Tidal effects on brown dwarfs: application to the eclipsing binary 2MASS J05352184-0546085

Abstract

<i>Context. <i/>2MASS J05352184-0546085 (2M0535-05) is the only known eclipsing brown dwarf (BD) binary, and so may serve as a 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 <i>≈<i/>10<sup>24<sup/> W) than expected. Previous explanations for the temperature reversal have invoked reduced convective efficiency in the structure of the primary, connected to magnetic activity and to surface spots, but these explanations cannot account for the enhanced luminosity of the secondary. Previous studies also considered the possibility that the secondary is younger than the primary.<i>Aims. <i/>We study the impact of tidal heating to the energy budget of both components to determine if it can account for the observed temperature reversal and the high luminosity of the secondary. We also compare various plausible tidal models to determine a range of predicted properties.<i>Methods. <i/>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. The four models differ in their assumptions about the rotational behavior of the bodies, the system's eccentricity and putative misalignments <i>ψ<i/> between the bodies' equatorial planes and the orbital plane of the system.<i>Results. <i/> 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 would have to be 10 and the secondary needs a spin-orbit misalignment of <i>≳<i/>. However, tidal synchronization time scales for 2M0535-05 restrict the tidal dissipation function to log() <i>≳<i/> 4.5 and rule out intense tidal heating in 2M0535-05. We provide the first constraint on <i>Q<i/> for BDs.<i>Conclusions. <i/>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. The heating could have slowed down the BDs' shrinking and cooling processes after the birth of the system <i>≈<i/>1 Myr ago, leading to a feedback between tidal inflation and tidal heating. Observations of old BD binaries and measurements of the Rossiter-McLaughlin effect for 2M0535-05 can provide further constraints on .