1. Galactic Super Massive Binary Black Hole Mergers Galactic Super Massive Binary Black Hole Mergers Dr. Peter Berczik Astronomisches Rechen-Institut (ARI), Zentrum für Astronomie Univ. Heidelberg, Germany Dr. Peter Berczik Astronomisches Rechen-Institut (ARI), Zentrum für Astronomie Univ. Heidelberg, Germany berczik@ari.uni-heidelberg.de Second RSDN meeting, 25-27 Nov. 2005, Hoher List, Germany Second RSDN meeting, 25-27 Nov. 2005, Hoher List, Germany

2. Collaborators: David Merritt, David Merritt, Rochester Institute of Technology, NY, USA Rainer Spurzem, ARI, Zentrum für Astronomie Univ. Heidelberg Rainer Spurzem, ARI, Zentrum für Astronomie Univ. Heidelberg Gabor Kupi, ARI, Zentrum für Astronomie Univ. Heidelberg Gabor Kupi, ARI, Zentrum für Astronomie Univ. Heidelberg Stefan Harfst, Stefan Harfst, Rochester Institute of Technology, NY, USA David Merritt, David Merritt, Rochester Institute of Technology, NY, USA Rainer Spurzem, ARI, Zentrum für Astronomie Univ. Heidelberg Rainer Spurzem, ARI, Zentrum für Astronomie Univ. Heidelberg Gabor Kupi, ARI, Zentrum für Astronomie Univ. Heidelberg Gabor Kupi, ARI, Zentrum für Astronomie Univ. Heidelberg Stefan Harfst, Stefan Harfst, Rochester Institute of Technology, NY, USA Grants: AST-0206031, AST-0420920 & AST-0437519 from the NSF AST-0206031, AST-0420920 & AST-0437519 from the NSF NNG04GJ48G from NASA NNG04GJ48G from NASA HST-AR-09519.01-A from STScI HST-AR-09519.01-A from STScI SFB-439 from the Deutsche Forschungsgemeinschaft SFB-439 from the Deutsche Forschungsgemeinschaft AST-0206031, AST-0420920 & AST-0437519 from the NSF AST-0206031, AST-0420920 & AST-0437519 from the NSF NNG04GJ48G from NASA NNG04GJ48G from NASA HST-AR-09519.01-A from STScI HST-AR-09519.01-A from STScI SFB-439 from the Deutsche Forschungsgemeinschaft SFB-439 from the Deutsche Forschungsgemeinschaft Publications: Berczik, Merritt & Spurzem, 2005, ApJ, 633, 680, [astro-ph/0507260] Berczik, Merritt & Spurzem, in prep… Berczik, Merritt & Spurzem, 2005, ApJ, 633, 680, [astro-ph/0507260] Berczik, Merritt & Spurzem, in prep…

3. Galaxy Collisions:

4. BH’s in galaxies (MW - Sgr A*):

5. Galaxy Collisions ≈ BH’s collisions: Multiple Massive Black Holes NGC6240 strong ongoing merger… Multiple Massive Black Holes NGC6240 strong ongoing merger…

6. Future Observations: Gravitational Wave Detection - LISA 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

7. Milosavljevich 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] Szell A., Merritt D. & Seppo M., 2005, [astro-ph/0502198] Some of the previous works: Dynamical Modeling Methods: Direct N-body method: - As much as possible accurate… - Symmetry of the problem is irrelevant… - (-) Very compute intensive!!!

8. Basic idea of the N-body code:

9. Hierarchical Block Time Steps Our own GRAPE+N-body1 parallel code: 4th order Hermite scheme

10. ~N ~N^2 GRAPE = GRAvity PipE

11. GRAPE = GRAvity PipE – more detail…

12. 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 ~128 Gflops for a price ~5K USD Memory for N, up to 128K particles GRAPE6a PCI board

13. 32 dual-Xeon 3.0 GHz nodes 32 GRAPE6a 14 TB RAID Infiniband switch (10 Gb/s) Speed: ~4 Tflops N up to 4M Cost: ~500K USD Funding: NSF/NASA/RIT RIT & ARI 32 node GRAPE6a clusters 32 dual-Xeon 3.2 GHz nodes 32 GRAPE6a 32 FPGA 7 TB RAID Dual port Infiniband switch (20 Gb/s) Speed: ~4 Tflops N up to 4M Cost: ~350K EUR Funding: Vwagen/BW/ARI

14. RIT & ARI 32 node GRAPE6a clusters

15. Parallel PP on GRAPE6a cluster N N N/N p N act

16. Parallel PP on GRAPE6a cluster

20. X Y Z Two equal-mass black holes near center of Plummer-model galaxy Initial Conditions - I:

21. Some Theory: Example: loss-cone around a binary black hole. Stars scattered into the binary are ejected via the gravitational slingshot. The binary responds by shrinking. In a real galaxy, the shrinking rate (d/dt)(1/a) would be limited by the rate of diffusion of stars into the loss cone. binary black hole θ star N-body Integration of Binary Black Hole Dynamical Evolution Full loss-coneDiffuse regime

22. Results – I (Plummer):

24. X Y Z Two equal-mass black holes near center of King-model (W0=6) galaxy Initial Conditions - II:

25. Results – II (King):

26. Results – I (Plummer) + II (King):

27. Double check of the Results:

29. BH collisions? 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!!! d ~10*R_BH ???

30. Initial data… Initial data… No equilibrium… No equilibrium… Higher initial eccentricity… Higher initial eccentricity… New code: ε=0 New code: ε=0 regularization (CHAIN - ?, KS - ?)… regularization (CHAIN - ?, KS - ?)… Larger direct N simulations: Larger direct N simulations: AC neighbor scheme… AC neighbor scheme… N-body + GAS (SPH) N-body + GAS (SPH) Hardware solution for SPH calculations (FPGA) Hardware solution for SPH calculations (FPGA) Initial data… Initial data… No equilibrium… No equilibrium… Higher initial eccentricity… Higher initial eccentricity… New code: ε=0 New code: ε=0 regularization (CHAIN - ?, KS - ?)… regularization (CHAIN - ?, KS - ?)… Larger direct N simulations: Larger direct N simulations: AC neighbor scheme… AC neighbor scheme… N-body + GAS (SPH) N-body + GAS (SPH) Hardware solution for SPH calculations (FPGA) Hardware solution for SPH calculations (FPGA) Possible way of “solution”:

31. First large direct N ~1M parallel GRAPE6a cluster simulations… First large direct N ~1M parallel GRAPE6a cluster simulations… The BBH decay rate is N dependent! ~400K – 1M particle is already enough to have a near “diffuse” regime… The BBH decay rate is N dependent! ~400K – 1M particle is already enough to have a near “diffuse” regime… The initial rotation of the host galaxy is very important for the BBH orbital evolution. For larger rotation we see the clear “fixation” of decay rate… The initial rotation of the host galaxy is very important for the BBH orbital evolution. For larger rotation we see the clear “fixation” of decay rate… Some of the highly rotating models can produce the BBH with a very high eccentricity e~1. Possible source of the low frequency GW (LISA)… Some of the highly rotating models can produce the BBH with a very high eccentricity e~1. Possible source of the low frequency GW (LISA)… First large direct N ~1M parallel GRAPE6a cluster simulations… First large direct N ~1M parallel GRAPE6a cluster simulations… The BBH decay rate is N dependent! ~400K – 1M particle is already enough to have a near “diffuse” regime… The BBH decay rate is N dependent! ~400K – 1M particle is already enough to have a near “diffuse” regime… The initial rotation of the host galaxy is very important for the BBH orbital evolution. For larger rotation we see the clear “fixation” of decay rate… The initial rotation of the host galaxy is very important for the BBH orbital evolution. For larger rotation we see the clear “fixation” of decay rate… Some of the highly rotating models can produce the BBH with a very high eccentricity e~1. Possible source of the low frequency GW (LISA)… Some of the highly rotating models can produce the BBH with a very high eccentricity e~1. Possible source of the low frequency GW (LISA)… Conclusions: Thank you for attention... Thank you for attention...