Supermassive Black Hole Growth and Merger Rates From Cosmological N-Body Simulations

1. Supermassive Black Hole Growth and Merger Rates From Cosmological N-Body Simulations Miroslav Micic, Steinn Sigurdsson, Tom Abel, Kelly Holley-Bockelmann Abel et al. 2002 Chandra Chandra Pop III stars, z>12, 100Mסּ<m<1000Mסּ HST Starburst M82, MBH~1000Mסּ Spiral M74, 100Mסּ<MBH<10000Mסּ • - N-body simulations • - DMH at high redshifts • MBH at the centers of DMH • MBH kicks from grav. recoil • - Merger tree for DMH and MBH • - Buildup of IMBH and SMBH • - IMBH merger rates • - Grav. waves from IMBH mergers Globular Cluster G1, MBH~18000Mסּ Chandra 1 Sagittarius A*, M~3x106Mסּ

2. Simulation Setup • SIM1; SIM2a; SIM2b • - Assume single epoch of IMBH formation at z=8.16 • Identify IMBHs in DMH ; • NIMBH = 2869 • Assign IMBHs at z=8.16 with Gaussian velocity distribution • 0 km/s ≤ Vkick ≤ 150 km/s ; Vkick_mean = 75 km/s • 125 km/s ≤ Vkick ≤ 275 km/s ; • Vkick_mean = 200 km/s • - Track IMBHs trajectories 1 ≤ z ≤ 8.16 ΛCDM, ΩM=0.3, ΩΛ=0.7, h=0.7, 1 ≤ z ≤ 40 2 Mpc 4.9x106 high-res. particles; Mhr=8.85x105Mסּ 2.0x106 low-res. particles; Mlr=5.66x107Mסּ - Kick ranges suggested by Favata et al. 2004, but we do know now the “real kicks” from the recent works in numerical relativity 10 Mpc Micic et al. 2006, MNRAS, 372, 1540 2

3. black – escape velocity for the DMH centers • red and blue – kicks assigned to the BH • If kicks > escape velocity – BH ejected • If kicks < escape velocity – BH sinks back z=8.16 Micic et al. 2006, MNRAS, 372, 1540 3

4. z = 8.16 → NIMBH = 2869 z=1: SIM1 → N = 1958 inside primary halo ~ ¾ NIMBH SIM2a → N = 1944, 1851 of them are SIM1 IMBHs SIM2b → N = 1795, 1630 of them are SIM1 IMBHs 4 Micic et al. 2006, MNRAS, 372, 1540

5. Largest DMH Micic et al. 2006, MNRAS, 372, 1540 • - max. escape velocity is a measure of strength of DMH’ gravitational potential • - Largest DMH in the simulation governs the dynamics (primary halo) • - V esc, max = 700 km/s at z=1 for largest DMH • Even when ejected with substantial kicks, BH sink back due to rapid increase in • DMH gravitational potential 5

6. Post – merger evolution Primary halo at redshift z=1 M = 8x1012Mסּ Rvir = 370 kpc σ = 157 km/s ln Λ ~ 10 tfric = 1.17 r2σ / GMsubhaloln Λ SIM1: Rsink = Rvir / 30 → 83 IMBH, ~ 4 % RLISA ~ 100 year -1 MSMBH = 7x107 Mסּ SIM2a: Rsink = Rvir / 100 → 4 - 5 IMBH, ~ ¼ % RLISA ~ 5 year -1 SIM2b: only one IMBH originating from the ancestor of primary halo at z=8.16 is inside Rvir / 100 BH distributions inside primary kick I no kick kick II BH distributions relative to “no kick” case Micic et al. 2006, MNRAS, 372, 1540 6

7. Dark Matter Halos’ Merger Tree - all previous works on BH merger rates are approximate - t dynamical friction = 0 Numerical simulations vs Press-Schechter theory structure evolution probability evolution M1 + M2≠ M M1 + M2= M Nagashima et al. 2005 Volonteri et al. 2002 minimum halo mass M = 3x109 Mסּ M = 1011Mסּ resolved with 10 particles! no substructures? FOF algorithm - we improve these approximate models: - minimum 32 particles per halo. - minimum halo mass M = 2.8x107 Mסּ - FOF + SUBFIND algorithm + 200 x ρaverage + Mvir>108Mסּ[(1+z)/10] -1.5 - seeding redshift: 12 < z < 20 (Wise & Abel 2005); Mseed=200Mסּ - Salpeter gas accretion: BH doubles its mass 40Myrs after galaxies merge - Proper treatment of the problem would be to form, identify, seed and merge DMH and BH while simulating. 7

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13. Milky Way ! Sd galaxies ? G1 ? NGC 4395 ? M33 ? - galaxies with no or small bulge might not have SMBH at their centers - Some globular clusters do have IMBH 13

14. M31 SMBH - If merging DMH with mass ratios 4:1 and smaller are allowed to have gas accreting SMBH, it is easy to grow Sagittarius A* size black hole. Sagittarius A* - If mass ratio is 10:1, M31 SMBH can form. 4:1 mergers would give the same result if allowed larger simulation box - DMH gain mass through cycle of steady accretion and rapid mergers (z=11, 6, 3) 14

15. - When compared to the M-σ relation from Merritt & Ferrarese 2001, SMBH of ~ 3x107 Mסּ has velocity dispersion of σ=120km/s at z=0 which matches the SMBH mass in 10:1 growth scenario. 15

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17. 10 : 1 growth scenario 17

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19. SUMMARY - We used a high-resolution cosmological N-body simulation to study the formation and growth of seed black holes into SMBHs and derived black hole merger rates. We used physically-motivated formalisms for seeding DMH with black holes. - Our improved, but still approximate, model gives us Rmax ~ 55 year -1 at z=11 or Rtotal ~ 1000 per year per galaxy per Hubble time due to t dynamical friction = 0 - IMBH mergers combined with IMBH gas accretion can explain growth of SMBH in our Galaxy as well as in Andromeda galaxy. - We showed that z=6 may be a critical redshift for the transition from the AGN duty cycle dominated by high mass ratio DMH mergers to a starburst galaxy phase where low mass ratio DMH mergers supply a galaxy with a population of ULXs which is constant up to z=2. - This model also shows that Sd galaxies form without SMBH as the result of isolation from DMH mergers. 19

20. FUTURE - We will study whether LISA observations will be able to distinguish between different assembly scenarios. • We will calculate LISA detectability of IMBH mergers for different mass ranges 102 Mסּ <mBH < 108 Mסּ and binary mass ratios 1<m1/m2 < 106. At this point, rough estimates can be made from Figure 4, considering the known ranges for LISA sensitivity. In case of dry growth (Fig 4g), a black hole binary with mass 105 Mסּ<mBH < 106 Mסּ is in the LISA range with very high merger rate R~15 yr −1. Interestingly, just as SMBHs dim electromagnetically at z=6, they turn on in the gravitational wavebands. - There are a number of processes that might suppress massive black hole merger rates. We assumed that every first star will produce black hole as opposed to neutron star or pair detonation with no remnant. We also assume that black holes merge efficiently and that recoil ejection which is a function of spin, orientation, eccentricity, and mass ratio of merging black holes is negligible. All of these processes will be addressed in the follow up paper. - We would like to thank NASA’s Columbia High End Computing program for a generous time allocation, and the Center for Gravitational Wave Physics at Pennsylvania State University for sponsoring this research. 20