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Dynamical Models for LISA and SKA – Multiple Black Holes in Galactic Nuclei

Dynamical Models for LISA and SKA – Multiple Black Holes in Galactic Nuclei. Rainer Spurzem, Astronomisches Rechen-Institut Zentrum für Astronomie Univ.Heidelberg, Germany. spurzem@ari.uni-heidelberg.de http://www.ari.uni-heidelberg.de/mitarbeiter/spurzem/. (ARI). Talk Summary:

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Dynamical Models for LISA and SKA – Multiple Black Holes in Galactic Nuclei

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  1. Dynamical Models for LISA and SKA – Multiple Black Holes in Galactic Nuclei Rainer Spurzem, Astronomisches Rechen-Institut Zentrum für Astronomie Univ.Heidelberg, Germany spurzem@ari.uni-heidelberg.de http://www.ari.uni-heidelberg.de/mitarbeiter/spurzem/

  2. (ARI) Talk Summary: • Multiple Black Holes in Galactic Nuclei • Gravitational Waves • Software/Hardware Stellar Dynamics Group @ ARI: Christoph Eichhorn, Peter Berczik, Gabor Kupi, … in VESF/LSC collaboration: on gravitational wave modelling from dense star clusters: G. Schäfer, A. Gopakumar (Univ. Jena, D) M. Benacquista (MSU Billing, USA) Pau Amaro-Seoane (AEI, Potsdam, D) Further collaborations: Sverre Aarseth (IoA Cambridge UK) David Merritt (RIT, USA) Birmingham 06

  3. Galactic Nuclei, Black Holes • Galaxien-Crash (Antennen-Galaxien) Birmingham 06

  4. Galactic Nuclei, Black Holes Semi-Analytical Study: Volonteri, Haardt, Madau 2003 Number of Mergers of large galaxies: ~10 What happens to Black Holes? Birmingham 06

  5. Galactic Nuclei, Black Holes Sesana et al. 2004 Extending study of Volonteri et al. 03: Rate of expected Black Hole Mergers in Galaxies Birmingham 06

  6. Galactic Nuclei, Black Holes Komossa et al. 2002: NGC6240: merger in progress Je ein AGN in beiden Kernen (Sep. ca. 1kpc) (Chandra X-Ray) Birmingham 06

  7. Galactic Nuclei, Black Holes (Viewgraph by D.Merritt) Birmingham 06

  8. Galactic Nuclei, Black Holes Cosmological Galaxy Formation → Mergers with Black Holes Begelman, Blandford & Rees 1980 Superelastic Scattering? Third Process: Superelastic Scattering → Binary Hardening Birmingham 06

  9. Galactic Nuclei, Black Holes • Superelastic Scattering: Resonant 3-body Encounters Starlab Simulation S.L.W. McMillan http://www.physics.drexel.edu/~steve/ -> Three-Body-Problem Birmingham 06

  10. Galactic Nuclei, Black Holes Some previous work: • Milosavljevic M. & Merritt D., 2001, ApJ, 563, 34 • Hemsendorf M., Sigurdsson S. & Spurzem R., 2002, ApJ, 581, 1256 • Chatterjee P., Hernquist L. & Loeb A., 2003, ApJ, 592, 32 • Makino J. & Funato Y., 2004, ApJ, 602, 93 • Laun F. & Merritt D., 2004, [astro-ph/0408029] • Berczik P., Merritt D., Spurzem R., 2005, ApJ, 633, 680 • Berczik P., Merritt D., Spurzem R., Bischof, H.P. 2006, ApJL in press. Birmingham 06

  11. ARI 32 node GRACE cluster The GRACE Project – Supercomputers – Black Holes State of Baden-Württemberg Univ. of Heidelberg, Germany 3.2 Tflops sustained for NBODY; of 4.0 Tflops peak Birmingham 06

  12. Galactic Nuclei, Black Holes Results – I (Plummer): low ecc. Berczik, Merritt & Spurzem (2005) Birmingham 06

  13. Galactic Nuclei, Black Holes Standard Case: here non-rotating King model W0=6 (25000 particles) (Berczik, Merritt & Spurzem in prep.) – e remains small. Birmingham 06

  14. Galactic Nuclei, Black Holes Christoph Eichhorn (Diploma Thesis Univ. Heidelberg), Eichhorn & Spurzem 2005 (in prep) Birmingham 06

  15. Galactic Nuclei, Black Holes Christoph Eichhorn (Diploma Thesis Univ. Heidelberg), Eichhorn & Spurzem 2005 (in prep) Birmingham 06

  16. Galactic Nuclei, Black Holes Christoph Eichhorn (Diploma Thesis Univ. Heidelberg), Eichhorn & Spurzem 2005 (in prep) Birmingham 06

  17. Galactic Nuclei, Black Holes • Hemsendorf, Sigurdsson, Spurzem, 2002 , Astroph. Jl. • Cf. also Aarseth & Mikkola (2003), Funato & Makino (2005), Makino et al. 1993 But: other authors (Milosavljevic & Merritt 2001, Berczik, Merritt & Spurzem 2005) find: eccentricity remains small if N is large enough! Birmingham 06

  18. Eichhorn & Spurzem 2005 (in prep), cf. also Hemsendorf, Sigurdsson & Spurzem 2002 Birmingham 06

  19. Galactic Nuclei, Black Holes Birmingham 06

  20. Galactic Nuclei, Black Holes Results – II (King): rotating -> high ecc.! up to 1 mill. part.! Berczik, Merritt, Spurzem, & Bischof, Apj 2006 in press. Birmingham 06

  21. Galactic Nuclei, Black Holes Non-Standard Case: here rotating King model W0=6 w0=1.8 (25k up to 1M particles) (Berczik, Merritt & Spurzem, Bischof, 2006, ApJ in press) Birmingham 06

  22. Galactic Nuclei, Black Holes • Movie to show the evolution prepared with Spiegel Software of Hans-Peter Bischoff http://www.cs.rit.edu/~grapecluster/ • cf. also xnbody – a visualization toolkit for NBODY6++ and others, maintained and provided by ZAM Jülich http://www.fz-juelich.de/zam/xnbody/ http://documentation.wikicities.com/wiki/Xnbody Birmingham 06

  23. Gravity Waves • Two of the strongest potential sources in the • low-frequency (LISA) regime are: • Coalescence of binary supermassive black holes • Extreme-mass-ratio inspiral into supermassive black holes Birmingham 06

  24. Gravity Waves ??? BH mergers – conservative view:? d ~10*R_BH If we scaled up our numerical results, for the typical galaxy bulge (~10^9 Mo & ~3 kpc: 10 Gyr = 130) we see that the BH’s separation never come closer ~1 – 0.1 pc… For the typical BH’s mass (10^6 Mo) the “gravitational merging” regime start with ~10^-6 pc!!! Birmingham 06

  25. Peters & Mathews 1963: Distribution of Power in Harmonics for Eccentric Orbits Birmingham 06

  26. Gmax : Power radiated in maximum harmonic relative to circular orbit (2nd harmonic) Nmax: Number of maximum power harmonic (Piero et al. 2001) Birmingham 06

  27. Gravity Waves Peters, P.C., Phys. Rev. 1964, 136, 1224 Peters, P.C., Mathews, J., 1963, Phys. Rev. 131, 435 Birmingham 06

  28. Gravity Waves What happens? Use Post-Newtonian approximation... + c-5 H2.5 + c-7 H3.5 • Non-Dissipative Terms, so-called PN 1,2,3.... (Perihel Shifts) • Dissipative Terms PN 2.5, 3.5 (Emission of Energy in gravitational waves, emission of linear momentum!) • Spin-Spin, Spin-Orbit-Couplings PN 3.5! • Schäfer, Gauge Theor. Grav. 36, 2223 (2004) • Memmesheimer, Gopakumar, Schäfer, Phys. Rev.D 70, 104011 (2004) Birmingham 06

  29. Gravity Waves What happens afterwards? Post-Newton Order „2.5“... Kupi & Spurzem 2004 Final Ring-Down and Merger  grav. wave signal! tGW = 1.1  106 a M8-5/3 (P/a) 8/3 (1+q)²/q (Jaffe & Backer 2003) Birmingham 06

  30. Gravity Waves Kupi & Amaro-Seoane & Spurzem 2005, in prep. Cluster of 1000 very massive black Holes. Gravitational Radiation Emission at high eccentricities! Birmingham 06

  31. Gravity Waves Sesana et al. 2004 Birmingham 06

  32. Galactic Nuclei, Black Holes Volonteri et al. 2003 Assumptions: Every Galaxy has a Black Hole... Simple Ideas for dynamical Friction and Merger timescales Of Binary Black Holes... ... There are Triple-Black Holes! Birmingham 06

  33. Motion of three black holes in star cluster of 64000 stars Galactic Nuclei, Black Holes C. Eichhorn Diploma Thesis Univ. of Heidelberg 2004 Extremely high e = 0.999… sometimes… (Kozai cycles, Makino & Funato 2005) Birmingham 06

  34. Galactic Nuclei, Black Holes Benacquista, Lommen, Makino, Spurzem, Eichhorn, in prep. detectable time residual in T Example now: Period: 240 yrs, d=130ns T=3.3yrs rmax = 6 Mpc e=0.9 Period: 24000 yrs rmax = 58 Mpc e=0.99 Example SKA: Period: 240 yrs,d=30ns T=4.0 yrs rmax = 27 Mpc e=0.9 Period: 24000 yrs rmax = 250 Mpc e=0.99 T=8.0 yrs rmax = 10 Gpc future? All such objects in the universe may be detectable! Birmingham 06

  35. Conclusions: • First large direct up to N ~1M parallel GRAPE6a cluster simulations on titan GRACE cluster… • The initial rotation of the host galaxy is very important for the BBH orbital evolution. For larger rotation we see bar formation, radial orbit instability… • Some of the highly rotating models or triple BHs can produce a BBH with a very high eccentricity e~1. Much higher detection possibility with pulsar timing or other low frequency GW instruments (LISA)… • Modelling presently still not complete – need (gas) physics and even more computer time for better parameter studies! Birmingham 06

  36. T. Prince (Caltech), Project Scientist, LISA: Two of the outstanding theoretical issues to be addressed if LISA is to succeed are: • “Formation and evolution of nuclear star clusters around supermassive black holes” • “Understanding the fate of supermassive black holes in galaxy mergers” The GRACE cluster will be a premier computational instrument in the world for answering these questions. Birmingham 06

  37. The GRACE Project – Supercomputers – Black Holes GRACE Project = GRAPE + MPRACE Astrophysical Computer Simulations using Programmable Hardware R. Spurzem, R. Männer, A. Burkert with G. Lienhart, M. Wetzstein (with P. Berczik, G. Kupi, A. Ernst, …) • Hardware • Software, Algorithms • Binary Black Holes in Galactic Nuclei • Gravity Waves Interdisciplinary: Computer Science and Astrophysics Univ. Heidelberg (ARI-ZAH), Munich (USM) Univ. Mannheim (Techn. Informatik) Project Key Data: 3 Years (2005-2007) Total 800 kEUR 3 Postdocs (HD, MA, M each one) 380 kEUR hardware Birmingham 06

  38. (Funded by: VW-Stiftung, Land BW, part for SFB439) Collaboration with VESF and SFB-TR7 G. Achamveedu, G. Schäfer Further International Collaboration: Sverre Aarseth (IoA Cambridge UK) David Merritt (RIT, USA) Naohito Nakasato Tsuyoshi Hamada (RIKEN Institute Tokyo Japan) D. Sugimoto, J. Makino, T. Fukushige, ... Birmingham 06

  39. RIT & ARI 32 node GRAPE6a clusters • 32 dual-Xeon 3.0 GHz nodes • 32 GRAPE6a • 14 TB RAID • Infiniband link (10 Gb/s) • Speed: ~4 Tflops • N up to 4M • Cost: ~500K USD • Funding: NSF/NASA/RIT • 32 dual-Xeon 3.2 GHz nodes • 32 GRAPE6a • 32 FPGA • 7 TB RAID • Dual port Infiniband link (20 Gb/s) • Speed: ~4 Tflops • N up to 4M • Cost: ~380K EUR • Funding: Volkswagen/Baden-Württemberg Infiniband Dual 20Gb/s Birmingham 06

  40. GRAPE Hardware New Jersey, Indiana, Heidelberg Birmingham 06

  41. GRAPE Hardware GRAPE6a PCI board GRAPE6a - PCI Board for PC-Clusters, recent development of the University of Tokyo ~128 Gflops for a price ~5K USD Memory for N, up to 128K particles Birmingham 06

  42. GRACE • GRACE Complexity (simple algorithm NBODY4) T = α N + β N2 ...put 2nd part on special accelerator board.... ...fine for N-body, but many astrophysical complications... Better Algorithms (NBODY6) T = α N + β N2 / γ + δ N Nn ...put 3rd part on reconfigurable logics board... ...fine in particular for coupling with gas dynamics using particles (SPH method) Birmingham 06

  43. GRACE • G.Lienhart • Kugel • R. Männer • Univ. Mannheim • coop. With • ARI/MPIA and • U Tokyo Acceleration of SPH simulation with ReconfIgurable Computing for AStroPHysics Birmingham 06

  44. GRACE MPRACE Board GRAPE • GRAPE moves the bottleneck to neighbour calculation • Use FPGA-platform for accelerating neighbour algorithm • (SPH, NBODY6++) Birmingham 06

  45. Smoothed Particle Hydrodynamics (SPH) GRACE Hydrodynamic equation of motion, gravity for neighbour forces in NBODY6++ SPH formulation Birmingham 06

  46. Birmingham 06

  47. Birmingham 06

  48. Birmingham 06

  49. www.riken.jp The Institute of Physical and Chemical Research PGR and demonstration software by: Tsuyoshi Hamada and Naohito Nakasato in Computational Astrophysics Lab., RIKEN. Hardware: "Bioler-3" jointly developed by RIKEN and Chiba University. "PROGRAPE-3 System" Bioler-3 Birmingham 06

  50. GRACE • FPGA designs for SPH have been completed • FPGA designs for gravitational force interface completed • Measured performance 4.7 GFlops on mpRACE • Funding by Birmingham 06

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