Estimating the total infrared luminosity of galaxies up to z similar to 2 from mid- and far-infrared observations

Aims. We present the observed correlations between rest-frame 8, 24, 70 and 160 mu m monochromatic luminosities and measured total infrared luminosities LIR of galaxies detected by Spitzer. Methods. Our sample consists of 372 star-forming galaxies with individual detections and flux measurements at 8, 24, 70 and 160 mu m. We have spectroscopic redshifts for 93% of these sources, and accurate photometric redshifts for the remainder. We also used a stacking analysis to measure the IR fluxes of fainter sources at higher redshifts. Results. We show that the monochromatic mid and far-infrared luminosities are strongly correlated with the total infrared luminosity and our stacking analysis confirms that these correlations also hold at higher redshifts. We provide relations between monochromatic luminosities and total infrared luminosities L-IR that should be reliable up to z similar to 2 (z similar to 1.1) for ULIRGs (LIRGs). In particular, we can predict L-IR with accuracies of 37% and 54% from the 8 and 24 mu m fluxes, while the best tracer is the 70 mu m flux. Combining bands leads to slightly more accurate estimates. For example, combining the 8 and 24 mu m luminosities predicts L-IR with an accuracy of 34%. Our results are generally compatible with previous studies, and the small changes are probably due to differences in the sample selection criteria. We can rule out strong evolution in dust properties with redshift up to z similar to 1. Finally, we show that infrared and sub-millimeter observations are complementary means of building complete samples of star-forming galaxies, with the former being more sensitive for z less than or similar to 2 and the latter at higher z greater than or similar to 2.