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 ( \lesssim 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 3 K , 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 temperatures 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 .