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Appendix A: Testing the SED fitting technique

As described in Sect. 3.1, our fitting approach consists of using 5 SFG templates, derived from a sample of local star-forming galaxies and an empirically derived AGN template (Mullaney et al. 2011) modified by an extinction law (with A_V ≈ 0−30 mag). We applied these templates to decompose the total SEDs of high redshift sources (z ≤ 3) into AGN and galaxy components. To determine the best-fitting solutions, we firstly fit to the Spitzer and Herschel photometric data a simple model including only the SFG template, using χ² minimisation, yielding 5 SED solutions (one for each SFG template). We then fit the data with a more complex SFG + AGN (plus extinction on the AGN component only) model, using an f-test to determine the best-fitting solutions. The criteria we used to choose whether the AGN component significantly improves the fit are: i) an f-test probability >90% confidence when adding the AGN template to the fit; ii) this first condition must be met in the majority of the SED fitting solutions (i.e. at least 3 out of 5).

This SED fitting approach (Sect. 3.1) and the criteria chosen to identify the best-fit models were selected based on the results of careful tests performed on a sample of 30 sources in the VLA/24 μm detected sample (Sect. 2) for which Spitzer IRS low-resolution spectroscopy is available (covering the wavelength range λ ≈ 3−20  μm, rest-frame; Kirkpatrick et al. 2012; Murphy et al. 2009; Pope et al. 2008). These sources are all detected in the X-ray band (Alexander et al. 2003) and the majority of them are also detected in at least one of the Herschel bands at 100, 160 and/or 250 μm (29/30 sources; Table 4). Our tests consist of two main steps:

• 1.

  constraining the AGN and star formation components using theIRS spectra (plus Herschel data), which providemore detailed information (e.g. PAH features or featurelesspower-law continuum) than photometry alone on the sourceemission at MIR wavelengths, where the AGNcontribution affects the SED the most(λ ≲ 30 − 40  μm);

• 2.

  performing the SED fits using only Spitzer and Herschel photometric points (not including the IRS spectra), testing various criteria to select, amongst the different solutions, the best-fitting models that more closely matched the IRS spectral fitting results.

In analysing the IRS spectra, we also included the Herschel 100, 160 and 250 μm flux densities to help constrain the SEDs in the FIR band, as the spectra alone cover too small a wavelength range to allow a reliable extrapolation of the SEDs in the broad IR band. In fact, fitting just the IRS spectra (not including the Herschel data) tend to underestimate the amount of star formation contribution to the total emission, favoring higher contribution from the AGN component, instead.

Since the Spitzer IRS spectra provide a large amount of data for fitting our SED templates, we fitted the spectra (and Herschel data) directly using a model including both SFG and AGN (plus extinction) templates described in Sect. 3.1 to measure galaxy and AGN contributions to the total IR emission. We note that because the IRS data have much smaller uncertainties compared to the Herschel data, we increased the errors on the IRS spectra by a constant factor to be of the same order of magnitude of the Herschel data errors¹³ (when S/N > 3); this is to avoid the SED fitting results being dominated by the Spitzer IRS data (which would have much more “weight” on the resulting χ² than the Herschel data), and also to account for the intrinsic scatter between our 5 discrete SFG templates. We adopted χ² minimisation to evaluate the best fit of the 5 SFG templates. We note that due to the high signal-to-noise ratio of the IRS spectra (despite the enhancement applied to the errors), the resulting χ² values for all the fits are very high (χ²/d.o.f. ≫ 1) and therefore cannot be used as an absolute measure of the goodness of the fit in the usual way (see also Mullaney et al. 2011). However, since the χ² calculation is affected by this issue in the same way for each solution, a comparison between χ² values can still be used to identify the best-fit amongst the five different solutions: the spectral fit yielding the minimum χ² was chosen as the best-fitting solution. It is important to note however, that in some cases the difference in χ² between different solutions is small, and therefore, the chosen best-fit model is not the only acceptable solution to reproduce the data. To overcome this issue, instead of choosing one solution as the best-fit, we used a weighted mean between the five different fitting solutions to retrieved the 6 μm luminosity of the AGN (from the fitted AGN component), the FIR fluxes and the q values for the sources. The χ² values were used to calculate appropriate weights in order to give the maximum weight to the solution with the minimum χ² (i.e. ). A dominant AGN component (i.e. L_6  μm,AGN/L_6  μm,tot > 0.5) was measured in 16 cases. From these IRS spectra (+Herschel) fits, we also determined that when the AGN is found to contribute less than ~30% to the total (AGN + SFG) emission at 6 μm, the total SED is not significantly affected by the presence of the AGN component compared to that of a pure SFG. Therefore, when the AGN is not significantly detected with our SED fitting approach (i.e. when using photometric Spitzer and Herschel data only), we chose the upper limit for the AGN luminosity at 6 μm to be 30% of the total 6 μm luminosity (see Sect. 5.1).

After using the IRS spectra to obtain good constraints on the AGN and star formation components, we then performed several sets of SED fits to these sources using Spitzer 8, 16, 24 μm and Herschel 100, 160, 250 μm flux densities only (not including the IRS spectra), testing different criteria to select the best-fitting solutions, in particular to establish the significance of the AGN component in the fits. These tests were performed to find the best “recipe” to recover, with these sparse photometric data points (which is the approach adopted in this paper; see Sect. 3.1), the results obtained from the IRS spectral (plus Herschel data) fits (Fig. A.2 and Table 4). As for the IRS spectra, the Spitzer photometric data have much smaller uncertainties than the Herschel data; we therefore increased the errors on the 8, 16 and 24 μm flux densities (by constant factors for all of the sources) during the SED fitting process in order for each data point to have a similar “weight” in the fit and to allow for the intrinsic scatter on the templates. We note, however, that in these SED fits, as for the IRS + Herschel data fits, the reduced χ² alone (i.e. χ²/d.o.f. ≈ 1) is not a reliable indicator of the goodness of fit since the χ² is very sensitive to the errors on the data points used in the fits, especially when the number of data points is limited, as in our case. Nevertheless, as we pointed out above, the relative χ² can still be used to determine the best-fit model between two sets of solutions (SFG only, or SFG + AGN; Fig. 3), so we performed an f-test, which compares the χ² values and d.o.f. of the two models (see Sect. 3.1), to measure the improvement of the fit obtained by including the AGN component to the model.

We tested the reliability of the best-fitting solutions by varying the f-test probability threshold between the two adopted models (SFG and SFG + AGN) and also varying the number of solutions that needed to pass this threshold for the model to be accepted as the best-fit. A higher confidence level (e.g. 95% or 99%) allowed us to recover the AGN component detected in the IRS spectra only in a small number of cases, while missing some very obvious, strong IR AGN, where the AGN emission found from the IRS contributes 100% to the total 6 μm luminosity. We therefore lowered the confidence level threshold from the f-test to be at least 90%. The f-test was performed between each pair of SED fitting solutions (i.e. for each SFG template) in order to verify whether the need of the AGN component was dependent on the SFG template used in the fits. Indeed, we recognised that the fits performed with one particular SFG template (“SB5” in Mullaney et al. 2011) typically required an AGN component with higher confidence than the others. To avoid biases on the results due to the choice of SFG template and thus to remove the dependence of the fitting solutions on any specific templates, we decided to accept the AGN component as significant only if the f-test criterion was met in at least 3 of the 5 SED fitting solutions, otherwise we conservatively assumed the simple SFG model as the best-fit.

As previously seen from the Spitzer IRS spectral fits, in some cases different fitting solutions yielded small differences in χ² values meaning that a unique solution could not be defined. Therefore, once we established the best-fit model (SFG or SFG + AGN), we obtained the 6 μm luminosity of the AGN, the total FIR fluxes and the q values for our sources using a weighted average of the values calculated from all the best-fit model solutions¹⁴ (as for the fits of the Spitzer IRS spectra + Herschel data); the errors on the estimated averages were calculated as weighted average variances.

To test the results for our chosen SED fitting approach, we compared the 6 μm luminosity of the AGN obtained from the IRS spectral fitting (+Herschel data) to that obtained from the SED fitting performed using Spitzer and Herschel photometry (Fig. A.1). In Fig. A.1 we distinguish between sources with a dominant AGN component at 6 μm (IR AGN: L_{6  μm,  AGN}/L_{6  μm,  tot} > 0.5) from those where the AGN component is not significantly detected (IR SFG: L_{6  μm,  AGN}/L_{6  μm,  tot} < 0.5). In ≈87% of the cases the IR classification of the sources obtained from the IRS spectra and the SED fits are consistent with each other (12 IR AGN and 14 IR SFGs) and the 6 μm luminosities measured from the two types of analysis are in good agreement (Table 4). In the remaining cases (≈13%), the two different analyses yielded different results: the IRS spectral analysis identified an AGN component in four further sources, which are missed by our SED fitting analysis; this is because the criteria we adopted in defining the AGN component as significant in our SED fits are very conservative and thus, while we can easily identify the AGN where L_{6  μm,  AGN}/L_{6  μm,  tot} ≫ 0.5, we are likely to miss some cases where the AGN component is not strongly dominant in the MIR band. With this in mind, we can consider the detection of the AGN emission component through our SED fitting approach as robust.

Fig. A.1 Comparison of the AGN 6 μm luminosity obtained from the SED fitting of the photometric Spitzer and Herschel data points (νL6  μm, SED) versus the L6  μm estimated from the IRS spectral (+ Herschel data points) fitting (νL6  μm, IRS). For the IR SFGs, where the AGN component was not significantly detected, we plotted an upper limit of the AGN L6  μm (i.e., 30% of the total 6 μm luminosity; see Appendix A). Sources where the classification from the two analyses agree are shown as filled symbols: IR AGN (filled squares) and IR SFG (filled circles). The AGN identified only from the IRS spectral fit are shown as open squares.

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As a final verification of the reliability of our SED fitting approach, we plot in Fig. A.2 the best-fit SEDs (using Spitzer and Herschel photometric points only) for the 30 sources analysed here in comparison to the Spitzer IRS spectra; we showed only one of the best-fitting solutions for each source. The SEDs were fitted using only Spitzer 8, 16, 24 μm, and Herschel 100, 160, 250 μm photometric points (black circles); the Spitzer-IRAC data points at 3.6, 4.5, and 5.8 μm (red triangles) and the VLA radio data points (black star) are over-plotted to the SEDs (not used in the fits) to show the agreement with the resulting SEDs. The Spitzer IRS spectra (cyan line) are also shown, but they are not included in the SED fits. The panels on the top right of each plot is a zoom on the IRS spectra (2.5−25  μm rest-frame) to better show the comparison between the best-fit SEDs and the spectra. In general, there is very good agreement with the resulting SED and the IRS spectra, even though we stress that here the spectra were not used to constrain the SEDs. This result is a confirmation of the validity of our templates and SED fitting approach. The only few cases (2/30; i.e. CXOJ123555.13+620901.7 and CXOJ123726.51+622026.8) where the SEDs differ from the MIR IRS spectra are those where deep silicate features are present; in these cases the photometric data points do not provide enough information to predict the amount of extinction needed to reproduce these strong features. However, since the purpose of our analysis is not to measure the strength of the spectral features, such as silicate absorption/emission features or PAH emission lines, but to estimate the AGN and SFG contribution to the overall IR SEDs, we can ignore the discrepancies between SEDs and spectra for these sources.

Fig. A.2 Best-fitting solutions to the spectral energy distributions (SEDs) of the X-ray detected sources in GOODS-N with Spitzer-IRS spectroscopy (Kirkpatrick et al. 2012; Murphy et al. 2009; Pope et al. 2008). The dotted lines represent the AGN component and the dashed lines indicate the SFG component; the total SEDs are represented as solid lines. The Spitzer 8, 16, 24 μm and the Herschel 100, 160, 250 μm data points (black circles) have been used to constrain the SEDs, while the Spitzer-IRAC 3.6, 4.5, 5.8 μm (red stars) and the VLA 1.4 GHz (black star) radio data points are over plotted on the SEDs but they are not included in the fit. The Spitzer-IRS spectrum is also shown (cyan line), but it is NOT used to constrain the SEDs. On the top right-hand side of each plot, a zoom on the Spitzer-IRS spectrum is shown (2.5–25 μm); our best-fit SEDs are typically in very good agreement with the Spitzer-IRS spectra.

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Appendix B: SEDs of the radio-excess sources

In this appendix the best-fit SED plots for the entire radio-excess sample (51 sources) are reported (Fig. B.1); for each source we only plotted the SED with the lowest χ² value amongst the best-fitting model solutions (see Sects. 3.1 and Appendix A).

Fig. B.1 Best-fit SEDs for the 51 sources in the radio-excess sample. The total SEDs are shown as black solid lines, the AGN templates are shown as dotted lines and the SFG templates as dashed lines. Filled circles represent the Spitzer 8, 16, 24 μm and the Herschel 100, 160, 250 μm flux densities, which are used to constrain the SEDs. Open symbols indicate the data that were not included in the SED fitting process: red triangles are Spitzer-IRAC 3.6, 4.5, 5.8 μm flux densities, black open circles are SPIRE 350 and 500 μm, and black squares are VLA 1.4 GHz flux densities; the blue stars represent the 6 μm luminosity of the AGN predicted from the X-ray luminosity (2–10 keV, rest-frame) using the Lutz et al. (2004) relation for local unobscured AGN; we note that these points do not always match the IR AGN component because the X-ray luminosity tends to underestimate the intrinsic AGN power if the AGN emission is heavily absorbed. For the passive sources we plotted the SFG template upper limit (grey line) and an elliptical galaxy template (long dashed line; Sect. 4.3) to show that it could well represent the data, although we stress that this latter template is not included in our SED fitting analysis. The rise of the IRAC data point at short wavelengths observed for many sources is due to the emission from the galaxy old stellar population.

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© ESO, 2012