Solution pixel approach to estimate α_{¹²CO(1−0)}. Left: from the scatter minimization approach, described by Leroy et al. (2011) and Sandstrom et al. (2013), we obtain estimates of α_{¹²CO(1−0)} and DGR. The top panels (i) show the hexagons that illustrate the individual solution pixels for both ¹²CO(1–0) and (2–1) transmission. The solution pixels consist of 37 underlying, half-beam spaced lines of sight. We note that the underlying hexagon tiling is meant to show the results in each solution pixel (the actual solution pixels have 40% overlap). In the maps, we highlight an individual solution pixel. We vary α_{¹²CO(1−0)} and compute the DGR following Eq. (12). We select the value for which the variation in DGR is minimal. The bottom left panel (ii) shows the variation of the DGR as a function of different α_{¹²CO(1−0)}. The variation for the selected solution pixel is minimal for α_{¹²CO(1−0)} labeled B. We perform this analysis for each solution pixel. The bottom right panel (iii) illustrates why the variance differs when changing α_{¹²CO(1−0)}. Here we combine all significant points from the solution pixel indicated in panel (i) from both CO lines. The black lines point to the solution pixel where the individual lines of sight are drawn from. We correct the ¹²CO(2–1) data with the average line ratio of the solution pixel. The panel illustrates the differences in DGR for three selected α_{¹²CO(1−0)} (labeled A, B, and C). Based on the selection of α_{¹²CO(1−0)} the DGR values will be positively or negatively correlated (as illustrated by the colored line, which is drawn schematically to guide the eye). Right: the resulting α_{¹²CO(1−0)} value for each solution pixel based on the combined ¹²CO(1–0) and ¹²CO(2–1) integrated intensities.