Ly-alpha emitters (LAEs) are seen everywhere in the redshift domain from local to z~7. Far-infrared (FIR) counterparts of LAEs at different epochs could provide direct clues on dust content, extinction, and spectral energy distribution (SED) for these galaxies. We search for FIR counterparts of LAEs that are optically detected in the GOODS-North field at redshift z~2.2 using data from the Herschel Space Telescope with the Photodetector Array Camera and Spectrometer (PACS). The LAE candidates were isolated via color-magnitude diagram using the medium-band photometry from the ALHAMBRA Survey, ancillary data on GOODS-North, and stellar population models. According to the fitting of these spectral synthesis models and FIR/optical diagnostics, most of them seem to be obscured galaxies whose spectra are AGN-dominated. From the analysis of the optical data, we have observed a fraction of AGN or composite over source total number of ~0.75 in the LAE population at z~2.2, which is marginally consistent with the fraction previously observed at z=2.25 and even at low redshift (0.2<z<0.45), but significantly different from the one observed at redshift ~3, which could be compatible either with a scenario of rapid change in the AGN fraction between the epochs involved or with a non detection of obscured AGN in other z=2-3 LAE samples due to lack of deep FIR observations. We found three robust FIR (PACS) counterparts at z~2.2 in GOODS-North. This demonstrates the possibility of finding dust emission in LAEs even at higher redshifts.
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