Planck intermediate results. XXIX. All-sky dust modelling with Planck,
  IRAS, and WISE observations
  We present all-sky modelling of the high resolution Planck, IRAS, and WISE
infrared (IR) observations using the physical dust model presented by Draine
and Li in 2007 (DL). We study the performance and results of this model, and
discuss implications for future dust modelling. The present work extends the DL
dust modelling carried out on nearby galaxies using Herschel and Spitzer data
to Galactic dust emission. We employ the DL dust model to generate maps of the
dust mass surface density, the optical extinction Av, and the starlight
intensity parametrized by Umin. The DL model reproduces the observed spectral
energy distribution (SED) satisfactorily over most of the sky, with small
deviations in the inner Galactic disk and in low ecliptic latitude areas. We
compare the DL optical extinction Av for the diffuse interstellar medium with
optical estimates for 2 10^5 quasi-stellar objects (QSOs) observed in the Sloan
digital sky survey. The DL Av estimates are larger than those determined
towards QSOs by a factor of about 2, which depends on Umin. The DL fitting
parameter Umin, effectively determined by the wavelength where the SED peaks,
appears to trace variations in the far-IR opacity of the dust grains per unit
Av, and not only in the starlight intensity. To circumvent the model
deficiency, we propose an empirical renormalization of the DL Av estimate,
dependent of Umin, which compensates for the systematic differences found with
QSO observations. This renormalization also brings into agreement the DL Av
estimates with those derived for molecular clouds from the near-IR colours of
stars in the 2 micron all sky survey. The DL model and the QSOs data are used
to compress the spectral information in the Planck and IRAS observations for
the diffuse ISM to a family of 20 SEDs normalized per Av, parameterized by
Umin, which may be used to test and empirically calibrate dust models.
