The insignificance of P-R drag in detectable extrasolar planetesimal belts

This paper considers a simple model in which dust produced in a planetesimal belt migrates in toward the star due to P-R drag suffering destructive collisions with other dust grains on the way. Assuming the dust is all of the same size, the resulting surface density distribution can be derived analytically and depends only on the parameter eta(0) = 5000 tau(eff)(r(0))root(M star/r0) over bar/beta; this parameter can be determined observationally with the hypothesis that beta = 0.5. For massive belts in which eta(0) >> 1 dust is confined to the planetesimal belt, while the surface density of more tenuous belts, in which eta(0) << 1, is constant with distance from the star. The emission spectrum of dust from planetesimal belts at different distances from different mass stars shows that the dust belts which have been detected to date should have eta(0) >> 1; dust belts with eta(0) << 1 are hard to detect as they are much fainter than the stellar photosphere. This is confirmed for a sample of 37 debris disk candidates for which eta(0) was determined to be > 10. This means that these disks are so massive that mutual collisions prevent dust from reaching the inner regions of these systems and P-R drag can be ignored when studying their dynamics. Models for the formation of structure in debris disks by the trapping of particles into planetary resonances by P-R drag should be reconsidered. However, since collisions do not halt 100% of the dust, this means that in the absence of planetary companions debris disk systems should be populated by small quantities of hot dust which may be detectable in the mid-IR. Even in disks with eta(0) << 1 the temperature of dust emission is shown to be a reliable tracer of the planetesimal distribution meaning that inner holes in the dust distribution imply a lack of colliding planetesimals in the inner regions.