JWST/MIRI 15 μm Thermal Phase Curves

• The paper demonstrates that JWST/MIRI 15 μm phase curves serve as a diagnostic tool by tracking mid-IR flux variations to distinguish surface and atmospheric properties.
• It details a methodology combining forward modeling, spectral diagnostics, and dual-band comparisons to differentiate airless rocky bodies from those with molecular-rich atmospheres.
• Key findings indicate that precise 15 μm observations constrain heat transport efficiency and atmospheric composition, crucial for assessing exoplanet habitability and evolution.

JWST/MIRI 15 μm thermal phase curves are a fundamental observational tool for characterizing the surface and atmospheric properties of rocky and gaseous exoplanets and brown dwarfs. By measuring the temporal modulation of a planet’s mid-infrared thermal emission as a function of orbital or rotational phase, these observations can disentangle physical scenarios ranging from bare rocks with no energy redistribution to worlds with dense, molecular atmospheres exhibiting heat transport, temperature inversions, and complex circulation. The 15 μm channel, accessible through JWST’s Mid-Infrared Instrument (MIRI), is exceptionally sensitive to the ν2 bending mode of CO₂ and a key probe of both surface and atmospheric physical conditions due to its placement in the thermal infrared, high stellar–planet contrast, and relative insensitivity to stellar contamination or clouds.

1. Principles of Thermal Phase Curve Measurement

Thermal phase curves track the change in apparent infrared flux from an exoplanet or brown dwarf as it moves through different orbital longitudes or rotates, often with a focus on tidally locked objects orbiting M dwarfs or brown dwarfs themselves. The fundamental observable is the time-dependent planet-to-star flux ratio, $F_\mathrm{p}(t)/F_\ast$, within a specific wavelength band (most commonly the F1500W filter, centered at 15 μm). This ratio is proportional to the disk-integrated brightness temperature of the planet’s visible hemisphere and modulated by both the incident stellar flux and the planet’s energy redistribution efficiency.

For a rocky body without an atmosphere, local surface temperature is set by

$$T(\theta) = \left[\, \frac{F_\ast\,(1-A)\,\cos\theta}{\sigma} \,\right]^{1/4}$$

where $\theta$ is local zenith angle, $A$ the Bond albedo, and $\sigma$ the Stefan–Boltzmann constant. The resulting emission is highly asymmetric between day and night hemispheres, producing phase curves with large amplitude and negligible nightside flux (Selsis et al., 2011, Maurin et al., 2011, Hammond et al., 6 Sep 2024, Gillon et al., 2 Sep 2025).

Atmospheric models introduce radiative, convective, and dynamical transport. The observed phase curve amplitude (peak-to-trough flux difference) becomes a direct probe of the ratio between atmospheric dynamical to radiative timescales ($t_\mathrm{wave}/t_\mathrm{rad}$), the longwave optical depth at the surface ($\tau_\mathrm{LW}$), and the efficiency of heat redistribution (Koll et al., 2014, Selsis et al., 2011).

2. Mid-Infrared Band Sensitivity and Spectral Diagnostics

The 15 μm band is specifically sensitive to the ν2 CO₂ vibrational mode and probes a regime where molecular absorption and thermal emission compete. In atmospheres with modest to high CO₂ partial pressure, the brightness temperature in this band reveals both the vertical temperature structure and molecular abundance, as the emission layer is located where the band-integrated optical depth $\tau_{15μm} \sim 1$.

Spectrally resolved or dual-band measurements (e.g., 12.8 μm versus 15 μm in TRAPPIST-1 b studies) allow discrimination between surface- or atmosphere-dominated emission. For example, an airless planet produces a relatively featureless blackbody curve across mid-IR bands, while an atmosphere with a thermal inversion can reverse CO₂ absorption to emission, creating a 15 μm flux excess relative to shorter wavelengths (Ducrot et al., 16 Dec 2024). This contrast is particularly sensitive to photochemical hazes and high-altitude absorption/emission phenomena.

The following table summarizes spectral diagnostics from observations in the mid-IR for representative scenarios:

Scenario	15 μm Phase Curve Amplitude	Distinguishing Spectral Feature
Airless rocky surface	Large; zero nightside	Flat or monotonic spectrum
Dense CO₂ atmosphere	Small; nonzero nightside	Absorption at 15 μm (unless inverted)
CO₂ + photochemical haze/inversion	Variable; emission feature	Increased 15 μm relative to 12.8 μm
O₂-dominated thin atmosphere	Moderate; weak variation	Weak feature, possibly with water
Steam atmosphere	Moderate; nearly isothermal	Complex with H₂O features

3. Thermal Phase Curve Modeling and Retrieval Techniques

Quantitative interpretation of thermal phase curves employs forward models coupled to retrieval frameworks, often featuring 3D general circulation models (GCMs) for exoplanets (Selsis et al., 2011, Koll et al., 2014, Hammond et al., 25 Apr 2024), radiative–convective equilibrium codes, or 1D radiative–convective models for spherically symmetric atmospheres.

The basic phase curve is typically modeled as

$$F_\mathrm{p}(t)/F_\ast = \frac{1}{2} [1 + \cos(\theta(t) - \delta)] \cdot \frac{F_\mathrm{day,max}}{F_\ast} \cdot \Omega(t)$$

where $\delta$ is any phase offset from heat transport, and $\Omega(t)$ accounts for planetary occultation. For airless bodies, quasi-Lambertian models using $[ \cos(\theta/2) ]^{\gamma}$ are often preferred (Gillon et al., 2 Sep 2025).

Advanced analysis can use eclipse mapping with spherical harmonic expansions as in

$Z(\theta,\phi) = \sum_{i} c_{i} z_{i}(\theta,\phi)$

up to $\ell_\mathrm{max}=2$ or $3$, with Bayesian frameworks enforcing physicality and model parsimony (Hammond et al., 25 Apr 2024).

Modern data reduction leverages data-driven systematic models, notably frame-normalized principal component analysis (FN-PCA), to detrend instrument systematics—especially exponential ramps due to detector settling. The settling time is found empirically to scale as

$$T_\mathrm{set}[hr] = 0.063\,\exp(0.427\,m_K) - 0.657$$

where $m_K$ is the target’s K-band magnitude (Connors et al., 2 Jul 2025). Accurate systematics modeling is essential for extracting ppm-level signals characteristic of exoplanet phase curves.

4. Observational Results from JWST/MIRI 15 μm Phase Curves

Recent JWST/MIRI campaigns have yielded the first 15 μm phase curves for temperate terrestrial exoplanets and brown dwarfs. For TRAPPIST-1 b, dayside emission yields a brightness temperature of $490 \pm 17$ K, with nightside flux below $39_{-27}^{+55}$ ppm—consistent with a nearly airless ultramafic rocky surface and negligible redistribution (Gillon et al., 2 Sep 2025, Ducrot et al., 16 Dec 2024). There is no significant phase offset, and dense atmospheres ($p_s \gtrsim 1$ bar) are strongly disfavored.

TRAPPIST-1 c shows a lower dayside brightness ($369 \pm 23$ K) and equally undetectable nightside flux. Multiple modeling approaches suggest a bare rock with higher albedo or a tenuous, greenhouse-poor O₂-dominated atmosphere as possible scenarios, with Venus-like atmospheres excluded at high confidence. In both cases, the combined data indicate inefficient day–night energy redistribution (Lincowski et al., 2023, Gillon et al., 2 Sep 2025).

For WASP-43b, two-dimensional mapping of dayside thermal emission using spherical harmonics reveals a meridionally averaged eastward hot spot shift of $7.75 \pm 0.36^\circ$ and clear differentiation between longitudinal ($\sim$250 ppm) and latitudinal ($\sim$200 ppm) emission structures, matching predictions from atmospheric GCMs (Hammond et al., 25 Apr 2024).

Brown dwarf SIMP-0136 displays phase-dependent emission entirely attributable to temperature and auroral-driven thermal inversion (250–300 K at $P<10$ mbar), while patchy silicate clouds remain static in longitude (Nasedkin et al., 10 Jul 2025).

5. Diagnostic Power, Limitations, and Future Prospects

Thermal phase curves at 15 μm are currently the only unambiguous diagnostic for detecting atmospheres on rocky exoplanets, as dayside secondary eclipse depths alone are degenerate between high-albedo rocks and greenhouse-induced redistribution. Significant nonzero nightside emission in the F1500W filter is a “smoking gun” for atmospheric presence and heat transport (Hammond et al., 6 Sep 2024). High photometric precision ($\sim10^{-5}$ relative stability) over full orbital periods ($\gtrsim10$ days) is necessary for atmospheric constraints (Selsis et al., 2011, Maurin et al., 2011).

Degeneracies persist in distinguishing surface and hazy/inverted atmospheric scenarios when only two filters or broadband data are available (Ducrot et al., 16 Dec 2024). Multiwavelength, high-cadence phase curves combined with detailed spectral and eclipse mapping are essential for breaking these ambiguities.

Stellar variability, instrumental systematics (notably detector ramps), and intrinsic star–planet flux contrast remain observational challenges. Systematics can be mitigated with repeated cycles, simultaneous multi-band observations, and advanced detrending (e.g., FN-PCA) (Connors et al., 2 Jul 2025).

Future prospects include orders-of-magnitude expansion in the accessible population for atmospheric characterization beyond transiting planets, improved constraints on atmospheric mass and surface pressure for habitability studies, and refined diagnostics of atmospheric evolution and loss (Koll et al., 2014, Gillon et al., 2 Sep 2025).

6. Comparative Table: Diagnostic Features in JWST/MIRI 15 μm Phase Curves

Scenario	Dayside Temp (K)	Nightside Flux (ppm)	Phase Offset (deg)	Atmosphere Constraint
TRAPPIST-1 b	$490 \pm 17$	$39^{+55}_{-27}$	$-6.5 \pm 6.4$	Airless, ultramafic rock
TRAPPIST-1 c	$369 \pm 23$	$62^{+60}_{-43}$	$10^{+25}_{-22}$	Thin O₂ or bare rock
WASP-43b (hot Jupiter)	$\sim$1500	Nonzero (complex)	$7.75 \pm 0.36$	Zonal wind, superrotation
SIMP-0136 (brown dwarf)	$1243$–$1248$	$+5$\% phase change	0	Auroral inversion present

This table illustrates key parameters retrieved from recent 15 μm JWST/MIRI phase curve observations, emphasizing the diagnostic power of nightside flux and phase offset constraints.

7. Implications for Comparative Planetology and Exoplanet Assessment

The application of JWST/MIRI 15 μm phase curves has transformed the capacity to probe atmosphere retention, surface composition, and atmospheric evolution for rocky and gaseous exoplanets. Null detection of nightside emission in TRAPPIST-1 b and c marks a turning point, conclusively ruling out thick atmospheres and implying divergent volatile loss pathways even within the same system (Gillon et al., 2 Sep 2025). For objects with tenuous atmospheres, broadband phase curve amplitude constrains surface pressure to within a factor of two, delivering key inputs for habitability and atmospheric evolution studies (Koll et al., 2014).

The 15 μm data also extend to brown dwarfs, revealing non-standard heating processes (auroral-driven inversions) and providing analogues for directly imaged exoplanets (Nasedkin et al., 10 Jul 2025). Overall, JWST/MIRI 15 μm phase curves constitute a unique window into the fundamental processes that govern surface–atmosphere interaction, energy redistribution, and evolutionary fate for diverse classes of substellar objects.