tokens: is in good agreement with the correlation coefficient measured from the 545 and 857GHz dust maps in the Planck Sky Model (dashed lines). Dust is more than 99percent correlated between these frequencies. In the Planck 2013 analysis of cosmological parameters, the following simple parameteric model for the dust power spectrum was adopted: The parameters , c and are fixed by matching to the mask-differenced dust power spectra. Given the universality of the dust power spectrum, neither the choice of frequency nor mask sizes are critical in fixing these parameters. Using the 857GHz mask 40mask 25 spectrum, we find 0.387, c 162.9 and 0.168, so that asymptotically . This dependence at high multipoles is compatible with previous high-resolution measurements of the dust power spectrum in high Galactic latitude cirrus clouds, C 2.7 0.1 (Miville-Deschnes, Lagache Puget 2002 ; Miville-Deschnes etal. 2010 ), although our mask-differenced results consistently give slopes at the shallower end of this range. For a given mask, the dust power in the spectrum is specified by the parameter . For the values of , c and given above, is the dust power at multipole 10. The solid black lines in Fig. 4 show the model of equation ( 4 ) compared to the mask 40mask 25 and mask 50mask 25 spectra for the 353, 545 and 857GHz spectra. The model provides a reasonably good fit but one can see evidence for an excess at 500. We have therefore fit the dust spectra to a slightly more complicated fitting function: where B , 2 , 2 , c 2 , 2 and are parameters that we fit to the 857857 mask 50mask 25 spectrum. The best-fitting parameters are B 0.74, 2 0.19, 0.58, c 2 543.1, 2 11.6 and 0.07. We normalize the template at 10, so that the dust amplitudes derived using the templates of equations ( 5 ) and ( 4 ) can be compared directly. The best-fitting template of equation( 5 ) is shown by the red lines in Fig. 4 . Equation ( 5 ) provides a better fit to both the mask 40mask 25 and mask 50mask 25 spectra than equation ( 4 ), capturing the small excess at 500. Unless otherwise stated, we use the template shape of equation ( 5 ) in our baseline analysis. In summary, using mask-differenced spectra to isolate the contribution from Galactic dust, we find that the dust power spectrum has a nearly universal shape independent of frequency and sky fraction up to mask 60. For larger sky fractions, we see relatively small departures from universality that depends on the point source mask and are most likely associated with the anisotropy of the point source masks at low Galactic latitudes. The shape of the dust power spectrum is modelled accurately by the fitting function of equation( 5 ), which provides a template shape used in our likelihood analysis. We have verified that the dust power spectra are almost perfectly correlated over the frequency range 353857GHz. We therefore solve for three dust amplitudes, , and in our likelihood analysis assuming that the dust power spectrum is completely
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