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Tidal effects on brown dwarfs: Application to the eclipsing binary 2MASSJ05352184-0546085 - The anomalous temperature reversal in the context of tidal heating

2MASSJ05352184-0546085 (2M0535-05) is the only known eclipsing brown dwarf (BD) binary, and so may serve as an important benchmark for models of BD formation and evolution. However, theoretical predictions of the system's properties seem inconsistent with observations: i. The more massive (primary) component is observed to be cooler than the less massive (secondary) one. ii. The secondary is more luminous (by roughly 10^{24} W) than expected. We study the impact of tidal heating to the energy budget of both components. We also compare various plausible tidal models to determine a range of predicted properties. We apply two versions of two different, well-known models for tidal interaction, respectively, (i.) the 'constant-phase-lag' model and (ii.) the 'constant-time-lag' model, and incorporate the predicted tidal heating into a model of BD structure. We find that the contribution of heat from tides in 2M0535-05 alone may only be large enough to account for the discrepancies between observation and theory in an unlikely region of the parameter space. The tidal quality factor of BDs, Q_{BD}, would have to be 10^{3.5} and the secondary needs a spin-orbit misalignment greater than 50 degrees. However, tidal synchronization time scales for 2M0535-05 restrict the tidal dissipation function Q_{BD} to values greater than 10^{4.5} and rule out intense tidal heating in 2M0535-05. We provide the first constraint on Q_{BD}. Tidal heating alone is unlikely to be responsible for the surprising temperature reversal within 2M0535-05. But an evolutionary embedment of tidal effects and a coupled treatment with the structural evolution of the BDs is necessary to corroborate or refute this result.