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 v halo, and hence a relation between SMBH and dark matter halo mass. Black-Hole & Dark-Matter Halo Masses Ferrarese (2002)

Three assumptions: Both M bh ~v halo 5 and M bh ~M halo 5/3 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? 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

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 M bh -M halo 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.

Large Scale Distribution of Quasars From 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 M bh ~ v halo 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 (M bh ~v halo 5 ) More luminous samples are more highly clustered. Clustering increases with redshift in a flux limited sample. Preliminary SDSS data

What if M bh ≈M halo 2/3 With No Redshift Dependence? Black-holes comprise a larger fraction of a galaxies mass at earlier times Preliminary SDSS data

No evolution in the M bh -M halo relation implies Super-Eddington accretion at z~3 The Correlation Length Favours Larger M bh /M halo at High Redshift

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