Models of the escape and retention of volatiles by minor icy objects exclude any presence of volatile ices on the surface of TNOs smaller than ~1000km in diameter at the typical temperature in this region of the solar system, whereas the same models show that water ice is stable on the surface of objects over a wide range of diameters. Collisions and cometary activity have been used to explain the process of surface refreshing of TNOs and Centaurs. These processes can produce surface heterogeneity that can be studied by collecting information at different rotational phases. The aims of this work are to study the surface composition of (20000)Varuna, a TNO with a diameter ~650km and to search for indications of rotational variability. We observed Varuna during two consecutive nights in January 2011 with NICS@TNG obtaining a set of spectra covering the whole rotation period of Varuna. After studying the spectra corresponding to different rotational phases, we did not find any indication of surface variability. In all the spectra, we detect an absorption at 2{mu}m, suggesting the presence of water ice on the surface. We do not detect any other volatiles on the surface, although the S/N is not high enough to discard their presence. Based on scattering models, we present two possible compositions compatible with our set of data and discuss their implications in the frame of the collisional history of the Kuiper Belt. We find that the most probable composition for the surface of Varuna is a mixture of amorphous silicates, complex organics, and water ice. This composition is compatible with all the materials being primordial. However, our data can also be fitted by models containing up to a 10% of methane ice. For an object with the characteristics of Varuna, this volatile could not be primordial, so an event, such as an energetic impact, would be needed to explain its presence on the surface.
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