GMF G214.5-1.8 as traced by CO: I -- cloud-scale CO freeze-out as a result of a low cosmic-ray ionisation rate

We present an analysis of the outer Galaxy giant molecular filament (GMF) G214.5-1.8 (G214.5) using IRAM 30m data of $^{12}$CO, $^{13}$CO and C$^{18}$O. We find that the $^{12}$CO (1-0) and (2-1) derived excitation temperatures are near identical and are very low, with a median of 8.2 K, showing that the gas is extremely cold across the whole cloud. Investigating the abundance of $^{13}$CO across G214.5, we find that there is a significantly lower abundance along the entire 13 pc spine of the filament, extending out to a radius of $\sim 0.8$ pc, corresponding to $A_v \gtrsim 2$ mag and $T_{dust} \lesssim 13.5$ K. Due to this, we attribute the decrease in abundance to CO freeze-out, making G214.5 the largest scale example of freeze-out yet. We construct an axisymmetric model of G214.5's $^{13}$CO volume density considering freeze-out and find that to reproduce the observed profile significant depletion is required beginning at low volume densities, $n\gtrsim2000$ cm$^{-3}$. Freeze-out at this low number density is possible only if the cosmic-ray ionisation rate is $\sim 1.9 \times 10^{-18}$ s$^{-1}$, an order of magnitude below the typical value. Using timescale arguments, we posit that such a low ionisation rate may lead to ambipolar diffusion being an important physical process along G214.5's entire spine. We suggest that if low cosmic-ray ionisation rates are more common in the outer Galaxy, and other quiescent regions, cloud-scale CO freeze-out occurring at low column and number densities may also be more prevalent, having consequences for CO observations and their interpretation.