Cold dust grains emission in the FIR/submm is usually expressed as a modified black body law in which the dust mass absorption coefficient (MAC), is described with a temperature- and wavelength-independent emissivity spectral index, beta. However, numerous data from space and balloon-born missions and recently from Herschel and Planck show that dust emission is not well understood, as revealed by the observed anti-correlation of beta with the grain temperature. In order to give astronomers the necessary data to interpret FIR/submm observations, we synthesised analogues of interstellar amorphous and crystalline silicate grains, rich in Mg and Ca, and having stiochiometry of olivine and pyroxene and measured their MAC, in the 100-1000/1500 mum range for grain temperatures varying from 300 to 10 K. We find that the grain MAC decreases when the grain temperature decreases and that the local spectral index, beta, defined as the slope of the MAC curve, is anti-correlated with the grain temperature. These variations, which are not observed in the crystallised samples, are related to the amorphous nature of the samples. In addition, the spectral shape of the MAC is complex: at short wavelengths (lambda < 500/700 mum), beta is in the range 1.6 - 2.1 for all grain temperature and grain composition whereas at longer wavelengths (lambda > 500/700 mum), beta < 2 for samples with a pyroxene stoichiometry and beta > 2 for samples with an olivine stoichiometry. Hence, the simplifying asymptotic expression based on a single temperature- and wavelength-independent spectral index used by astronomers is not appropriate to describe the dust MAC and thus the dust emission, and may induce significant errors on the derived parameters such as the dust mass and the dust physical and chemical properties. Instead, dust emission models should use the dust MAC as a function of wavelength and temperature.
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