Short period (<50 days) low-mass (<10Mearth) exoplanets are abundant and the few of them whose radius and mass have been measured already reveal a diversity in composition. Some of these exoplanets are found on eccentric orbits and are subjected to strong tides affecting their rotation and resulting in significant tidal heating. Within this population, some planets are likely to be depleted in volatiles and have no atmosphere. We model the thermal emission of these Super Mercuries to study the signatures of rotation and tidal dissipation on their infrared light curve. We compute the time-dependent temperature map at the surface and in the subsurface of the planet and the resulting disk-integrated emission spectrum received by a distant observer for any observation geometry. We calculate the illumination of the planetary surface for any Keplerian orbit and rotation. We include the internal tidal heat flow, vertical heat diffusion in the subsurface and generate synthetic light curves. We show that the different rotation periods predicted by tidal models (spin-orbit resonances, pseudo-synchronization) produce different photometric signatures, which are observable provided that the thermal inertia of the surface is high, like that of solid or melted rocks (but not regolith). Tidal dissipation can also directly affect the light curves and make the inference of the rotation more difficult or easier depending on the existence of hot spots on the surface. Infrared light curve measurement with the James Webb Space Telescope and EChO can be used to infer exoplanets rotation periods and dissipation rates and thus to test tidal models. This data will also constrain the nature of the (sub)surface by constraining the thermal inertia.
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