There is currently debate over whether the dust content of planetary systems is stochastically regenerated or originates in planetesimal belts evolving in quasi-steady state .
In this paper a simple model for the steady state evolution of debris disks due to collisions is developed and confronted with the properties of the emerging population of 7 sun-like stars that have hot dust at < 10 AU .
The model shows that there is a maximum possible disk mass at a given age , since more massive primordial disks process their mass faster .
The corresponding maximum dust luminosity is f _ { max } = 0.16 \times 10 ^ { -3 } r ^ { 7 / 3 } t _ { age } ^ { -1 } , where r is disk radius in AU and t _ { age } is system age in Myr .
The majority ( 4/7 ) of the hot disks exceed this limit by a factor \gg 1000 and so can not be the products of massive asteroid belts , rather the following systems must be undergoing transient events characterized by an unusually high dust content near the star : \eta Corvi , HD69830 , HD72905 and BD+20307 .
It is also shown that the hot dust can not originate in a recent collision in an asteroid belt , since there is also a maximum rate at which collisions of sufficient magnitude to reproduce a given dust luminosity can occur in a disk of a given age .
For the 4 transient disks , there is at best a 1 : 10 ^ { 5 } chance of witnessing such an event compared with 2 % of stars showing this phenomenon .
Further it is shown that the planetesimal belt feeding the dust in these systems must be located further from the star than the dust , typically at \gg 2 AU .
Other notable properties of the 4 hot dust systems are : two also have a planetesimal belt at > 10 AU ( \eta Corvi and HD72905 ) ; one has 3 Neptune mass planets at < 1 AU ( HD69830 ) ; all exhibit strong silicate features in the mid-IR .
We consider the most likely origin for the dust in these systems to be a dynamical instability which scattered planetesimals inwards from a more distant planetesimal belt in an event akin to the Late Heavy Bombardment in our own system , the dust being released from such planetesimals in collisions and possibly also sublimation .
Further detailed study of the planet , planetesimal and dust populations in these rare objects has the potential to uncover the chaotic evolutionary history of these systems and to shed light on the history of the solar system .