The Third Option: Color Phase Curves to Characterize the Atmospheres of Temperate Rocky Exoplanets

TL;DR

This paper introduces color phase curves (CPC) as a third approach to characterize temperate rocky exoplanet atmospheres, using the ratio of two long-wavelength infrared bands (e.g., $21\,rac{m}{\mu}$m) to isolate planetary thermal emission from the host star and instrumental systematics. CPCs are designed to measure longitudinal heat transport, with a particular emphasis on synchronously rotating planets and targets around M-dwarfs; the method can be applied to non-transiting planets as well, and relies on self-consistent physical models to render heat-redistribution estimates quasi-inclination-independent via mass-radius constraints. The paper demonstrates the concept with Proxima Centauri b (and d) through toy climate and GCM models, showing that amplitudes of a few tens to ~100 ppm are detectable with JWST/MIRI given realistic observing campaigns, and that multi-planet CPCs can be decomposed to retrieve individual amplitudes and infer atmospheric presence and properties. Beyond Proxima, CPCs could probe atmospheres for a wider set of nearby planets, including non-transiting systems, offering a practical, spectroscopy-light route to assess heat transport and atmospheric viability in temperate rocky worlds.

Abstract

Detecting and characterizing the atmospheres of rocky exoplanets has proven to be challenging for JWST. Transit spectroscopy of the TRAPPIST-1 planets has been impacted by the effects of spots and faculae on the host star. Secondary eclipses have detected hot rocks, but evidence for atmospheres has been difficult to obtain. However, there is a third option that we call color phase curves. This method will apply to synchronously rotating non-transiting planets as well as transiting planets. A color phase curve uses photometry at a long-IR wavelength near the peak of the planetary thermal emission (e.g., 21 microns) divided by photometry at a shorter wavelength where the star dominates more strongly (e.g., 12 microns). We avoid wavelengths having potentially strong molecular absorption (e.g., 15 microns) to minimize degeneracies in the color phase curve, and we aim to detect and characterize the planetary atmosphere via its longitudinal heat transfer. The ratio of two wavelengths observed nearly simultaneously is designed to isolate thermal emission from the planet, discriminate against the star, and largely cancel instrumental systematic effects. Moreover, we show that invoking mass-radius relations, and using self-consistent physical models, will permit the longitudinal heat transfer to be measured independent of the orbital inclination. Radial velocity surveys are detecting many new exoplanets, including temperate rocky worlds with Earth-like masses. Most of those planets will not transit, but color phase curves have the potential to detect and characterize their atmospheres.

Figures (6)

• Figure 1: Color phase curves (CPCs) for the sum of planets 'b' and 'd' in the Proxima Centauri system. The CPC is the ratio of the flux in the 21 $\mu$m to 12.8 $\mu$m JWST/MIRI filters, normalized to the stellar flux, with the median value subtracted from the normalized ratio. The CPCs are the sum of both planets, and are shown here for the 2027 visibility period for JWST (lighter when not visible). Two cases are shown: using a hot rock model for 'b', and a GCM (see text). Planet 'd' is modeled as a hot rock in both cases.
• Figure 2: Color phase curves (CPCs) for planets 'b' and 'd' in the Proxima Centauri system, as in Figure \ref{['fig: curves1']}, except that the CPC for the 'b' planet is here also plotted separately, in addition to being summed with 'd'. Both planets are represented by the two-column model of lincowski_2023 (see text for description).
• Figure 3: Corner plot for multi-variate linear regression results from 50,000 sets of simulated CPC data for the Proxima system. Each data set is based on 25 observations of the CPCs shown in Figure \ref{['fig: curves1']}, with 8 ppm error bars. The planets are taken to be coplanar, and the regression solves for the CPC amplitudes of planets 'b' and 'd', as well as the amplitude of stellar variation. The orbital inclination is varied for each simulated dataset, with the amplitude of variations corresponding to the current observational uncertainties (Table \ref{['tab: params']}).
• Figure 4: Corner plot for the sum of Proxima 'd', and 'b', assuming a hot rock model for 'd' (as in Figure \ref{['fig: corner1']}), but using our two-column model for planet 'b'.
• Figure 5: Possible mass and orbital inclination of Proxima Centauri b as a function of the amplitude of the CPC (21- vs. 12.8 $\mu$m), where each curve is constrained by a mass radius relation. The phase curve amplitudes (X-axis) are based on the toy models from kreidberg_2016 (see text). We adopt M(R) relations from otegi_2020 and muller_2024 in order to show that the result is not critically dependent on the exact form of M(R). Dotted lines show the $\pm1\sigma$ error ranges due to imprecision in M(R). Because the curves for different values of heat redistribution are nearly vertical, an observed CPC amplitude will intersect only a small range of heat redistribution values (see text).