/sci/ - Science & Math

1996 Pahre, Djorgovski, and de Carvalho (PDdC hereafter) applied the Tolman test by studying the SB of elliptical galaxies in 3 clusters up to z=0.4. It was concluded that the data are in good agreement with the expectations for an expanding Universe, while the non-expanding model was ruled out at the better of 5-sigma significance level.

To cope with the strong SB-radius correlation of elliptical galaxies, PDdC compared the SB at a fixed physical radius of 1 kpc computed for the expanding Universe, adopting H0=75km s^−1Mpc^−1,ΩM=0.2, ΩΛ=0. Unfortunately, they used the same SBs computed for the expanding case to test also the nonexpanding one. This is invalid; all the transformations from apparent to physical sizes must be properly computed for the static model using the linear d-z relation in order to actually test the static model. When this is done, we see that the SBs used by PDdC refer to physical radii of 1.4 kp cat z=0.23 and 1.7 kpc at z= 0.4. For consistency with PDdC we use H0=75 km s−1 Mpc−1. Due to this effect at z=0.4 (pictured), an artificial SB dimming of ~0.5 magnitude is introduced (remember that luminosity decay I mentioned earlier?). This is fully responsible for the failure of the non-expanding model claimed by PDdC. Note that VEGA magnitudes are used in this work, so a (1+z) dimming is expected for the static case. This is shown in >>6624030 where the corrected data for the static model are compared with the predictions.

This is why you don't use the prediction of expansion to account for redshift dimming when testing expansion as being responsible for redshift dimming.