ner_tags: O O O O O B-Software O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: noise random number generator within GILDAS . However, the data cube has undergone many transformations and the true noise may not be precisely Gaussian. Thus, we extract contiguous channels from signal-free regions of the cube which we use as noise. In fact, as any transformations were designed to preserve particularly the region where signal is present, this is a sort of worst-case noise. We first examine what we obtain from mock clouds with no velocity gradient, that is to say with v xy constant. Figure 13 shows the results for T max = 200 mK using both purely random noise and noise taken from signal-free but unoptimized regions of the cube. The gradients, for equivalent clouds and noise levels, are clearly more dispersed with the “real” cube noise. The dispersions, as measured by the full width at half power of the distribution (divided by 2.35 to give the equivalent for a Gaussian), are approximately 0.008 and 0.015 km s −1 pc −1 for the random and cube noise injection. T max = 200 mK corresponds roughly to the median signal in the cloud sample. Fig. 13 Histogram of gradients from noise. The black line shows the distribution of the gradients for purely random noise. The red line shows the distribution when noise is from signal-free regions of the cube. No velocity gradient has been injected here. We have also tested with higher and lower S/N levels. For T max = 100 mK, the dispersion increases to 0.014 and 0.029 km s −1 pc −1 for respectively random and cube noise. For T max = 400 mK, the dispersion decreases to 0.005 and 0.0085 km s −1 pc −1 for respectively random and cube noise. 5 Evaluating uncertainties on cloud rotation The same operations were done with the observed gradients, creating the same clouds but injecting the velocity gradient deduced from the observations for each cloud. Should there be a link between size or shape and the velocity gradient deduced from calculating the first moment, the link would be preserved in these tests. Figure 14 shows the distribution of the retrieved gradients. The clouds were created with the observed gradients and shapes and then noise was added and the gradients remeasured. This can be directly compared with Fig. 10 . The distribution in Fig. 14 is of course wider because the gradients from Fig. 10 have been injected and then noise added. The process was repeated with T max = 100 mK and the distribution is significantly wider but the prograde-retrograde asymmetry is nonetheless preserved. We are thus confident that the gradients retrieved reflect the true distribution of velocity gradients, although the distribution is likely broadened by the presence of the noise in the datacube. Fig. 14 Like Fig. 13 except that the observed gradients (see Fig. 10 ) have been injected, noise added, and the gradients recovered. Black line shows the distribution of the gradients for purely random noise. The red line shows the distribution when noise from signal-free regions of the cube. As in Fig. 13 , T