2010ApJ...719.1699H

A numerical model of a circumstellar debris disk is developed and applied to observations of the circumstellar dust orbiting β Pictoris. The model accounts for the rates at which dust is produced by collisions among unseen planetesimals, and the rate at which dust grains are destroyed due to collisions. The model also accounts for the effects of radiation pressure, which is the dominant perturbation on the disk's smaller but abundant dust grains. Solving the resulting system of rate equations then provides the dust abundances versus grain size and dust abundances over time. Those solutions also provide the dust grains' collisional lifetime versus grain size, and the debris disk's optical depth and surface brightness versus distance from the star. Comparison to observations then yields estimates of the unseen planetesimal disk's radius, and the rate at which the disk sheds mass due to planetesimal grinding. The model can also be used to measure or else constrain the dust grain's physical and optical properties, such as the dust grains' strength, their light-scattering asymmetry parameter, and the grains' efficiency of light scattering Q_s . The model is then applied to optical observations of the edge-on dust disk orbiting β Pictoris, and good agreement is achieved when the unseen planetesimal disk is broad, with 75 ≲ r ≲ 150 AU. If it is assumed that the dust grains are bright like Saturn's icy rings (Q_s= 0.7), then the cross section of dust in the disk is A_d=~ 2x10²⁰ km2 and its mass is M_d=~ 11 lunar masses. In this case, the planetesimal disk's dust-production rate is quite heavy, {dot}M_d∼9 M_⊕/Myr, implying that there is or was a substantial amount of planetesimal mass there, at least 110 Earth masses. If the dust grains are darker than assumed, then the planetesimal disk's mass-loss rate and its total mass are heavier. In fact, the apparent dearth of any major planets in this region, plus the planetesimal disk's heavy mass-loss rate, suggests that the 75 ≲ r < 150 AU zone at β Pic might be a region of planetesimal destruction, rather than a site of ongoing planet formation.