The masses of supermassive black holes correlate almost perfectly with the velocity dispersions of their host bulges, M • ∝ σ α , where α = 4.8 ± 0.5. The relation is much tighter than the relation between M • and bulge luminosity, with a scatter no larger than expected on the basis of measurement error alone. Black hole masses estimated by Magorrian et al. (1998) lie systematically above the M • − σ relation defined by more accurate mass estimates, some by as much as two orders of magnitude. The tightness of the M • − σ relation implies a strong link between black hole formation and the properties of the stellar bulge.

We present here the Ðnal results of the Hubble Space T elescope (HST ) Key Project to measure the Hubble constant. We summarize our method, the results, and the uncertainties, tabulate our revised distances, and give the implications of these results for cosmology. Our results are based on a Cepheid calibration of several secondary distance methods applied over the range of about 60È400 Mpc. The analysis presented here beneÐts from a number of recent improvements and reÐnements, including (1) a larger LMC Cepheid sample to deÐne the Ðducial period-luminosity (PL) relations, (2) a more recent HST Wide Field and Planetary Camera 2 (WFPC2) photometric calibration, (3) a correction for Cepheid metallicity, and (4) a correction for incompleteness bias in the observed Cepheid PL samples. We adopt a distance modulus to the LMC (relative to which the more distant galaxies are measured) of mag, or 50 kpc. New, revised distances are given for the 18 spiral galaxies for k 0 (LMC) \ 18.50^0.10 which Cepheids have been discovered as part of the Key Project, as well as for 13 additional galaxies with published Cepheid data. The new calibration results in a Cepheid distance to NGC 4258 in better agreement with the maser distance to this galaxy. Based on these revised Cepheid distances, we Ðnd values (in km s~1 Mpc~1) of (random)^6 (systematic) (Type Ia supernovae),

We present improved black hole masses for 35 active galactic nuclei (AGNs) based on a complete and consistent reanalysis of broad emission-line reverberation-mapping data. From objects with multiple line measurements, we find that the highest precision measure of the virial product cτ ∆V 2 /G, where τ is the emission-line lag relative to continuum variations and ∆V is the emission-line width, is obtained by using the crosscorrelation function centroid (as opposed to the cross-correlation function peak) for the time delay and the line dispersion (as opposed to full width half maximum) for the line width and by measuring the line width in the variable part of the spectrum. Accurate line-width measurement depends critically on avoiding contaminating features, in particular the narrow components of the emission lines. We find that the precision (or random component of the error) of reverberation-based black hole mass measurements is typically around 30%, comparable to the precision attained in measurement of black hole masses in quiescent galaxies by gas or stellar dynamical methods. Based on results

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