19$\times$106 | 3.21$\times$106
Planetary Parameters
Mass, $M_{p}$ [$\rm M_{J}$] | 0.0166iifootnotemark:  | 0.0839iifootnotemark:  | 0.0686$\pm$0.02eefootnotemark:
Radius, $R_{p}$ [$\rm R_{J}$] | 0.192$\pm$0.009aafootnotemark:  | 0.499$\pm$0.03ggfootnotemark:  | 0.346$\pm$0.01eefootnotemark:
Equilibrium temperature, $T_{eq}$ [K] | 968$\pm$36aafootnotemark:  | 981$\pm$31ggfootnotemark:  | 1841$\pm$41eefootnotemark:
Surface gravity, log(g) [cgs] | 3.05iifootnotemark:  | 2.92iifootnotemark:  | 3.15$\pm$0.13eefootnotemark:
System Parameters
Systemic velocity, $\gamma$ [km/s] |  $-$16.31$\pm$0.20ddfootnotemark:  | +14.644$\pm$0.136hhfootnotemark:  | +34.78$\pm$0.64ddfootnotemark:
Period, $P$ [days] | 7.10793$\pm$0.0004aafootnotemark:  | 8.24958$\pm$0.00072ggfootnotemark:  | 1.6739035$\pm$0.0000004eefootnotemark:
Inclination, $i$ [∘] | 89.38${}^{+0.43}_{-0.64}$aafootnotemark:  | 88.49${}^{+092}_{-0.72}$ggfootnotemark:  | 81.27$\pm$0.37eefootnotemark:
Scaled semi-major axis, $a/R_{\star}$ | 16.95${}^{+0.34}_{-0.82}$aafootnotemark:  | 13.19$\pm$0.55ggfootnotemark:  | 5.21$\pm$0.13eefootnotemark:
Radius ratio, $R_{p}/R_{\star}$ | 0.02161$\pm$0.00055aafootnotemark:  | 0.0381$\pm$0.0017ggfootnotemark:  | 0.02867$\pm$0.00028eefootnotemark:
Mid-transit time, $T_{0}$ [BJD] |  $2458916.4526^{+0.0032}_{-0.0027}$aafootnotemark:  |  $2457064.2797\pm 0.0034$ggfootnotemark:  |  $2457140.71941\pm 0.00027$eefootnotemark:
Transit duration [days] | 0.134$\pm$0.0014aafootnotemark:  | 0.194$\pm$0.005ggfootnotemark:  | 0.067$\pm$0.0006eefootnotemark:

##  2 Observations & Data Reduction

###  2.1 Observations

We observed a single transit each of V1298 Tau c, HD 63433b, and K2-100b with
Keck II/NIRSPEC (McLean et al., 1998; Martin et al., 2018) on UT 17 Dec 2020,
UT 24 Dec 2020, and UT 08 Jan 2021, respectively. Our observations were taken
as part of Program N165 (PI: Alam) using the NIRSPEC-1 filter, which covers
the $Y$-band (0.947–1.121 $\mu$m; NIRSPEC orders 68-80) at a spectral
resolution of R$\sim$25,000. Here we present the extracted NIRSPEC order 70
(1.0799–1.1014 $\mu$m) spectra only, which covers the metastable helium
triplet at 1.0833 $\mu$m.

To mitigate fringing effects, we did not use the ‘Thin’ blocking filter (e.g.,
Kasper et al. 2020; Kirk et al. 2022). At the beginning and end of our transit
observations, we obtained a set of 11 darks (including bias frames), 11 lamp
flats, and two arcs (each composed of 10 co-added Ne, Ar, Xe, and Kr arc
lamps). We obtained 28 spectra for V1298 Tau c ($J$=8.6) with exposure times
of 300 seconds each over 182 minutes, and acquired an additional 6 out-of-
transit spectra for this target on UT 08 Jan 2021111The first night of V1298
Tau data was severely affected by bad weather, limiting the number of out-of-
transit exposures to 3.. For HD 63433b ($J$=5.6), we acquired 372 spectra with
exposure times of 30 seconds over the course of 303 minutes. For K2-100b
($J$=9.4), we obtained 26 600-second spectra over 255 minutes. For all of our
observations, we used an ABBA nod pattern to remove sky background by A-B pair
subtraction. We achieved an average SNR per pixel per exposure in order 70 of
199, 213, and 191 for V1298 Tau c, HD 63433b, and K2-100b, respectively.

###  2.2 Data Reduction

We reduced our observations using the
REDSPEC222https://www2.keck.hawaii.edu/inst/nirspec/redspec.html software
(McLean et al., 2003, 2007), which performs spatial rectification of tilted
spectral orders on the detector, bad pixel interpolation, flat-fielding, and
dark and bias subtraction. For the dark subtraction and flat-field correction
steps in REDSPEC, we created a main dark and a main flat by median-combining
our 22 darks and 22 flats, respectively. We used a second-order polynomial to
correct for the tilt of the spectral orders on the detector. We then performed
a wavelength calibration for order 70 using our arc lamp spectra and a second-
order polynomial to map the measured arc line locations to the theoretical
values. The spectra were then extracted in differenced A-B nod pairs to remove
the sky background and OH emission lines, with an aperture width of 11 pixels.

###  2.3 Post-Processing

We post-processed the extracted stellar spectra following the prescription
outlined in Kirk et al. (2022), which we briefly summarize here. After
extracting the wavelength-calibrated time-series spectra, we continuum-
normalized the spectra using iSpec333https://www.blancocuaresma.com/s/iSpec
(Blanco-Cuaresma et al., 2014; Blanco-Cuaresma, 2019). We fit cubic splines to
the 1.080-1.095 $\mu$m portion of order 70, masking the helium triplet from
our continuum calculation.

We then used
molecfit444https://www.eso.org/sci/software/pipelines/skytools/molecfit
(Kausch et al., 2015; Smette et al., 2015) to remove telluric features. We
selected telluric absorption lines away from stellar absorption lines to
constrain the molecfit model, fitting for atmospheric H2O only. For HD 63433b,
we used seven telluric absorption lines and three for K2-100b. For V1298 Tau
c, we used four telluric absorption lines for the December observations and
three for the January observations. We fitted the telluric absorption lines
with a Gaussian with a FWHM initiated at 3.5 pixels. The FWHM of the Gaussian
was fixed to 3.5 pixels for K2-100b following (Zhang et al. 2021; Kirk et al.
2022), due to difficulties in the ability of the data to constrain this
parameter for this night. The fitted FWHMs of the telluric models for the
other two targets were $3.33\pm 0.16$ pixels (HD 63433b) and $3.73\pm 0.26$
pixels (V1298 Tau c). Example telluric-corrected spectra are shown in Figure
1.

To check our systematic errors in the wavelength solution near the He triplet,
we cross-correlated our stellar spectra with model spectra that combined
PHOENIX stellar atmosphere models (Husser et al., 2013) with a telluric model
from the
molecfit555https://www.eso.org/sci/software/pipelines/skytools/molecfit
software (Kausch et al., 2015; Smette et al., 2015). By cross-correlating sub-
sections of the spectral order, we found that the bluest wavelengths ($\leq
1.087$ $\mu$m) were shifted from the truth by $\sim$30 km s-1 for K2-100b,
$\sim$12 km s-1 for HD 63433b and $\sim$-10 km s-1 for V1298 Tau c. However,
at the reddest wavelengths ($\geq 1.092$ $\mu$m) the spectra were shifted by
–2 km s-1, –5 km s-1 and 1 km s-1, respectively. We corrected for this
wavelength distortion by fitting a quadratic polynomial to our wavelength-
dependent cross-correlation results. As a final check to our wavelength
solution, we fit a Voigt absorption profile to a non-saturated absorption line
at 1.0842 $\mu$m in the same spectral order and measured the center of the
fitted profile for each exposure. We then calculated its shift in Doppler
velocity space from the average stellar spectrum, and correct the wavelength
solution in the He triplet region based on this systematic Doppler velocity
shift; this procedure was repeated for each exposure.

Figure 1: Examples of pre- (black) and post-telluric corrected spectra for
K2-100b (green), HD 63433b (purple), and V1298 Tau c (orange). The best-
fitting molecfit H2O models are shown in light blue. The telluric OH emission
occurs in the shaded gray region, however, this feature is successfully
removed by the A-B nod pair subtraction. The dashed gray lines indicate the
location of the He triplet which are different in the observer frame due to
the combination of the barycentric and systemic velocities.

We then shifted all of the spectra from the observer rest frame to the stellar
rest frame by correcting for the barycentric, systemic, and stellar reflex
velocities (Wright & Eastman, 2014). To account for cosmic rays in our
datasets, we constructed a median-combined spectrum and compared each spectral
frame to the combined spectrum. We replaced data points that deviated by
$>$4$\sigma$ from the median spectrum to the median of the surrounding pixels.
We flagged 11 outliers for HD 63433b and 14 outliers for V1298 Tau c within
$\pm$20 km/s of the helium triplet in the planets’ rest frames but opted not
to replace these to avoid removing real planetary signal. Due to the larger
amplitude and greater number of outliers in the K2-100 data set (26 pixels
within $\pm$20 km/s of the helium triplet, equal to 5% of the total pixels) we
replaced these to avoid anomalous signals caused by outliers.

##  3 Time-Series Analysis

We first generated the mean in-transit and out-of-transit spectra in order to
determine the in-transit excess absorption signal. We constructed the in-
transit spectrum by computing the weighted mean (weighted by the spectral
uncertainties) of spectra taken between the second and third contact points;
the out-of-transit spectrum was constructed by computing the weighted mean of
the spectra taken before first contact and after fourth contact. To determine
the contact points, we used the ephemerides of V1298 Tau c, HD 63433b, and
K2-100b from David et al. (2019), Mann et al. (2020), and Barragán et al.
(2019), respectively. The individual order 70 spectra, as well as the mean in-
and out-of-transit spectra, for the planets in our sample are shown in Figures
2, 3, and 4. We find that there is no apparent excess absorption centered on
the helium triplet for any of the planets in our sample. We also constructed
phase-resolved maps centered on the helium line in our search for excess
absorption around 1.083 $\mu$m, computed by dividing each spectrum of the
time-series by the mean out-of-transit spectrum. The phase-resolved excess
absorption maps are shown in Figures 5, 6, and 7.

We then constructed the helium transmission spectra for K2-100b, HD 63433b,
and V1298 Tau c, by shifting the excess absorption to each planet’s respective
rest frame, which are shown in Figure 8. Since the native uncertainties in the
transmission spectra are not representative of the scatter in the data due to
the presence of correlated noise, we inflated our uncertainties to account for
the actual scatter in the data. This step was necessary as, without it, we
could infer anomalous or overly precise measurements of planetary absorption.
We do this by setting the uncertainties in the helium transmission spectra to
be equal to the standard deviation of the transmission spectra. From our
spectra, we place 3$\sigma$ upper limits on the excess He absorption of 0.56%
for K2-100b, 0.47% for HD 63433b and 1.13% for V1298 Tau c. These upper limits
are equal to three times the standard deviation of the (flat) transmission
spectra taken from $\pm$10 Å around the He triplet. We also calculate upper
limits on the equivalent width (EW) by integrating the transmission spectra
between 10831–10835 Å. This leads to upper limits on the EW of $<$4.44 mÅ for
K2-100b, $<$2.52 mÅ for HD 63433b and $<$8.49 mÅ for V1298 Tau c. From both
the mean in-transit and out-of-transit spectra as well as the excess
absorption maps, we do not identify excess absorption for the planets in our
sample. We use the p-winds (Dos Santos et al., 2022) code to place upper
limits on the in-transit He absorption (§4.2).

##  4 Helium Non-Detections in Context

We consider our non-detections of excess helium absorption in light of the
effects of stellar winds and magnetic fields on depopulating the metastable
helium line (§4.1), 1D isothermal escape models (Parker winds; §4.2), and
photoevaporation-driven hydrodynamic escape models (§4.3).

###  4.1 Stellar Winds & Magnetic Fields

Given our non-detections, we should assess whether they agree with the basic
predictions of outflow models. A hydrodynamically launched outflow can only be
accelerated up to trans-sonic velocities. Beyond the sonic regime, the
velocity remains approximately constant (e.g., Lammer, 2013) and the density
profile falls off as $1/r^{2}$. When the helium triplet state is depopulated
by electron collisions (rather than photoionizations), as is expected for
K-stars (Oklopčić, 2019), the helium triplet fraction is roughly constant at
large radius. This means that the helium absorption is dominated by the
contribution from large radius, rather than close to the planet. Therefore,
the helium absorption signal is dominated by how far the outflow extends
spherically away from the planet. In the case of limited stellar wind, the
outflow can ultimately only remain spherical out to the Hill sphere; whereas a
strong stellar wind can crush the planetary outflow to a fraction of its Hill
sphere (Carolan et al., 2020). Given a maximum radius out to which the outflow
remains spherical ($R_{\rm out}$), the maximum possible excess absorption is:

$\approx\left[1-\left(\frac{R_{p}}{R_{\rm
out}}\right)^{2}\right]\left(\frac{R_{\rm out}}{R_{*}}\right)^{2}$ (1)

in the case that the outflow is optically thick in transmission at $R_{\rm
out}$. Setting $R_{\rm out}$ to the Hill sphere radius $R_{\rm H}$ yields
maximum excess optical depths of 1.9%, 8.4%, and 4.7% for K2-100b, HD 63433b,
and V1298 Tau c, respectively. The fact that these maximal excess depths are
only a factor of $\sim$4 larger than our upper limits for K2-100b and V1298
Tau c implies that a transmission optical depth in helium of $\lesssim 0.25$
would be sufficient to render the helium absorption below our detection limit.
Thus, since the helium line is normally optically thin, these non-detections
are not surprising. For an optically thin $1/r^{2}$ density profile, the
excess absorption becomes:

$\approx 2\sigma_{\rm He3}\pi n_{He3}(R_{\rm out})R_{\rm
out}\left(1-\frac{R_{p}}{R_{\rm out}}\right)\left(\frac{R_{\rm
out}}{R_{*}}\right)^{2}$ (2)

where $\sigma_{\rm He3}$ is the cross-section at 10830 Å (appropriately
averaged over our R$\sim$25,000 spectral resolution) and $n_{He3}(R_{\rm
out})$ is the density of metastable helium at $R_{\rm out}$. Even with the
optimistic assumption that all helium is neutral and an extreme helium triplet
fraction of $10^{-5}$, for a Solar ratio of hydrogen to helium the excess
helium absorption remains below our upper limits for K2-100b and V1298 Tau c
with mass-loss rates up to $10^{11}$ and $3\times 10^{11}$ g s-1,
respectively. These limits are consistent with typical energy-limited mass-
loss rates.

Applying the same methodology to HD 63433b would require a mass-loss rate
below $10^{10}$ g s-1 due to its larger Hill sphere – but this estimate is in
tension with model expectations, of several $10^{10}$ g s-1. One immediate
solution would be to reduce the outer radial extent of the outflow by its
interaction with the stellar wind. To crush the planetary outflow to a
sufficiently small size to be consistent with our non-detection would require
a stellar wind with a velocity at the planet of several hundred km s-1 to have
an outflow rate of $\sim$$10^{-12}~{}$M⊙ yr-1, approximately a hundred times
larger than that of the Sun. Given the young age of the HD 63433 system and
its observed X-ray properties, such a large stellar wind outflow rate is
consistent with empirical scaling relationships (e.g. Wood et al., 2005;
Johnstone et al., 2015; Blackman & Owen, 2016). We note that a study using
Zeeman-Doppler Imaging infers stellar mass-loss rates in the range $1-4\times
10^{-13}$ M⊙ yr-1 (Bellotti et al., 2024).

An alternative explanation for HD 63433b is the presence of a strong planetary
magnetic field. Schreyer et al. (2023) demonstrated that any planetary
magnetic field can suppress the helium transmission signal. This arises from
two interrelated effects. Firstly, since the majority of the gas is confined
by closed planetary magnetic fields, it cannot expand and cool as a result of
stellar XUV heating. Thus, the gas is heated to $\sim$$10^{4}$ K where
Lyman-$\alpha$ cooling becomes efficient, thermostating the gas at
$\sim$$10^{4}$ K (e.g., Murray-Clay et al., 2009; Owen & Wu, 2016). Around
K-stars, the helium triplet state is depopulated by collisions with electrons
(Oklopčić, 2019) and populated by recombinations – processes that both happen
less efficiently at high temperatures, resulting in a significantly lower
population of metastable helium (Biassoni et al., 2023).

Secondly, the outflowing regions near the pole have lower densities than a
spherically symmetric outflow. This is because the outflow – forced to follow
planetary magnetic field lines – has a streamline divergence that falls faster
than $1/r^{2}$. In the outflow regions near the pole, the streamline
divergence falls off as $1/r^{3}$ (Adams, 2011; Owen & Adams, 2014). This
difference is important because for a $1/r^{2}$ density profile the helium
absorption signal is dominated by absorption far from the planet, where it
covers a larger area of the star (Equation 2); whereas for $1/r^{3}$ the
absorption is more weighted toward the regions closer to the planet where they
cover less of the star’s area. As Schreyer et al. (2023) demonstrated, this
effect significantly reduces the helium absorption for a planet with a strong
magnetic field, where the excess absorption for a $1/r^{3}$, compared to a
$1/r^{2}$ density profile is of order $R_{p}/R_{\rm out}$ smaller, which is
$\sim$0.1 for HD 63433b. As discussed by Zhang et al. (2022b), planetary
magnetic fields could be responsible for the He non-detection. Following the
methodology in Owen & Adams (2014), we estimate a surface dipole planetary
magnetic field strength of $\sim$4-5 G to close $>$50% of the planetary field
lines.

###  4.2 Parker Wind Models

We modeled the helium transmission spectra presented in §3 for HD 63433b,
K2-100b, and V1298 Tau c using the one-dimensional atmospheric escape model
p-winds666https://github.com/ladsantos/p-winds (Dos Santos et al., 2022; Dos
Santos & Vissapragada, 2023). This open-source Python-based code is based on
the framework of Oklopčić & Hirata (2018) and Lampón et al. (2020), and has
been benchmarked against the EVaporating Exoplanets (EVE) code (Bourrier &
Lecavelier des Etangs 2013; Bourrier et al. 2015). The model treats the
escaping material as an isothermal Parker wind (Parker, 1958) composed only of
hydrogen and helium, finds the steady-state recombination/ionization solutions
for the distribution of neutral hydrogen and helium in the planetary upper
atmosphere, and solves the radiative transfer equation to determine the in-
transit absorption due to the escaping planetary material. The p-winds code
requires as input high-energy spectral energy distributions (SEDs) of the host
stars HD 63433, K2-100, and V1298 Tau. The SEDs of V1298 Tau and HD 63433 that
we use are adapted from Duvvuri et al. (2023) and Zhang et al. (2022c),
respectively. For K2-100, since there is no archival high-energy spectrum
available, we adopted the SED of the similarly young (600 Myr) and solar-type
star $\iota$ Horologii (Sanz-Forcada et al., 2019) scaled to the system’s
stellar radius and semi-major axis. For these models, we assume that the
outflow is composed solely of H and He, and that H/He ratio is 90/10 in number
of particles. We adopt the stellar and planetary parameters in Table 1.

Correlated noise is prevalent in the excess absorption spectra shown in Figure
8. Potential sources of correlated noise in the data may be instrumental or
astrophysical in origin, including not limited to telluric contamination,
wavelength calibration, stellar activity, and temporal variability in the the
deep Mg 10811 Å, Si 10827 Å, and Si 10844 Å lines (e.g., Guilluy et al. 2023;
Zhang et al. 2023; Vissapragada et al. 2024). Therefore, we model the excess
absorption spectra as a planetary absorption combined with correlated noise.
To accurately constrain the mass loss, outflow temperature, and outflow
velocity, we employ the use of Gaussian processes (GPs) to account for
systematic uncertainties and model the correlated noise (Rasmussen & Williams,
2006). The Matérn-3/2 kernel is used as the covariance function for the GPs,
allowing for smoothness in our correlated noise functions (Foreman-Mackey et
al., 2017). Gaussian processes allow for the fitting of the true helium
absorption signal, removing the correlated noise present in the data. The use
of Gaussian processes introduces two parameters (the systematics amplitude
$\sigma$ and length scale $\rho$), which, when paired with the three p-winds
parameters (mass-loss rate, outflow temperature, and outflow radial velocity),
creates a five-dimensional model. The systematics and planetary absorption are
fitted simultaneously. The Bayesian inference we designed avoids overfitting
by applying a prior for the GP parameters inferred from the transmission
spectrum outside of the He feature. This methodology will be discussed in more
detail in an upcoming paper (McCreery et al., in prep.). When constraining the
posteriors of these five parameters given the transmission spectra, we use
nested sampling (Speagle, 2020). Nested sampling is advantageous over Monte
Carlo methods in this situation due to our poor prior information and nested
sampling’s ability to estimate the marginal likelihood, which aids in model
selection.

In summary, our model uses nested sampling to perform fits of the helium
absorption spectrum of HD 63433b, K2-100b, and V1298 Tau c using p-winds to
fit for the helium signature and Gaussian processes to account for correlated
noise. The resulting best-fit systematics and planetary signals are shown in
Figure 9. We found that the nested sampling results favor a non-detection for
HD 63433b with more than 95% confidence, a tentative detection at high blue-
shifted velocities (-17 km s-1) for K2-100b, and a marginal detection at high
red-shifted velocities (+21 km s-1) for V1298 Tau c. To confirm that our model
is not overfitting the data, we also ran fits only including the GP component.
Table 2 compares the results for the p-winds+GP models to GP only models. We
find similar posterior distributions from this exercise compared to the
p-winds+GP fits for V1298 Tau c and HD 63433b. For K2-100b, the p-winds+GP
models are favored at the $\sim$3$\sigma$ level because – although the length-
scale of the GP is similar to the p-winds feature, the amplitude is clearly
larger at the location of the He line.

| K2-100b | V1298 Tau c | HD 63433b
---|---|---|---
$\log z_{\text{GP}}$ | 461.17 | 392.43 | 490.59
$\log z_{\text{GP+}\texttt{p-winds}}$ | 464.53 | 391.57 | 489.17
$|\Delta\log z|,|\log B_{m}|$ | 3.36 | .85 | 1.42
$p$-value | .03 | .70 | .81
Table 2: Model comparisons between the Gaussian Process-only models and the
full Gaussian Process + p-winds models using log-evidence ($\log z$). The
Bayes factor, $B_{m}$, indicates that there are no significant differences in
the model fits to the transmission spectra for V1298 Tau c and TOI-1726b. For
K2-100b, however, the GP + p-winds model is moderately favored over the GP-
only model.

Most detections of helium outflows in transiting exoplanets have been found to
exhibit blue-shifted velocities up to $\sim$$-10$ km s-1 (McCreery et al., in
prep.), a result that is theoretically expected for confined winds (MacLeod &
Oklopčić, 2022; Nail et al., 2023). Slightly red-shifted helium signals are
expected for outflows in magnetized exoplanets (Schreyer et al., 2023). The
outflow velocities measured by the nested sampling have never been observed
before, are not predicted by state-of-the-art hydrodynamic escape models, and
are likely spurious signals. The posterior distributions of the retrieved
parameters from our p-winds modeling are shown in Table 3 and Figures 10, 11,
and 12.

Table 3: Parker-wind model constraints estimated for the observed transmission spectra Planet | Excess Absorption | log $\dot{m}$ (g s-1) | T ($\times 10^{3}$ K) | v (km s-1)
---|---|---|---|---
HD 63433b |  $<$2.52 mÅ |  $<10.9$ (95% conf.) |  $>5000$ (prior) | No constraint
V1298 Tau c |  $<$8.49 mÅ |  $<11.9$ (95% conf.) |  $>5000$ (prior) | $+21^{+23}_{-50}$
K2-100b |  $<$4.44 mÅ | $11.10^{+0.23}_{-0.22}$ | $7.2^{+2.3}_{-1.5}$ | $-17.0^{+3.0}_{-2.0}$

###  4.3 Photoevaporation-driven Hydrodynamic H/He Models

Additionally, we modeled HD 63433b, K2-100b, and V1298 Tau c using the one-
dimensional hydrodynamic model described in Allan et al. (2024). This model
self-consistently solves the hydrodynamic equations of atmospheric escape
simultaneously with equations tracking the state of hydrogen, as well as
helium in its $1^{1}S$, $2^{1}S$, $2^{3}S$, singly and doubly ionized states.
It considers the following hydrogen and helium processes: recombination,
radiative decay, charge exchange between hydrogen and helium particles,
collisional excitation, collisional ionization and photoionization. Fluxes in
specified X-ray, soft and hard EUV, and mid-UV wavelength bins (see Table 1)
are required as input in order to model photoionizations. To this end, we use
the same SEDs described in §4.2. Table 1 lists the resulting band integrated
fluxes adopted in our modeling. Having modeled the hydrodynamics, we then
utilize the ray tracing model also described in Allan et al. (2024) to perform
helium triplet transmission spectroscopy.

Predicted helium triplet absorptions for our three planets using the Allan et
al. (2024) model are shown on the left-hand side of Figure 13. The models have
been convolved to the spectral resolution (R$\sim$25,000) of our observations.
The solid lines show the mean average of phases between the transit’s first
and fourth points of contact, while the shaded region encompasses all phases
between first-contact and mid-transit. The right-hand side of Figure 13
displays each planet’s helium triplet extinction map across the stellar disk,
as marked by the dashed circle. The displayed extinction is the sum of the
individual extinction of each of the three lines of the triplet.

Despite assuming a large helium to hydrogen number fraction of He/H=0.1, the
model predicts very weak absorption ($<$0.05%) for HD 63433b, in agreement
with the observations presented in Section §3. Its low mass-loss rate
prediction of 2.8 $\times 10^{10}$ g s-1 is responsible for its low density
and ultimately its weak helium triplet extinction, relative to the other
planets.

The model for V1298 Tau c predicts a larger absorption more in line with the
literature’s current sample of detections with a mean predicted excess of 0.6%
assuming He/H=0.1, although we note that this prediction is still below the
upper limit of 1.13% we set from our observations. The predicted excess drops
to 0.2% if we instead assume He/H=0.02 in the hydrodynamic model, as shown by
the gray dashed line. Accordingly, re-observing V1298 Tau c with tighter
uncertainties could help constrain the fraction of helium in this planet’s
atmosphere. Of the three planets, we predict V1298 Tau c to have the highest
mass-loss rate, 2.2 $\times 10^{11}$ g s-1. The greater atmospheric escape
rate is due to a favorable combination of high EUV flux and low surface
gravity (Allan & Vidotto, 2019). The large escape rate, combined with a mid-UV
flux sufficiently low so as to prevent significant depopulation of helium
triplet by mid-UV photoionization, are responsible for its greater He transit
absorption predicted in our modeling.

The predicted phase averaged excess absorption for K2-100b is $\sim$0.15%,
also below the 3$\sigma$ upper limit of 0.56% we get from the observation.
Despite the low excess absorption, a large mass-loss rate of 1.1 $\times
10^{11}$ g s-1 is predicted by the model. The right-hand side of Figure 13
reveals that the weak absorption is partially due to its large impact
parameter of 0.79$\rm R_{\star}$.

##  5 Discussion

###  5.1 Comparison to Previous Observations

####  5.1.1 K2-100b

High-resolution short-cadence spectroscopy from Subaru/IRD for K2-100b (Gaidos
et al., 2020) yielded an upper limit on the planet’s helium absorption of 5.7
mÅ in equivalent width and mass loss of $5.7\times 10^{10}$ g s-1 (0.3
$M_{\oplus}$ Gyr-1) using a Parker wind model with temperatures below $10^{4}$
K. With the Keck II/NIRSPEC data presented in this work, we can place tighter
upper limits of $<$4.44 mÅ (0.56%) excess helium absorption. From our He
transmission spectrum, we measure a mass-loss rate of $1.25\times 10^{11}\,\rm
g\,s^{-1}$ from our Parker wind models (see §4.2), which is $\sim$5$\times$
higher than that of Gaidos et al. (2020) and consistent with the §4.3 models.
However, as we discussed in §4.2, our 1D Parker wind models for K2-100b
converge to fit a likely spurious bump in our transmission spectrum and
therefore our mass-loss measurements from this model are unreliable. Our
theoretical 1D hydrodynamic models (§4.3) predict a mass-loss rate of
1.1$\times 10^{11}$ g s-1, which would correspond to He absorption of 0.15%
and is below our detection threshold (0.56%). Gaidos et al. (2020) have a
tighter upper limit on the mass-loss than we obtain from our 1D hydrodynamic
models, despite having a looser upper limit on the helium equivalent width.
This suggests that the differences in the mass-loss predictions from their
study and ours may originate from the different model flux inputs, which would
influence the resulting inferred transit absorptions.

####  5.1.2 HD 63433b

Previous Keck II/NIRSPEC observations of the HD 63433 system (Zhang et al.,
2022c) placed an upper limit on HD 63433b’s helium absorption of 0.5 %, which
is consistent with the 0.47 % upper limit that we derive in this work. Zhang
et al. (2022c) also noted that the stellar helium line varied during their
transit observations, demonstrated by a darkening in the helium absorption map
during the transit of HD 63433b. This darkening matches what we see in the
data presented here (Figure 6), and induces an apparent helium emission
feature (negative excess absorption) in the planet’s transmission spectrum
(Figure 8). Similar to Zhang et al. (2022c), we attribute this apparent
emission to a darkening in the stellar helium triplet that is unrelated to the
planet’s atmosphere, suggesting that the stellar helium triplet is variable
over the timescale of a transit observation. Zhang et al. (2022c) observed HD
63433b on 2021 January 7, two weeks after our observations. If this
variability was to be seen in further subsequent epochs to have a period
commensurate with the planet’s orbital period, this could point to star-planet
interactions, as has been proposed to explain the observed variation in the
helium triplet for AU Mic (Klein et al., 2022a).

Using 3D hydrodynamic mass-loss models, Zhang et al. (2022c) compute a mass-
loss rate of $6.6\times 10^{10}$ g s-1 (0.35 $M_{\oplus}$ Gyr-1) for HD
63433b, which implies a mass-loss timescale of 80 Myr. This timescale is
consistent with the 95th percentile upper limit on the mass loss rate of
$7.9\times 10^{10}\,\rm g\,s^{-1}$ (0.42 $M_{\oplus}$ Gyr-1) derived from our
Parker wind models, but higher than the rate $2.8\times 10^{10}$ g s-1 (0.15
$M_{\oplus}$ Gyr-1) inferred from our self-consistent hydrodynamic models
(§4.2 and 4.3), respectively. Given the age of HD 63433b ($414\pm 23$ Myr;
Mann et al. 2020), our p-winds and self-consistent model findings agree with
Zhang et al. (2022c) in demonstrating that it is unlikely that the planet has
retained a H/He atmosphere.

Our 1D hydrodynamic modeling yields a mass-loss rate that is $\sim$2.3 times
smaller than the Zhang et al. (2022c) estimates, which consequently results in
a smaller overall estimated outflow density. Although our model uses the same
high-energy stellar SED as Zhang et al. (2022c), their model differs from ours
in their treatment of the heating/cooling processes of the atmosphere. They
also include the interaction with a stellar wind, but we believe the former
difference is the likely cause of our differing evaporation rates. Because of
the smaller escape rates and densities of our spherically symmetric models, it
is expected that our excess helium absorption would differ from theirs: in
fact, our excess helium absorption at the line center ($<$0.05%) is an order
of magnitude smaller than the model from Zhang et al. (2022c) for HD 63433b.

####  5.1.3 V1298 Tau c

Vissapragada et al. (2021) used narrowband photometry from Palomar/WIRC to
search for helium in V1298 Tau c, but were unable to detect the planet’s
transit likely due to correlated noise in the data. Their non-detection is
consistent with our findings for this planet (Figure 8), however, our upper
limit on the excess helium absorption of 1.13% (EW $<$ 8.49 mÅ) is the first
quantitative upper limit for this planet. We checked whether our result was
sensitive to our choice of ephemeris by re-doing our analysis with the
ephemeris of Feinstein et al. (2022) and found a consistent upper limit to
when we used the ephemeris from David et al. (2019). High-resolution optical
spectra from GRACES on Gemini-North (Feinstein et al., 2021) revealed a
tomographic signal in the Ca II triplet attributed to possible star-planet
interactions, as well as excess H$\alpha$ absorption smoothly decreasing
during the planet’s transit that can be explained by starspots and faculae
rotating into and out of view.

Since the Ca II triplet arises in the chromosphere, searching for variability
in other chromospheric lines may corroborate the star-planet interactions
hypothesis (Feinstein et al., 2021). Given that the helium triplet is also a
chromospheric line, we can search for variability in this line (Klein et al.,
2022b). However, the variability we see in the stellar helium line, combined
with the poor weather conditions during our observations, prevents us from
testing the possibility of star-planet interactions.

Variability in V1298 Tau’s stellar helium line has been seen on a number of
previous occasions (e.g., Vissapragada et al., 2021; Gaidos et al., 2022;
Krolikowski et al., 2024). Vissapragada et al. (2021) measured a difference in
the stellar helium equivalent width of 0.15 Å over a two month timescale in
addition to a flare in the helium line during a transit of V1298 Tau c. Gaidos
et al. (2022) found a 50 % variability in the stellar helium line during a
transit observation V1298 Tau b. In this case, the variability is neither due
to stellar variability due to the short time scale involved, nor planet
variability given the orbital phases at which this absorption is seen. Gaidos
et al. (2022) instead suggest that the absorption they see could be associated
with a transit of V1298 Tau d, which would be consistent with Vissapragada et
al. (2021). We rule out seeing variability in the stellar He line at the
amplitudes and timescales that Gaidos et al. (2022) see, reinforcing the
conclusion that they were seeing absorption from V1298 Tau d.

V1298 Tau was also observed as part of Krolikowski et al. (2024)’s program to
monitor the stellar He equivalent width of exoplanet host stars. For V1298
Tau, the youngest star in their sample, they observed variability in the He
equivalent width with a median absolute deviation of $61.5^{+8.4}_{-7.8}$ mÅ
or equivalently $3.93^{+0.54}_{-0.50}$ % in absorption depth over their
observing baseline of $\sim$1.5 years. Over a three week time scale, the
difference between our transit observations and subsequent additional out-of-
transit baseline for V1298 Tau, Krolikowski et al. (2024) measure variability
of $\sim$80 mÅ, serving as a cautionary tale against using out of transit data
from different epochs for these young systems.

We also measure variability in the stellar helium line between our December
and January out-of-transit observations. Over this 3 week time scale, the
helium equivalent width varied from 453.784 mÅ to 418.649 mÅ (integrated
between 10831.58 Å and 10835.48 Å). The equivalent widths and variability are
similar to that seen by Krolikowski et al. (2024). We were motivated to use
the January out-of-transit spectra because we were only able to acquire three
out-of-transit spectra immediately before the December transit due to poor
weather. However, in doing so, we are insensitive to planetary absorption
because of the large amplitude variability in the stellar helium line. For
this reason, we recalculated V1298 Tau c’s transmission spectrum using only
the December out-of-transit data. This approach also reveals no in-transit He
absorption with an upper limit of 0.55 %, which is consistent with our
original approach of using the January data, and hence does not change our
conclusions.

###  5.2 Young Planets in Context

To contextualize the helium non-detections presented here for K2-100b, HD
63433b, and V1298 Tau c, we compare our derived He upper limits to measured
helium equivalent widths from the literature for sub-Jovian ($\rm R_{\oplus}$
$\leq$ 6) planets orbiting K dwarfs and other stellar host types in Figure 14.
We also compare these helium measurements to 1D hydrodynamic modeling
predictions with planetary evolution. We extend upon the work of Allan et al.
(2024), by computing two new self-consistent model sets better suited to the
three planets discussed in this work, namely a smaller 0.1 $\rm M_{J}$ planet
orbiting the same K-type star at 0.045 au, again considering both 2% and 10%
He abundances. For the radius evolution input, we use the models of Fortney &
Nettelmann (2010) for a 0.1 $\rm M_{J}$ planet, with a 25 $\rm M_{\oplus}$
planetary core. Over the considered evolution timeframe of 16 to 5000 Myr, the
radius evolves from 0.83 to 0.55 $\rm R_{J}$, closer to – but still above –
the radii of the planets here (0.346, 0.192, 0.499 and $\rm R_{J}$ for
K2-100b, HD 63433b, and V1298 Tau c, respectively). Other than these smaller
radius and mass inputs, the modeling of the evolution predictions presented
here is identical to the F2 and F10 model sets of Allan et al. (2024).

Compared to these previous larger, inflated models, the two new self-
consistent evolution model sets experience a stronger gravitational force due
to the smaller planetary radius (despite the lower planetary mass assumed).
Consequently, the predicted atmospheric escape is also lower. During transit,
this, in addition to the smaller planetary radii results in relatively reduced
coverage of the stellar disk by atmospheric triplet-state helium and
ultimately a lower predicted observability of escape. However, the overall
trend of weaker He absorption with evolution noted in Allan et al. (2024)
remains in the new 0.1 $\rm M_{J}$ model-sets, with the solid and dashed
profiles of Figure 14 corresponding to 2% and 10% He abundances.

Considering the non-detections we find here and the high estimated mass-loss
rates from both our hydrodynamic escape models (isothermal Parker wind and
photoevaporation-driven escape), we consider the ages of the systems in our
sample and the timescales of photoevaporation assuming a constant mass-loss
rate with evolution. For HD 63433 b, the self-consistent model’s predicted
mass-loss rate of $2.8\times 10^{10}$ g s-1 gives an evaporation timescale of
215 Myr if we adopt the same envelope fraction of 0.6% (Zhang et al., 2022c).
This rough estimation is also likely underestimated due to our assumption of a
constant mass-loss rate with evolution, due to the escape likely being
stronger at ages younger than the sampled age in reality. Given HD 63433 b’s
predicted age (414$\pm$23 Myr; Mann et al. 2020), both p-winds and our
hydrodynamic models are consistent with (Zhang et al., 2022b) in demonstrating
that it is unlikely that the planet has retained a H/He atmosphere.

Applying the constant mass loss with evolution approximation to V1298 Tau c
and K2-100 b results in photoevaporation timescales of 140 and 225 Myr,
respectively. Using a more ample envelope fraction of 2% for mini-Neptunes
leads to timescales of 465 and 740 Myr. Regardless of the assumed envelope
fraction, the very expected young age of V1298 Tau c ($23\pm 4$ Myr) suggests
that it should still have its primordial atmosphere. K2-100b – with its age of
$750\pm 5$ Myr – may be close to its photoevaporation lifetime, depending on
the mass fraction of the envelope. Furthermore, the hydrodynamic modeling
(which assumes a primordial atmosphere) shows that the loss of the primordial
atmosphere is not required to explain the non-detections – the low number
density of helium triplet material obscuring the disk alone is enough to do
so.

We therefore propose three different explanations for the He non-detections
presented here: i) it is possible that the planets formed with a low He
abundance; ii) stellar winds and/or magnetic field effects quash the He signal
(§4.1); or iii) escape is occurring, but helium is not in the metastable state
(§4.3) and thus not observable with our 1.083 $\mu$m data. Magnetic fields are
consistent with the HD 63433b non-detection, while the K2-100 and V1298 Tau c
non-detections do not require magnetic fields and can instead be explained by
a combination of the Hill radii and likely optically thin nature of He being
less than our detection threshold, combined with some potential stellar wind
confinement.

Intriguingly, the majority of previously published He i observations for young
sub-Jovian planets have yielded several non-detections (e.g., Gaidos et al.
2020; Vissapragada et al. 2021; Zhang et al. 2022c, 2023) – contrary to
theoretical predictions of higher or ongoing atmospheric escape rates early on
in the evolutionary timescales of these systems. Long-term monitoring of
stellar helium variability for a sample of mostly young stars (Krolikowski et
al., 2024) – including the three planets that are the subject of this study –
show that exoplanet helium absorption is typically less than the stellar
helium variability at ages $<300$ Myr. This presents another confounding
factor for better understanding young planets.

##  6 Conclusions

Using Keck II/NIRSPEC, we observed the helium transmission spectra for three
young ($<$800 Myr) sub-Jovian (0.2–0.5 $\rm R_{J}$) planets: HD 63433b,
K2-100b, and V1298 Tau c. We find upper limits on the excess helium absorption
ranging from 0.47–1.13% for all three planets in this sample, with upper
limits on their mass-loss rates of $7.9\times 10^{10}-7.9\times 10^{11}$ g s-1
from Parker wind models (§4.2). These observed upper limits are consistent
with the analytical maximum excess absorption predictions at 1.083 $\mu$m
($\sim$2–8%; §4.1) and estimates of $<$0.04–0.6% from 1D hydrodynamic escape
models (§4.3). In the context of other He observations of sub-Jovian planets
in both young and older systems, our results follow theoretical predictions
for the exponential decay of helium absorption in sub-Jovians as a function of
system age. Further 1.083 $\mu$m observations for a larger sample of sub-
Jovian planets at a range of ages is crucial for better understanding the
temporal evolution of the helium triplet.

## Acknowledgments

We thank Jorge Sanz-Forcada for kindly sharing the high-energy SED of $\iota$
Horologii. We acknowledge W. M. Keck Observatory, which is operated as a
scientific partnership among the California Institute of Technology, the
University of California and the National Aeronautics and Space
Administration. The Observatory was made possible by the generous financial
support of the W.M. Keck Foundation. The authors wish to recognize and
acknowledge the very significant cultural role and reverence that the summit
of Maunakea has always had within the indigenous Hawaiian community. We are
most fortunate to have the opportunity to conduct observations from this
mountain. JK acknowledges financial support from Imperial College London
through an Imperial College Research Fellowship grant. APA and AAV acknowledge
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (grant agreement No 817540,
ASTROFLOW). R. A. is a Trottier Postdoctoral Fellow and acknowledges support
from the Trottier Family Foundation. This work was supported in part through a
grant from the Fonds de Recherche du Québec - Nature et Technologies (FRQNT).
This work was funded by the Institut Trottier de Recherche sur les Exoplanètes
(iREx). This work has been carried out within the framework of the NCCR
PlanetS supported by the Swiss National Science Foundation under grants
51NF40$\\_$182901 and 51NF40$\\_$205606\. This project has received funding
from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (project Spice Dune, grant agreement No
947634).

Figure 2: In-transit (green) and out-of-transit (black) stellar spectra of
K2-100b for all individual spectral frames (top) and the mean spectra
(middle), as well as the excess absorption (bottom) centered on the helium
triplet (dashed black lines). The OH emission (light gray) and H2O absorption
(dark gray) telluric regions are also indicated. Figure 3: In-transit (purple)
and out-of-transit (black) stellar spectra of HD 63433b for all spectral
frames (top) and the mean spectra (middle), as well as the excess absorption
(bottom) centered on the helium triplet (dashed black lines). The OH emission
(light gray) and H2O absorption (dark gray) telluric regions are also
indicated. Figure 4: In-transit (orange) and out-of-transit (black) stellar
spectra of V1298 Tau c for all spectral frames (top) and the mean spectra
(middle), as well as the excess absorption (bottom) centered on the helium
triplet (dashed black lines). The OH emission (light gray) and H2O absorption
(dark gray) telluric regions are also indicated. Figure 5: Phase-resolved
signal-to-noise map for K2-100b centered on the helium triplet in the stellar
rest frame, compared to the first and fourth contact points (solid white
lines) and the planet’s orbital motion (dashed white lines). Figure 6: Phase-
resolved signal-to-noise map of absorption for the partial transit (no pre-
ingress baseline) of HD 63433b centered on the helium triplet in the stellar
rest frame, compared to fourth contact (solid white line) and the planet’s
orbital motion (dashed white lines).  Figure 7: Phase-resolved signal-to-noise
map for the partial transit of V1298 Tau c centered on the helium triplet in
the stellar rest frame, compared to the first contact point (solid white
lines) and the planet’s orbital motion (dashed white lines). Figure 8: The He
transmission spectrum for K2-100b (top), HD 63433b (middle), V1298 Tau c
(bottom) centered on the helium triplet (dashed gray lines). The dark and
light shaded colored regions correspond to the 1$\sigma$ and 3$\sigma$
uncertainties, respectively. Telluric regions are shown in the shaded gray
regions, as in Figures 2, 3, and 4.

Figure 9: Best-fit results for simultaneously modeling the instrumental
systematics and atmospheric escape signal. Figure 10: Posterior distributions
of retrieved parameters from our 1D p-winds models. Figure 11: Same as Figure
10, but for HD 63433b. Figure 12: Same as Figure 10, but for V1298 Tau c.
Figure 13: Helium triplet excess absorption predictions (left) and their
corresponding mid-transit extinction maps (right), obtained with the model of
Allan et al. (2024) as described in §4.3. For the excess absorption profiles,
solid lines indicate mean phase averaged (T1-T4) profiles while shaded region
encompasses all phases between first contact and mid-transit. For the
extinction maps, the dashed circle marks the stellar disk. The displayed
extinction is the sum of the three individual extinctions of each of the
triplet lines. A helium to hydrogen number fraction of He/H=0.1 was assumed
for each planet, with He/H=0.02 also being tested in the case of V1298 Tau c
as shown by the gray dashed profile. Additional planetary and stellar
parameters listed in Table 1 were used. Figure 14: The measured equivalent
width of the metastable helium line as a function of age for Neptunes (4
$\leq$ $\rm R_{\oplus}$ $\leq$ 6) around K stars (triangles) and M stars
(diamonds), and sub-Neptunes ($\rm R_{\oplus}<$ 4) around K stars (circles)
and around G and M stars (squares). The upper limits from our sample are shown
for K2-100b (green), V1298 Tau c (orange), and HD 63433b (purple). The He
equivalent width for HD 63433b from Zhang et al. (2022c) is shown in the open
purple square. We also show predicted trends between helium absorption and age
from hydrodynamic models (Allan et al., 2024) for 2% (solid black line) and
10% (dashed black line) He abundance. These models are calibrated for a 0.1
MJup planet orbiting a K-type star at 0.045 au (details in text). Literature
helium values are taken from Allart et al. (2018); Gaidos et al. (2023);
Kasper et al. (2020); Krishnamurthy et al. (2021); Nortmann et al. (2018);
Orell-Miquel et al. (2022, 2023); Zhang et al. (2021, 2022a, 2023).

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