The search for rocky exoplanets plays an important role in our quest for extra-terrestrial life. Here, we discuss the extreme physical properties possible for the first characterized rocky super-Earth, CoRoT-7b (R_pl = 1.58 \pm 0.10 R_Earth, Mpl = 6.9 \pm 1.2 M_Earth). It is extremely close to its star (a = 0.0171 AU = 4.48 R_st), with its spin and orbital rotation likely synchronized. The comparison of its location in the (Mpl, Rpl) plane with the predictions of planetary models for different compositions points to an Earth-like composition, even if the error bars of the measured quantities and the partial degeneracy of the models prevent a definitive conclusion. The proximity to its star provides an additional constraint on the model. It implies a high extreme-UV flux and particle wind, and the corresponding efficient erosion of the planetary atmosphere especially for volatile species including water. Consequently, we make the working hypothesis that the planet is rocky with no volatiles in its atmosphere, and derive the physical properties that result. As a consequence, the atmosphere is made of rocky vapours with a very low pressure (P \leq 1.5 Pa), no cloud can be sustained, and no thermalisation of the planetary is expected. The dayside is very hot (2474 \leq 71 K at the sub-stellar point) while the nightside is very cold (50 to 75 K). The sub-stellar point is as hot as the tungsten filament of an incandescent bulb, resulting in the melting and distillation of silicate rocks and the formation of a lava ocean. These possible features of CoRoT-7b could be common to many small and hot planets, including the recently discovered Kepler-10b. They define a new class of objects that we propose to name "Lava-ocean planets"

Aims. We use the super Earth 55 Cnc e as a case study to address an observable effect of tidal heating. This transiting short-period planet belongs to a compact multiple system with massive planets. We investigate whether planet-planet interactions can force the eccentricity of this planet to a level affecting the eclipse depth observed with Spitzer. Methods. Using the constant time lag tidal model, we first calculate the observed planet flux as a function of albedo and eccentricity, for different tidal dissipation constants and for two extreme cases: a planet with no heat redistribution and a planet with full heat redistribution. We derive the values of albedo and eccentricity that match the observed transit depth. We then perform N-body simulations of the planetary system including tides and general relativity to follow the evolution of the eccentricity of planet e. We compare the range of eccentricities given by the simulations with the eccentricities required to alter the eclipse depth. Results. Using our nominal value for the dissipation constant and the most recent estimates of the orbital elements and masses of the 55 Cnc planets, we find that the eccentricity of planet e can be large enough to contribute at a measurable level to the thermal emission measured with Spitzer. This affects the constraints on the albedo of the planet, which can be as high as 0.9 (instead of 0.55 when ignoring tidal heating). We also derive a maximum value for the eccentricity of planet e directly from the eclipse depth: e < 0.015 assuming Earth's dissipation constant. Conclusions. Transiting exoplanets in multiple planet systems -like 55 Cancri -are exceptional targets for testing tidal models because their tidal luminosity may be observable. Future multi-wavelengths observations of eclipse depth and phase curves (for instance with EChO and JWST) should allow us to better resolve the temperature map of these planets and break the degeneracy between albedo and tidal heating that remains for single band observations. In addition, an accurate determination of the eccentricity will make it possible to constrain the dissipation rate of the planet and to probe its internal structure.