Steady State Evolution of Debris Disks around A Stars

In this paper a simple analytical model for the steady-state evolution ofdebris disks due to collisions is confronted with Spitzer observations of mainsequence A stars. All stars are assumed to have planetesimal belts with adistribution of initial masses and radii. In the model disk mass is constantuntil the largest planetesimals reach collisional equilibrium whereupon themass falls off oc 1/t. We find that the detection statistics and trends seen atboth 24 and 70um can be fitted well by the model. While there is no need toinvoke stochastic evolution or delayed stirring to explain the statistics, amoderate rate of stochastic events is not ruled out. Potentially anomaloussystems are identified by a high dust luminosity compared with the maximumpermissible in the model (HD3003, HD38678, HD115892, HD172555). Theirplanetesimals may have unusual properties (high strength or low eccentricity)or this dust could be transient. While transient phenomena are also favored fora few systems in the literature, the overall success of our model, whichassumes planetesimals in all belts have the same strength, eccentricity andmaximum size, suggests a large degree of uniformity in the outcome of planetformation. The distribution of planetesimal belt radii, once corrected fordetection bias, follows N(r) oc r^{-0.8+-0.3} for 3-120AU. Since the inner edgeis often attributed to an unseen planet, this provides a unique constraint onthe planetary systems of A stars. It is also shown that P-R drag may sculpt theinner edges of A star disks close to the Spitzer detection threshold (HD2262,HD19356, HD106591, HD115892). This model can be readily applied to theinterpretation of future surveys, and predictions are made for the upcomingSCUBA-2 survey, including that >17% of A stars should be detectable at 850um.Comment: Accepted by Ap