Resonant Relaxation in Protoplanetary Disks

Resonant relaxation is a novel form of two-body relaxation that arises innearly Keplerian disks such as protoplanetary disks. Resonant relaxation doesnot affect the semimajor axes of the particles, but enhances relaxation ofparticle eccentricities and inclinations. The equilibrium state after resonantrelaxation is a Rayleigh distribution, with the mean-square eccentricity andinclination inversely proportional to mass. The rate of resonant relaxationdepends strongly on the precession rate of the disk. If the precession due tothe disk's self-gravity is small compared to the total precession, then therelaxation is concentrated near the secular resonance between each pair ofinteracting bodies; on the other hand if the precession rate is dominated bythe disk's self-gravity then relaxation occurs through coupling to thelarge-scale low-frequency m=1 normal modes of the disk. Depending on the diskproperties, resonant relaxation may be either stronger or weaker than the usualnon-resonant relaxation.Comment: 19 pages, 1 figure, LaTeX, submitted to A