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

Abstract

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).

Figures (13)

• Figure 1: The RGB-stacked colored image with the three NIRCam filters: F150W2 (blue), F356W (green) and F444W (red) using DS9 software ds9.The location of white dwarf WD0806 is shown in the orange circle and the location of WD0806 b is illustrated by the orange arrow.
• Figure 2: Top panel: the solid black and orange lines show the NIRSpec/G395M spectrum and the best-fit retrieval spectrum respectively. The inset plot shows the JWST NIRCam F150W2, F200W, and the HST F110W broadband photometry, which are plotted in black dots. The integrated band photometry of the best-fit retrieval spectrum area plotted in orange plus signs. Bottom panel: the difference between the NIRSpec spectrum and the best-fit retrieval that is normalized by the full uncertainty ($\sigma_{full}$), which includes NIRSpec/G395M data uncertainty and the two the marginalized uncertainty parameters described in Section \ref{['sec:noise']}.
• Figure 3: The combination of JWST NIRCam photometry, HST photometry, JWST NIRSpec G395M spectrum, JWST MIRI LRS spectrum, and MIRI photometry covers 91% of the bolometric luminosity of WD0806$\,$b. We also include the transmission curve of the broadband filters that share the same colors with the photometric points. The plotted photometric points from short to long wavelengths are HST/WFC3 F110W, NIRCam F150W2, NIRCam F200W, NIRCam F356W, NIRCam F444W, MIRI F1200W, MIRI F1500W, MIRI F1800W, and MIRI F2100W respectively. The MIRI photometric points are adopted from voyer2025 and the HST F110W are adopted from luhman2014.
• Figure 4: Upper panel: the best-fit Elf-Owl (orange line) and ATMOS++ (blue line) model spectra compared to the JWST G395M spectrum (black line). Bottom panel: The residuals between the models and data normalized by the total uncertainties. The sharp positive residual feature at 4.55 $\mathrm{\,\mu m}$ of Elf-Owl model arises from the model CH4 opacity line list that includes CH3D at solar mixing ratio.
• Figure 5: Left panel: The best-fit PICASO retrieval temperature-pressure (TP) profile is plotted as a solid blue line with the temperature-pressure knots indicated in solid blue circles. The light blue shaded region indicates the 3$\sigma$ confidence interval of the retrieved TP profiles. The tightly constrained TP profiles in the 1--10 bar range match with the peak of the 3--5$\mathrm{\,\mu m}$ contribution function plotted in the right panel. The retrieved TP profile based on MIRI-LRS 5--11.7$\mathrm{\,\mu m}$ spectrum in voyer2025 is plotted in solid purple along with the 3$\sigma$ uncertainty plotted as light-purple shaded region. The condensation curves of H2O, Na2S, and KCl at solar metallicity are plotted with blue, orange, and green dashed lines respectively. For reference, the solid black line shows the TP profile of the best-fit Elf Owl grid model ([M/H] = -1, C/O = 1.5, log(g) = 3.23, log($K_{zz}$) = 7, T$_{\mathrm{eff}}$ = 350 K). Right panel: The contribution function map of the best-fit PICASO retrieval results shows that most of the 3--5$\mathrm{\,\mu m}$ flux is emitted from 0.1--10 bar region.