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)

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M bh

Mhalo

=ε Mhalo

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

Mhalo

=ε Mhalo

1012

⎛ ⎝ ⎜

⎞ ⎠ ⎟23(1+ z)

52

€

M bh

Mhalo

=ε Mhalo

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

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LB = 5.73 ×1011η Mbh

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

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LB = 3.6 ×1011 εεSIS

⎛ ⎝ ⎜

⎞ ⎠ ⎟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 εεSIS

⎛ ⎝ ⎜

⎞ ⎠ ⎟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

Summary