The Ability of the 200-INCH Telescope to Discriminate Between Selected World Models.

The present paper reviews several tests which can be performed to decide between world models. Each test is discussed in terms of the capabilities of the 200-inch Hale telescope. The tests include (1) the deviation from linearity of the red-shift-magnitude relation, (2) the galaxy-count-magnitude relation, (3) the angular-diameter-red-shift relation treated for both metric and isophotal diameters, and (4) the time scale. Selected exploding models of the Friedman type and the steady-state model are considered. The object of the tests is to determine observationally the deceleration parameter qo. Once qo is known, the world model follows from equations given in Section I. It appears possible to find qo from the magnitude-red-shift relation. At a red shift (Ax/ 0) of z = 0.5, a difference of 0.9 mag. exists in the m, z relation between a closed, elliptical universe with qo = +1 and the steady-state model with qo = -1. Such a difference can possibly be detected if the aperture effect for the measurement of intensities and if the Scott effect of observational selection can be allowed for. The value of qo is presently estimated to lie between 0 and +3. The most probable value is qo = 1 + 22. The predictions of steady-state cosmology would appear to be inconsistent with present information. The N(m) relation for galaxy counts is derived for all models considered. Galaxy counts are insensitive to the model. At the limit of the 200-inch, an observational error of only Am = 0.28 mag. can change the counts from indicating a closed universe with qo = +1 to an open, empty model with qo = 0. There seems to be no hope of finding qo from the N(m) counts because the predicted differences between the models are too small compared with the known fluctuations of the distribution. The angular diameters of clusters of galaxies and of galaxies themselves are discussed. The angular diameter subtended by a linear distance y is shown to change with z in a different way than the isophotal diameters. Both types of diameters are considered, and a test for qo seems to be possible with the 200-inch, but the test will be difficult and perhaps marginal Equations for the time t0 since the beginning of the expansion are derived. It is shown that to is a function of the Hubble parameter H0 and qo alone for exploding models with A = 0. The present value of H0 and the age of the oldest stars are shown to be incompatible. If qo = +1, then to = 0.571 H-02= 7.42 x 100 years (assuming H0 = 75 km/sec 100 pc). However, the age of the oldest stars in our Galaxy is computed to be greater than 15 X 10 years if the most recent stellar models of Hazelgrove and Hoyle are used. These values are too uncertain to claim that exploding models with A = 0 are incorrect, but the data, as given, would so require. It is shown in the final section that exploding models of the LemaftreEddington type approach asymptotically qo = -1 and are therefore like the steady-state model. In the limit both models predict the same fm, z] and 0, z relations Consequently, tests of the type considered in this paper cannot decide between these particular models Appeal to the time independence of the steady- state model must then be made for a test. Appendix A gives the explicit equations for N(m) for various qo values.