Feedback from AGN is thought to be key in shaping the life cycle of their host galaxies by regulating star-formation activity. Therefore, to understand the impact of AGN on star formation, it is essential to trace the molecular gas out of which stars form. In this paper we present the first systematic study of the CO properties of AGN hosts at z~2 for a sample of 27 X-ray selected AGN spanning two orders of magnitude in AGN bolometric luminosity (Lbol= 10^44.7-10^46.9 erg/s) by using ALMA Band 3 observations of the CO(3-2) transition (~1 angular resolution). To search for evidence of AGN feedback on the CO properties of the host galaxies, we compared our AGN with a sample of inactive (i.e., non-AGN) galaxies from the PHIBSS survey with similar redshift, stellar masses, and SFRs. We used the same CO transition as a consistent proxy for the gas mass for the two samples in order to avoid systematics involved when assuming conversion factors. By adopting a Bayesian approach to take upper limits into account, we analyzed CO luminosities as a function of stellar masses and SFRs, as well as the ratio LCO(3-2)/M* (proxy for the gas fraction). The two samples show statistically consistent trends in the LCO(3-2)-Lfir and LCO(3-2)-M* planes. However, there are indications that AGN feature lower CO(3-2) luminosities (0.4-0.7 dex) than inactive galaxies at the 2-3sigma level when we focus on the subset of parameters where the results are better constrained and on the distribution of the mean LCO(3-2)/M*. Therefore, even by conservatively assuming the same excitation factor r31, we would find lower molecular gas masses in AGN, and assuming higher r31 would exacerbate this difference. We interpret our result as a hint of the potential effect of AGN activity (e.g., radiation and outflows), which may be able to heat, excite, dissociate, and/or deplete the gas reservoir of the host galaxies. (abridged)
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