On the Use of Scaling Relations for the Tolman Test

Citations Over TimeTop 11% of 1998 papers

Abstract

The use of relations between structural parameters of early-type galaxies to perform the Tolman test for the expansion of the universe is reconsidered. Scaling relations such as the fundamental plane or the Kormendy relation require the transformation from angular to metric sizes, to compare the relation at different z-values. This transformation depends on the assumed world model: galaxies of a given angular size, at a given z, are larger (in units of kiloparsecs) in a nonexpanding universe than in an expanding one. Furthermore, the luminosities of galaxies are expected to evolve with z in an expanding model. These effects are shown to conspire to reduce the difference between the predicted surface brightness (SB) change with redshift in the expanding and nonexpanding cases. We have considered expanding models with passive luminosity evolution. We find that their predictions for the visible photometric bands are very similar to those of the static model until z ∼ 1, and therefore the test cannot distinguish between the two world models. Recent good-quality data on the Kormendy relation and the fundamental plane at intermediate redshifts are consistent with the predictions from both models. In the K band, where the expected (model) luminosity evolutionary corrections are smaller, the differences between the expanding and static models amount to ∼0.4 (0.8) mag at z = 0.4 (1). It is shown that, owing to that small difference between the predictions in the covered z-range, and to the paucity and uncertainties of the relevant SB photometry, the existing K-band data are not adequate to distinguish between the different world metrics and cannot yet be used to discard the static case. It is pointed out that the scaling relations could still be used to rule out the nonevolving case if it could be shown that the coefficients change with the redshift. © 1993. The American Astronomical Society. All rights reserved.

Related Papers

• → Scaling of the Turbulence Transition Threshold in a Pipe(2003)268 cited
• → Unified Scaling Law for flux pinning in practical superconductors: II. Parameter testing, scaling constants, and the Extrapolative Scaling Expression(2016)21 cited
• → Old and new scaling laws in quantum quench(2016)22 cited
• → One Parameter Scaling Theory for Stationary States of Disordered Nonlinear Systems(2010)