The nature of the red disk-like galaxies at high redshift: dust attenuation and intrinsically red stellar populations

We investigate which conditions of dust attenuation and stellar populations allow models of dusty, continuously star-forming, bulge-less disk galaxies at 0.8<z<3.2 to meet the different colour selection criteria of high-z ``red'' galaxies (e.g. Rc-K>5.3, Ic-K>4, J-K>2.3). As a main novelty, we use stellar population models that include the thermally pulsating Asymptotic Giant Branch (TP-AGB) phase of stellar evolution. The star formation rate of the models declines exponentially as a function of time, the e-folding time being longer than 3 Gyr. In addition, we use calculations of radiative transfer of the stellar and scattered radiation through different dusty interstellar media in order to explore the wide parameter space of dust attenuation. We find that synthetic disks can exhibit red optical/near-infrared colours because of reddening by dust, but only if they have been forming stars for at least about 1 Gyr. Extremely few models barely exhibit Rc-K>5.3, if the inclination i=90 deg and if the opacity 2*tauV>6. Hence, Rc-K-selected galaxies at 1<z<2 most probably are either systems with an old, passively evolving bulge or starbursts. Synthetic disks at 1<z<2 exhibit 4<Ic-K<4.8, if they are seen edge on (i.e. at i about 90 deg) and if 2*tauV>0.5. This explains the large fraction of observed, edge-on disk-like galaxies with Ks<19.5 and F814W-Ks>4. Finally, models with 2<z<3.2 exhibit 2.3<J-K<3, with no bias towards i about 90 deg and for a large range in opacity (e.g. 2*tauV>1 for i about 70 deg). In conclusion, red disk-like galaxies at 0.8<z<3.2 may not necessarily be dustier than nearby disk galaxies (with 0.5<2*tauV<2) and/or much older than about 1 Gyr. This result is due both to a realistic description of dust attenuation and to the emission contribution by TP-AGB stars... (Abridged)