We present the infrared (IR) and X-ray properties of a sample of 33 mid-IR luminous quasars (νL6 μm ≥ 6 × 1044 erg s−1) at redshift z ≈ 1–3, identified through detailed spectral energy distribution analyses of distant star-forming galaxies, using the deepest IR data from Spitzer and Herschel in the GOODS–Herschel fields. The aim is to constrain the fraction of obscured, and Compton-thick (CT, NH > 1.5 × 1024 cm−2) quasars at the peak era of nuclear and star formation activities. Despite being very bright in the mid-IR band, ≈30 per cent of these quasars are not detected in the extremely deep 2 and 4 Ms Chandra X-ray data available in these fields. X-ray spectral analysis of the detected sources reveals that the majority (≈67 per cent) are obscured by column densities NH > 1022 cm−2; this fraction reaches ≈80 per cent when including the X-ray-undetected sources (9 out of 33), which are likely to be the most heavily obscured, CT quasars. We constrain the fraction of CT quasars in our sample to be ≈24–48 per cent, and their space density to be Φ = (6.7 ± 2.2) × 10−6 Mpc−3. From the investigation of the quasar host galaxies in terms of star formation rates (SFRs) and morphological distortions, as a sign of galaxy mergers/interactions, we do not find any direct relation between SFRs and quasar luminosity or X-ray obscuration. On the other hand, there is tentative evidence that the most heavily obscured quasars have, on average, more disturbed morphologies than the unobscured/moderately obscured quasar hosts, which preferentially live in undisturbed systems. However, the fraction of quasars with disturbed morphology amongst the whole sample is ≈40 per cent, suggesting that galaxy mergers are not the main fuelling mechanism of quasars at z ≈ 2.
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