A massive HI-absorption-selected galaxy at $z\approx2.356$

We use the Karl G. Jansky Very Large Array (VLA) and the Atacama Large Millimeter/submillimeter Array (ALMA) to detect $\rm CO(1-0)$, $\rm CO(3-2)$, and rest-frame 349-GHz continuum emission from an HI-selected galaxy, DLA1020+2733g, at $z\approx2.3568$ in the field of the $z=2.3553$ damped Lyman-$\alpha$ absorber (DLA) towards QSO J1020+2733. The VLA $\rm CO(1-0)$ detection yields a molecular gas mass of $(2.84\pm0.42)\times10^{11}\times(\alpha_{\rm CO}/4.36)\,\rm{M_\odot}$, the largest ever measured in an HI-selected galaxy. The DLA metallicity is $+0.28 \pm 0.16$, from the ZnII$\, \lambda2026$\r{A} absorption line detected in a Keck Echellette Spectrograph and Imager spectrum. This continues the trend of high-metallicity DLAs being frequently associated with massive galaxies. We obtain a star-formation rate (SFR) of $\lesssim400~$M$_\odot~$yr$^{-1}$ from the rest-frame 349-GHz continuum emission, and a relatively long molecular gas depletion timescale of $\gtrsim0.6~$Gyr. The excitation of the J=3 rotational level is sub-thermal, with $r_{31}\equiv{L'_{\rm{CO(3-2)}}/L'_{\rm{CO(1-0)}}}=0.513\pm0.081$, suggesting that DLA1020+2733g has a low SFR surface density. The large velocity spread of the CO lines, $\approx500~\rm km~s^{-1}$, and the long molecular gas depletion timescale suggest that DLA1020+2733g is likely to be a cold rotating-disk galaxy.