Transmission Spectroscopy of the Habitable Zone Exoplanet LHS 1140 b with JWST/NIRISS

LHS 1140 b is the second-closest temperate transiting planet to the Earth with an equilibrium temperature low enough to support surface liquid water. At 1.730$\pm$0.025 R$_\oplus$, LHS 1140 b falls within the radius valley separating H$_2$-rich mini-Neptunes from rocky super-Earths. Recent mass and radius revisions indicate a bulk density significantly lower than expected for an Earth-like rocky interior, suggesting that LHS 1140 b could either be a mini-Neptune with a small envelope of hydrogen ($\sim$0.1% by mass) or a water world (9--19% water by mass). Atmospheric characterization through transmission spectroscopy can readily discern between these two scenarios. Here, we present two JWST/NIRISS transit observations of LHS 1140 b, one of which captures a serendipitous transit of LHS 1140 c. The combined transmission spectrum of LHS 1140 b shows a telltale spectral signature of unocculted faculae (5.8 $\sigma$), covering $\sim$20% of the visible stellar surface. Besides faculae, our spectral retrieval analysis reveals tentative evidence of residual spectral features, best-fit by Rayleigh scattering from an N$_2$-dominated atmosphere (2.3 $\sigma$), irrespective of the consideration of atmospheric hazes. We also show through Global Climate Models (GCM) that H$_2$-rich atmospheres of various compositions (100$\times$, 300$\times$, 1000$\times$solar metallicity) are ruled out to $>$10 $\sigma$. The GCM calculations predict that water clouds form below the transit photosphere, limiting their impact on transmission data. Our observations suggest that LHS 1140 b is either airless or, more likely, surrounded by an atmosphere with a high mean molecular weight. Our tentative evidence of an N$_2$-rich atmosphere provides strong motivation for future transmission spectroscopy observations of LHS 1140 b.


INTRODUCTION
Whether temperate rocky planets orbiting low-mass stars have an atmosphere is arguably one of the most important scientific questions of the James Webb Space Telescope (JWST) mission (Gardner et al. 2023), one that can only be answered if a significant fraction of its lifetime is dedicated to this endeavour (Cowan et al. 2015;de Wit et al. 2023;Doyon 2024).Answering this question is an essential first step in assessing the habitability of nearby worlds and identifying the best targets for biosignature searches.The first 18 months of JWST observations have highlighted both its power and versatility for studying the atmospheres of small exoplanets.While the first atmospheric reconnaissance of TRAPPIST-1 b (Greene et al. 2023) and TRAPPIST-1 c (Zieba et al. 2023) through eclipse photometry suggests that those two planets may be airless worlds, the presence of atmospheres on these planets has not been definitively ruled out (Zieba et al. 2023;Ih et al. 2023;Lincowski et al. 2023;Turbet et al. 2023;Ducrot et al. 2023).The first JWST transmission spectra of the TRAPPIST-1 planets, in general, show strong signs of stellar activity in the form of continuum variability, unocculted spots/faculae (Lim et al. 2023), and flares (Howard et al. 2023).Unocculted spots/faculae, responsible for the transit light source (TLS) effect (Rackham et al. 2018), pose a significant challenge as they can mimic genuine atmospheric signals, greatly complicating the interpretation of transmission spectra.The TLS effect is a recurrent theme of numerous Cycle 1 and Cycle 2 transmission spectroscopy programs (e.g., Lim et al. 2023;Moran et al. 2023;May et al. 2023;Fournier-Tondreau et al. 2024); a fundamental problem that has yet to be solved.
LHS 1140 (Dittmann et al. 2017;Ment et al. 2019;Lillo-Box et al. 2020;Cadieux et al. 2024) is a keystone system for habitability studies.This M4.5 dwarf (Dittmann et al. 2017) hosts two small transiting planets: an outer planet LHS 1140 b (R p = 1.73 R ⊕ ), a rare object in the middle of the radius valley (Fulton et al. 2017(Fulton et al. , 2018;;Cloutier & Menou 2020) on a 24.7-day temperate orbit, and an inner planet LHS 1140 c, a warm super-Earth (R p = 1.27R ⊕ ) orbiting every 3.78 days.The two planets receive 0.43 and 5.3 times the irradiation of Earth, respectively, with LHS 1140 b comfortably situated within the Water Condensation Zone (Turbet et al. 2023).Cadieux et al. (2024) recently presented a joint study of almost all transit and radial velocity observations to date, obtaining a precision of 3% on the masses and 2% on the radii of LHS 1140 b and c.Among the temperate rocky exoplanets, only those in the TRAPPIST-1 system are currently characterized to such precision.Their analysis of the composition of LHS 1140 b shows that the planet could be enveloped in hydrogen (∼0.1% H/He by mass), akin to a smaller version of the temperate mini-Neptune K2-18 b, which has a transmission spectrum characterized by prominent CH 4 and CO 2 absorption bands in the near-infrared (Madhusudhan et al. 2023).Alternatively, LHS 1140 b could be a water world with a surface layer of condensed water representing 9-19% of the total mass.A 3D Global Climate Model (GCM) of the water world scenario predicts liquid water at the substellar point for a large range of atmospheric compositions (Cadieux et al. 2024).The GCM also predicts a distinctive transmission spectrum featuring relatively small (∼15 ppm) CO 2 features at ∼2.8 and ∼4.3 µm.
Transmission spectroscopy with HST/WFC3 shows a tentative signal of H 2 O/CH 4 near 1.4 µm in a low mean molecular weight atmosphere (Edwards et al. 2021;Biagini et al. 2024), but a combination of unocculted spots and faculae offers an alternative explanation -a hypothesis also supported by ground-based measurements (Diamond-Lowe et al. 2020).These observations imply a large fractional coverage (>80%) of stellar active regions which is somewhat surprising given that LHS 1140 is a relatively old (>5 Gyrs; Cadieux et al. 2024), slowly rotating star (P rot = 131±5 days; Dittmann et al. 2017), with low levels of flaring activity (Medina et al. 2022).Recent observations of two transits of LHS 1140 b with JWST/NIRSpec (G235H/G395H, 1.7-5.2µm) ruled out an H 2 -rich atmosphere and favored a high mean molecular weight atmosphere (Damiano et al. 2024).Further TLS characterization with JWST is required, especially in the context of seeking the detection of small atmospheric signals that could be severely affected/biased by stellar activity.
This letter presents the results of a transmission spectroscopy program with JWST NIRISS/SOSS (0.6-2.8 µm) aimed at both characterizing the stellar activity of LHS 1140 and providing a strong discriminating test of the mini-Neptune/water-world scenarios of Cadieux et al. (2024).We show that TLS is clearly detected in LHS 1140 and that a cloud-free mini-Neptune atmosphere for LHS 1140 b is strongly excluded.
The letter is structured as follows.The observations and data reduction steps are presented in Section 2 followed by the transit modeling in Section 3 and spectral extraction analysis in Section 4. The retrieved atmospheric properties of LHS 1140 b and TLS constraints are presented and discussed in Section 5 followed by a discussion of proposed follow-up observations in Section 6.We then conclude in Section 7.

OBSERVATIONS
Two transits of LHS 1140 b were obtained with JWST using the NIRISS instrument (Doyon et al. 2023) on UT2023-12-01 and UT2023-12-26 as part of program DD6543 (PI: Cadieux & Doyon).The spectroscopic time series were carried using the SOSS mode (Albert et al. 2023), offering a spectral resolution R ≈ 650, with the SUBSTRIP256 subarray configuration to access the first two diffraction orders of NIRISS (0.6-2.8 µm).Each visit comprised 949 integrations, covering 2.58 hr before ingress, the 2.15-hour transit and 1.11 hr after egress.The second visit fully captured a transit of LHS 1140 c lasting 1.13 hr and starting approximately 34 min after first contact of LHS 1140 b.Each integration was composed of n group = 3 filling approximately 50% of the full well to minimize charge migration and non-linearity effects (Albert et al. 2023).We made use of two independent data reduction pipelines, namely SOSSISSE (Lim et al. 2023) and supreme-SPOON (Feinstein et al. 2023;Radica et al. 2023Radica et al. , 2024;;Benneke et al. 2024), both yielding consistent transmission spectra with a mean (median) absolute deviation of 0.72σ (0.60σ).More details of both pipelines and their comparison are provided in Appendix A. The SOSSISSE data products are hereafter used in the analysis.
During the first visit, the star LHS 1140 was erroneously positioned outside the target acquisition field of view, causing a displacement of the orders on the detector with offsets ∆x = −157 px (dispersion) and ∆y = −12 px (cross-dispersion) relative to their nominal positions.This offset was calculated by comparing the pixel-to-wavelength calibrations derived from the two visits.A modified wavelength solution for the shifted spectral trace was determined through a crosscorrelation between the stellar trace and a PHOENIX stellar atmosphere model (Husser et al. 2013), following the procedure described by Feinstein et al. (2023); Radica et al. (2023).The target acquisition failure is attributable to an incorrect epoch of proper motion entered during scheduling (LHS 1140 is a high proper motion target), which means this sequence was executed with blind guiding from the observatory.Fortunately, this data set can be fully recovered with a small wavelength shift in order 1 -0.70-2.67 µm compared to 0.85-2.83µm during visit 2 -and negligible change in order 2.
The first visit is also affected by a background star1 that overlaps the spectral trace of LHS 1140 for wave-lengths below 0.90 µm in order 1, and between 0.60-0.75µm in order 2, contaminating the flux at the 1-2% level.We estimate a spectral type M2.4±0.4V for the contaminant star using the G − G RP calibration of Kiman et al. (2019).The T eff estimate of 3516 K from Gaia DR3 (Gaia Collaboration et al. 2023) is also consistent with an M2V spectral type (Pecaut & Mamajek 2013).We constructed a model of the trace of the contaminant star from a M0V template (WASP-80; GTO 1201, PI: Lafrenière) observed with NIRISS.This template was aligned by maximizing the correlation coefficient between the derivatives in spatial direction x of the template and observations in regions (pixels) where only the contaminant is seen.Once the optimal shift was determined, we computed the amplitude of the contamination pixel by pixel, and use the median of these amplitudes to scale the template to match the contaminant trace.We then subtracted this contaminant model from the images leaving flux residuals of the order of 0.1% on the affected pixels of LHS 1140.Such residuals could decrease (dilute) the transit depth of LHS 1140 b by 10 ppm at most.This possible systematics is further mitigated in the next Sections by analysing both visits together, as visit 2 was not affected by a dispersed contaminant.

WHITE LIGHT CURVE ANALYSIS
One output of SOSSISSE is an amplitude time series a(t) that corresponds to broadband flux measurements (details in Appendix A), hereafter referred to as the 'white' light curve (WLC).The WLC is modeled with two components, one for transits and the other for treating systematic signals, both described below.The fit was performed using the juliet framework (Espinoza et al. 2019) that generates transit models with batman (Kreidberg 2015) and implements Gaussian Process (GP) regression with celerite (Foreman-Mackey et al. 2017).The posterior distribution is explored with nested sampling and 500 live points using the dynesty package (Speagle 2020) available in juliet.
The transit component assumes circular orbits for both planets (Gomes & Ferraz-Mello 2020).The orbital parameters of planet k (k: 'b', 'c') are the period P k fixed to the value from Cadieux et al. (2024), the time of inferior conjunction t 0,k , and the scaled semi-major axis a k /R ⋆ that we derive using a common stellar density ρ ⋆ .For ρ ⋆ , we use the same Gaussian prior as in Cadieux et al. (2024) constructed from stellar mass and radius estimates.For all other parameters, we adopt wide uniform priors.The transits of LHS 1140 b and c are parameterized with the planet-to-star radius ratio R p,k /R ⋆ and the impact parameter b k .We fit for quadratic limb-darkening parameters q 1 and q 2 defined in Kipping (2013) that ensure physical solutions for values between 0 and 1.
For the systematic component, we use GP regression to model two nuisance signals also reported in other NIRISS data sets (e.g., Coulombe et al. 2023;Radica et al. 2024;Benneke et al. 2024): a beat pattern introduced by the observatory thermal control (McElwain et al. 2023) and correlated structures on the timescale of a few minutes suggestive of stellar granulation (e.g., Kallinger et al. 2014;Grunblatt et al. 2017;Pereira et al. 2019).We use a combination of two simple harmonic oscillator (SHO) kernels in celerite to jointly model these systematic signals.We fix the period of the first SHO term to 204 s, corresponding to the dominant periodicity in the out-of-transit fluxes based on its power (highest peak) in the generalized Lomb-Scargle periodogram (Zechmeister & Kürster 2009).We fit for an amplitude σ beat and a quality factor Q beat for this oscillation.As in Radica et al. (2024), we use a critically damped SHO term (Q fixed to √ 0.5) for the granulationlike signal and fit for an amplitude σ gra and a timescale τ gra of this stochastic variation.An extra jitter term σ jitter is added in quadrature to the diagonal of the covariance matrix to account for excess noise.We also fit for a baseline flux and a temporal slope for each visit.We measure slopes of −0.26 and −0.36 ppm per min during visits 1 and 2, respectively, a flux variation approximately 20-30 times weaker than observed during the transits of TRAPPIST-1 b with NIRISS (Lim et al. 2023).This is consistent with the fact that LHS 1140 is a slow-rotating star with a flux level remarkably stable over a timescale of a few hours, as also confirmed by TESS (Ricker et al. 2015).
The WLC of the two visits were jointly fit with a common ρ ⋆ , q 1 , and q 2 to allow more precise constraints.The adopted priors and resulting posteriors (16 th , 50 th , and 84 th percentiles) of this fit are presented in Table 1.The best-fit transit and systematic components of the WLC are shown in the top panels of Figure 1.Fitting visit 1 and visit 2 independently yielded consistent parameters within the 1σ uncertainty, but we note a systematic increase of ∼40 ppm in the transit depth of LHS 1140 b during visit 2 due to the double transit.The joint fit alleviates the covariance between R p,b , R p,c , and b c in visit 2 by using the information of a single transit of planet b from visit 1.This same argument is later used to extract combined transmission spectra of LHS 1140 b and c by jointly fitting the two visits in each spectral channel.

SPECTROPHOTOMETRIC ANALYSIS
We binned the extracted spectroscopic time series from SOSSISSE to R ≈ 100 in both order 1 and order 2. We excluded wavelengths below (above) 0.86 µm in spectral order 1 (2), as these wavelengths are already covered by the other order at a higher throughput.Because of the wavelength coverage differing between the two data sets (see Sect. 2), this results in 145 spectrophotometric light curves for the first visit and 149 for the second visit.We also constructed a common wavelength grid at the native resolution corresponding to the average of the nearest pixels (in wavelength) between the two visits.This average grid deviates at most by 0.23 nm from the wavelength calibrations from individual visits.We combined the spectral time series of visit 1 and visit 2 using the common wavelength grid, then binned to a R ≈ 100 to end up with 142 joint spectrophotometric light curves.We then removed the systematic component determined from the WLC from all spectral light curves.At R ≈ 100, the median photometric precision of the light curves is approximately  800 ppm which prevents us from characterizing the beat pattern and granulation signals, both with amplitudes below 100 ppm (Table 1).
To derive the transmission spectra of LHS 1140 b and c, we fitted a transit model to each spectrophotometric light curve.Again, the fits were carried out with juliet using nested sampling and 500 live points for each spectral bin.We fixed P k , t 0,k , a k /R ⋆ , b k to the best-fit values from the WLC analysis (Table 1) and fit for R p,k /R ⋆ .The limb-darkening coefficients were calculated for all spectral channels with ExoTic-LD (Grant & Wakeford 2022) using a custom PHOENIX model input (T eff = 3100 K, log g = 5, [Fe/H] = 0.0) for LHS 1140.For the spectral fits, the corresponding q 1 and q 2 limbdarkening parameters are kept fixed.We allow for a baseline flux parameter and a σ jitter for each visit and all spectroscopic bins.Examples of 10 spectroscopic channels jointly fitting the transits of LHS 1140 b and c are shown in Figure 1.
The final combined transit spectrum of LHS 1140 b is presented in Figure 2 along with a binned version at R ∼ 20 to ease comparison with HST/WCF3 data.The spectrum is relatively flat above 1 µm, but features a clear 200-ppm decrease towards shorter wavelengths.We show in the next section that this is a signature of the TLS effect from unocculted faculae.The HST/WFC3 data are fairly consistent with NIRISS albeit for one or two data points with larger transit depth blueward of 1.4 µm which may have largely contributed to the tentative water/methane detection mentioned by Edwards et al. (2021) and Biagini et al. (2024).The transmission spectra of LHS 1140 b and c are available in Appendix B.

THE ATMOSPHERE OF LHS 1140 B
We now use the combined transmission spectrum of LHS 1140 b to jointly infer properties of the planetary atmosphere and stellar contamination from unocculted active regions resulting in stellar contamination (the transit light source, or 'TLS' effect).Our analysis considers the evidence for stellar contamination (Sect.5.1), evidence for a planetary atmosphere through retrievals (Sect.5.2), and finally a comparison with GCM pre-dictions of mini-Neptunes (Sect.5.3).We also provide a preliminary analysis of the transmission spectrum of LHS 1140 c in Appendix C showing that its spectrum is featureless and inconsistent with a cloud-free H 2 -rich atmosphere.

Transit Light Source Effect from LHS 1140
We first consider whether LHS 1140 b's transmission spectrum can be explained only by unocculted stellar active regions.We modeled the TLS effect using the transmission spectra stellar contamination module of the POSEIDON retrieval package (MacDonald & Madhusudhan 2017; MacDonald 2023).We generate model spectra by multiplying a bare-rock transmission term, (R p /R ⋆ ) 2 , by the wavelength-dependent stellar contamination factor from two distinct stellar heterogeneities (Equation 3, Fournier-Tondreau et al. 2024).The active region spectra are calculated by interpolating PHOENIX stellar models using the PyMSG package (Townsend & Lopez 2023).Our TLS model fits for the covering fractions and temperatures of the facula, spot, and quiet photosphere, yielding six free parameters: R p , f fac , f spot , T fac , T spot , and T phot .We fix the surface gravity of all active regions to log g = 5.04 (Cadieux et al. 2024).The priors are listed in Table D1 and mainly follow those in Fournier-Tondreau et al. ( 2024) for their two-heterogeneity model.Our POSEIDON model spectra are generated at R = 20 000 from 0.60 to 2.9 µm, convolved with a Gaussian kernel to the native resolution of NIRISS/SOSS (R ≈ 650), then multiplied by the instrument sensitivity function and binned down to the wavelength spacing of the data (R ≈ 100).The parameter space is explored via the nested sampling package PyMultiNest (Feroz & Hobson 2008;Buchner et al. 2014) with 2 000 live points.The posterior distributions for this TLS-only model are shown in orange in the bottom row of Figure 2 (also in Appendix D), with the median and 1σ confidence intervals listed in Table D1.
LHS 1140 b's transmission spectrum shows definitive evidence of unocculted stellar faculae.We detect faculae at 5.8 σ confidence (∆ ln Z = 14.91,where ∆ ln Z is the increase in log Bayesian evidence for stellar contamination over a flat line).Our 6-parameter TLS model (χ 2 ν = 1.73, with 136 degrees of freedom), shown in Figure 2, provides a significantly better fit compared to a flat line (χ 2 ν = 1.96, with 141 degrees of freedom).The reduced χ 2 of 1.73 may be indicative of underestimated error bars, or perhaps imperfect TLS modeling due to inherent uncertainties in stellar atmosphere models (Lim et al. 2023;Jahandar et al. 2024).We find unocculted faculae 72 +84 −32 K hotter than the photosphere covering 20 +17 −12 % of the visible stellar disk.There is no evidence for spots.A wide range of covering fractions are consistent with the data due to the degeneracy between f fac and ∆T = T fac − T phot (i.e., smaller/larger faculae need to be hotter/cooler to produce a similar spectral contamination).This level of stellar activity is consistent, within a factor of order unity, with the observed photometric peak-to-peak variability of ∼1% of LHS 1140 (Dittmann et al. 2017) inferred from a 2-year monitoring campaign with MEarth (Irwin et al. 2009).
We note that fitting a single stellar contamination model to LHS 1140b's combined spectrum amounts to assuming a similar surface distribution of unocculted heterogeneities during the times of the two visits separated by one orbital period of 24.7 days, equivalent to ∼20% of one stellar rotation.To validate this assumption, we also fit the same TLS-only model to the transmission spectrum of each individual visit, obtaining f fac = 0.18 +0.16  −0.11 and T fac = 3151 +77 −54 K for visit 1 and f fac = 0.06 +0.16  −0.03 and T fac = 3420 +237 −227 K for visit 2. We also observe consistent unocculted faculae properties from LHS 1140 c's transmission spectrum with f fac = 0.12 +0.18 −0.07 and T fac = 3293 +205 −111 K during visit 2 (Appendix C).This confirms that our two visits have consistent faculae properties, and hence it is valid to analyze the combined spectrum with a single TLS model.The consistent faculae parameters from our LHS 1140 b and LHS 1140 c analyses confirm that these unocculted faculae lie outside the stellar surface sampled by the two planetary transit chords.We additionally note that Damiano et al. (2024) reported a spot crossing event during a different set of two transits of LHS 1140 b observed with NIRSpec in July 2023.Their observations, conducted 124 days prior to our NIRISS data set (about one full rotation of LHS 1140), disfavor unocculted heterogeneities (their Table 4).However, the longer wavelengths covered by NIRSpec G235H and G395H are less sensitive to the TLS effect.Our analysis therefore critically underscore the need for NIRISS observations to characterize the nature and spectral impact of unocculted stellar active regions on transmission spectra.

Atmospheric Retrieval
We next establish whether there is any evidence of an atmosphere on LHS 1140 b.Given the presence of unocculted faculae established above, we performed a joint stellar contamination and planetary atmosphere retrieval analysis using POSEIDON.We consider a range of atmospheric retrieval models, including single-gas pure atmospheres, multiple gases, and atmospheres with or without aerosols.Our models consider the following gases (opacity sources in parentheses): CO 2 (Tashkun & Perevalov 2011) D1.The transmission spectrum of LHS 1140 b is mainly shaped by stellar contamination from unocculted faculae.A planetary atmosphere dominated by N2 or CO2 is compatible with the data, with the former pure composition being the maximum a posteriori model.A clear N2-rich atmosphere combined with unocculted faculae is preferred at 2.3 σ over faculae alone (see Sect. 5.2 and Fig. D1).(Yurchenko et al. 2017) For multi-gas models, the volume mixing ratios follow a permutation-invariant centered-log-ratio (CLR) prior (Benneke & Seager 2012), which allows for any molecule to be equally likely a priori to be the dominant gas.We assume isothermal atmospheres and fit for a reference radius, R p,ref , at a reference pressure of 1 bar.We include a two-parameter power-law prescription for hazes (MacDonald & Madhusudhan 2017) in all multi-gas atmospheric models.For the cloudy model, we assume an optically-thick gray opacity/surface with all layers deeper than P surf set to infinite opacity.We allow M p to vary as a free parameter following a Gaus-sian prior (5.60 ± 0.19M ⊕ ; Cadieux et al. 2024).For the stellar contamination, we use the same TLS parameterization as outlined above (i.e., 5 parameters to fit for both faculae and spots).We used 2 000 PyMultiNest live points for all retrievals.A summary of the free parameters and their priors is provided in Table D1.
Our retrieval analysis identifies tentative evidence for a cloud-free N 2 -dominated atmosphere on LHS 1140 b (2.3σ).We first considered models with a single-gas atmosphere with negligible cloud opacity in the upper atmosphere (all including stellar contamination), finding that the fit did not improve for CO 2 , H 2 O, CH 4 , or H 2 pure atmospheres.For example, our 100% CO 2 model has a lower Bayesian evidence compared to stellar contamination only (ln Z = 1141.02vs. 1142.15)reflectingthe 'Occam penalty' from adding one or more parameters that do not improve the fit (see e.g., Trotta 2008) -since there are no apparent CO 2 features in our NIRISS spectrum.Pure CO 2 atmospheres must have T < 233 K (2σ upper limit) to be compatible with our non-detection of CO 2 absorption (i.e., high-temperature pure CO 2 atmospheres are ruled out).However, our 100% N 2 model has the highest Bayesian evidence of all our models (ln Z = 1144.65),with a ∆ ln Z = 2.50 (2.8σ) for N 2 + stellar contamination over stellar contamination alone.The evidence for N 2 arises from a combination of a residual short-wavelength slope compatible with N 2 Rayleigh scattering and a weak feature near 2.2 µm attributable to N 2 -N 2 collision-induced absorption (CIA) -see Appendix D and Figure D1.Our multiple gas retrieval reaffirms that N 2 is the favored background gas, even when hazes are included in the model, with a retrieved abundance of 100 +0 −2 % (see Fig. 2, blue posteriors), indicating that our data rule out the tail to lower N 2 abundances present in the CLR prior.We rule out cloud-free H 2 O-rich, CH 4rich, and H 2 -rich atmospheres, with 2σ upper limits of log H 2 O < −2.94, log CH 4 < −2.78, and log H 2 < −0.95 (< 11%), respectively.While our multiple gas retrieval does allow for cold (T ≈ 100 K) CO 2 -rich atmospheres (corresponding to a relatively featureless atmospheric contribution to the spectrum), this solution is not statistically favored, as discussed above.To provide a more conservative estimate for the N 2 detection significance, we calculated the Bayesian evidence for a multiple gas model including all the other gases and hazes but without N 2 (ensuring the possibility of both CO 2 -dominated atmospheres and hazes are propagated into the Bayesian evidence), finding a conservative ∆ ln Z = 1.50 (2.3σ) in favor of an N 2 -dominated atmosphere.Our tantalizing evidence for a N 2 -dominated atmosphere on a habitable zone super-Earth raises a resounding call for additional observations of LHS 1140 b to confirm this result.
We additionally considered the potential for aerosols in LHS 1140 b's atmosphere.First, we reiterate that our multi-gas retrieval discussed above included a parametric prescription for atmospheric hazes in the form of a power law (MacDonald & Madhusudhan 2017).The haze parameters are unconstrained in all our retrievals (see posteriors in Appendix D).The reason for this is that hazes still exist within an atmosphere, providing an additional opacity enhancing the dominant Rayleigh slope, but the retrieval must first 'select' a background gas before the impact of a haze can be established.If N 2 is the background gas, N 2 Rayleigh scattering alone provides a good fit, and additional haze opacity is not needed (hazes are redundant parameters).If CO 2 is the dominant gas, then hazes have no spectral effect due to the high molecular weight and low temperature shrinking the scale height and hence flattening the spectrum.Therefore, allowing for hazes does not affect the inference of a clear N 2 -dominated atmosphere as the favored model.When we include a cloud/surface in our multigas retrieval we obtain a bimodal solution: (i) a clear ∼100% N 2 atmosphere, as above, or (ii) an opticallythick cloud deck at low P surf ∼ 10 −5 bar with no constraints on the atmospheric composition (i.e., such highaltitude clouds would render any transmission spectrum featureless, regardless of the atmospheric composition).The Bayesian evidence decreases when adding a cloud deck (see Table D1), indicating that this is a redundant parameter not required to explain LHS 1140 b's transmission spectrum.We also stress that such exceedingly high-altitude clouds are probably unrealistic.According to 3D GCMs of LHS 1140 b for both the water world (Cadieux et al. 2024) and hydrogen-rich scenarios (see below), a cloud deck (e.g., H 2 O, CO 2 clouds) should form much deeper in the atmosphere (P ≈ 1 bar).Therefore, while our present observations do not strongly favor a clear N 2 -dominated atmosphere over a high-altitude cloud deck, the latter scenario is less plausible from a GCM standpoint.
We examine the evidence for N 2 in the atmosphere of LHS 1140 b and present our full atmospheric retrieval results and posterior distributions in Appendix D.

3D GCM Forward Modeling
Here we compare the observed spectrum with realistic predictions from 3-D GCMs of a mini-Neptune with a 80 bar H 2 -rich atmosphere of various compositions: 100×, 300×, and 1000×solar metallicity.For this, we used the Generic PCM (Planetary Climate Model), historically known as the Generic LMD GCM, as in Cadieux et al. (2024).The model is capable of simulating various types of exoplanets, including terrestrial planets in the TRAPPIST-1 system (Turbet et al. 2018;Fauchez et al. 2019) and sub-Neptunes such as GJ 1214 b (Charnay et al. 2015) or K2-18 b (Charnay et al. 2021).The GCM simulations performed here closely follow the methodology described in Charnay et al. (2021), except that star and planet properties have been adapted to LHS 1140 b.The GCM experiments are described in more details in Appendix E.
Following the methodology of Fauchez et al. (2019), the outputs of the GCMs are used as inputs to the Planetary Spectrum Generator (Villanueva et al. 2018) to generate synthetic transmission spectra using the GlobES module (Villanueva et al. 2022) that consider the 3D nature of the atmosphere and cloud in a self-consistent manner.The simulations include atmospheric refrac-  2024) for an Earth-like atmosphere (1 bar N2, 400 ppm CO2) and a pure CO2 atmosphere at 5 bar.An H2-rich atmosphere for LHS 1140 b is formally rejected (>10σ) by the NIRISS/SOSS data.A flat solution (e.g., water world or airless planet) provides a significantly better fit but the reduced χ 2 of 1.75 may indicate an underestimation of error bars, an imperfect TLS correction, or the presence of residual spectral features (e.g., slope).An apparent linear trend with a slope of approximately 40 ppm across the NIRISS domain (dotted green line) improve the fit (χ 2 ν = 1.72), but is not predicted by our GCMs.
tion, collision-induced absorption (CIA) and multiple scattering.Irrespective of atmospheric composition, all forward models have a cold trap between ∼0.1 and 1 bar (see Fig. E1), favoring condensation of H 2 O into clouds.For these realistic cloudy mini-Neptune models, CH 4 and CO 2 (to a lesser extent) are the only observable transmission features in the near-infrared.Figure 3 compares the TLS-corrected transmission spectrum of LHS 1140 b with these updated mini-Neptune models along with water world GCMs taken from Cadieux et al. (2024) for an Earth-like atmosphere (1 bar N 2 , 400 ppm CO 2 ) and a pure CO 2 atmosphere at 5 bar.All hydrogen-rich GCMs are formally rejected by the data (fitting for an offset) with a confidence level exceeding 10 σ, with a ∆ ln Z = −326.90,−172.22,−84.98 for the 100×, 300×, and 1000×solar metallicity models, respectively, compared to a flat spectrum.The water world GCMs or a flat line (airless planet) provide a much better fit to the data.However, we note an apparent slope of ∼40 ppm in the spectrum that is not predicted by the GCMs explored in this study.The possible origin of this residual slope is discussed in Appendix D. One line of evidence supporting atmospheric retention on LHS 1140 b is that the planet is likely resilient to atmospheric mass loss of light elements (H 2 , He) from processes such as XUV-driven photoevaporation (Owen & Wu 2017) and core-powered mass loss (Ginzburg et al. 2018).According to Cadieux et al. 2024 (Figure 4, therein), an initial envelope mass fraction as low as ∼0.1% H/He could mostly persist after 10 Gyr thanks to the relatively low instellation of LHS 1140 b combined with its relatively high surface gravity.Based on these results, it is probable that an atmosphere composed of any elements heavier than hydrogen or helium would also be retained by the planet over similar timescales.
Another way to present this argument is illustrated in Figure 4, showing the instellation vs. the escape velocity of LHS 1140 b (S = 0.43 ± 0.03 S ⊕ , v esc = 20.13 ± 0.37 km/s; Cadieux et al. 2024) along with other exoplanets smaller than 1.8 R ⊕ using the NASA Exoplanet Archive (Akeson et al. 2013).This radius cut is chosen to focus on terrestrials, super-Earths, and potentially water worlds, excluding exoplanets predominantly composed of gas.The empirical "cosmic shore-line" (S ∝ v 4 esc ) of Zahnle & Catling (2017) based on Solar System objects appears as an orange band in the figure, a region that separates planets with an atmosphere from those without.Reconnaissance atmospheric characterization in transmission and/or in emission with JWST of a few key targets will be required to establish this shoreline across spectral types.As shown in this diagram, LHS 1140 b, TOI-1452 b (Cadieux et al. 2022), TRAPPIST-1 f and TRAPPIST-1 g (Agol et al. 2021) appear as the most favorable small exoplanets to host an (secondary) atmosphere.2017) based on Solar System bodies is depicted in orange with an arbitrary envelope to underscore uncertainty with spectral types.The size of data points scale with their Transmission and Emission Spectroscopy Metrics (Kempton et al. 2018) to highlight favorable targets for JWST atmospheric characterization.Targets with S < 10 S⊕ or with TSM/ESM above 90 th percentile are annotated.The TRAPPIST-1 system is abbreviated as "T-1".The optimistic habitable zone (Early Mars/Recent Venus) defined by Kopparapu et al. (2013) is shown in green (approximated for a range of spectral types).With a relatively high escape velocity and low instellation, LHS 1140 b likely retained an atmosphere.

Future observations
Considering the significant implications associated with the potential detection of a secondary atmosphere on LHS 1140 b, seeking unambiguous evidence warrants a combined approach of eclipse and transmission spec-troscopy.Here, we discuss the required observations to ascertain with high certainty the presence of a secondary atmosphere on LHS 1140 b (or lack thereof).It should be noted that due to the system's limited visibility with JWST, only 4 or 5 transits/eclipses of LHS 1140 b are observable in a given year.

Eclipse Photometry
Eclipse photometry centered on the 15-µm CO 2 absorption feature is a powerful tool for constraining the presence of an atmosphere on small rocky planets, e.g., TRAPPIST-1 b (Greene et al. 2023) and TRAPPIST-1 c (Zieba et al. 2023).The eclipse depth is given by F p /F ⋆ where F p and F ⋆ are respectively the flux from the dayside of the planet and the star during the eclipse.Assuming a BT-COND stellar atmosphere model (Allard et al. 2012) with an effective temperature of 3100 K anchored to the 2MASS J magnitude of LHS 1140, we find F ⋆ = 10.1 mJy for the F1500W MIRI filter.The observations of TRAPPIST-1 b at 15 µm suggest that the stellar model prediction for F ⋆ should be accurate to ∼10% (Greene et al. 2023).A blackbody is assumed for F p with the equilibrium temperature , where T eff is the effective temperature of the host star, R ⋆ its radius, a the planet semi-major axis, A B the planet Bond albedo and f the re-radiation factor that can take two extreme values: f = 1/4 corresponding to a homogeneous distribution of the energy across the planet and f = 2/3 corresponding to no heat redistribution to the night side (Esteves et al. 2013).
Figure 5 shows the predicted emission spectrum of LHS 1140 b for two airless models with different albedos and the two water world GCM cases of Cadieux et al. (2024).Three visits with MIRI would be sufficient to detect/exclude at the 3 σ level the most optimistic scenario (A B = 0, f = 2/3) corresponding to a dark, airless planet which is the coreless case inferred from the internal structure model of Cadieux et al. (2024).An airless Europa-like surface (A B = 0.6, Buratti & Veverka 1983) would require ∼19 visits to detect the secondary eclipse, i.e., observing every eclipse for nearly 5 years.Detecting and discriminating the water world cases (an Earth-like or CO 2 -rich atmosphere) is out of reach through eclipse photometry at 15 µm only, and would probably require the combination of many filters (e.g., 15 + 21 µm) over many eclipses.Cadieux et al. (2024) estimated that 12 transits (six times each of NIRSpec G235 and G395) would be required to detect the CO 2 features longward of 2.8 µm, The red cross, centered on the deepest airless case (AB = 0, f = 2/3), gives the predicted uncertainty at 15 µm for three visits needed to reach a 3-σ detection assuming photon-limited performance.Similarly, the green cross gives the number of visits needed (seven) for detecting the deepest eclipse at 21 µm.Each visit is assumed to last ∼7.5 hours (1 hr + 3 times the transit duration), a similar experimental design adopted by Greene et al. (2023) and Zieba et al. (2023) for the MIRI observations of TRAPPIST-1 b and c, respectively.

Transmission spectroscopy
an exposure time in line with the nine additional G395 visits proposed by Damiano et al. 2024 to detect the CO 2 feature at 4.3 µm.While G395 may be the most attractive mode for maximizing the signal-to-noise of the 4.3 µm feature, it comes with the significant scientific compromise that the atmospheric water abundance in the presence of TLS, as observed in LHS 1140 b, is likely to be poorly constrained.The same ambiguity issue between TLS and water detection associated with the G395 mode alone has been noted by other NIRSpec programs on warm super-Earths (e.g., Moran et al. 2023;May et al. 2023).Moreover, the G395 mode is insensitive to short wavelength spectral slopes associated with hazes and Rayleigh scattering.Our observations provide tantalizing evidence (2.3 σ) for a Rayleigh scattering slope and a CIA feature around 2.2 µm that could be explained by a N 2 -rich atmosphere.Such a signal could be confirmed with approximately 4 additional visits that should also include NIRSpec observations since the N 2 -N 2 CIA shows stronger opacity at 4.3 µm which is very close to the CO 2 feature.Clearly, the optimal experimental design for exploring the full diversity of secondary atmospheres (N 2 -or CO 2 -rich) along with proper TLS characterization calls for the widest pos-sible wavelength coverage as offered by the combination of NIRISS/SOSS and NIRSpec/G395.Observing within the same season (July or December) through two consecutive visits between NIRISS and NIRSpec minimizes the change in stellar rotation phase which is only ∼20% given the relative orbital period of LHS 1140 b (24.7 days) and the stellar rotation period of ∼131 days.
The two consecutive transits of LHS 11140 b observed with NIRISS that we presented in this letter is the proof of concept of this experimental design, showing that the TLS can vary weakly within one observing season, implying that the G395 and NIRISS data acquired within one season could be analyzed jointly under the reasonable assumption that both visits share a similar stellar heterogeneity configuration.

SUMMARY & CONCLUSION
We have presented the 0.65-2.7 µm transmission spectrum of the temperate planet LHS 1140 b obtained from two visits with JWST/NIRISS, the second of which coincidentally involved a transit of LHS 1140 c.All spectra exhibit a low level of stellar contamination caused by unocculted faculae with covering fractions at the level of ∼20%.GCMs of mini-Neptunes with various atmospheric compositions (100×, 300×, 1000×solar metallicity) are all excluded with a significance greater than 10 σ.A spectral retrieval analysis also excludes a clear H 2 -rich atmosphere, with the most likely atmospheric scenario being that of an N 2 -or CO 2 -dominated envelope.The former N 2 -rich atmospheric composition is favored by the data at 2.3 σ from a tentative detection of N 2 Rayleigh scattering combined with weak N 2 -N 2 CIA absorption near 2.2 µm.While an H 2 -rich atmosphere with a relatively high cloud deck is consistent with the NIRISS observations, such a muted spectrum is in contradiction with cloud formation simulated in GCMs and the relatively clear atmospheres detected on the temperate mini-Neptunes K2-18 b (Madhusudhan et al. 2023) and TOI-270 d (Benneke et al. 2024).
The NIRISS observations are more likely consistent with the water world scenarios presented by Cadieux et al. (2024), with or without a secondary atmosphere, a conclusion also supported by recent transmission spectroscopy data obtained with JWST/NIRSpec (Damiano et al. 2024).Of all nearby small temperate planets, LHS 1140 b is the most likely to have retained a secondary atmosphere based on its low instellation and high surface gravity.The next obvious step to better constrain LHS 1140 b's atmospheric composition is to perform a joint analysis of both NIRISS and NIRSpec datasets, ideally with a common data reduction methodology.
Only three visits of 15 µm eclipse photometry with MIRI is required to yield a 3-σ detection of the secondary eclipse associated with a dark, airless planet, but nearly five years (4-5 eclipses per year) is required if its albedo is closer to an icy surface (A B ∼ 0.5) as suggested by the relatively high water mass fraction (∼15%) of LHS 1140 b.Transmission spectroscopy is the most efficient method to detect the potential secondary atmosphere of LHS 1140 b through consecutive observations between NIRISS/SOSS and NIRSpec/G395 during the same season to allow for a proper characterization of stellar contamination at all epochs and explore N 2 -and CO 2 -dominated atmospheres.Given the limited visibility of LHS 1140 b, several years worth of observations may be required to detect its potential secondary atmosphere, a program that should be initiated as soon as possible given the limited lifetime of JWST.LHS 1140 b is arguably the best temperate transiting planet for which liquid surface water may be indirectly inferred through the detection of sufficient level of atmospheric CO 2 .The first transmission spectrum of the warm super-Earth LHS 1140 c is presented in Figure C1.We present here a first exploratory analysis of LHS 1140 c's NIRISS/SOSS spectrum by repeating the retrieval exercise outlined in Section 5.2 for the Flat line, TLS-only, and TLS + Multi-gas (Haze) models.All priors remain unchanged except for R p,ref and M p changed to U (1, 1.5) and N 1.91, 0.06 2 based on Cadieux et al. (2024), and T now allowed to go to higher temperatures (100-600 K).
A flat solution is favored for LHS 1140 c (2.1 σ) due to the lower signal-to-noise ratio spectrum derived from a single transit entirely confined into a transit of LHS 1140 b (double transit, Fig. 1).The Flat line model yields a ln Z = 1090.49,while the TLS-only and TLS + Multi-gas (Haze) retrieval runs end up with marginally lower Bayesian evidences of ln Z = 1089.34and 1088.83,respectively.and a joint stellar contamination and planetary atmosphere model (blue).The TESS and Spitzer photometric measurements (Cadieux et al. 2024) are shown in red.We have included the Spitzer point in the retrieval analysis, but its exclusion does not change the results.The NIRISS/SOSS observations is flat with marginal evidence of unocculted faculae consistent with the simultaneous transit of LHS 1140 b (Fig. 2).The spectrum covering 0.65-2.7 µm has an average transit depth that falls between those measured by TESS and Spitzer, resolving the 4 σ discrepancy in radius measurements between the two instruments noted by Cadieux et al. (2024).
The stellar contamination only model yields consistent unocculted heterogeneity properties compared to LHS 1140 b: f fac = 0.12 +0.18 −0.07 and T fac = 3293 +205 −111 K, with f spot consistent with 0. The TLS effect associated with LHS 1140 c is smaller by definition given the surface ratio of the planets (R p,c /R p,b ) 2 of about one half.
Our joint stellar contamination and planetary atmosphere retrieval (TLS + Multi-gas model) can inform on possible atmospheres on LHS 1140 c.The posterior distributions for this run are presented in Appendix D. We do not detect any molecular feature or a slope from hazes (haze parameters are unconstrained).The most likely composition favored by the data is a pure N 2 envelope at any T .Two other solutions exist that are approximately equally likely: a H 2 O-rich atmosphere at T ≈ 200 K or a CO 2 -rich atmosphere at T ≲ 500 K.The combination of a high mean molecular weight µ and/or low T for such atmospheres is sufficient to flatten the spectrum below the sensitivity of our NIRISS spectrum.The data is incompatible with clear CH 4 -rich and H 2 -rich atmospheres with 2σ upper limits of log CH 4 < −2.25 and log H 2 < −0.94 (< 11%), respectively.Here, we elucidate why our retrievals favor an N 2 -dominated atmosphere.The observed transmission spectrum is given by ∆ λ, obs = ϵ λ, star ∆ λ, atm , where ϵ λ, star is the 'stellar contamination factor' (e.g., Equation 3 in Fournier-Tondreau et al. 2024) and ∆ λ, atm is the 'regular' transmission spectrum of the planetary atmosphere.Given that unocculted faculae are the dominant wavelength-dependent effect sculpting LHS 1140 b's transmission spectrum, we first corrected our NIRISS/SOSS data by dividing out the best-fitting unocculted stellar contamination model (binned to the resolution of the data).This allows one to compare model atmosphere-transmission-only spectra, ∆ λ, atm , to an equivalent form of the data.
Figure D1 compares our stellar contamination-corrected transmission spectrum of LHS 1140 b to our best-fitting 100% N 2 and 100% CO 2 atmosphere models.The CO 2 model is essentially flat, consistent with a non-detection of CO 2 bands.The N 2 model, however, exhibits a clear Rayleigh slope in both the first and second orders of the NIRISS/SOSS data (alongside a weaker N 2 -N 2 collision-induced absorption feature near 2.2 µm).Both models allow for the possibility of power-law hazes, but N 2 Rayleigh scattering alone provides the necessary slope without any additional scattering opacity.We stress that the residual slope attributed here to N 2 relies on the assumption that the stellar contamination is well-described by our interpolated PHOENIX models for faculae.The best TLS model leaves a significant residual near 2.3 µm which is coincident with the CO bandhead, a well-known temperature-and gravity-sensitive spectral feature in M dwarf spectra.Given inherent uncertainties associated with stellar atmosphere models (e.g., Lim et al. 2023;Jahandar et al. 2024), one cannot rule out the possibility that the measured slope is an artifact of imperfect stellar contamination correction.The evidence for N 2 is only tentative at this stage (2.3 σ) and will need to be confirmed with future observations.

D.2. Atmospheric and Stellar Retrieval Results
The priors, posterior parameter constraints, and key statistics from our retrieval analysis of LHS 1140 b are presented in Table D1.The full posterior distributions are shown for the TLS-only model in Figure D2, TLS + N 2 (Clear) in Figure D3, TLS + Multi-gas (Haze) in Figure D4, and TLS + Multi-gas (Haze + Cloud) in Figure D5.Finally, the posterior distributions for the TLS + Multi-gas (Haze) retrieval of LHS 1140 c are presented in Figure D6.

E. GLOBAL CLIMATE MODEL SIMULATIONS AND SYNTHETIC OBSERVABLES
We performed a series of 3-D GCM (Global Climate Model) simulations designed to explore a large variety of plausible atmospheric compositions for LHS 1140 b.These simulations include (i) thick mini-Neptune atmospheres (80 bar H 2 -rich) with compositions of 100×, 300× and 1000×solar metallicity, described in the main text, (ii) compact secondary N 2 and CO 2 -rich atmospheres, described in Cadieux et al. (2024), and (iii) sensitivity experiments of H 2 -rich atmospheres on top of a dry surface or a global surface ocean a.k.a.'hycean'-type planet (Madhusudhan et al. 2021).
Figure E1 shows the temperature, water vapor mixing ratio and cloud profiles for the mini-Neptune cases, as well as for the Earth-like and CO 2 -dominated atmospheres for comparison.In all these simulations, cloud decks are located below atmospheric pressures of ∼0.1 bar, near the top of the tropospheric cold trap.Clouds therefore have a very limited impact on the transit spectra (see Fig. 3) for all the simulations explored in this work.Previous intercomparison works (Sergeev et al. 2022;Fauchez et al. 2022) have shown that cloud deck altitude can vary slightly from one model to another, but here cloud deck altitude would have to rise by at least two orders of magnitude to alter our conclusions.The presence of high-altitude hazes -which is not simulated here -could flatten the transit spectrum even in the case of an atmosphere rich in H 2 , but in this scenario we would expect to see a haze slope in the shortwave part of spectrum (Sing et al. 2011).Some simulated cases show a slight variability in the amplitude of transit spectra due to cloud variability (in time and location), as already shown in Charnay et al. 2021 in the case of K2-18 b.However, even at model timesteps where the terminator region is the cloudiest, the amplitude of the transit spectrum features for the mini-Neptune cases is far greater than the scatter of NIRISS observations, so these compositions can be formally rejected.
We ran additional sensitivity simulations in which we changed the boundary conditions for the mini-Neptune simulations.First, we added a dry surface at 10 bar atmospheric pressure, but in this case the synthetic spectra (not shown) are very similar to the mini-Neptune cases (see Fig. 3).Second, we added a surface entirely covered by an ocean also at 10 bar atmospheric pressure.This aquaplanet endowed with a thick H 2 -dominated atmosphere, also known as hycean planet, has a quite different behavior.In fact, the simulation enters runaway greenhouse, which forces the ocean to evaporate and the surface temperatures to rise.This result is compatible with previous calculations of the runaway greenhouse limit for hycean planets (Innes et al. 2023).As the simulation progresses, the amount of water vapor in the atmosphere increases at all altitude layers.The altitude of the water cloud deck also increases, similar to what has been shown already for N 2 -dominated atmospheres entering the runaway greenhouse (Chaverot et al. 2023).For all the hycean cases we have simulated, the amplitude of the spectral atmospheric features is far greater

Figure 1 .
Figure 1.Spectrophotometric transit fits of LHS 1140 b for visit 1 (UT2023-12-01, left) and visit 2 (UT2023-12-26, right) and LHS 1140 c for visit 2 only.The broadband ('white') light curves are shown in top panels with the best-fit full model (transit + systematics) shown in black and systematics component only in pink (scaled 10× for clarity).For both visits, examples of 10 systematics-corrected spectroscopic bins are depicted with colored points in bottom panels.

Figure 2 .
Figure 2. Combined transmission spectrum of LHS 1140 b with NIRISS/SOSS from two transits and POSEIDON retrieval analysis results.The binned spectrum at R ∼ 20 (white points) and at a higher R ∼ 100 (gray points) significantly improve upon the HST/WFC3 data from Edwards et al. (2021) (black diamonds).The median models with 1-2σ confidence envelopes are shown for a stellar contamination model (orange) and a joint stellar contamination and planetary atmosphere model (blue), with their respective posterior distributions shown in the bottom panels (same colors).Confidence intervals for each parameter are given in TableD1.The transmission spectrum of LHS 1140 b is mainly shaped by stellar contamination from unocculted faculae.A planetary atmosphere dominated by N2 or CO2 is compatible with the data, with the former pure composition being the maximum a posteriori model.A clear N2-rich atmosphere combined with unocculted faculae is preferred at 2.3 σ over faculae alone (see Sect. 5.2 and Fig.D1).

Figure 3 .
Figure3.Stellar contamination-corrected combined spectrum of LHS 1140 b using the best-fit solution of Figure2.The black points are binned to R ∼ 20 while the gray points are at a higher R ∼ 100.Dashed lines depict GCM-based forward models for mini-Neptune atmosphere (100×, 300×, 1000×solar metallicity) and solid lines the water world GCMs ofCadieux et al. (2024) for an Earth-like atmosphere (1 bar N2, 400 ppm CO2) and a pure CO2 atmosphere at 5 bar.An H2-rich atmosphere for LHS 1140 b is formally rejected (>10σ) by the NIRISS/SOSS data.A flat solution (e.g., water world or airless planet) provides a significantly better fit but the reduced χ 2 of 1.75 may indicate an underestimation of error bars, an imperfect TLS correction, or the presence of residual spectral features (e.g., slope).An apparent linear trend with a slope of approximately 40 ppm across the NIRISS domain (dotted green line) improve the fit (χ 2 ν = 1.72), but is not predicted by our GCMs.
A Secondary Atmosphere on LHS 1140 b?While an exceptionally cloudy mini-Neptune is compatible with our NIRISS spectrum, such a scenario would be in stark contrast with the relatively clear atmospheres predicted by self-consistent GCMs of LHS 1140 b.Recent observations of the temperate mini-Neptunes K2-18 b (Madhusudhan et al. 2023) and TOI-270 d (Benneke et al. 2024) have detected strong spectral features associated with H 2 -rich atmospheres, with relatively little cloud opacity.Instead, our tentative inference of an N 2 -dominated atmosphere suggests LHS 1140 b is a water world with a secondary atmosphere (Forget & Leconte 2014; Kite & Ford 2018; Kite & Barnett 2020; Marounina & Rogers 2020).

Figure 4 .
Figure4.Escape velocity-instellation diagram of small exoplanets (Rp < 1.8 R⊕).The empirical "cosmic shoreline" (S ∝ v 4 esc ) ofZahnle & Catling (2017) based on Solar System bodies is depicted in orange with an arbitrary envelope to underscore uncertainty with spectral types.The size of data points scale with their Transmission and Emission Spectroscopy Metrics(Kempton et al. 2018) to highlight favorable targets for JWST atmospheric characterization.Targets with S < 10 S⊕ or with TSM/ESM above 90 th percentile are annotated.The TRAPPIST-1 system is abbreviated as "T-1".The optimistic habitable zone (Early Mars/Recent Venus) defined byKopparapu et al. (2013) is shown in green (approximated for a range of spectral types).With a relatively high escape velocity and low instellation, LHS 1140 b likely retained an atmosphere.

Figure 5 .
Figure5.Predicted emission spectrum of LHS 1140 b for various scenarios including the Earth-like (1 bar N2, 400 ppm CO2) and pure CO2 (5 bar) atmosphere cases from the GCMs ofCadieux et al. (2024).Extreme Bond albedos cases (0 or Europa-like) with no atmospheric heat redistribution (f = 2/3) are shown with dashed lines.The grey enveloppe represents the 10% uncertainty of LHS 1140's stellar flux inferred from a BT-COND model.The red cross, centered on the deepest airless case (AB = 0, f = 2/3), gives the predicted uncertainty at 15 µm for three visits needed to reach a 3-σ detection assuming photon-limited performance.Similarly, the green cross gives the number of visits needed (seven) for detecting the deepest eclipse at 21 µm.Each visit is assumed to last ∼7.5 hours (1 hr + 3 times the transit duration), a similar experimental design adopted byGreene et al. (2023) andZieba et al. (2023) for the MIRI observations of TRAPPIST-1 b and c, respectively.

Figure C1 .
Figure C1.Transmission spectrum of LHS 1140 c from NIRISS/SOSS at a R ∼ 20 (white points) and at a higher R ∼ 100 (gray points).The best-fit models from POSEIDON with 1-2σ confidence envelopes are shown for a stellar contamination model (orange) and a joint stellar contamination and planetary atmosphere model (blue).The TESS and Spitzer photometric measurements(Cadieux et al. 2024) are shown in red.We have included the Spitzer point in the retrieval analysis, but its exclusion does not change the results.The NIRISS/SOSS observations is flat with marginal evidence of unocculted faculae consistent with the simultaneous transit of LHS 1140 b (Fig.2).The spectrum covering 0.65-2.7 µm has an average transit depth that falls between those measured by TESS and Spitzer, resolving the 4 σ discrepancy in radius measurements between the two instruments noted byCadieux et al. (2024).
D. SUPPLEMENTARY MATERIAL: ATMOSPHERIC INFERENCE ANALYSIS D.1.Evidence for a N 2 -Dominated Atmosphere on LHS 1140 b

Figure D1 .
Figure D1.Tentative evidence of an N2-dominated atmosphere on LHS 1140 b.The stellar contamination corrected LHS 1140 b NIRISS/SOSS transmission spectrum (black points for R ∼ 20, gray points for R ∼ 100) is compared to the best-fitting model transmission spectra for a 100% N2 atmosphere (green) and a 100% CO2 atmosphere (blue), plotted at R = 20.The N2 model has a best-fitting T = 399 K, while the CO2 model has T = 116 K.The N2 model provides a better fit (2.3 σ) due to the presence of a Rayleigh scattering slope and a weak N2-N2 collision-induced absorption feature.

Figure D3 .
Figure D3.Posterior distribution for the joint N2 atmosphere and stellar contamination retrieval of LHS 1140 b's combined NIRISS/SOSS transmission spectrum.Note that N2 does not show in the corner plot as a free parameter because the N2 abundance is fixed to 100% for this model.

Figure E1 .
Figure E1.Results of Global Climate Model (GCM) simulations of LHS 1140 b assuming mini-Neptune thick H2 atmosphere (100×, 300× and 1000×solar metallicity composition), an Earth-like atmosphere (1 bar N2, 400 ppm CO2), and a thick CO2dominated atmosphere (5 bar of CO2).Panels show vertical profiles of the atmospheric temperatures (left), water vapor mixing ratio (middle), and water cloud mixing ratios (right).The thick solid lines indicate the global mean vertical profiles, and the dotted lines indicate the terminator vertical profiles (impacting transit spectra).

Table 1 .
Transit and systematic parameters inferred from a joint fit of the white light curve of visits 1 and 2 , H 2 O (Polyansky et al. 2018), CH 4

Table B1 .
NIRISS SOSS transmission spectra of LHS 1140 b and c Central wavelength (µm) Bandwidth (µm) Depth b (ppm) Error b (ppm) Depth c (ppm) Error c (ppm) Order .PRELIMINARY ANALYSIS OF THE TRANSMISSION DATA OF LHS 1140 C C

Table D1 .
Retrieval analysis summary for LHS 1140 b's combined NIRISS/SOSS transmission spectrum