Tolman surface brightness test

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A Tolman surface brightness test is a comparison of 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.

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 400-inch Keck telescope to measure nearly a thousand galaxies' redshifts and the 94-inch HST 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.

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