The blue UV slopes of z ∼ 4 Lyman break galaxies: implications for the corrected star formation rate density

Context. Study of the dust extinction in high-redshift galaxies is fundamental to obtaining an estimate of the corrected star formation rate density (SFRD) and to put constraints on galaxy evolution models. Aims. We plan to analyse dust extinction in Lyman break galaxies (LBGs) by introducing a new and more reliable approach to their selection and to the characterization of their distribution of UV slopes beta, using deep IR images from HST. We fully discuss the methodology and the results, focusing on a robust sample of z similar to 4 LBGs. Methods. We exploit deep WFC3 IR observations of the ERS and HUDF fields over GOODS-South, combined with HST-ACS optical data, to select z similar to 4 LBGs through a new (B-V) vs. (V - H) colour diagram. The UV slope of the selected galaxies is robustly determined by a linear fit over their observed I, Z, Y, J magnitudes, coherently with the original definition of beta. The same fit is used to determine their rest-frame UV magnitudes M1600 through a simple interpolation. We estimate the effect of observational uncertainties with detailed simulations that we also exploit, under a parametric maximum-likelihood approach, to constrain the probability density function of UV slopes PDF(beta) as a function of rest-frame magnitude. Results. We find 142 robust LBGs in the ERS and 25 in the HUDF field, limiting our sample to S/N(H) > 10 objects. Our newly defined criteria improve the selection of z similar to 4 LBGs and allow us to exclude red interlopers at lower redshifts, especially z similar to 3-3.5 objects. We show that using a linear fit to estimate beta and accurately characterizing observational effects are required in this kind of analysis of flux-limited samples. We find that z similar to 4 LBGs are characterized by blue UV slopes, suggesting a low dust extinction: all L < L* galaxies have an average UV slope similar or equal to -2.1, while brighter objects are only slightly redder ( similar or equal to -1.9). We find an intrinsic dispersion similar or equal to 0.3 for PDF(beta) at all magnitudes. The SFRD at z similar to 4 corrected according to these estimates turns out to be lower than previously found: log(SFRD) similar or equal to -1.09 M circle dot/yr/Mpc(3). Finally, we discuss how the UV slope of z similar to 4 galaxies changes as a function of the dust-corrected UV magnitude (i.e. SFR). We show that most galaxies with high SFR (greater than or similar to 80 M-circle dot/yr) are highly extincted objects. Among galaxies with lower SFR, we detect many with a much lower amount of reddening, although current observational limits prevent us from detecting those with high extinction, if they exist.