Steady state evolution of debris disks around a stars

This paper confronts a simple analytical model for the steady state evolution of debris disks due to collisions with Spitzer observations of dust around main-sequence A stars. It is assumed that every star has a planetesimal belt, the initial mass and radius of which are drawn from distributions. In the model disk mass is constant until the largest planetesimals reach collisional equilibrium, whereupon mass falls alpha t(age)(-1). We find that the detection statistics and trends seen at 24 and 70 mu m 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 (HD 3003, HD 38678, HD 115892, HD 172555); their planetesimals may have unusual properties (high strength or low eccentricity), or this dust could be transient. The overall success of our model, which assumes planetesimals in all belts have the same strength, eccentricity, and maximum size, suggests the outcome of planet formation is reasonably uniform. The distribution of planetesimal belt radii, once corrected for detection bias, follows N(r) alpha r(-0.8 +/- 0.3) for 3-120 AU. Since belt boundaries may be attributed to unseen planets, this provides a unique constraint on A star planetary systems. It is also shown that P-R drag may sculpt the inner edges of A star disks close to the Spitzer detection threshold (HD 2262, HD 19356, HD106591, HD115892). This model can be readily applied to the interpretation of future surveys, and predictions for the upcoming SCUBA-2 survey include that 17% of A star disks should be detectable at 850 mu m.