Extremely red galaxies: dust attenuation and classification

We re-address the classification criterion for extremely red galaxies (ERGs) of Pozzetti & Mannucci, which aims to separate, in the I-c - K (or R-c - K) versus J - K colour-colour diagram, passively evolving, old (greater than or equal to 1 Gyr) stellar populations in a dust-free environment, associated with ellipticals (Es), from dusty starburst galaxies (DSGs), both at 1 < z < 2. We explore a category of objects not considered previously, i.e. galaxies forming in this redshift range on a short (0.1 Gyr) time-scale and also observed in their early, dusty post-starburst phase. We also investigate the impact of structure of the dusty medium and the amount of dust on the observed optical/near-infrared (near-IR) colours of high-z DSGs/dusty post-starburst galaxies (DPSGs), through multiple-scattering radiative transfer calculations for a dust/stars configuration and an extinction function calibrated with nearby dusty starbursts. As a main result, we find that DPSGs, with ages between 0.2 and 1 Gyr, at 1.3 < z < 2 mix with Es at 1 < z < 2 for a large range in the amount of dust. This 'intrusion' is a source of concern for the present two-colour classification of ERGs. On the other hand, we confirm, in agreement with Pozzetti & Mannucci, that DSGs are well separated from Es, both at 1 < z < 2, in the I-c - K versus J - K colour-colour diagram, whatever the structure (two-phase clumpy or homogeneous) of their dusty medium and the amount of dust. This result holds under the new hypothesis of high-z Es being as dusty as nearby ones. Thus the interpretation of the optical/near-IR colours of high-z Es may suffer from a multiple degeneracy among age, metallicity, dust and redshift. We also find that DPSGs at z similar to 1 mix with DSGs at 1 < z < 2, as a function of the amount of dust and the structure of the dusty medium. All of these results help to explain the complexity of the ERG classification that has emerged from recent surveys. Model DSGs/DPSGs with K < 20.5 and selected as ERGs on the basis of their observed optical/near-IR colours span a large range in absorption efficiency and/or intrinsic ultraviolet-to-optical luminosity ratio. Consequently, the total emission from dust in the rest-frame mid-IR-(sub) millimetre ranges from similar to 10(10) to similar to 5.6 x 10(12) L. for DPSGs to DSGs. This large dynamic range is consistent with estimates made from submillimetre observations of bright (K < 19.5-20) ERGs. Finally, we show that ERG samples are biased towards a lower fraction either of DSGs/DPSGs at 1.3 < z < 2 or of DSGs/DPSGs at z similar to 1, when selection is made via either the R-c - K greater than or equal to 5.3 or the I-c - K greater than or equal to 4 colour criterion.