The dust content of the Crab Nebula
  We have modelled the near-infrared to radio images of the Crab Nebula with a
Bayesian SED model to simultaneously fit its synchrotron, interstellar and
supernova dust emission. We infer an interstellar dust extinction map with an
average $A_{\text{V}}$=1.08$\pm$0.38 mag, consistent with a small contribution
(<22%) to the Crab's overall infrared emission. The Crab's supernova dust mass
is estimated to be between 0.032 and 0.049 M$_{\odot}$ (for amorphous carbon
grains) with an average dust temperature $T_{\text{dust}}$=41$\pm$3K,
corresponding to a dust condensation efficiency of 8-12%. This revised dust
mass is up to an order of magnitude lower than some previous estimates, which
can be attributed to our different interstellar dust corrections, lower SPIRE
flux densities, and higher dust temperature than were used in previous studies.
The dust within the Crab is predominantly found in dense filaments south of the
pulsar, with an average V-band dust extinction of $A_{\text{V}}$=0.20-0.39 mag,
consistent with recent optical dust extinction studies. The modelled
synchrotron power-law spectrum is consistent with a radio spectral index
$\alpha_{\text{radio}}$=0.297$\pm$0.009 and an infrared spectral index
$\alpha_{\text{IR}}$=0.429$\pm$0.021. We have identified a millimetre excess
emission in the Crab's central regions, and argue that it most likely results
from two distinct populations of synchrotron emitting particles. We conclude
that the Crab's efficient dust condensation (8-12%) provides further evidence
for a scenario where supernovae can provide substantial contributions to the
interstellar dust budgets in galaxies.
