All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1468fig1.eps} \end{figure}$ Figure 1: X-ray image in the 0.5-10 keV band (grey scale) with the 11 arcmin radius circle of the X-ray analysis and the deepest region ( $\sim$ 450 arcmin²) in the K-band (polygon) superimposed. The shallower K-band image covers the entire X-ray field of view. The X-ray sources associated with EROs are marked with circles.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1468fig2.eps} \end{figure}$ Figure 2: Observed magnitude distribution of the optical objects detected in the R band within a radius of 3 $^{\prime \prime }$ around each of the 87 X-ray sources (solid histogram), together with the expected distribution of background objects in the same area ( n(m), dashed histogram). The difference between these two distributions (dot-dot-dot dashed histogram) is the expected magnitude distribution of the optical counterparts. The smooth curve fitted to this histogram (dot-dot-dot dashed line) has been used as input in the likelihood calculation ( q(m)).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1468fig3.eps} \end{figure}$ Figure 3: The hardness ratio versus 2-10 keV flux for the hard X-ray selected sources in the "Daddi Field''. Sources with a secure optical ID (i.e. first part of Table 1) are indicated as filled symbols. The 8 hard X-ray detected EROs from the 5 $\sigma$ sample are plotted as filled triangles (see Table 3).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1468fig4a.eps}\par\vspace*{4mm} \includegraphics[width=8.8cm,clip]{1468fig4b.eps} \end{figure}$ Figure 4: Upper panel: R-band magnitude vs. hard X-ray flux for EROs, serendipitously detected in hard X-ray surveys. Large filled triangles are the 9 hard X-ray selected EROs of this work; circles correspond to the EROs in the "literature sample''; squares are sources from the Hellas2Xmm survey. As a comparison, broad-line AGN, i.e. sources with broad optical emission lines in the optical spectrum, detected in the CDF-S and CDF-N surveys are also reported as crosses. The shaded area represents the region typically occupied by known AGN (e.g. quasars and Seyferts) along the correlation log $({\rm X}/O)=0\pm 1$ . For comparison, we report the result of the stacking analysis performed on the K20 EROs in the CDF-S field not individually detected in the Chandra observation (asterisk at the faintest X-ray flux; Brusa et al. 2002). Lower panel: the same plot but in the K-band.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1468fig5.eps} \end{figure}$ Figure 5: The R-K color as a function of the X-ray to optical flux ratio (X/O) for EROs in the literature sample (empty circles are objects from the deep fields; filled triangles the EROs from this work; empty squares sources from Mignoli et al. 2004) and for BL AGN selected in the CDF-N and CDF-S fields (crosses). See text for details.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1468fig6a.eps}\par\vspace*{2mm} \includegraphics[width=8.8cm,clip]{1468fig6b.eps} \end{figure}$ Figure 6: Upper panel: the K magnitude as a function of redshift for EROs in the literature sample for which spectroscopic (filled circles) or photometric (empty circles) redshifts are available and for near-infrared selected EROs in the K20 survey (crosses: spectroscopic z; plus signs: photometric z). Lower panel: fraction of AGN ERO as a function of the K-band magnitudes, as computed from three different samples: this work, the Alexander et al. (2002) work (A02) and the Roche et al. (2003) sample.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1468fig7.eps} \end{figure}$ Figure 7: Logarithm of the absorbing column density ( $N_{\rm H}$ ) versus the logarithm of the unabsorbed X-ray luminosity in the 2-10 keV band for all the X-ray detected EROs with spectroscopic or photometric redshifts from the literature sample. Filled symbols are those with ${\rm X}/O >10$ (see text). In the upper right corner the "QSO2 locus'' is highlighted.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1468fig8.eps} \end{figure}$ Figure 8: K-band luminosities versus the 2-10 keV X-ray luminosities (filled triangles: our XMM EROs; filled circles: EROs with spectroscopic redshifts). The $M_{\rm BH}$ resulting from the K-band luminosity on the basis of the Marconi & Hunt (2003) relation are reported on the right axis of the figure. The two continuous lines represent the expected correlation between the two plotted quantities for two different assumptions on the bolometric correction ( $k_{\rm bol}=10$ and $k_{\rm bol}=30$ ) and for $L/L_{\rm Edd}=1$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1468fig1.eps} \end{figure}$	Figure 1: X-ray image in the 0.5-10 keV band (grey scale) with the 11 arcmin radius circle of the X-ray analysis and the deepest region ( $\sim$ 450 arcmin²) in the K-band (polygon) superimposed. The shallower K-band image covers the entire X-ray field of view. The X-ray sources associated with EROs are marked with circles.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1468fig3.eps} \end{figure}$	Figure 3: The hardness ratio versus 2-10 keV flux for the hard X-ray selected sources in the "Daddi Field''. Sources with a secure optical ID (i.e. first part of Table 1) are indicated as filled symbols. The 8 hard X-ray detected EROs from the 5 $\sigma$ sample are plotted as filled triangles (see Table 3).
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1468fig5.eps} \end{figure}$	Figure 5: The R-K color as a function of the X-ray to optical flux ratio (X/O) for EROs in the literature sample (empty circles are objects from the deep fields; filled triangles the EROs from this work; empty squares sources from Mignoli et al. 2004) and for BL AGN selected in the CDF-N and CDF-S fields (crosses). See text for details.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1468fig7.eps} \end{figure}$	Figure 7: Logarithm of the absorbing column density ( $N_{\rm H}$ ) versus the logarithm of the unabsorbed X-ray luminosity in the 2-10 keV band for all the X-ray detected EROs with spectroscopic or photometric redshifts from the literature sample. Filled symbols are those with ${\rm X}/O >10$ (see text). In the upper right corner the "QSO2 locus'' is highlighted.
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