Vega, Fomalhaut, and Beta Pictoris are the most prominent examples of
main-sequence stars surrounded by orbiting particulate matter which em
its strongly at far-infrared wavelengths. We interpret JCMT maps of th
e 800 mum emission from these three stars to indicate that they are no
t ringed by large reservoirs of distant orbiting dust particles that a
re too cold to have been detected by IRAS. We also searched for 800 mu
m emission from stars in the Pleiades aid Ursa Majoris open clusters.
In comparison with the mass of dust particles near T Tauri and Herbig
Ae stars, the JCMT data indicate a decline in dust mass during the ini
tial 3 x 10(8) yr that a star spends on the main sequence that is at l
east as rapid as (time)-2. Others have suggested that the particles th
at are observed to orbit Vega-like stars are not simply the decaying r
emnants of ''primordial'' disks that formed at the same time as the st
ars but, rather, the particulate matter is being replenished continual
ly, most probably from objects such as comets and/or asteroids. We pre
sent arguments in support of this model. By interpreting the dusty reg
ions as extrasolar analogs of the Kuiper comet belt region that has be
en proposed to lie between 20 and 50 AU from the Sun, we estimate that
in the Kuiper belt the ratio of total mass carried by small particles
to that carried by comets is orders of magnitude smaller than this ra
tio is 1 AU from the Sun. If recent 800 mum opacities calculated by Po
llack et al. (1993) are correct, then the particles with radii less th
an 100 mum that dominate the far-IR fluxes measured by IRAS cannot ent
irely account for the measured 800 mum fluxes at Vega, beta Pic, and F
omalhaut; larger particles must be present also.