Top: variations of the square root of the CRB of T_ex 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 T_ex and N values whichlead to singular Fisher matrices. For this analysis, σ_b = 100 mK, Δ_V = 1.1 km s⁻¹ and σ_V = 0.61 km s⁻¹. The constant σ_V,0 = 1 km s⁻¹ is introduced to have expressions in (d–f) that depend on σ_V, but remain homogeneous to a temperature.