Tolman surface brightness test
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.
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. 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:
Surface brightness
The overall brightness of an extended astronomical object such as a galaxy, star cluster, or nebula, can be measured by its total magnitude, integrated magnitude or integrated visual magnitude; a related concept is surface brightness, which specifies the brightness of a standard-sized piece of an...
of galaxies
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
as a function of their redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
(measured as z). Such a comparison was first proposed in 1930 by Richard C. Tolman
Richard C. Tolman
Richard Chace Tolman was an American mathematical physicist and physical chemist who was an authority on statistical mechanics. He also made important contributions to theoretical cosmology in the years soon after Einstein's discovery of general relativity...
as a test of whether the universe is expanding or static
Static universe
A static universe, also referred to as a "stationary" or "Einstein" universe, is a model in which space is neither expanding nor contracting. Albert Einstein proposed such a model as his preferred cosmology in 1917...
. 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. 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.