A warm Neptune's methane reveals core mass and vigorous atmospheric mixing
Observations of transiting gas giant exoplanets have revealed a pervasive depletion of methane, which has only recently been identified atmospherically. The depletion is thought to be maintained by disequilibrium processes such as photochemistry or mixing from a hotter interior. However, the interiors are largely unconstrained along with the vertical mixing strength and only upper limits on the CH$_4$ depletion have been available. The warm Neptune WASP-107 b stands out among exoplanets with an unusually low density, reported low core mass, and temperatures amenable to CH$_4$ though previous observations have yet to find the molecule. Here we present a JWST NIRSpec transmission spectrum of WASP-107 b which shows features from both SO$_2$ and CH$_4$ along with H$_2$O, CO$_2$, and CO. We detect methane with 4.2$\sigma$ significance at an abundance of 1.0$\pm$0.5 ppm, which is depleted by 3 orders of magnitude relative to equilibrium expectations. Our results are highly constraining for the atmosphere and interior, which indicate the envelope has a super-solar metallicity of 43$\pm$8$\times$ solar, a hot interior with an intrinsic temperature of T$_{\rm int}$=460$\pm$40 K, and vigorous vertical mixing which depletes CH4 with a diffusion coefficient of Kzz = 10$^{11.6\pm0.1}$ cm$^2$/s. Photochemistry has a negligible effect on the CH$_4$ abundance, but is needed to account for the SO$_2$. We infer a core mass of 11.5$_{-3.6}^{+3.0}$ M$_{\odot}$, which is much higher than previous upper limits, releasing a tension with core-accretion models.