A Physical Model for Co-evolution of QSOs and of their Spheroidal

Hosts

Gianfranco De Zotti

with: Francesco Shankar, Andrea Lapi, Luigi Danese, Gian Luigi Granato, Michele Cirasuolo, Paolo Salucci, Laura Silva

Observational connections between galaxy and BH properties

• BH are generally connected with the (generally old) bulge stellar population not with the younger disk population (Kormendy & Gebhardt 2001; Kormendy & Ho 2000; Salucci et al. 2000)

• Tight relationship between BH mass and stellar velocity dispersion (Tremaine et al. 2002):

• M_BH is also well correlated with the mass in stars (Häring & Rix 2004):

• Further relationships can be derived comparing the Galactic Halo Mass Function with the Stellar and BH mass functions or with the velocity dispersion function (Shankar et al. 2005):

where the GHMF is derived from the halo mass function (Sheth & Tormen 2002), adding the contribution of sub-halos (Vale & Ostriker 2004) and subtracting that of groups and clusters (Martinez et al. 2002)

Examples:

• Mass in stars vs halo mass

Different behaviour above and below Mh~2.5 1011 Msun !

The -Vvir relation and the Velocity Dispersion Function(Loeb & Peebles 2003; Cirasuolo et al 2005)

The -Vvir relation is a key ingredient to connect theoretical predictions with observations

Vvir is controlled by dynamics of halos, while feels the effect of dissipative baryon setting

From observational point of view:(L) + (L- relation) ()

From theoretical point of view:n(Mvir, zvir) + v2

vir (vvir)

PS+ST GMvir/rvir

Loeb & Peebles (2003)

The -Vvir relation and the Velocity Dispersion Function

= 0.57 ± 0.05 V= 0.57 ± 0.05 Vvirvir = 0.57 ± 0.05 V= 0.57 ± 0.05 Vvirvir

Dynamical attractor (Gao et al. 2004)? Major mergers rarer in sufficiently massive halos?

A simplified feedback model(Shankar et al. 2005; Granato et al. 2004)

• The gas, heated at virial temperature, cools down and falls towards the central star-forming region at a rate

where

and

fcosm= b/DM0.19

• The time derivative of the cold, star-forming gas mass is

where R0.3 for a Salpeter IMF and

Dezotti:

is the effective efficiency of cold gas removal by SN feedback

Dezotti:

is the effective efficiency of cold gas removal by SN feedback

so that the efficiency of gas removal by SN feedback is

Setting

The differential equation can be solved to give:

where = 1– R + and

At the present time

For and 1-Rconst.

so that consistent with the data For small masses,

so that

with a much flatter slope than inferred from the data (effect of reheating?)

BH growth

Radiation drag dissipates the angular momentum of gas clouds allowing them to infall toward the central BH at a rate (Kawakatu & Umemura 2002):

The final BH mass is then:

After Granato et al. (2004):

since and, for

, Thus, for large masses, and

For small masses ( « 1)

consistent with the steepening indicated by the data:

whence

AGN energy transferred to the gas

• Kinetic luminosity (Granato et al. 2004), erg/s

• For Eddington limited accretion:

with for = 0.1, so that

for and

e.g.:

Dezotti:

f_c: covering factor of AGN-driven winds

N_22: gas column densityi n 10^22 cm^-2

f_h: fraction of AGN kinetic power transferred to the gas

Dezotti:

f_c: covering factor of AGN-driven winds

N_22: gas column densityi n 10^22 cm^-2

f_h: fraction of AGN kinetic power transferred to the gas

Halos form, gas is shock heated to virial T

Scheme of our semi analytical model at high z

Gas cools, collapse and forms stars directly, in small halos SNae quench SF, in big ones nothing prevents a huge burst of SF ('1000 M¯/yr over 0.5 Gyr), SMGs phase

(almost) passive evolution of stellar population follows. ERO phase with dormant SMBH

SF promotes the growth of a SMBH, powering high z QSO. QSO activity expels the ISM, terminating SF and its own growth. QSO phase

INGREDIENTS of physical model (zvir>1.5, logM vir>11.5)

1. formation of dark matter halos, starting from primordial density fluctuations. PS (ST) formalism is used

2. shock-heating & radiative cooling of gas in DM halos

3. collapse of cold gas & star formation from cold gas

4. chemical and energetic feedback from stars (SNae)

5. formation of low angular momentum reservoir with a rate SFR (radiation drag Umemura 2001)

6. Growth of SMBH, limited by Eddington, viscosity, fuel availability

7. Feed-back on cold gas due to increasing QSO activity

8. luminosity evolution of stellar populations

9. absorption of starlight by dust & re-emission in IR+sub-mm (our GRASIL, Silva et al 1998)

Evolution of galaxyEvolution of SMBH

Mvir=2e12

Mvir=1e13

Example at zvir=4

accretionrate

SFR

Evolution faster in more massive halosGranato et al 2004

Chemical abundances (in stars) at z=0 as a function of M(halo)

Granato et al 2004

K band local Luminosity function of spheroids

Data:Huang et al 2003Kochanek et al 2001

Granato et al 2004

Silva et al 2005

Star forming

Passive

<—— Cimatti et al. (2002)

<—— Somerville et al. (2004)

z = 0.5

z = 0.9

z =1.3

z = 1.8

Fontana et al 2004: galaxy stellar mass function in K20 sample

Standard SAMsGranato et al 2004

Standard SAMs underproduce massive galaxy, by a fraction increasing with z

ABC scenario naturally reproduces SMGs statistic

5.7 mJy z dist MEDIAN QUARTILE

Chapman et al 2005 (73 sources)

2.2 1.7-2.8

Model 2.2 1.6-3.3

SCUBA 850 m

MAMBO 1200 m

model

data

The central BH

= 0.57 ± 0.05 V= 0.57 ± 0.05 Vvirvir = 0.57 ± 0.05 V= 0.57 ± 0.05 Vvirvir

Steepening at low (due to greater effectiveness of SNae and lower

dispersion interpreted as different virialization epochs

Tighter MBH-M*?

MBH vs Mh (1)

MBH vs Mh (2)

Mass function of local SMBH

observations

model

THE PRE-QSO PHASEThe build up by accretion of the SMBH, promoted by SF and before the bright optical QSO phase, gives rise to a mild AGN activity in sub-mm galaxies detectable in hard-X.Indeed ~75% of >4 mJy SCUBA sources host an X-ray AGN with intrinsic LX[0.5-8]1043-1044 erg s-1 (Alexander et al 03,04,05)

dM/dt(BH)>0.02 M¯/yr ) L(0.5-8)>1E43 erg/s

dM/dt(BH)>0.2 M¯/yr ) L(0.5-8)>1E44 erg/s

dM/dt(BH)>1 M¯/yr ) L(0.5-8)>5E44 erg/s

QSO luminosity functions (work in progress)

+ slow decrease of Lbol/ LEdd with z, from 4 at >6 to 0.8 at <2

Optical LF (1)

z=1.5tvis=3 107 yr

Optical LF (2)

z=3.1 tvis=4 107 yr

z=4.5tvis=4 107 yr

Optical LF (3)

Optical LF (4)

z=6 tvis=4 107 yr

Evolution of the optical luminosity function

Models in which a fraction of the halo mass is accreted at each major merger, when normalized to produce the density of QSO at z»6, tend to overproduce the density at lower z (Bromley et al. 2004).

QSOs with L>3 1047 erg/s

Our model is not affected by this problem!(and without tuning of parameters)

..the cosmic accretion rate is in agreement with results of optical surveys (e.g. Fan et al. 2003)

Unabsorbed X-ray (0.5-8 keV) light curve of QSOszvir=4

Mh=2.5 1012 Msun

Mh=2.5 1013 Msun

X-ray binaries AGN activity

Hard X-ray luminosity function (1)

z=1.5 tvis= 108 yr

Ueda et al. (2003)

Barger et al. (2005)

Hard X-ray luminosity function (2)

Ueda et al. (2003)

La Franca et al. (2005)

Barger et al. (2005)

z=1.5 tvis= 3 108 yr

Hard X-ray luminosity function (3)

La Franca et al. (2005)

Ueda et al. (2003)

Barger et al. (2005)

z=2.5 tvis= 108 yr

Clustering

SCUBA - QSO - EROs are subsequent stages inside large DM halos highly and similarly clustered.

Z 1.2

EROEROss

rr00 5-12 Mpc/h 5-12 Mpc/h(Daddi et al. 2003)

Z > 1.5

SCUBA galaxiesSCUBA galaxies

rr00= 8= 83 3 MpMpcc/h/h

(Smail et al. 2003)

Z 0

Bright Bright EllipticalsEllipticals

rr00= 8-11 Mpc/h= 8-11 Mpc/h(Norberg et al. 2003)

QSOsrr00 6.46.4 Mpc/h Mpc/h

(Grazian et al. 2004)

Conclusions (1)

• A simple physical recipe accounts for the observed galaxy & AGN “downsizing” in the framework of the standard hierarchical clustering scenario

• Key role played by SN and AGN feedback; the relative importance varies with Mh

• Faster and earlier evolution for more massive objects• Data consistent with basic galaxy and AGN properties

in large halos (Mh 2.5 1011 Msun) established at the virialization epoch; subsequent merging and baryon dissipation have apparently little effect

Conclusions (2)

• The model successfully reproduces:o the observational relationships between Mh, Mbulge,

and MBH

o the the galaxy velocity dispersion function and the fundamental plane relationships (Cirasuolo et al. 2005)

o the local BH mass function (Shankar et al. 2005a)o the galaxy and QSO epoch-dependent luminosity

functions in different bands

Conclusions (3)

•The model yields: o an extended dust-obscured phase of BH growtho a fast increase of the MBH/Mstar ratio in the pre-optical

QSO phase (cf. Borys et al. 2005)o mildly differential evolution of the LFo optical visibility time 1 e-folding timeo hard X-ray visibility time 3–4 e-folding timeso higher luminosity sources are less absorbed (cf. La

Franca et al. 2005)o high metallicity and -enhancement associated to high-

z quasars; metallicity increases with luminosity (cf. Roberto Maiolino’s talk)

Conclusions (4)o faster high-z decline of QSO luminosity density,

compared with SFRo MBH – Mstar and MBH – relations established at

high z in the optically bright QSO phase and unchanged during the subsequent passive evolution (ERO) phase

o a prolonged “starving” phase of massive BHs (low radiative/accretion efficiency, ADAF, C-DAF, ADIOS ...)

•Additional ingredients required for less massive halos, which evolve more slowly, are mostly associated with disk galaxies, and are found in lower density environments