Hubble WFC3 Spectroscopy of the Habitable-zone Super-Earth LHS 1140 b

Our analysis started from the raw spatially scanned spectroscopic images which were obtained from the Mikulski Archive for Space Telescopes.⁴ Two transit observations of LHS 1140b were acquired for proposal 14888 (PI: Jason Dittmann) and were taken in 2017 January and December. Both visits utilized the GRISM256 aperture, and 256 × 256 subarray, with an exposure time of 103.13 s which consisted of 16 up-the-ramp reads using the SPARS10 sequence. The visits had different scan rates with 010 s⁻¹ and 014 s⁻¹ used for January and December respectively, resulting in scan lengths of 109 and 159.

We used Iraclis,⁵ a specialized, open-source software for the analysis of WFC3 scanning observations (Tsiaras et al. 2016b) and the reduction process included the following steps: zero-read subtraction, reference pixel correction, nonlinearity correction, dark current subtraction, gain conversion, sky-background subtraction, flat-field correction, and corrections for bad pixels and cosmic rays. For a detailed description of these steps, we refer the reader to the original Iraclis paper (Tsiaras et al. 2016b).

Although two transits of LHS 1140 b were obtained, one of these was affected due to large shifts in the location of the spectrum on the detector. These changes in position are shown in Figure 1 and, when the white light curve was extracted, large spikes were seen in the flux as shown in Figure 2. The presence of such shifts are known to dominate the systematics and reduce precision if the position of the spectrum is not well known (e.g., Stevenson & Fowler 2019; Tsiaras & Ozden 2019). We attempted to remove the bad frames but still could not recover a satisfactory fit. Additionally, exposures that seemed to give reasonable data in the extracted white light curve also showed obvious degradation when the fits files were visually inspected, potentially due to an unusually high number of cosmic-ray impacts. Figure 3 displays an example raw image from each data set and the degradation is easily visible for the January observation. We therefore discarded the initial observation and so only the December data set was utilized.

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For this observation, the reduced spatially scanned spectroscopic images were then used to extract the white (from 1.1–1.7 μm) and spectral light curves. The spectral light-curve bands were selected such that the signal-to-noise ratio (S/N) is approximately uniform across the planetary spectrum. We then discarded the first orbit of each visit as they present stronger wavelength-dependent ramps, and the first exposure after each buffer dump as these contain significantly lower counts than subsequent exposures (e.g., Deming et al. 2013; Tsiaras et al. 2016b).

We fitted the light curves using our transit model package PyLightcurve (Tsiaras et al. 2016a) which utilizes the Markov Chain Monte Carlo (MCMC) code ecmee (Foreman-Mackey et al. 2013) and, for the fitting of the white light curve, the only free parameters were the mid-transit time and planet-to-star ratio. The other planet parameters were fixed to the values from Ment et al. (2019; $a/{R}_{* }=95.34$, i = 8989) while the limb-darkening coefficients were computed using the formalism from Claret et al. (2012, 2013) and the stellar parameters from Ment et al. (2019; ${T}_{* }=3216\,$ K, $\mathrm{log}(g)=5.0$).

It is common for WFC3 exoplanet observations to be affected by two kinds of time-dependent systematics: the long-term and short-term ramps. These systematics were fitted using

$$\begin{eqnarray}&&{R}_{w}(t)={n}_{w}^{\mathrm{scan}}(1-{r}_{a}(t-{T}_{0}))(1-{r}_{{b}_{1}}{e}^{-{r}_{{b}_{2}}(t-{t}_{0})}),\end{eqnarray} \tag{ 1 }$$

where t is time, ${n}_{w}^{\mathrm{scan}}$ is a normalization factor, T₀ is the mid-transit time, t_o is the time when each HST orbit starts, r_a is the slope of a linear systematic trend along each HST visit, and (${r}_{{b}_{1}},{r}_{{b}_{2}}$) are the coefficients of an exponential systematic trend along each HST orbit. The normalization factor we used (${n}_{w}^{\mathrm{scan}}$) was changed to ${n}_{w}^{\mathrm{for}}$ for upward scanning directions (forward scanning) and to ${n}_{w}^{\mathrm{rev}}$ for downward scanning directions (reverse scanning). The reason for using different normalization factors is the slightly different effective exposure time due to the known upstream/downstream effect (McCullough & MacKenty 2012).

We fitted the white light curve using the formulae above and the uncertainties per pixel, as propagated through the data reduction process. However, it is common in HST WFC3 data to have additional scatter that cannot be explained by the ramp model. For this reason, we scaled up the uncertainties in the individual data points, for their median to match the standard deviation of the residuals, and repeated the fitting, which is the standard practice for the Iraclis code (e.g., Tsiaras et al. 2018; Skaf et al. 2020).

Next, we fitted the spectral light curves with a transit model (with the planet-to-star radius ratio being the only free parameter) along with a model for the systematics (R_λ) that included the white light curve (divide-white method; Kreidberg et al. 2014)) and a wavelength-dependent, visit-long slope (Tsiaras et al. 2018) parameterized by

$$\begin{eqnarray}&&{R}_{\lambda }(t)={n}_{\lambda }^{\mathrm{scan}}(1-{\chi }_{\lambda }(t-{T}_{0}))\displaystyle \frac{{{LC}}_{w}}{{M}_{w}},\end{eqnarray} \tag{ 2 }$$

where ${\chi }_{\lambda }$ is the slope of a wavelength-dependent linear systematic trend along each HST visit, LC_w is the white light curve, and M_w is the best-fit model for the white light curve. Again, the normalization factor we used, (${n}_{\lambda }^{\mathrm{scan}}$), was changed to (${n}_{\lambda }^{\mathrm{for}}$) for upward scanning directions (forward scanning) and to (${n}_{\lambda }^{\mathrm{rev}}$) for downward scanning directions (reverse scanning).

The white light-curve fit is shown in Figure 4 and the subsequent spectral light-curve fits are shown in Figure 5. A full list of stellar and planet parameters used in this study is given in Table 1 while the limb-darkening coefficients and extracted spectrum are in Table 2.

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Table 1.  Stellar and Planetary Parameters Used or Derived in This Work

Parameter	Value
R.A. [J2000]	00h44m593
decl. [J2000]	−15° 1' 18''
KS	8.821 ± 0.024
Rs (R⊙)	0.2139 ± 0.0041
Ms (M⊙)	0.179 ± 0.014
Ts (K)	3216 ± 39
$\mathrm{log}(g)$	5.0
Fe/H	−0.24 ± 0.10
Rp/Rs	0.07390 ± 0.00008
${M}_{{\rm{p}}}$ (M⊕)	6.98 ± 0.89
Rp (R⊕)	1.727 ± 0.032
ρ (ms−2)	7.5 ± 1.0
g (ms−2)	23.7 ± 2.7
Teff (K)	235 ± 5
S (S⊕)	0.503 ± 0.030
a (au)	0.0936 ± 0.0024
a/Rs	95.34 ± 1.06
i (deg)	${89.89}_{-0.03}^{+0.05}$
e	<0.06*
Porb (days)	24.7369148 ± 0.0000058†
Tmid [BJDTDB]	2457187.81760 ± 0.00012†
*Fixed to zero	†This work

Note. Data is from Ment et al. (2019) unless otherwise stated.

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The retrieval of the transmission spectra was performed using the publicly available retrieval suite TauREx 3 (Al-Refaie et al. 2019).⁶ We included the molecular opacities from the ExoMol database (Tennyson et al. 2016), the high-resolution transmission molecular absorption database (HITRAN; Gordon et al. 2016), and the the high-temperature molecular spectroscopic database (HITEMP; Rothman et al. 2010) for H₂O (Polyansky et al. 2018), CH₄ (Yurchenko & Tennyson 2014), CO (Li et al. 2015), CO₂ (Rothman et al. 2010), and NH₃ (Yurchenko et al. 2011). On top of this, we also included collision-induced absorption (CIA) from H₂–H₂ (Abel et al. 2011; Fletcher et al. 2018) and H₂–He (Abel et al. 2012) as well as Rayleigh scattering for all molecules. The priors used are listed in Table 3. We allowed the bounds on the volume mixing ratio (VMR) of each molecular species to vary from 1 to 1e⁻¹², allowing for both low and high mean molecular weight atmospheres. Our retrievals used 500 live points with an evidence tolerance of 0.5 and all retrievals for this study were performed on a single core of a 2017 MacBook Pro.

We calculated the potential effect of the stellar spots on the transmission spectrum using the model from Rackham et al. (2018). LHS 1140 is known to have ∼1% stellar brightness variability with a period of 131 days at optical wavelengths (Dittmann et al. 2017). Assuming that the variability is caused by stellar rotation, we infer that the stellar surface is not homogeneous. We adopted four cases of the stellar spot distribution: giant spots, solar-type spots, giant spots with faculae, and solar-type spots with faculae. These are depicted in Figure 6 and the spot covering fraction values for each case are imported from the values for M4 stars in Rackham et al. (2018), as the stellar effective temperature and brightness variability are very similar to the values from their study.

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In Rackham et al. (2018), they calculate the total stellar flux by iteratively adding spots to random locations and derive the best spot covering fraction that represents a 1% variation in brightness. Note that the amplitude of the brightness variability is not proportional to the spot covering fraction, since the size of each spot is defined (R_spot = 2^o for solar-like spots and ${R}_{\mathrm{spot}}={7}^{{\rm{o}}}$ for giant spots), and multiple spots are distributed over the stellar surface in all cases. We assumed the photosphere to be at 3100 K, a spot temperature of 2700 K, and faculae with temperatures of 3200 K. We used theoretical BT-Settl models of the stellar flux⁷ calculated for each temperature component, at $\mathrm{log}g=5$ and [Fe/H] = 0. The effects on the transmission spectrum at each wavelength, the contamination factor, are calculated by Equation (3) in Rackham et al. (2018). The derived contamination factor values are multiplied by a flat transit depth model, and we compared the atmospheric and stellar spots models to check which more adequately describes the observed transmission spectrum.

Accurate knowledge of exoplanet transit times is fundamental for atmospheric studies. To ensure that LHS 1140b can be observed in the future, we used our HST white light-curve mid-time, along with data from the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2014), to update the ephemeris of the planet. TESS data is publicly available through the Mikulski Archive for Space Telescopes (MAST) and we use the pipeline developed in Edwards et al. (2020) to download, clean, and fit the 2 minute cadence presearch data conditioning (PDC) light curves (Smith et al. 2012; Stumpe et al. 2012, 2014). LHS 1140b had been studied in Sector 3 and, after excluding bad data, we recovered a single transit. Again we fitted only for the transit mid-time and planet-to-star radius ratio, with all other values being fixed to those from Ment et al. (2019). For the limb-darkening coefficients we utilize the values from Claret (2017). The extracted light curve is given in Table 4 while the best-fit model is shown in Figure 7 and the mid-time, which was used for refining the ephemeris, is given in Table 5. To get the period of the planet we fitted a linear function to the observations using a least-squared fit.

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The recovered spectrum is given in Table 2 and while we ran atmospheric retrievals searching for a number of molecules, the only one for which the data supported any evidence for was H₂O. The best-fit spectrum is shown in Figure 8 while Figure 9 displays the posteriors of the H₂O-only retrieval, which suggest an abundance of ${\mathrm{log}}_{10}({\text{}}{V}_{{{\rm{H}}}_{2}{\rm{O}}})=-{2.94}_{-1.49}^{+1.45}$. However, we note that the significance of the detection is relatively low. We compared the Bayesian log evidence (log(E)) for this retrieval to one which contained no molecular opacities. For this second retrieval the only fitted parameters were the planet radius, planet temperature, and cloud-top pressure. Rayleigh scattering and CIA were also included. The difference in Bayesian log evidence was computed to be 2.26 in favor of the fit including H₂O, providing positive evidence for the detection of molecular features (Kass & Raftery 1995). This is equivalent to the atmospheric detectability index (ADI), as defined in Tsiaras et al. (2018), or 2.65σ.

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We note that the bounds used, which are given in Table 3, allow for higher mean molecular weight atmospheres, dominated by water, but the retrieval did not favor such a solution. Nevertheless, given the debate around the nature of such planets, we also attempted a retrieval which forced an atmosphere with a significant abundance of water ($\gt 10 \%$), with the subsequent posteriors shown in Figure 10. In the baseline retrieval, the mean molecular weight was inferred to be ${2.31}_{-0.00}^{+0.28}$, while this second case gives a value of ${6.59}_{-2.13}^{+5.73}$ due to the VMR of water being retrieved, to 1σ, as between 13.8% and 65.6%. The forced retrieval does, in fact, give a marginally better fit to the data (log(E) = 195.21 versus log(E) = 194.47) and, compared to the flat model, is preferred by 2.95σ. However, given the small difference in evidence between the two retrievals including water, and that the Bayesian evidence is sensitive to the prior, one cannot use statistical means to preferentially select either (Kass & Raftery 1995).

As in Tsiaras et al. (2019), we also performed a retrieval which included nitrogen to increase the mean molecular weight without adding additional molecular absorption features. In this case, a water abundance of ${\mathrm{log}}_{10}({\text{}}{V}_{{{\rm{H}}}_{2}{\rm{O}}})=-{2.96}_{-1.73}^{+1.49}$ was recovered while the N₂/H₂ ratio was best fit as $-{4.75}_{-3.42}^{+3.22}$, as shown in Figure 11. The Bayesian evidence (log(E) = 192.51) is again similar to the other models. Hence, while all our retrievals point to the presence of water, the nature of the atmosphere (i.e., primary or secondary) cannot be ascertained. Additionally, while comparing the Bayesian evidence from different retrievals that favor those with water, the difference in the evidence in all of the cases is small and it is worth noting that, compared to the flat model, the water-only retrieval has but a single additional fitting parameter (${\mathrm{log}}_{10}({\text{}}{V}_{{{\rm{H}}}_{2}{\rm{O}}})$). The water opacity adds great freedom to the model to fit the modulation without overly penalizing the resulting Bayes factor for this increase dimensionality. For completeness, we also report the results of two retrievals with H₂O, NH₃, CH₄, CO, and CO₂ as active absorbers: one where all molecules could form up to 100% of the atmosphere and a second where all but water were capped at 10%. These resulted in water abundances of ${\mathrm{log}}_{10}({\text{}}{V}_{{{\rm{H}}}_{2}{\rm{O}}})=-{3.31}_{-4.11}^{+1.93}$ and $-{3.74}_{-4.39}^{+1.80}$, respectively, with evidences of log(E) = 194.51 and 194.33. Again positive evidence is found for atmospheric features but, in the latter case, the significance of the detection is reduced: the dimensionality of the fit has increased but the quality of it has not. Hence, while comparing the evidence from models is crucial, it must be done cautiously, with an understanding of the underlying statistical implications and the effects of the choice of one's priors: fine tuning one's priors can lead to apparent increases or decreases in the significance of a detection.

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The models of potential contamination are also plotted in Figure 8. For each, we compute the chi-squared as a means of comparing the ability of the model to fit the data. We additionally used the same metric to analyze the fit of the models from our retrievals. For simplicity, we chose to only compare the flat model and primary atmosphere containing water. As shown in Table 6, the preferred case is still an atmosphere containing H₂O. We note that none of the starspot models alone provide convincing fits to the data, with the features induced coming at longer wavelengths and being broader than those seen in the data.

Table 6.  Chi-squared (χ²) and Reduced Chi-squared (${\bar{\chi }}^{2}$) Values for Different Atmospheric and Stellar Contamination Models for the HST WFC G141 Data

Model		χ2	${\bar{\chi }}^{2}$
Atmosphere	H2O	29.48	1.40
	Flat	35.82	1.63
Giant spots	Mean	35.43	1.61
	Max	35.11	1.60
Solar spots	Mean	34.76	1.58
	Max	51.83	2.36
Giant spots + faculae	Mean	35.86	1.71
	Max	36.05	1.72
Solar spots + faculae	Mean	33.67	1.60
	Max	34.18	1.63

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Spectroscopic ground-based observations of LHS 1140b were recently presented by Diamond-Lowe et al. (2020). They observed two transits of the planet and simultaneously monitored them with the IMACS and LDSS3C multi-object spectrographs on the twin Magellan telescopes. Their spectroscopic measurements resulted in a spectrum with a median error of 260 ppm which is significantly larger than the ∼70 ppm achieved here.

We note that the compatibility of different data sets is hard to confirm, particularly without spectral overlap, as the use of different limb-darkening coefficients or orbital parameters, imperfect correction of instrument systematics, or stellar activity and stellar variability can all cause variations in the transit depth observed (e.g., Tsiaras et al. 2018; Alexoudi et al. 2018; Yip et al. 2020a, 2020b; Changeat et al. 2020; Pluriel et al. 2020). Diamond-Lowe et al. (2020) used the same orbital parameters, from Ment et al. (2019), but used logarithmic limb-darkening coefficients. However, the TESS depth recovered here matches well with the ground-based data and was derived using the four-coefficient law from Claret (2017). In Figure 8, the data from Diamond-Lowe et al. (2020) is plotted alongside the HST and TESS transit depths recovered here.

The ground-based data set appears to show a shallower transit depth than any of the stellar contamination models but the solar spots with the faculae model provide the best fit as demonstrated by the chi-squared values in Table 7. The plotted data in Figure 8 assumes no offsets between data sets but, to ensure we do not draw false conclusions because of one, we renormalize the stellar contamination models. To do this we sample various offsets for each stellar model, finding the best-fit value using the chi-squared metric. These are shown in Figure 12 and the chi-square values are again given in Table 7.

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Table 7.  Chi-squared Values for Different Atmospheric and Stellar Contamination Models for the Data from Diamond-Lowe et al. (2020)

No Renormalization
Model		χ2	${\bar{\chi }}^{2}$
Giant spots	Mean	95.43	5.61
	Max	107.45	6.32
Solar spots	Mean	239.39	14.08
	Max	840.16	49.42
Giant spots + faculae	Mean	73.82	4.61
	Max	62.67	3.92
Solar spots + faculae	Mean	30.05	1.88
	Max	120.6	7.54
With Renormalization
Giant spots	Mean	33.8	1.99
	Max	36.0	2.12
Solar spots	Mean	61.11	3.59
	Max	186.8	10.99
Giant spots + faculae	Mean	29.15	1.82
	Max	25.74	1.61
Solar spots + faculae	Mean	28.09	1.76
	Max	34.1	2.13

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Table 8.  Retrieved Water Abundance after Accounting for Different Stellar Contamination Models

Stellar Model		Water Abundance	log(E) Water	log(E) Flat	Δlog(E)	Sigma
Giant spots	Mean	$-{2.85}_{-1.69}^{+1.48}$	194.07	192.43	1.64	2.37
	Max	$-{2.98}_{-1.69}^{+1.68}$	194.17	192.51	1.66	2.38
Solar spots	Mean	$-{4.31}_{-4.75}^{+2.57}$	193.12	192.71	0.41	0.26
	Max	$-{7.11}_{-3.32}^{+3.41}$	184.30	184.50	−0.20	⋯
Giant spots + faculae	Mean	$-{2.92}_{-1.42}^{+1.51}$	194.50	192.07	2.43	2.73
	Max	$-{2.78}_{-1.41}^{+1.36}$	194.58	192.04	2.54	2.77
Solar spots + faculae	Mean	$-{2.78}_{-1.70}^{+1.43}$	195.37	193.24	2.13	2.60
	Max	$-{5.57}_{-4.27}^{+3.20}$	193.57	193.11	0.46	0.26
None		$-{2.94}_{-1.49}^{+1.45}$	194.47	192.21	2.26	2.65

Note. The Bayesian evidence for the models with and without water are also given along with the sigma level for each.

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Given the downward slope seen in this data set, this would appear to rule out the case of solar spots without faculae, which would provide the largest modulation in the HST wavelength range. Of the stellar models computed, before renormalization the mean coverage of solar spots with faculae provides the best fit to the slope seen in this ground-based data set: the same model also best fits the HST data. After renormalization, solar spots and faculae in both coverage cases give a reasonable fit. Additionally, giant spots and faculae, with either mean or maximum coverage, also provide good fits to the IMACS/LDSS3C data set and these do not cause modulation in the WFC3 bandpass.

Of course, one would not expect the spectrum to be explained entirely by the stellar model unless LHS 1140b were to have no atmosphere. Hence, the signal seen should be a combination of contributions. To explore the effect of stellar contamination on the retrieved atmosphere, and thus the significance of the water detection, we tested subtracting our spot models from both our HST data set and the observations from Diamond-Lowe et al. (2020). The effect of stellar contamination is greater in the visible. Hence, we use this to rule out spot contamination models which would imply nonphysical atmospheric features in the data from Diamond-Lowe et al. (2020). A similar approach was taken by Wakeford et al. (2019) for TRAPPIST-1 g. While a slope that increases at shorter wavelengths can be described by Rayleigh scattering, a negative one would be more difficult to describe. If solar spots were the correct contamination model, the atmospheric feature would be around 40 scale heights in the max coverage case, or 30 in the mean, and thus is not feasible. Other models still have large feature sizes, 10–20 scale heights, but the data is relatively noisy and the error bars are of the order of several scale heights.

For the HST data, we also accounted for each stellar contamination model by subtracting the contribution and conducting two retrievals on the resultant spectrum: one with water and one without. The only three models which cause significant modulation in the HST WFC3 bandpass are solar spots, both mean and max coverage, and the max coverage of solar spots with faculae. Subtracting each of these essentially completely removed any evidence for water in the atmosphere. However, as mentioned, the visible data could not be explained in the solar spots case. Plots of the subsequent HST WFC3 data, with best-fit models, are given in Figure 13. The corrected spectrum in the max solar spots case is strange and the retrieval tries to use CIA to explain the modulation. The maximum coverage of solar spots and faculae is the only stellar contamination model which leads to no evidence for water in the atmosphere of LHS 1140b and is not ruled out by the visible data.

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Having accounted for all other models, our retrievals still favored the presence of water with a confidence of 2.38–2.77σ and with an abundance similar to that from our baseline retrieval on the unmodified HST data, as shown in Table 8.

The spectrum obtained using HST WFC3 contains 25 data points but the evidence for water is likely to be driven by only a few of these: those around 1.4 μm where the feature is the strongest. Therefore we attempted retrievals on data sets where we removed individual data points. Each time we ran the model with and without water and compared the difference in the global log evidence. Our analysis found that removing the data point at 1.38 μm eliminates all indications from water being present with the removal of the 1.36 μm data point reducing the confidence to 2.01σ. Meanwhile, deducting the spectral data at 1.40 or 1.42 μm changes the confidence of the models that water is present to 2.57 and 2.9σ, respectively. Such results are expected given the narrow wavelength region means only one water feature is probed.

To further explore the quality of the spectral light-curve fitting, and thus of the water detection, we also produced a spectrum at the native resolution of the G141 grism (R ∼ 130 at 1.4 μm). A peak of several data points is seen in this data set around the 1.4 μm water feature, as seen in Figure 14, suggesting the peak seen is not due to a narrowband contamination of the spectra. Additionally, we studied the autocorrelation function of each spectral light-curve fit. Various correlations are calculated (e.g., between one point and the next) using the numpy.correlate package and the maximum value is reported. Figure 15 shows that the 1.38 μm data point, the one on which the water detection hinges, appears to be well fitted and thus reliable.

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The choice of limb-darkening coefficients can also have profound effects on the recovered spectrum, particularly for cooler stars (e.g., Kreidberg et al. 2014), and several different limb-darkening laws are available. We attempted fits with precomputed linear, square-root, and quadratic coefficients, again calculated using ExoTETHyS (Morello et al. 1919), but only the linear values provided usable fits to the white light curve. Additionally, we fitted the data with claret coefficients for different stellar temperatures. The linear law and additional claret fits all resulted in spectra which agree with the one originally derived to within 1σ, as shown in Figure 16. Nevertheless, we performed retrievals on these spectra, finding that they preferred a solution with water to 2.98 and 2.92σ for claret coefficients at 3150 and 3250 K, respectively, while the linear coefficients resulted in a 3.22σ detection of water.

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Finally, a recent study used ESPRESSO and TESS data to provide updated system parameters (Lillo-Box et al. 2020). Hence we tried fitting the light curves using their parameters (a/R_s = 96.4, i = 89.877°) as well as performing retrievals using their revised mass (M_p = 6.38 M_⊕). The resultant spectrum, and best-fit retrieval, is shown in Figure 17. The spectrum still shows evidence for water with an abundance of ${{\rm{log}}}_{10}({{\rm{V}}}_{{{\rm{H}}}_{2}{\rm{O}}})={3.01}_{+1:59}^{-1:58}$ and a significance of 2.57σ. On this alternate spectrum we also conducted a retrieval with CH₄ as the main absorber, resulting in an abundance of ${\rm{lo}}{{\rm{g}}}_{10}({{\rm{V}}}_{{{\rm{CH}}}_{4}})={3.37}_{-5:01}^{+2:48}$, but the model did not provide a significantly better fit than the at model (log(E) = 191.01 versus log(E) = 190.47).

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