Abstract
The space mission will cover over $14\,000\ $ with two optical and near-infrared spectro-photometric instruments, and is expected to detect around ten million active galactic nuclei (AGN). This unique data set will make a considerable impact on our understanding of galaxy evolution in general, and AGN in particular. For this work we identified the best colour selection criteria for AGN, based only on photometry or including ancillary photometric observations, such as the data that will be available with the Rubin Legacy Survey of Space and Time (LSST) and observations already available from Spitzer /IRAC. The analysis was performed for unobscured AGN, obscured AGN, and composite (AGN and star-forming) objects. We made use of the spectro-photometric realisations of infrared-selected targets at all-$z$ ( ) to create mock catalogues mimicking both the Euclid Wide Survey (EWS) and the Euclid Deep Survey (EDS). Using these mock catalogues, we estimated the best colour selection, maximising the harmonic mean (F1) of: (a) completeness, that is, the fraction of AGN correctly selected with respect to the total AGN sample; and (b) purity, that is, the fraction of AGN inside the selection with respect to the selected sample. The selection of unobscured AGN in both surveys (Wide and Deep) is possible with photometry alone with $ F1=0.22$--0.23 (Wide and Deep), which can increase to $ F1=0.43$--0.38 (Wide and Deep) if we limit out study to objects at $z>0.7$. Such a selection is improved once the Rubin/LSST filters, that is, a combination of the $u$, $g$, $r$, or $z$ filters, are considered, reaching an F1 score of 0.84 and 0.86 for the EDS and EWS, respectively. The combination of a colour with the $ colour, which is possible only in the EDS, results in an F1 score of 0.59, improving the results using only filters, but worse than the selection combining and LSST colours. The selection of composite AGN =0.05$--0.65 at 8--40$\ and obscured AGN is challenging, with $ F1 even when including Rubin/LSST or IRAC filters. This is unsurprising since it is driven by the similarities between the broad-band spectral energy distribution of these AGN and star-forming galaxies in the wavelength range 0.3--5\,micron
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