JWST Spectral Retrieval of Cold Directly Imaged Planet WD 0806 b and the First Measurement of Altitude-dependent <i>K</i> _<i>zz</i> in Exoplanet Atmospheres

Abstract WD 0806 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 350 K, 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 μ m Near-Infrared spectroscopy (NIRSpec) G395M spectrum obtained with the James Webb Space Telescope. 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 zz ) at multiple quenched pressures. We find that the eddy diffusion coefficients decrease from around 10 4 –10 2 cm 2 s −1 as the atmospheric pressure decreases from from 50 to 20 bar. 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 μ m NIRCam, NIRSpec, and the previously published MIRI data, we measure the bolometric luminosity to be log( L / L ⊙ ) = −6.75 ± 0.01 and derive the mass to be 8 ± 1 M J . The retrieval results suggest that WD 0806 b has an elevated C/O ratio of 0.76, or 1.3× solar, subsolar metallicity ([M/H ]= −0.25), and a nearly solar C/S ratio (1.17x solar).