5 Contribution to the extragalactic background light

The samples of sources discussed allow us to estimate how much of the mid-IR extragalactic light detected in the mid-IR surveys is due to AGNs. We can derive this quantity in a direct way by simply computing the total of the mid-IR fluxes of the sources whose emission is dominated by AGNs and dividing this by the total of the mid-IR fluxes of the sources in the area. In this case, we can estimate only the AGN contribution within the sensitivity limits of the surveys and not to the total extragalactic background mid-IR light (more than 30% and 60% of the 15 $\mu$m background is resolved at the flux limits of the Lockman Hole and HDF-N surveys, respectively). Alternatively, we can use the median $\alpha _{\rm IX}$ for different classes of contributors to the X-ray background to estimate the total contribution to the mid-IR extragalactic background (following Severgnini et al. 2000).

5.1 Estimating the AGN contribution to mid-IR surveys

We can derive the AGN contribution in the case of HDF-N and Lockman surveys for which we have the complete information on X-ray and mid-IR sources. To do this, we have to select on the basis of the optical, X-ray and mid-IR properties, the subsamples of sources whose mid-IR emission is dominated by AGNs.

In the case of the Lockman Hole, we have seen that almost all the galaxies in the sample have high X-ray luminosity and low $\alpha _{\rm IX}$ values. Therefore, we conservatively assume that the mid-IR emission of all the galaxies in the sample is due to AGNs.

In the case of the HDF-N, we have seen that Chandra observations are so deep that X-ray emission from starburst galaxies is also detected. Thus, in order to estimate the AGN contribution to the mid-IR total emission we have to select the galaxies whose mid-IR emission is dominated by the AGN. We base our selection on the X-ray luminosity (see Fig. 7) and on the shape of the SED from radio to X-ray wavelengths (see Fig. 9).

Figure 9: Radio, mid-IR, near-IR, optical and X-ray data for sources in the HDF-N (numbered as in Table 4) superimposed to scaled SEDs of template galaxies (A: Arp 220, B: M 82, C: NGC 6240, D: Circinus). The fit with the lowest $\chi ^2$ (see values in the upper left corner) is shown.

Out of 16 sources with flux greater than 0.1 mJy, four have a high X-ray luminosity ( $L_{\rm X} > 10^{43}$ erg s^-1) and another four are faint in the X-ray ( $L_{\rm X} \le 10^{40}$ erg s^-1). In these cases, we assume that the mid-IR emission is dominated by AGN and star-formation activity, respectively. Moreover, since the source #172 is detected also in the ultra-hard band, we consider that it is dominated by AGN activity. We classify all the other sources, which have an intermediate X-ray luminosity, by comparing their radio, mid-IR, near-IR, optical and X-ray data with the SEDs of two star formation-dominated and two type-2 AGNs (Arp 220, M 82, Circinus and NGC 6240) for which we have the SED from radio to X-ray frequences. Radio data at 8.5 GHz come from Richards et al. (1998) and at 1.4 GHz from Richards (2000). In the 1.4 GHz case, we also retrieved the image to estimate the 1.4 GHz flux of the source #155. For each galaxy we fitted the data to the template SEDs scaled in luminosity choosing the fit with the lowest $\chi ^2$ value. Figure 9 shows the $\chi ^2$ values for each SED and the the best fit superimposed to the data. In the fit we considered also upper limits on the hard X-ray fluxes. This means that the $\chi ^2$ of the NGC 6240 and Circinus SEDs are typically underestimated. For comparison, in the same figure, the SED of two bright X-ray sources (#163 and #142) and one faint X-ray source (#160) are also shown (the best fit is obtained with the NGC 6240, Circinus and M 82 SEDs, respectively). The sources with intermediate X-ray luminosity are all well fitted with the M82 SED, except for #136 which is fitted by the Arp 220 SED. We note that also the variable X-ray source ("Var'') follows the M 82 SED very well. Therefore, in these cases we assume that the mid-IR emission of these sources is not dominated by the presence of an AGN.

Figure 10: On the left: histogram of LW3 fluxes in the Lockman and HDF-N surveys. Sources detected in the X-ray are shaded, while the black histogram shows the sources dominated by AGN emission. On the right: ratio of integrated 15 $\mu$m flux of AGN-dominated sources to that of all the mid-IR extragalactic sources as a function of limiting flux. The 0.1 mJy points comes from the HDF-N survey, while the other points are computed on the basis of the Lockman survey. The horizontal band shows the percentage of background light due to AGN emission according to the analysis based on the $\alpha _{\rm IX}$ index (see the text).

In Fig. 10 we summarise the contribution of AGNs to the mid-IR extragalactic background as a function of the flux. The bin between 0.1 mJy and 0.5 mJy has been defined using the HDF-N data, since the sources detected in this field cover this range of fluxes well and the HDF-N is complete for fluxes greater than 0.1 mJy (Aussel et al. 1999). Due to its small size, there are no sources in the HDF-N with fluxes greater than 0.5 mJy. Hence, the contribution in the other two bins is based on the Lockman Hole data which are more than 80% complete at the flux of 0.5 mJy (Fadda et al. 2002).

In the HDF-N there are 42 sources for a total of 9.9 mJy in the 0.1-0.5 mJy bin, five of which are classified by us as AGN-dominated (#142, #144, #163, #171 and #172). This implies an AGN contribution in this flux bin of $(17.8 \pm 7)\%$.

The Lockman Hole survey covers well the 0.5-3 mJy flux interval where we find 103 sources for a total of 81.8 mJy with 13 sources which are AGN-dominated, leading to a total contribution of $(14.6 \pm 4.7)\%$. In Fig. 10, we report the contribution in two bins: 0.5-0.8 mJy ( $(14.3 \pm 6)\%$) and 0.8-3 mJy ( $(14.8 \pm 7)\%$). The contribution in this interval is probably slightly underestimated because, as is clear from Fig. 7, XMM-Newton observations may miss a population of fainter X-ray sources that contain highly obscured AGNs. The effect should not be dramatic because, as we have seen in our analysis of the HDF-N sources, the mid-IR emission of most of these intermediate X-ray luminous sources is not dominated by the AGN activity.

From these estimates, we can derive the AGN contribution to the fraction of the mid-IR extragalactic background due to the emission of 0.1-3 mJy sources, which constitute $\sim$70% of the measured background. The 0.1-0.5 mJy and 0.5-3 mJy sources contribute 48% and 23% of the observed mid-IR background, respectively (Elbaz et al. 2002). Therefore, AGNs contribute $(16.8\pm6.2)\%$ of the fraction of the mid-IR extragalactic background for which are responsible the sources detected in the 0.1-3 mJy flux interval.

5.2 Estimating AGN contribution with median mid-IR to X-ray spectral indices

In order to exploit all the existing information from the deep HDF-N data to the shallow ELAIS-S1 observations, we can estimate the AGN contribution to the mid-IR background using the mean $\alpha _{\rm IX}$ indices of bright and faint X-ray sources of the X-ray background with mid-IR emission (see Severgnini et al. 2000 for an application of this technique to the SCUBA sources).

To apply this method we have to know the values of the X-ray and mid-IR backgrounds. We compute the 5 keV X-ray background using the estimation of the 1-7 keV background by Chen et al. (1997), which is in good agreement with recent Chandra and XMM counts. In particular, the counts by Brandt et al. (2001a) clearly flatten at low fluxes, indicating that almost all the background is resolved in this survey. Assuming the background of Chen et al. (1997), Alexander et al. (2001a) evaluate that $\sim$$86\%$ of the 2-8 keV background is resolved by Chandra observations in the HDF-N region. The recent estimation by Vecchi et al. (1999) with Beppo-SAX observations seems to be too high to agree with recent deep observations of XMM and Chandra satellites. In the case of 15 $\mu$m, the total background has not yet been measured. Observational values are the upper limit of 5 nW m^-2 sr^-1 established by Stanev & Franceschini (1998) measuring the optical depth at high energies due to the $\gamma \longrightarrow \gamma$ interaction with the background infrared photons and the lower limit of $\nu I(\nu) \vert _{15~\mu \rm m} = 2.4$ nW m^-2 sr^-1 obtained by Elbaz et al. (2002) integrating the flux of all the sources in the deep ISOCAM surveys down to the flux limit of 0.05 mJy. Franceschini et al. (2001), on the basis of their evolutionary model, which takes into account counts in the mid-IR, far-IR and sub-mm, and measurement of the far-IR background, expect that the contribution of fainter sources would bring the total background to $\nu I(\nu) \vert _{15~\mu \rm m} = 3.3$ nW m^-2 sr^-1. This value, which is not far from values predicted by other models (Chary & Elbaz 2001; Xu 2000) and from values found by Altieri et al. (1999) using cluster-lensed data, has been adopted in our analysis.

The horizontal band in Fig. 8 represents the $\alpha _{\rm IX}$ of the cosmic background, assuming that most of the flux in the two spectral windows comes from sources with a similar distribution of redshifts centred around z=1. Therefore, this value should correspond to the mid-IR to X-ray index of the population which dominates the X-ray background if the same population were responsible for the totality of the mid-IR background. Otherwise, fitting both backgrounds requires a combination of AGN and star formation activity.

The flattening of the 2-8 keV counts in the HDF-N deep Chandra survey (Brandt et al. 2001a) clearly shows that almost all the hard X-ray background is resolved at the sensitivity of this survey. Since these counts agree very well with the counts by Mushotzky et al. (2000), extrapolating their result we can say that about 85% of the 2-10 keV background is resolved at a flux of $0.5\times10^{-15}$ erg s^-1 cm^-2 (see also Alexander et al. 2001a). We do not consider sources with fluxes less than this value because most of them have only upper limits on the flux and are probably starburst galaxies (according to their low X-ray luminosity).

To evaluate the AGN contribution to the mid-IR background we divide the sources in two groups according to their X-ray fluxes: sources brighter than 10^-14 erg s^-1 cm^-2 and faint sources with 2-10 keV flux in the range $0.5\times10^{-15}$-10^-14 erg s^-1 cm². In these flux ranges the sources have similar $\alpha _{\rm IX}$ values (see Fig. 8). Using the counts of Brandt et al. (2001a) and the results of Ueda et al. (1999) and Mushotzky et al. (2000), sources brighter than 10^-14 erg s^-1 cm^-2contribute $40 \pm 10\%$ of the hard X-ray background, while sources with flux in the range $0.5\times10^{-15}$-10^-14 erg s^-1 cm²contribute $45 \pm 5\%$ of the hard X-ray background.

We can evaluate the AGN contribution to the mid-IR background by means of the median spectral indices of bright and faint X-ray sources. Bright sources, most of them are in the Elais-S1 survey, have a median $\alpha _{\rm IX}$ of 1.15, which corresponds to only 6% of the value required to fill the mid-IR background. Therefore, bright hard X-ray sources contribute to the mid-IR background $(40\pm10)\%\times6\%=(2.4\pm0.6)\%$, i.e. in a negligible way.

The median value of $\alpha _{\rm IX}$ for faint sources is 1.30, which corresponds to 33% of the mid-IR background. Hence, faint hard X-ray sources contribute to the mid-IR background $(45\pm5)\%\times33\%=(14.8\pm 1.7)\%$. Combining these results, we conclude that sources making up $\sim$85% of the 2-10 keV background contribute $(17.2\pm2.3)\%$ of the mid-IR background.

Considering that the infrared spectra of typical AGNs, due to a dusty-torus reprocessed emission, peak around 20 $\mu$m (e.g. Granato et al. 1997), the LW3 ISOCAM band is expected to be quite efficient in selecting AGNs at moderate redshifts, more than far-IR or sub-millimeter observations. Due to the more diffuse and lower-intensity energy sources, starburst spectra should peak at significantly longer infrared wavelengths, as observed. This indicates that our estimated limit of $\sim$17% of mid-IR background as due to X-ray loud AGNs may be considered as an upper limit for the AGN contribution to the CIRB energy density. This obviously cannot account for possible contribution of AGNs completely opaque below 10 keV and longwards of 20 $\mu$m, i.e. hidden by extremely high column density material.