Planck intermediate results. XIV. Dust emission at millimetre wavelengths in the Galactic plane

We use Planck HFI data combined with ancillary radio data to study the emissivity index of the interstellar dust emission in the frequency range 100-353 GHz, or 3-0.8 mm, in the Galactic plane. We analyse the region l = 20 degrees-44 degrees and vertical bar b vertical bar <= 4 degrees where the free-free emission can be estimated from radio recombination line data. We fit the spectra at each sky pixel with a modified blackbody model and two opacity spectral indices, beta(mm) and beta(FIR), below and above 353 GHz, respectively. We find that beta(mm) is smaller than beta(FIR), and we detect a correlation between this low frequency power-law index and the dust optical depth at 353 GHz, tau(353). The opacity spectral index beta(mm) increases from about 1.54 in the more diffuse regions of the Galactic disk, vertical bar b vertical bar = 3 degrees-4 degrees and tau(353) similar to 5 x 10(-5), to about 1.66 in the densest regions with an optical depth of more than one order of magnitude higher. We associate this correlation with an evolution of the dust emissivity related to the fraction of molecular gas along the line of sight. This translates into beta(mm) similar to 1.54 for a medium that is mostly atomic and beta(mm) similar to 1.66 when the medium is dominated by molecular gas. We find that both the two-level system model and magnetic dipole emission by ferromagnetic particles can explain the results. These results improve our understanding of the physics of interstellar dust and lead towards a complete model of the dust spectrum of the Milky Way from far-infrared to millimetre wavelengths.