ACCRETION MODELS FOR
BLACK HOLE EVOLUTION
In collaboration with:
D. Weinberg
J. Miralda-Escude’
L. Ferrarese
A. Cavaliere
S. Mathur
Francesco Shankar
CCAPP/OSU BH WORKSHOP
10/2/07
GOAL:
•
EMPIRICALLY CONSTRAIN
BLACK HOLE EVOLUTION IN A
STATISTICAL SENSE
TOOLS:
•
WE USE:
-LOCAL BH MASS FUNCTION
-AGN BOL. LUMINOSITY FUNCTION
- AGN
CLUSTERING
How many? How Much?
MBH - Lbulge
Φ(L)→Φ(Lbulge)
()= (L) +L-
Ф(MBH)
MBH - 
• For All relations convolve with an
“intrinsic” scatter!
The Local Black Hole Mass Function
Log MPEAK~8.5
Systematic and shape uncertainties….
The Bolometric AGN Luminosity Function

SMBH from Merging/Dark Accretion or
through Visible Accretion detected in the
AGN luminosity Functions?
Soltan
argument
2

LBol  L  K Bol   M
ACC c


M
BH  (1   ) M ACC
 total  K Bol
z max

dz
0
dt
dz

Lmax
Lmin
Single object
(1   ) L
 ( L, z ) dL
2
c

dV
L 
n( S , z ) dS dz   ( L, z ) dL
dz  S 
2
dz
4

D
L 

DL
dV  ( DA2 c dt ) (1  z ) 3
 (1  z ) 2
DA
K (1   )
 total  Bol 2
c
z max

0
dz (1  z )

S max
S min
4
n ( S , z ) S dS
c
independent of cosm. par. but very
dependent on the ratio Kbol/ε !
Parallel growth of Stars and Black Holes
Soltan’s constraint: 0.055 <  < 0.11
The ratio <MBH/MSTAR> probably was nearly constant
at all times….
Shankar et al. 2007
Shankar & Mathur 2007
Shankar, 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
Bias in the MBH-n relation??
Shankar & Ferrarese 2007
The Reference Model matches
the Clustering of luminous AGNs

 n( M
M HALO

HALO
)dM HALO 
 n( M
M BH
BH
)dM BH
CONCLUSIONS
0.06<<0.11
More Massive+Sub-Edd
Less Massive+Edd
dm/dt~0.5
+AGN LF
Merging
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

b ( z) 

LMIN
b( L[ M ], z ) ( L, z )dL


LMIN
 ( L, z )dL
-Need to relate BHs to
Dark Matter
-Further independent test
for accretion parameters
 AGN ( L, z )  P( M , z )n( M , z )dM
IDEA: Use the duty-cycles
as produced from accretion
Shankar & Weinberg 2007
Varying the accretion rate: L~dm/dtMBH~MH
Remember: L~(dm/dt)MBH~MH
High Duty cycle at z~6 excluded by the bias…
Successful model:
P(z=6)~0.5-1
dm/dt~1
STAR/Vvir~0.55-0.6
Data from Shen et al.
Shankar, Miralda-Escude’ et al. 2007
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…
A sequence of very strong decreasing dm/dt can explain both Clustering and SED…
Shankar 2007
Changing the Luminosity Function of AGNs…
The Bolometric AGN Luminosity Function
2

yi  y( xi ; a1 , a2 , a3 ,....)
2
 


i2
i
2

BH
A First Estimate of Clustering:
The Space Density of AGNs Hosts!
Here I am using an empirical relation calibrated
with a one-to-one approximation…
Lradio~fradioLkin
Lkin ~fkinL
L~dm/dt c2
The Soltan argument can also be applied to
Radio AGNs only…
Shankar, Cavaliere et al. 2007
Constrain the relation between
Luminosity and halo mass…
Independent of duty-cycle
It can give “hints” on the best relation between MBH and MH
Which fits the bias…
But then take care to fit the LF!!


b ( z) 
LMIN
Shankar & Weinberg 2007
b( L[ M ], z )( L, z )dL


LMIN
( L, z )dL
Further constraints from AGN BIAS

b ( z) 

LMIN
b( L[ M ], z ) ( L, z )dL


LMIN
 AGN ( z )  

M MIN
 ( L, z )dL
P ( M , z )n( M , z )dM

b( M , z )n( M , z )dM
M MIN
tH (M , z)
b ( z) 

n( M , z )dM
M MIN t H (M , z )
IDEA: Use the duty-cycles
as produced from accretion
Shankar & Weinberg 2007
-Need to relate BHs to
Dark Matter
-Further independent test
for accretion parameters
Massive Dark Objects  observed in all bulged-galaxies
 strong link with the host spheroid M/n/
Marconi & Hunt
MBHRe2
Log MBH~0.25 dex
=kVc
+
VC+DM profile 
VVIR(zvir=0)(Mvir )1/3
What are MDOs? How and why are they
connected with spheroids and DM? What is
their role in shaping galaxies?
The XRBG is mostly made of..AGNs!!!
Evolving the black hole
Accreted Mass Function….
insert  and dm/dt
 c 2   (m
 )m
 Ml
L  M
0 .1
evolve masses at each
timestep
M
 (t )
M (t  t )  M (t )  m
t
ts
average rate proportional
to “probability”
“probability” given by
the fraction of active BHs
 (t ) ( M , t )   Pj ( M , t ) m
j
m
j
 ( L, z ) dL
P( M , t ) ~
n( M , z ) dM
Require initial duty-cycle but at z<3.5 mass function
evolves INDEPENDENT of the ansatz…