The dust and gas content of the Crab Nebula
  We have constructed MOCASSIN photoionization plus dust radiative transfer
models for the Crab Nebula core-collapse supernova (CCSN) remnant, using either
smooth or clumped mass distributions, in order to determine the chemical
composition and masses of the nebular gas and dust. We computed models for
several different geometries suggested for the nebular matter distribution but
found that the observed gas and dust spectra are relatively insensitive to
these geometries, being determined mainly by the spectrum of the pulsar wind
nebula which ionizes and heats the nebula. Smooth distribution models are ruled
out since they require 16-49 Msun of gas to fit the integrated optical nebular
line fluxes, whereas our clumped models re quire 7.0 Msun of gas. A global
gas-phase C/O ratio of 1.65 by number is derived, along with a He/H number
ratio of 1.85, neither of which can be matched by current CCSN yield
predictions. A carbonaceous dust composition is favoured by the observed
gas-phase C/O ratio: amorphous carbon clumped model fits to the Crab's Herschel
and Spitzer infrared spectral energy distribution imply the presence of
0.18-0.27 Msun of dust, corresponding to a gas to dust mass ratio of 26-39.
Mixed dust chemistry models can also be accommodated, comprising 0.11-0.13 Msun
of amorphous carbon and 0.39-0.47 Msun of silicates. Power-law grain size
distributions with mass distributions that are weighted towards the largest
grain radii are derived, favouring their longer-term survival when they
eventually interact with the interstellar medium. The total mass of gas plus
dust in the Crab Nebula is 7.2 +/- 0.5 Msun, consistent with a progenitor star
mass of 9 Msun.
