The characterization of dust properties in the interstellar medium (ISM) is key for star formation. Mass estimates are crucial to determine gravitational collapse conditions for the birth of new stellar objects in molecular clouds. However, most of these estimates rely on dust models that need further observational constraints from clouds to prestellar and protostellar cores. We present results of a study of dust emissivity changes based on mm-continuum data obtained with the NIKA camera at the IRAM-30m telescope. Observing dust emission at 1.15 mm and 2 mm allows us to constrain the dust emissivity index ($beta$) in the Rayleigh-Jeans tail of the dust spectral energy distribution (SED) far from its peak emission, where the contribution of other parameters (i.e. dust temperature) is important. Focusing on the Taurus molecular cloud, a low-mass star-forming regions in the Gould Belt, we analyze the emission properties of several distinct objects in the B213 filament: three prestellar cores, two Class-0/I protostellar cores and one Class-II object. By means of the ratio of the two NIKA channel-maps, we show that in the Rayleigh-Jeans approximation the dust emissivity index varies among the objects. For one prestellar and two protostellar cores, we produce a robust study using Herschel data to constrain the dust temperature of the sources. By using the Abel transform inversion technique we get accurate radial $beta$ profiles. We find systematic spatial variations of $beta$ in the protostellar cores that is not observed in the prestellar core. While in the former case $beta$ decreases toward the center, in the latter it remains constant. Moreover, $beta$ appears anticorrelated with the dust temperature. We discuss the implication of these results in terms of dust grain evolution between pre- and protostellar cores.
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