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Register a new userAn Observed Fundamental Plane Relation for Supermassive Black Holes
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Philip F. Hopkins
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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.
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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.
Supermassive black holes have generally been recognized as the most destructive force in nature. But in recent years, they have undergone a dramatic shift in paradigm. These objects may have been critical to the formation of structure in the early universe, spawning bursts of star formation and nucleating proto-galactic condensations. Possibly half of all the radiation produced after the Big Bang may be attributed to them, whose number is now known to exceed 300 million. The most accessible among them is situated at the Center of Our Galaxy. In the following pages, we will examine the evidence that has brought us to this point, and we will understand why many expect to actually image the event horizon of the Galaxys central black hole within this decade.
We investigate the correlations between the black hole mass $M_{BH}$, the velocity dispersion $sigma$, the bulge mass $M_{Bu}$, the bulge average spherical density $rho_h$ and its spherical half mass radius $r_h$, constructing a database of 97 galaxies (31 core ellipticals, 17 power-law ellipticals, 30 classical bulges, 19 pseudo bulges) by joining 72 galaxies from the literature to 25 galaxies observed during our recent SINFONI black hole survey. For the first time we discuss the full error covariance matrix. We analyse the well known $M_{BH}-sigma$ and $M_{BH}-M_{Bu}$ relations and establish the existence of statistically significant correlations between $M_{Bu}$ and $r_h$ and anti-correlations between $M_{Bu}$ and $rho_h$. We establish five significant bivariate correlations ($M_{BH}-sigma-rho_h$, $M_{BH}-sigma-r_h$, $M_{BH}-M_{Bu}-sigma$, $M_{BH}-M_{Bu}-rho_h$, $M_{BH}-M_{Bu}-r_h$) that predict $M_{BH}$ of 77 core and power-law ellipticals and classical bulges with measured and intrinsic scatter as small as $approx 0.36$ dex and $approx 0.33$ dex respectively, or 0.26 dex when the subsample of 45 galaxies defined by Kormendy and Ho (2013) is considered. In contrast, pseudo bulges have systematically lower $M_{BH}$, but approach the predictions of all the above relations at spherical densities $rho_hge 10^{10} M_odot/kpc^3$ or scale lengths $r_hle 1$ kpc. These findings fit in a scenario of co-evolution of BH and classical-bulge masses, where core ellipticals are the product of dry mergers of power-law bulges and power-law Es and bulges the result of (early) gas-rich mergers and of disk galaxies. In contrast, the (secular) growth of BHs is decoupled from the growth of their pseudo bulge hosts, except when (gas) densities are high enough to trigger the feedback mechanism responsible for the existence of the correlations between $M_{BH}$ and galaxy structural parameters.
We perform a detailed study of the location of brightest cluster galaxies (BCGs) on the fundamental plane of black hole (BH) accretion, which is an empirical correlation between a BH X-ray and radio luminosity and mass supported by theoretical models of accretion. The sample comprises 72 BCGs out to $zsim0.3$ and with reliable nuclear X-ray and radio luminosities. These are found to correlate as $L_mathrm{X} propto L_mathrm{R}^{0.75 pm 0.08}$, favoring an advection-dominated accretion flow as the origin of the X-ray emission. BCGs are found to be on average offset from the fundamental plane such that their BH masses seem to be underestimated by the $M_mathrm{BH}-M_mathrm{K}$ relation a factor $sim$10. The offset is not explained by jet synchrotron cooling and is independent of emission process or amount of cluster gas cooling. Those core-dominated BCGs are found to be more significantly offset than those with weak core radio emission. For BCGs to on average follow the fundamental plane, a large fraction ($sim40%$) should have BH masses $> 10^{10}$ M$_{odot}$ and thus host ultramassive BHs. The local BH-galaxy scaling relations would not hold for these extreme objects. The possible explanations for their formation, either via a two-phase process (the BH formed first, the galaxy grows later) or as descendants of high-z seed BHs, challenge the current paradigm of a synchronized galaxy-BH growth.
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