  Several studies in the recent past have inferred the existence of thermal
inversions in some transiting hot Jupiter atmospheres. Given the limited data
available, the inference of a thermal inversion depends critically on the
chemical composition assumed for the atmosphere. In this study, we explore the
degeneracies between thermal inversions and molecular abundances in four highly
irradiated hot Jupiter atmospheres, day-side observations of which were
previously reported to be consistent with thermal inversions based on Spitzer
photometry. The four systems are: HD 209458b, HAT-P-7b, TrES-4, and TrES-2. For
each system, we explore the model parameter space with ~ 10^6 models using a
Markov chain Monte Carlo routine. Our results primarily suggest that a thorough
exploration of the model parameter space is necessary to identify thermal
inversions in hot Jupiter atmospheres. We find that existing observations of
TrES-4 and TrES-2 can both be fit very precisely with models with and without
thermal inversions, and with a wide range in chemical composition. On the other
hand, observations of HD 209458b and HAT-P-7b are better fit with thermal
inversions than without, as has been reported before. We do not see a
correlation between irradiation levels and thermal inversions, given current
data. Before JWST becomes available, near-IR observations from ground and with
HST, along with existing Spitzer observations, can potentially resolve thermal
inversions in some systems.
