SELF-CONSISTENT SIZE AND VELOCITY DISTRIBUTIONS OF COLLISIONAL CASCADES
- Department of Astronomy, University of California, Berkeley, CA 94720 (United States)
The standard theoretical treatment of collisional cascades derives a steady-state size distribution assuming a single constant velocity dispersion for all bodies regardless of size. Here we relax this assumption and solve self-consistently for the bodies' steady-state size and size-dependent velocity distributions. Specifically, we account for viscous stirring, dynamical friction, and collisional damping of the bodies' random velocities in addition to the mass conservation requirement typically applied to find the size distribution in a steady-state cascade. The resulting size distributions are significantly steeper than those derived without velocity evolution. For example, accounting self-consistently for the velocities can change the standard q = 3.5 power-law index of the Dohnanyi differential size spectrum to an index as large as q = 4. Similarly, for bodies held together by their own gravity, the corresponding power-law index range 2.88 < q < 3.14 of Pan and Sari can steepen to values as large as q = 3.26. Our velocity results allow quantitative predictions of the bodies' scale heights as a function of size. Together with our predictions, observations of the scale heights for different-sized bodies for the Kuiper belt, the asteroid belt, and extrasolar debris disks may constrain the mass and number of large bodies stirring the cascade as well as the colliding bodies' internal strengths.
- OSTI ID:
- 22016225
- Journal Information:
- Astrophysical Journal, Vol. 747, Issue 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
Similar Records
THE IRREGULAR SATELLITES: THE MOST COLLISIONALLY EVOLVED POPULATIONS IN THE SOLAR SYSTEM
After runaway: The trans-Hill stage of planetesimal growth