Keck/NIRSPEC Studies of He i in the Atmospheres of Two Inflated Hot Gas Giants Orbiting K Dwarfs: WASP-52b and WASP-177b

WASP-52b, discovered by Hébrard et al. (2013), is an inflated hot Saturn (R_P = 1.253 ± 0.027 R_Jup, M_P = 0.434 ± 0.024 M_Jup, T_eq = 1315 ± 26 K, Mancini et al. 2017) orbiting a young and active K2 dwarf (age $=\,{0.4}_{-0.2}^{+0.3}$ Gyr, $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }=-4.4\pm 0.2$; Hébrard et al. 2013).

Previous studies of the planet's atmosphere in transmission are broadly consistent with muted spectral features, likely due to clouds in the planet's atmosphere (Kirk et al. 2016; Chen et al. 2017; Louden et al. 2017; Mancini et al. 2017; Alam et al. 2018; May et al. 2018); however, water has been detected in the near-IR (Bruno et al. 2018, 2020), and Na, K, and Hα have been detected at high resolution (Chen et al. 2017, 2020). Additionally, these previous studies have revealed in-transit light-curve anomalies from the optical to the near-IR associated with the planet occulting stellar magnetic regions (Kirk et al. 2016; Louden et al. 2017; Mancini et al. 2017; Bruno et al. 2018; May et al. 2018), highlighting the active nature of the host. Furthermore, WASP-52b is a James Webb Space Telescope (JWST) Guaranteed Time Observation target for transit and eclipse observations (PIDs: 1201 and 1224).

In Kirk et al. (2020), we identified WASP-52b as a promising target for studies of atmospheric escape via helium due to its low surface gravity, large atmospheric scale height, and K-type host. Recently, Vissapragada et al. (2020) presented a photometric transit observation of WASP-52b in a narrow filter (FWHM = 0.635 nm) centered on the He i triplet. In this filter, they measured the planet's transit depth to be 2.97% ± 0.13%, which was 1.6σ deeper than the transit depth observed by Alam et al. (2018) between 898.5 and 1030.0 nm.

In this study, we present the first high-resolution observation and detection of He i in WASP-52b's atmosphere, which extends over 66 ± 5 atmospheric scale heights (H).

WASP-177b, discovered by Turner et al. (2019), is another inflated hot gas giant (${R}_{{\rm{P}}}={1.58}_{-0.36}^{+0.66}$ R_Jup, M_P = 0.508 ± 0.038 M_Jup, T_eq = 1142 ± 32 K) orbiting an old K2 dwarf (age =9.7 ± 3.9 Gyr). WASP-177b is in a grazing transit configuration with an impact parameter of ${0.980}_{-0.060}^{+0.092}$ (Turner et al. 2019). The WASP data reveal the stellar photometry to modulate with a period of 14.86 ± 0.14 days and amplitude of 5 ± 1 mmag, indicating stellar magnetic regions. There have been no further studies of this planet.

Similar to WASP-52b, we also identified WASP-177b as a promising target for helium studies in Kirk et al. (2020) due to the planet's low surface gravity and large scale height, and the K-type host star.

In this study, we present the first atmospheric follow-up of WASP-177b. We see tentative hints of He i absorption extending across 23 ± 5 H; however, as we discuss in Section 4.3, we do not interpret this as significant evidence for He i absorption.

The rest of the paper is structured as follows. In Sections 2 and 3 we describe our observations and data reduction. In Section 4 we detail our data analysis and results, including our helium transmission spectra in Section 4.3. In Section 5 we present our 1D atmospheric escape modeling of WASP-52b and WASP-177b's He i transmission spectra. We discuss our results in Section 6 and conclude in Section 7.

To reduce our NIRSPEC data we used the NIRSPEC-specific REDSPEC software (McLean et al. 2003, 2007), which is written in IDL. This was the same software as we used in Kirk et al. 2020 to reduce our WASP-107b data.

In short, REDSPEC performs dark and bias subtraction, flat-fielding, bad pixel interpolation, and standard spectral extraction following the spatial rectification of tilted spectra on the detector.

For the dark and flat-field corrections we median-combined the 22 darks and 22 flats to create a master dark and master flat for each night. We restricted our analysis to spectral orders 70 (1.080–1.101 μm) and 71 (1.065–1.086 μm) since these are the orders that cover the helium triplet at 1.0833 μm (wavelength in vacuum). For WASP-52b, we achieved an average signal-to-noise ratio of 128 per pixel per exposure for order 70, and 134 for order 71. For WASP-177b these values were 94 and 97, respectively. For both nights, and for both orders, we used a fourth-order polynomial to correct for the tilted nature of the spectra on the detector.

The next step in REDSPEC is to perform the wavelength calibration, which we did using our arc lamp spectra. For WASP-52b, we found that a cubic polynomial was able to map the measured locations of the arc lines to the theoretical values to within 0.01 pixels.

For WASP-177b, we were unable to get a satisfactory wavelength solution from the arc lamps. This was because we chose to keep the slit position angle fixed at 12° to avoid a nearby star falling within the slit. This had the effect of shifting the stellar spectra and arc lamps, making accurate wavelength calibration difficult from the arcs. For WASP-52b, we allowed the sky to rotate on the slit, which gives the most precise radial velocities for NIRSPEC, ⁸ and found the arc solution to be satisfactory. For WASP-177b, we instead used the OH emission lines in the science spectra for our wavelength calibration.

We then extracted the spectra in differenced AB nod pairs, to remove the sky background and OH emission lines, using an aperture of 15 pixels. For WASP-177's spectra, where we did use the "Thin" blocking filter (Section 2), we additionally had to perform a fringing correction. We did this using REDSPEC's fringing correction tool, which involved manually identifying and removing peaks in the power spectra calculated for each stellar spectrum. The flux uncertainties were calculated by considering the photon noise, read noise, dark current, and sky background.

Due to the intermittent clouds in the first six frames of WASP-52b's observations, the sky background brightness varied between the A and B nod positions. This meant that a straightforward A–B subtraction did not adequately remove the OH emission lines from these frames. We experimented by adding an extra step in our spectral extraction process, by fitting the sky background with polynomials in the cross-dispersion direction, but found that this led to greater noise in the stellar spectra due to the uncertainty in the sky polynomial fit. Ultimately we found that our sigma-clipping step (Section 3.2) was able to remove the residual OH emission from these six frames. We also note that the OH emission lines were well seperated from the He i triplet for this observation (Figure 1).

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Following the extraction of the wavelength-calibrated stellar spectra using REDSPEC, we then post-processed our data to continuum normalize our spectra, correct for residual wavelength shifts, and remove telluric (primarily H₂O) absorption.

To continuum normalize our data, we used iSpec (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma 2019) to fit cubic splines to a portion of each order's wavelength range (10800–10950 Å for order 70 and 10700–10850 Å for order 71), and masked the He i triplet from our continuum calculation. We focused on these portions to improve our continuum normalization in the vicinity of the He i triplet (at 10833 Å) while leaving enough telluric absorption features to allow for accurate correction.

To remove the telluric absorption, we used molecfit (Kausch et al. 2015; Smette et al. 2015), which has been used in a number of high-resolution ground-based transmission spectroscopy studies (e.g., Allart et al. 2017, 2019; Nortmann et al. 2018; Kirk et al. 2020). molecfit uses Global Data Assimilation System ⁹ profiles which contain weather information for user-specified observatory coordinates, airmasses, and times. It then models the telluric absorption lines in the observed spectra using this information.

For WASP-52, order 70, we used six telluric absorption lines, free of significant stellar absorption, to constrain the molecfit model. For WASP-177, order 70, we used four telluric absorption lines to constrain the molecfit model.

We chose to fit only for the atmospheric H₂O content, with CH₄ and O₂ fixed. We also fixed the FWHM of the Lorentzian used to fit the telluric absorption to 3.5 pixels based upon our experience in analyzing NIRSPEC data, while also to overcome the impacts of the poorly removed OH emission lines in the six frames at the beginning of WASP-52b's observations (Section 3). We did this as the residual OH emission impacted molecfit's ability to model the nearby H₂O absorption if the FWHM was allowed to vary (Figure 1). We note that Zhang et al. (2021) similarly fixed this parameter to 3.5 pixels in their molecfit modeling of NIRSPEC data.

Given that order 71's wavelength coverage included fewer telluric absorption lines, we were not able to obtain a satisfactory fit to order 71 in isolation. Instead we found that using the best-fitting parameters from order 70 (i.e., depth of the water column etc.) gave good fits when applied to order 71.

Figure 1 shows example WASP-52 and WASP-177 spectra before and after the telluric correction using molecfit. This also demonstrates the proximity of the He i triplet to OH emission lines on both nights. However, aside from the first six frames for WASP-52b, our A–B nod subtraction effectively removed these emission lines from our science spectra.

There appear to be some residual oscillations in the example spectrum of WASP-177 (Figure 1, bottom panel). One possibility behind these is residual fringing from our use of the Thin blocking filter (Section 2), despite our fringing correction. However, the amplitudes of oscillations in the master spectra of WASP-177 (Figure 3) are not significantly greater than those of WASP-52 (Figure 2), for which we did not use the Thin blocking filter and thus avoided significant fringing. Therefore, we do not believe fringing is significantly affecting our results for WASP-177b.

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Following the removal of telluric absorption from our spectra, we then shifted each of our spectra from the observer frame into the stellar rest frames and checked the accuracy of our wavelength solution. To shift our spectra into the stellar frame we corrected for the barycentric velocity, via astropy's (Astropy Collaboration et al. 2013, 2018) implementation of Wright & Eastman (2014)'s method, in addition to the systemic velocity and stellar reflex velocity caused by the close-in gas giant (using the parameters in Table 1). To confirm our wavelength solutions, we cross-correlated our stellar spectra with Phoenix (Husser et al. 2013) model spectra for both stars. We found in both cases the wavelength solutions needed small corrections (∼1 km s⁻¹). Despite these being small corrections (∼1/3 pixel) we applied them since we are sensitive to velocity shifts in the planets' He i absorption of ∼1 km s⁻¹ (Section 4.3).

Table 1. The System Parameters of WASP-52b and WASP-177b Used in the Data Reduction and Analysis

Parameter	Symbol	Unit	WASP-52b	WASP-177b
Time of mid-transit	T0	BJD	2456862.79776 ± 0.00016 a	2457994.37140 ± 0.00028
Orbital period	P	d	1.74978119 ± 0.00000052 a	3.071722 ± 0.000001
Orbital inclination	i	◦	85.15 ± 0.06 a	${84.14}_{-0.83}^{+0.66}$
Continuum transit depth	${({R}_{p}/{R}_{* })}^{2}$		0.02686 ± 0.00016	${0.0185}_{-0.0014}^{+0.0035}$
Semimajor axis	a	au	0.02643 ± 0.00055 a	0.03957 ± 0.00058
Scaled semimajor axis	a/R*		7.23 ± 0.03 a	${9.61}_{-0.53}^{+0.42}$
Stellar mass	M*	M⊙	0.804 ± 0.050 a	0.876 ± 0.038
Planet mass	Mp	MJ	0.434 ± 0.024 a	0.508 ± 0.038
Planet radius	Rp	RJ	1.253 ± 0.027 a	${1.58}_{-0.36}^{+0.66}$
Planet surface gravity	$\mathrm{log}{g}_{p}$	cgs	2.84 ± 0.02 a	${2.67}_{-0.31}^{+0.22}$
Planet equilibrium temperature	Teq	K	1315 ± 26 a	1142 ± 32
Semi-amplitude	K*	m s−1	84.3 ± 3.0 b	77.3 ± 5.2
Systemic velocity	γ	km s−1	0.48 ± 0.33 d	−6.41 ± 1.18 d
Stellar effective temperature	Teff	K	5000 ± 100 b	5017 ± 70
Stellar metallicity	[Fe/H]	dex	0.03 ± 0.12 b	0.25 ± 0.04
Stellar surface gravity	$\mathrm{log}g$	cgs	4.553 ± 0.010 a	4.486 ± 0.049

Notes. These values are from Hébrard et al. (2013), Mancini et al. (2017), and Alam et al. (2018) for WASP-52b, and Turner et al. (2019) for WASP-177b. The systemic velocities are from Gaia DR2 (Gaia Collaboration et al. 2016, 2018).

^a Mancini et al. (2017). ^b Hébrard et al. (2013). ^c Alam et al. (2018). ^d Gaia DR2 (Gaia Collaboration et al. 2016, 2018).

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At this stage, we had normalized, telluric-corrected stellar spectra in the stellar rest frame. However, we still needed to account for the poorly removed OH emission in WASP-52b's first six frames and cosmic rays in the spectra of both WASP-52 and WASP-177. To do this, we performed a sigma-replacement method (e.g., Allart et al. 2017). Specifically, we made a median-combined spectrum for both WASP-52 and WASP-177 and compared each spectral frame to the combined median. We then replaced any data points that deviated by >4 median absolute deviations from the combined median, with the corresponding median-combined data point.

To avoid clipping out real planetary signal from our spectra, we masked the spectra within ±20 km s⁻¹ of the He i triplet in the planets' rest frames. Instead, for outliers in the He i triplet in the planets' rest frames, we removed whole frames from our analysis based on a fit to the planets' He i light curves (see Appendix A). This meant that we were neither clipping real signal nor being biased by outlying frames. By this method we removed frames 7 and 10 from order 70, and frames 8, 11, and 15 from order 71 for WASP-52 (10% of our spectra). For WASP-177 we removed no frames from order 70 and frames 47 and 56 from order 71 (2% of our spectra).

Our data analysis started with generating master in- and out-of-transit spectra so that we could obtain the in-transit excess absorption signal. The in- and out-of-transit spectra were constructed by taking the weighted mean of spectra that fell between the second and third contact points, and before and after the first and fourth contact points of the transit, respectively. These contact points were determined using the ephemerides of Mancini et al. (2017) for WASP-52b and Turner et al. (2019) for WASP-177b.

Figures 2 and 3 show the individual and master spectra for both WASP-52 and WASP-177. In these figures, we have combined orders 70 and 71 into a single spectrum. Figures 2 and 3 demonstrate that there is excess absorption of ∼4% centered on He i for WASP-52b but no immediately apparent excess absorption for WASP-177b. We investigate this excess absorption in the following subsections.

Figures 4 and 5 show the phase-resolved excess absorption for WASP-52b and WASP-177b. These figures show each spectral frame divided by the master out-of-transit spectrum. This was performed separately for order 70 and 71 for each planet. However, we then combined the residual spectra from both orders for our analysis. For WASP-52b (Figure 4), there is clear excess in-transit absorption while there is no significant phase-resolved absorption for WASP-177b (Figure 5).

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Figure 6 shows the velocity, in the stellar frame, of WASP-52b's peak excess He i absorption during its transit, calculated via fitting Gaussians to the He i transmission spectrum in each frame. This demonstrates it is consistent with both the planet's orbital velocity and no velocity shift, when considering the resolution element of NIRSPEC (12 km s⁻¹). We note that the final spectrum is at low signal-to-noise and so do not take this as evidence for blueshifted material.

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By shifting the excess absorption to each planet's rest frame (e.g., Wyttenbach et al. 2015, 2017; Allart et al. 2017 ), we were able to construct the He i transmission spectra for both WASP-52b and WASP-177b. These are shown in Figures 7 and 8.

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Similar to our treatment of WASP-107b's transmission spectrum in Kirk et al. (2020), we initially analyzed the transmission spectra by fitting the summation of two Gaussians (which we refer to as a "double Gaussian") to quantify the excess absorption and wavelength shift. One Gaussian was centered on the weaker, bluer line at 10832.06 Å with the other centered on the two stronger, and blended, lines at 10833.22 and 10833.31 Å (vacuum wavelengths). We fitted for a wavelength shift (Δλ) in the means of the two Gaussians to account for potential Doppler-shifted absorption. This wavelength shift was shared by both components of the Gaussian and was defined relative to the vacuum wavelengths of the helium triplet. The FWHM of the two Gaussians were set to be equal, given we expect the same instrumental and velocity broadening to apply to both components of the He i absorption. The amplitudes of the two Gaussians (A₁ and A₂) were allowed to vary independently. We additionally fitted for a parameter (C) to account for imperfect normalization of the transmission spectrum, which effectively moved the double Gaussian up and down in y.

In total, the transmission spectrum was fitted with five parameters (FWHM, Δλ, A₁, A₂, and C). We used Markov chain Monte Carlo (MCMC) to explore the parameter space via the emcee Python package (Foreman-Mackey et al. 2013). We ran the MCMC with 42 walkers for 10,000 steps each and discarded the first 5000 steps as burn-in. Following this initial run, we then rescaled the photometric uncertainties so that the best-fitting model gave a reduced χ² = 1 to account for red noise not taken into account by the photometric uncertainties. We then ran a second MCMC with the same setup.

For WASP-52b, we find the amplitude of the two Gaussians to be ${0.26}_{-0.17}^{+0.24}$ and 3.44% ± 0.31% (11σ), respectively. We detected no velocity offset in WASP-52b's absorption (Δv = 0.00 ± 1.19 km s⁻¹).

For WASP-177b, the transmission spectrum shows evidence for excess absorption around the He i triplet, although at a lower amplitude than for WASP-52b, which is also consistent with the amplitude of systematic noise in the data (Figure 8). Nevertheless, we also fitted WASP-177b's transmission spectrum with the same double Gaussian model, finding amplitudes of ${0.25}_{-0.17}^{+0.23}$% and ${1.28}_{-0.29}^{+0.30}$%. However, this absorption is redshifted by +6.02 ± 1.88 km s⁻¹.

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The systematic around the Si line in WASP-177b's transmission spectrum, and this apparent redshifted He absorption, may be due to imperfect wavelength calibration for this night. This is apparent when looking at the master-in and master-out spectra of WASP-177 (Figure 3). Given the systematics in WASP-177b's transmission spectrum, we encourage additional observations to test the repeatability of this signal.

Taking the residual spectra (stellar spectra divided by the master out-of-transit spectrum) in the planet rest frame, we generated light curves by integrating the residual flux in a bin centered on the He i triplet. For the purposes of determining the transit depth as a function of bin width, we generated multiple light curves by varying the bin width from the resolution of NIRSPEC (0.43 Å ≈ 4 pixels) to 15 Å in increments of 0.5 Å. For WASP-52b, we additionally created a light curve using a bin of width 6.35 Å to match the FWHM of the filter used by Vissapragada et al. (2020).

For both WASP-52b and WASP-177b, we fixed the planets' orbital periods, time of mid-transits, scaled semimajor axes, and inclinations to the values given in Table 1. We fixed the quadratic limb-darkening coefficients to values calculated by LDTk (Parviainen & Aigrain 2015), using the stellar parameters listed in Table 1. We fitted only for R_P /R_*.

We used batman (Kreidberg 2015) to generate the light curves and fitted this using MCMC, again with emcee (Foreman-Mackey et al. 2013). In both cases we ran 20 walkers for 2000 steps each, discarding the first 1000 as burn-in. We then again rescaled the photometric uncertainties to give a reduced χ² = 1 and then ran the MCMC chains for a second time.

Figures 9 and 10 show the light curves corresponding to the narrowest-wavelength bins multiplied by the continuum light curves (from Alam et al. 2018 for WASP-52b and Turner et al. 2019 for WASP-177b). This multiplication is necessary to convert from excess absorption to absolute absorption. These figures also include the change in transit depth as a function of bin width.

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Fitting WASP-52b's helium light curve, we find that the excess transit depth is 3.44% ± 0.36% in our narrowest bin, which is consistent with our transmission spectrum (Figure 7). The light curve is largely symmetric about the midpoint. To estimate the excess transit duration we observe, we resampled our fitted transit light curve (red line, Figure 9) to a time resolution of 30 s. Comparing this with the transit duration corresponding to Alam et al. (2018)'s optical light curve, we find that WASP-52b's transit duration is 11 minutes longer at the location of the He i triplet in a 0.43 Å wide bin.

In our bin matching the filter used by Vissapragada et al. (2020; green line, Figure 9), we measure excess absorption of 0.66 ± 0.14% for WASP-52b. Vissapragada et al. place a 95th percentile upper limit on excess absorption in the helium bandpass of 0.47%. Therefore in the same bandpass our result is 1.4σ deeper than that of Vissapragada et al.

The JWST will be able to observe the He i triplet with a maximum resolution of R = 2700 with the G140H grism on the NIRSpec instrument, or equivalently Δλ = 4 Å. At this resolution, we predict excess He i absorption of ∼1% (Figure 9) for WASP-52b. This should be readily detectable if NIRSpec can reach its predicted noise floor of ∼20 ppm (e.g., Greene et al. 2016; Batalha et al. 2017).

For WASP-177b (Figure 10), we detect no significant in-transit absorption from the He i light curves.

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Following the approach of other ground-based high-resolution studies of narrow absorption lines (e.g., Redfield et al. 2008; Salz et al. 2018; Alonso-Floriano et al. 2019), we performed a bootstrap analysis as another check of the significance of our detection. For both orders 70 and 71, we randomly selected half of the in- and out-of-transit frames and calculated the median absorption in a 20 km s⁻¹ wide bin centered on the two redder lines of the helium triplet. We repeated this process 5000 times.

Figure 11 shows the results of this bootstrap analysis for WASP-52b, which reveals the in-minus-out distribution is >0 at 4.2σ confidence, while the out-minus-out distribution is centered on 0%, as expected.

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Figure 12 shows the bootstrap analysis results for WASP-177b, revealing no significant excess in-transit absorption. We discuss this finding in the context of WASP-177b's transmission spectrum (Figure 8) in Section 6.

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As we showed in Section 4.3, we measured significant (11σ) excess absorption by helium in WASP-52b's atmosphere and found tentative evidence for redshifted He i absorption for WASP-177b, which is not confirmed by our light curve or bootstrap analysis.

For WASP-52b, we observe excess helium absorption of 3.44% ± 0.31%. This excess absorption corresponds to 66 ± 5 atmospheric scale heights, where the scale height of the planet is 688 km using the parameters in Table 1. This in turn means that at the location of the helium triplet, and at the resolution of NIRSPEC, WASP-52b's excess helium absorption extends to 1.51 ± 0.04 R_P. Using the approximation of Eggleton (1983) and the planet parameters given in Table 1, we calculate WASP-52b's Roche radius to be 1.72 R_P. This means that the helium absorption we detect is close to filling the planet's Roche radius (0.88 ± 0.02 × the Roche radius). Using 1D isothermal Parker wind models, we calculate WASP-52b's mass-loss rate to be 1.4 × 10¹¹ g s⁻¹ or equivalently 0.5% of its mass per Gyr. We discuss the possible consequences of 3D models in Section 6.3.

For WASP-177b, we see evidence for redshifted absorption (Δv = 6.02 ± 1.88 km s⁻¹) with an amplitude of ${1.28}_{-0.29}^{+0.30}$% (equal to 23 ± 5 H). However, the amplitude of this absorption is comparable to a systematic in the transmission spectrum associated with poor removal of the stellar Si line (Figure 8), which we believe may be caused by imperfect wavelength calibration for WASP-177. This redshift amounts to approximately two pixels or half the resolution element.

Furthermore, our light curve (Section 4.4) and bootstrapping (Section 4.5) do not confirm any significant He i absorption from WASP-177b. We therefore encourage additional observations of this planet to confirm or refute this possible hint of He i.

If we instead place a 3σ upper limit on WASP-177b's He i absorption based upon the standard deviation of its transmission spectrum (1.25%), we find this is equal to an upper limit of 22 H, where we calculate the scale height of the planet to be 872 km using the parameters in Table 1.

However, we also note that since the planet has a grazing transit (Figure 10), it is possible that these numbers are underestimated. Taking the R_P /R_* (${0.1360}_{-0.0052}^{+0.0129}$) and impact parameter ($b={0.980}_{-0.060}^{+0.092}$) of WASP-177b (Turner et al. 2019), we calculate that at mid-transit ${55}_{-14}^{+21}$% of WASP-177b's atmosphere is being probed. Therefore, taking the 1σ lower bound on the amount of the planet's atmosphere that is being probed at mid-transit (41%), and scaling our 22 H upper limit, the upper limit on WASP-177b's He i absorption could be as high as 54 H, assuming spherically symmetric He i absorption.

WASP-52 is an active star with numerous observations of magnetic activity regions occulted during transits of the planet (Kirk et al. 2016; Louden et al. 2017; Mancini et al. 2017; Bruno et al. 2018; May et al. 2018). Despite this activity, we interpret the helium absorption we detect as being planetary, not stellar, in nature. In a simulation study, Cauley et al. 2018 showed that the 10833 Å He i triplet could be contaminated at the 0.1% level in specific cases, but that these would likely lead to a dilution of the signal, not an enhancement/spurious detection. This is significantly smaller than the 3.44% ± 0.31% signal that we observe (Figure 7). Additionally, in Chen et al.'s (2020) study of WASP-52b's H-α absorption, the authors demonstrated that the 0.86% ± 0.13% absorption they detected was not replicated in the activity indicator lines they used as a control sample. Finally, the good agreement between our study and that of Vissapragada et al. (2020; Figure 9), for which the observation epochs were separated by a year, suggests non-variable planetary absorption. Taken together, we attribute the absorption we detect to WASP-52b's atmosphere, not stellar activity.

For WASP-177, Turner et al. (2019) attributed modulation in its photometry to active regions on the host star. However, given it is the same spectral type as WASP-52 but older (9.7 ± 3.9 Gyr as opposed to ${0.4}_{-0.2}^{+0.3}$ Gyr; Hébrard et al. 2013), similar arguments apply and therefore we do not believe that our observations of WASP-177b are significantly impacted by activity.

We have so far discussed inferences from spherical models of escaping planetary outflows. In reality, planetary winds escape in an orbiting frame and are shaped by the stellar wind environment of their host stars. Thus, the geometry of the escaped planetary material can be distorted by orbital effects and the interaction with the stellar wind (e.g., McCann et al. 2019; Wang & Dai 2021). This can, in turn, affect the overall strength of the absorption signal and how it relates to the properties of the planetary outflow, such as the mass-loss rate.

These effects can only be fully studied in three dimensions with simulation models catered to a particular planet's parameters. Performing Bayesian inference with these sorts of models remains computationally intractable because of their expense. However, our use of 1D atmospheric profiles to infer the planetary mass-loss rate is justified by the fact that the both WASP-52b's helium absorption (Figure 7) and light curve (Figure 9) are symmetric, which also suggests we are probing the thermosphere and not the exosphere (e.g., see Figure 4 of Allart et al. 2019).

Recent 3D simulations by MacLeod & Oklopčić (2022) show that, in cases of relatively weak and moderate confinement of the planetary outflow by the stellar wind, the helium absorption originates from a region of unshocked planetary material which is not significantly affected by the interaction with the stellar wind (see Figure 2 of MacLeod & Oklopčić 2022). As a result, the helium light curve has a high degree of symmetry around the transit midpoint, similar to what we see for WASP-52b (Figure 9), and the absorption depth is consistent with the predictions of the spherically symmetric Parker wind models which do not include stellar winds at all. In the case of strong confinement by the stellar wind, the planetary outflow gets distorted, which results in a boosted absorption signal (compared to the 1D Parker wind model predictions) and an asymmetric light curve with a prolonged helium egress, i.e., a helium "tail."

Given the predicted ∼1% amplitude of WASP-52b's He i absorption at the resolution of the JWST (Section 4.4), future observations with the JWST could provide a more finely sampled light curve which is needed to fully assess the impact of stellar wind on the escaping material.

Previous studies of exoplanetary helium absorption suggested evidence for a potential relation between XUV irradiation and the amplitude of He i absorption observed for gas giant exoplanets (e.g., Nortmann et al. 2018; Alonso-Floriano et al. 2019; dos Santos et al. 2020). However, more recent results (Casasayas-Barris et al. 2021; Fossati et al. 2022) are in disagreement with this tentative relation.

Figure 18 shows all exoplanets with well-constrained He i absorption ¹¹ , along with our new findings for WASP-52b and WASP-177b. Following our 1D modeling (Section 5), we adopted eps Eri for WASP-52 and HD 40307 for WASP-177 to calculate the planets' XUV irradiation. Following Kasper et al. (2020) and Zhang et al. (2020), we assume that our estimated XUV fluxes are accurate to within a factor of three, based on typical uncertainties in the reconstruction of stellar EUV fluxes (e.g., Oklopčić 2019). However, this is likely an underestimation, since the gyrochronological and isochronal ages for WASP-52 and WASP-177 (Hébrard et al. 2013; Mancini et al. 2017; Turner et al. 2019) lead to significantly different XUV fluxes when using empirical age–XUV luminosity relations (e.g., Sanz-Forcada et al. 2011). For the purposes of Figure 18, we estimate ${{\rm{F}}}_{\mathrm{XUV}}={24.8}_{-16.6}^{+49.7}$ W m⁻² for WASP-52b and ${{\rm{F}}}_{\mathrm{XUV}}={3.5}_{-2.3}^{+7.0}$ W m⁻² for WASP-177b.

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Our new results, taken together with recent results for WASP-76b (Casasayas-Barris et al. 2021), HAT-P-18b (Paragas et al. 2021), WASP-80b (Fossati et al. 2022), and HAT-P-32b (Czesla et al. 2022), suggest a shallower relation between XUV irradiation and He i, if indeed such a relation exists. However, it is important to consider that WASP-177b's transit is grazing, and so its amplitude may be as large as 54 H (Section 6.1), while HAT-P-18b's detection resulted from a narrowband filter which may also be underestimating the full amplitude of its He i absorption. Futhermore, the observations of WASP-76b were hampered by telluric absorption (Casasayas-Barris et al. 2021). Therefore additional observations are needed to test the existence of such a relation.

While this paper was under review, Poppenhaeger (2022) published a subset of literature He i results, finding that the amplitude of exoplanetary He i absorption is more strongly correlated to narrowband EUV fluxes that take into account the stellar coronal iron abundances. We will look for a similar correlation in the updated sample of He i-targeted exoplanets in a future work.

The Neptune Desert is the name given to the observed dearth of short-period Neptunes in the exoplanet population (e.g., Mazeh et al. 2016). It has been suggested that this is the result of atmospheric loss; planets that initially fell within this desert were quickly stripped of their atmospheres and subsequently migrated out of the desert toward smaller masses and radii (e.g., Kurokawa & Nakamoto 2014; Matsakos & Königl 2016; Owen & Lai 2018; Allan & Vidotto 2019; Hallatt & Lee 2022).

Given the rapid increase in the number of exoplanets that have been the focus of published helium observations, we can start to interpret these in the context of the Neptune Desert. Figure 19 shows the sample of published exoplanetary helium observations (Table 3) along with the boundaries of the Neptune Desert as defined by Mazeh et al. (2016). This figure reiterates the finding of Oklopčić (2019) that K stars are the most favorable for studies of helium as most exoplanets with helium detections orbit stars with T_eff ≈ 5000 K.

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Table 3. Published Detections and Robust Upper Limits of Exoplanetary Helium Absorption in the Literature as Plotted in Figures 18 and 19

Planet	FXUV (W m−2)	δ RP /Heq	References
WASP-69b	4.170 ± 0.566 a	85.5 ± 3.6	Nortmann et al. (2018), (also Vissapragada et al. 2020)
HD 189733b	16.75 ± 0.028 a	77.2 ± 4.8	Nortmann et al. (2018), (also Salz et al. 2018; Guilluy et al. 2020)
HD 209458b	1.004 ± 0.284 a	46.9 ± 4.8	Alonso-Floriano et al. (2019), (also Nortmann et al. 2018)
HAT-P-11b	2.109 ± 0.124 a	103.4 ± 11.3	Allart et al. (2018), (also Mansfield et al. 2018)
WASP-107b	2.664 ± 1.05 a	88.7 ± 2.1	Kirk et al. (2020), (also Spake et al. 2018; Allart et al. 2019; Spake et al. 2021)
GJ 436b	0.197 ± 0.007 a	≤37.5	Nortmann et al. (2018)
KELT-9b	≤0.15 a	≤41	Nortmann et al. (2018)
WASP-127b	0.058 ± 0.034 a	≤18.77	dos Santos et al. (2020)
GJ 1214b	${0.3}_{-0.2}^{+0.6}$ a	57 ± 10	Orell-Miquel et al. (2022),
			(also Kasper et al. 2020; Petit dit de la Roche et al. 2020)
GJ 9827d	${2.4}_{-1.6}^{+4.8}$ a	≤17	Kasper et al. (2020), (also Carleo et al. 2021)
HD 97658b	${1.1}_{-0.73}^{+2.2}$ a	≤74	Kasper et al. (2020)
GJ 3470b	1.435 ± 0.008 a	77 ± 9	Palle et al. (2020), (also Ninan et al. 2020)
55 Cnc e	${7.4}_{-4.9}^{+14.8}$ b	≤11	Zhang et al. (2020)
HAT-P-18b	${8}_{-5}^{+16}$ b	14.3 ± 3.5	Paragas et al. (2021)
HD 73583b/TOI-560b	5.1 ± 1.3 b	123 ± 10	Zhang et al. (2022a)
HAT-P-32b	90 ± 12 a	72.6 ± 3.4 c	Czesla et al. (2022)
WASP-80b	${6.281}_{-3.141}^{+6.281}$ b	≤39	Fossati et al. (2021)
WASP-76b	≤94 a	≤35	Casasayas-Barris et al. (2021)
GJ 9827b	${37}_{-25}^{+74}$ b	≤83	Carleo et al. (2021)
TRAPPIST-1b	3 ± + 0.4 b , d	≤1.6	Krishnamurthy et al. (2021)
TRAPPIST-1e	0.4 ± 0.07 b , d	≤4.2	Krishnamurthy et al. (2021)
TRAPPIST-1f	0.27 ± + 0.04 b , d	≤1.5	Krishnamurthy et al. (2021)
WASP-52b	${24.8}_{-16.6}^{+49.7}$ a	66 ± 5	This work
WASP-177b	${3.5}_{-2.3}^{+7.0}$ a	≤22	This work

Notes. The first reference in the reference column is that from which the values are taken or derived. Additional references to studies of these planets are also given.

^a For λ < 504 Å. ^b For λ < 912 Å. ^c Error calculated assuming same fractional uncertainty as in the equivalent width. ^d Calculated from Wheatley et al. (2017).

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If atmospheric loss is responsible for the Neptune Desert, we might expect planets falling within the boundaries of the desert to be losing their atmospheres. Figure 19 shows that several exoplanets with non-detections of helium absorption reside within the boundaries of the desert. However, since these planets do not orbit K stars, it is possible that they are losing their atmospheres but helium is not a sensitive probe.

Considering only WASP-52b and WASP-177b on Figure 19, we see that WASP-52b sits inside the Neptune Desert and is losing its atmosphere at a significant rate. WASP-177b sits at the edge of the desert and due to systematics in our data and its grazing transit, we cannot say with confidence whether the planet is or is not losing its atmosphere. Nevertheless, Figure 19 demonstrates the potential of the 10830 Å He i triplet to probe the origins of the Neptune Desert, which motivates further observations of exoplanets in this parameter space.