Observational tests of world models

Observational cosmologists owe a great debt to H. P. Robertson not only because his work clarified much of the confusion which surrounded the observational approach to the cosmological problem in the 1930’s but also because his rigorous derivation of the two fundamental equations which connect theory and observation (i.e. the metrical and apparent luminosity relations) established beyond doubt their validity. During his career, Robertson returned again and again to the problem, each time with new insight, and each time to clarify the observational approach. He, together with Heckmann and McVittie, were foremost in casting the theoretical equations exclusively in terms of observables such as redshift, apparent luminosity, and angular diameter, which can be determined at the telescope. The influence of Robertson on the observers was enormous. He took great interest in the new developments connected with the 200-inch project, and his council concerning theoretical interpretation of the observations was always given liberally. It is my privilege in this memorial symposium to retrace some of the logical development of the theory, to show how observational relations follow from Robertson’s methods in deriving the models, and finally to indicate where progress has been made in comparing the resulting predictions with the real world

The age of the galactic disk

The galactic disk is a dissipative structure and must, therefore be younger than the halo if galaxy formation generally proceeds by collapse. Just how much younger the oldest stars in the galactic disk are than the oldest halo stars remains an open question. A fast collapse (on a time scale no longer than the rotation period of the extended protogalaxy) permits an age gap of the order of approximately 10 to the 9th power years. A slow collapse, governed by the cooling rate of the partially pressure supported falling gas that formed into what is now the thick stellar disk, permits a longer age gap, claimed by some to be as long as 6 Gyr. Early methods of age dating the oldest components of the disk contain implicit assumptions concerning the details of the age-metallicity relation for stars in the solar neighborhood. The discovery that this relation for open clusters outside the solar circle is different that in the solar neighborhood (Geisler 1987), complicates the earlier arguments. The oldest stars in the galactic disk are at least as old as NGC 188. The new data by Janes on NGC 6791, shown first at this conference, suggest a disk age of at least 12.5 Gyr, as do data near the main sequence termination point of metal rich, high proper motion stars of low orbital eccentricity. Hence, a case can still be made that the oldest part of the galactic thick disk is similar in age to the halo globular clusters, if their ages are the same as 47 Tuc

Confirmation of previous ground-based Cepheid P-L zero-points using Hipparcos trigonometric parallaxes

Comparisons show agreement at the 0.1-mag level between the calibration of the Cepheid period-luminosity (P-L) relation by Feast & Catchpole (FC) using the early release of Hipparcos data and four previous ground-based calibrations, three of which are either largely or totally independent of the distance to the Large Magellanic Cloud (LMC). Each of the comparisons has the sense that the FC calibration is brighter, but only at the level of ≲ 0.1 mag. In contrast, FC argue that their Hipparcos recalibration leads to a 0.2-mag revision in the distance to the LMC, and thereby to a 10 per cent decrease in the Hubble constant. We argue differently. The comparison of the Hipparcos recalibration with others should be made using only local Galactic Cepheids, not based on Cepheids in the LMC that require a set of precepts that are not germane to the direct Hipparcos recalibration. The comparison made here, using only Galactic Cepheids, gives a correction of ∽ 4 per cent or less to our value of H0 based on Type Ia supernovae, keeping all other factors and precepts the same. A second success of the Hipparcos mission is the calibration of the position of the main sequence in the Hertzsprung—Russell diagram as a function of metallicity using local subdwarfs. These data have been used by Reid and by Gratton et al. to obtain, similarly to FC, a brighter absolute magnitude of RR Lyrae stars by ∽0.3 mag from that often currently adopted. These new calibrations confirm the earlier brighter calibrations by Walker, by Sandage, and by Mazzitelli, D'Antona & Caloi, thereby reducing the ages of globular clusters by ∽30 per cent. This removes most of the cosmological time-scale problem if H0∽55 km s−1 Mpc−1. A similar conclusion, based on pulsation theory and MACHO data, has been reached by Alcock et a

The Tolman Surface Brightness Test for the Reality of the Expansion. III. HST Profile and Surface Brightness Data for Early-Type Galaxies in Three High-Redshift Clusters

Photometric data for 34 early-type galaxies in the three high-redshift clusters Cl 1324+3011 (z = 0.76), Cl 1604+4304 (z = 0.90), and Cl 1604+4321 (z = 0.92), observed with the Hubble Space Telescope (HST) and with the Keck 10-meter telescopes by Oke, Postman & Lubin, are analyzed to obtain the photometric parameters of mean surface brightness, magnitudes for the growth curves, and angular radii at various Petrosian eta radii. The angular radii at eta = 1.3 mag for the program galaxies are all larger than 0.24". All of the galaxies are well resolved at this angular size using HST whose point-spread function is 0.05", half width at half maximum. The data for each of the program galaxies are listed at eta = 1.0, 1.3, 1.5, 1.7, and 2.0 mag. They are corrected by color equations and K terms for the effects of redshift to the rest-frame Cape/Cousins I for Cl 1324+3011 and Cl 1604+4304 and R for Cl 1604+4321. The K corrections are calculated from synthetic spectral energy distributions derived from evolving stellar population models of Bruzual & Charlot which have been fitted to the observed broad-band (BVRI) AB magnitudes of each program galaxy. The listed photometric data are independent of all cosmological parameters. They are the source data for the Tolman surface brightness test made in Paper IV.Comment: 17 pages, 7 figures; accepted for publication in the Astronomical Journa

The Tolman Surface Brightness Test for the Reality of the Expansion. II. The Effect of the Point-Spread Function and Galaxy Ellipticity on the Derived Photometric Parameters

To complete the Tolman surface brightness test on the reality of the expansion of the Universe, we need to measure accurately the surface brightness profiles of the high-redshift galaxy sample. We, therefore, investigate the effects of various sizes of point-spread-functions composed of telescope diffraction, CCD pixel resolutions, and ground-based seeing on the measurements of mean surface brightness. We have done the calculations using two synthetic galaxies of effective radii of 0.70" and 0.25" with point-spread functions of 0.1, 0.3, and 0.9 arcseconds. We have also compared actual observations of three high-redshift galaxies in the cluster Cl 1324 + 3011 (z = 0.76) made both with the Keck telescopes in seeing of about 0.9" and with HST which has a PSF that is approximately ten times smaller. The conclusion is that HST data can be used as far into the galaxy image as a Petrosian metric radius of eta = 1.3 magnitudes, whereas the ground-based data will have systematic errors of up to 2.9 magnitudes in the mean surface brightness at eta values of less than 2.2 magnitudes. In the final section, we compare the differences in derived average surface brightness for nearly circular galaxy images compared with highly flattened images. The comparison is made by using the two reduction procedures of (1) integrating the profile curves using circular apertures, and (2) approximating an ``equivalent circular'' galaxy that is highly elongated by using an ``effective'' radius of sqrt{ab}, where a and b are the semi-major and semi-minor axis, respectively, of the best-fitting ellipse. The conclusion is that the two methods of reduction give nearly identical results and that either method can be used to analyze the low and high-redshift galaxy samples used in the Tolman test.Comment: 15 pages, 9 figures; accepted for publication in Astronomical Journa