A series of gravitational instabilities in a circumnuclear gas disk (CND) are required to trigger gas transport to a central supermassive black hole (SMBH) and ignite Active Galactic Nuclei (AGNs). A test of this scenario is to investigate whether an enhanced molecular gas mass surface density ($Sigma_{rm mol}$) is found in the CND-scale of quasars relative to a comparison sample of inactive galaxies. Here we performed sub-kpc resolution CO(2-1) observations with ALMA of four low-redshift ($z sim 0.06$), luminous ($sim 10^{45}$ erg s$^{-1}$) quasars with each matched to a different star-forming galaxy, having similar redshift, stellar mass, and star-formation rate. We detected CO(2-1) emission from all quasars, which show diverse morphologies. Contrary to expectations, $Sigma_{rm mol}$ of the quasar sample, computed from the CO(2-1) luminosity, tends to be smaller than the comparison sample at $r < 500$ pc; there is no systematic enhancement of $Sigma_{rm mol}$ in our quasars. We discuss four possible scenarios that would explain the lower molecular gas content (or CO(2-1) luminosity as an actual observable) at the CND-scale of quasars, i.e., AGN-driven outflows, gas-rich minor mergers, time-delay between the onsets of a starburst-phase and a quasar-phase, and X-ray-dominated region (XDR) effects on the gas chemical abundance and excitation. While not extensively discussed in the literature, XDR effects can have an impact on molecular mass measurements particularly in the vicinity of luminous quasar nuclei; therefore higher resolution molecular gas observations, which are now viable using ALMA, need to be considered.
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