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Register a new userThe slope of the black-hole mass versus velocity dispersion correlation
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Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object M and the velocity dispersion sigma of the host galaxy, of the form log(M/M_sun) = a + b*log(sigma/sigma_0); however, published estimates of the slope b span a wide range (3.75 to 5.3). Merritt & Ferrarese have argued that low slopes (<4) arise because of neglect of random measurement errors in the dispersions and an incorrect choice for the dispersion of the Milky Way Galaxy. We show that these explanations account for at most a small part of the slope range. Instead, the range of slopes arises mostly because of systematic differences in the velocity dispersions used by different groups for the same galaxies. The origin of these differences remains unclear, but we suggest that one significant component of the difference results from Ferrarese & Merritts extrapolation of central velocity dispersions to r_e/8 (r_e is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the measurements. A new determination of the slope using 31 galaxies yields b=4.02 +/- 0.32, a=8.13 +/- 0.06, for sigma_0=200 km/s. The M-sigma relation has an intrinsic dispersion in log M that is no larger than 0.3 dex. In an Appendix, we present a simple model for the velocity-dispersion profile of the Galactic bulge.
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The recent discovery of a correlation between nuclear black hole mass, M_bh, and the stellar velocity dispersion (Gebhardt et al. 2000, Ferrarese and Merritt 2000), in elliptical galaxies and spiral bulges, has raised the question whether such a relationship exists for AGN. Estimates of M_bh for many AGN, made using reverberation mapping techniques, allow exploration of the relationship between black hole mass, the host galaxy and the energetics of nuclear emission. However, since only a few AGN have both M_bh and velocity dispersion measurements, we use the [OIII] 5007 emission line widths on the assumption that for most AGN the forbidden line kinematics are dominated by virial motion in the host galaxy bulge. We find that a relation does exist between M_bh and [OIII] line width for AGN which is similar to the one found by Gebhardt et al. 2000, although with more scatter as expected if secondary influences on the gas kinematics are also present. Our conclusion is that both active and inactive galaxies follow the same relationship between black hole mass and bulge gravitational potential. We find no compelling evidence for systematic differences in the mass estimates from reverberation mapping and stellar dynamics. We also find that for radio quiet AGN the radio power and black hole mass are highly correlated linking emission on scales of kiloparsecs with the nuclear energy source.
We describe a correlation between the mass M_BH of a galaxys central black hole and the luminosity-weighted line-of-sight velocity dispersion sigma_e within the half-light radius. The result is based on a sample of 26 galaxies, including 13 galaxies with new determinations of black hole masses from Hubble Space Telescope measurements of stellar kinematics. The best-fit correlation is M_BH = 1.2 (+-0.2) x 10^8 M_sun (sigma_e/200 km/s)^(3.75 (+-0.3))over almost three orders of magnitude in M_BH; the scatter in M_BH at fixed sigma_e is only 0.30 dex and most of this is due to observational errors. The M_BH-sigma_e relation is of interest not only for its strong predictive power but also because it implies that central black hole mass is constrained by and closely related to properties of the host galaxys bulge.
The correlation between black hole mass M(BH) and stellar velocity dispersion sigma in nearby elliptical galaxies affords a novel way to determine M(BH) in active galaxies. We report on measurements of sigma from optical spectra of 7 BL Lac host galaxies. The derived values of sigma are in the range of 160 - 290 km/s corresponding to M(BH) of 5 x 10^7 to 1 x 10^9 Msun. The average ratio of M(BH) to the host galaxy mass is 1.4 x 10^-3, consistent with that estimated in other active and inactive galaxies. The velocity dispersions and the derived values of M(BH) of the BL Lacs are similar to those obtained for low redshift radio galaxies, in good agreement with the predictions of the unified models for radio-loud active galaxies.
Observational data show that the correlation between supermassive black holes (MBH) and galaxy bulge (Mbulge) masses follows a nearly linear trend, and that the correlation is strongest with the bulge rather than the total stellar mass (Mgal). With increasing redshift, the ratio Gamma=MBH/Mbulge relative to z=0 also seems to be larger for MBH >~ 10^{8.5} Msol. This study looks more closely at statistics to better understand the creation and observations of the MBH-Mbulge correlation. It is possible to show that if galaxy merging statistics can drive the correlation, minor mergers are responsible for causing a *convergence to linearity* most evident at high masses, whereas major mergers have a central limit convergence that more strongly *reduces the scatter*. This statistical reasoning is agnostic about galaxy morphology. Therefore, combining statistical prediction (more major mergers ==> tighter correlation) with observations (bulges = tightest correlation), would lead one to conclude that more major mergers (throughout an entire merger tree, not just the primary branch) give rise to more prominent bulges. With regard to controversial findings that Gamma increases with redshift, this study shows why the luminosity function (LF) bias argument, taken correctly at face value, strengthens rather than weakens the results. However, correcting for LF bias is unwarranted because the BH mass scale for quasars is bootstrapped to the MBH-Sigma* correlation in normal galaxies at z=0, and quasar-quasar comparisons are internally consistent. In Monte-Carlo simulations, high Gamma objects are under-merged galaxies that take longer to converge to linearity via minor mergers. Another evidence that the galaxies are undermassive at z >~ 2 for their MBH is that the quasar hosts are very compact for their expected mass.
We investigate a mechanism for a super-massive black hole at the center of a galaxy to wander in the nucleus region. A situation is supposed in which the central black hole tends to move by the gravitational attractions from the nearby molecular clouds in a nuclear bulge but is braked via the dynamical frictions by the ambient stars there. We estimate the approximate kinetic energy of the black hole in an equilibrium between the energy gain rate through the gravitational attractions and the energy loss rate through the dynamical frictions, in a nuclear bulge composed of a nuclear stellar disk and a nuclear stellar cluster as observed from our Galaxy. The wandering distance of the black hole in the gravitational potential of the nuclear bulge is evaluated to get as large as several 10 pc, when the black hole mass is relatively small. The distance, however, shrinks as the black hole mass increases and the equilibrium solution between the energy gain and loss disappears when the black hole mass exceeds an upper limit. As a result, we can expect the following scenario for the evolution of the black hole mass: When the black hole mass is smaller than the upper limit, mass accretion of the interstellar matter in the circum-nuclear region, causing the AGN activities, makes the black hole mass larger. However, when the mass gets to the upper limit, the black hole loses the balancing force against the dynamical friction and starts spiraling downward to the gravity center. From simple parameter scaling, the upper mass limit of the black hole is found to be proportional to the bulge mass and this could explain the observed correlation of the black hole mass with the bulge mass.
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