The Thermal Emission Spectrum of the Nearby Rocky Exoplanet LTT 1445A b from JWST MIRI/LRS

The secondary eclipse observations of LTT 1445A b are most sensitive to the planet-to-star flux ratio (F_p/F_*) through the eclipse depth, where the planet flux at MIRI wavelengths is dominated by thermal emission, and to the eccentricity e and argument of periastron ω, through the eclipse timing and duration. The information on other stellar and planetary parameters is minimal. In this work, we adopted stellar and planetary parameters derived from E. K. Pass et al. (2023), which are the most recent global analysis of the system, shown in Table 1. E. K. Pass et al. (2023) obtained new transit data for planet c from Hubble Space Telescope (HST) using WFC3/UVIS combined with existing data from the Transiting Exoplanet Survey Satellite (TESS), radial velocity (RV) data from ESPRESSO, HARPS, HIRES, MAROON-X, PFS, plus additional 85 ESPRESSO RVs from B. Lavie et al. (2023) to help constrain parameters, making this the most comprehensive fit to the system published to date. A circular orbit (e = 0) is assumed in this joint analysis, and we verify in this work that the eccentricity of planet b is indeed small. E. K. Pass et al. (2023) did not rederive an effective temperature for the star, instead using T_*,eff = 3340 ± 150 K, from J. G. Winters et al. (2022), which included an extra-cautious uncertainty to account for systematic uncertainties in M dwarf bolometric corrections. To get a precise timing of the eclipse, we estimated light-travel time delay in the system to be 2a/c = 38 s, where a is semimajor axis, and c is speed of light. Then, we added this value to the quoted T_C value (transit midpoint) to account for the delay between the position of the planet at transit to its position at eclipse.

Table 1. Median and 68% Confidence Intervals of Stellar and Planetary Parameters Used in This Work

Parameters	Units	Values	References
Stellar Parameters:
M*	Mass (M⊙)	0.257 ± 0.014	E. K. Pass et al. (2023)
R*	Radius (R⊙)	0.271	E. K. Pass et al. (2023)
ρ*	Density (cgs)	18.2	calculated from E. K. Pass et al. (2023) values
	Surface gravity (cgs)	4.982	calculated from E. K. Pass et al. (2023) values
T*,eff	Effective Temperature (K)	3340 ± 150	J. G. Winters et al. (2022)
	Metallicity (dex)	−0.34 ± 0.09	J. G. Winters et al. (2022)
d	Distance (pc)	6.8638 ± 0.0012	Gaia DR 3 (Gaia Collaboration et al. 2023, 2016)
Planetary Parameters:
P	Period (days)	5.3587635	E. K. Pass et al. (2023)
a	Semimajor axis (AU)	0.03810	E. K. Pass et al. (2023)
Rp/R*	Planet-to-star radius ratio	0.0454 ± 0.0012	E. K. Pass et al. (2023)
Rp	Radius (RE)	1.34	E. K. Pass et al. (2023)
Mp	Mass (ME)	2.73	E. K. Pass et al. (2023)
TC	Time of conjunction (BJDTDB)a	2458412.70954	E. K. Pass et al. (2023)
T14	Total transit duration (days)	0.05691	E. K. Pass et al. (2023)
i	Inclination (Degrees)	89.53	E. K. Pass et al. (2023)
e	Eccentricityb	<0.110	J. G. Winters et al. (2022)
ρp	Density (cgs)	6.2	E. K. Pass et al. (2023)
Teq	Equilibrium temperaturec (K)	431 ± 23	E. K. Pass et al. (2023)
S	Instellation (S⊕)	5.7	E. K. Pass et al. (2023)

Notes. Most values are updated in E. K. Pass et al. (2023) from J. G. Winters et al. (2022) by adding HST WFC3/UVIS data and redoing a joint fit between new HST data and TESS data.

^aWe show T_C as measured by a clock located at LTT 1445A b’s position at the time of eclipse. We calculate this light-travel time corrected T_C by adding 2a/c = 38 s to the transit-referenced T_C = 2458412.70910 quoted in E. K. Pass et al. (2023). ^b2σ (95%) upper limit. Note that E. K. Pass et al. (2023) assumed e = 0. ^cAssumes no albedo and perfect heat redistribution.

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We used two data reduction pipelines to ensure the robustness of final spectroscopic light curves: Eureka! (T. J. Bell et al. 2022)¹¹ and Simple Planetary Atmosphere Reduction Tool for Anyone (SPARTA; first described in E. M.-R. Kempton et al. 2023).¹² These are both open-source packages specifically developed for JWST time-series observations.

3.2.1. Eureka!

3.2.2. SPARTA

We imported the optimal extracted spectroscopic light curves from Eureka! (optimal extraction) and SPARTA, using chromatic,¹³ a Python-based tool for reading and visualizing JWST data. We then truncated the Eureka! products below 5 and above 12 μm to match the wavelength range of data products from SPARTA. Next, we normalized the data by dividing by the median spectrum across all integrations. We flagged outliers more than 10σ away from each wavelength’s median-filtered light curve and excluded them from future binning or analysis, removing 16 outlying wavelength/time pairs for SPARTA and 71 for Eureka!. The processed data are shown in Figure 1, averaged with inverse-variance weighting into Δλ = 0.1 μm wavelength bins and Δt = 60 s time bins, for visual clarity.

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The most notable systematic is an exponential ramp at the beginning of each observation. Such exponential ramps are common in infrared instruments including Spitzer/IRAC (E. Agol et al. 2010), HST/WFC3 (Z. K. Berta et al. 2012; Y. Zhou et al. 2017), and JWST MIRI/LRS (T. J. Bell et al. 2023; J. Bouwman et al. 2023) and have been attributed to charge-trapping. However, beyond 10.6 μm, we observed a sudden change in ramp behavior, from a downward lower amplitude ramp to an upward higher-amplitude ramp (see Figure 1). This is consistent with the “shadowed” region described by T. J. Bell et al. (2023), where pixels on either side of this wavelength may experience qualitatively different illumination histories. This phenomenon appears to be common but not universal across MIRI/LRS observations, seen in T. J. Bell et al. (2024), E. M.-R. Kempton et al. (2023), M. Zhang et al. (2024), R. Hu et al. (2024), and M. W. Mansfield et al. (2024), but not in L. Welbanks et al. (2024), Q. Xue et al. (2024).

To mitigate the charge-trapping ramp, we removed the first 20 minutes of data from all three visits (red vertical ticks in Figure 1), during which this effect was strongest. While this cutoff does not completely eliminate the charge-trapping ramp, especially in the shadowed region where the direction of the ramp changes from fading to brightening, it significantly simplifies the systematic so that it can be well-modeled with a single exponential function during light-curve fitting (see Section 3.5). During the third visit, we observed a sudden drop in flux in both Eureka! and SPARTA products (see Figure 1 bottom panel), at around the 350 ppm level spanning approximately 9 minutes (broadband light curve from 5–12 μm). This drop occurred at BJD time = 2460162.280 (about 1 hr from the start of the observation). This drop is not at the gap of a data sector nor is it likely to be our target’s secondary eclipse (the calculated eclipse depth is 28 ppm at 8.54 μm). This flux drop is similar to one seen in the MIRI/LRS observation of GJ 367b in M. Zhang et al. (2024); it is not immediately clear whether its cause is a detector state change or something else. We did not find any correlation associate with FGS data using Spelunker (D. Deal & N. Espinoza 2024), so we think that this is not a mirror-tilt event. We mitigate this sudden drop by trimming off an additional 50 minutes (a total of 70 minutes) for the third visit.

It is crucial to determine the host star spectrum at MIRI/LRS wavelengths to be able to compare the planet’s thermal emission to theoretical models. The measured secondary eclipse depth is a planet-to-star relative flux contrast (D_sec = F_p/F_*), and it needs to be multiplied by a stellar spectrum to convert to the planet’s intrinsic dayside thermal emission flux. In this section, we will explore different options for stellar spectra of LTT 1445A and estimate the uncertainty on our adopted spectrum. Figure 2 shows LTT 1445A spectra from different sources as described below. In all cases, the stellar flux is represented at the surface of the star, as the Wm⁻² μm⁻¹ that could be multiplied by the stellar surface area to get to the star’s luminosity.

• 1.  
  The SPHINX model. A. R. Iyer et al. (2023) designed this grid to improve the treatment of broadband molecular features in M dwarf stars and benchmarked it against empirical spectra. We interpolated the precalculated grid spectra to the parameters in Table 1 assuming a solar C/O ratio of 0.5. We performed trilinear interpolation in log-surface gravity (), log-metallicity (), and log stellar effective temperature (), since fluxes per wavelength can grow where x ≠ 1. We identified stellar effective temperature (T_*,eff = 3340 ± 150 K, 4.5% uncertainty; J. G. Winters et al. 2022) as the main source of uncertainty in our stellar spectra. We perturbed T_*,eff by ±150 K (T_*,eff = 3190, 3490 K) resulting in spectra that are, on average, 6% higher and 7% lower (shown by the blue shading in Figure 2). We adopt this model and uncertainty as our reference stellar spectrum for the rest of this work.
• 2.  
  BT-Settl model. H. Diamond-Lowe et al. (2024) published a panchromatic spectral energy distribution comprising empirical data in X-ray, UV, and blue optical, estimates of EUV, Lyα line reconstruction, and BT-Settl (CIFIST) model for the rest of optical and infrared. In the MIRI/LRS wavelength range, the spectrum is just the BT-Settl (CIFIST) model (F. Allard et al. 2003; E. Caffau et al. 2011) using stellar parameters as in J. G. Winters et al. (2022). H. Diamond-Lowe et al. (2024) verified that the normalization of this spectrum closely matches the observe low-resolution prism spectrum of LTT 1445A from Gaia. This empirically informed BT-Settl model is higher than one produced by SPHINX model by about 1% and well within our adopted SPHINX uncertainty.
• 3.  
  Eureka! MIRI/LRS spectrum. We derived flux-calibrated stellar spectra from Visit 1 with Eureka! by turning on calibrated_spectra, and with guidance and caution about the reliability of this process from Eureka! developers (Taylor Bell, private communication). To better capture the full stellar flux for the intrinsic stellar spectrum, we used a box extraction with spectral aperture (spec_hw) and background half-width (bg_hw) of 9 and 15 pixels, respectively, larger than the 4 and 9 pixels used for time-series extraction (see Section 3.2.1). We then performed an aperture correction to translate from finite spectral aperture to infinite aperture using JWST’s jwst_miri_apcorr_0012.fits file and translated the observed flux at JWST into a stellar surface flux in Wm⁻²μm⁻¹ assuming the distance and radius reported in Table 1. When compared to the SPHINX model, the time-integrated observed flux from Eureka! at spec_hw = 9 is ∼10% lower than the T_*,eff = 3340 K SPHINX model on average, about 1σ–2σ given the estimated SPHINX uncertainty.
• 4.  
  SPARTA MIRI/LRS spectrum. We performed a similar reduction to that described in Section 3.2.2; however, using a simpler box extraction with an aperture half-width of 20 pixels. Using a larger aperture window ensures that we have captured almost all of the flux and that the aperture correction array is almost 1.0 across the wavelength range (max correction is 1.0035). The SPARTA spectrum agrees closely with the adopted SPHINX spectrum, although with systematic offsets up to 5% at longer wavelengths.
• 5.  
  STScI pipeline (x1dints) MIRI/LRS spectra. We downloaded the Visit 1 flux-calibrated JWST official x1dints file from the MAST portal and compared it to other spectra. We found mostly agreement with other spectra below 10 μm; however, as this default pipeline product does not include background subtraction, it may be increasingly subject to telescope thermal radiation at longer wavelengths.
• 6.  
  Planck thermal spectrum. For reference, we show a simple Planck thermal emission spectrum with T_*,eff = 3340 K. It overestimates the stellar flux by 10%–20% and entirely misses the broad jump at 6–7 μm present in the other theoretical and empirical spectra (see Figure 2, bottom panel).

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We performed light-curve fitting using chromatic_fitting (C. Murray 2025), a Python-based open-source tool specifically designed for multiwavelength light-curve fitting. This tool uses PyMC3 for efficient inference of parameter posterior probability distributions (J. Salvatier et al. 2016). For all eclipse fits in this paper, we use EclipseModel, which is a wrapper of the starry package (R. Luger et al. 2019).

For nonzero eccentricities (e > 0), directly including the argument of periastron ω as a model parameter can be challenging due to its degeneracy with ω + π. One approach is to re-parameterize in and , which ties strongly with observable eclipse timing and duration, respectively (J. N. Winn 2010). However, sampling in and induces a linear prior in e when applying a uniform prior in and (see detailed discussions in E. B. Ford 2006; J. Eastman et al. 2013). Instead, we opted to re-parameterize in and , as suggested by D. R. Anderson et al. (2011), which simplifies model ambiguities associated with the ω parameter while correcting for a uniform prior in e.

After carefully examining the data, we employed the following combination of systematic and eclipse models:

Here, F_eclipse(t, λ) represents the flux computed from the EclipseModel within chromatic_fitting. F_systematics(t, λ) is the systematics model built from a combination of PolynomialModel and ExponentialModel models in chromatic_fitting:

F_time = p_t,0 + p_t,1t_rel is a first-order polynomial in relative time, (where is the mean time of the trimmed data), used to correct for any linear trends and the baseline stellar flux. is an exponential ramp in relative time aimed at describing the residual charge-trapping ramp common in mid-infrared instruments (e.g., E. Agol et al. 2010; Z. K. Berta et al. 2012; Y. Zhou et al. 2017; T. J. Bell et al. 2023) while t_rel,0 is a relative start time of the time series after cutting off the first 20 minutes of the data (70 minutes in visit 3). Notably, the exponential amplitude A can be positive or negative to account for the different ramp behavior for wavelengths shorter or longer than 10.6 μm. F_y = 1.0 + p_y,1y(t) and F_x = 1.0 + p_x,1x(t) are linear functions of the y (spectral axis) and x (spatial axis) centroids in each frame, respectively, for data from the SPARTA pipeline. For Eureka! data, instead of the spectral axis (y) centroid, we used the provided spatial width of the point-spread function (σ_y). Note that Eureka! rotated each frame by 90°, so the x- and y-axes were swapped from the convention (and the SPARTA pipeline).

For all fitting, we binned the data to a time increment of 1 minute to improve computational efficiency and account for correlated noise on a shorter timescale. We fixed the stellar radius, stellar mass, orbital period, time of conjunction, orbital inclination, planet mass, and planet radius to the values in Table 1. We fixed the stellar amplitude to 1.0 to migrate any baseline in normalized stellar flux to the p_t,0 term in F_time. We also set the stellar and planet brightness maps to be uniform so other Starry parameters will not affect our light curve. The secondary eclipse depth then can be directly interpreted as a planet brightness map overall amplitude, which is propositional to the planet’s luminosity. The priors of eclipse depth and [], which ultimately control eclipse timing, will be later discussed in Sections 3.5.1 and 3.5.2.

The PyMC3 module (J. Salvatier et al. 2016), integrated into chromatic_fitting, was employed for parameter space exploration using No-U-Turn Sampler (NUTS; M. D. Hoffman et al. 2014) Markov Chain Monte Carlo (MCMC) techniques with 80,000 burn-in steps and 50,000 subsequent runs utilizing four chains. We initialize NUTS sampling with optimal parameters from pymc_ext.optimize. We included an uncertainty inflation ratio (n_σ,fitting) to account for extra scatter in flux. The uncertainty inflation ratio during the fitting (n_σ,fitting) is defined as the fitted parameter needed to inflate the light-curve uncertainty until a reduced χ² of 1 is met. Hence, one can use to assess the goodness-of-fit similar to reduced χ². The Gelman–Rubin diagnostic test (A. Gelman & D. B. Rubin 1992; S. P. Brooks & A. Gelman 1998) was used to indicate convergence, with , where is the variance of the posterior between chains, and W is the variance within each chain.

3.5.1. Broadband Fit to Orbital Parameters

3.5.2. Spectrophotometric Light-curve Fitting

Figure 1 shows the extracted fluxes from SPARTA and Eureka! are broadly similar, but the most direct quantitative way to compare them is through the residuals to model fits. We performed broadband and spectrophotometric fits for both pipelines’ extracted time-series spectra. In the broadband fits (Section 3.5.1), the expected per-point uncertainty from SPARTA is 35 ppm at 1 minute cadence, and the achieved scatter of the residuals to the broadband eclipse is 41, 44, and 42 ppm for the three visits. For Eureka!, the expected per-point uncertainty at the same cadence is 32 ppm, while the achieved scatter of the residuals is 52, 50, and 53 ppm for the three visits, ∼20% higher than with SPARTA. For the spectrophotometric fits, Figure 3 compares the measured scatter in the model residuals for both extractions, in 20 wavelength bins for the three visits. At the longest wavelengths, where the photon noise is intrinsically higher due to low stellar flux and instrument throughput, the two pipelines closely agree. Toward shorter wavelengths, where the photon noise is lower and subtleties of the extraction matter more, the Eureka! residuals show approximately 10%–15% higher scatter than SPARTA. Given SPARTA’s slight improvement in all fits, we adopt these results for our primary conclusions throughout the rest of the paper. In all analyses, we confirmed that Eureka! light curves lead to consistent results, albeit with slightly larger final uncertainties.

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Before delving into details about the constraints on eccentricity and the emission spectra, it is crucial to confirm that we have captured the secondary eclipse of LTT 1445A b. The planet’s thermal emission is close to the noise level, and given the potential of the inner planet LTT 1445A c (historically discovered after planet b) to excite eccentricity that might move LTT 1445A b’s eclipse away from the time predicted for a circular orbit, we first demonstrate that we clearly detect the eclipses in this MIRI/LRS data set.

Secondary eclipses of LTT 1445A b are not easily visible in the raw data (Figure 1). However, if we use the best-fit (means of posterior distributions) model parameters from a simultaneous eclipse and systematics fit (Equation (2)) for each visit, and remove the systematics contribution from the model (Equation (3)), the eclipses emerge. Figures 4 and 5 show systematics-corrected light curves for the broadband (1 wavelength bin) and spectrophotometric (20 wavelength bins) fits, respectively. We overplot individual-visit eclipse model fits using solid lines. We also included the inverse-variance weighted average of the three visits along with an eclipse model generated from the final eclipse depths in the far-right column (see Section 4.4 and Table 2 for the complete set of depths). Figure 6 shows the same systematics-corrected and combined data set as the last column of Figure 5, binned and rendered as 2D flux maps. Eclipses occur with consistent timing and depths across the three independent visits, and the eclipse depth grows toward longer wavelengths, as qualitatively expected for thermal emission at these wavelengths. These two independent pieces of evidence (the eclipse timing and the depth) emphasize that we truly detected the secondary eclipse of LTT 1445A b.

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The observations were planned assuming a near-circular orbit, but we test that assumption by allowing for a nonzero eccentricity that might change the eclipse’s timing through or its duration through . If the eccentricity is large, assuming a perfectly circular orbit could bias eclipse depths by missing the eclipse time or using the wrong eclipse duration. Here we summarize what we learn about e and ω through fits to the broadband light curves.

Even though we fit for and , the results in this section will be mainly given in and since it ties more strongly with observables. We calculated and by transforming MCMC samples in , to eccentricity e = + and argument of periastron ω = . Then, we reconstruct and , showing their posteriors in Figure 7. In the limit of small eccentricity, we can add a second x-axis to the top panel of Figure 7 as the offset of the mid-eclipse time from the e = 0 prediction (Δt_{e = 0}) using Equation (33) in J. N. Winn (2010):

where P is the planet’s orbital period and the light-travel-time delay has been accounted for in Table 2. Likewise, for the bottom panel, we can translate to duration ratio (T_ecl/T_tra) using Equation (34) in J. N. Winn (2010):

where T_tra and T_ecl are the transit and secondary eclipse durations, respectively.

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We observed good agreement within 1σ of between the first visit, = 0.00069 ± 0.00042, and the second visit, = 0.00031 ± 0.00037. While the posterior peak in for visit 3 is higher, at 0.0027 ± 0.0129, a greater uncertainty is observed due to a shorter out-of-eclipse baseline, even shorter than the in-eclipse duration (note that we also observed a bump in the visit 3 posterior, overlapping with peaks from the first and second visit). We calculated the weighted average of all visits as 0.00048 ± 0.00028, which translates to 2.4 ± 1.4 minutes later than the e = 0 (circular orbit) expectation, shown as the purple dashed line in the top panel of Figure 7. The combined value is consistent with 0 at 1.7σ.

For , constraints from the eclipse duration are less precise than , as expected, but they have good agreement across the three visits (see Figure 7; bottom). The best-fit value for is −0.0005 ± 0.0173 (purple dashed vertical line in bottom panel), statistically indistinguishable from circular. This value of also translates to the eclipse-to-transit duration ratio (T_ecl/T_tra) of 1.00 ± 0.04.

Moreover, constraints on and act as an independent check on the presence of eclipses. Given our wide uniform priors on [, ], the eclipses could theoretically fall outside our observation windows (indicated as colored shade in Figure 7). However, the fact that the posteriors find consistent eclipse timings and durations (that are also very close to circular) is another indication that real eclipses are detected.

Although not discussed in detail, Eureka!’s products’ best-fit and also agreed well within 1σ with best-fit = 0.00030 ± 0.00035, and = −0.0002 ± 0.0219 translates to eclipse time delay of 1.5 ± 1.7 minutes and eclipse-to-transit duration ratio of 1.00 ± 0.04.

With the eclipse timing and duration fixed to the values reported in Section 4.3 (translated back to and ), we obtained the emission spectra in terms of the eclipse depth (D), a planet-to-star flux ratio, from fits to broadband and spectroscopic light curves. Because eclipse depth is a nearly linear parameter and could go negative in these fits, the posteriors for eclipse depths were all well-described by symmetric Gaussian distributions. Figure 8 and Table 2 show these eclipse depths for the individual and combined visits at different binnings. Results are shown for SPARTA light curves, but the Eureka! depths are consistent to much better than 1σ for most bins (and no worse than 2σ across any bins; see Appendix A.1).

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Larger wavelength bins have lower noise and average more strongly over possible interwavelength correlations, but they hide the details of the planetary emission that grows sharply across this wavelength range. Smaller wavelength bins are noisier, but they better reveal the shape of the emission spectrum and could potentially show atmospheric absorption features. Even though we observed broadly consistent depths across the wavelength range (5–12 μm) as shown in Figure 8 and Table 2, we decided to exclude data points at wavelengths longer than 10.6 μm (gray shaded region in Figure 8) due to contamination from the shadowed region, and proceed with the more reliable shorter wavelength bins for comparison to theoretical models. This will make the comparison between each binning scheme more direct and easier to interpret. Therefore, the binning scheme is now 1, 4, 8, and 16 bins, instead of 1, 5, 10, and 20 bins, as described in Section 3.5.2.

Also, instead of using individual visits in our statistical analysis and interpretation that might be too noisy, we combined the depths of all three visits using inverse-variance weighting. The skewed central wavelength of each data point in Figure 8 indicates the “effective wavelength,” the inverse-variance weighted-averaged wavelength. The effective wavelengths differ from the central bin wavelength the most in broadband and are less pronounced as the bin size decreases.

Overall, the emission spectra show good agreement between visits 1 and 3, with broadband eclipse depths of 37 ± 6 ppm and 30 ± 8 ppm, respectively, while visit 2 shows a deeper broadband eclipse depth at 62 ± 8 ppm with = 1.35 ± 0.10, 1.50 ± 0.15, and 1.41 ± 0.16 for first, second, and third visit. We deployed the χ² statistic to these three visits’ broadband depths compared to the combined depth and got χ² = 9.19 with 3-1 = 2 degrees of freedom (dof), which translated to a p-value of 0.01. We did not find the cause of deeper eclipse depth in visit 2 from modeled systematics, guide star data, and residuals. Therefore, we artificially inflated the uncertainties of visits-combined broadband data point by a factor of n_σ,combined = so that we can can capture this unknown cause and assume that all three measured eclipse depths were drawn from the same underlying distribution. This uncertainty inflation factor (n_σ,combined) brings the reduced chi-square () of the three visits’ broadband eclipse depths compared to the combined depth close to 1. Similarly, we calculated the uncertainty inflation ratio as described above for each binning scheme, which yielded factors of 1.72, 1.40, and 1.30 for the 4, 8, and 16 wavelength binning schemes, respectively. These inflation ratios met our expectation that smaller wavelength bin sizes exhibit more photon noise and are therefore less sensitive to systematic noise, resulting in smaller required n_σ,combined. We then applied these uncertainty inflation ratios to the last column (combined) depths in Figure 8 and Table 2.

For context, Figure 8 shows the expected contrast for uniform, isothermal, Planck thermal emission from the planet’s dayside as dashed gray lines, according to

where B_p(λ, T_p) is the Planck thermal emission intensity as a function of planet temperature (T_p) and wavelength (λ). indicates the SPHINX stellar spectrum as described in Section 3.4. We also compared the approximation of a single dayside temperature to a sum of different temperature Planck spectra (from hottest at substellar point to coolest at the limb). We found that the difference is minimal: the sum of different temperature spectra is ∼1% higher at 5 μm and ∼3% lower at 12 μm. Therefore, we proceed with the single temperature approximation.

In the calculation of the Planck spectra above, we did not yet consider the uncertainties associated with the system’s parameters (T_*,eff = 3340 ± 150 K, a/R_* = 30.2 ± 1.7, R_p/R_* = 0.0454 ± 0.0012; Table 1). We translate these parameters into a model uncertainty (σ_model) and include them in the χ² calculations as

where D and D_model are the observed and modeled eclipse depths. σ_{depth,combined} is the inflated, combined visits uncertainties on eclipse depths (as shown in the last column of Table 2) while σ_model represents the model uncertainties estimated via propagation of errors as

where the partial derivatives of the depth with respect to each parameter were evaluated numerically. Figure 8 shows these model uncertainties as shaded swaths surrounding each model. Comparing to some key dayside temperature models for each binning, we find:

• 1.  
  The null hypothesis of there being no eclipse (0 K Planck spectrum) can be ruled out at 4.6σ, 6.0σ, 7.7σ, and 9.2σ, for 1, 4, 8, and 16 bins. Therefore, we solidly detect the planet’s thermal emission.
• 2.  
  The most basic thick-atmosphere hypothesis of zero albedo, full heat redistribution, and f = 1/4 (431 K Planck spectrum) can be marginally disfavored at 2.0σ, 2.3σ, 3.3σ, and 4.6σ for 1, 4, 8, and 16 bins.
• 3.  
  The slightly bolder thick-atmosphere hypothesis with α_B = 0.77 (resemble Venus), full heat redistribution, and f = 1/4 (297 K Planck spectrum) can be ruled out at 4.2σ, 5.4σ, 6.9σ, and 8.4σ for 1, 4, 8, and 16 bins.
• 4.  
  The most basic no-atmosphere hypothesis of zero albedo, no heat redistribution, f = 2/3 (549 K Planck spectrum) is consistent with the data at 0.4σ, 0.3σ, 0.9σ, and 1.9σ for 1, 4, 8, and 16 bins.

The eccentricity of LTT 1445A b is very close to zero. The and inferred from the eclipse timing and duration are each consistent at <2σ with 0, and we place an upper limit of e < 0.0059 at 95% confidence from the visit-combined posterior distribution.

In an ensemble analysis, S. Sagear & S. Ballard (2023) found that eccentricities of single transiting planets around M dwarfs can be large or small, whereas systems with multiple transiting planets around M dwarfs almost exclusively have small eccentricities. LTT 1445A b verifies this trend, now with an individually precisely measured small eccentricity in a compact multiple. B. Quarles et al. (2020) examined the planetary system’s orbital stability in the face of perturbations from the BC component of the LTT 1445ABC triple and found the planets orbit tightly enough to be relatively unaffected by the two distant stars. The circular and coplanar orbits of the LTT 1445A planets point toward a cool dynamical history, free from major disruption by external perturbers, with any initial eccentricities for the planets likely erased by tidal circularization.

One way to assess the presence of the atmosphere on LTT 1445A b is through the overall energy budget: incoming radiation gets thermally reradiated from the planet’s dayside, which is detectable at secondary eclipse. Here, we assume the planet’s dayside is isothermal and infer a posterior distribution for its emission temperature. We define model depths (D_model,binned) similar to Equation (6) but binned onto the same wavelength grid as the data by integrating the photon counts received by the planet and star within each bin:

where E_λ = hc/λ is the energy of a photon at wavelength λ, converting fluxes from energy units to photon counts, which is appropriate for MIRI’s photon-counting detector, and W(λ) is the MIRI/LRS instrumental throughput,¹⁴ weighting wavelengths according to the efficiency with which JWST can count their photons. Uncertainties were propagated into the binned model depths as in Equation (8). This integration is particularly important for wide wavelength bins across which the stellar flux drops dramatically and the planet’s thermal emission rises sharply. We use PyMC3 as described above to infer the dayside temperature T_day as one free parameter.

The best-fit dayside temperatures are T_day = 513 ± 33 K, 511 ± 22 K, 515 ± 17 K, and 525 ± 15 K for the 1, 4, 8, and 16 binning schemes, respectively. Figure 9 shows the 16-bin spectrum converted into flux units along with the best-fit isothermal model, along with the stellar spectrum. The dayside temperature uncertainties do not account for uncertainties in the stellar and planetary parameters. To more accurately include them, we calculate a temperature ratio (R) between the fitted dayside brightness temperature (T_day) and the maximum expected dayside temperature (assuming zero albedo and instant heat reradiation; = 2/3) as

and propagated the uncertainty on T_eq = 431 ± 23 K into the uncertainty on R, where f_eq = 1/4 is the f-factor for fully redistribution. For 1, 4, 8, and 16 wavelength bins, we achieve a temperature ratio R of 0.930 ± 0.077, 0.928 ± 0.064, 0.935 ± 0.059, and 0.952 ± 0.057. Qualitatively, the R uncertainties decreasing from 1–16 wavelength bins is consistent with the fact that a smaller uncertainty inflation ratio (n_σ,combined) was applied to the higher-resolution combined emission spectra (Section 4.4). The fitted R ratios all agreed with each other within 1σ level, and they are all consistent with instant reradiation from a dark rocky surface. Compared to the SPARTA-derived 16-bin temperature ratios of R = 0.952 ±0.057, for Eureka! we derive a comparable temperature ratio of R = 0.944 ± 0.058, differing by only 0.8% and well within the 1σ uncertainty.

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We then compared these temperature ratios (R) to simplified heat redistribution models from D. D. B. Koll (2022). An analytic model connects atmospheric surface pressure to the heat redistribution parameter (f-factor) with simplifying assumptions (D. D. B. Koll 2022):

where p_s represents the surface pressure. We linearly interpolated equivalent long-wave gray optical thickness τ_LW as a function of p_s from τ_LW = [0.2170, 0.5533, 1.1497, 3.5244, 7.0824] calculated assuming pure CO₂ atmosphere in Section 5.3 when p_s = [0.01, 0.1, 1.0, 10.0, 100.0] bar, respectively.

captures additional planetary properties that have minimal effects across different planetary systems (mostly of order unity). We adopt parameter values from D. D. B. Koll (2022) for high-MMW atmospheres: (R, c_p) = (, ), C_d = 1.9 × 10⁻³, L = R_p, χ = 0.2, where n_LW = 2 indicates opacity is dependent on pressure (pressure broadening). Additionally, we calculated g = 14.93 m s⁻² for LTT 1445A b (using parameters from Table 1), yielding k_LTT1445Ab = 2.77. We used Equations (11) and (1) to calculate the expected dayside temperature, although the model predictions are robust to uncertainties in the system parameter in Table 1. The exact quantitative relationship between surface pressure and dayside temperature depends on the details of the above parameter assumptions.

Figure 10 shows these calculated temperatures as a function surface pressure (p_s), for different assumed Bond albedos (α_B), compared to the planet’s dayside temperature posteriors inferred from this work. In this model, the planet’s dayside might be cooler either because an atmosphere distributes the incoming radiation to the nightside or because the planet reflects some of the incoming light before it can be absorbed, either off the surface or a reflective cloud deck. For context, M. Mansfield et al. (2019) identified α_B ≈ 0.4 as an approximate upper limit for the expected albedo of warm rocky surfaces; in Figure 10, that implies that a dayside temperature cooler than 483 K could only be achieved through an atmosphere. At all binnings, the observed dayside temperatures are warmer than this limit. The dayside temperature disfavors atmospheres that are extremely reflective and/or very thick, but many atmospheric scenarios cannot be explicitly distinguished from bare rock, such as moderately thick (Earth-like) and thin (Mars-like) atmospheres.

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Figure 11 shows the analytic temperature calculation expressed as the temperature ratio R, as a 2D map of surface pressure and albedo. Posteriors for the observed temperature ratio R = 0.952 ± 0.057 (from the 16 bin fit) are shown, where the uncertainty includes both JWST measurement uncertainties and from the intrinsic system parameter uncertainties. The observed temperature ratio disfavors thick (p_s > 100 bar) atmospheres with Bond albedos >0.08 at the 3σ confidence interval. These thick atmospheres too effectively transport heat to the nightside, thus cooling the dayside below the observed temperature ratio. Additionally, the temperature ratio rules out a bright (α_B > 0.62) bare rock at 3σ confidence with the same logic.

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We include solar system rocky worlds in Figure 11 for comparison. Even though their Bond albedos would be different if irradiated by a cooler M dwarf compared to the Sun, a qualitative comparison is still beneficial for understanding the atmospheric possibilities on LTT 1445A b. Venus has a thick (p_s = 92 bar)¹⁵ mainly CO₂ atmosphere with reflective clouds (α_B = 0.77). A true Venus-like atmosphere is not aligned with our derived surface pressure and Bond albedo from the observations and can be ruled out at ∼7σ confidence. Titan with α_B = 0.265 (L. Li et al. 2011), p_s = 1.5 bar (G. Lindal et al. 1983), and Earth (α_B = 0.294, p_s = 1 bar) are good examples of moderate surface pressures and albedos; we slightly disfavor such atmospheres at ∼1.6σ but cannot rule them out. Thin atmospheres like the one on Mars (α_B = 0.250, p_s = [4.0–8.7] × 10⁻³ bar) or nonexistent atmospheres like that of Mercury (α_B = 0.068, p_s ≲ 5 × 10⁻¹⁵ bar) and the Moon (α_B = 0.11, p_s ≲ 3 × 10⁻¹⁵ bar) are all consistent with the observed temperature ratio within 1σ.

It is worth noting that we observed statistically different emission spectra from each visit, especially the second visit (shown in Figure 8). Such differences might result either from uncorrected systematics or from astrophysical time variability on the planet’s flux. We accounted for the inconsistent depths by inflating the emission spectrum uncertainties, but if we had used only the two most consistent visits (1 + 3), the resulting lower eclipse depth would imply a cooler temperature ratio of R = 0.914 ± 0.057. This would still reject reflective Venus-like atmospheres at ∼6σ but it would not reject thick (∼100 bar) but dark (α_B < 0.25) atmospheres from an overall energy budget perspective.

In addition to the overall energy balance argument above, an atmosphere might be revealed through the detection of molecular absorption features in the emission spectrum. Here, we compare the MIRI/LRS emission spectrum of LTT 1445A b to forward models of simple atmospheres. We constructed model emission spectra using calculations as in C. V. Morley et al. (2017), assuming 100% CO₂ atmospheres of varying surface pressures of [0.01, 0.1, 1.0, 10.0, 100.0] bar. Temperature–pressure profiles follow a dry adiabat from the surface up until they reach the skin temperature, above which they are isothermal. For all models, the Bond albedo was assumed to be α_B = 0.1 for both the overall energy balance of the atmosphere and for the planet’s surface. The D. D. B. Koll (2022) analytic heat redistribution is included with a self-consistent infrared opacity (f = [0.662, 0.619, 0.434, 0.272, 0.252] for p_s = [0.01, 0.1, 1.0, 10.0, 100.0] bar, respectively), so thicker atmospheres have lower f, distributing more energy to the nightside and thus requiring less total heat be emitted from the dayside visible during eclipse.

Figure 12 compares these model spectra to our 16-bin measured emission spectrum. For each model, we calculate the χ² statistic including the model uncertainty using Equation 7, where the numerical derivatives needed for Equation 8 were calculated from model emission spectra generated for two closely separated equilibrium temperatures. Comparing the achieved χ² to the probability distribution for χ² assuming 16 dof, we calculate the probability at which a given model can be disfavored and translate that into a number of σ away from a Gaussian distribution.

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Figure 12 shows the thinner atmospheres are most consistent with the data, with emission spectra that are effectively closer to the warm isothermal spectrum explored in Section 5.2. Surface pressures ≤0.1 bar do not perfectly match to the data, but are still allowed within 3σ. For these simple atmospheres, thicker ≥1 bar surface pressures are progressively worse fits, with stronger absorption features resulting in too little flux in CO₂ bands and too much flux in atmospheric windows where hotter temperatures from deep in the atmosphere shine through; the tested atmospheres are all disfavored at >4σ.

Taken together, the lack of deep CO₂ absorption features (Figure 12) and the dayside temperature being broadly consistent with instant reradiation from a rocky surface (Figure 11) point toward disfavoring the presence of a thick ∼100 bar atmosphere on LTT 1445A b. An important caveat is that we only explored the most basic atmospheric forward models with pure CO₂ composition and monotonically decreasing temperature–pressure profiles. Such simple modeling is reasonable given that the data are consistent with isothermal emission spectra at 2σ (Figure 12).

However, it is possible that a more complete exploration of atmospheric compositions and thermal structures might better explain the marginally significant low-level wiggles in the emission spectrum. For example, the shallow depths at 6.3 and 8.7 μm appear to align with atmospheric CO₂ opacity windows, suggesting they could potentially trace cool near-surface emission peeking out from under a hotter upper atmosphere. To explore this possibility, we used PICASO N. E. Batalha et al. (2019) to generate atmospheres with thermal inversions. We tested different surface pressures (0.01–100 bar) and compositions (CO₂ and CO₂/O₃ mixtures), and used Levenberg–Marquardt to optimize the strength of the inversion (parameterized as in T. Guillot 2010) to match the eclipse depths. The best models we found were effectively isothermal, producing no better χ² values than the pure Planck spectra in Figure 12.

Fundamentally, more precise data and more detailed atmospheric modeling will likely be required to definitely characterize whatever atmosphere might remain around LTT 1445A b.

We compare LTT 1445A b, a rocky planet for which MIRI/LRS disfavors thick Venus-like atmospheres, with other worlds with and without atmospheres. Figure 13 presents proposed “cosmic shorelines,” potentially separating planets with and without atmospheres (K. J. Zahnle & D. C. Catling 2017). Exoplanet data were drawn from the NASA Exoplanet Archive¹⁶ pscomppars table, and limited to systems with better than 20% uncertainties on the planet mass and radius, curated to replace bad parameter choices for a few important nearby systems, and filtered to include only planets smaller than 2 R_⊕ to exclude most thick H/He-dominated envelopes, focusing on secondary rocky atmospheres. Solar system data for planets, satellites, and small bodies were drawn from JPL Solar System Dynamics,¹⁷ again eliminating (the four) gas and ice giants with thick H/He-envelopes.

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Bolometric flux and escape velocity are calculated straightforwardly from system parameters. The “estimated time-integrated XUV flux” is calculated via the commonly used but extremely oversimplified approximation from K. J. Zahnle & D. C. Catling (2017) that the cumulative XUV energy output of a star ∫L_XUVdt is set by a proportionality with the star’s instantaneous bolometric luminosity as . Qualitatively, this very rough tracer has the effect that lower-luminosity M dwarf planets appear additionally more highly irradiated. Quantitatively, this cumulative XUV tracer approximating polynomial scalings from H. Lammer et al. (2009) has enormous uncertainties because it is derived from incomplete X-ray data extrapolated into the mostly unobserved EUV. It does not incorporate the intrinsic spread in XUV fluxes at fixed age, and it does not actually use individual exoplanet ages so that young and old planets would inaccurately appear to have absorbed the same integrated XUV over their lifetimes. Given these concerns, relative XUV histories might easily be uncertain to more than an order of magnitude, possibly including systematic trends and should be viewed with utmost skepticism.

Figure 13 draws dark blue circles around planets if there is strong evidence of the presence of an atmosphere thicker than 1 mbar. For the solar system, the only such rocky atmospheres are Venus, Earth, Mars, and Titan, and for the exoplanets this so far includes only 55 Cnc e (R. Hu et al. 2024; J. A. Patel et al. 2024), which sits at extremes in both irradiation and size. Venus and Earth are the only two planets known so far that have ∼100 bar CO₂ atmospheres (considering the CO₂ locked by liquid water into Earth’s global limestone deposits), therefore indicated by green circles in Figure 13. Exoplanets that have been observed in thermal emission with JWST or Spitzer to test for atmospheres are marked as solid circles without blue circles (even if observations might not have been sensitive to all millibar atmospheres). Exoplanets observed by JWST that showed a slightly cool dayside that might indicate a presence of a thin atmosphere or nonzero albedo are indicated by orange circles. Solar system bodies with atmospheres in vapor pressure equilibrium with large reservoirs of condensed surface volatiles like Pluto are denoted with dashed outlines, as are transient tenuous atmospheres fed by volcanism like the Galilean moons.

Power laws in each panel of Figure 13 aim to delineate planets that have atmospheres from those without, each normalized to Mars as a planet that has experienced significant but incomplete atmospheric loss (B. Jakosky et al. 2018). The blue lines are the proposed empirical cosmic shorelines from K. J. Zahnle & D. C. Catling (2017), originally drawn to connect hot hydrogen-rich exoplanets with tenuous cold atmospheres like Pluto. The gray lines indicate another simple shoreline set by a constant ratio between the planet’s escape velocity v_escape and the thermal velocity v_thermal of atmospheric molecules, effectively a line of constant Jeans escape parameter λ = E_{gravitational}/E_thermal quantifying whether gas particles have the kinetic energy to escape the planet’s gravity. With v_thermal ∝ T^1/2 and equilibrium temperatures set by insolation as T ∝ I^1/4, constant values of v_escape/v_thermal will follow , thus appearing steeper in the plots. Thermal velocities calculated from the bolometric flux represents particle speeds for the planet’s equilibrium temperature, which is reasonably well known (assuming similar albedos) but might be much cooler than the temperatures in the exosphere where escape occurs; using average XUV irradiation might be a better tracer of exospheric heating, but it relies on uncertain inputs and neglects the difficult-to-predict balance with exospheric cooling.

LTT 1445 A b’s apparent lack of such a thick CO₂ atmosphere makes more sense in the bottom panel of Figure 13, where its enhanced XUV moves it farther up, away from the solar system planets. We observe that LTT 1445A b is below the Mars-normalized shoreline in the bolometric panel, but above it in the time-integrated XUV panel. This may potentially point toward the unsurprising conclusion that XUV irradiation matters for atmospheric evolution, but we caution against too strongly interpreting these simple shorelines since they neglect many important factors governing atmospheric retention and delivery (stellar winds, magnetic fields, chemistry, impacts, tides, outgassing).

H. Diamond-Lowe et al. (2024) investigated LTT 1445 A’s current high-energy spectrum in the X-ray and UV using data from Chandra and Hubble COS + STIS. Though no flares have been seen in the optical, flares were detected at both UV and X-ray wavelengths. Given the observed XUV activity and their poorly constrained lower limit age of 2.2 Gyr, they proposed that LTT 1445A b would be able to retain a pure CO₂ atmosphere if it started with 10% or more of Earth’s total CO₂ budget. If LTT 1445A b started with a total CO₂ budget that was <10% of Earth’s total CO₂ budget (according to their simplified model), it would not be able to retain its CO₂ atmosphere, and that might be one of the reasons for the observed lacking Venus-like atmosphere.

While not shown in the main figures, Figure 14 and Table 3 show that both SPARTA's (colored) and Eureka!'s (grey) eclipse depths are all agree with 2σ, with most data points agreeing within 1σ except nine out of 80 points. If we further exclude points within the shadowed region, only three points do not agree within 1σ but rather 2σ, and all of the points in combined visits agree within 1σ. This result emphasized the robustness of the emission spectra.

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