  This paper presents an all-sky model of dust emission from the Planck 857,
545 and 353 GHz, and IRAS 100 micron data. Using a modified black-body fit to
the data we present all-sky maps of the dust optical depth, temperature, and
spectral index over the 353-3000 GHz range. This model is a tight
representation of the data at 5 arc min. It shows variations of the order of 30
% compared with the widely-used model of Finkbeiner, Davis, and Schlegel. The
Planck data allow us to estimate the dust temperature uniformly over the whole
sky, providing an improved estimate of the dust optical depth compared to
previous all-sky dust model, especially in high-contrast molecular regions. An
increase of the dust opacity at 353 GHz, tau_353/N_H, from the diffuse to the
denser interstellar medium (ISM) is reported. It is associated with a decrease
in the observed dust temperature, T_obs, that could be due at least in part to
the increased dust opacity. We also report an excess of dust emission at HI
column densities lower than 10^20 cm^-2 that could be the signature of dust in
the warm ionized medium. In the diffuse ISM at high Galactic latitude, we
report an anti-correlation between tau_353/N_H and T_obs while the dust
specific luminosity, i.e., the total dust emission integrated over frequency
(the radiance) per hydrogen atom, stays about constant. The implication is that
in the diffuse high-latitude ISM tau_353 is not as reliable a tracer of dust
column density as we conclude it is in molecular clouds where the correlation
of tau_353 with dust extinction estimated using colour excess measurements on
stars is strong. To estimate Galactic E(B-V) in extragalactic fields at high
latitude we develop a new method based on the thermal dust radiance, instead of
the dust optical depth, calibrated to E(B-V) using reddening measurements of
quasars deduced from Sloan Digital Sky Survey data.
