The Hubble Space Telescope Key Project on the Extragalactic Distance Scale. XXVII. A derivation of the hubble constant using the fundamental plane and D-n-sigma relations in Leo I, Virgo, and Fornax

Using published photometry and spectroscopy, we construct the fundamental p lane and D-n-sigma relations in Leo I, Virgo, and Fornax. The published Cep heid period-luminosity (PL) relations to spirals in these clusters fixes th e relation between angular size and metric distance for both the fundamenta l plane and D-n-sigma relations. Using the locally calibrated fundamental p lane, we infer distances to a sample of clusters with a mean redshift of ct approximate to 6000 km s(-1), and derive a value of H-0 = 78 +/- 5 +/- 9 k m s(-1) Mpc(-1) (random and systematic errors, respectively) for the local expansion rate. This value includes a correction for depth effects in the C epheid distances to the nearby clusters, which decreased the deduced value of the expansion rate by 5% +/- 5%. If one further adopts the metallicity c orrection to the Cepheid PL relation as derived by the Key Project, the val ue 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 un certainty in the distance to the Large Magellanic Cloud, a +/-4% error due to uncertainties in the WFPC2 calibration, and several small sources of unc ertainty in the fundamental plane analysis, yield a total systematic uncert ainty of +/-11%. We find that the values obtained using either the cosmic m icrowave background (CMB) or a how-held model, for the reference frame of t he distant dusters, agree to within 1%. The D-n-sigma relation also produce s similar results, as expected from the correlated nature of the two scalin g 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.