Coeval Evolution of Galaxies and Supermassive Black Holes : Cosmological Simulations

J. A. de Freitas Pacheco Charline Filloux

Fabrice Durier Matias Montesino

Collaborators J. Silk – Oxford

T.P. Idiart – USP Miguel Preto - Heidelberg

The Facts

Observational evidences for the existence of massive BH in the core of galaxies

Sagittarius A* - galactic centre

Ghez et al. 1998

DMO in M87, M84 and NGC4261

Black holes and galaxies

Strong correlations are observed between the black hole mass and :

Stellar velocity dispersion :

Stellar bulge mass :

Stellar bulge luminosity :

Co-evolution of SMBH and galaxies

Dark halo mass :

3.5 4.5M ˜

1.12lgbu eM M˜

1.26BM L˜

Tremaine et al. 2002 ; Gebhardt et al.2000

Haring and Rix, 2004

Marconi and Hunt, 2003

1.27haloM M˜Baes et al. 2003

Lower Mass Limits

* Lower limits

- negative searches for intermediate

mass black holes

- upper limits for M33 (3103 M ) and

NGC 205 (3.8104 M )

-indirect evidence for IMBH in NLSeyf1

(8104 - 8106 M )

Origin & Evolution of SMBH

Origin of Seeds

(*) Intermediate mass black holes (103-104 M) formed in : a) the collapse of primordial gas clouds (Haehnelt & Rees 1993)b) the core collapse of star clusters formed in starburts (Shapiro 2004)

(*) Collapse of primordial massive stars (100-300 M) formed in highdensity peaks of the primordial fluctuation spectrum

Cosmological simulations

Advantages

• follow up of seeds• gas dynamics & merger tree• follow up of the star formation history

Difficulties

Two extreme scales :Galaxies interactions : several kpcBlack hole physics : sub-pc scales

Number of Particles Mass resolution (gas)

V=(50 Mpc)3

CPU/hours/run

(128 processors)

21603 5.35108 M 4 000

21923 3.09108 M 12 000

22563 1.30108 M 60 000

v=0.7 m=0.3 bh2= 0.0224 h=0.70 8=0.9

The Code

GADGET-IISpringel 2005

Gravitation(tree code)

Hydrodynamics(SPH)

DARK MATTER GASSMBH

Introduction of BH seeds at potential

minima (z=15)

BH Growth(« disk » and HLB mode)

AGN activity (feedback)

STARS

Star formation (conversion of gas

into tars)

Ionisation, heating and

radiative cooling

Supernovae (type Ia and II)

Galactic winds

Metal enrichment

SMBH coalescences during galaxy

mergers

Code Parameters

,

510.03 0.2

10Ia II

SNE erg

Energy injected by supernovae

1n

wr

Weight for the blast energy per particle i SNi N

ii

w E

Nw

’’turbulent’’ diffusion efficiency 20.1 0.2tD t

L

Accretion mode spherical (Bondi – Hoyle) ’’disk’’ 2

6 sc VdM

dt QG

AGN feedback

gravitational energy

rotational energy

0.1J AGN bol AGNL L 2

2 2

max2J horA

c SL H cr

V S

Jet angle 20 ,45 ,180o o o Jet length 100 - 400 kpc

Detection of Structures

FoF SubFind

Davis et al, 1985 ; Huchra and Geller, 1982 Springel et al, 2001

Structure determination

Properties of Galaxies

Dynamical Properties of Simulated Galaxies

Faber-Jackson & Tully-Fisher relations Angular momenta of blue & red galaxies

’’Red’’ galaxies (U-V)>1.1 and (B-V)>0.8’’Blue’’ galaxies otherwise

Properties of Simulated Galaxies

Grey zone – SDSS data from Gallazzi et al. 2005

Properties of Simulated Black Holes

The mass function at z=0

All simulations give similar results, with BHMF slightly overestimated for M● >107M

BH seeds of 100 M: evolution of massive pop III stars

192/160 : resolution disk/kerr : AGN feedback from accretion /rotation

S : with higher SNIa efficiency

Evolution of the Black hole mass density

Simulation ρ●(z=0) [M.Mpc-3]

MBH,min

[M]

160kerr 5.0 x 105 2.4 x 104

160disk 9.6 x 105 1.8 x 104

160diskS 7.4 x 105 3.7 x 103

192disk 8.2 x 105 1.2 x 103

Estimates : ρ●= 2 - 9 x 105 M.Mpc-3

Chokshi and Turner 1992 ; Salucci et al., 1999 ; Aller and Richstone, 2002 ; Marconi et al, 2004, …

192/160 : resolution disk/kerr : AGN feedback from accretion /rotation

S : with higher SNIa efficiency

Assuming bolometric luminosity proportional to the accretion rate

Black hole mass density at z=0

The M● - σ relation

Cygnus A, NGC 5252, NGC 3115 and NGC 4594

Good agreement, except for the four galaxies having black holes apparently too massive.

192disk simulation

The M● - Mhalo relation

Good agreement with Baes et al, 2003.

Mhalo is directly extracted from simulations.

192disk simulation

Some problems: no SMBH at z ~ 6!

No supermassive black holes at z=6 hierarchical growth

No super-Eddington accretion rates are observed (resolution effect?)

Gravitational Waves from Coalescences

Coalescence of two massive BHs

tThre

Four regimes can be recognized:i) adiabatic – sequence of quasi-circular geodesic orbitsii) transition – near the innermost stable orbitiii) plunge – merger of the two horizonsiv) ring-down – normal modes of the distorted black hole

Maximum mean frequencies – adiabatic regime

21 2

1 2

0.052( )gw

M ME c

M M

Total energy radiated under theform of GW in the adiabatic phase

5682( )gw lso Hz

M

Frequency near the ’’last stable orbit’’

Expected contribution to the background

max 2

min 1

1/3 7 /3 30

( ') '( ) ( , ')

(1 ') (1 ')o

z

o z v m

c z dzK P z d

H v z z

Expected flux at the observer’s frame

With 1 21/3

1 2( )

M M

M M

and ( )z total merger rate per

comoving volume

3

1( ) oo

gw gwc c

Equivalent density parameter

( , )P z Fraction of mergers with a parameter occurring at z

Ring-down contribution to the background

Expected flux

max

min

3 2

4 30

( ') '( ( ') /(1 ') )

(1 ') (1 ')o

z

oo z v m

c G z dzG z z

H z z

Equivalent density parameter 3

1( ) oo

gw oc c

0.3

2

100 63 ( )( ) 12 1 ( ) ( )

37 37

c J zG z a z kHz a z

GM

2

1

3 2

300 0

2 ( ') '( ) ( ') ( , ')

3000 (1 ')

Mz z

gw s

Mv m

c r z dzD z dR z M M z dM

H z

Duty cycle

Ring-down background(shot-noise – D <<1)

Spin data: Daly 2009 Shot-noise

I. Conclusions

• Cosmological simulations are the best tool to study the coeval evolution of galaxies and their central black holes

• Properties of gas, galaxies and the growth of supermassive black holes depend strongly on feedback mechanisms, in particular the downsizing effect

• Simulated galaxies have adequate mass profiles, satisfying the Faber-Jackson (red galaxies), the Tully-Fisher (blue galaxies) and the mass-metallicity relation

II. Conclusions• Seeds ( ~ 100 M) originated from the evolution of zero metallicity massive stars

are able to explain SMBH, by growing through accretion and coalescences

• Simulated SMBH satisfy the mass distribution observed in the local universe as well as the evolution of the BH mass density, the M● vs and the M● vs Mhalo relations

• Gravitational waves can put strong constraints on the coalescence history of seeds

• However, difficulties exist such:

a) no SMBH are seen at z ~ 6

b) density of massive galaxies are overestimated

c) simulated <Fe> and Mg2 indices still do not reproduce adequately the observations

d) blue galaxies do not have enough angular momentum