Encoding of the infrared excess in the NUVrK color diagram for star-forming galaxies

We present an empirical method of assessing the star formation rate (SFR) of star-forming galaxies based on their locations in the rest-frame color-color diagram (NUV - r) vs (r - K). By using the Spitzer 24 mu m sample in the COSMOS field (similar to 16400 galaxies with 0.2 <= z <= 1.3) and a local GALEX-SDSS-SWIRE sample (similar to 700 galaxies with z <= 0.2), we show that the mean infrared excess < IRX > = < L-IR/L-UV > can be described by a single vector, NRK, that combines the two colors. The calibration between < IRX > and NRK allows us to recover the IR luminosity, L-IR, with an accuracy of sigma similar to 0.21 for the COSMOS sample and 0.27 dex for the local one. The SFRs derived with this method agree with the ones based on the observed (UV+IR) luminosities and on the spectral energy distribution(SED) fitting for the vast majority (similar to 85%) of the star-forming population. Thanks to a library of model galaxy SEDs with realistic prescriptions for the star formation history, we show that we need to include a two-component dust model (i.e., birth clouds and diffuse ISM) and a full distribution of galaxy inclinations in order to reproduce the behavior of the < IRX > stripes in the NUVrK diagram. In conclusion, the NRK method, based only on rest-frame UV/optical colors available in most of the extragalactic fields, offers a simple alternative of assessing the SFR of star-forming galaxies in the absence of far-IR or spectral diagnostic observations.