Abstract
Abstract It is now well established that many galaxies have nuclear star clusters (NCs) whose total masses correlate with the velocity dispersion σ of the galaxy spheroid in a very similar way to the well-known supermassive black hole (SMBH) M−σ relation. Previous theoretical work suggested that both correlations can be explained by a momentum feedback argument. Observations further show that most known NCs have masses ≲108 M⊙, while SMBHs frequently have measured masses ≳108 M⊙, which remained unexplained in earlier treatments. We suggest here that this changeover reflects a competition between the SMBH and nuclear clusters in the feedback they produce. When one of the massive objects reaches its limiting M−σ value, it drives the gas away and hence cuts off its own mass and also the mass of the ‘competitor’. The latter is then underweight with respect to the expected M−σ mass. More specifically, we find that the bulge dynamical time-scale is a steeply rising function of velocity dispersion, and that the NC–SMBH changeover occurs where the dynamical time is about equal to the Salpeter time. We propose that SMBHs, growing on the Salpeter time-scale, are unable to reach their M−σ mass quickly enough in small bulges. The central regions of these bulges are swamped with gas which fragments into stars, creating the nuclear clusters. The latter then limit their own growth by the feedback they produce, settling on their (offset) M−σ relation. The SMBH in such bulges should be underweight as their growth is curtailed before they reach the M−σ mass. In large bulges, on the other hand, the SMBH catches up quickly enough to settle on its M−σ relation. Nuclear star clusters may also exist in such bulges but they should be underweight with respect to their M−σ sequence.
Highlights
It is well known that the masses of the supermassive black holes (SMBHs) in the nuclei of early-type galaxies and bulges correlate with the velocity dispersions of the stellar spheroids (e.g. Ferrarese & Merritt 2000; Gebhardt et al 2000; Tremaine et al 2002)
SMBH growth is limited by the Eddington accretion rate, M Edd = LEdd/( c2), where ∼ 0.1 is the radiative efficiency of accretion
We have seen that momentum feedback gives a simple physical explanation of why galaxy bulges are dominated by nuclear clusters for low velocity dispersions and by SMBHs for high dispersions
Summary
It is well known that the masses of the supermassive black holes (SMBHs) in the nuclei of early-type galaxies and bulges correlate with the velocity dispersions of the stellar spheroids (e.g. Ferrarese & Merritt 2000; Gebhardt et al 2000; Tremaine et al 2002). McLaughlin, King & Nayakshin (2006) proposed that the observed MNC−σ relation for dwarf elliptical galaxies follows naturally from an extension of the above argument (King 2003, 2005) to the outflows from young star clusters containing massive stars These individual stars are Eddington limited, and produce outflows with momentum outflow rate ∼LEdd/c where LEdd is calculated from the star’s mass. Milosavljevic (2004) argues against this possibility due to the short time-scales available for this process, and argues instead that these clusters may form in situ We agree with this point, and further note that observations of young massive stars in the central parsec of the Milky Way offer direct support to the in situ formation model (Nayakshin & Cuadra 2005; Paumard et al 2006; Nayakshin & Sunyaev 2005). The exact geometrical arrangement of the forming stars (a thick disc or a quasi-spherical cluster) is irrelevant on the scales of the parent galaxy
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