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Dust masses and grain size distributions of a sample of Galactic pulsar wind nebulae

We calculate dust spectral energy distributions (SEDs) for a range of grain sizes and compositions, using physical properties appropriate for five pulsar wind nebulae (PWNe) from which dust emission associated with the ejecta has been detected. By fitting the observed dust SED with our models, with the number of grains of different sizes as the free parameters, we are able to determine the grain size distribution and total dust mass in each PWN. We find that all five PWNe require large ($\ge 0.1 \, {\rm μm}$) grains to make up the majority of the dust mass, with strong evidence for the presence of micron-sized or larger grains. Only two PWNe contain non-negligible quantities of small ($<0.01 \, {\rm μm}$) grains. The size distributions are generally well-represented by broken power laws, although our uncertainties are too large to rule out alternative shapes. We find a total dust mass of $0.02-0.28 \, {\rm M}_\odot$ for the Crab Nebula, depending on the composition and distance from the synchrotron source, in agreement with recent estimates. For three objects in our sample, the PWN synchrotron luminosity is insufficient to power the observed dust emission, and additional collisional heating is required, either from warm, dense gas as found in the Crab Nebula, or higher temperature shocked material. For G$54.1$+$0.3$, the dust is heated by nearby OB stars rather than the PWN. Inferred dust masses vary significantly depending on the details of the assumed heating mechanism, but in all cases large mass fractions of micron-sized grains are required.