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For refcode 1988ApJ...331..583S:
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1988ApJ...331..583S A CASE FOR H_0_ = 42 AND {OMEGA}_0_ = 1 USING LUMINOUS SPIRAL GALAXIES AND THE COSMOLOGICAL TIME SCALE TEST ALLAN SANDAGE Center for Astrophysical Sciences in the Department of Physics and Astronomy, The Johns Hopkins University; and Space Telescope Science Institute Received 1987 May 29; accepted 1987 September 9 ABSTRACT There are two internally self-consistent methods of finding the Hubble velocity-distance ratios for individual galaxies. In the first, one assumes a linear velocity-distance relation, from which relative distances are found from the velocities. A system of absolute magnitudes is obtained thereby, later zero-pointed using Cepheid distances to local calibrating galaxies. In the second, one uses some parameter such as 21 cm line width, or the internal velocity dispersion, or the de Vaucouleurs {LAMBDA}-index, etc., to which is assigned a fixed absolute magnitude <M> for each value of the parameter, again zero-pointed later from the Cepheid calibrating galaxies. Neither of the two methods can be faulted by considering only the internal data of a flux-limited sample, yet one or the other gives the wrong mean Hubble constant unless external information is known, either on the form of the velocity field (i.e., whether the redshift-distance relation is linear), or on the dispersion of the luminosity function. The self-consistency can be broken by adding data from a fainter flux-limited sample, seeking a contradiction in one of the methods. The test of which method is in error, and therefore whether the high or low value of H_0_ is correct, is made here by combining redshift and magnitude data for bright ScI galaxies from the RSA with faint ScI galaxies from two catalogs in the literature to demonstrate the bias in the second method directly. It is shown that the method of assigning a fixed <M> to each ScI galaxy in the bright sample (or to any other parameter that might be adopted as a distance indicator) produces an artificially compressed distance scale, imitating a varying Hubble ratio that appears to increase outward. However, adding the bright and faint samples gives a list that approaches a volume-limited catalog for redshifts smaller than ~4000 km s^-1^, from which it is demonstrated that (1) the local velocity-distance relation is linear over this redshift range (2), the ScI luminosity function is broad with {sigma}<M> = 0.7 mag, and (3) the value of the Hubble constant is low. Calibration of the ScI magnitude and redshift data in the v approaches 0 limit, using M31, M81, and M101 as calibrators, gives H_0_= 42 +/- 11 km s^-1^ Mpc^-1^, where the error is estimated by assigning an absolute magnitude uncertainty of 0.6 mag for the combined errors of (1) the calibration of the relevant ScI zero point from only three local galaxies, and (2) the uncertainty of the apex magnitude (<M_B_T__> at v approaches 0) which is determined from the upper and lower envelope fits to the M_B_T__, log v_0_ diagram. Cepheid distances to many more ScI calibrating galaxies, and a complete (volume-limited) survey for such galaxies will be needed to improve the value of H_0_ via this method. The age of the globular clusters is adopted to be 13.5 +/- 1 Gyr from the precision measurement of the age of 47 Tuc (Hesser et al.) using VandenBerg isochrones that permit [O/Fe] to vary with [Fe/H], now required from the recent subdwarf data. From the globular cluster age, plus the gestation period of galaxies, the age of the universe is put at 14.9 +/- 2 Gyr, giving H_0_ T_U_ = 0.64 +/- 0.19 and thereby {OMEGA}_0_= 1.2^+3^_-0.9_. Although the errors on {OMEGA}_0_ are large, the increase in the H^-1^_0_ Hubble time to ~23 Gyr if H_0_ = 42, and the decrease in the globular cluster ages to ~14 Gyr now permits {OMEGA}_0_ = 1 with {LAMBDA}=0 from the time scale test, whereas earlier literature values on ages did not. Subject headings: cosmology - galaxies: distances
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