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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
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• EMPIRICALLY CONSTRAIN BLACK HOLE EVOLUTION IN A STATISTICAL SENSE
• WE USE: -LOCAL BH MASS FUNCTION -AGN BOL. LUMINOSITY FUNCTION - AGN CLUSTERING
GOAL:
TOOLS:
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• 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-
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The Local Black Hole Mass Function
Systematic and shape uncertainties….
Log MPEAK~8.5
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The Bolometric AGN Luminosity Function
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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?
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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
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Varying the Reference Model…
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Consequences on BH accretion…dm/dt(z)
dm/dt(MBH) Only works with P(z=6)~0.02 and Super-Edd accretion
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Shankar & Ferrarese 2007
Bias in the MBH-n relation??
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The Reference Model matches the Clustering of luminous AGNs
BHHALO M
BHBH
M
HALOHALO dMMndMMn )()(
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CONCLUSIONS
0.06<<0.11
dm/dt~0.5
More Massive+Sub-EddLess Massive+Edd
Merging
+AGN LF
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A Reference Model
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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
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The Effect of Merging…
Negligible effect on accretion histories and duty cycles:
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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
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Varying the accretion rate: L~dm/dtMBH~MH
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Remember: L~(dm/dt)MBH~MH
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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.
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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)…
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Again Radio AGNs..Clustering useful here as well…
Shankar 2007
A sequence of very strong decreasing dm/dt can explain both Clustering and SED…
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Changing the Luminosity Function of AGNs…
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The Bolometric AGN Luminosity Function
i i
ii aaaxyy2
2321
22 ,....),,;(
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BH
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A First Estimate of Clustering:The Space Density of AGNs Hosts!
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Here I am using an empirical relation calibratedwith a one-to-one approximation…
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The Soltan argument can also be applied toRadio AGNs only…
Shankar, Cavaliere et al. 2007
Lradio~fradioLkin
Lkin ~fkinLL~dm/dt c2
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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
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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
![Page 31: ACCRETION MODELS FOR BLACK HOLE EVOLUTION Francesco Shankar In collaboration with: D. Weinberg J. Miralda-Escude’ L. Ferrarese A. Cavaliere S. Mathur CCAPP/OSU](https://reader030.vdocuments.net/reader030/viewer/2022032523/56649d775503460f94a5a012/html5/thumbnails/31.jpg)
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
+
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The XRBG is mostly made of..AGNs!!!
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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…