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We model the thermal dust emission from dust grains heated by synchrotronradiation and by particle collisions, under conditions appropriate for fourdifferent shocked and unshocked gas components of the Cassiopeia A (Cas A)supernova remnant (SNR). By fitting the resulting spectral energy distributions(SEDs) to the observed SNR dust fluxes, we determine the required mass of dustin each component. We find the observed SED can be reproduced by $\sim 0.6 \,{\rm M_\odot}$ of silicate grains, the majority of which is in the unshockedejecta and heated by the synchrotron radiation field. Warmer dust, located inthe X-ray emitting reverse shock and blastwave regions, contribute to theshorter wavelength infrared emission but make only a small fraction of thetotal dust mass. Carbon grains can at most make up $\sim 25 \%$ of the totaldust mass. Combined with estimates for the gas masses, we obtain dust-to-gasmass ratios for each component, which suggest that the condensation efficiencyin the ejecta is high, and that dust in the shocked ejecta clumps is wellprotected from destruction by sputtering in the reverse shock.

The mass, location and heating of the dust in the Cassiopeia A supernova remnant