(Abridged) Since the discovery of the first directly-imaged, planetary-mass object, 2MASS 1207 b, several works have sought to explain a disparity between its observed temperature and luminosity. Given its known age, distance, and spectral type, 2MASS 1207 b is under-luminous by a factor of ~10 (~2.5 mags) when compared to standard models of brown-dwarf/giant-planet evolution. In this paper, we study three possible sources of 2MASS 1207 b's under-luminosity. First, we investigate Mohanty et al. (2007)'s hypothesis that a near edge-on disk might be responsible for 2MASS 1207 b's under-luminosity. We conclude that the hypothesis is unlikely due to the lack of variability seen in multi-epoch photometry and unnecessary due to the increasing sample of under-luminous brown-dwarfs/giant-exoplanets that cannot be explained by an edge-on disk. Next, we test the analogous possibility that a spherical shell of dust, could explain 2MASS 1207 b's under-luminosity. Models containing enough dust to create ~2.5 mags of extinction, placed at reasonable radii, are ruled out by our new Gemini/T-ReCS 8.7 micron photometric upper-limit for 2MASS 1207 b. Finally, we investigate the possibility that 2MASS 1207 b is intrinsically cooler than the commonly used AMES-DUSTY fits to its spectrum, and thus it is not, in fact, under-luminous. New, thick cloud model grids by Madhusudhan et al. (2011) fit 2MASS 1207 b's 1-10 micron SED well, but they do not quite fit its near-infrared spectrum. However, we suggest that with some "tuning", they might be capable of simultaneously reproducing 2MASS 1207 b's spectral shape and luminosity. In this case, the whole class of young, under-luminous brown-dwarfs/giant-exoplanets might be explained by atmospheres that are able to suspend thick, dusty clouds in their photospheres at lower temperatures than field brown-dwarfs.Comment: 35 pages, 9 figures, accepted to Ap
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