# Non-detection of Helium in the Hot Jupiter WASP-48b

Katherine A. Bennett Department of Earth and Planetary Sciences, Johns Hopkins
University, Baltimore, MD 21218, USA  Astronomy Department, Wesleyan
University, Van Vleck Observatory, Middletown, CT, 06459, USA  Seth Redfield
Astronomy Department, Wesleyan University, Van Vleck Observatory, Middletown,
CT, 06459, USA  Antonija Oklopčić Anton Pannekoek Institute of Astronomy,
University of Amsterdam, 1098 XH Amsterdam, Netherlands  Ilaria Carleo
Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain
Joe P. Ninan Department of Astronomy and Astrophysics, Tata Institute of
Fundamental Research, Mumbai, 400005, India  Michael Endl Department of
Astronomy, The University of Texas at Austin, Austin, TX, 78712, USA

###### Abstract

Hot Jupiters orbiting extremely close to their host star may experience
atmospheric escape due to the large amounts of high-energy radiation they
receive. Understanding the conditions under which this occurs is critical, as
atmospheric escape is believed to be a driving factor in sculpting planetary
populations. In recent years, the near-infrared 10833 Å helium feature has
been found to be a promising spectral signature of atmospheric escape. We use
transmission spectroscopy to search for excess helium absorption in the
extended atmosphere of WASP-48b, a hot Jupiter orbiting a slightly evolved,
rapidly-rotating F star. The data were collected using the Habitable Zone
Planet Finder spectrograph on the Hobby-Eberly Telescope. Observations were
taken over the course of seven nights, from which we obtain three transits. No
detectable helium absorption is seen, as absorption depth is measured to
$-0.0025\pm 0.0021$, or $1.2\sigma$ from a null detection. This non-detection
follows our current understanding of decreasing stellar activity (and thus
high-energy radiation) with age. We use a 1D isothermal Parker wind model to
compare with our observations and find our non-detection can best be explained
with a low planetary mass-loss rate and high thermosphere temperature. We
explore our results within the context of the full sample of helium detections
and non-detections to date. Surprisingly, comparing helium absorption with the
stellar activity index $\rm log\;R^{\prime}_{HK}$ reveals a large spread in
the correlation between these two factors, suggesting that there are
additional parameters influencing the helium absorption strength.

Exoplanet astronomy (486) — Exoplanet atmospheres (487) — Hot Jupiters (753) —
High resolution spectroscopy (2096) — Transmission spectroscopy (2133)

††facilities: Hobby-Eberly Telescope (Habitable-Zone Planet Finder)††software:
astropy (Astropy Collaboration et al., 2013, 2018, 2022), barycorrpy (Kanodia
& Wright, 2018; Wright & Eastman, 2014), matplotlib (Hunter, 2007), numpy
(Harris et al., 2020), pandas (Wes McKinney, 2010), radvel (Fulton et al.,
2018), scipy (Virtanen et al., 2020),

##  1 Introduction

With the explosion of exoplanet detections in the last decade, an increasing
focus has been on understanding planetary demographics and evolution.
Atmospheric escape of close-in exoplanets is a phenomenon that can help us
answer both of these questions. It is thought to be a partial explanation for
the dearth of planets between 1.5–2 $R_{\earth}$, known as the radius valley
(Fulton et al., 2017), because it may drive enough atmospheric mass loss on
planets of a certain size threshold to significantly affect how a planet
evolves (e.g., Owen & Wu 2013). Additionally, quantifying mass loss rates
through studies of atmospheric escape provides insight into atmospheric
durability over a planet’s lifetime, which in turn is important for
understanding habitability (Lammer et al., 2014).

Thought to be driven primarily by high-energy ultraviolet (UV) and X-ray
stellar radiation (e.g., Lammer et al. 2003; Murray-Clay et al. 2009),
atmospheric escape was first directly observed in the atmosphere of HD 209458b
(Vidal-Madjar et al., 2003) via the detection of the Ly-$\alpha$ hydrogen
transition in the planetary atmosphere using UV transmission spectroscopy.
However, to date only a handful of detections using this marker have been made
(e.g, Lecavelier des Etangs et al. 2012; Ehrenreich et al. 2012; Kulow et al.
2014). Though the line has a large cross section (Owen, 2019), the lack of
ease of detection is attributable to the fact that the line is in the
ultraviolet regime (at 1215 Å) and thus cannot be observed using high-
resolution ground-based facilities. In addition, the core of the line is
altered by heavy absorption by the interstellar medium (ISM) (Wood et al.,
2005; Edelman et al., 2019) and Earth’s own geocoronal emission (e.g., Vidal-
Madjar et al. 2003).

In addition to Ly-$\alpha$, the H$\alpha$ line of the Balmer series has also
been observed in a handful of exoplanetary atmospheres (e.g., Jensen et al.
2012; Yan & Henning 2018). However, there have been controversies over whether
some detections of H$\alpha$ are due to stellar activity or planetary
absorption (e.g., Barnes et al. 2016; Cauley et al. 2017).

Metals, including OI (Vidal-Madjar et al., 2004; Ben-Jaffel & Ballester,
2013), CII (Vidal-Madjar et al., 2004; Linsky et al., 2010), MgI (Vidal-Madjar
et al., 2013), and MgII and FeII (Sing et al., 2019) have also been used as
indicators of atmospheric escape. Additionally, broadband X-ray transit
observations of HD 189733b have shown a discrepancy between the X-ray and
optical transit depths, supporting the existence of escaping metals (which
absorb at X-ray wavelengths) in planetary exospheres (Poppenhaeger et al.,
2013).

The metastable helium feature at 10833 Å has also emerged in recent years as a
marker of atmospheric escape. It is less susceptible to stellar activity than
H$\alpha$ and is not affected by absorption from the ISM like Ly-$\alpha$. In
addition, a huge advantage of using this feature over Ly-$\alpha$ is that is
in the infrared regime, meaning it can be observed using ground-based
telescopes.

While it was first predicted to be a strong absorption feature of transmission
spectroscopy in 2000 (Seager & Sasselov, 2000), this triplet feature was not
detected in an exoplanetary atmosphere until 2018, when it was observed in the
atmosphere of WASP-107b using narrowband photometry with the Wide Field Camera
3 (WFC3) onboard the Hubble Space Telescope (HST) (Spake et al., 2018). Since
then, the number of helium detections has exploded. To date, more than 30
planets have been investigated for the 10833 Å helium line. Of these, most
have been nondetections (e.g., Kasper et al. 2020; Krishnamurthy et al. 2021;
Vissapragada et al. 2021; Zhang et al. 2021; Kawauchi et al. 2022), but there
have been many detections as well (e.g., Nortmann et al. 2018; Allart et al.
2018; Salz et al. 2018; Ninan et al. 2020; Paragas et al. 2021).

The helium absorption feature at 10833 Å is due to resonance scattering of
neutral helium from the $\rm 2^{3}S$ to the $\rm 2^{3}P$ state (Oklopčić &
Hirata, 2018). There are two main pathways to populate the $\rm 2^{3}S$
metastable state: photoionization-recombination and collisional excitation
(Oklopčić & Hirata, 2018). In the photoionization-recombination pathway, EUV
photons are responsible for ionizing neutral helium, which then recombines to
the metastable $\rm 2^{3}S$ state. In exoplanets, this is the dominant pathway
populating the metastable helium state. Therefore, the population of this
state (and thus helium absorption at 10833 Å) is thought to be driven
primarily by the amount of EUV flux received from the host star (Oklopčić,
2019). Accordingly, an intense amount of focus has been placed on determining
a correlation between EUV flux and helium absorption depth.

On the other hand, the metastable $\rm 2^{3}S$ state is ionized and
depopulated by mid-UV flux (Oklopčić, 2019). This suggests larger helium
absorption features may be expected from planets orbiting stars with high
amounts of EUV radiation, which originates from the stellar corona (Nortmann
et al., 2018), but low amounts of mid-UV blackbody radiation. The optimal
ratio of EUV to mid-UV flux was found by Oklopčić (2019) to exist around
K-type stars, and this finding has largely skewed the sample of helium studies
toward K-type stars.

Additionally, because EUV flux originates from stellar magnetic activity in
the corona, and stars are most active in their younger years (Ribas et al.,
2005), emphasis has also been placed on helium searches for planets orbiting
young, active stars. While it is important to continue to study atmospheric
escape in these types of environments, in order to fully comprehend the
relationship between high-energy radiation and helium absorption, environments
other than planets orbiting young, K-type stars must be considered. Only with
a more complete sample can we begin to sketch the story of how atmospheric
escape drives planetary evolution across all stellar types and ages.

In this paper, we use transmission spectroscopy to examine the 10833 Å line in
the atmosphere of a hot Jupiter orbiting a slightly evolved star. WASP-48 is
an F-type star with an age of approximately 7.9 Gyr (Enoch et al., 2011), and
its sole known planet is a hot Jupiter with a period of 2.14 days. Stellar and
planetary parameters are given in Table 1. This system is very similar to that
of HAT-P-32, which has one of the strongest helium signals detected to date
(Czesla et al., 2022). Though the HAT-P-32 system is likely younger than the
WASP-48 system, both consist of hot Jupiters with similar planet properties
orbiting an F-star at approximately 0.034 au (see Table 5).

By investigating a non K-type star that is off the main sequence, we hope to
contribute to a more complete sample of helium observations, which is
important in order to uncover the full picture of how EUV flux impacts
atmospheric escape over the course of a planet’s lifetime. To the best of our
knowledge, this is only the second time a star off the main sequence has been
targeted in the metastable helium search. The first was WASP-12b (Kriedberg &
Oklopčić, 2018), in which helium was not detected.

While the host star has a low stellar activity index (log $\rm
R^{\prime}_{HK}=-5.135$), it is rotating at $v\,{\rm sin}\,i\sim 12.2\;{\rm
km\,s^{-1}}$, a rapid rate for a star of its age. This make it an intriguing
candidate for a metastable helium study, as a higher rotation rate is
suggestive of greater stellar activity. Therefore, a search for helium in this
exoplanet will provide insight into whether evolved stars can indeed show high
levels of EUV flux and thus drive atmospheric escape beyond the time frame
accepted in our current models.

Table 1: Parameters of WASP-48b and its host star

Parameter | Value
---|---
Distance (pc) | 460 ± 5
Stellar Radius ($R_{\odot}$) | 1.75 ± 0.09
Stellar Mass ($M_{\odot}$) | 1.19 ± 0.05
Stellar $T_{\rm eff}\,$ (K) | 5920 ± 150
Stellar Age (Gyr) | $7.9^{+2.0}_{-1.6}$
Spectral Type | F
V magnitude | 11.72 ± 0.14
log $g_{\odot}$ $(\rm cm\;s^{-2}$) | 4.03 ± 0.04
$\rm[Fe/H]$ | $-0.12\pm 0.12$
$v\,{\rm sin}\,i\;({\rm km\,s^{-1}})$ | 12.2 ± 0.7
Planet Radius ($R_{J}$) | 1.67 ± 0.10
Planet Mass ($M_{J}$) | 0.984 ± 0.085
Planet Density ($\rho_{J}$) | 0.21 ± 0.04
Planetary $T_{\rm eff}$ (K) | 2035 ± 52
$a$ (au) | 0.0344 ± 0.0026
$P$ (days) | 2.14363592 ± 0.0000046
log $g_{P}$ $(\rm cm\;s^{-2}$) | 2.91 ± 0.06
Transit Duration (min) | 192.20 ± 1.73
$T_{c}(0)\;(\rm BJD_{TDB})$ | 2455364.55217 ± 0.00020
Inclination (degrees) | 80.09 ± 0.55

Note. — Values taken from Enoch et al. (2011) and Turner et al. (2016).

We detail the observations and analysis in Section 2. In Section 3, we examine
how our observations compare to the model derived by Oklopčić & Hirata (2018)
and perform a more robust statistical examination of the result. We examine
our findings in the context of the complete sample of helium literature in
Section 4 and work toward uncovering a relationship between helium absorption
and measures of stellar activity.

##  2 Observations and Data Analysis

###  2.1 Observations and Data Reduction

Observations were taken using the Habitable-Zone Planet Finder (HPF), a fiber-
fed NIR echelle spectrograph on the 10 m Hobby-Eberly Telescope (HET). Though
HPF was originally designed to detect low-mass planets around M dwarfs using
precision radial velocity techniques (Mahadevan et al., 2012), it has become
widely used in the search for helium in exoplanets (e.g., Ninan et al. 2020;
Krishnamurthy et al. 2021; Vissapragada et al. 2021). HPF has a wavelength
range coverage of 8079–12786 Å and resolving power of R$\sim$55,000 (Ninan et
al., 2020).

Observations were taken on seven nights between 2019 May 16 UT and 2019 June
29 UT. These are detailed in Table 2. Due to the design of the HET,
observations can only take place over a limited time span, so observing a full
transit from ingress to egress in one night is not possible. Instead,
observations are taken on multiple nights to piece together as much of the
transit as possible. Across these seven nights of observations, three transits
were observed: on 2019 May 19 UT, 2019 June 16 UT, and 2019 June 18 UT.

Table 2: HPF Spectrographic Observations of WASP-48b.  Date | Time | In vs. Out | Average
---|---|---|---
(UT) | (UT) | of Transit | SNR
2019 May 16 | 08:06:44 | out | 112.3
2019 May 16 | 08:22:33 | out | 112.9
2019 May 16 | 08:38:21 | out | 105.4
2019 May 17 | 07:55:23 | out | 66.2
2019 May 17 | 08:11:11 | out | 84.0
2019 May 17 | 08:27:00 | out | 90.0
2019 May 19 | 07:21:18 | out | 92.8
2019 May 19 | 07:37:07 | in | 110.2
2019 May 19 | 07:52:56 | in | 121.8
2019 May 19 | 08:08:45 | in | 120.5
2019 May 19 | 08:24:33 | in | 108.1
2019 May 19 | 08:40:22 | in | 105.0
2019 Jun 16 | 05:44:02 | in | 59.1
2019 Jun 16 | 05:59:50 | in | 61.1
2019 Jun 16 | 06:15:39 | in | 98.3
2019 Jun 16 | 06:31:28 | in | 92.0
2019 Jun 16 | 06:47:17 | in | 88.0
2019 Jun 16 | 07:04:31 | in | 74.1
2019 Jun 18 | 05:56:08 | out | 94.3
2019 Jun 18 | 06:11:57 | out | 91.9
2019 Jun 18 | 06:27:46 | out | 79.8
2019 Jun 18 | 06:43:34 | out | 73.4
2019 Jun 18 | 10:20:41 | in | 78.6
2019 Jun 18 | 10:36:30 | in | 92.2
2019 Jun 18 | 10:52:19 | in | 31.7
2019 Jun 18 | 11:08:08 | out | 49.5
2019 Jun 19 | 05:38:12 | out | 62.2
2019 Jun 19 | 05:54:01 | out | 75.6
2019 Jun 19 | 06:09:50 | out | 82.2
2019 Jun 19 | 06:25:39 | out | 76.2
2019 Jun 29 | 09:56:16 | out | 105.1
2019 Jun 29 | 10:12:05 | out | 98.2
2019 Jun 29 | 10:27:54 | out | 90.1
2019 Jun 29 | 10:43:43 | out | 86.6

In our analysis, we include exposures with an average SNR of greater than 50,
which excludes the exposures from 2019 Jun 18 10:52 UT and 2019 Jun 18 11:08
UT. This decision was supported by the fact that a strong stellar silicon
feature occurring just blue-ward of the helium triplet (see Figure 1) was
absent in these two exposures but present in all other exposures, suggesting
that WASP-48 was not successfully observed in these two cases.

Two more exposures, those from 2019 Jun 16 05:44 UT and 2019 Jun 16 05:59 UT
were also eventually discarded due to an imperfect data analysis process that
proved to be particularly errant for these two exposures. More details on this
realization and justification are provided in Section 3.

The data were reduced using the HPF extraction pipeline (Ninan et al., 2018).
After accounting for bias removal, nonlinearity correction, and cosmic ray
correction, this algorithm nondestructively measures the rate of charge
accumulation per pixel in an “up-the-ramp” fashion. These 3D data are then
collapsed to a 2D flux image, which is flat-fielded and rectified (Kaplan et
al., 2019). Finally, an optimal extraction algorithm (Horne, 1986) is used to
weight the data by its uncertainty and cross-dispersion profile and collapse
it into a 1D spectrum.

Each resulting exposure contains a science, sky, and calibration fiber
spectrum, with all wavelengths being measured in vacuum. The metastable helium
feature is actually a triplet with rest vacuum wavelengths of 10832.07,
10833.22, and 10833.31 Å. We calculate these values by converting the air
wavelengths of the helium triplet, given on the NIST Atomic Spectra
Database111https://www.nist.gov/pml/atomic-spectra-database, into vacuum
wavelengths. A first glimpse of the spectrum around 10833 Å can be seen in
Figure 1. A stellar silicon line and several telluric features are visible.
These telluric features include an OH emission doublet at 10832.10 and
10832.41 Å, another strong but blended OH emission doublet at 10834.24 and
10834.33 Å, and two water vapor absorption lines at 10835.07 and 10836.94 Å.
The identities of these features were uncovered using the HITRAN (high-
resolution transmission molecular absorption) database222https://hitran.org.

Figure 1: Example spectrum from 2019 May 19 08:08 UT in the topocentric rest
frame. Rest wavelengths of HITRAN derived OH and $\rm H_{2}O$ features are
shown with vertical green and yellow dashed lines, respectively. These
coincide with the emission lines seen in the spectrum, confirming they are
telluric features originating in the Earth’s atmosphere. The expected location
of the stellar silicon feature and any planetary helium feature is also
plotted. Note that the location of the predicted helium feature varies across
exposures due to changing barycentric and planetary velocity corrections.

###  2.2 Analysis

Telluric lines pepper our observations and must be removed before preceding.
In particular, we focus on the OH telluric emission lines closest to the 10833
$\rm\AA$ line. When shifting the spectra into a stellar rest frame, the blue-
most OH emission doublet overlays the redward components of the helium triplet
(10833.22 and 10833.31 Å), which will interfere with our ability to detect any
planetary helium in exposures close to mid-transit, where the planetary
velocity shifts are relatively small.

To remove these telluric emission lines, we subtract the sky fiber from the
science fiber. For each spectra, we first remove the sky flux continuum and
interpolate the sky fiber to the science fiber. We calculate a scaling ratio
for the sky spectrum to correct for the varying intensity of the OH peaks
between the sky and science fibers. We apply this scaling ratio to the sky
spectrum between 10831–10835 $\rm\AA$. Though the scaling ratio does have a
chromatic dependence, the two OH peaks are very close in wavelength, and one
scaling factor should suffice. Once the scaling factor is applied, we subtract
the interpolated sky spectrum from the science spectrum. This technique
reveals a shallow stellar helium feature underneath the OH emission lines, as
shown in Figure 2.

Figure 2: Science fiber in the topocentric rest frame, both before (light blue
line) and following (dark blue line) sky flux subtraction. This exposure is
from 2019 May 19 08:08 UT. We have zoomed in to see the sky subtraction has
successfully removed the OH emission lines and has revealed a stellar helium
line underneath the small OH doublet.

By examining Figure 2, we can see that the closest telluric water absorption
lines falls about 2 Å from the stellar helium feature. We calculate that the
maximum planetary radial velocity in-transit is $\rm 32.7\;km\;s^{-1}$, which
translates into a $\rm 1.2\;\AA$ shift at 10833 Å. Because this is smaller
than the wavelength difference between helium and the telluric water lines, we
are justified in disregarding those telluric absorption lines. (We also
conducted a visual examination of each in-transit spectrum in the planet rest
frame to confirm that the expected planetary helium feature location does not
overlap in any instance with the telluric water lines.)

Once the telluric features have been accounted for, we create a master out-of-
transit spectrum. First, the spectra are normalized by dividing each science
spectra by a third-order polynomial fitted to the stellar continuum, following
Salz et al. (2018). Next, each out-of-transit spectrum is shifted from a
topocentric rest frame into the stellar rest frame. To do this, the spectra
are first shifted into a barycentric rest frame using the barycorrpy Python
package developed by Kanodia & Wright (2018), which is based on the IDL code
by Wright & Eastman (2014). We then immediately shift each spectrum into
WASP-48’s stellar rest frame by accounting for the systemic radial velocity of
WASP-48 ($-19.740$ $\rm km$ $\rm s^{-1}$, taken from the SIMBAD Astronomical
Database333http://simbad.u-strasbg.fr/simbad/). We ignore the reflex stellar
radial velocity from the motion of the planet, because we calculate the radial
velocity semiamplitude of the star to be only $0.14$ $\rm km$ $\rm s^{-1}$. At
10833 $\rm\AA$, this translates to a shift of $\rm 0.0050\;\AA$, which is less
than the spectral resolution of HPF at this wavelength ($\rm\sim 0.2\;\AA$).

Next, we interpolate each individual out-of-transit spectrum to a single
reference wavelength grid using the scipy cubic interpolation function. We sum
the spectra together, with each spectrum weighted by the inverse of its
variance following Salz et al. (2018) and Ninan et al. (2020), to arrive at
our master out-of-transit spectrum.

Before shifting the in-transit spectra into their appropriate planetary rest
frames, we can create an analogous master in-transit spectrum in the stellar
rest frame to compare with the out-of-transit spectrum. This provides a quick
visual inspection of the helium feature to see if there is any hint of
planetary helium. As shown in Figure 3, no visible planetary helium is present
when examining the master in-versus-out spectrum.

Figure 3: In-versus-out of transit spectrum in the stellar rest frame. The
individual spectra have been interpolated and undergone a weighted sum with
their inverse variances used as weights. No planetary helium signal is
visible.

To create the transmission spectrum, we interpolate the master out-of-transit
spectrum to each individual in-transit spectrum and calculate:

$\frac{F_{\rm in}-F_{\rm out}}{F_{\rm out}}=\frac{F_{\rm in}}{F_{\rm out}}-1,$
(1)

to create a series of “ratio spectra”. We then shift these spectra into their
planetary rest frames by using the radvel package (Fulton et al., 2018) to
calculate planetary radial velocity for each in-transit exposure, which is
then converted into a wavelength shift. We interpolate the ratio spectra to a
single reference grid and sum them using their inverse variances as weights.
This brings us to the final transmission spectrum, shown in Figures 4 and 5.
The spectrum is quite flat, demonstrating that there is no obvious planetary
helium absorption in the atmosphere of WASP-48b. We additionally examine the
transmission spectra per night and find they are also flat.

Figure 4: Final transmission spectrum in the planetary rest frame centered on
the 10831–10835 $\rm\AA$ range. Planetary absorption would be seen as a
negative value, so this flat spectrum shows no indication of helium
absorption. One example of the 1D Parker wind model is overplotted with the
spectrum. This example depicts various mass-loss rates
($\rm\dot{M}=10^{9}-10^{11}\;g\;s^{-1}$) with a thermosphere temperature of
9500 K. Absorption signature increases with mass-loss rate at this
thermosphere temperature.

Figure 5: Final transmission spectrum in the planetary rest frame. Same as
Figure 4, but with varying thermosphere temperatures ($\rm T=7000-10000\;K$)
at a constant mass loss rate of $\rm\dot{M}=10^{10}\;g\;s^{-1}$. At this mass
loss rate, helium absorption increases with decreasing temperature.

##  3 Results

In the formulation in Equation 1, planetary absorption is expressed as as a
negative value, emission as a positive value, while a value of zero indicates
no planetary absorption or emission. To calculate the average absorption
depth, we take the average of the absorption depth over a narrow range of
wavelengths (10833.10–10833.49 $\rm\AA$) centered on the two red components of
the helium triplet, following Alonso-Floriano et al. (2019) and Kirk et al.
(2020). Because the blue-most helium line (at 10832.07 $\rm\AA$) is much
weaker than the redder two lines (e.g., Oklopčić & Hirata 2018), we exclude
this portion of the wavelength range. We calculate the the average absorption
to be $-0.0025\pm 0.0021$ with a significance of $1.2\sigma$. Therefore, this
is a non-detection of metastable helium in the atmosphere of WASP-48b.

###  3.1 Empirical Monte Carlo

To examine the impact individual exposures taken over the course of many
nights have on the final transmission spectrum, we turn to the empirical Monte
Carlo (EMC) diagnostic (Redfield et al., 2008). This is a technique that aims
to assess any underlying systematic errors in our analysis, including those
arising from the data analysis itself as well as from astrophysical sources
including stellar variability.

The EMC applies our data analysis pipeline to a random subset of observations
to arrive at a final absorption depth. It then conducts this random selection
many times. Assuming no subset of exposures is skewing our overall result, the
resulting histogram of absorption values should be centered around the
absorption depth of $-0.0025\pm 0.0021$. To preserve the integrity of our
analysis, a random selection of five in-transit and eight out-of-transit
exposures is selected for each iteration, so that the ratio of in-transit to
out-of-transit exposures in the EMC most closely matches the true ratio of all
the in-transit exposures (11) to out-of-transit exposures (19).

In addition to conducting the EMC for in-transit versus out-of-transit
exposures (“in-out”), we also apply the EMC to compare a random subset of in-
transit exposures with the rest of the in-transit exposures (“in-in”). We do
the same for out-of-transit exposures (“out-out”). These comparisons are done
to ensure there is no systematic deviation within the in-transit or out-of-
transit data. The absorption depth for both of these comparisons should be
zero, signifying that there is no difference between various in-transit
exposures (and the same for out-of-transit exposures). As in the “in-out”
comparison, we preserve the in/out ratio for these two cases as closely as
possible.

The EMC was run for 330 iterations in all three scenarios: “in-out”, “out-
out”, and “in-in”. 330 iterations is the maximal possible number of
combinations for the “in-in” scenario and thus became the limiting factor.

At this stage, two more exposures were excluded in the analysis: 2019 Jun 16
05:44 UT and 2019 Jun 16 05:59 UT. When running the EMC with these two
exposures included, instead of a Gaussian shape centered around the calculated
absorption value, there is a clear bimodal distribution in the “in-out”
scenarios. This indicates that a small subset of exposures is largely skewing
the data. When these two exposures are removed, the bimodal nature of the “in-
out” distribution disappears. These two exposures also had the lowest SNR of
our sample and were causing errant emission in our transmission spectrum.

The final EMC is seen in Figure 6, and the calculated absorption and standard
deviation for the three scenarios are shown in Table 3. From Figure 6, though
the distributions in the three scenarios do not perfectly align, there is no
indication that the “in-out” data are significantly different from the “in-in”
or “out-out” scenarios. This is supported by Table 3, which demonstrates that
all three scenarios are within 1$\sigma$ of zero absorption (and within
2$\sigma$ of each other), further supporting our conclusion. We can also
compare the calculated absorption and standard deviation from the transmission
spectrum (black lines in Figure 6) to the mean and standard deviation of the
“in-out” scenario of the EMC (magenta lines in Figure 6; see also Table 3).
From the transmission spectrum, we measure absorption to be $-0.0025\pm
0.0021$, and in the EMC, we measure $-0.0023\pm 0.0057$. This is within
$0.1\sigma$ of the calculated absorption value, and so we can confirm that we
sufficiently accounted for systematic errors in our analysis.

Figure 6: Final version of EMC, showing absorption depth at the 10833 $\rm\AA$ helium line across randomly selected subsets of in and out-of-transit exposures. The solid and dotted black lines depict the calculated absorption depth and error from the transmission spectrum. The corresponding magenta lines show the average absorption and standard deviation calculated in the EMC. The lines are within $0.1\sigma$ of each other, suggesting we have correctly accounted for systematic errors in the analysis. Table 3: EMC distribution properties.  | $\mu$ | $\sigma$
---|---|---
In-In | 0.0014 | 0.0044
Out-Out | $-0.0043$ | 0.0050
In-Out | $-0.0023$ | 0.0057

###  3.2 Modeling

We use the 1D isothermal Parker wind model developed by Oklopčić & Hirata
(2018) to constrain the mass loss rate of WASP-48b based on helium absorption.
Briefly, the model uses input parameters of the stellar spectrum, planetary
mass and radius, planetary atmospheric composition, temperature of the
thermosphere, and mass-loss rate to derive density and velocity profiles of
the atmosphere as a function of altitude. These profiles are used to determine
the population levels of helium atoms as a function of radius, which are then
used to ultimately calculate the column density of the metastable $\rm 2^{3}S$
state as a function of radius. From the column density profile, the predicted
metastable helium absorption is calculated by integrating the optical depth
from the planetary radius to the planetary Hill radius.

Input parameters of planetary mass and radius are given in Table 1. Solar
composition (9:1 hyrogen-to-helium ratio) and solar input spectrum are
assumed. As described in Oklopčić (2019), the solar spectrum is derived from
the Solar Radiation and Climate Experiment (SORCE) solar spectral irradiance
data from the Laboratory for Atmospheric and Space Physics (LASP) Interactive
Solar Irradiance Data Center444http://lasp.colorado.edu/lisird/. This spectrum
includes the region 5–395 Å and $\sim$1150–23700 Å. To account for the EUV
irradiance between $\sim$400–1150 Å, the Ly$\alpha$ scaling relation described
in Linsky et al. (2014) is applied. The complete input solar spectrum for this
work can be viewed as the G2 model in Figure 1 of Oklopčić (2019).

Unfortunately, it is difficult to a priori estimate the planetary thermosphere
temperature and mass loss rate without information about the the high-energy
spectrum of the star. The XUV spectrum of WASP-48b is virtually unknown, but
we can estimate a range of predicted mass-loss rates using the energy-limited
formula (e.g., Murray-Clay et al. 2009):

$\dot{M}\approx\frac{\epsilon\pi R^{3}_{P}F_{XUV}}{GM_{P}}.$ (2)

Using solar XUV luminosity from the input solar spectrum, we calculate
$\dot{M}\approx 9\times 10^{9}$ $\rm g\;s^{-1}$. We can also take the XUV
luminosity for HAT-P-32 reported in Czesla et al. (2022) and calculate
$\dot{M}\approx 2\times 10^{12}$ $\rm g\;s^{-1}$. (Recall that HAT-P-32 is the
system very similar to the WASP-48 system.) We therefore expect the mass-loss
rate to be on the order of magnitude between $\rm 10^{9}-10^{12}\;g\;s^{-1}$.
We know HAT-P-32 is likely younger than WASP-48, and we therefore can expect
the XUV luminosity of WASP-48 to be slightly lower than that of HAT-P-32.
Because of this, helium absorption for WASP-48b has been modeled over
$10^{9}-10^{11.5}$ $\rm g$ $\rm s^{-1}$ for mass-loss rate. We also model the
thermosphere temperature between 6000–10000 K, which is a typical prediction
for close-in, highly irradiated planets.

Helium absorption predicted by the isothermal model at a thermosphere
temperature of 9500 K across a range of mass-loss rates is shown in Figure 4.
While keeping all stellar parameters constant, as mass-loss rate increases, so
does the absorption depth of the helium feature. We can compare this to Figure
4 in Lampón et al. 2020, which demonstrates how the density of the metastable
state increases with increasing mass-loss rate. This may occur because an
increasing mass-loss rate increases corresponds to an increase in atmospheric
density and thus free electron density (Oklopčić 2019; also see Figure 6 in
Lampón et al. 2020). Because free electrons are responsible for recombining
ionized helium to the metastable triplet state, the helium absorption
signature is strengthened.

Likewise, we can examine how thermosphere temperature drives the absorption
feature by plotting a range of temperatures across a single mass-loss rate
($\rm\dot{M}=10^{10}$ $\rm g$ $\rm s^{-1}$). This is shown in Figure 5. From
the figure, there is an inverse relationship between helium absorption and
thermosphere temperature. We again compare this with Figure 4 in Lampón et al.
2020, which shows a decrease in density of the metastable state with
increasing thermosphere temperature. This may be due to the fact that lower
temperatures lead to higher atmospheric and electron density by slowing the
rate of outflow (Spake et al., 2022). Higher levels of helium ionization due
to higher temperatures may also lead to a lower metastable helium abundance.

To more fully constrain the parameters of WASP-48b’s atmosphere, we create a
contour plot depicting the predicted helium absorption signature across the
full range of thermosphere temperature and mass-loss rate space. We calculate
how well different combinations of thermosphere temperatures and mass-loss
rates agree with our observations. This is seen in Figure 7, which measures
the number of $\sigma$ deviations between the transmission spectrum and model
across a range of parameter space. The $\chi^{2}_{\nu}$ value between the data
and model is calculated for the range 10831–10835 Å, and this is converted
into a $\sigma$ value. Blue contours represent a sigma deviation of less than
$3\sigma$, while contours in red represent a sigma deviation of greater than
$3\sigma$. In other words, a larger signal is expected in the red regions.
Since we do not see evidence of a signal in our data, the areas in red can be
rejected.

Figure 7: The number of standard deviations between the transmission spectrum
and model in the range 10831–10835 Å, measured across the full range of
parameter space. A line is drawn around the $3\sigma$ contour to show that
anything higher than this value (red on the plot) can be rejected. The
apparent decrease in absorption at high mass-loss rates may be a model
artifact due to the fact that our model does not take into account helium that
exists beyond the Hill radius.

We can safely reject low thermosphere temperatures ($\sim$ 6000 K) between
$\rm\dot{M}\approx 10^{9}-10^{11.4}\;g\;s^{-1}$. However, increasing the
thermosphere temperature decreases the range of mass-loss rates that can be
rejected. As discussed above, low mass-loss rates and high thermosphere
temperatures both decrease the atmospheric density, thereby decreasing the
metastable helium population. At low thermosphere temperatures but moderate
mass loss rates ($\rm\dot{M}=10^{10}-10^{11}\;g\;s^{-1}$), the metastable
helium population is maximized (Oklopčić, 2019); we see that a smaller signal
is expected as thermosphere temperature increases in this mass loss range. At
high mass loss rates, the atmospheric density can become too high for the EUV
radiation to ionize helium atoms low in the thermosphere, meaning metastable
helium only forms in a detached shell that gets thinner and thinner as it
approaches the Hill radius. At the highest mass-loss rates, helium mostly
forms outside the Hill radius. This is beyond the range considered by our
model, which relies on spherical symmetry and therefore breaks down outside
the Hill radius. The apparent decrease in absorption at high mass-loss rates
therefore may not be entirely physical.

From Figure 7, we conclude that our non-detection is most likely in agreement
with a low mass-loss rate and high thermosphere temperature. In reality, these
parameters are correlated with the incident stellar flux (Oklopčić, 2019).
Further observational and theoretical work is needed to tease out the
interplay between them.

##  4 Discussion

Our non-detection of planetary helium in WASP-48b can be explained through low
levels of EUV radiation and atmospheric escape, low helium abundances, or
stellar winds and other sources of stellar variability. The most
straightforward explanation is the first, but other explanations should be
considered. There could still be ongoing atmospheric escape, but the
thermosphere temperature may be high enough to ionize a majority of the helium
population (Owen, 2019). Another possibility is that there is stellar
variability due to XUV luminosity variability, stellar winds, shear
instability, or stellar flares (Zhang et al., 2022a). This variability would
lead to varying planetary outflows and thus a time-dependent absorption
feature that is only detectable during certain epochs.

However, though stellar winds could induce a variable helium feature, they are
unlikely to suppress it entirely (Zhang et al., 2021). Additionally, while it
is possible that high thermosphere temperatures are attenuating the population
of metastable helium, the most plausible explanation is that the amount of EUV
irradiation by the star is insufficient to support ongoing atmospheric escape.
This is supported by the fact that the stellar helium feature seen in Figure 2
appears weaker than in HAT-P-32 (see Figures C.1 and C.2 in Czesla et al.
2022), suggesting that stellar radiation is the main culprit. (Recall that
HAT-P-32b, which is very similar to WASP-48b, has a strong helium detection.)
Because the same photoionization-recombination pathway that populates the $\rm
2^{3}S$ metastable state in planetary atmospheres also populates the
metastable state in stellar chromospheres, the fact that the stellar signal is
weaker in WASP-48 may be an indicator that WASP-48’s stellar radiation field
is less optimal for the excitation of helium atoms to the metastable state
compared to HAT-P-32.

Because EUV radiation decreases with stellar age (e.g., Ribas et al. 2005;
Sanz-Forcada et al. 2011), this conclusion also makes sense in light of the
fact that WASP-48 is an old, slightly evolved star. Indeed, the only other
helium paper examining a planet orbiting an evolved star (WASP-12b) was also a
non-detection (Kriedberg & Oklopčić, 2018). Though WASP-48 is rotating
rapidly, which would hint at higher stellar activity, we do not see any
indication that activity is driving atmospheric escape in WASP-48b.

###  4.1 Helium and EUV Flux

EUV flux is thought to be the main driver behind metastable helium absorption,
but EUV stellar radiation is difficult to observe due to its high absorption
by the interstellar medium (Sanz-Forcada et al., 2011). To date, only one
space mission, the Extreme Ultraviolet Explorer (EUVE), has been commissioned
for the purpose of studying stellar EUV emission. This leaves astronomers to
predict stellar EUV flux by deriving scaling relationships between EUV flux
and observable parameters such as age (Sanz-Forcada et al., 2011), the stellar
activity index log $\rm R^{\prime}_{HK}$ (Sreejith et al. 2020), and stellar
rotation rate (Wright et al., 2011).

Oklopčić (2019) also found that it is not simply EUV flux that should
correlate with helium absorption, but the ratio of EUV flux to mid-UV flux.
While EUV flux populates the $\rm 2^{3}S$ state by ionizing neutral helium,
thereby initializing the photoionization-recombination pathway, the mid-UV
flux directly ionizes the $\rm 2^{3}S$ state and depopulates it. Thus, stars
with low mid-UV flux (due to lower effective temperatures) but high EUV flux
(due to stellar activity) should optimize helium absorption. Oklopčić (2019)
found that planets orbiting K-type stars are the most promising candidates
given these constraints.

Recall that WASP-48b orbits an old ($\sim 7.9$ Gyr), slightly evolved F star.
According to the discussion above, neither F-type stars nor old stars are
ideal for the detection of helium. WASP-48’s low log $\rm R^{\prime}_{HK}$
value ($-5.135$) further supports the notion that this is an inactive star,
and thus has low amounts of high-energy radiation being emitted from the
corona. However, its high rotation rate ($v{\rm\;sin}\;i\sim
12.2\;{\rm\;km}\;{\rm\;s^{-1}}$), particularly for a star of its age, suggests
that perhaps its activity level could be higher than anticipated. Our non-
detection in spite of this high rotation rate hints that perhaps rotation rate
is not the best proxy for stellar activity or that age is a more dominant
factor.

Though the non-detection of helium in WASP-48b seems to not raise any
questions in light of current understandings of EUV flux, stellar activity,
and age, to more robustly investigate these relationships, the full suite of
helium detections and non-detections should be considered. Only then can we
draw conclusions about the observational veracity of these theoretical
assumptions.

###  4.2 Comparison with Helium Literature

In order to tease out the influence of various stellar and planetary
parameters, we examine our non-detection in the context of all helium
detections and non-detections to date. To the best of our knowledge, WASP-48b
is the $\rm 37^{th}$ planet to be investigated for the detection of helium.
Table 4 gives an overview of all the helium detections and non-detections by
spectral type. (We utilized both the NASA Astrophysics Data
System555https://ui.adsabs.harvard.edu and the IAC ExoAtmospheres
database666http://research.iac.es/proyecto/exoatmospheres/ to conduct our
search.) One can see that there have been more non-detections (21) than
detections (16), and for spectral types F, G, and M, the majority of
investigations have been non-detections. Only one planet orbiting a hot A-type
star has been investigated (KELT-9b), and this was a non-detection (Nortmann
et al., 2018). Notably, 18 out of the 37 planets investigated orbit K stars,
and of these, more than half have been detections. While this supports the
finding from Oklopčić (2019) that K stars are the most promising candidates,
the sample is still relatively small and skewed toward K stars to draw any
final conclusion. In addition, there have been several non-detections around K
stars, as well as detections around other spectral types.

Table 4: Distribution of helium detections and non-detections in the literature by spectral type.  Spectral Type | Detections | Non-Detections
---|---|---
A | 0 | 1
F | 1 | 3
G | 1 | 4
K | 12 | 6
M | 1 | 6
T Tauri | 1 | 1
Total | 16 | 21

Still, the majority of the findings around F, G, and M stars have thus far
been non-detections. The sole detection around an F star was for the hot
Jupiter HAT-P-32b (Czesla et al., 2022), which, as noted, is very similar to
the WASP-48 system, albeit likely younger.

The full table of stellar and planetary parameters for each planet are found
in Table 5. These parameters have been taken from the literature. To the best
of our knowledge, this is the most complete sample of helium literature to
date. While there are inhomogeneities in the way that the data are derived
(e.g., some stellar ages are derived through isochrone fitting, while others
are derived using gyrochronology), this can be used as a starting point to
compare various parameters with helium absorption.

To compare helium findings across the literature, we measure the height of the
planetary atmosphere following Fossati et al. (2022), in which the effective
planet radius ($R_{\rm{eff}}$) at 10833 Å (in units of $R_{P}$) is calculated
from

$\frac{R_{\rm{eff}}}{R_{P}}=\sqrt{\frac{\delta+c}{\delta}},$ (3)

where $R_{P}$ is the planet radius, $\delta$ is the transit depth, and $c$ is
the helium absorption depth or upper limit. From here, we calculate a change
in transit depth, $\delta_{R_{P}}$, which represents the height of an opaque
atmosphere that causes the inflated planetary effective radius at 10833 Å and
produces the absorption signature in the transmission spectrum (Nortmann et
al., 2018). $\delta_{R_{P}}$ is given by

$\delta_{R_{P}}=\frac{R_{\rm{eff}}}{R_{P}}-1.$ (4)

$\delta_{R_{P}}$ is then normalized to the scale height, $H_{eq}$, following
Nortmann et al. (2018). To calculate $H_{eq}$, we use the planetary
equilibrium temperature, $T_{eq}$, and set the atmospheric mean molecular
weight to 2.3 times the mass of hydrogen, assuming H/He planetary atmospheres
with solar abundances.

We examine the correlation between the normalized atmospheric height of the
helium signature ($\delta_{R_{P}}/H_{eq}$) and several stellar and planetary
parameters, including the stellar activity index log $\rm R^{\prime}_{HK}$,
stellar age, stellar rotation rate, metallicity, planetary surface gravity,
and semimajor axis. We exclude directly comparing $\delta_{R_{P}}/H_{eq}$ with
high-energy EUV or XUV flux, as has been done in several other helium papers
(e.g., Nortmann et al. 2018; Alonso-Floriano et al. 2019; Kasper et al. 2020;
Casasayas-Barris et al. 2021; Orell-Miquel et al. 2022; Fossati et al. 2022),
because the X-ray luminosity for WASP-48 is not available. Instead of moving
through multiple layers of analytic scaling relations to estimate the X-ray
luminosity and in turn the EUV flux onto the planet, we elect instead to
compare $\delta_{R_{P}}/H_{eq}$ with only directly measured parameters found
in the literature.

We do not see any correlation with the stellar and planetary parameters listed
above, with the exception of the stellar activity index log $\rm
R^{\prime}_{HK}$. log $\rm R^{\prime}_{HK}$ was first described in Noyes et
al. (1984), and measures the ratio of the emission of Ca II H and K lines
(3933 Å and 3968 Å) originating in the chromosphere compared to the total
stellar bolometric luminosity. The correlation between log $\rm
R^{\prime}_{HK}$ and $\delta_{R_{P}}/H_{eq}$ was first noted in Nortmann et
al. (2018), and we find that using log $\rm R^{\prime}_{HK}$ is advantageous
because it is easily found in the literature and involves optical emission
lines that can be measured from the ground (Sreejith et al., 2020). However,
because the $\rm Ca\leavevmode\nobreak\ II$ lines originate in the
chromosphere, they do probe a spatially independent region from the corona and
transition region, where EUV radiation originates (Nortmann et al., 2018;
Sreejith et al., 2020). Additionally, this measurement is not available for
all stellar types, as late-type stars have very low luminosity in the optical
region. Still, log $\rm R^{\prime}_{HK}$ is widely used as a method to
quantify the stellar magnetic activity.

Figure 8: Normalized helium absorption versus log $\rm R^{\prime}_{HK}$, with
spectral type designated by color. Vertical error bars are depicted for all
data points, though some are quite small and are not visible. Error bars on
log $\rm R^{\prime}_{HK}$ are included where available. Non-detections (upper
limits on helium absorption) are depicted with vertical arrows. There appears
to be a slight positive correlation between $\delta_{R_{P}}/H_{eq}$ and log
$\rm R^{\prime}_{HK}$, hinting at a relationship between helium absorption and
stellar activity. WASP-48b is in the lower left corner at a
$\delta_{R_{P}}/H_{eq}$ value of $\sim 16.3$ and log $\rm R^{\prime}_{HK}$
value of $-5.135$.

We plot $\delta_{R_{P}}/H_{eq}$ vs. log $\rm R^{\prime}_{HK}$ for those stars
in our sample with available log $\rm R^{\prime}_{HK}$ values in the
literature in Figure 8. We include only planets for which helium absorption is
derived spectroscopically, as photometric measurements typically have a
diluted $\delta_{R_{P}}$ due to the narrowband filter’s response function.
They therefore require a scaling factor in order to be accurately compared
with spectroscopic measurements.

In Figure 8, spectral types are delineated by color, and non-detections are
marked by a vertical downward arrow. At first glance, there does appear to be
some positive correlation between these two parameters. Using a Pearson
correlation coefficient to measure the linear correlation between these
parameters for detections only, we find a correlation coefficient of $+0.29$,
indicating a weak to moderate positive correlation.

Still, Figure 8 must be interpreted with a grain of skepticism. Because we
calculate $\delta_{R_{P}}/H_{eq}$ using values taken from various literature
sources, this is in no way a homogeneous sample. Helium absorption depths are
measured differently using different telescopes, and several assumptions go
into the predicted scale height of an atmosphere. Additionally, applying a
scale height normalization may actually obscure the relationship between
$\delta_{R_{P}}/H_{eq}$ and $\rm R^{\prime}_{HK}$ if the scale height, which
is related to the lower hydrostatic atmosphere, is uncorrelated to the height
of the thermosphere. Both detections and non-detections have been reported for
the same planet (e.g., helium in WASP-52b was not detected in Vissapragada et
al. 2020 but was detected in Kirk et al. 2022), and absorption values are
constantly updated. We must keep these factors in the back of our mind when
interpreting such a plot. A greater sample size with more diversity in
spectral type will help us uncover whether there is truly a relationship
between log $\rm R^{\prime}_{HK}$ values and helium absorption.

Indeed, while many papers report a positive trend between helium absorption
and EUV or XUV flux (e.g., Nortmann et al. 2018; Poppenhaeger 2022), others
are beginning to question whether this simple correlation is the only factor
or whether the relationship is shallower than previously assumed (e.g.,
Alonso-Floriano et al. 2019; Fossati et al. 2022; Kirk et al. 2022). Next
steps should consider comparing the “hardness” of the high-energy stellar
spectra, i.e. the ratio between the EUV and mid-UV flux as described in
Oklopčić (2019).

##  5 Conclusion

In this paper, we search for metastable helium absorption in the extended
atmosphere of WASP-48b, a hot Jupiter orbiting a slightly evolved, rapidly
rotating F-type star. We use high-resolution ground-based transmission
spectroscopy using the Habitable-Zone Planet Finder. Our resulting
transmission spectrum is flat. No planetary helium appears to be present in
the extended atmosphere of WASP-48b, suggesting that there is no ongoing
atmospheric escape occurring on this planet.

We compare our findings with a 1D isothermal Parker wind model (Oklopčić,
2019), which allows us to constrain the expected thermosphere temperature and
mass-loss rate of the planet. We find that our non-detection can be explain by
a high thermosphere temperature and low mass-loss rate, or a high mass-loss
rate.

To understand this non-detection to the fullest extent, we compare our
findings to all other published helium works. We normalize helium absorption
to the planetary atmospheric scale height, $H_{eq}$, and plot these values
against a variety of stellar and planetary parameters. We find that only the
log $\rm R^{\prime}_{HK}$ index shows any correlation with helium absorption.

Oklopčić (2019) predicts that close-in planets orbiting K stars are the most
likely to experience high levels of atmospheric escape and provide the most
promising candidates for helium absorption. While there has certainly been the
largest number of detections around K stars, there have also been detections
around other spectral types (F, G, M, and T Tauri stars) as well as several
non-detections around K stars. More investigations of planets around a variety
of stellar types and ages need to be done to observationally validate the
prediction that K-type stars are optimal for helium detections.

To strengthen the veracity of atmospheric escape studies, we should couple
helium observations with Ly-$\alpha$ (for stars closer than 50 pc) and/or
H$\alpha$ studies to corroborate findings when possible. This has been done
for some planets, including HD 189773b (Vidal-Madjar et al., 2003; Jensen et
al., 2012; Salz et al., 2018), 55 Cnc e (Ehrenreich et al., 2012; Zhang et
al., 2021), and GJ 9827b and d (Carleo et al., 2021). Additionally, multiple
transits should be observed when possible, because it has become increasingly
apparent that stellar variability plays a meaningful role in fluctuating mass
loss and helium absorption over short timescales. HD 189733b has been shown to
exhibit XUV variability of up to 33% (Pillitteri et al., 2022; Zhang et al.,
2022a), which greatly impacts the amount of helium absorption detected.

As more planets are investigated and comparative studies expand, one of the
fundamental goals of the exoplanet atmospheric research community must be to
fully elucidate the timeline of atmospheric escape, the stellar and planetary
environment in which it occurs, and its impact on atmospheric evolution over a
planet’s lifetime. This is just one small piece of the exoplanet
characterization puzzle, but it will bring us closer to understanding the
architecture and habitability of planetary systems within our Galaxy.

=2.75in

Table 5: Stellar parameters for exoplanets with published helium results.

Planet | Distance (pc) | Spectral Type |  $T_{\rm eff}$ (K) | Age (Gyr) | Radius ($R_{\odot}$) | Mass ($M_{\odot}$) | [Fe/H] |  $v$ $\rm sin$ $i$ ($\rm km$ $\rm s^{-1}$) |  $\rm log$ $\rm R^{{}^{\prime}}_{HK}$
---|---|---|---|---|---|---|---|---|---
WASP-107b | $64.7414{{{}^{+0.2617}_{-0.2596}}}$ | $\rm K6V^{1}$ | $4425\pm 70^{2}$ | $6.9^{+3.7^{2}}_{-3.4}$ | $0.67\pm 0.02^{2}$ | $0.683^{+0.017^{2}}_{-0.016}$ | $+0.02\pm 0.09^{2}$ | $2.5\pm 0.8^{1}$ | $-$
WASP-69b | $49.9605^{+0.1320}_{-0.1313}$ | $\rm K5V^{4}$ | $4700\pm 50^{4}$ | $1.10\pm 0.15^{4}$ | $0.813\pm 0.028^{4}$ | $0.826\pm 0.029^{4}$ | $+0.15\pm 0.08^{4}$ | $2.2\pm 0.4^{4}$ | $-4.54^{4}$
HAT-P-11b | $37.7647^{+0.0337}_{-0.0336}$ | $\rm K4V^{6}$ | $4850\pm 50^{6}$ | $6.5^{+5.9^{6}}_{-4.1}$ | $0.75\pm 0.02^{6}$ | $0.81^{+0.02^{6}}_{-0.03}$ | $+0.31\pm 0.05^{6}$ | $1.5\pm 1.5^{6}$ |  $-$ $-4.584^{6}$
HD 189733b | $19.7638{{}^{+0.0128}_{-0.0127}}$ | $\rm K2V^{8}$ | $5050\pm 50^{8}$ | $5.2\pm 3.5^{9}$ | $0.76\pm 0.01^{8}$ | $0.82\pm 0.03^{8}$ | $-0.03\pm 0.04^{8}$ | $3.5\pm 1.0^{8}$ | $-4.5\pm 0.007^{75}$
WASP-12b | $427.246^{+6.068}_{-5.903}$ | $\rm F^{13}$ | $6300\pm{200}$ | $2\pm 1^{13}$ | $1.57\pm 0.07^{13}$ | $1.35\pm 0.14^{13}$ | $+0.30^{14}$ | $2.2\pm 1.5^{13}$ | $-5.500^{14}$
HAT-P-18b | $161.400^{+0.610}_{-0.605}$ | $\rm K2V^{16}$ | $4803\pm 80^{16}$ | $12.4^{+4.4^{16}}_{-6.4}$ | $0.749\pm 0.037^{16}$ | $0.770\pm 0.031^{16}$ | $+0.10\pm 0.08^{16}$ | $0.5\pm 0.5^{16}$ | $-4.73^{77}$
HD 209458b | $48.3016^{+0.1240}_{-0.1234}$ | $\rm G0V^{18}$ | $6071\pm 20^{18}$ | $3.5\pm 1.4^{18}$ | $1.20\pm 0.05^{18}$ | $1.26\pm 0.15^{18}$ | $+0.02\pm 0.03^{20}$ | $3.75\pm 1.25^{21}$ | $–4.92\pm 0.029^{75}$
55 Cnc e | $12.5855^{+0.0124}_{-0.0123}$ | $\rm G8V^{25}$ | $5172\pm 18^{26}$ | $8.6\pm 1.0^{27}$ | $0.943\pm 0.010^{27}$ | $0.905\pm 0.015^{27}$ | $+0.35\pm 0.1$ | $<1.23\pm 0.01^{27}$ | $–5.03^{27}$
GJ 1214b | $14.6427\pm 0.0372$ | $\rm M4.5V^{29}$ | $3250\pm 100^{29}$ | $5-10^{30}$ | $0.2213\pm 0.0043^{29}$ | $0.176\pm 0.009^{29}$ | $+0.1\pm 0.1^{29}$ | $<2.0^{31}$ | $-5.149^{85}$
GJ 9827d | $29.6610^{+0.0543}_{-0.0541}$ | $\rm K6V^{34}$ | $4255\pm 110^{34}$ | $\leavevmode\nobreak\ 10^{49}$ | $0.651\pm 0.065^{34}$ | $0.659\pm 0.060^{34}$ | $-0.28\pm 0.12^{34}$ | $2\pm 1^{34}$ | $-$
HD 97658b | $21.5618^{+0.0254}_{-0.0253}$ | $\rm K1V^{36}$ | $5192\pm 122^{36}$ | $3.9\pm 2.6^{37}$ | $0.746\pm 0.034^{36}$ | $0.77\pm 0.05^{36}$ | $-0.23\pm 0.03^{38}$ | $0.5\pm 0.5^{38}$ | $-4.975\pm 0.025^{38}$
GJ 436b | $9.75321^{+0.00898}_{-0.00896}$ | $\rm M2.5V^{39}$ | $3479\pm 60^{40}$ | $6.5^{39}$ | $0.449\pm 0.019^{40}$ | $0.445\pm 0.044^{40}$ | $-0.03\pm 0.20^{23}$ | $0.33\pm 0.091^{40}$ | $-5.09\pm 0.001^{75}$
V1298b | $108.199^{+0.704}_{-0.696}$ | T $\rm Tauri^{42}$ | $4970\pm 120^{42}$ | $0.023\pm 0.004^{42}$ | $1.345^{+0.056^{42}}_{-0.051}$ | $1.101^{+0.049^{42}}_{-0.051}$ | $-$ | $-$ | $-$
V1298d | $108.199^{+0.704}_{-0.696}$ | T $\rm Tauri^{42}$ | $4970\pm 120^{42}$ | $0.023\pm 0.004^{42}$ | $1.345^{+0.056^{42}}_{-0.051}$ | $1.101^{+0.049^{42}}_{-0.051}$ | $-$ | $-$ | $-$
GJ 3470b | $29.4214^{+0.0508}_{-0.0507}$ | $\rm M1.5V^{44}$ | $3652\pm 50^{44}$ | $0.3-3^{44}$ | $0.48\pm 0.04^{44}$ | $0.51\pm 0.06^{44}$ | $+0.20\pm 0.10^{44}$ | $-$ | $-4.86\pm 0.0038^{75}$
KELT-9b | $204.455^{+1.582}_{-1.558}$ | $\rm A0V^{47}$ | $10170\pm 450^{47}$ | $0.3^{47}$ | ${2.362^{+0.075}_{-0.063}}^{47}$ | ${2.52^{+0.25}_{-0.20}}^{47}$ | $-0.030\pm 0.200^{47}$ | $111.4\pm 1.3^{47}$ | $-$
GJ 9827b | $29.6610^{+0.0543}_{-0.0541}$ | $\rm K6V^{34}$ | $4255\pm 110^{34}$ | $10^{49}$ | $0.651\pm 0.065^{34}$ | $0.659\pm 0.060^{34}$ | $-0.28\pm 0.12^{34}$ | $2\pm 1^{34}$ | $-$
WASP-80b | $49.78760\pm 0.11605$ | $\rm K7V^{51}$ | $4150\pm 100^{10}$ | $1.601\pm 0.202^{52}$ | $0.571\pm 0.016^{10}$ | $0.570\pm 0.050^{10}$ | $-0.14\pm 0.16^{51}$ | $3.46\pm 0.35^{51}$ | $-4.04^{54}$
WASP-76b | $194.459^{+6.206}_{-5.839}$ | $\rm F7V^{55}$ | $6250\pm 100^{55}$ | $5.3\pm 2.9^{55}$ | $1.73\pm 0.04^{55}$ | $1.46\pm 0.07^{55}$ | $+0.23\pm 0.10^{55}$ | $3.3\pm 0.6^{55}$ | $-$
TRAPPIST-1b | $12.47\pm 0.01$ | $\rm M8V^{57}$ | $2566\pm 26^{58}$ | $7.6\pm 2.2^{59}$ | $0.1192\pm 0.0013^{58}$ | $0.0898\pm 0.0023^{58}$ | $+0.040\pm 0.080^{57}$ | $6\pm 2^{57}$ | $-$
TRAPPIST-1e | $12.47\pm 0.01$ | $\rm M8V^{57}$ | $2566\pm 26^{58}$ | $7.6\pm 2.2^{59}$ | $0.1192\pm 0.0013^{58}$ | $0.0898\pm 0.0023^{58}$ | $+0.040\pm 0.080^{57}$ | $6\pm 2^{57}$ | $-$
TRAPPIST-1f | $12.47\pm 0.01$ | $\rm M8V^{57}$ | $2566\pm 26^{58}$ | $7.6\pm 2.2^{59}$ | $0.1192\pm 0.0013^{58}$ | $0.0898\pm 0.0023^{58}$ | $+0.040\pm 0.080^{57}$ | $6\pm 2^{57}$ | $-$
HD 63433b | $22.4035\pm 0.0225$ | $\rm G2V^{62}$ | $5640\pm 74^{62}$ | $0.414\pm 0.023^{62}$ | $0.912\pm 0.034^{62}$ | $0.990\pm 0.030^{62}$ | $+0.04\pm 0.05^{62}$ | $7.3\pm 0.3^{62}$ | $-4.39\pm 0.05^{62}$
HD 63433c | $22.4035\pm 0.0225$ | $\rm G2V^{62}$ | $5640\pm 74^{62}$ | $0.414\pm 0.023^{62}$ | $0.912\pm 0.034^{62}$ | $0.990\pm 0.030^{62}$ | $+0.04\pm 0.05^{62}$ | $7.3\pm 0.3^{62}$ | $-4.39\pm 0.05^{62}$
HAT-P-32b | $289.205^{+5.355}_{-5.167}$ | $\rm F^{64}$ | $6207\pm 88^{10}$ | $3.8\pm 1.5^{64}$ | $1.219\pm 0.016^{64}$ | $1.160\pm 0.041^{64}$ | $-0.04\pm 0.08^{64}$ | $20.7\pm 0.5^{64}$ | $-4.62^{64}$
HD 73583b | $31.5666^{+0.0321}_{-0.0320}$ | $\rm K4V^{66}$ | $4511\pm 110^{66}$ | $0.48\pm 0.19^{66}$ | $0.65\pm 0.02^{66}$ | $0.73\pm 0.02^{66}$ | $0.00\pm 0.09^{66}$ | $3.5\pm 0.5^{66}$ | $-4.465\pm 0.015^{66}$
TOI-2136b | $33.36310\pm 0.06425$ | $\rm M4.5V$ | $3373\pm 108^{68}$ | $4.6\pm\textpm 1.0^{69}$ | $0.3440\pm 0.0099^{68}$ | $0.3272\pm 0.0082^{68}$ | $+0.02\pm 0.14^{68}$ | $0.21\pm 0.012^{68}$ | $-$
WASP-52b | $174.818^{+1.343}_{-1.323}$ | $\rm K2V^{70}$ | $5000\pm 100^{70}$ | $0.4\pm 0.3^{70}$ | $0.79\pm 0.02^{70}$ | $0.87\pm 0.03^{70}$ | $+0.03\pm 0.12^{70}$ | $3.6\pm 0.9^{70}$ | $-4.4\pm 0.2^{70}$
WASP-127b | $159.507^{+1.210}_{-1.191}$ | $\rm G5V^{72}$ | $5620\pm 85^{72}$ | $11.41\pm 1.80^{72}$ | $1.39\pm 0.03^{72}$ | $1.08\pm 0.03^{72}$ | $-0.18\pm 0.06^{72}$ | $0.3\pm 0.2^{72}$ | $-$
WASP-177b | $176.818^{+2.428}_{-2.364}$ | $\rm K2V^{74}$ | $5017\pm 70^{74}$ | $2.5\pm 1.7^{74}$ | $0.885\pm 0.046^{74}$ | $0.876\pm 0.038^{74}$ | $0.25\pm 0.04^{74}$ | $2.9\pm 0.2^{74}$ | $-$
HAT-P-26b | $141.837^{+1.152}_{-1.133}$ | $\rm K1V^{76}$ | $5079\pm 88^{76}$ | $9.0^{+3.0^{76}}_{-4.9}$ | $0.788^{+0.098^{76}}_{-0.043}$ | $0.816\pm 0.033^{76}$ | $-0.04\pm 0.08^{76}$ | $1.8\pm 0.5^{76}$ | $-4.992^{76}$
NGTS-5b | $306.779^{+2.601}_{-2.558}$ | $\rm K2V^{78}$ | $4987\pm 41^{78}$ | $-$ | $0.739^{+0.014\;78}_{-0.012}$ | $0.661^{+0.068\;78}_{-0.061}$ | $0.12\pm 0.10^{78}$ | $-$ | $-4.63^{77}$
TOI-1807b | $42.5775^{+0.0622}_{-0.0620}$ | $\rm K3V^{79}$ | $4730\pm 75^{80}$ | $0.3\pm 0.08^{80}$ | $0.690\pm 0.036^{80}$ | $0.76\pm 0.03^{80}$ | $-0.04\pm 0.02^{80}$ | $4.2\pm 0.5^{80}$ | $-4.363\pm 0.002^{80}$
TOI-2076b | $41.9091^{+0.0528}_{-0.0526}$ | $\rm K0V^{79}$ | $5187^{+54\;81}_{-53}$ | $0.2\pm 0.05^{81}$ | $0.7622^{+0.0157\;81}_{-0.0159}$ | $0.850^{+0.025\;81}_{-0.026}$ | $-0.032^{+0.048\;81}_{-0.047}$ | $4.3\pm 0.5^{81}$ | $-4.271\pm 0.056^{81}$
TOI-1430.01 | $41.17\pm 0.04$ | $\rm K1V^{82}$ | $5067\pm 60^{82}$ | $0.165\pm 0.03^{82}$ | $0.784^{+0.018^{82}}_{-0.014}$ | $0.85\pm 0.10^{82}$ | $-$ | $6.9^{82}$ | $-$
TOI-1683.01 | $51.19\pm 0.14^{82}$ | $\rm K4V^{82}$ | $4539\pm 100^{82}$ | $0.5\pm 0.15^{82}$ | $0.636^{+0.031^{82}}_{-0.017}$ | $0.69\pm 0.09^{82}$ | $-$ | $2.8^{82}$ | $-$
WASP-48b | $454.144^{+4.465}_{-4.381}$ | $\rm F^{83}$ | $5920\pm 150^{83}$ | $7.9^{+2.0\;83}_{-1.6}$ | $1.75\pm 0.09^{83}$ | $1.19\pm 0.05^{83}$ | $-0.12\pm 0.12^{83}$ | $12.2\pm 0.7^{83}$ | $-5.135^{84}$

Note. — Values taken from NASA Exoplanet
Archive777https://exoplanetarchive.ipac.caltech.edu unless otherwise noted.
Error bars are taken from the literature or, if missing, estimated by taking
the average error from the remaining data. See page 16 for references.

=2.25in

Table 6: Planetary parameters for exoplanets with published helium results.

Planet | Radius ($R_{J}$) | Mass ($M_{J}$) |  $a$ (au) |  $T_{\rm eq}$ (K) |  $\rm log$ $g_{P}$ ($\rm cm\;s^{-2}$) | $\delta_{R_{P}}$ | $\delta_{R_{P}}/H_{eq}$ | Detection?
---|---|---|---|---|---|---|---|---
WASP-107b | $0.94\pm 0.02^{1}$ | $0.096\pm 0.005^{2}$ | $0.055\pm 0.001^{1}$ | $770\pm 60^{1}$ | $2.49\pm 0.05^{1}$ | $1.12\pm 0.10^{3}$ | $84.2\pm 6.6^{3}$ | Yes
WASP-69b | $1.057\pm 0.047^{4}$ | $0.260\pm 0.017^{4}$ | $0.04525\pm 0.00053$ | $963\pm 18$ | $2.726\pm 0.046^{4}$ | $0.74\pm 0.13^{5}$ | $85.6\pm 1.6^{5}$ | Yes
HAT-P-11b | $0.422\pm 0.014^{6}$ | $0.081\pm 0.009^{6}$ | $0.0530^{+0.0002}_{-0.0008}$ | $878\pm 15$ | $3.05\pm 0.06^{6}$ | $1.06\pm 0.11^{7}$ | $113.6\pm 1.9^{7}$ | Yes
HD 189733b | $1.138\pm 0.027^{10}$ | $1.123\pm 0.045^{10}$ | $0.0313\pm 0.0004^{8}$ | $1201\pm 13^{23}$ | $3.3\pm 0.03^{10}$ | $0.17\pm 0.06^{12}$ | $69.5\pm 0.8^{12}$ | Yes
WASP-12b | $1.825\pm 0.091^{10}$ | $1.39\pm 0.12^{10}$ | $0.02312^{+0.00094^{10}}_{-0.00100}$ | $2516\pm 36^{13}$ | $2.99\pm 0.03^{13}$ | $0.002\pm 0.134^{15}$ | $0.29\pm 0.004^{15}$ | No
HAT-P-18b | $0.995\pm 0.052^{16}$ | $0.197\pm 0.013^{16}$ | $0.0559\pm 0.0007^{16}$ | $852\pm 28^{16}$ | $2.69\pm 0.05^{16}$ | $0.12\pm 0.15^{17}\tablenotemark{*}$ | $13.3\pm 0.4^{17}\tablenotemark{*}$ | Yes
HD 209458b | $1.359^{+0.016^{10}}_{-0.019}$ | $0.682^{+0.014^{10}}_{-0.015}$ | $0.0490\pm 0.0020^{18}$ | $1459\pm 12^{22}$ | $2.963\pm 0.005^{23}$ | $0.29\pm 0.10^{24}$ | $50.0\pm 0.4^{24}$ | Yes
55 Cnc e | $0.1673\pm 0.00287^{27}$ | $0.0251\pm 0.00104^{27}$ | $0.01544\pm 0.00005^{27}$ | $1990^{28}$ | $3.35\pm 2.00$ | $0.32\pm 0.10^{28}$ | $12.1\pm 0.6^{28}$ | No
GJ 1214b | $0.254\pm 0.018^{32}$ | $0.0197\pm 0.0027^{32}$ | $0.01411\pm 0.00032^{32}$ | $604\pm 19^{29}$ | $2.88\pm 2.07$ | $0.046\pm 0.148^{33}$ | $2.9\pm 0.5^{33}$ | No
GJ 9827d | $0.185\pm 0.0125^{35}$ | $0.016^{+0.006}_{-0.004}$ | $0.05615\pm 0.00091^{35}$ | $680\pm 25^{35}$ | $3.07\pm 0.12^{35}$ | $0.34\pm 0.27^{33}$ | $21.4\pm 0.8^{33}$ | No
HD 97658b | $0.2055\pm 0.009814^{36}$ | $0.0246\pm 0.00173^{36}$ | $0.0831\pm 0.0011^{38}$ | $751\pm 12^{37}$ | $3.16\pm 2.09$ | $0.90\pm 0.26^{33}$ | $71.1\pm 6.1^{33}$ | No
GJ 436b | $0.366\pm 0.014^{41}$ | $0.0799^{+0.0066^{40}}_{-0.0063}$ | $0.0308\pm 0.0013^{41}$ | $649\pm 60^{23}$ | $3.17\pm 2.13$ | $0.26\pm 0.14^{5}$ | $43.0\pm 5.6^{5}$ | No
V1298b | $0.916^{+0.052^{42}}_{-0.047}$ | $-$ | $0.1688\pm 0.0026^{42}$ | $677\pm 22^{42}$ | $-$ | $0.036\pm 0.218^{43}$ | $-$ | No
V1298d | ${0.572^{+0.040}_{-0.035}}^{42}$ | $-$ | $0.1083\pm 0.0017^{42}$ | $845\pm 27^{42}$ | $-$ | $0.10\pm 12^{43}$ | $-$ | Yes
GJ 3470b | $0.346\pm 0.029^{44}$ | ${0.03958^{+0.00412}_{-0.00403}}^{44}$ | $0.0348\pm 0.0014^{45}$ | $615\pm 16^{45}$ | $2.91\pm 2.04$ | $0.93\pm 0.32^{46}$ | $85.7\pm 11.7^{46}$ | Yes
KELT-9b | ${1.891^{+0.061}_{-0.053}}^{47}$ | $2.88\pm 0.84^{47}$ | $0.03462\pm 0.00110^{47}$ | $4050\pm 180^{47}$ | $3.30\pm 0.11^{47}$ | $0.22\pm 0.11^{5}$ | $40.8\pm 1.8^{5}$ | No
GJ 9827b | ${0.1407^{+0.0024}_{-0.0028}}^{48}$ | $0.0154\pm 0.0015^{48}$ | ${0.01880^{+0.00020}_{-0.00014}}^{48}$ | $1114\pm 46^{49}$ | $3.29\pm 2.12$ | $1.66\pm 0.82^{50}$ | $81.5\pm 6.5^{50}$ | No
WASP-80b | ${0.952^{+0.026}_{-0.027}}^{10}$ | ${0.540^{+0.036}_{-0.035}}^{10}$ | ${0.03427^{+0.00096}_{-0.00100}}^{10}$ | $825\pm 19^{53}$ | $3.178\pm 0.013^{51}$ | $0.11\pm 0.08^{54}$ | $39.1\pm 0.9^{54}$ | No
WASP-76b | $1.83\pm 0.06^{53}$ | $0.92\pm 0.03^{53}$ | $0.0330\pm 0.0005^{53}$ | $2160\pm 40^{53}$ | $2.80\pm 0.02^{53}$ | $0.32\pm 0.10^{56}$ | $34.2\pm 0.6^{56}$ | No
TRAPPIST-1b | ${0.09956^{+0.00125}_{-0.00107}}^{58}$ | $0.004323\pm 0.000217^{58}$ | $0.01154\pm 0.00010^{58}$ | $400\pm 9^{57}$ | $3.03\pm 1.71^{58}$ | $0.040\pm 0.115^{60}$ | $2.1\pm 0.1^{60}$ | No
TRAPPIST-1e | ${0.0821^{+0.0012}_{-0.0011}}^{58}$ | $0.00218\pm 0.00007^{58}$ | $0.02925\pm 0.00250^{58}$ | $251.3\pm 4.9^{61}$ | $2.90\pm 1.38^{58}$ | $0.070\pm 0.161^{60}$ | $3.6\pm 0.1^{60}$ | No
TRAPPIST-1f | ${0.09323^{+0.00116}_{-0.00107}}^{58}$ | $0.003269\pm 0.000098^{58}$ | $0.03849\pm 0.00033^{58}$ | $219.0\pm 4.2^{61}$ | $2.97\pm 1.38^{58}$ | $0.020\pm 0.132^{60}$ | $1.6\pm 0.1^{60}$ | No
HD 63433b | $0.192\pm 0.009^{62}$ | $-$ | ${0.0719^{+0.0031}_{-0.0044}}^{62}$ | $969\pm 13^{54}$ | $-$ | $2.42\pm 0.57^{63}$ | $-$ | No
HD 63433c | $0.238\pm 0.011^{62}$ | $-$ | ${0.1458^{+0.0062}_{-0.0101}}^{62}$ | $680\pm 9^{54}$ | $-$ | $1.82\pm 0.46^{63}$ | $-$ | No
HAT-P-32b | $1.789\pm 0.025^{10}$ | $0.75\pm 0.13^{10}$ | ${0.03427^{+0.00040}_{-0.00042}}^{10}$ | $1786\pm 26^{64}$ | $2.82\pm 0.10^{64}$ | $0.83\pm 0.05^{65}$ | $108.8\pm 1.6^{65}$ | Yes
HD 73583b | $0.249\pm 0.009^{66}$ | ${0.0321^{+0.0107}_{-0.0098}}^{66}$ | ${0.0604^{+0.0027}_{-0.0026}}^{66}$ | $714\pm 21^{66}$ | $3.11\pm 2.66^{66}$ | $1.32\pm 0.17^{67}$ | $118.3\pm 42.1^{67}$ | Yes
TOI-2136b | $0.20\pm 0.0062^{68}$ | $0.015\pm 0.0098^{68}$ | $0.0533\pm 0.0015^{68}$ | $378\pm 13^{68}$ | $2.98\pm 2.8^{68}$ | $1.25\pm 0.89^{68}$ | $125.3\pm 82.9^{68}$ | No
WASP-52b | $1.27\pm 0.03^{70}$ | $0.46\pm 0.02^{70}$ | $0.0272\pm 0.0003^{70}$ | $1315\pm 35^{70}$ | $2.81\pm 0.03^{70}$ | $0.50\pm{0.08}^{71}$ | $62.6\pm 1.7^{71}$ | Yes
WASP-127b | $1.37\pm 0.04^{72}$ | $0.18\pm 0.02^{72}$ | $0.0520\pm 0.0005^{72}$ | $1400\pm 24^{72}$ | $2.33\pm 0.06^{72}$ | $0.19\pm 0.17^{73}$ | $7.8\pm 0.1^{73}$ | No
WASP-177b | ${1.58^{+0.66}_{-0.36}}^{74}$ | $0.508\pm 0.038^{74}$ | $0.03957\pm 0.00058^{74}$ | $1142\pm 32^{74}$ | $2.67\pm 0.31^{74}$ | $0.17\pm{0.85}^{71}$ | $22.6\pm 0.6^{71}$ | No
HAT-P-26b | $0.565^{+0.072\;76}_{-0.032}$ | $0.059\pm 0.007^{76}$ | $0.0479\pm 0.0006^{76}$ | $1001^{+66\;76}_{-37}$ | $2.65^{+0.08\;76}_{-0.10}$ | $0.25\pm{0.37}^{77}\tablenotemark{*}$ | $12.7\pm 0.8^{77}\tablenotemark{*}$ | Yes
NGTS-5b | $1.136\pm 0.023^{78}$ | $0.229\pm 0.037^{78}$ | $0.0382\pm 0.0013^{78}$ | $952\pm 24^{78}$ | $2.643^{+0.066\;78}_{-0.078}$ | $0.19\pm 0.11^{77}\tablenotemark{*}$ | $19.5\pm 0.5^{77}\tablenotemark{*}$ | Yes
TOI-1807b | $0.122\pm 0.008^{80}$ | $0.00809\pm 0.00157^{80}$ | $0.0120\pm 0.0003^{80}$ | $2100^{+39\;81}_{-40}$ | $3.13\pm 2.20$ | $7.58\pm 25.52^{79}$ | $118.3\pm 14.1^{79}$ | No
TOI-2076b | $0.223\pm 0.005^{81}$ | $-$ | $0.0631\pm 0.0027^{81}$ | $870\pm 13^{81}$ | $-$ | $2.50\pm 0.13^{82}$ | $-$ | Yes
TOI-1430.01 | $0.188\pm 0.018^{82}$ | $-$ | $0.0705^{82}$ | $813^{82}$ | $-$ | $2.41\pm 0.33^{82}$ | $-$ | Yes
TOI-1683.01 | $0.205\pm 0.027^{82}$ | $-$ | $0.036^{82}$ | $927^{82}$ | $-$ | $1.94\pm{0.45}^{82}$ | $-$ | Yes
WASP-48b | $1.67\pm 0.1^{83}$ | $0.984\pm 0.085^{83}$ | $0.0344\pm 0.0026^{83}$ | $2035\pm 52^{83}$ | $2.91\pm 0.06^{83}$ | $0.15\pm 0.28$ | $16.3\pm 0.4$ | No

Note. — Values taken from NASA Exoplanet Archive unless otherwise noted. Error
bars are taken from the literature or, if missing, estimated by taking the
average error from the remaining data. See page 16 for references.

References for Table 5: 1\. Anderson et al. (2017); 2. Piaulet et al. (2021);
3. Kirk et al. (2020); 4. Anderson et al. (2014); 5. Nortmann et al. (2018);
6. Bakos et al. (2010); 7. Allart et al. (2018); 8. Bouchy et al. (2005); 9.
Boyajian et al. (2015); 10. Bonomo et al. (2017); 11. Barstow et al. (2017);
12. Salz et al. (2018); 13. Hebb et al. (2009); 14. Turner et al. (2016); 15.
Kriedberg & Oklopčić (2018); 16.Hartman et al. (2011a); 17. Paragas et al.
(2021); 18. del Burgo & Allende Prieto (2016); 19. Melo et al. (2006); 20.
Santos et al. (2004); 21. Queloz et al. (2000); 22. Southworth (2010); 23.
Torres et al. (2008); 24. Alonso-Floriano et al. (2019); 25. von Braun et al.
(2011); 26. Yee et al. (2017); 27. Bourrier et al. (2018a); 28. Zhang et al.
(2021); 29. Gillon et al. (2014); 30. Lalitha et al. (2014); 31. Charbonneau
et al. (2009); 32. Harpsøe et al. (2013); 33. Kasper et al. (2020); 34.
Niraula et al. (2017); 35. Rodriguez et al. (2018); 36. Guo et al. (2020); 37.
Ellis et al. (2021); 38. Howard et al. (2011); 39. Salz et al. (2015); 40.
Bourrier et al. (2018b); 41. Lanotte et al. (2014); 42. David et al. (2019);
43. Vissapragada et al. (2021); 44. Kosiarek et al. (2019); 45. Bonfils et al.
(2012); 46. Palle et al. (2020); 47. Gaudi et al. (2017); 48. Rice et al.
(2019); 49. Prieto-Arranz et al. (2018); 50. Carleo et al. (2021); 51. Triaud
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Gillon et al. (2016); 58. Agol et al. (2021); 59. Burgasser & Mamajek (2017);
60. Krishnamurthy et al. (2021); 61. Gillon et al. (2017); 62. Mann et al.
(2020); 63. Zhang et al. (2022c); 64. Hartman et al. (2011b); 65. Czesla et
al. (2022); 66. Barragán et al. (2022); 67. Zhang et al. (2022b); 68. Kawauchi
et al. (2022); 69. Gan et al. (2022); 70. Hébrard et al. (2013);71. Kirk et
al. (2022); 72. Lam et al. (2017); 73. dos Santos et al. (2020); 74. Turner et
al. (2019); 75. Sreejith et al. (2020); 76. Hartman et al. (2011a); 77.
Vissapragada et al. (2022); 78. Eigmüller et al. (2019); 79. Gaidos et al.
(2023); 80. Nardiello et al. (2022); 81. Hedges et al. (2021); 82. Zhang et
al. (2023); 83. Enoch et al. (2011); 84. O’Rourke et al. (2014); 85. Boro
Saikia et al. (2018)

We would like to thank our reviewer for their very helpful and thoughtful
comments. Their insightful improved the quality of this paper. A.O. gratefully
acknowledges support from the Dutch Research Council NWO Veni grant.

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