  We present high-resolution Keck optical spectra of the very young substellar
eclipsing binary 2MASS J05352184-0546085, obtained during eclipse of the
lower-mass (secondary) brown dwarf. The observations yield the spectrum of the
higher-mass (primary) brown dwarf alone, with negligible (~1.6%) contamination
by the secondary. We perform a simultaneous fine-analysis of the TiO-epsilon
band and the red lobe of the KI doublet, using state-of-the-art PHOENIX Dusty
and Cond synthetic spectra. Comparing the effective temperature and surface
gravity derived from these fits to the {\it empirically} determined surface
gravity of the primary (logg=3.5) then allows us to test the model spectra as
well as probe the prevailing photospheric conditions. We find that: (1) fits to
TiO-epsilon alone imply Teff=2500 \pm 50K; (2) at this Teff, fits to KI imply
logg=3.0, 0.5 dex lower than the true value; and (3) at the true logg, KI fits
yield Teff=2650 \pm 50K, ~150K higher than from TiO-epsilon alone. On the one
hand, these are the trends expected in the presence of cool spots covering a
large fraction of the primary's surface (as theorized previously to explain the
observed Teff reversal between the primary and secondary). Specifically, our
results can be reproduced by an unspotted stellar photosphere with Teff=2700K
and (empirical) logg=3.5, coupled with axisymmetric cool spots that are 15%
cooler (2300K), have an effective logg=3.0 (0.5 dex lower than photospheric),
and cover 70% of the surface. On the other hand, the trends in our analysis can
also be reproduced by model opacity errors: there are lacks in the synthetic
TiO-epsilon opacities, at least for higher-gravity field dwarfs. Stringently
discriminating between the two possibilities requires combining the present
results with an equivalent analysis of the secondary (predicted to be
relatively unspotted compared to the primary).
