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Continuum Models of Globular Cluster Dynamics

Continuum Models of Globular Cluster Dynamics. Rainer Spurzem, Astronomisches Rechen-Institut Heidelberg, Germany. spurzem@ari.uni-heidelberg.de http://www.ari.uni-heidelberg.de/mitarbeiter/spurzem/. Continuum models. Main Collaborators:

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Continuum Models of Globular Cluster Dynamics

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  1. Continuum Models of Globular Cluster Dynamics Rainer Spurzem, Astronomisches Rechen-Institut Heidelberg, Germany spurzem@ari.uni-heidelberg.de http://www.ari.uni-heidelberg.de/mitarbeiter/spurzem/

  2. Continuum models.... Main Collaborators: M. Giersz (CAMK Warsaw, Poland) E. Kim, H.M. Lee (Seoul Nat. Univ., Korea) S. Aarseth (Inst. Of Astron. Cambridge UK)... ...and students...: P. Amaro-Seoane, S. Deiters, J. Fiestas, E. Khalisi... • Introduction • Rotation • Binaries • Black Holes, Grav. Rad. HYDRA CGWP Workshop

  3. (ARI) Foundation Document of ARI May 10, 1700 Calendar Patent of Duke of Brandenburg ARI Fieldsof Work today: • Astrometry • (Hipparcos, GAIA) • Stellar Dynamics • (Galaxies, Star Clusters) • Calendar Data • Bibliography • (Astronomy and Astroph. • Abstracts, ceased 2001) CGWP Workshop

  4. Introduction: History S.v. Hoerner, Z.f.Astroph. 1960, 63 Siemens 2002 N=4,8,12,16 (4 Trx) N=16,25 (40 Trx) see also v. Hoerner 2001, in star2000-Proceedings... CGWP Workshop

  5. Introduction: Star Clusters • Dynamical Time Scale • Relaxation Time Scale • Age of Universe Laboratories for gravothermal N-Body Systems! Note: Cosmological and Galactic N-Body Simulations need few crossing times, and less than a relaxation time, while gravothermal systems need multiples of N crossing times, several relaxation times! Complexity goes as N3 ! 106 yrs 108 yrs 1010 yrs ← Virial Equilibrium → CGWP Workshop

  6. Introduction: Star Clusters • Stellar Evolution Time • Stellar CollisionTime • Readjustment of Collision Products • Star Formation Time • Binary Evolution Laboratories for dissipative or chemodynamical N-Body Systems! 105-10yrs 104-6yrs 103 yrs 106 yrs 104-10 yrs CGWP Workshop

  7. Continuum models.... • S.J.Aarseth, S. Mikkola (ca. 20.000 lines): • Hierarchical Block Time Steps • Ahmad-Cohen Neighbour Scheme • Kustaanheimo-Stiefel and Chain-Regular. • for bound subsystems of N<6 • 4th order Hermite scheme (pred/corr) • Bulirsch-Stoer (for KS) CGWP Workshop

  8. Continuum models.... Some methods for studying the evolution of globular clusters (by D.C.Heggie) Hybrid (Giersz & Spurzem 2000) Monte Carlo (Giersz 1998) CGWP Workshop

  9. Continuum models.... Where it does work.... (Spurzem & Aarseth 1996) (Giersz & Spurzem 1994) N-Body / N-Body N-Body / Fokker-Planck In spherical symmetry ...but... CGWP Workshop

  10. N-body .vs. Continuum model w. rotation Kim, Lee, Spurzem, 2003 (in prep.) Decay of rotational energy by relaxation and tidal field CGWP Workshop

  11. Physical and Numerical Methods: Modelling the Dynamics Full Fokker-Planck Equation, use Liouville‘s Theorem and Rosenbluth Potentials (local equation): CGWP Workshop

  12. Physical and Numerical Methods: Modelling the Dynamics Rosenbluth Potentials (Rosenbluth, McDonald & Judd 1956) Diffusion Coefficients (Local) Gas Models: up to l=2 for background f (in principle higher possible) CGWP Workshop

  13. Physical and Numerical Methods: Modelling the Dynamics Orbit averaged Fokker-Planck Equation (here in the 2D form for axisymm. systems, Einsel & Spurzem 1999) CGWP Workshop

  14. Physical and Numerical Methods: Modelling the Dynamics Flux Conserving Form of Fokker-Planck Equation (Einsel & Spurzem 1999), Chang-Cooper Scheme (1970) CGWP Workshop

  15. Rotation - Initial models • Rotating King model * two parameter family * W0 = 3,6 & ω0 = 0.0 ... 2.4 • Mass function * single mass system * two-component model * continuous mass spectrum (10 comp), • Boundary condition * tidally limited/isolated system CGWP Workshop

  16. Rotation – single mass Rotation accelerates core collapse significantly and takes away flattening (Einsel & Spurzem 1999) (Kim, Einsel, Lee, Spurzem & Lee 2002) CGWP Workshop

  17. Rotation - Effect of mass function Kim, Lee, Spurzem, 2003 (in prep.) CGWP Workshop

  18. & Kim, Lee, Spurzem, 2003 (in prep.) CGWP Workshop

  19. Gas Monte Carlo Hybrid Model and Binaries Ns =300.000, N b=30.000 Giersz & Spurzem (2000, 2003) Fully self-consistent evolution of cluster and Binaries...3b and 4b integration of encounters using Regularisation techniques. No assumptions about any cross sections, but still point mass ...remain challenges for theory AND modelling... CGWP Workshop

  20. Gas Model and relativistic binaries? CGWP Workshop

  21. Gas Model and Black Hole • Loss Cone Theory standard diffusive picture - fast out – slow in, Liouville Theorem ok, orbit averaged Fokker-Planck equation • Non-standard cases (re Milosavljevic, Phd thesis 2002) • Ejection (binary black hole) instead of tidal disruption θlc large! • Binary black hole gets kicks • External perturbations (fueling, bars, mergers) • Orbit „diffusion“ in non-spherical potentials can be fast(Malkov, Vilkoviski, Nuzhnova, Spurzem, 1993, in Russian) • Stars return in case of ejection tout=n tcross ; n > 1 • → time-dep. loss-cone required! CGWP Workshop

  22. Gas Model and Black Hole Milosavljevic 2002 CGWP Workshop

  23. Gas Model and Black Hole • Time-Dep. Loss-Cone Diffusion (Milos. & Merritt, 2003) in orbit averaged Fokker-Planck model • Anisotropic gaseous model (Louis & Spurzem 1991, Spurzem 1994) plus local simplified diffusion equation (Amaro-Seoane, Freitag, Spurzem, in prep.) • Using gaseous model: http://www.gaseous.model.de (S. Deiters) CGWP Workshop

  24. Gas Model - Example of Black Hole Growth Amaro-Seoane, Spurzem, 2001 Amaro-Seoane, Spurzem, 2003, in prep. Black Hole Growth Self-Regulation Gas Model single mass CGWP Workshop

  25. Gas Model – Multi-Mass with Black Hole Amaro-Seoane, Freitag, Spurzem, 2003, in prep. Black Hole Growth Self-Regulation Gas Model multi-mass CGWP Workshop

  26. Gas Model and Star-Gas Drag Exotic Processes... Star-Gas Interactions Just (2003) CGWP Workshop

  27. Gas Model and Radiative Transfer • Ongoing Project: High-Resolution 1D Chemo+Stellar Dynamics • Stellar Dynamical Equations • Gas Dynamics, 1D Radiative Transfer (Yorke, 1980) • Stellar Collisions, Star-Gas Interaction CGWP Workshop

  28. Status of Continuum Models ☼yellow sun: accomplished green key: in progress or straightforward ☼ CGWP Workshop

  29. Status of Continuum Models ☼yellow sun: accomplished green key: in progress or straightforward CGWP Workshop

  30. Future Modelling Required for Galactic Nuclei Credit: R. Blandford, in Active Galactic Nuclei 1991, Saas Fee Lecture 20 CGWP Workshop

  31. Spin-Orbit Couplings Black Holes / Stellar Orbits? Can we detect them? Yu & Lu 2001 CGWP Workshop

  32. Conclusion • Continuum Models still very fast even in times of GRAPE-6,8,...,NBODY6++,... • Continuum Models help understanding physics • Continuum Models are far from being exploited to their limits – much to do still! • Comparisons with NBODY and Monte-Carlo should be continued (KyotoII) CGWP Workshop

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