The Black-Hole – Halo Mass Relation and High Redshift Quasars

1. 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 Black-Hole – Halo Mass Relation and High Redshift Quasars Stuart Wyithe Avi Loeb (The University of Melbourne) (Harvard University)

2. Black-Hole & Dark-Matter Halo Masses • 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. Ferrarese (2002)

3. How is the SMBH Related to its Host Halo at Larger Redshifts? • Both Mbh~vhalo5 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? Three assumptions: SMBH mass dependent on halo mass SMBH mass dependent on halo velocity

4. Quasars • 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.

5. The Quasar Correlation Function. • 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. Three assumptions:

6. 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)

7. Comparison with Observed Quasar Correlation Function Assuming Mbh ~ vhalo5 Croom et al. (2000,2001) Correlation Length • The correlation function is in agreement with quasars that shine near their limiting rate.

8. Evolution of Clustering Length With Redshift and Luminosity (Mbh~vhalo5) Preliminary SDSS data • Clustering increases with redshift in a flux limited sample. • More luminous samples are more highly clustered.

9. What if Mbh≈Mhalo2/3 With No Redshift Dependence? Preliminary SDSS data • Black-holes comprise a larger fraction of a galaxies mass at earlier times

10. The Correlation Length Favours Larger Mbh/Mhalo at High Redshift • No evolution in the Mbh-Mhalo relation implies Super-Eddington accretion at z~3

11. Summary • 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