The formation of the first supermassive black holes

Transcription

1 The formation of the first supermassive black holes Zoltán Haiman Columbia University Collaborators: Eli Visbal (Columbia) Kohei Inayoshi (Columbia) Taka Tanaka (Stony Brook/NYU) Jemma Wolcott-Green (Columbia) Greg Bryan (Columbia) ICTP Colloquium Sao Paulo, Brazil 12 August 2015

2 Outline High-redshift quasars observations [3] The first stars and their BH remnants theory [6] Using stellar-mass seed BHs to build SMBHs [6] Rapid direct collapse in more massive halos [12] [ Probing SMBH assembly with future observations... 4 ]

3 Bright Quasars at z>6 Rare ( 5σ ) objects: 10 found in SDSS at z>6 20 in CFHQS + few others Record: z = 7.08 (t=0.77 Gyr, UKIDDS) Mortlock et al Tip of the iceberg (?): Space density ~1 Gpc -3 Mass estimates Willott et al M bh = L obs /L Edd M (Eddington luminosity) M halo M (match space density)

4 Maximum SMBH Masses e-folding (Edd) time: M/(dM/dt) = 4 (ε/0.1) 10 7 yr Age of universe (z=6-7) (0.8 1) x 10 9 yr Must start early! Accretion rate must keep up w/ Eddington most of the time Obvious alternatives: (1) merge many BHs (2) grow faster Masses estimated from: Fan+ (2006); Willott+ (2010); Mortlock+ (2011); Wu+ (2015)

5 Can we be fooled? Short answer: NO. Several 10 9 M masses are here to stay. Gravitational lensing? No. (Keeton, Kuhlen & Haiman 2004) Strong beaming? No. (Haiman & Cen 2002; Willott et al. 2003) Empirical measurement of L/L edd from CIV and MgII line widths, calibrated by reverberation mapping (Vestergaard 2004; Kurk et al Jiang et al. 2009)

6 Outline High-redshift quasars observations The first stars and their BH remnants theory Using stellar-mass seed BHs to build SMBHs Rapid direct collapse in more massive halos Probing z>6 SMBH assembly with future observations

7 Stellar seed vs direct collapse STELLAR SEEDS uninterrupted near-eddington accretion onto ~ M seeds - continuous gas supply - avoid radiative feedback depressing accretion rate - must avoid ejection from halos and loosing BHs - avoid overproducing total ρ BH (in ~10 6 M holes) DIRECT COLLAPSE (A.K.A. HEAVY SEEDS ) rapid formation of M black holes at z>10 by direct collapse of gas or via intermediary (supermassive star, quasi-star, or ultra-dense star cluster) - gas must be driven in rapidly (deep potential) - transfer angular momentum outward - must avoid fragmentation - avoid cooling via H 2 to T ~ few 100 K and fragmenting

8 Seed Fluctuations on Small Scales extrapolation by a factor of about 100 in linear scale CMB LSS Dark Age Wayne Hu www mass function of DM halos directly tested in simulations at z=30; M=10 6 M e.g. Lukic et al. (2007) Reed et al. (2007) No SMBHs in m x <kev WDM (Barkana, ZH, Ostriker 2001)

9 3D Simulation of a Primordial Gas Cloud Greif et al. (2012) Abel et al. (2002), Bromm et al. (2002), Yoshida, Omukai & Hernquist (2008), Cosmological mini-halo: M halo M z coll 20 Protostar(s) in core: T few 100 K n cm -3 M * M

10 Upper limit on stellar mass Gas infall at sound speed: c s 1-2 km/s dictated by H 2 Mass accretion rate: M acc c 3 s /G = few 10-3 M yr -1 Star s mass: M M acc t KH M acc 10 5 yr = few 10 2 M Result: massive stars and stellar-mass BH remnants Final stellar masses can be reduced by: - fragmentation (Greif et al. 2013) - radiation of protostar (43 M - Hosokawa et al. 2012)

11 Final Masses Reduced? FRAGMENTATION Using sink particles to follow post-1 st -clump evolution ~10 fragments with heaviest mass reduced to M=??? Driven by turbulence and disk self-gravity Greif et al. (2013); Prieto et al. (2011), Clark et al. (2010); Stacy et al. (2010) RADIATIVE SELF-REGULATION Analytic models for protostellar evolution with H 2 -photodissociation, Lyα radiation pressure, HII region: M=140 M McKee & Tan (2008) Hydro simulations: M=43 M Hosokawa et al. (2012)

12 Remnants of Massive Stars Heger et al (for single, non-rotating stars) Z=Z metalicity Z=0 10M 25M 40M 140M 260M

13 Outline High-redshift quasars observations The first stars and their BH remnants theory Using stellar-mass seed BHs to build SMBHs Rapid direct collapse in more massive halos Probing z>6 SMBH assembly with future observations

14 Growing SMBHs by Accretion + Mergers z~6 M bh = few 10 9 M M halo = several M CDM merger tree z~30 M halo ~10 5 M v esc ~ few km/s Merger trees : Haiman & Loeb (2001); Haiman (2004); Yoo & Miralda-Escude (2004); Sesana et al. (2004); Bromley et al. (2004); Volonteri & Rees (2006), Shapiro (2005); Tanaka & Haiman (2009), Volonteri & Natarajan (2010), Hydro simulations: Li et al. (2007); Pelupessy et al. (2007); Sijacki et al. (2009) Bellovary et al. (2011), di Matteo et al. (2012),

15 Growing SMBHs by Accretion + Mergers Tanaka, Perna & Haiman (2012) Construct Monte-Carlo DM halo merger trees from z=6 to z> M M halo M (M res = M ; N~10 5 trees; V eff ~5 Gpc 3 ) Q1: Fraction of minihalos forming stellar BH seeds? - f seed depends on IMF (M * = M M seed =2-125 M ) - f seed ~ 1 (requires only one star with M * >20 M - most can be low-mass ) Q2: Time-averaged mass accretion rate? - duty cycle f duty for Eddington-lim accretion with ε=0.07 (0.5 f duty 1.0) - impose additional Bondi ( ρm BH 2 /c s 3 ) upper limit - density profile either ρ r -2.2 (cool gas) or flat core (dep. on T IGM ) (Ricotti 2009) Q3: What happens to the BHs when halos merge? - gas drag leads to coalescence of BHs - gravitational recoil: v kick - spins aligned, random mag (Lousto et al. 2010) - follow kicked BH trajectory - damped oscillation (gas drag)

16 Making the ~10 9 M SMBHs Tanaka, Perna & Haiman (2012) redshift M BH [M ] ρ BH [M Mpc -3 ] age of universe (Gyr) 10 9 M BHs from unusually massive (10 2 M ) runaway early seeds (z>20) that avoided ejection at merger: asymmetric mass ratio q<0.01

17 Making the ~10 9 M SMBHs Tanaka, Perna & Haiman (2012) redshift M BH [M ] ρ BH [M Mpc -3 ] age of universe (Gyr) Local SMBH Mass density: ρ tot M Mpc M BHs from unusually massive (10 2 M ) runaway early seeds (z>20) that avoided ejection at merger: asymmetric mass ratio q<0.01

18 Eliminating unwanted ~10 6 M BHs (without suppressing most massive ones) Internal feedback: (e.g. Volonteri & Natarajan 2010) - M BH limited in each halo by M BH σ relation No BH seeds after PopIII PopII? - Requires sharp cut at z~25 and low f seed ~ 10-3 (mutually exclusive ) External radiation backgrounds: (Tanaka & Haiman 2009) (Tanaka et al. 2012) - stars and their BH remnants build early IR/UV/X-ray - affect H 2 chemistry, heat IGM these backgrounds regulate early star formation history

19 X-rays from Mini-Quasars Multi-color disk + corona Emission peaks at 1-5 kev No significant IR or UV X-rays heat IGM (by fast photo electrons): 1. increase Jeans mass in IGM 2. decrease central density in halos Ricotti & Ostriker (2004) Madau et al. (2004)

20 Self-regulation by X-ray Global Warming Tanaka, Perna & Haiman (2012) redshift M BH [M ] ρ BH [M Mpc -3 ] age of universe (Gyr) Local SMBH Mass density: ρ tot M Mpc -3 Total BH mass density remains below 10% of its present-day value NB: recent low Planck τ is ndependent evidence for suppression (Visbal, Haiman & Bryan 2015 arxiv: )

21 Self-regulation by X-ray Global Warming Tanaka, Perna & Haiman (2012) redshift M BH [M ] ρ BH [M Mpc -3 ] age of universe (Gyr) Local SMBH Mass density: ρ tot M Mpc -3 Total BH mass density remains below 10% of its present-day value NB: recent low Planck τ is ndependent evidence for suppression (Visbal, Haiman & Bryan 2015 arxiv: )

22 Outline High-redshift quasars observations The first stars and their BH remnants theory Using stellar-mass seed BHs to build SMBHs Rapid direct collapse in more massive halos Probing z>6 SMBH assembly with future observations

23 Alternative: Direct Gas Collapse RAPID GAS INFALL - must exceed Eddington rate 10-2 (ε/0.1) -1 (M BH / M ) M yr -1 - but need ~1M yr -1 to accrete ~10 5 M in KH time of 10 5 yr ANGULAR MOMENTUM - large viscosity (global dynamical instabilities) - use low-j tail (either rare halos or fraction of gas in given halo) AVOIDING FRAGMENTATION - must avoid cooling to T 10 4 K - avoid H 2 formation (otherwise: popiii stars as in mini-halos) LAST TWO CRITERIA ARE RELATED - BH fueling problem for quasars (Schlosman & Begelman 1989; Goodman 2003) - key: stable locally (gravity vs pressure/turbulence) unstable globally (rotational vs potential energy) - sims to ~0.1pc (Mayer et al. 2009, Levine et al. 2008; Hopkins & Quataert 2010)

24 A promising site: T vir >10 4 K halos? Super-Eddington growth if gas remains T=10 4 K (due to lack of H 2 ) and cools via atomic H: M acc c s 3 1 M yr -1 Jeans mass M J T 3/2 /ρ 1/ M Mo-Mao-White disk with isothermal gas at T=10 4 K ~ T vir is thick and Toomre-stable, gas could avoid local fragmentation (Oh & Haiman 2002) No fragmentation seen in simulations (Bromm & Loeb 2003; Wise & Abel 2007; Regan & Haehnelt 2009; Regan et al. 2015) Gas can collapse rapidly onto a seed BH (Volonteri & Rees 2005) or collapse directly into a ~10 5 M SMS by global instability (Koushiappas et al. 2004; Begelman et al 2006; Spaans & Silk 2006; Lodato & Natarajan 2006; Wise & Abel 2007; Regan & Haehnelt 2008) or fragment into ultra-dense M star cluster via metals/dust IMBH (Omukai, Schneider & ZH 2008; Devecchi & Volonteri 2009; Alexander & Natarajan 2014)

25 3D proto-galaxy simulation with J UV =10 3 Enzo - atomic cooling halos with M halo 10 8 M z coll 14 Fernandez, Bryan, Haiman & Li (2013) Gas stays near 10 4 K never forms enough H 2 to cool further density Temperature Δ-.v Mach number

26 Mass of Central Object t acc (yr) M gas /M

27 Mass of Central Object t acc (yr) Kelvin-Helmoltz time M Pop III star M gas /M 10 5 M supermassive star/bh Abel et al.; Bromm et al.; Yoshida et al. (M acc ~ 1 M yr -1 )

28 SMBH by direct collapse: summary In-fall proceeds at sound speed c s 10 km/s Mass accretion rate M acc c s 3 ~ 1 M yr -1 Fragmentation is not seen in simulations Central object has mass M 10 5 M (cf. M 10 2 M with H 2, when c s 1-2 km/s) - BUT Worry 1: is such large UV flux possible? Worry 2: fragments ultimately? Worry 3: metals present and cool the gas?

29 Synchronized pairs of atomic cooling halos Visbal, Haiman & Bryan (2014) - dynamical time in core of atomic cooling halo t dyn ~ 10 Myr - require that halo is illuminated by J>J crit during this time - flux can be provided by neighboring halo at a distance d=0.5kpc with f * ~ 1-20% if stars are 20-5 M - same neighbor would photoevaporate the target halo s progenitor in ~20 Myr two halos must be synchronized to Δt sync ~ 10 Myr - orbital separation r>0.2 kpc to avoid ram pressure stripping

30 (Sub)halo pairs N-body simulations - Five Gadget-2 runs (768 3 particles, L=15 cmpc) - Halos and subhalos are identified with ROCKSTAR Behroozi et al. (2013) 2 suitable pairs found forming within 10 Myr < Δt form < 20 Myr staying within 0.2 kpc < Δr < 0.5 (for +10 Myr )

31 Synchronized pairs to z=6 quasar BHs Visbal, Haiman & Bryan (2014) - Abundance of z>6 SMBHs with M bh ~10 9 M is n ~ 1 cgpc -3 - Need only ~1 candidate per 60 N-body boxes M z=10 seed can grow to 10 9 M at Eddington by z~6 - Extrapolate w/analytic model: enough pairs with much tighter synchronization (Δt sync ~0.2 Myr) - This can help to avoid external metal pollution: DCBH seed forms (or gets past point of no return) before stars in neighbor produce SNe and metals reach DCBH host

32 OUCH! Fragmentation?

33 Fragmentation? Regan et al. (2014) Rf 0.1pc nf >10 8 cm -3 Mclump > 20Msun

34 Toy model for fragmenting disk Inayoshi & Haiman (2014) Analytic toy model of a compact, metal-free, marginally unstable (Q T =1), nuclear protogalactic accretion disk Steady state, constant dm/dt = 0.1 M yr 1 viscous heating balanced by cooling (via free-bound H - ) Yields unique viscosity (α) and surface density (Σ) Assume viscosity from self-gravity, fragments if α α f =1 Examine properties and fate of clumps formed in the disc

35 Fragmentation scale Interior to a characteristic radius R f = few 10 2 pc, the disk fragments into O(10-100) clumps with M c 30 M agrees well with Regan et al. 2014; lower accretion rate version of model with dm/dt = 10-3 M yr 1 agrees well with surface density, disk size, number and mass of clumps in Greif central star clump ionized wind accretion disk

36 Fragmentation? Inayoshi & Haiman (2014) Compact central disk in atomic cooling halo may fragment (or may not? Van Borm et al. 2014) However, toy model suggest even if disk fragments, this is not an obstacle to direct formation of heavy SMBH: - most fragments sink to center before they evolve into stars (migration faster than Kelvin Helmholtz time) - a few of the fragments could evolve into massive stars, but are unable to suppress global accretion rate More simulations needed to track fate of unstable disks

37 Outline High-redshift quasars observations BH remnants of the first stars theory Using stellar-mass seed BHs to build SMBHs Rapid direct collapse in more massive halos Probing z>6 SMBH assembly with future observations

38 Future Observational Probes 1. SMBHs with <10 6 M should be directly detectable at z~10 (i) optical/ir with JWST (~10 njy at few μm) (ii) radio with EVLA, SKA (~1-10μJy at 1-10 GHz) (iii) X-rays: CXO deep fields correspond to ~ M (IXO 2021) 2. Accreting BHs can cause pre-ionizaton at z>10 topology: swiss-cheese vs. nearly uniform due to X-rays. power spectrum (21cm, ksz) depressed on scales < m.f.p. 3. elisa event rates (z>6): 0 to ~30 event/yr/dz mass ratio is a diagnostic, Einstein Telescope to stellar mass BHs 4. Fossil evidence in z=0 dwarf galaxies: BH occupation fraction Menou et al. (2001); Van Wassenhove et al. (2010)

39 Reionization by Stars vs BHs note: photon mean free path ~ Gpc (E/1 kev) 3 [(1+z)/10] -3 f HI -1 Stars only: Photon m.f.p. << source sep. swiss cheese Stars + BH mix: Photon m.f.p. ~< source sep. Blurred swiss cheese Accreting BHs dominate: Photon m.f.p. >~ source sep. Nearly uniform ionization

40 elisa/ngo sensitivity Amaro-Seoane et al. (2012)

41 Fossil Evidence in z=0 dwarfs Menou et al. (2001); Van Wassenhove et al. (2010) Occupation fraction M bh -σ relation

42 Conclusions 1. Growing z>6 SMBHs with ~10 9 M requires extreme assumptions: (i) stellar seeds grow at Eddington rate without interruption, or (ii) rapid direct collapse in rare special environments with no metals 2. Extra challenge (i): not to overproduce number of ~ M SMBHs. seed formation AND growth are suppressed by X-ray global warming 3. Extra challenge (ii): not to cool by H 2 and fragment. requires large Lyman-Werner flux (J 21 ~ 10 3 ), achieved in close halo pairs 4. Future Observations: faint-end quasar LF (optical/radio/x-ray) to ~ M (e.g. JWST) GWs from elisa up to ~100 merger events/yr smooth reionization topology (e.g. 21cm, ksz) to diagnose X-rays fossil BHs in local Milky Way dwarfs

43 Le Fin

44 Can we be fooled? Short answer: NO. Several 10 9 M masses are here to stay. Gravitational lensing? No. (Keeton, Kuhlen & Haiman 2004) Strong beaming? No. (Haiman & Cen 2002; Willott et al. 2003) Empirical measurement of L/L edd from CIV and MgII line widths, calibrated by reverberation mapping (Vestergaard 2004; Kurk et al Jiang et al. 2009) and if L>>L edd then dm/dt = L/εc 2 is large BH anyway accretes 4 x 10 9 M in << 4 x (ε/0.1) yr

45 Global Radiative Feedback Wolcott-Green & Haiman (2012) Dominant process to manufacture molecular H 2 at z~20: H + e - H - +γ H + H - H 2 + e - Early radiation backgrounds build up at frequencies at which the IGM is optically thin: (1) E~12 ev Lyman Werner: H 2 + γ H (*) 2 H+H+γ (2) E~1 kev soft X-rays: H + γ H - + e - [ heating ] (3) E~1 ev infrared: H - +γ H + e - These backgrounds self-regulate early star-formation history Which is most important? Depends on masses of first stars - M * = 100 M (BHs, X-ray binaries): #2 X-rays - M * = 10 M (no BH remnants): #1 Lyman-Werner - M * = 1 M (no UV): #3 infrared

46 N-body simulations Visbal, Haiman & Bryan (2014) look for (sub) halo pairs forming within 10 Myr < Δt form <20 Myr of one another staying within 0.2 kpc < Δr < 0.5, 0.75, 1kpc (for +10 Myr ) - Five independent Gadget-2 runs particles, L=15 cmpc 100 particles per atomic halo (can be identified and tracked as subhalos of larger systems) - z in = 200, 20 outputs between 10 < z < 12 (every 3 Myr) - Halos and subhalos are identified with ROCKSTAR Behroozi et al. (2013)

47 N-body simulations: Results 2, 5, 17 suitable pairs forming within 10 Myr < Δt form < 20 Myr staying within 0.2 kpc < Δr < 0.5, 0.75, 1kpc (for +10 Myr )

48 3D proto-galaxy simulation with J 21 =10 3 Fernandez, Bryan, Haiman & Li (2013) Temperature number density

49 Avoiding cooling/fragmentation with UV [ H 2 -formation rate ρ 2 ] = [ photo-dissoc. rate Jρ ] Critical flux: J ρ J 21,crit low ~ in low-mass mini-halos (n ~ cm -3 ) Compare to J ~ 1 (at z~3) or J~ 10 (at reionization) In more massive (atomic cooling) halos: avoid H 2 -cooling up to critical density of H 2 : n ~ 10 4 cm -3 J 21,crit increased to ~10 3 (Wolcott-Green, ZH Bryan 2011) (Sugimura et al. 2015) Omukai, Schneider & Haiman (2008)

50 How to avoid cooling/fragmentation? Omukai, Schneider & Haiman (2008) To avoid this fate, gas must get to safe zone at n>n crit =10 4 cm -3 - Destroy H 2 with huge LW flux: J 21 (crit) 10 4 In minihalos gas cools and forms PopIII stars - Shock in dense n >10 4 cm -3 core: v s (crit) 10 km/s In T vir >10 4 K halos (with no prior PopIII starformation), gas cools via Lyα high density 3 H 2 cooling M acc c s ~ 10-2 M yr -1 similar to popiii! - Heat gas by primordial magnetic field: B(crit) 3 ng - Trap Lyα radiation for a free-fall time (high n HI & N HI ) Shang et al. (2010) Inayoshi & Omukai(2012) Sethi & Haiman (2010) Silk & Spaans (2008)

51 Critical UV flux [ H 2 -formation rate ρ 2 ] = [ photo-dissoc. rate Jρ ] Critical flux: J ρ J 21,crit low ~ in low-mass mini-halos (n ~ cm -3 ) Compare to J ~ 1 (at z~3) or J~ 10 (at reionization) In more massive (atomic cooling) halos: avoid H 2 -cooling up to critical density of H 2 : n ~ 10 4 cm -3 J 21,crit increased to ~10 3 NB: H 2 self-shielding crucial (Wolcott-Green, Haiman, Bryan 2011) (Sugimura et al. 2015)

52 Fragmentation scale Interior to a characteristic radius R f = few 10 2 pc, the disk fragments into O(10-100) clumps with M c 30 M [agrees well with Regan et al. 2014; lower accretion rate version of model with dm/dt = 10-3 M yr 1 agrees well with surface density, disk size, number and mass of clumps in Greif ] temperature surf.density viscosity param

53 Fate of clumps Migration Accretion UV feedback Migration: faster than KH time most clumps merge with central object before evolving into stars

54 Fate of clumps Migration + Accretion + Feedback central star clump ionized wind Some clumps could survive (either formed farther out, or lucky ) and evolve to ZAMS stars photoionization heating limits these star s mass to ~40 M, but unable to reduce global dm/dt in disk

55 Ionizing shocks in dense halo core? Gas directly heated up into safe zone Look for shocks in core with Mach number > 3-4 Fernandez, Bryan & Haiman (2012) Inayoshi & Omukai (2012) density Temperature Δ-.v Mach number

56 Ionizing shocks in dense halo core? Fernandez, Bryan & Haiman (2012) Temperature number density

57 Self-Shielding of H 2 Lyman Werner lines Wolcott-Green, Haiman & Bryan (2011) Critical for SMBH formation: f shield = J(N H2 )/J(N H2 =0) several 0.01 Two-step process: H 2 +γ H 2 (*) H+H+γ Radiative transfer must be followed for O(10) lines in ground state; dozens at T=few 1000 K Also: anisotropic density, velocity, temperature gradients Previous works assume optically thin gas, or (mis)use local N H2 with f shield (N H2 ) from Draine & Bertoldi 1996 J(crit) reduced by a factor of >10 to J crit 10 3 Achieved in close (~10kpc) pairs of 10 8 M halos Dijkstra et al. (2009)

58 Self-Shielding of H 2 Lyman Werner lines Contribution of 76 (gs) lines saw-tooth background spectrum Haiman, Abel & Rees (2000) Haiman, Rees & Loeb (1997)

59 IGM evolution with/without X-ray heating exponential Bondi-limited IGM is heated to T= K Jeans filtering of M= M halos redshift redshift

60 A global controversy

61 Final Stellar Mass? Shang, Bryan & Haiman (2010) t acc (yr) M gas/m dm/dt = M yr -1

62 Final Stellar Mass? Shang, Bryan & Haiman (2010) t acc (yr) Kelvin-Helmoltz time M gas/m M Pop III star Abel et al.; Bromm et al.; Yoshida et al...

63 Avoiding H 2 cooling with UV flux Shang, Bryan & Haiman (2010) Simulations with enzo: 3 halos with M ~10 8 M identified in 1 Mpc box re-simulate each halo, refinement levels, with J=0, 10, 100, 10 4, 10 5 Collapse with PopII UV spectrum (T*=10,000 K) Expected background flux at z~10: J(UV) ~ < J crit < 300 (PopII) 10 4 < J crit < 10 5 (PopIII)

64 Self-Shielding of H 2 Lyman Werner lines Wolcott-Green, Haiman & Bryan (2011) Critical for SMBH formation: f shield = J(N H2 )/J(N H2 =0) several 0.01 Two-step process: H 2 +γ H 2 (*) H+H+γ Known cross-sections (Abgrall et al. 1993) and dissociation fractions (Abgrall et al. 2000) Radiative transfer must be followed for O(10) lines in ground state; dozens at T=few 1000 K Anisotropic density, velocity, temperature gradients Previous works assume optically thin gas, or (mis)use local N H2 with f shield (N H2 ) from Draine & Bertoldi 1996

65 Self-Shielding of H 2 Lyman Werner lines Exact line transfer in 3D (Wolcott-Green, Haiman & Bryan 2011) Approximate methods overestimate shielding - factor >10 in relevant range - mostly from inaccurate extrapolation of f shield from DB96 to high T (LTE populations) Important for Jcrit: - J shield reduced to ~10 3 Many more candidate halos see this flux

66 SMBH by direct collapse possible (?) Shang, Bryan & Haiman (2010) t acc (yr) M gas/m

67 SMBH by direct collapse possible (?) Shang, Bryan & Haiman (2010) t acc (yr) Kelvin-Helmoltz time M gas/m M Pop III star 10 5 M supermassive star/bh Abel et al.; Bromm et al.; Yoshida et al. Fuller, Woosley & Weaver (1986)

68 Can we have sufficiently large UV flux? Dijkstra, Haiman, Mesinger & Wyithe (2008) Need: J(LW) erg s cm -2 Hz -1 sr -1 Factor of ~100 above mean. Must come from nearby sources. High-redshift halos are strongly clustered J=10 3 from a galaxy 3kpc away - vs J=50

69 UV Flux PDF Sampled by Halos - (non-linear) source clustering. - Poisson fluctuations in # of neighbors. - UV luminosity scatter Dijkstra, Haiman Mesinger & Wyithe (2008) 1 in ~10 6 halos has a close ( 10 kpc) bright and synchronized neighbor, so flux is ~ 30 mean N~10 3 Gpc -3 halos, could all end up in z=6 QSO hosts

70 Direct SMBH formation: impact of metals Including the effect of (1) irradiation and (2) metals Omukai, Schneider & Haiman (2008)

71 Direct SMBH formation: Summary Two conditions needed to avoid fragmentation: (i) J(LW) few erg s cm -2 Hz -1 sr -1 (ii) Z Z First condition can be satisfied in rare case of very close, bright & synchronized neighbors (Dijkstra, Haiman, Wyithe & Mesinger 2008) Gas with trace metals forms dense cluster of low-mass stars collapse to IMBH of 10 4 M (Omukai et al. 2008) First condition eased for normal IMF (H - -dissociation) (Shang, Bryan & Haiman 2010) Second condition eased by factor of 100 if no dust (CII and OI cooling).

72 Alternative heating: magnetic field Sethi, Haiman & Pandey (2010) Primordial magnetic field can be generated during phase transitions in the early universe Current best upper limit from CMB anisotropy: B~1nG Ambipolar diffusion heating can balance HI cooling

73 Growing SMBHs by Accretion + Mergers Tanaka & Haiman (2009) Construct Monte-Carlo DM halo merger trees from z=6 to z> M M halo M (M res =few 10 5 M ; N~10 5 trees) Q1: Fraction of minihalos forming stellar BH seeds? - f seed depends on IMF and feedback (e.g: H 2 +γ H 2 (*) H+H+γ) - f seed ~ (M seed ~ M ) Q2: Time-averaged mass accretion rate? - duty cycle f duty for accretion (f duty 1.0) - maximum of Bondi ( ρm BH 2 /c s 3 ) and Eddington rate - density profile either ρ r -2.2 (cool gas) or flat core (adiabatic) Q3: What happens when halos merge? - gas drag leads to coalescence of BHs - gravitational recoil: v kick - spins random or aligned (Baker et al. 2008) - follow kicked BH trajectory - damped oscillation (gas drag)

74 SMBH mass functions at z=6 f seed =10-3 f seed =10-2 f seed =10-1 f seed = 1 log(nbh/gpc -3 ) log(m bh /M )

75 f seed f seed =10-3 f seed =10-2 f seed =10-1 f seed = 1 log(nbh/gpc -3 ) log(m bh /M )

76 f seed f seed =10-3 f seed =10-2 f seed =10-1 f seed = 1 random spin aligned log(nbh/gpc -3 ) log(m bh /M )

77 f seed f seed =10-3 f seed =10-2 f seed =10-1 f seed = 1 random spin aligned log(nbh/gpc -3 ) f duty log(m bh /M )

78 Total mass in >10 5 M SMBHs: overproduced by a factor of Tanaka & Haiman (2009) Local SMBH mass density: ρ tot M Mpc -3 At most ~10% can come from z > 6 Over-prediction is generic in all models z seed Introduce redshift cutoff: no new seeds below z cut (for low f seed )

79 Distribution of recoil velocities Tanaka & Haiman (2009) spin magnitudes chosen randomly from 0<a 1,2 <0.9 v kick below v esc for unequal mass mergers q=m 1 /M 2 < 0.01 irrespective of spin

80 SMBHs from stellar seeds: Summary (i) density cusp (ii) f seed 10-3 (iii) f duty 0.8 } very optimistic assumptions required! Making few 10 9 M BHs by z=6 without overproducing the number of few 10 5 M BHs (ρ BH M Mpc -3 ) suggests f seed 10-2 and negative feedback at z~20 H2-dissociation by soft UV? X-ray heating from BHs? Growth self-regulates? No BH seeds after PopIII PopII? The 10 9 M BHs result from runaway early seeds (z>25) that avoided ejection at merger: asymmetric mass ratio Kick and spin alignment makes little difference for low f seed

81 SMBH by direct collapse possible (?) Shang, Bryan & Haiman (2010) Normal stars (soft UVB) Pop III stars (hard UVB)

82 SMBH by direct collapse possible (?) Shang, Bryan & Haiman (2010) Kelvin-Helmoltz time M Pop III star Abel et al.; Bromm et al.; Yoshida et al M supermassive star/bh Fuller, Woosley & Weaver( 1986)

83 Direct SMBH formation in T vir >10 4 K halos? log( cooling rate / erg s -1 cm 3 ) COSMIC TIME MASS SCALE log( Temperature / K ) cf. Halo virial temperature: Gas collapses to M SMBH directly, or via a supermassive star or a dense stellar cluster - gas driven in rapidly (deep potential) - no fragmentation (avoid cooling) - shed angular momentum (global instability)

84 A possible obstacle: gravitational recoil Gravitational radiation produces sudden recoil kick velocity depends on mass ratio and on spin vectors typical v(kick) ~ few 100 km/s (Baker et al. 2006, 2007 maximum v(kick) ~ 4,000 km/s Gonzalez et al. 2007) v(kick) 1 km/s for unequal BH masses (q < 0.01) Most important at high redshift when halos are small escape velocities from z>6 halos is few km/s Is there a sweet spot for fraction of halos with BH seeds?

85 Time-averaged Mass Accretion Rate? LIMIT FROM AMBIENT CONDITIONS - Bondi rate ( ρm BH 2 /c s 3 ) initially sub-eddington - Quickly catches up with Eddington rate, if ρ high LIMIT BY RADIATIVE FEEDBACK - Radiation from star + hole ionizes and heats gas - No steady-state solution in spherical symmetry - Episodic accretion with time-averaged f duty ~ 0.3 Milosavljević et al. (2009) SUPER-EDDINGTON MASS ACCRETION? - Radiation trapped and advected with flow (RIAF s) - Problem: winds only few % of mass reaches BH - Radiation leaks out photon bubble MHD instability - f duty ~ 2-3 possible (?)

86 Do Most Minihalos Form Stars? Minihalos are fragile - many possible feedback effects LOCAL FEEDBACK IN & NEAR MINIHALO - UV flux unbinds gas - supernova expels gas, sweeps up shells - H 2 chemistry (positive and negative) - metals enhance cooling GLOBAL (FAR REACHING OR LONG LASTING) - H 2 chemistry (LW: negative X-rays: positive) - entropy floor (inactive fossil HII regions or X-rays) - photo-evaporation (minihalos with σ < 10 km/s) - photo-heating (halos with 10 km/s < σ < 50 km/s) - global dispersion of metals (pop III pop II) - mechanical (SN blast waves)

87 Halo Collapse in ΛCDM Smallest scales condense first collapse redshift log (Mass/ M ) Jeans mass: ~10 4 M possible further delay in gas by Δz~4: Tseliakovich & Hirata (2010) Greif et al. (2011) Stacy et al (2010) Maio et al. (2010)

88 Alternative: Direct Gas Collapse ANGULAR MOMENTUM - large effective viscosity (global dynamical instabilities?) - use low-j tail (either rare halos or fraction of gas in given halo) AVOIDING FRAGMENTATION - must avoid cooling to T 10 4 K - avoid cooling by metals and dust - avoid H 2 formation (otherwise: fragmentation, star-formation will be similar to mini-halos) THESE TWO CRITERIA MAY BE RELATED - age-old BH fueling problem for quasars - key: stable locally (gravity vs pressure/turbulence) unstable globally (rotational vs potential energy) - recent simulations to 0.1pc (Mayer et al. 2009, Levine et al Hopkins & Quataert 2010)

89 BH trajectory : dynamical friction vs. gas Tanaka & Haiman (2009) DM halo NFW gas with flat core (Shapiro et al. 1999) gas with steep cusp (Abel et al Bromm et al Yoshida et al. 2003) Asymmetry in 3D makes return harder (Guedes et al. 2009)

90 Stellar seed vs direct collapse STELLAR SEEDS uninterrupted near-eddington accretion - continuous gas supply - avoid radiative feedback depressing accretion rate - must avoid ejection from halos (loosing the seeds) (Tanaka & Haiman 2010) DIRECT COLLAPSE rapid formation of M black holes by (super-eddington) collapse of gas to a SMBH either directly or via a supermassive star or dense stellar cluster - gas must be driven in rapidly (deep potential) - must avoid fragmentation until high densities - transfer angular momentum (Shang, Haiman & Bryan 2010)

91 LISA event rate: M-σ model Tanaka & Haiman (2009) 10 4 M < (1+z)M bh < 10 7 M Aligned Random Internal feedback regulates BH mass set to maintain extrapolated M-σ relation Growth driven by mergers: slow accretion, tracks halo growth on Hubble time Many ejections can exceed half ρ BH

92 Quasar BH Signatures in 21cm Blurred HII bubble boundary for hard sources - suppression of 21cm power spectrum Iliev, Shapiro, Furlanetto et al. - parameter-fitting through linear perturbation approach Zhang, Hui & Haiman (2007) - imaging individual bubbles: diagnose quasars, constrain spectrum Kramer & Haiman (2008); Zaroubi & Silk (2005) Fossil quasar bubbles - grey bubbles, modify power spectra - constrain quasar duty cycle and clumping Furlanetto, Haiman & Oh (2008) Finite-speed-of light distorts the shapes of quasar bubbles - observable as an anisotropy in the power spectrum (MWA)? - diagnose quasar contribution, constrain abundance/lifetime Sethi & Haiman (2008)

93 Alternative heating: magnetic field Sethi & Haiman (in prep) electron fraction H 2 molecule fraction

94 Can we have sufficiently large UV flux? Dijkstra, Haiman, Mesinger & Wyithe (2008) Ahn et al. (2009) Need: J(LW) erg s cm -2 Hz -1 sr -1 Factor of ~100 above mean. Must come from nearby sources. High-redshift halos are strongly clustered (Barkana & Scannapieco)

95 Direct SMBH formation in Irradiated Gas? Evolution of irradiated, metal-free gas: J 21 (crit) 10 3 Omukai, Schneider & Haiman (2008)

96 Critical UV flux: 3D simulations Normal stars PopIII stars T(K) 30 < J crit < < J crit < 10 5 Hydro (enzo) simulation of collapse with UV flux f(e) Shang Bryan & Haiman (2010) f(h 2 ) Expected background flux at z~10: J(UV) ~ 10

97 Avoiding steep BH mass function: Require low f seed 10-2 to spread seeds in redshift Also require high cutoff redshift z cut 30 Other ideas to flatten the BH mass function : start with much more massive seeds (lowers z cut ) internal feedback always maintains M BH -σ relation - many more mergers in this model (good news for LISA) - also solves puzzle of connecting z>6 and z<6 universe

98 Ultra-Early Pause in Structure Formation? Soft UV background: this background inevitable destroys molecules H 2 dissociated by ev Lyman-Werner photons: H 2 +γ H 2 (*) H+H+γ Soft X-ray background: this background from BHs themselves (or X ray binaries?) ~ 1 kev photons produce fast photoelectrons H+γ H + +e - H 2 cooling in minihalos suppressed already when J 21 ~ 0.01 early partial (pre)ionization and IGM heating Haiman, Rees & Loeb 1997 Mesinger, Bryan & Haiman 2008 Madau et al Ricotti & Ostriker 2004

99 Negative Feedback in Reionization History Haiman & Bryan (2006) ionized volume fraction τ=0.19 τ=0.09 Optical depth redshift efficiency Minihalo contribution suppressed by a factor of ~10 (2σ)

100 Direct SMBH formation in T vir >10 4 K halos? Highly super-eddington growth may be possible if gas remains T=10 4 K (due to lack of H 2 ) and cools via atomic H Jeans mass M J T 3/2 /ρ 1/ M A Mo-Mao-White disk model with isothermal gas at T=10 4 K is Toomre-stable, gas could avoid fragmentation (Oh & Haiman 2002) No fragmentation seen in simulations (Bromm & Loeb 2003; Wise & Abel 2007; Regan & Haehnelt 2009; Shang et al. 2010) Gas can collapse rapidly onto a seed BH (Volonteri & Rees 2005) or collapse directly into M SMBH by global instability (Koushiappas et al. 2004; Begelman et al 2006; Spaans & Silk 2006; Lodato & Natarajan 2006; Wise & Abel 2007; Regan & Haehnelt 2008)

101 If gas in T vir >10 4 K halos cools to ~100K: (Oh & Haiman 2002; Shang et al. 2010) Similar to mini-halos: Rely on H 2 cooling and fragment on similar (~ 100 M ) scales; no rapid in-fall (c s vs v ff ) Main differences: 1. contract to high densities less susceptible to feedback 2. HD possibly lowers mass (bad for SMBH formation) cf: SMBHs Volonteri &Rees 2005 Bromm & Loeb 2005 Begelman et al Lodato et al Spaans & Silk 2006 cf: HD reduces temperature and fragmentation scale? Uehara & Inutsuka 2000 Machida et al Johnson & Bromm 2005 but: Mc Greer & Bryan 2008

102 A Perturbation Theory of Reionization Zhang, Hui & Haiman (2007); Iliev et al. (2007, 2008) Power spectrum of fluctuations (HI, HII) will be smoothed on scales below the mean free path of ionizing photons leaking into the IGM We will need parameterized model to fit to future data (e.g. 21cm or ksz power spectra) that probe the ionization topology On large scales (k 0.1 Mpc -1 ), linear perturbation theory should be adequate Linear perturbation theory solves ionization balance and radiative transfer, and can predict power spectra as a function of parameters Example: typical spectral slope β = - d lnf ν / d lnν

103 A Perturbation Theory of Reionization Zhang, Hui & Haiman (2007) Soft spectrum z=10 z=9 z=13 z=20 Hard spectrum

104 The Shapes of Quasar HII Regions Finite speed of light distorts apparent shape of quasar HII region (Cen & Haiman 2000 Wyithe & Loeb 2004; Yu 2005): Effect is large when spheres are large and expand at v ~ c (short-lived, bright quasars) Asymmetry confirms quasar origin, and constrains a combination of (t Q,, t rec,, t nr ) and therefore (t Q,, x HI,, C)

105 Can We Detect The Distortion? 21cm is best bet, since it offers 3D tomographic information (another signature is modulation in the spatial distribution of Lyα emitters?) Has to be statistical, involving 100s of quasars, to average out intrinsic non-sphericities Effect is ~10 percent for quasars ~10 times less luminous than the SDSS quasars at z~6 There could be up to ~10 such quasars deg -2, ionizing up to ~10% of the IGM volume, consistent with observed LF, lensing, and XRB (Dijkstra, Haiman & Loeb 2005; Sbrinovsky & Wyithe 2007; Richards et al. 2006)

106 Quasar HII Region Shapes in 21cm Quasar HII region appears as a hole, surrounded by ring of emission, in the 21cm maps Tozzi et al. (2000) Imaging individual HII regions (although high S/N may require sensitivity of SKA) Wyithe, Loeb & Barnes (2005) Alternatives: statistical detection in the small-scale 21cm power spectrum, or by stacking? Sethi & Haiman (2007) Best case scenario: large quasar bubbles, expanding relativistically into a partially ionized IGM, fill a few percent of the IGM volume without overlapping significantly

107 21cm Power Spectrum Anisotropy Sethi & Haiman (2007) When T spin T spin, 21cm emission given by local neutral hydrogen density: We need correlation function ξ of x HI : Model: randomly distributed distorted spheres

108 Expected Anisotropy in ξ(r,θ) Sethi & Haiman (2007) t Q =10 7 yr t Q = yr t Q = yr t Q = yr , 45 18, 31 z=8 f ion = 0.8 C=5-20 N= s -1 MWA can detect ~10% anisotropy in few days T B = 2.2K ξ = K 2

109 Fossil Quasar Bubbles Many pieces of evidence that bright quasar phase is short: 10 7 years t Q 10 8 years (e.g. Martini 2004) Fiducial recombination time in z>6 IGM: t rec t Hubble years at mean density at z=8 fossils outnumber active bubbles by factor t rec /t Q 5-50 Fossils affect the IGM, and are useful probes: large (40-50 comoving Mpc), prime targets for 21cm imaging probe quasar properties (Wyithe, Loeb & Barnes 2005; Zaroubi & Silk 2005; Kramer & ZH 2007) probe IGM properties (Lidz et al., Alvarez & Abel, Geil & Wyithe) entropy floor even in recombined fossils (Oh & ZH 2003) H 2 formation (Ricotti et al. 02; Kuhlen & Madau 05; Mesinger et al. 07)

110 How does HII region recombine? Recombination must be inhomogeneous: over-dense regions recombine quickly under-dense regions remain ionized for longer than t rec Pre-existing galaxies: mean free path in fossil starts much higher than outside can pre-existing galaxies keep most of the fossil ionized? (easier than to ionize the region to begin with) How do we distinguish fossils? grey bubble: reduced contrast relative to active bubbles but ionization nearly uniform large size distinguishes them from rare large galaxy-bubbles

111 Fossil Recombination With Zero Flux z=6 z=6 z=14 z=9 Assume Γ bg =0 Follow -dependent recombination cf: equivalent crit with P( ) from MHR00 Miralda-Escude, Haehnelt & Rees (2000) Compute m.f.p. (including the under-dense voids) m.f.p. remains ~Mpc if x HI 10-3 (at ~1)

112 Fossil Evolution vs Global Reionization Semi-analytical reionization model Follow mean x HI in z=10 fossil vs globally Additionally: follow -dependent x HI inside fossils Compute m.f.p. using MHR00 c.f. clustering length of pre-existing galaxies uniform, high ionization

113 An Early Fossil (z=15) Probably much rarer than fossils from z=10 Still remains highly ionized different from z=10 fossil: m.f.p. drops below galaxy clustering length will develop (reduced contrast) swiss-cheese

114 Check validity of MHR00 m.f.p. Assume uniform Γ bg z=14 z=7 neglect self-shielding Compute optical depth τ across one MHR00 m.f.p., including the under-dense voids z=9 z=7 z=10 fossil: x HI 10-3 τ=0.9, 0.5, 0.4 z=15 fossil: τ=13, 4.5, 1.5, 0.7, 0.1