Context. Since the mid-1990s, the sample of Lyman break galaxies (LBGs) has been growing thanks to the increasing sensitivities in the optical and in near-infrared telescopes for objects at z > 2.5. However, the dust properties of the LBGs are poorly known because the samples are small and/or biased against far-infrared or sub-mm observations. Aims. This work explores from a statistical point of view the far-infrared (far-IR) and sub-millimeter (sub-mm) properties of a large sample of LBGs at z ∼ 3 that cannot be individually detected from current far-infrared observations. Methods. We select a sample of 22, 000 LBGs at 2.5 < z < 3.5 in the COSMOS field using the dropout technique. The large number of galaxies included in the sample allows us to split it in several bins as a function of UV luminosity (L FUV ), UV continuum slope (β UV ) and stellar mass (M * ) to better sample their variety. We stack in PACS (100 and 160 µm) images from PACS Evolution Probe survey (PEP), SPIRE (250, 350 and 500µm) images from the Herschel Multi-tied Extragalactic Survey (HerMES) programs and AzTEC (1.1 mm) images from the Atacama Submillimetre Telescope Experiment (ASTE). Our stacking procedure corrects the biases induced by galaxy clustering and incompleteness of our input catalogue in dense regions. Results. We obtain the full infrared spectral energy distributions (SED) of subsamples of LBGs and derive the mean IR luminosity as a function of L FUV , β UV and M * . The average IRX (or dust attenuation) is roughly constant over the L FUV range, with a mean of 7.9 (1.8 mag). However, it is correlated with β UV , A FUV = (3.15 ± 0.12) + (1.47 ± 0.14) β UV , and stellar mass, log (IRX) = (0.84 ± 0.11) log M * /10 10.35 + 1.17 ± 0.05. We investigate using a statistically-controlled stacking analysis as a function of (M * , β UV ) the dispersion of the IRX-β UV and IRX-M * plane. On the one hand, the dust attenuation shows a departure by up to 2.8 mag above the mean IRX-β UV relation, when log(M * [M ]) increases from 9.75 to 11.5 in the same β UV bin. That strongly suggests that M * plays an important role in shaping the IRX-β UV plane. On the other hand, the IRX-M * plane is less dispersed for variation in the β UV . However, the dust attenuation shows a departure by up to 1.3 mag above the mean IRX-M * relation, when β UV increases from -1.7 to 0.5 in the same M * bin. The low stellar mass LBGs (log(M * [M ]) < 10.5) and red β UV (β UV > −0.7), 15% of the total sample, present a large dust attenuation than the mean IRX-M * , but they still are in agreement with the mean IRX-β UV relation. We suggest that we have to combine both, IRX-β UV and IRX-M * , relations to obtain the best estimation of the dust attenuation from the UV and NIR properties of the galaxies (L FUV , β UV , M * ). Our results enable us to study the average relation between star-formation rate (SFR) and stellar mass, and we show that our LBG sample lies on the main sequence of star formation at z ∼ 3. we demonstrate that the SFR is underestimate for LBGs with hig...
