KASHz+SUPER: Evidence of cold molecular gas depletion in AGN hosts at cosmic noon

The energy released by AGN has the potential to heat or remove the gas of the ISM, thus likely impacting the cold molecular gas reservoir of host galaxies at first, with star formation following on longer timescales. Previous works on high-z galaxies have yielded conflicting results, possibly due to selection biases and other systematics. To provide a reliable benchmark for galaxy evolution models at cosmic noon (z=1-3), two surveys were conceived: SUPER and KASHz, both targeting unbiased X-ray-selected AGN at z>1 that span a wide bolometric luminosity range. In this paper, we assess the effects of AGN feedback on the molecular gas content of host galaxies in a statistically robust, uniformly selected, coherently analyzed sample of AGN at z=1-2.6, drawn from the KASHz and SUPER surveys. By using ALMA data in combination with dedicated SED modeling, we retrieve CO and FIR luminosity as well as $M_*$ of SUPER and KASHz AGN. We selected non-active galaxies from PHIBBS, ASPECS and multiple ALMA/NOEMA surveys of sub-mm galaxies. By matching the samples in z, $M_*$ and $L_{FIR}$, we compared the properties of AGN and non-active galaxies within a Bayesian framework. We find that AGN hosts at given $L_{FIR}$ are on average CO depleted compared to non-active galaxies, confirming what was previously found in the SUPER survey. Moreover, the molecular gas fraction distributions of AGN and non-active galaxies are statistically different, with that of of AGN being skewed to lower values. Our results indicate that AGN can indeed reduce the total cold molecular gas reservoir of their host galaxies. Lastly, by comparing our results with predictions from three cosmological simulations (TNG, Eagle and Simba) filtered to match the observed properties, we confirm already known discrepancies and highlight new ones between observations and simulations.[Abridged]