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

Abstract

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. To quantify this accuracy, we 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 for galaxies whose effective (half-light) radii range from 0.70" to 0.17". 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", full width at half maximum. We have also compared actual observations of three high-redshift galaxies in the cluster Cl 1324+3011 (z=0.76) made both with the ground-based Keck 10 m telescopes in seeing of about 0.9" and with the Hubble Space Telescope (HST) with a point-spread function that is approximately 10 times smaller. The conclusion is that HST data can be used as far into the galaxy image as a Petrosian metric radius of η=1.3 mag, whereas the ground-based data will have systematic errors of up to 2.9 mag in the mean surface brightness at η values of less than 2.2 mag for all but the largest galaxies at redshifts of z~0.7. In the final section, we compare the differences in derived average surface brightness for nearly circular galaxy images 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 (ab)^1/2, where a and b are the semimajor and semiminor 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.