Limitations in determining vturb and Tkin from the two direct methods. Panels a) and b) show the relative error in vturb for a given (vturb/cs) as a function of the temperature a) and line width b) corresponding to the direct method with a known excitation temperature and the co-spatial method, respectively. Panel c) shows the relative error in Tkin from the co-spatial method as a function of relative error in line width. The left panel does not take into account errors in the line width. The dashed contour lines show 10, 5, and 3σ limits.
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