Monday, January 14, 2013

Jerusalem WS lecture notes: 12. Galactic dynamics II

By R. Sari, slides of both talks here.
  • stability: dispersion relation
  • spiral density waves: leading and trailing, pattern speed
  • resonances: co-rotation, Lindblad resonances: drift through arms: epicyclic motion of particles in the disk. Pressure: away from CR, gravity: towards the center. Each epicyclic period a particle drifts one potential peak
  • migration: dynamical friction, one-sided torques from the outer disk and the inner disks: push from inner side stronger than pull from the outer (? shouldn't it be the inverse?)
  • marginally stable galaxies
  • centrifugal barrier: disk stability
  • 18 \pi^2: overdensity
    • final semi-major axis of the overdense region:
    • Keplerian elliptical orbit: t_{vir} = 2\pi/(sqrt(GM/a^3))
    • density ratio: \rho_0(r_0/a)^3/\rho_0*(t_{vir}/t0) = r_0^3/a^3 \cdot 4\pi^2/GMt^2_0 = 9/4 \cdot v_0^2 \cdot 4 \pi^2/1/2 v_0^2 = 18 \pi^2
  • virial theorem:
    • relaxation: two-body, resonant (in almost Keplerian systems), violent. two-body relaxation time t_{rd} = R/V\cdot N/lnN
    • tidal breakup: binaries (interaction with BH), stars, extended objects: 'black hole worshipping' - BH destroys objects, relaxation brings them back
    • binaries destruction: r_{tidal}: when the rotation period of the binary is equal to rotation around the BH (forces are equal)
    • differential force for the binary system: r_{tidal} = a(M_{BH}/m)^{1/3}
    • density: spread out the masses
    • largest orbital velocity for a binary member: v_{esc}, few hundred km/s for MS stars. BHs enhance the velocity by orders of magnitude -> hypervelocity stars
  • loss cone
  • filling rates

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