We present an extinction map of the Polaris molecular cirrus cloud derived from star counts and compare it with the Schlegel et al. (1998) extinction map derived from the far--infrared dust opacity. We find that, within the Polaris cloud, the Schlegel et al. Av values are a factor 2 to 3 higher than the star count values. We propose that this discrepancy results from a difference in $tau_{FIR}/ A_V$ between the diffuse atomic medium and the Polaris cloud. We use the difference in spectral energy distribution, warm for the diffuse atomic medium, cold for the Polaris cloud, to separate their respective contribution to the line of sight integrated infrared emission and find that the $tau_{FIR}/ A_V$ of cold dust in Polaris is on average 4 times higher than the Schlegel et al. value for dust in atomic cirrus. This change in dust property could be interpreted by a growth of fluffy particles within low opacity molecular cirrus clouds such as Polaris. Our work suggests that variations in dust emissivity must be taken into account to estimate Av from dust emission wherever cold infrared emission is present (i.e. molecular clouds).
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