We investigate which conditions of dust attenuation and stellar populations allow models of dusty , continuously star-forming , bulge-less disk galaxies at 0.8 \la z \la 3.2 to meet the different colour selection criteria of high- z “ red ” galaxies ( e.g . R _ { c } - K > 5.3 , I _ { c } - 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 \sim 1 Gyr .
Extremely few models barely exhibit R _ { c } - K > 5.3 , if the inclination i = 90 °and if the opacity 2 \times \tau _ { \mathrm { V } } \ga 6 .
Hence , R _ { c } - K -selected galaxies at 1 \la z \la 2 most probably are either systems with an old , passively evolving bulge or starbursts .
Synthetic disks at 1 \la z \la 2 exhibit 4 < I _ { c } - K < 4.8 , if they are seen edge on ( i.e .
at i \sim 90 ° ) and if 2 \times \tau _ { \mathrm { V } } \ga 0.5 .
This explains the large fraction of observed , edge-on disk-like galaxies with K _ { s } < 19.5 and F 814 W - K _ { s } \ga 4 .
Finally , models with 2 \la z \la 3.2 exhibit 2.3 < J - K < 3 , with no bias towards i \sim 90 °and for a large range in opacity ( e.g . 2 \times \tau _ { \mathrm { V } } > 1 for i \sim 70 ° ) .
In conclusion , red disk-like galaxies at 0.8 \la z \la 3.2 may not necessarily be dustier than nearby disk galaxies ( with 0.5 \la 2 \times \tau _ { \mathrm { V } } \la 2 ) and/or much older than \sim 1 Gyr .
This result is due both to a realistic description of dust attenuation and to the emission contribution by TP-AGB stars , with ages of 0.2 to 1–2 Gyr and intrinsically red colours .