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Collisionless Dynamics V: Relaxation and Equilibrium

Collisionless Dynamics V: Relaxation and Equilibrium. Review. Tensor virial theorem relates structural properties (d 2 I ij /dt 2 ) to kinematic properties (random KE + ordered KE + potential E). Scalar virial theorem: 2K + W [+ SP] = 0 . Applications:

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Collisionless Dynamics V: Relaxation and Equilibrium

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  1. Collisionless Dynamics V:Relaxation and Equilibrium

  2. Review • Tensor virial theorem relates structural properties (d2Iij/dt2) to kinematic properties (random KE + ordered KE + potential E). • Scalar virial theorem: 2K + W [+ SP] = 0. • Applications: • Mvir from half-light radius and velocity dispersion. • M/L from S, s (assuming spherical, non-rot) • Flattening of spheroids v/s. • Jeans theorem: Can express any DF as fcn of integrals of motion (E, Lz, L, I3, …).

  3. Summary • Relaxation is driven by phase mixing and chaotic mixing, with violent relaxation being dominant in collisionless mergers. • The end state of merging appears to be not fully relaxed; the origin of NFW-like profiles still not fully understood. • Dynamical friction (braking due to wakes) can cause orbital decay in several orbital times. • Heat capacity of gravitating systems is negative, hence cuspy systems with short relaxation time undergo gravothermal collapse (e.g. globulars).

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