Encoding the infrared excess (IRX) 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 micron sample in the COSMOS field (~16400 galaxies with 0.2 = can be described by a single vector, NRK, that combines the two colors. The calibration between and NRK allows us to recover the IR luminosity, L_IR, with an accuracy of ~0.21 dex 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 fitting for the vast majority (~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 stripes in the NUVrK diagram. In conclusion, the NRK method, based only on rest-frame UV and 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.