As gas giant planets and brown dwarfs radiate away the residual heat from their formation, they cool through a spectral type transition from L to T, which encompasses the dissipation of cloud opacity and the appearance of strong methane absorption. While there are hundreds of known T-type brown dwarfs, the first generation of directly-imaged exoplanets were all L-type. Recently, Kuzuhara et al. (2013) announced the discovery of GJ 504 b, the first T dwarf exoplanet. GJ 504 b provides a unique opportunity to study the atmosphere of a new type of exoplanet with a ~500 K temperature that bridges the gap between the first directly imaged planets (~1000 K) and our own Solar Systems Jupiter (~130 K). We observed GJ 504 b in three narrow L-band filters (3.71, 3.88, and 4.00 microns), spanning the red end of the broad methane fundamental absorption feature (3.3 microns) as part of the LEECH exoplanet imaging survey. By comparing our new photometry and literature photometry to a grid of custom model atmospheres, we were able to fit GJ 504 bs unusual spectral energy distribution for the first time. We find that GJ 504 b is well-fit by models with the following parameters: T_eff=544+/-10 K, g<600 m/s^2, [M/H]=0.60+/-0.12, cloud opacity parameter of f_sed=2-5, R=0.96+/-0.07 R_Jup, and log(L)=-6.13+/-0.03 L_Sun, implying a hot start mass of 3-30 M_jup for a conservative age range of 0.1-6.5 Gyr. Of particular interest, our model fits suggest that GJ 504 b has a super-stellar metallicity. Since planet formation can create objects with non-stellar metallicities, while binary star formation cannot, this result suggests that GJ 504 b formed like a planet, not like a binary companion.
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