Census of High- and Medium-mass Protostars V. CO Abundance and the Galactic $X_{\text{CO}}$ Factor

We present the second dust continuum data release in the Census of High- and Medium-mass Protostars (CHaMP), expanding the methodology trialed in Pitts et al. 2019 to the entire CHaMP survey area ($280^{\circ}<l<300^{\circ}$, $-4^{\circ}<b<+2^{\circ}$). This release includes maps of dust temperature ($T_d$), H$_2$ column density ($N_{H_2}$), gas-phase CO abundance, and temperature-density plots for every prestellar clump with Herschel coverage, showing no evidence of internal heating for most clumps in our sample. We show that CO abundance is a strong function of $T_d$, and can be fit with a second-order polynomial in log-space, with a typical dispersion of a factor of 2--3. The CO abundance peaks at $20.0^{+0.4}_{-1.0}$ K with a value of $7.4^{+0.2}_{-0.3}\times10^{-5}$ per H$_2$; the low $T_d$ at which this maximal abundance occurs relative to laboratory results is likely due to interstellar UV bombardment in the largest survey fields. Finally, we show that, as predicted by theoretical literature and hinted at in previous studies of individual clouds, the conversion factor from integrated $^{12}$CO line intensity ($I_{^{12}CO}$) to $N_{H_2}$, the $X_{CO}$-factor, varies as a broken power-law in $I_{^{12}CO}$ with a transition zone between 70 and 90 K km$^{-1}$. The $X_{CO}$-function we propose has $N_{H_2}\propto I_{^{12}CO}^{0.51}$ for $I_{^{12}CO}\lesssim70$ K km$^{-1}$ and $N_{H_2}\propto I_{^{12}CO}^{2.3}$ for $I_{^{12}CO}\gtrsim90$ K km$^{-1}$. The high-$I_{^{12}CO}$ side should be generalizable with known adjustments for metallicity, but the influence of interstellar UV fields on the low-$I_{^{12}CO}$ side may be sample specific. We discuss how these results expand upon previous works in the CHaMP series, and help tie together observational, theoretical, and laboratory studies on CO over the past decade.