Collisionless Dynamics II: Orbits Collisionless Dynamics II: Orbits.

Collisionless Collisionless Dynamics II:Dynamics II:

OrbitsOrbits

ReviewReview Self-consistency problem:Self-consistency problem: Find DF evolution Find DF evolution

(i.e. orbits) that yield consistent density-(i.e. orbits) that yield consistent density-potential pairs.potential pairs.

Timescales: Timescales: ttdyndyn < t < tHH < t < trelaxrelax.. Power-law and double power-law spherical Power-law and double power-law spherical

density profiles: density profiles: vvcc22 r r2-a2-a, M(<r) , M(<r) r r3-a3-a..

For deviations from spherical, use expansion For deviations from spherical, use expansion in in LegendreLegendre polynomials. polynomials.

Disk potentials written in terms of Disk potentials written in terms of Bessel Bessel fcnsfcns..

f = -Lx=dqi/dt

Orbit families in merger Orbit families in merger remnantremnant

(from Josh Barnes)(from Josh Barnes) BoxBox

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