Resolving the physics of Quasar Ly$α$ Nebulae (RePhyNe): II. The dense and clumpy CGM of Quasars at $z \sim$ 3.5

Abstract: The small scale density distribution of the cold circumgalactic medium (CGM) plays a central role in galaxy evolution, yet it is still poorly understood. We provide new constraints on the cold CGM density distribution by comparing the CGM emission from MUSE observations of quasar (QSO) nebulae at $z \sim 3.8$ with mock observations generated from the new DaLya simulation suite under the assumption of maximal fluorescence. These are further complemented by mock observations generated from the COLIBRE (m5 and m6 resolutions) and HELLO simulations. We first investigate the distribution of the observed and simulated Ly$α$ surface brightness (SB) values, which directly depend on the cold gas density distribution under our assumption, finding stark differences between observations and upper limits provided by simulations with the exception of the COLIBRE higher-resolution run (m5). The observations generally show a much larger covering fraction of regions with relatively large Ly$α$ SB values and suggest that densities reaching at least 10 cm$<sup>{-3}$ must be present in the CGM of QSOs within a radial distance of 50 to 200 ckpc. To understand the origin of this discrepancy, we study the cold CGM density distribution finding in all cases simulated PDFs consistent with skewed lognormal ones with medians $\sim 10<sup>{-2}$ cm$<sup>{-3}$ and clumping factors between 16 and 102. We compare the broadness of these distributions to the one implied by the observed HeII/Ly$α$ CGM ratio, which is independent on the assumption of maximum fluorescence. Assuming lognormal PDFs with median values similar to the simulations, the observed ratio requires a broader PDF with a clumping factor at least 8 times larger than predicted by simulations. These results suggest that higher resolution and/or additional physical mechanisms are needed to reproduce the observed CGM of QSOs at these redshifts.