estimate the contribution from star-formation processes to the 2–10 keV luminosities assuming the relation reported in Ranalli et al. (2003) and the SFRs obtained from SED fitting ($\S$2). The derived values are $\approx1.9\times10^{42}$ [erg s$^{-1}$]{} (SDP.9) and $\approx3.3\times10^{42}$ [erg s$^{-1}$]{} (SDP.11), i.e., the X-ray intrinsic luminosities are a factor $\approx$3–4.5 higher than those possibly associated with stellar processes. Recently, based on the analysis of the 6Ms CDFS data, Lehmer et al. (2016) have derived more refined scaling relations between the X-ray luminosity of galaxies and their SFR, stellar mass and redshift of the form $L_{2-10keV}=\alpha M_\star+\beta SFR$, where $\alpha$ and $\beta$ increase with redshift. By applying the scaling relations of Lehmer et al. (2016; see their Table 4), the 2-10 keV luminosities that can be ascribed to stellar processes would be $\sim30\%$ higher than those estimated with the Ranalli et al. relation. We note that because of the large, $\approx 30-40\%$ uncertainties in the measured X-ray luminosities, dominated by the low photon statistics, the measured values would still be compatible within $\sim2.0-2.5\sigma$ with being produced by star formation. However, the systematically higher measured values point again towards an AGN-related nature.

We finally note that any X-ray emission associated with star 