The SUPERCOLD-CGM survey: \\ I. Probing the extended CO(4-3) Emission of the Circumglactic medium in a sample of 10 Enormous Ly$\alpha$ Nebulae at $z\sim2$

To understand how massive galaxies at high-$z$ co-evolve with enormous reservoirs of halo gas, it is essential to study the coldest phase of the circum-galactic medium (CGM), which directly relates to stellar growth. The SUPERCOLD-CGM survey is the first statistical survey of cold molecular gas on CGM scales. We present ALMA+ACA observations of CO(4-3) and continuum emission from 10 Enormous Ly$\alpha$ Nebula (ELANe) around ultraluminous type-I QSOs at $z\sim2$. We detect CO(4-3) in 100$\%$ of our targets, with 60$\%$ showing extended CO on scales of 15$-$100 kpc. Q1228+3128 reveals the most extended CO(4-3) reservoir of $\sim$100 kpc and is the only radio-loud target in our sample. The CO reservoir is located along the radio axis, which could indicate a link between the inner radio-jet and cold halo gas. For the other five radio-quiet ELANe, four of them show extended CO(4-3) predominantly in the direction of their companions. These extended CO(4-3) reservoirs identify enrichment of the CGM, and may potentially contribute to widespread star formation. However, there is no evidence from CO(4-3) for diffuse molecular gas spread across the full extent of the Ly$\alpha$ nebulae. One target in our sample (Q0107) shows significant evidence for a massive CO disk associated with the QSO. Moreover, 70$\%$ of our QSO fields contain at least one CO companion, two of which reveal extended CO emission outside the ELANe. Our results provide insight into roles of both the cold CGM and companions in driving the early evolution of massive galaxies.