Revealing The CO X-factor In Dark Molecular Gas through Sensitive ALMA
  Absorption Observations
  Carbon-bearing molecules, particularly CO, have been widely used as tracers
of molecular gas in the interstellar medium (ISM). In this work, we aim to
study the properties of molecules in diffuse, cold environments, where CO tends
to be under-abundant and/or sub-thermally excited. We performed one of the most
sensitive (down to $\mathrm{\tau_{rms}^{CO} \sim 0.002}$ and
$\mathrm{\tau_{rms}^{HCO^+} \sim 0.0008}$) sub-millimeter molecular absorption
line observations towards 13 continuum sources with the ALMA. CO absorption was
detected in diffuse ISM down to $\mathrm{A_v< 0.32\,mag}$ and \hcop was down to
$\mathrm{A_v < 0.2\,mag}$, where atomic gas and dark molecular gas (DMG) starts
to dominate. Multiple transitions measured in absorption toward 3C454.3 allow
for a direct determination of excitation temperatures $\mathrm{T_{ex}}$ of
4.1\,K and 2.7\,K, for CO and for \hcop, respectively, which are close to the
cosmic microwave background (CMB) and provide explanation for their being
undercounted in emission surveys. A stronger linear correlation was found
between $\mathrm{N_{HCO^+}}$ and $\mathrm{N_{H_2}}$ (Pearson correlation
coefficient P $\sim$ 0.93) than that of $\mathrm{N_{CO}}$ and
$\mathrm{N_{H_2}}$ (P $\sim$ 0.33), suggesting \hcop\ being a better tracer of
H$_2$ than CO in diffuse gas. The derived CO-to-\h2 conversion factor (the CO
X-factor) of (14 $\pm$ 3) $\times$ 10$^{20}$ cm$^{-2}$ (K \kms)$^{-1}$ is
approximately 6 times larger than the average value found in the Milky Way.
