Top: variations of the square root of the CRB of Tex in Kelvin as a function of the column density and the excitation temperature. Bottom: functions of the line opacities. Left: only 13CO (1−0) is analyzed. Middle: only 13CO(2−1) is analyzed. Right: both 13CO(1−0) and 13CO(2− 1) are analyzed simultaneously. In (a) and (b) pixels in grey correspond to Tex and N values whichlead to singular Fisher matrices. For this analysis, σb = 100 mK, ΔV = 1.1 km s−1 and σV = 0.61 km s−1. The constant σV,0 = 1 km s−1 is introduced to have expressions in (d–f) that depend on σV, but remain homogeneous to a temperature.
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