High-resolution Spectroscopic Reconnaissance of a Temperate Sub-Neptune

We observed time-series spectroscopy of the host star TOI-732 (LTT 3780) using the IGRINS infrared spectrograph on Gemini-South. The observations were carried out as part of the Gemini GO program GS-2021A-Q-201 (PI: Valencia) and included observations during two primary transits on the nights of 2021 January 6 (Night 1) and 2021 February 24 (Night 2), for ∼3 hr each. We assess data from both nights but report results only for Night 2 in the present work. The data from Night 1 are presented in Appendix A. The data from Night 2 displayed significantly higher quality, a result of both ideal photometric conditions and excellent air mass over the observing duration (z spanned 1.08–1.18, with a minimum of 1.05). Our choice to exclude Night 1 is primarily due to its lower S/N and limited out-of-transit baseline (exposures from each night are compared in Appendix A). Our study aims to provide a proof of concept for HRCCS, which is best served by the higher S/N data set. For completion, we performed our full analysis on Night 1, which did not yield any statistically significant detections, as discussed in Appendix A.

On Night 2, we acquired in total 33 4-minute exposures (16 in-transit, 17 out-of-transit), where each exposure constitutes an A/B pair. IGRINS simultaneously captures H-band and K-band spectra, with coverage spanning 1.45–2.45 μm at spectral resolution R ∼ 45,000. Each spectral order was treated independently throughout our analysis until aggregation of their respective cross-correlation functions (CCFs; see Section 2.5). IGRINS has 54 spectral orders in total. However, only a subset of the orders outside of severe telluric contaminated zones were used (see below for masking details).

The data reduction, spectral extraction, and wavelength calibration were performed using the IGRINS Pipeline Package (PLP; Lee & Gullikson 2017) by the IGRINS instrument team. The resulting spectral data cubes were used for the HRCCS analysis in the present work. A telluric standard A0V star was observed before and after the science exposures. The time-series spectra were divided by the spectrum of the later telluric standard, which provides a preliminary continuum normalization (these data correspond to the spec_a0v reduced PLP products). The typical pixel S/N was ∼300 (Figure 1). However, the S/N exceeded 400 in the stellar continuum, near the peak of the instrument response and outside of telluric bands.

Zoom In Zoom Out Reset image size

The most evident features in the source spectra are bands of strong telluric contamination, predominantly due to absorption by H₂O, CH₄, and CO₂, as well as the blaze function inherent to the instrument's spectral response. The telluric standard division essentially removes the blaze component and significantly reduces the presence of tellurics. The telluric standard used for the initial division was the one observed after science exposures in the standard IGRINS observing procedure. Additional preprocessing steps were taken in order to remove remaining broadband variations, time-dependent features, and the most contaminated wavelength ranges. We place the spectra into a 2D array, each column representing a wavelength bin and each row representing an exposure (or, equivalently, time or orbital phase). First, we divide each spectrum by its median value in order to normalize throughput. Although corrected spectra were already continuum normalized, we continued to remove any remaining broadband trends. We apply a sliding 31-pixel filter, which selects for the 95th percentile value within its window. These values serve as approximate samples of the spectrum's continuum. We then fit a quadratic function to these values and finally divide the spectrum by this fit.

We proceed to mask orders that fell in significant water absorption bands, in order to mitigate the effects of telluric contamination. Specifically, the following orders were masked: 1, 2, 3, 4, 5, 6, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 49, 50, 51, 52, 53, 54. More columns were masked in the remaining orders based on their contamination level. The masking consistently included the first 400 pixels and the last 100 pixels, which were affected by edge effects. We used a blaze-corrected, telluric standard spectrum taken on Night 1 to mask additional wavelength channels. Specifically, any channel with flux below 0.99 in the blaze-corrected spectrum was flagged and subsequently masked from our primary science spectra. In addition to remaining, shallow, telluric features, the M dwarf host imparts a rich molecular absorption spectrum. These lines are removed by detrending the time-series spectra as follows.

Each spectral order bears a unique distribution of exoplanetary, stellar, and telluric features. We detrend the spectra in order to isolate the exoplanet's atmospheric signal. For close-in HRCCS targets, the atmospheric signal is significantly Doppler shifted throughout the transit. In contrast, stellar and telluric features are approximately stationary, and they are present in all frames. They may be efficiently removed via singular value decomposition (SVD; de Kok et al. 2013). SVD can also identify and remove telluric trends related to the time-variable column density of the absorber. In our case, the planetary Doppler shift is a moderate ∼0.12 km s⁻¹ (0.06 pixels) between consecutive exposures. However, the atmospheric signal is present during in-transit exposures only. Our out-of-transit baseline therefore establishes telluric and stellar features as the dominant trends, and the atmospheric signal contributes negligibly to the leading-order singular vectors (Appendix B). In our implementation, we compute a low-rank approximation of the spectra with SVD, divide the data by this approximation, and finally subtract unity, thereby isolating features in the transmission spectrum. Optimizations to this procedure are discussed in Section 2.5.

It is important to note that the original spectra are in the geocentric rest frame, and as a result, stellar features are further Doppler shifted by the barycentric correction velocity. This quantity varies by ∼0.34 km s⁻¹ throughout the 33-frame time series. In-transit spectra experience ∼0.16 km s⁻¹ of this drift, which also shifts the atmospheric signal. Nevertheless, we find that the stellar features are largely removed in the detrending process, and our injection/recovery procedure demonstrates our robustness to these effects.

We generate a library of simulated transmission spectra for cross-correlation with the data (Figure 2) using the AURA atmospheric modeling and retrieval framework (Pinhas et al. 2018; Welbanks et al. 2019; Constantinou et al. 2023). The atmosphere at the day–night terminator is modeled in plane-parallel geometry under the assumption of hydrostatic equilibrium and isothermal temperature structure. Transmission spectra are generated through a radiative transfer calculation at a resolution of R = 300,000.

Zoom In Zoom Out Reset image size

The chemical composition of the model atmosphere is uniform and set through the individual mixing ratios of trace molecular species, with the remainder made up of H₂ and He in solar elemental ratio. The spectral baseline of the resulting transmission spectrum is provided by H₂–H₂ and H₂–He collision-induced absorption (Borysow et al. 1988; Orton et al. 2007; Abel et al. 2011; Richard et al. 2012). The model can also include spectral absorption contributions from H₂O (Barber et al. 2006; Rothman et al. 2010), CH₄ (Yurchenko & Tennyson 2014), and NH₃ (Yurchenko et al. 2011). All three molecules are expected to be primary elemental carriers in temperate H₂-dominated atmospheres (Burrows & Sharp 1999; Lodders & Fegley 2002). The cross sections of all molecular species are computed following Gandhi & Madhusudhan (2017) and Gandhi et al. (2020) and account for pressure broadening due to H₂. We specifically consider mixing ratios corresponding to 10× solar elemental abundances under thermochemical equilibrium. These are 10⁻² for H₂O, 5 × 10⁻³ for CH₄ and 10⁻³ for NH₃. The isothermal temperature in the atmosphere is nominally assumed to be 350 K, consistent with the zero-albedo equilibrium temperature of the planet with efficient day–night redistribution.

In addition to spectral contributions from gaseous species, the model atmosphere can also include extinction arising from atmospheric aerosols. We follow a parametric approach, modeling atmospheric aerosols as a gray opacity across the observed wavelength range, described by a cloud-top pressure P_c . For all models, we additionally include extinction arising as a result of H₂ Rayleigh scattering.

Following standard HRCCS practices (e.g., Brogi et al. 2012), we cross-correlate our atmospheric models with the detrended transmission spectra. This step accumulates signal from the multitude of weak atmospheric features. Our analysis uses the X-COR pipeline (Hawker et al. 2018; Cabot et al. 2019), with details as follows. The CCF between the Doppler-shifted model template m(λ∣v) and observed transmission spectra f(λ, t) is given as

$$\begin{eqnarray}&&\mathrm{CCF}(v,t)=\displaystyle \frac{\sum _{\lambda }f(\lambda ,t)w(\lambda )}{\sum _{\lambda }w(\lambda )},\,w(\lambda )=\displaystyle \frac{m(\lambda | v)}{{\sigma }^{2}(\lambda )},\end{eqnarray} \tag{ 1 }$$

where λ represents the wavelength channel, t the time of exposure, and v the planetary radial velocity. The sum is weighted by a factor w, which includes the inverse of each channel's time-axis (column) variance σ²(λ), thereby minimizing contributions from cores of stellar or telluric lines. From each row of the CCF (i.e., corresponding to each exposure), we further subtract its median value (the result at this stage is shown in the grayscale arrays in Figure 3). Finally, we shift each row of the CCF by the expected planetary velocity, given by $v(t)={K}_{p}\sin \phi +{V}_{\mathrm{sys}}+{v}_{\mathrm{bary}}$ for semiamplitude K_p , systemic velocity V_sys, and barycentric correction velocity v_bary. We then sum the CCFs across in-transit exposures. This process was repeated for other orbital solutions (i.e., alternate values for K_p and V_sys), which provide a noise distribution for gauging significance.

Zoom In Zoom Out Reset image size

Detrending parameters can significantly influence the statistical significance and robustness of observed signals (Cabot et al. 2019; Cheverall et al. 2023). In our analysis, we determine the number of singular vectors (n_SV) to remove for each order. We choose n_SV based on ΔCCF optimization (Holmberg & Madhusudhan 2022; Spring et al. 2022; Cheverall et al. 2023). For each order, we select n_SV, which maximizes the S/N of ΔCCF. Here ΔCCF = CCF_inj − CCF_obs, where CCF_obs is the CCF computed from the observed data and CCF_inj is the same plus an additional transmission model injected at 1× nominal strength under the system's known K_p ≈ 68 and V_sys ≈ 0 km s⁻¹ (Nowak et al. 2020; Bonfanti et al. 2024). We find better injection recovery by optimizing the peak of the ΔCCF as opposed to the value at the exact injected (K_p , V_sys). We adopt this practice throughout our optimizations. As is standard, the noise baseline is derived from CCF_obs (computed row-wise for each frame, and excluding the region ∣V_sys∣ < 100 km s⁻¹). This approach maximizes recovery of the injected signal while mitigating coherent accumulation of noise from different spectral orders. Note that we repeat the full optimization and cross-correlation procedure for each atmospheric model considered.

At the outset, we highlight the quality of our observations against those obtained in previous studies. TOI-732 is representative of the bright, sub-Neptune-hosting M dwarfs discovered by TESS. However, at H = 8.44, it is somewhat fainter compared to the typical HRCCS targets hosting giant exoplanets. For example, the well-studied hot Jupiter hosts HD 189733 and HD 209458, which were subjects of near-infrared (NIR) atmospheric transmission spectroscopy (Snellen et al. 2010; Brogi et al. 2018; Sánchez-López et al. 2019, e.g.,), have H-band magnitudes 5.59 and 6.37, respectively (Cutri et al. 2003). Nevertheless, our spectra attained remarkably high S/N stemming from favorable observing conditions. In particular, observations were conducted at low air mass; midtransit corresponded to z = 1.068. In Figure 1, we plot the S/N of one representative spectrum from our study (red curve), which reached over 400 in some of the orders. This quality is comparable to that obtained using the same instrument for a confident detection of multiple molecules in a hot Jupiter orbiting the Sun-like star WASP-77 A (H = 8.37) using emission spectroscopy (Line et al. 2021). The S/N for one representative spectrum of WASP-77 A is also plotted in Figure 1. We do note that there are some differences between our analysis and Line et al. (2021). The latter probes a much stronger signal originating from dayside emission features, and the atmospheric features exhibit significantly greater Doppler shift than in the present case. Nevertheless, and as we will show in Section 3.3, the high fidelity of our data enables our sensitivity to molecular species in the atmosphere of TOI-732 c.

We perform cross-correlation with atmospheric models of CH₄, NH₃, and H₂O—each a key molecule expected in temperate H₂-rich atmospheres, as shown in Figures 3 and 4. We do not detect any of the molecules at high statistical significance, but we see nominal evidence for some trends. We report marginal (2σ–3σ) evidence for CH₄, based on CCF enhancement near the expected K_p and V_sys (the values of n_SV for each order, based on ΔCCF optimization, are listed in Table 1). The enhancement matches the morphology of signals recovered in injection tests (in particular, the cloudy models explored in Section 3.4). We find no evidence of either NH₃ or H₂O. In the case of NH₃, injection tests demonstrate high sensitivity to absorption by the molecule. However, our masking has removed regions with the strongest H₂O absorption features, and the remaining coverage has low sensitivity to the molecule. The top row of Figure 3 shows S/N maps from the cross-correlation for pairs of (K_p , V_sys).

The weak CH₄ signal manifests as a broad, vertical enhancement in its corresponding S/N map, near the planet's K_p and V_sys. It is slightly offset from the expected V_sys, with significance reaching 2.2σ–3.4σ at offsets of −4 to −7 km s⁻¹ (we show 1D profiles at the signal's peak in Figure 5). As such, we conservatively quote evidence for the molecule at the 2.2σ level. This confidence is supported by a bootstrap-based robustness test, included in Appendix B.2. Vertical structure in the signal is expected, and it is also present for injected signals described in Sections 3.3 and 3.4. This structure arises because the transit composes a very small portion of the planet's orbit (−0.0023 ≲ ϕ ≲ + 0.0023), and the change in the planet's radial velocity Δv_p is only 1.84 km s⁻¹. The process of shifting CCFs by the planet's velocity and then aggregating across exposures provides quantitatively similar results for various K_p . In other words, K_p is poorly constrained from the atmospheric cross-correlation analysis, even though it is known at high precision based on the system parameters derived from radial velocities and transit photometry (Cloutier et al. 2020; Nowak et al. 2020; Bonfanti et al. 2024). As seen in Figure 5, at the peak V_sys = − 7 km s⁻¹, values of K_p ranging from −213 km s⁻¹ up to the top boundary of the velocity K_p space exhibit S/N in excess of 2.4σ (i.e., within 1σ of the peak). On the other hand, V_sys shows a tighter distribution constrained from −10 to −5 km s⁻¹, again localized around the peak.

We perform an additional robustness test on the tentative CH₄ signal by repeating the analysis described above but swapping the in-transit frames with out-of-transit frames. Specifically, in ΔCCF optimization, the artificial signal is injected only into out-of-transit frames, and only the CCFs of out-of-transit frames are combined when we aggregate the planetary signal. All 17 out-of-transit frames are used in this test. The result is shown in Figure 4 and indicates that the CH₄ signal is not present in the out-of-transit spectra. This finding lends evidence that the nominal signal is not telluric in origin (or stellar, perhaps through a spurious peak in the cross-correlation of stellar lines and CH₄ features).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The slight offset in the CH₄ signal is not immediately reconcilable but could be explained by a number of factors. Similar blueshifted offsets on the order of several kilometers per second are commonplace for detections in hot Jupiter atmospheres (e.g., Sánchez-López et al. 2019). In those cases, blueshifted signals have been explained theoretically by high-altitude winds propagating from dayside to nightside (Miller-Ricci Kempton & Rauscher 2012). It is not clear if a similar process could apply for the present temperate sub-Neptune. Other potential explanations could be unaccounted-for instrumental effects or model uncertainties.

It is worth discussing additional structure in the S/N map, especially peaks of comparable strength to the putative CH₄ signal. Indeed, the presence of such structure means that more robust observations are needed to definitively confirm or rule out CH₄. It is possible that spurious peaks and troughs are due to unmitigated stellar or telluric residuals. For example, we performed a close inspection of one spurious peak at V_sys ≈ − 75 and K_p ≈ 100 km s⁻¹. We find significant contribution to this peak from two unmasked orders, between 1.68 and 1.73 μm. These orders contain particularly deep stellar lines, which are incompletely removed during SVD detrending. Similarly, strong positive and negative features also appear during the out-of-transit test in Figure 4, which may be attributed to similar causes. Our nominal CH₄ signal, however, arises from the full set of detrended orders and is not strongly present in any small subset. Since detrending is performed in the geocentric frame, residuals from deep stellar lines may persist owing to the barycentric correction velocity, leading to spurious cross-correlation peaks that diminish the S/N of the main CH₄ signal. We note that spurious structure can also influence the quoted S/N, through the calculation of the baseline standard deviation in Section 2.5. We chose a baseline V_sys region that appeared clear of gradients in the CCF matrix; however, when extending the baseline significantly (e.g., to −500 to +500 km s⁻¹), our tentative CH₄ signal becomes slightly diminished, with significances of 1.7σ−2.8σ at offsets between −4 and −7 km s⁻¹.

Neither the NH₃ nor H₂O S/N maps show any significant extended features near the expected K_p and V_sys. We performed additional cross-correlation experiments in search of an H₂O signal. In particular, we modified our mask in order to admit more spectral orders, including regions with stronger H₂O absorption. When including these data in the cross-correlation analysis, we found a feature in excess of 5σ significance near the expected orbital parameters; however, we believe this to be an artifact from incomplete removal of stellar H₂O absorption in the transmission spectra. While absorption by telluric water vapor should be removed during the detrending process (as telluric CH₄ was successfully removed), Earth's barycentric motion would have shifted the stellar photospheric H₂O lines by 0.34 km over the course of the night. Stellar lines are also affected, to a lesser extent, by the star's orbital motion around the system barycenter and by the Rossiter–McLaughlin effect during transit. Indeed, we found that stellar and telluric residuals in the CCF were suppressed only with significant detrending (n_SV ≥ 14). With this level of processing, injected atmospheric H₂O signals are significantly degraded. More sophisticated methods may be necessary to make robust HRCCS detections of species shared between the exoplanet, Earth, and host star, for V_sys ≈ 0 km s⁻¹.

We test our detection sensitivity to these species via injection/recovery tests. The row of Figure 3 shows the results of an identical analysis to the top row, except a model atmospheric transmission spectrum was injected (and cross-correlation was optimized) at K_p = 68 and V_sys = 80 km s⁻¹. The model was injected at 1 × its nominal strength, after first convolving it to match the spectral resolution of IGRINS.

For CH₄ and NH₃ we recover 5.6σ and 3.7σ signals, respectively. Therefore, we establish that the observations are indeed sensitive to these two species in the case of a clear atmosphere. This is consistent with similar analyses on low-velocity planets carried out using injections of cloud-free model spectra into this data set, as reported by Cheverall & Madhusudhan (2024). Recovery of H₂O is achieved at only a 2.9σ level, which we attribute to its relatively weak features in the unmasked channels. Remarkably, the Doppler shift of the planetary signal throughout transit is only Δv_p = 1.84 km s⁻¹. For hot Jupiter case studies in the HRCCS literature, this value typically reaches tens of kilometers per second (e.g., Brogi et al. 2018). Nevertheless, our injected CH₄ and NH₃ signals remain preserved through the detrending process.

An argument may be made that V_sys ∼ 0 presents further challenges to atmospheric detection, since atmospheric spectral features will more closely align with the cores of telluric lines. The atmospheric signal may therefore have lower S/N, or be more degraded by detrending. We therefore repeated the above injection test using the orbital parameters K_p = − 68 km s⁻¹ and V_sys = 0 km s⁻¹. This injected signal may more closely mimic the statistical properties of the true atmospheric transmission spectrum of this target. CH₄ and NH₃ are still recovered, albeit at the lower significances of 2.6σ and 1.6σ, respectively. H₂O is recovered at the 1.2σ level.

We therefore conclude that the combination of a low-significance inference of CH₄ and no indication of NH₃ in Section 3.2 is consistent with more CH₄ absorption relative to NH₃ in the atmosphere. Alternatively, if the CH₄ signal is spurious, then both species may be depleted, or the atmosphere may be cloudy (discussed in Section 3.4). The latter scenario could also point toward an atmosphere that is not H₂ dominated, or the species being photochemically destroyed.

We additionally consider the possibility of high-altitude clouds in the atmosphere of the planet that could be obscuring the molecular signatures. In particular, we investigate whether the low-significance inference of CH₄ in the data can be explained by the presence of high-altitude clouds. To test this scenario, we perform injection recovery tests using CH₄-only models with a gray cloud deck with different cloud-top pressures (P_c ), spanning from 10⁻² to 10⁻⁶ bar, with lower pressures implying higher in the atmosphere. The CH₄ abundance was set at 1%. We inject the models at V_sys = 80 and K_p = 68 km s⁻¹ and, as in the previous sections, attempt to recover the signal using ΔCCF optimization for each model individually. The results are shown in Figure 6.

Zoom In Zoom Out Reset image size

We find that the detection significance of the cloudy model decreases with the cloud-top pressure, which is consistent with expectations. At the deeper end with P_c = 10⁻² bar, or 10 mbar, the detection significance is lowered to 4.7σ, i.e., nearly 1σ lower than the equivalent cloud-free CH₄-only model. Importantly, for P_c below 10⁻⁴ bar, the detection significance is under 3σ. As such, our 2σ significance with the CH₄-only model is arguably consistent with the presence of a high-altitude cloud deck at P_c below 0.1 mbar. We also conduct similar injection tests for NH₃ and find that the detection significance reduces to the noise level for a cloud deck below 0.1 mbar, also consistent with our cross-correlation results.

For completion, we present spectra attained on Night 1; however, these spectra were excluded from the primary analysis of this manuscript. In total, 27 4-minute (A/B pair) exposures were attained. The exposures capture the full transit of TOI-732 c, but only one exposure occurred during the post-transit baseline. The data are of generally lower quality compared to Night 2, as the typical S/N per pixel is ∼200 (Figure 7). This is in part due to the substantially higher air mass of the observations (Figure 8), in the range z = 2.15 → 1.20, which also induces severe H₂O telluric contamination. We tested for the presence of CH₄ with our cross-correlation pipeline but did not identify a statistically significant signal near the expected V_sys or K_p of the system. Furthermore, when we injected our model CH₄ transmission spectrum, the cross-correlation signal was consistently recovered at low confidence (≲1.5σ), for injections at both V_sys = 80 and V_sys = 0 km s⁻¹. These poor statistical properties, in conjunction with Night 1's severe telluric contamination, led us to exclude it from our nominal analysis.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The necessity of out-of-transit baseline exposures for isolating the atmospheric signal is established. As discussed in Section 2.3, SVD can flexibly identify and remove telluric and stellar features but runs a risk of degrading the atmospheric signal (Birkby et al. 2013; de Kok et al. 2013), especially with a higher number of removed singular vectors. This risk is present in our analysis of TOI-732 c, whose low semiamplitude induces only a moderate Doppler shift across in-transit frames. However, our significant out-of-transit baseline helps mitigate this effect. Approximately half of our exposures are out-of-transit, which helps prevent the atmospheric signal from being captured in the leading singular components. The effect of fewer out-of-transit exposures is shown in Figure 9, via the recovery of a synthetic atmospheric signal injected into the data at V_sys = 80 and K_p = 68 km s⁻¹ prior to the analysis. Out-of-transit exposures are gradually cropped from either end of the time series, and as a result, the significance of the recovered signal is substantially reduced.

Zoom In Zoom Out Reset image size

A bootstrap analysis is conducted to further test the robustness of our tentative CH₄ signal. Spectra are cleaned, continuum normalized, and assigned orbital phases and in-transit/out-of-transit designations, per Section 2. In one bootstrap trial, we resample (with replacement) the spectral time series. Specifically, the fluxes in each wavelength channel of one spectrum are replaced with the fluxes in the corresponding channels of a different, randomly selected spectrum, and this process is repeated for all 33 spectra in the time series. In each case, the replacement spectrum may be selected from either the original in-transit or out-of-transit sample. Detrending with ΔCCF optimization is then performed, followed by cross-correlation. The S/N values across pairs of K_p , V_sys are recorded. We repeat for 1000 bootstrap trials.

For each bootstrap trial, we isolate S/N values lying in the ranges −10 km s⁻¹ ≤ V_sys ≤ + 1 km s⁻¹ and +30 km s⁻¹ ≤ K_p ≤ + 250 km s⁻¹. This restriction acts as an approximate prior on velocities. That is, if a statistically significant signal was detected in this range, it may be plausibly atmospheric in origin. The range roughly accounts for systematic and model uncertainties and the statistical properties of the data. Next, we benchmark our CH₄ signal to the distribution of bootstrapped S/N values. In Figure 10, we plot two distributions: the dotted profile ("All Samples" distribution) corresponds to all 2,652,000 S/N values resulting from all bootstrap trials, and the subsequent velocity range restriction. The tan histogram ("Trial Maxima" distribution) corresponds to the maximum of S/N values in each bootstrap trial (here, there are 1000 total samples, one for each bootstrap trial). With the observed CH₄ signal peaking at S/N = 3.4σ, 0.15% of samples in the "All Samples" distribution lie at greater S/N. Under a normal distribution, this position in the tail implies a 3.0σ outlier. Separately, 1.5% of samples in the "Trial Maxima" distribution lie at greater S/N than our tentative CH₄ signal, which corresponds to a 2.2σ outlier. Therefore, the 3.4σ S/N of the CH₄ inference is well calibrated to the statistical properties of the data. Furthermore, the peak remains an outlier across bootstrap trials, suggesting that there are no trends or artifacts in the data that would consistently generate this signal through resampling spectra.

Zoom In Zoom Out Reset image size