EROs found behind lensing clusters -: I.: Stellar population and dust properties of optical dropout EROs and comparison with related objects

Context. On the nature, redshift, stellar populations and dust properties of optically faint or non-detected extremely red objects. Aims. Determining the nature, redshift, stellar populations and dust properties of optically faint or non-detected, extremely red objects (ERO) found from our survey of the lensing clusters A1835 and AC114 (Richard et al. 2006, A&A, 456, 861). Comparison with properties of related galaxies, such as IRAC selected EROs and a z similar to 6.5 post-starburst galaxy candidate from the Hubble Ultra Deep Field. Methods. Using an updated version of Hyperz (Bolzonella et al. 2000, A&A, 363, 476) and a large number of spectral templates we perform broad-band SED fitting. The photometric observations, taken from Hempel et al. (2007, A&A, submitted), include deep optical, ACS/HST, ISAAC/VLT, IRAC/Spitzer data, and for some objects 24 mu m MIPS/Spitzer and sub-mm data as well. Results. For most of the lensed EROs we find photometric redshifts showing a strong degeneracy between low-z (z similar to 1-3) and high-z (z similar to 6-7). Although formally best fits are often found at high-z, their resulting bright absolute magnitudes, the number density of these objects, and in some cases Spitzer photometry or longer wavelength observations, suggest strongly that all of these objects are at low-z. The majority of these objects are best fitted with relatively young (less than or similar to 0.5-0.7 Gyr) and dusty starbursts. Three of our objects show indications for strong extinction, with A(V) similar to 2.4-4. The typical stellar masses of our objects are M-* similar to (0.5-5) x 10(10) M-circle dot after correction for lensing; for the most extreme ERO in our sample, the sub-mm galaxy SMMJ14009+0252 most likely at z(fit) similar to 3, we estimate M-* similar to 6. x 10(11) M-circle dot. For dusty objects star formation rates (SFR) have been estimated from the bolometric luminosity determined after fitting of semi-empirical starburst, ERO, and ULIRG templates. Typically we find SFR similar to (1-18) M-circle dot yr(-1). Again, SMMJ14009+0252 stands out as a LIRG with SFR similar to 1000 M-circle dot yr(-1). Finally, we predict the mid-IR to sub-mm SED of the dusty objects for comparison with future observations with APEX, Herschel, and ALMA. Concerning the comparison objects, we argue that the massive post-starburst z similar to 6.5 galaxy candidate HUDF-J2 showing observed properties very similar to our EROs, is more likely a dusty starburst at z similar to 2.3-2.6. This interpretation also naturally explains the observed 24 mu m emission from this object and we predict its IR to sub-mm SED. Both empirically and from our SED fits we find that the IRAC selectec EROs from Yan et al. (2004, ApJ, 616, 63) show very similar properties to our lensed EROs. Reasonable fits are found for most of them with relatively young and dusty stellar populations.