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Because of the Herschel and Planck satellite missions, there is stronginterest in the interpretation the sub-millimetre dust spectra frominterstellar clouds. Much work has been done to understand the dependencebetween the spectral index beta_Obs and the colour temperature T_C that ispartly caused by the noise. The (T_C, beta_Obs) confidence regions areelongated, banana-shaped structures. We studied under which conditions theseexhibit anomalous, strongly non-Gaussian behaviour that could affect theinterpretation of the observed (T_C, beta_Obs) relations. We examined modifiedblack body spectra and spectra calculated from radiative transfer models offilamentary clouds at wavelengths 100um-850um. We performed modified black bodyfits and examined the structure of the chi^2(T_, beta_Obs) function. We showcases where, when the signal-to-noise ratio is low, the chi^2 has multiplelocal minima in the (T_C, beta_Obs) plane. A small change in the weighting ofthe data points can cause the solution to jump to completely different values.In particular, noise can lead to the appearance of a separate population ofsolutions with low colour temperatures and high spectral indices. The anomaliesare caused by the noise but the tendency to show multiple chi^2 minima dependson the model and the wavelengths analysed. Deviations from the assumed singlemodified black body spectrum are not important. The presence of local minimaimplies that the results obtained from the chi^2 minimisation depend on thestarting point of the optimisation and may correspond to non-global minima. The(T_C,beta_Obs) distributions may be contaminated by a few solutions withunrealistically low colour temperatures and high spectral indices. Properweighting must be applied to avoid the determination of the beta_Obs(T_C)relation to be unduly affected by these measurements.

The degeneracy between the dust colour temperature and the spectral index. The problem of multiple chi^2 minima