Steady State Evolution of Debris Disks around A Stars

Abstract

In this paper a simple analytical model for the steady-state evolution of debris disks due to collisions is confronted with Spitzer observations of main sequence A stars. All stars are assumed to have planetesimal belts with a distribution of initial masses and radii. In the model disk mass is constant until the largest planetesimals reach collisional equilibrium whereupon the mass falls off oc 1/t. We find that the detection statistics and trends seen at both 24 and 70um can be fitted well by the model. While there is no need to invoke stochastic evolution or delayed stirring to explain the statistics, a moderate rate of stochastic events is not ruled out. Potentially anomalous systems are identified by a high dust luminosity compared with the maximum permissible in the model (HD3003, HD38678, HD115892, HD172555). Their planetesimals may have unusual properties (high strength or low eccentricity) or this dust could be transient. While transient phenomena are also favored for a few systems in the literature, the overall success of our model, which assumes planetesimals in all belts have the same strength, eccentricity and maximum size, suggests a large degree of uniformity in the outcome of planet formation. The distribution of planetesimal belt radii, once corrected for detection bias, follows N(r) oc r^{-0.8+-0.3} for 3-120AU. Since the inner edge is often attributed to an unseen planet, this provides a unique constraint on the planetary systems of A stars. It is also shown that P-R drag may sculpt the inner edges of A star disks close to the Spitzer detection threshold (HD2262, HD19356, HD106591, HD115892). This model can be readily applied to the interpretation of future surveys, and predictions are made for the upcoming SCUBA-2 survey, including that >17% of A stars should be detectable at 850um.