The Importance of Physical Models for Deriving Dust Masses in Supernova Ejecta I: Radiatively Heated Dust Surrounding the Crab's Pulsar Wind Nebula

Recent far-infrared (IR) observations of supernova remnants (SNRs) have revealed significantly large amounts of newly-condensed dust in their ejecta, comparable to the total mass of available refractory elements. The dust masses derived from these observations assume that all the grains of a given species radiate at the same temperature, regardless of the dust heating mechanism or grain radius. In this paper, we derive the dust mass in the ejecta of the Crab Nebula, using a physical model for the heating and radiation from the dust. We adopt a power-law distribution of grain sizes and two different dust compositions, and calculate the heating rate of each dust grain by the radiation from the pulsar wind nebula (PWN). We find that the grains attain a continuous range of temperatures, depending on their size and composition. The best-fit model to the observed IR spectrum consist of amorphous carbon grains with a total mass of 0.027+/-0.003 Msun. We find that the power-law size distribution of dust grains is characterized by a power-law index of 3.5 and a maximum grain size larger than 0.6 microns. The grain sizes and composition are consistent with what is expected for dust grains formed in a Type IIP SN. Our derived dust mass is significantly less than the 0.11-0.24 Msun reported in previous studies of the Crab Nebula that are based on a simplified two-temperature models. These models also require a larger mass of refractory elements to be locked up in dust than was likely available in the ejecta. The results of this study shows that a physical model resulting in a realistic distribution of dust temperatures can significantly affect derived dust masses. Our study has therefore important implications for dust mass estimates in other SNRs and for the ultimate question of whether SNe are major sources of dust in the Galactic interstellar medium (ISM) an in external galaxies.