The Black-Hole – Halo Mass Relation and High Redshift Quasars Stuart Wyithe Avi Loeb (The University of Melbourne) (Harvard Fan et al. (2001) -SMBHs and dark matter halos -SMBHs and quasars -The quasar correlation function -Extending the SMBH -- halo relation to earlier times. Is dark matter halo mass or velocity more important for formation?
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The Black-Hole – Halo Mass Relation and High Redshift Quasars Stuart Wyithe Avi Loeb (The University of Melbourne) (Harvard University) Fan et al. (2001)
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The Black-Hole – Halo Mass Relation and High
Redshift Quasars
Stuart Wyithe Avi Loeb (The University of Melbourne) (Harvard University)
Fan et al. (2001)
-SMBHs and dark matter halos
-SMBHs and quasars
-The quasar correlation function
-Extending the SMBH -- halo relation to earlier times. Is dark matter halo mass or velocity more important for formation?
• The bulges of all local galaxies contain SMBHs.
• There is a tight relation between and SMBH mass (e.g. Merritt & Ferrarese 2001; Tremaine et al.
2002).
• There is a relation between and vhalo, and hence a relation between SMBH and dark matter halo mass.
Black-Hole & Dark-Matter Halo Masses
Ferrarese (2002)
€
M bh
M halo
=ε M halo
1012Mother
⎛
⎝ ⎜
⎞
⎠ ⎟
2 / 3
€
Mbh = 1.9 × 108 vhalo
350km/s
⎛
⎝ ⎜
⎞
⎠ ⎟5
Msolar
€
εSIS =10−5.8
εNFW =10−5.2
Three assumptions:• Both Mbh~vhalo
5 and Mbh~Mhalo5/3 valid at z=0.
• At higher redshift, galaxies form out of a denser background, have a larger binding energy per unit mass, and therefore a larger circular velocity.
• Is halo mass or velocity the determining factor?
How is the SMBH Related to its Host Halo at Larger Redshifts?
€
M bh
M halo
=ε M halo
1012
⎛ ⎝ ⎜
⎞ ⎠ ⎟
23(1+ )z
52
€
M bh
M halo
=ε M halo
1012
⎛ ⎝ ⎜
⎞ ⎠ ⎟
23
SMBH mass dependent on halo mass
SMBH mass dependent on halo velocity
• Quasars are powered by accretion onto a SMBH.
• The velocity dispersion -- SMBH mass relation is also seen in quasars. (e.g. McLure & Dunlop 2002)
• Accretion is near the Eddington Rate. (e.g. Willott et al. 2003; Elvis et al. 1994)
Boyle et al. (2000)
• Quasars offer a pointer to the evolution of the SMBH population to z~6.
Quasars
€
LB = 5.73×1011ηMbh
108Msolar
⎛
⎝ ⎜
⎞
⎠ ⎟LB ,solar
Three assumptions:• The quasar correlation function measures, as a function of distance R, the excess probability above random that two quasars will be separated by R.
• Larger halos are more highly clustered.
• The Mbh-Mhalo relation, and accretion at the Eddington rate relate luminosity to halo mass; and therefore the quasar correlation function to the dark matter halo correlation function.
The Quasar Correlation Function.
€
LB = f (Mhalo)
€
ξ R,Mhalo,z( )⇒ ξ R,mB ,z( )
€
mB = f (LB ,z)
Large Scale Distribution of QuasarsFrom the 2dF Quasar Redshift Survey
• Redshifts for 25,000 quasars in two strips.
• The correlation function tests the relation between luminosity and halo mass.
Croom et al. (2000,2001)
Comparison with Observed Quasar Correlation Function Assuming Mbh ~ vhalo
5
• The correlation function is in agreement with quasars that shine near their limiting rate.
Correlation Length
Croom et al. (2000,2001)
Evolution of Clustering Length With Redshift and Luminosity (Mbh~vhalo
5)
• More luminous samples are more highly clustered.
• Clustering increases with redshift in a flux limited sample.
Preliminary SDSS data
What if Mbh≈Mhalo2/3 With No Redshift
Dependence?
• Black-holes comprise a larger fraction of a galaxies mass at earlier times
Preliminary SDSS data
€
LB = 3.6 ×1011 ε
εSIS
⎛
⎝ ⎜
⎞
⎠ ⎟η med
Mhalo
1012
⎛
⎝ ⎜
⎞
⎠ ⎟5 / 3
1+ z
4
⎛
⎝ ⎜
⎞
⎠ ⎟5 / 2
• No evolution in the Mbh-Mhalo relation implies Super-Eddington accretion at z~3
€
LB = 3.6 ×1011 ε
εSIS
⎛
⎝ ⎜
⎞
⎠ ⎟η med
Mhalo
1012
⎛
⎝ ⎜
⎞
⎠ ⎟5 / 3
The Correlation Length Favours Larger Mbh/Mhalo at High Redshift
€
ε εSIS( )η med
€
εSIS =10−5.8
εNFW =10−5.2
• The quasar clustering length and its evolution with redshift and luminosity are reproduced if SMBH mass scales only with halo circular velocity.
• The evolution of the clustering length is too rapid if SMBH mass scales only with halo mass.
• This may imply that the mass of a SMBH is regulated by the depth of the potential well of the galaxy.
Black-holes comprise a larger fraction of a galaxies mass at high redshift