Towards an understanding of the evolution of the scaling relations for supermassive black holes

It has long been recognised that the growth of BHs is likely self-regulated (Silk & Rees 1998) and that these tight correlations indicate that the growth of BHs is tightly intertwined with the physical processes that drive galaxy for-⋆ E-mail: booth@strw.leidenuniv.nl (CMB) mation. However, despite a wide variety of theoretical and observational studies, the origin of these relations is still debated. The study of the evolution of the BH scaling relations therefore represents a crucial aspect of the galaxy formation process that may provide us with additional clues regarding the physical processes that give rise to the BH scaling relations.

Addressing these questions observationally is challenging. Due to their extremely high luminosities, bright quasars provide a promising route to measuring BH masses at high redshift through the widths of low-ionization lines that are associated with the broad-line region close to the BH and using the assumption of virial equilibrium (e.g. Vestergaard 2002). It has, however, been claimed that this procedure systematically underestimates BH masses (Jarvis & McLure 2002). Measuring galaxy masses for these objects is very difficult as the BH outshines the galaxy by a large factor (see e.g. the discussion in Merloni et al. 2010). Since AGN surveys are biased towards more massive black holes, selection effects also need to be taken into account (e.g. Shen & Kelly 2009;Bennert et al. 2010), which can make it difficult to distinguish between evolution in the normalization and in the scatter in the scaling relations (Lauer et al. 2007). In spite of these difficulties, measurements of the BH scaling relations have been made as far out as redshift three. McLure et al. (2006) found that the BHs associated with radio loud AGN residing in galaxies of a given stellar mass are a factor of four more massive at redshift two than in the local Universe. Decarli et al. (2010) studied the C IV line associated with the quasar broad line region in R-band selected hosts at both redshifts zero and three and found that BHs are typically a factor of seven more massive at high redshift for a given galaxy mass. These results are consistent with other observational studies (Walter et al. 2004;Peng et al. 2006a,b;Merloni et al. 2010;Greene et al. 2010;Bennert et al. 2010). Taken together, these papers suggest an emerging consensus that at higher redshift BHs in hosts of a given mass are systematically more massive than in the local Universe, although see Jahnke et al. (2009) for one study that finds no significant evolution.

The evolution of the relation between BH mass, mBH, and stellar velocity dispersion, σ * , has been studied utilising the width of the O III line as a proxy for stellar velocity dispersion (Nelson & Whittle 1996). These studies suggest that the mBHσ * relation either does not evolve (Shields et al. 2003;Gaskell 2009), or does so weakly, with BHs ∼ 0.1-0.3 dex more massive at z = 1 (Salviander et al. 2006;Gu et al. 2009;Woo et al. 2008;Treu et al. 2007).

The evolution of the BH scaling relations has also been studied using numerical simulations (e.g. Robertson et al. 2006;Johansson et al. 2009) and semi-analytic models (e.g. Malbon et al. 2007;Lamastra et al. 2010;Kisaka & Kojima 2010). Robertson et al. (2006) employed simulations of idealised galaxy mergers, initialised to have properties typical of merger progenitors at various redshifts, to construct the relation between galaxy stellar mass, m * , and σ * as a function of redshift and found that, at a given value of σ * , the corresponding mBH decreases mildly with increasing redshift. At z = 1 the simulations of Di Matteo et al. (2008) have BHs that lie slightly above the z = 0 normalization of the mBHσ relation. However, these simulations were stopped at z = 1 and so cannot inform us about the evolution of the mBHσ * toward lower redshift. However, for z > 1 they predict a weak evolution in the mBH -σ * relation such that at higher redshift galaxies of a given velocity dispersion contain slightly less massive BHs. Johansson et al. (2009) employed similar numerical techniques to argue that it is unlikely that BHs are able to form significantly before their host bulges. Semi-anal

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