The Sonora Substellar Atmosphere Models. IV. Elf Owl: Atmospheric Mixing and Chemical Disequilibrium with Varying Metallicity and C/O Ratios

Disequilibrium chemistry due to vertical mixing in the atmospheres of many brown dwarfs and giant exoplanets is well-established. Atmosphere models for these objects typically parameterize mixing with the highly uncertain $K_{\mathrm{z}\mathrm{z}}$ diffusion parameter. The role of mixing in altering the abundances of C-N-O-bearing molecules has mostly been explored for solar composition atmospheres. However, atmospheric metallicity and the C/O ratio also impact atmospheric chemistry. Therefore, we present the $\mathtt{\text{Sonora}}\mathtt{\text{Elf}}\mathtt{\text{Owl}}$ grid of self-consistent cloud-free 1D radiative-convective equilibrium model atmospheres for JWST observations, which includes a variation of $K_{\mathrm{z}\mathrm{z}}$ across several orders of magnitude and also encompasses sub-solar to super-solar metallicities and C/O ratios. We find that the impact of $K_{\mathrm{z}\mathrm{z}}$ on the $T(P)$ profile and spectra is a strong function of both $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$ and metallicity. For metal-poor objects $K_{\mathrm{z}\mathrm{z}}$ has large impacts on the atmosphere at significantly higher $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$ compared to metal-rich atmospheres where the impact of $K_{\mathrm{z}\mathrm{z}}$ is seen to occur at lower $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$. We identify significant spectral degeneracies between varying $K_{\mathrm{z}\mathrm{z}}$ and metallicity in multiple wavelength windows, in particular at 3-5 $\mu$m. We use the $\mathtt{\text{Sonora}}\mathtt{\text{Elf}}\mathtt{\text{Owl}}$ atmospheric grid to fit the observed spectra of a sample of 9 early to late T- type objects from $T_{\mathrm{e}\mathrm{f}\mathrm{f}}=550-1150$ K. We find evidence for very inefficient vertical mixing in these objects with inferred $K_{\mathrm{z}\mathrm{z}}$ values lying in the range between $\sim$ 10${}^1$-10${}^4$ cm${}^2$s${}^{-1}$. Using self-consistent models, we find that this slow vertical mixing is due to the observations probing mixing in the deep detached radiative zone in these atmospheres.