We study the dynamics of a vertically thin, dispersion-dominated disk of planetesimals with eccentricities "eand inclinations i (normalized in Hill units) satisfying e >> 1, << 1. This situation may be typical(even if only temporarily) for, e.g., a population of protoplanetary cores in the end of the oligarchic phase ofplanet formation. In this regime of orbital parameters, planetesimal scattering has an anisotropic character and strongly differs from scattering in thick (i~e) disks. We derive analytical expressions for the planetesimalscattering coefficients and compare them with numerical calculations. We find significant discrepancies in theinclination scattering coefficients obtained by the two approaches and ascribe this difference to the effectsnot accounted for in the analytical calculation: multiple scattering events (temporary captures, which may berelevant for the production of distant planetary satellites outside the Hill sphere) and distant interaction ofplanetesimals prior to their close encounter. Our calculations show that the inclination of a thin, dispersion-dominated planetesimal disk grows exponentially on a very short timescale implying that (1) such disksmust be very short-lived and (2) planetesimal accretion in this dynamical phase is insignificant. Our resultsare also applicable to the dynamics of shear-dominated disks switching to the dispersion-dominated regime.
展开▼
