The<i>Hubble Space Telescope</i>Key Project on the Extragalactic Distance Scale. XXVII. A Derivation of the Hubble Constant Using the Fundamental Plane and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $D_{n}$ \end{document} ‐σ Relations in Leo I, Virgo, and Fornax

Using published photometry and spectroscopy, we construct the fundamental plane and D n -σ relations in Leo I, Virgo, and Fornax. The published Cepheid period-luminosity (PL) relations to spirals in these clusters fixes the relation between angular size and metric distance for both the fundamental plane and D n -σ relations. Using the locally calibrated fundamental plane, we infer distances to a sample of clusters with a mean redshift of cz ≈ 6000 km s -1 , and derive a value of H 0 = 78 ± 5 ± 9 km s -1 Mpc -1 (random and systematic errors, respectively) for the local expansion rate. This value includes a correction for depth effects in the Cepheid distances to the nearby clusters, which decreased the deduced value of the expansion rate by 5% ± 5%. If one further adopts the metallicity correction to the Cepheid PL relation as derived by the Key Project, the value of the Hubble constant would decrease by a further 6% ± 4%. These two sources of systematic error, when combined with a ±6% error due to the uncertainty in the distance to the Large Magellanic Cloud, a ±4% error due to uncertainties in the WFPC2 calibration, and several small sources of uncertainty in the fundamental plane analysis, yield a total systematic uncertainty of ±11%. We find that the values obtained using either the cosmic microwave background (CMB) or a flow-field model, for the reference frame of the distant clusters, agree to within 1%. The D n -σ relation also produces similar results, as expected from the correlated nature of the two scaling relations. A complete discussion of the sources of random and systematic error in this determination of the Hubble constant is also given, in order to facilitate comparison with the other secondary indicators being used by the Key Project.

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