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Register a new userBeyond the Bulge: a Fundamental Relation Between Supermassive Black Holes and Dark Matter Halos
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Authors
Laura Ferrarese
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The possibility that the masses of supermassive black holes (SBHs) correlate with the total gravitational mass of their host galaxy, or the mass of the dark matter halo in which they presumably formed, is investigated using a sample of 16 spiral and 20 elliptical galaxies. The bulge velocity dispersion, typically defined within an aperture of size less than 0.5 kpc, is found to correlate tightly with the galaxys circular velocity, the latter measured at distances from the galactic center at which the rotation curve is flat, 20 to 80kpc. By using the well known M-sigma relation for SBHs, and a prescription to relate the circular velocity to the mass of the dark matter halo in a standard CDM cosmology, the correlation between velocity dispersion and circular velocity is equivalent to one between SBH and halo masses. Such a correlation is found to be nonlinear, with the ratio between the two masses decreasing from 2X10^-4 for halos of 10^14 solar masses, to 10^-5 for halos of 10^12 solar masses. Preliminary evidence suggests that halos smaller than ~5X10^11 solar masses are increasingly less efficient -- perhaps unable -- at forming SBHs.
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We study the relations between the mass of the central black hole (BH) $M_{rm BH}$, the dark matter halo mass $M_{rm h}$, and the stellar-to-halo mass fraction $f_starpropto M_star/M_{rm h}$ in a sample of $55$ nearby galaxies with dynamically measured $M_{rm BH}>10^6,{rm M}_odot$ and $M_{rm h}>5times10^{11},{rm M}_odot$. The main improvement with respect to previous studies is that we consider both early- and late-type systems for which $M_{rm h}$ is determined either from globular cluster dynamics or from spatially resolved rotation curves. Independently of their structural properties, galaxies in our sample build a well defined sequence in the $M_{rm BH}$-$M_{rm h}$-$f_star$ space. We find that: (i) $M_{rm h}$ and $M_{rm BH}$ strongly correlate with each other and anti-correlate with $f_star$; (ii) there is a break in the slope of the $M_{rm BH}$-$M_{rm h}$ relation at $M_{rm h}$ of $10^{12},{rm M}_odot$, and in the $f_star$-$M_{rm BH}$ relation at $M_{rm BH}$ of $sim10^7!-!10^8,{rm M}_odot$; (iii) at a fixed $M_{rm BH}$, galaxies with a larger $f_star$ tend to occupy lighter halos and to have later morphological types. We show that the observed trends can be reproduced by a simple equilibrium model in the $Lambda$CDM framework where galaxies smoothly accrete dark and baryonic matter at a cosmological rate, having their stellar and black hole build-up regulated both by the cooling of the available gas reservoir and by the negative feedback from star formation and active galactic nuclei (AGN). Feature (ii) arises as the BH population transits from a rapidly accreting phase to a more gentle and self-regulated growth, while scatter in the AGN feedback efficiency can account for feature (iii).
We study observed correlations between supermassive black hole (BHs) and the properties of their host galaxies, and show that the observations define a BH fundamental plane (BHFP), of the form M_BH sigma^(3.0+-0.3)*R_e^(0.43+-0.19), or M_BH M_bulge^(0.54+-0.17)*sigma^(2.2+-0.5), analogous to the FP of elliptical galaxies. The BHFP is preferred over a simple relation between M_BH and any of sigma, M_bulge, M_dyn, or R_e alone at >99.9% significance. The existence of this BHFP has important implications for the formation of supermassive BHs and the masses of the very largest black holes, and immediately resolves several apparent conflicts between the BH masses expected and measured for outliers in both the M_BH-sigma and M_BH-M_bulge relations.
We analyze the intriguing possibility to explain both dark mass components in a galaxy: the dark matter (DM) halo and the supermassive dark compact object lying at the center, by a unified approach in terms of a quasi-relaxed system of massive, neutral fermions in general relativity. The solutions to the mass distribution of such a model that fulfill realistic halo boundary conditions inferred from observations, develop a highly-density core supported by the fermion degeneracy pressure able to mimic massive black holes at the center of galaxies. Remarkably, these dense core-diluted halo configurations can explain the dynamics of the closest stars around Milky Ways center (SgrA*) all the way to the halo rotation curve, without spoiling the baryonic bulge-disk components, for a narrow particle mass range $mc^2 sim 10$-$10^2$~keV.
Observational studies of nearby galaxies have demonstrated correlations between the mass of the central supermassive black holes (BHs) and properties of the host galaxies, notably the stellar bulge mass or central stellar velocity dispersion. Motivated by these correlations, the theoretical paradigm has emerged, in which BHs and bulges co-evolve. However, this picture was challenged by observational and theoretical studies, which hinted that the fundamental connection may be between BHs and dark matter halos, and not necessarily with their host galaxies. Based on a study of 3130 elliptical galaxies $-$ selected from the Sloan Digital and ROSAT All Sky Surveys $-$ we demonstrate that the central stellar velocity dispersion exhibits a significantly tighter correlation with the total gravitating mass, traced by the X-ray luminosity of the hot gas, than with the stellar mass. This hints that the central stellar velocity dispersion, and hence the central gravitational potential, may be the fundamental property of elliptical galaxies that is most tightly connected to the larger-scale dark matter halo. Furthermore, using the central stellar velocity dispersion as a surrogate for the BH mass, we find that in elliptical galaxies the inferred BH mass and inferred total gravitating mass within the virial radius (or within five effective radii) can be expressed as $M_{rm{BH}} propto M_{rm tot}^{1.6^{+0.6}_{-0.4}} $ (or $M_{rm{BH}} propto M_{rm{5r_{eff}}}^{1.8^{+0.7}_{-0.6}}$). These results are consistent with a picture in which the BH mass is directly set by the central stellar velocity dispersion, which, in turn, is determined by the total gravitating mass of the system.
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