Abstract
Abstract The longest dust trail among those so detected at optical wavelengths was found along the orbit of 4P/Faye in the 2006 return. It extended as long as 10° in the backward direction. The surface brightness increases monotonically with the distance from the nucleus between $0\rlap{.}^\circ5$ and 3°, but decreases slowly beyond 4°. The observed brightnesses of the dust trail and the tail are reasonably explained by our dust ejection model. The model shows that the dust trail is composed of cm-sized particles ejected during previous returns, and the derived power indices of the size distribution function of dust particles ejected from the nucleus ($-$3.5) and those remaining in the trail ($-$1.9) have a big difference for each other. The averaged mass-loss rate (20 kg s$^{-1}$) derived from the model is comparable to those of known IRAS dust trail comets.
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