The Kuiper Belt in our own Solar System and the dust disks around Vega-like stars are both thought to be of similar origin. The dust in these systems is continuously produced by destruction of long-lived large bodies, probably in collisions. Replenishing the dust is necessary since the lifetime of dust particles in orbits around these stars is at most a few million years, and much shorter in systems with a lot of dust , For an overview of the properties of Vega-like dust disks, see contributions of Backman and Krivova in this volume.
Recent observations with the Infrared Space Observatory (ISO) [2,3] combined with new age determinations of nearby main sequence stars  have revealed that most stars arrive on the main sequence with a strong infrared excess attributed to debris dust. The amount of dust is measured by the ratio of the infrared to the bolometric luminosity, tjr. Typical values for tir are around 10-4. The main result of the ISO study was that most stars younger that 400 Myrs have a detectable dust disk. After 400 Myrs, most stars do not show a measurable IR excess which means that tir has dropped below 10~5. This indicates that the cloud of comets responsible for the dust replenishment has a life time of about 400 Myrs. On the other hand, a few stars in the sample studied are several billion years old and still show a strong infrared excess. It has been suggested that these stars started out with a much more massive cometary disk so that they can still produce dust today. In this contribution we explore a simple model for the collisional evolution of the cometary cloud in order to discuss possible causes for the observed 400 Myr timescale.
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