Sunday, 11 May 2014

Tolman surface brightness test


From Wikipedia, the free encyclopedia
The Tolman surface brightness test is one out of a half-dozen cosmological tests that was conceived in the 1930s to check the viability of and compare new cosmological models. Tolman's test compares the surface brightness of galaxies as a function of their redshift (measured as z). Such a comparison was first proposed in 1930 by Richard C. Tolman as a test of whether the universe is expanding or static. Different physicists have claimed that the results support different models.[who?]

In a simple (static and flat) universe, the light received from an object drops inversely with the square of its distance, but the apparent area of the object also drops inversely with the square of the distance, so the surface brightness would be independent of the distance. 

In an expanding universe, however, there are two effects that reduce the power detected coming from distant objects. First, the rate at which photons are received is reduced because each photon has to travel a little farther than the one before. Second, the energy of each photon observed is reduced by the redshift. At the same time, distant objects appear larger than they really are because the photons observed were emitted at a time when the object was closer. Adding these effects together, the surface brightness in a simple expanding universe (flat geometry and uniform expansion over the range of redshifts observed) should decrease with the fourth power of (1+z).

To date, the best investigation of the relationship between surface brightness and redshift was carried out using the 10m Keck telescope to measure nearly a thousand galaxies' redshifts and the 2.4m Hubble Space Telescope to measure those galaxies' surface brightness.[1] The exponent found is not 4 as expected in the simplest expanding model, but 2.6 or 3.4, depending on the frequency band. The authors summarize:

We show that this is precisely the range expected from the evolutionary models of Bruzual & Charlot. We conclude that the Tolman surface brightness test is consistent with the reality of the expansion.

Time Dilation in Type Ia Supernova Spectra at High Redshift
S. Blondin (Harvard-Smithsonian Ctr. Astrophys.) , T.M. Davis (Bohr Inst. & Queensland U.) , K. Krisciunas (Texas A-M) , B.P. Schmidt (Australian Natl. U., Canberra) , J. Sollerman (Bohr Inst.) , W.M. Wood-Vasey (Harvard-Smithsonian Ctr. Astrophys.) , A.C. Becker (Washington U., Seattle, Astron. Dept.) , P. Challis (Harvard-Smithsonian Ctr. Astrophys.) , A. Clocchiatti (Rio de Janeiro, Pont. U. Catol.) , G. Damke (Cerro-Tololo InterAmerican Obs.) et al. Show all 32 authors
Apr 2008 - 14 pages
Abstract (arXiv)
We present multiepoch spectra of 13 high-redshift Type Ia supernovae (SNe Ia) drawn from the literature, the ESSENCE and SNLS projects, and our own separate dedicated program on the ESO Very Large Telescope. We use the Supernova Identification (SNID) code of Blondin & Tonry to determine the spectral ages in the supernova rest frame. Comparison with the observed elapsed time yields an apparent aging rate consistent with the 1/(1+z) factor (where z is the redshift) expected in a homogeneous, isotropic, expanding universe. These measurements thus confirm the expansion hypothesis, while unambiguously excluding models that predict no time dilation, such as Zwicky's 'tired light' hypothesis. We also test for power-law dependencies of the aging rate on redshift. The best-fit exponent for these models is consistent with the expected 1/(1+z) factor.

Note: 14 pages (emulateapj), 10 figures/ accepted for publication in ApJ. Version with full-resolution figures available at http://www.cfa.harvard.edu/~sblondin/publications/timedilation/

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The Tolman Surface Brightness Test for the Reality of the Expansion. V. Provenance of the Test and a New Representation of the Data for Three Remote HST Galaxy Clusters

Allan Sandage
May 2009 - 51 pages



Abstract (arXiv)
A new reduction is made of the HST photometric data for E galaxies in three remote clusters at redshifts near z=0.85 in search for the Tolman surface brightness (SB) signal for the reality of the expansion. Because of the strong variation of SB of such galaxies with intrinsic size, and because the Tolman test is about surface brightness, we must account for the variation. In an earlier version of the test, Lubin & Sandage calibrated the variation out. In contrast, the test is made here using fixed radius bins for both the local and remote samples. Homologous positions in the galaxy image at which to compare the surface brightness values are defined by radii at five Petrosian eta values ranging from 1.0 to 2.0. 

Sersic luminosity profiles are used to generate two diagnostic diagrams that define the mean SB distribution across the galaxy image. A Sersic exponent, defined by the r^n family of Sersic profiles, of n=0.46 fits both the local and remote samples. Diagrams of the dimming of the <SB> with redshift over the range of Petrosian eta radii shows a highly significance Tolman signal but degraded by luminosity evolution in the look-back time. The expansion is real and a luminosity evolution exists at the mean redshift of the HST clusters of 0.8 mag in R_cape and 0.4 mag in the I_cape photometric rest-frame bands, consistent with the evolution models of Bruzual and Charlot.

Note: * Brief entry *


 Record created 2009-05-20, last modified 2014-03-07
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