ACCRETION MODELS FOR BLACK HOLE EVOLUTION

Francesco

ShankarIn collaboration with: D. Weinberg J. Miralda-Escude’ L. Ferrarese A. Cavaliere S. Mathur

CCAPP/OSU BH WORKSHOP 10/2/07

• EMPIRICALLY CONSTRAIN BLACK HOLE EVOLUTION IN A STATISTICAL SENSE

• WE USE: -LOCAL BH MASS FUNCTION -AGN BOL. LUMINOSITY FUNCTION - AGN CLUSTERING

GOAL:

TOOLS:

• For All relations convolve with an “intrinsic” scatter!

How many? How Much?How many? How Much?

Φ(L)→Φ(Lbulge)

MBH - Lbulge

Ф(MBH)

MBH - ()= (L) +L-

The Local Black Hole Mass Function

Systematic and shape uncertainties….

Log MPEAK~8.5

The Bolometric AGN Luminosity Function

Soltan argument

maxmax

min0

2

2

),()1(

)1(z

L

LBoltotal

ACCBH

ACCBolBol

dLzLc

L

dz

dtdzK

MM

cMKLL

Single object

maxmax

min0

2

232

2

),(4

)1()1(

)1()1()(

4),(),(

zS

S

Boltotal

A

LA

L

dSSzSnc

zdzc

K

zD

DzdtcDdV

D

LSdz

dz

dVdLzLdzdSzSn

independent of cosm. par. but very dependent on the ratio Kbol/ε !

SMBH from Merging/Dark Accretion or through Visible Accretion detected in the

AGN luminosity Functions?

Parallel growth of Stars and Black Holes

The ratio <MBH/MSTAR> probably was nearly constantat all times….

Soltan’s constraint: 0.055 < < 0.11

Shankar et al. 2007Shankar & Mathur 2007Shankar, Cavaliere et al. 2007

Varying the Reference Model…

Consequences on BH accretion…dm/dt(z)

dm/dt(MBH) Only works with P(z=6)~0.02 and Super-Edd accretion

Shankar & Ferrarese 2007

Bias in the MBH-n relation??

The Reference Model matches the Clustering of luminous AGNs

BHHALO M

BHBH

M

HALOHALO dMMndMMn )()(

CONCLUSIONS

0.06<<0.11

dm/dt~0.5

More Massive+Sub-EddLess Massive+Edd

Merging

+AGN LF

A Reference Model

CONCLUSIONS

• Normalization --> Radiative Efficiency

0.06<<0.11

• Peak+Clustering --> Edd. ratio of massive BHs dm/dt~0.5 probably

significantly decreasing at z<1

• High End --> Merging events NOT much

The Effect of Merging…

Negligible effect on accretion histories and duty cycles:

Further constraints from AGN BIAS

dMzMnzMPzL

dLzL

dLzLzMLbzb

AGN

L

L

MIN

MIN

),(),(),(

),(

),()],[()(

IDEA: Use the duty-cycles as produced from accretion

-Need to relate BHs to Dark Matter-Further independent test for accretion parameters

Shankar & Weinberg 2007

Varying the accretion rate: L~dm/dtMBH~MH

Remember: L~(dm/dt)MBH~MH

Shankar, Miralda-Escude’ et al. 2007

High Duty cycle at z~6 excluded by the bias…

Successful model:P(z=6)~0.5-1dm/dt~1STAR/Vvir~0.55-0.6

Data from Shen et al.

CONCLUSIONS

•Use of the Local Mass Function and AGN Luminosity Functions to constrain dm/dt and

•Use AGN clustering to constrain further duty-cycles and where Soltan is not sensitive and also probe dependencies on mass/luminosity of dm/dt

FOR THE FUTURE….even worse…

•Towards a multiple dm/dt…build a general P(dm/dt,z,MBH) to compare to the data

•Insert HOD models for AGNs, which could be derived from those of galaxies and apply our average P(M,t)…

Again Radio AGNs..Clustering useful here as well…

Shankar 2007

A sequence of very strong decreasing dm/dt can explain both Clustering and SED…

Changing the Luminosity Function of AGNs…

The Bolometric AGN Luminosity Function

i i

ii aaaxyy2

2321

22 ,....),,;(

BH

A First Estimate of Clustering:The Space Density of AGNs Hosts!

Here I am using an empirical relation calibratedwith a one-to-one approximation…

The Soltan argument can also be applied toRadio AGNs only…

Shankar, Cavaliere et al. 2007

Lradio~fradioLkin

Lkin ~fkinLL~dm/dt c2

Constrain the relation between Luminosity and halo mass…

Independent of duty-cycleIt can give “hints” on the best relation between MBH and MH

Which fits the bias…But then take care to fit the LF!!

MIN

MIN

L

L

dLzL

dLzLzMLbzb

),(

),()],[()(

Shankar & Weinberg 2007

Further constraints from AGN BIAS

MIN

MIN

MIN

MIN

MIN

MH

MH

MAGN

L

L

zMtdMzMnzMtdMzMnzMb

zb

dMzMnzMPz

dLzL

dLzLzMLbzb

),(),(

),(),(),(

)(

),(),()(

),(

),()],[()(

IDEA: Use the duty-cycles as produced from accretion

-Need to relate BHs to Dark Matter-Further independent test for accretion parameters

Shankar & Weinberg 2007

Massive Dark Objects observed in all bulged-galaxies strong link with the host spheroid M/n/

What are MDOs? How and why are they connected with spheroids and DM? What is their role in shaping galaxies?

Marconi & HuntMBHRe2

Log MBH~0.25 dex

VC+DM profile VVIR(zvir=0)(Mvir )1/3

=kVc

+

The XRBG is mostly made of..AGNs!!!

Evolving the black hole Accreted Mass Function….

dM

dL

zMn

zLtMP

mtMPtMtm

tt

MtmtMttM

MlmmcML

jjj

s

),(

),(~),(

),(),()(

)()()(

)(1.02

insert and dm/dt

evolve masses at each timestep

average rate proportionalto “probability”

“probability” given bythe fraction of active BHs

Require initial duty-cycle but at z<3.5 mass functionRequire initial duty-cycle but at z<3.5 mass functionevolves INDEPENDENT of the ansatz…evolves INDEPENDENT of the ansatz…