JWST spectral retrieval of cold directly imaged planet WD0806 b and the first measurement of altitude-dependent K$_{zz}$ in exoplanet atmospheres

WD0806 b is a rare exoplanet companion orbiting a white dwarf, currently with a projected orbital distance of 2500 au. The Spitzer mid-IR photometry suggests that the temperature is as cold as 350K, making it one of the coldest directly imaged exoplanets. In this paper, we present the Near-infrared Camera (NIRCam) F150W2, F200W, F356W, and F444W broadband photometry and a 3–5\um Near-Infrared spectroscopy (NIRSpec) G395M spectrum obtained with the James Webb Space Telescope (JWST). We develop a new retrieval framework based on the open-source PICASO software that includes additive and multiplicative systematic parameters. Our retrieval results reveal bounded abundances of H$_2$S, CO$_2$, CO, NH$_3$, H$_2$O, and CH$4$. We present a new chemical analysis framework that utilizes retrieved abundances to measure altitude-dependent eddy diffusion coefficients (K${\mathrm zz}$) at multiple quenched pressures. We find that the eddy diffusion coefficients decrease from around $10^4$ to $10^2$ $\rm cm^2/s$ as the atmospheric pressure decreases from from 50 to 20 bars. To our knowledge, this is the first study to report altitude-dependent vertical mixing (or, equivalently, quenched-species-dependent vertical mixing) based on the measured molecular abundances of CO, CH$_4$, and CO$2$. With the 1–21\um NIRCam, NIRSpec and the previously published MIRI data, we measure the bolometric luminosity to be log(L/L${\odot}$) = $-6.75\pm0.01$ and derive the mass to be $8\pm 1 \mathrm{M_J}$. The retrieval results suggest that \target has an elevated C/O ratio of 0.76, or 1.3$\times$ solar, sub-solar metallicity ([M/H ]= -0.25), and a nearly solar C/S ratio (1.17x solar).

💡 Research Summary

This paper presents the first comprehensive JWST characterization of the ultra‑cold directly imaged exoplanet WD 0806 b, a planetary‑mass companion to the white dwarf WD 0806‑661 at a projected separation of ~2500 au. Previous Spitzer photometry indicated a temperature near 350 K, making it one of the coldest known exoplanets. The authors obtained broadband NIRCam photometry in four filters (F150W2, F200W, F356W, F444W) covering 1.06–4.9 µm and a medium‑resolution NIRSpec IFU spectrum (G395M, 2.87–5.10 µm) with a total exposure of 6302 s. Together with previously published MIRI LRS spectra (5–14 µm) and photometry up to 21 µm, the data set spans 1–21 µm, capturing roughly 91 % of the planet’s bolometric output.

Data reduction employed the latest JWST pipeline (CAL = 1.14.1) and custom outlier‑rejection routines. Aperture photometry was optimized per filter, and absolute flux calibration used the encircled‑energy curves. The NIRSpec line‑spread function was empirically measured from a planetary‑nebula calibration target, allowing accurate convolution of model spectra.

For atmospheric retrieval the authors built a new framework on the open‑source PICASO code. Unlike traditional retrievals that assume a single, altitude‑independent eddy diffusion coefficient (Kzz), this framework treats Kzz as a function of pressure, enabling the inference of altitude‑dependent vertical mixing. Both additive (background) and multiplicative (scale) systematic parameters are fitted simultaneously, and Bayesian sampling (EMCEE) explores the posterior distribution with physically motivated priors.

The retrieval yields well‑constrained volume mixing ratios for six molecules: H₂S, CO₂, CO, NH₃, H₂O, and CH₄. The detection of H₂S and relatively high CO₂ abundances is notable for such a low‑temperature atmosphere. By comparing the retrieved abundances to equilibrium chemistry predictions, the authors identify distinct quench pressures for each species: CO and CH₄ quench near 30–45 bar, while CO₂ quenches at ~20 bar. Using the relation τmix ≈ L²/Kzz (with a characteristic mixing length L), they invert the quench pressures to obtain Kzz values that decrease from ~10⁴ cm² s⁻¹ at 50 bar to ~10² cm² s⁻¹ at 20 bar. This is the first observational demonstration that Kzz varies with altitude in an exoplanet atmosphere, providing a direct test of non‑equilibrium chemistry models that have long assumed a constant Kzz.

The integrated spectral energy distribution yields a bolometric luminosity of log(L/L☉) = ‑6.75 ± 0.01. Combining this luminosity with the white‑dwarf age (2 ± 0.5 Gyr) and the Sonora‑Bobcat evolutionary tracks gives a planetary mass of 8 ± 1 MJ, a surface gravity log g ≈ 4.5 (cgs), a radius ≈ 1 RJ, and an effective temperature consistent with the earlier estimate (~350 K).

Chemical analysis shows an elevated carbon‑to‑oxygen ratio C/O = 0.76, about 1.3 × solar, a sub‑solar metallicity