A Large Molecular Gas Reservoir in the Protocluster SPT2349$-$56 at $z\,{=}\,4.3

We present Atacama Compact Array (ACA) Band-3 observations of the protocluster SPT2349$-$56, an extreme system hosting ${\gtrsim}\,12$ submillimeter galaxies (SMGs) at $z\,{=}\,4.3$, to study its integrated molecular gas content via CO(4-3) and long-wavelength dust continuum. The $\sim$30-hour integration represents one of the longest exposures yet taken on a single pointing with the ACA 7-m. The low-resolution ACA data ($21.0''\,{\times}\,12.2''$) reveal a 75% excess CO(4-3) flux compared to the sum of individual sources detected in higher-resolution Atacama Large Millimeter Array (ALMA) data ($1.0''\,{\times}\,0.8''$). Our work also reveals a similar result by tapering the ALMA data to $10''$. In contrast, the 3.2mm dust continuum shows little discrepancy between ACA and ALMA. A single-dish [CII] spectrum obtained by APEX/FLASH supports the ACA CO(4-3) result, revealing a large excess in [CII] emission relative to ALMA. The missing flux is unlikely due to undetected faint sources but instead suggests that high-resolution ALMA observations might miss extended and low-surface-brightness gas. Such emission could originate from the circum-galactic medium (CGM) or the pre-heated proto-intracluster medium (proto-ICM). If this molecular gas reservoir replenishes the star formation fuel, the overall depletion timescale will exceed 400Myr, reducing the requirement for the simultaneous SMG activity in SPT2349$-$56. Our results highlight the role of an extended gas reservoir in sustaining a high star formation rate (SFR) in SPT2349$-$56, and potentially establishing the ICM during the transition phase to a mature cluster.