Planetesimal Initial Mass Functions and Creation Rates Under Turbulent Concentration Using Scale-Dependent Cascades

The initial accretion of primitive bodies from freely-floating nebula particles remains problematic. Traditional growth-by-sticking models in turbulent nebulae encounter a "meter-size barrier" due to both drift and destruction, or even a millimeter-to-centimeter-size "bouncing" barrier. Recent suggestions have been made that some "lucky" particles might be able to outgrow the collision and/or drift barriers, and lead to so-called "streaming instabilities" or SI. However, new full models of growth by sticking in the presence of radial drift show that lucky particles (the largest particles, at the tail of the size distribution, that grow beyond the nominal fragmentation and drift barriers) are far too rare to lead to any collective effects such as streaming or gravitational instabilities. Thus we need to focus on typical radii gamma(sub M) which contain most of the mass. Our models of disks with weak-to-moderate turbulence, which include all the most recent experimental constraints on collisional growth, erosion, bouncing, and fragmentation, as well as radial drift, find that growth stalls quite generally at sizes gamma(sub M) which are too small to settle into layers which are dense enough for any collective effects (streaming or gravitational instabilities) to arise. Even if growth by sticking could somehow breach the nominal barriers (perhaps if the actual sticking or strength is larger than current estimates for pure ice or pure silicate, with specific grain sizes), turbulent nebulae present subsequent formidable obstacles to incremental growth through the 1-10km size range. On the other hand, non-turbulent nebulae alpha is less than 10(Sup -4).