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We present a detailed analysis of the dayside atmosphere of the hot-NeptuneGJ~436b, based on recent Spitzer observations. We report statisticalconstraints on the thermal and chemical properties of the planetary atmosphere,study correlations between the various molecular species, and discuss scenariosof equilibrium and non-equilibrium chemistry in GJ 436b. We model theatmosphere with a one-dimensional line-by-line radiative transfer code withparameterized molecular abundances and temperature structure. We explore themodel parameter space with 10^6 models, using a Markov chain Monte Carloscheme. Our results encompass previous findings, indicating a paucity ofmethane, an overabundance of CO and CO2, and a slight underabundance of H2O, ascompared to equilibrium chemistry with solar metallicity. The concentrations ofthe species are highly correlated. Our best-fit, and most plausible,constraints require a CH4 mixing ratio of 1.0E-7 to 1.0E-6, with CO >= 1.0E-3,CO2 ~ 1.0E-6 to 1.0E-4, and H2O <= 1.0E-4; higher CH4 would require much higherCO and CO2. Based on calculations of equilibrium and non-equilibrium chemistry,we find that the observed abundances can potentially be explained by acombination of high metallicity (~ 10 x solar) and vertical mixing with Kzz ~10^6 - 10^7 cm^2/s. The inferred metallicity is enhanced over that of the hoststar which is known to be consistent with solar metallicity. Our constraintsrule out a dayside thermal inversion in GJ 436b. We emphasize that theconstraints reported in this work depend crucially on the observations in thetwo Spitzer channels at 3.6 micron and 4.5 micron. Future observations withwarm Spitzer and with the James Webb Space Telescope will be extremelyimportant to improve upon the present constraints on the abundances of carbonspecies in the dayside atmosphere of GJ 436b.

High Metallicity and Non-equilibrium Chemistry in the Dayside Atmosphere of hot-Neptune GJ 436b