Tolman surface brightness test

Last updated

The Tolman surface brightness test is one out of six cosmological tests that were 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. It is a unique test of cosmology, as it is independent of dark energy, dark matter and Hubble constant parameters, testing purely for whether Cosmological Redshift is caused by an expanding universe or not. [1]

In a simple (static and flat) universe, the light received from an object drops proportional to the square of its distance and the apparent area of the object also drops proportional to the square of the distance, so the surface brightness (light received per surface area) would be constant, independent of the distance. In an expanding universe, however, there are two effects that change this relation. 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.

One of the earliest and most comprehensive studies was published in 1996, as observational requirements limited the practicality of the test till then. This test found consistency with an expanding universe. [2] However, therein, the authors note that:

"The results of any Tolman SB test where galaxies must be corrected to a standard condition will involve some dependence on the assumed cosmology, but as will be described below, for the redshifts of interest here, the effect of cosmology is quite small compared to the predicted difference between the expansion and tired-light models."

A later paper that reviewed this one removed their assumed expansion cosmology for calculating SB, to make for a fair test, and found that the 1996 results, once the correction was made, did not rule out a static universe. [3]

To date, the most complex investigation of the relationship between surface brightness and redshift was carried out using the 10 m Keck telescope to measure nearly a thousand galaxies' redshifts and the 2.4 m Hubble Space Telescope to measure those galaxies' surface brightness. [4] 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."

However, the authors tested a specific Einstein Desitter static universe model where one of the effects of expansion that contributes a (1+z) term, namely time dilation, was left in. [3] [4] In order to test a truly static universe with no time dilation effects from expansion, this term was removed and corrected for, and it was Found that these previous results did not rule out a static universe. [3] [5]

As the predicted effects between static and expansion diverge dramatically towards higher redshifts, the most comprehensive test done to date was out to z=5, much larger than the previous largest which only went to z=0.9: this test found their results to be consistent with a static universe, but unable to rule out expansion if significant galaxy evolution was expected. [3]


See also

Footnotes

  1. Richard, Tolman (1934). "Relativity Thermodynamics and Cosmology". International Series of Monographs on Physics. (Oxford). 18 (231): 327–328. doi:10.2307/3605486. JSTOR   3605486.
  2. Pahre, Michael A.; Djorgovski, S. G.; Carvalho, R. R. de (10 January 1996). "A Tolman Surface Brightness Test for Universal Expansion and the Evolution of Elliptical Galaxies in Distant Clusters* **". The Astrophysical Journal. 456 (2): L79. doi:10.1086/309872. ISSN   0004-637X. S2CID   14419860.
  3. 1 2 3 4 Lerner, Eric J.; Falomo, Renato; Scarpa, Riccardo (1 May 2014). "UV surface brightness of galaxies from the local universe to z ~ 5". International Journal of Modern Physics D. 23 (6): 1450058. arXiv: 1405.0275 . doi:10.1142/S0218271814500588. ISSN   0218-2718. S2CID   119272816.
  4. 1 2 Allan Sandage and Lori M. Lubin, 2271-88; Lori M. Lubin and Allan Sandage, "The Tolman Surface Brightness Test for the Reality of the Expansion. II. The Effect of the Point-Spread Function and Galaxy Ellipticity on the Derived Photometric Parameters," Astronomical Journal 121 (2001): 2289-300; Lori M. Lubin and Allan Sandage, "The Tolman Surface Brightness Test for the Reality of the Expansion. III. Hubble Space Telescope Profile and Surface Brightness Data for Early-Type Galaxies in Three High-Redshift Clusters," Astronomical Journal 122 (2001): 1071-83; Lori M. Lubin and Allan Sandage, "The Tolman Surface Brightness Test for the Reality of the Expansion. IV. A Measurement of the Tolman Signal and the Luminosity Evolution of Early-Type Galaxies," Astronomical Journal, 122 (2001): 1084-1103.
  5. Lerner, Eric J (July 2018). "Observations contradict galaxy size and surface brightness predictions that are based on the expanding universe hypothesis". Monthly Notices of the Royal Astronomical Society. 477 (3): 3185–3196. arXiv: 1803.08382 . doi:10.1093/mnras/sty728.

Related Research Articles

<span class="mw-page-title-main">Big Bang</span> How the universe expanded from a hot, dense state

The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The overall uniformity of the Universe, known as the flatness problem, is explained through cosmic inflation: a sudden and very rapid expansion of space during the earliest moments. However, physics currently lacks a widely accepted theory of quantum gravity that can successfully model the earliest conditions of the Big Bang.

<span class="mw-page-title-main">Quasar</span> Active galactic nucleus containing a supermassive black hole.

A quasar is an extremely luminous active galactic nucleus (AGN). It is sometimes known as a quasi-stellar object, abbreviated QSO. The emission from an AGN is powered by a supermassive black hole with a mass ranging from millions to tens of billions of solar masses, surrounded by a gaseous accretion disc. Gas in the disc falling towards the black hole heats up because of friction and releases energy in the form of electromagnetic radiation. The radiant energy of quasars is enormous; the most powerful quasars have luminosities thousands of times greater than that of a galaxy such as the Milky Way. Quasars are usually categorized as a subclass of the more general category of AGN. The redshifts of quasars are of cosmological origin.

<span class="mw-page-title-main">Redshift</span> Change of wavelength in photons during travel

In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation. The opposite change, a decrease in wavelength and simultaneous increase in frequency and energy, is known as a negative redshift, or blueshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. The three main causes of electromagnetic redshift in astronomy and cosmology are, first, radiation traveling between objects that are moving apart ; second, the gravitational redshift due to radiation traveling towards an object in a weaker gravitational potential; and third, the cosmological redshift due to radiation traveling through expanding space. All sufficiently distant light sources show redshift for a velocity proportionate to their distance from Earth, a fact known as Hubble's law.

<span class="mw-page-title-main">Accelerating expansion of the universe</span> Cosmological phenomenon

Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered during 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which both used distant type Ia supernovae to measure the acceleration. The idea was that as type Ia supernovae have almost the same intrinsic brightness, and since objects that are farther away appear dimmer, we can use the observed brightness of these supernovae to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the farther an object is from us, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerated rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.

<span class="mw-page-title-main">Hubble's law</span> Observation in physical cosmology

Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible spectrum.

A non-standard cosmology is any physical cosmological model of the universe that was, or still is, proposed as an alternative to the then-current standard model of cosmology. The term non-standard is applied to any theory that does not conform to the scientific consensus. Because the term depends on the prevailing consensus, the meaning of the term changes over time. For example, hot dark matter would not have been considered non-standard in 1990, but would be in 2010. Conversely, a non-zero cosmological constant resulting in an accelerating universe would have been considered non-standard in 1990, but is part of the standard cosmology in 2010.

<span class="mw-page-title-main">Observable universe</span> All of space observable from the Earth at the present

The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. Initially, it was estimated that there may be 2 trillion galaxies in the observable universe, although that number was reduced in 2021 to only several hundred billion based on data from New Horizons. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical region centered on the observer. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth.

<span class="mw-page-title-main">Halton Arp</span> American astronomer

Halton Christian "Chip" Arp was an American astronomer. He was known for his 1966 Atlas of Peculiar Galaxies, which catalogues many examples of interacting and merging galaxies, though Arp disputed the idea, claiming apparent associations were prime examples of ejections. Arp published Seeing Red: Redshift, Cosmology and Academic Science in 1998. Arp was also known as a critic of the Big Bang theory and for advocating a non-standard cosmology incorporating intrinsic redshift.

Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors.

<span class="mw-page-title-main">Allan Sandage</span> American astronomer

Allan Rex Sandage was an American astronomer. He was Staff Member Emeritus with the Carnegie Observatories in Pasadena, California. He determined the first reasonably accurate values for the Hubble constant and the age of the universe.

In physical cosmology, the age of the universe is the time elapsed since the Big Bang. Astronomers have derived two different measurements of the age of the universe: a measurement based on direct observations of an early state of the universe, which indicate an age of 13.787±0.020 billion years as interpreted with the Lambda-CDM concordance model as of 2021; and a measurement based on the observations of the local, modern universe, which suggest a younger age. The uncertainty of the first kind of measurement has been narrowed down to 20 million years, based on a number of studies that all show similar figures for the age. These studies include researches of the microwave background radiation by the Planck spacecraft, the Wilkinson Microwave Anisotropy Probe and other space probes. Measurements of the cosmic background radiation give the cooling time of the universe since the Big Bang, and measurements of the expansion rate of the universe can be used to calculate its approximate age by extrapolating backwards in time. The range of the estimate is also within the range of the estimate for the oldest observed star in the universe.

Tired light is a class of hypothetical redshift mechanisms that was proposed as an alternative explanation for the redshift-distance relationship. These models have been proposed as alternatives to the models that require metric expansion of space of which the Big Bang and the Steady State cosmologies are the most famous examples. The concept was first proposed in 1929 by Fritz Zwicky, who suggested that if photons lost energy over time through collisions with other particles in a regular way, the more distant objects would appear redder than more nearby ones. Zwicky himself acknowledged that any sort of scattering of light would blur the images of distant objects more than what is seen. Additionally, the surface brightness of galaxies evolving with time, time dilation of cosmological sources, and a thermal spectrum of the cosmic microwave background have been observed—these effects should not be present if the cosmological redshift was due to any tired light scattering mechanism. Despite periodic re-examination of the concept, tired light has not been supported by observational tests and remains a fringe topic in astrophysics.

<span class="mw-page-title-main">History of the Big Bang theory</span> History of a cosmological theory

The history of the Big Bang theory began with the Big Bang's development from observations and theoretical considerations. Much of the theoretical work in cosmology now involves extensions and refinements to the basic Big Bang model. The theory itself was originally formalised by Belgian Catholic priest, theoretical physicist, mathematician, astronomer, and professor of physics Georges Lemaître. Hubble's Law of the expansion of the universe provided foundational support for the theory.

In cosmology, a static universe is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contracting. Such a universe does not have so-called spatial curvature; that is to say that it is 'flat' or Euclidean. A static infinite universe was first proposed by English astronomer Thomas Digges (1546–1595).

The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion; the universe does not expand "into" anything and does not require space to exist "outside" it. To any observer in the universe, it appears that all but the nearest galaxies recede at speeds that are proportional to their distance from the observer, on average. While objects cannot move faster than light, this limitation only applies with respect to local reference frames and does not limit the recession rates of cosmologically distant objects.

In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter of the universe, caused by acoustic density waves in the primordial plasma of the early universe. In the same way that supernovae provide a "standard candle" for astronomical observations, BAO matter clustering provides a "standard ruler" for length scale in cosmology. The length of this standard ruler is given by the maximum distance the acoustic waves could travel in the primordial plasma before the plasma cooled to the point where it became neutral atoms, which stopped the expansion of the plasma density waves, "freezing" them into place. The length of this standard ruler can be measured by looking at the large scale structure of matter using astronomical surveys. BAO measurements help cosmologists understand more about the nature of dark energy by constraining cosmological parameters.

<span class="mw-page-title-main">Calán/Tololo Survey</span>

The Calán/Tololo Supernova Survey was a supernova survey that ran from 1989 to 1995 at the University of Chile and the Cerro Tololo Inter-American Observatory to measure a Hubble diagram out to redshifts of 0.1. It was founded by Mario Hamuy, José Maza Sancho, Mark M. Phillips, and Nicholas B. Suntzeff in 1989 out of discussions at the UC Santa Cruz meeting on supernovae on how to improve the Hubble diagram using Type Ia supernovae. It was also motivated by the suggestion of Allan Sandage to restart a supernova survey after the Sandage and Tammann survey failed due to poor quality photographic plates in 1986. The Survey built on the original supernova survey of Maza done at the f/3 Maksutov Camera at the Cerro Roble Observatory of the University of Chile between 1979 and 1984. The Survey used the CTIO Curtis Schmidt telescope with IIa-O photographic plates, each plate covering a field of 25 sq-deg on the sky. The plates were developed and sent to Santiago Chile the next morning and searched for supernovae at the Department of Astronomy at the University of Chile. Any supernova candidates were then observed the next night using the 0.9m telescope at CTIO with a CCD camera. This was one of the first studies done in astronomy where the telescope time was scheduled to observe objects not yet discovered.

<span class="mw-page-title-main">UDFy-38135539</span> Distant galaxy in the constellation Fornax

UDFy-38135539 is the Hubble Ultra Deep Field (UDF) identifier for a galaxy which was calculated as of October 2010 to have a light travel time of 13.1 billion years with a present proper distance of around 30 billion light-years.

The cosmic age problem is a historical problem in astronomy concerning the age of the universe. The problem was that at various times in the 20th century, the universe was estimated to be younger than the oldest observed stars. Estimates of the universe's age came from measurements of the current expansion rate of the universe, the Hubble constant , as well as cosmological models relating to the universe's matter and energy contents. Issues with measuring as well as not knowing about the existence of dark energy led to spurious estimates of the age. Additionally, objects such as galaxies, stars, and planets could not have existed in the extreme temperatures and densities shortly after the Big Bang.

<span class="mw-page-title-main">GN-z11</span> High-redshift galaxy in the constellation Ursa Major

GN-z11 is a high-redshift galaxy found in the constellation Ursa Major. It is among the farthest known galaxies from Earth ever discovered. The 2015 discovery was published in a 2016 paper headed by Pascal Oesch and Gabriel Brammer. Up until the discovery of JADES-GS-z13-0 in 2022 by the James Webb Space Telescope, GN-z11 was the oldest and most distant known galaxy yet identified in the observable universe, having a spectroscopic redshift of z = 10.957, which corresponds to a proper distance of approximately 32 billion light-years.