Sachs-Wolfe effect
Encyclopedia
The Sachs–Wolfe effect, named after Rainer Kurt Sachs
and Arthur Michael Wolfe
, is a property of the cosmic microwave background radiation
(CMB), in which photons from the CMB are gravitationally redshifted
, causing the CMB spectrum to appear uneven. This effect is the predominant source of fluctuations in the CMB for angular scales above about ten degrees.
, so it is not part of the primordial CMB
. It occurs when the Universe
is dominated in its energy density by something other than matter. If the Universe is dominated by matter, then large-scale gravitational potential energy
wells and hills do not evolve significantly. If the Universe is dominated by radiation
, or by dark energy
, though, those potentials do evolve, subtly changing the energy of photons passing through them.
There are two contributions to the ISW effect. The "early-time" ISW occurs immediately after the (non-integrated) Sachs–Wolfe effect produces the primordial CMB, as photons course through density fluctuations while there is still enough radiation
around to affect the Universe's expansion. Although it is physically the same as the late-time ISW, for observational purposes it is usually lumped in with the primordial CMB, since the matter fluctuations that cause it are in practice undetectable.
, or the cosmological constant
, starts to govern the Universe's expansion. Unfortunately, the nomenclature is a bit confusing. Often, "late-time ISW" implicitly refers to the late-time ISW effect to linear/first order in density perturbations. This linear part of the effect entirely vanishes in a flat universe with only matter, but dominates over the higher-order part of the effect in a universe with dark energy. The full nonlinear (linear + higher-order) late-time ISW effect, especially in the case of individual voids and clusters, is sometimes known as the Rees–Sciama effect, since Martin Rees and Dennis Sciama elucidated the following physical picture.
Accelerated expansion due to dark energy causes even strong large-scale potential wells (supercluster
s) and hills (voids
) to decay over the time it takes a photon
to travel through them. A photon gets a kick of energy going into a potential well (a supercluster), and it keeps some of that energy after it exits, after the well has been stretched out and shallowed. Similarly, a photon has to expend energy entering a supervoid, but will not get all of it back upon exiting the slightly squashed potential hill.
A signature of the late-time ISW is a non-zero cross-correlation function
between the galaxy density (the number of galaxies per square degree) and the temperature of the CMB, because superclusters gently heat photons, while supervoids gently cool them. This correlation has been detected at moderate to high significance.
In May 2008, Granett, Neyrinck & Szapudi showed that the late-time ISW can be pinned to discrete supervoids and superclusters identified in the SDSS
Luminous Red Galaxy catalog. Their ISW detection is arguably the clearest to date, producing an image of the mean effect supervoids and superclusters have on the CMB.
Rainer Kurt Sachs
Rainer Kurt Sachs is a German-American computational radiation biologist and astronomer. In particular he and Arthur Michael Wolfe were the authors of the Sachs-Wolfe effect, which concerns a property of the Cosmic microwave background radiation.- Life and career :He was born in Frankfurt am Main...
and Arthur Michael Wolfe
Arthur Michael Wolfe
Arthur Michael Wolfe is an American astrophysicist, professor and the former Director of the Center for Astrophysics & Space Sciences at the University of California, San Diego. Together with Rainer Kurt Sachs, he authored the Sachs-Wolfe effect.-External links:*...
, is a property of the cosmic microwave background radiation
Cosmic microwave background radiation
In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....
(CMB), in which photons from the CMB are gravitationally redshifted
Gravitational redshift
In astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...
, causing the CMB spectrum to appear uneven. This effect is the predominant source of fluctuations in the CMB for angular scales above about ten degrees.
Non-integrated Sachs–Wolfe effect
The non-integrated Sachs–Wolfe effect is caused by gravitational redshift occurring at the surface of last scattering. The effect is not constant across the sky due to differences in the matter/energy density at the time of last scattering.Integrated Sachs–Wolfe effect
The integrated Sachs–Wolfe effect is also caused by gravitational redshift, however it occurs between the surface of last scattering and the EarthEarth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
, so it is not part of the primordial CMB
CMB
CMB can mean:*The IATA airport code for Bandaranaike International Airport, Colombo – Sri Lanka's only international airport*C.M.B., the debut album of American R&B and pop group Color Me Badd...
. It occurs when the Universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
is dominated in its energy density by something other than matter. If the Universe is dominated by matter, then large-scale gravitational potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...
wells and hills do not evolve significantly. If the Universe is dominated by radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
, or by dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
, though, those potentials do evolve, subtly changing the energy of photons passing through them.
There are two contributions to the ISW effect. The "early-time" ISW occurs immediately after the (non-integrated) Sachs–Wolfe effect produces the primordial CMB, as photons course through density fluctuations while there is still enough radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
around to affect the Universe's expansion. Although it is physically the same as the late-time ISW, for observational purposes it is usually lumped in with the primordial CMB, since the matter fluctuations that cause it are in practice undetectable.
Late-time integrated Sachs–Wolfe effect
The "late-time" ISW effect arises quite recently in cosmic history, as dark energyDark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
, or the cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
, starts to govern the Universe's expansion. Unfortunately, the nomenclature is a bit confusing. Often, "late-time ISW" implicitly refers to the late-time ISW effect to linear/first order in density perturbations. This linear part of the effect entirely vanishes in a flat universe with only matter, but dominates over the higher-order part of the effect in a universe with dark energy. The full nonlinear (linear + higher-order) late-time ISW effect, especially in the case of individual voids and clusters, is sometimes known as the Rees–Sciama effect, since Martin Rees and Dennis Sciama elucidated the following physical picture.
Accelerated expansion due to dark energy causes even strong large-scale potential wells (supercluster
Supercluster
Superclusters are large groups of smaller galaxy groups and clusters and are among the largest known structures of the cosmos. They are so large that they are not gravitationally bound and, consequently, partake in the Hubble expansion.-Existence:...
s) and hills (voids
Void (astronomy)
In astronomy, voids are the empty spaces between filaments, the largest-scale structures in the Universe, that contain very few, or no, galaxies. They were first discovered in 1978 during a pioneering study by Stephen Gregory and Laird A. Thompson at the Kitt Peak National Observatory...
) to decay over the time it takes a photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
to travel through them. A photon gets a kick of energy going into a potential well (a supercluster), and it keeps some of that energy after it exits, after the well has been stretched out and shallowed. Similarly, a photon has to expend energy entering a supervoid, but will not get all of it back upon exiting the slightly squashed potential hill.
A signature of the late-time ISW is a non-zero cross-correlation function
Correlation function
A correlation function is the correlation between random variables at two different points in space or time, usually as a function of the spatial or temporal distance between the points...
between the galaxy density (the number of galaxies per square degree) and the temperature of the CMB, because superclusters gently heat photons, while supervoids gently cool them. This correlation has been detected at moderate to high significance.
In May 2008, Granett, Neyrinck & Szapudi showed that the late-time ISW can be pinned to discrete supervoids and superclusters identified in the SDSS
Sloan Digital Sky Survey
The Sloan Digital Sky Survey or SDSS is a major multi-filter imaging and spectroscopic redshift survey using a dedicated 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico, United States. The project was named after the Alfred P...
Luminous Red Galaxy catalog. Their ISW detection is arguably the clearest to date, producing an image of the mean effect supervoids and superclusters have on the CMB.
External links
- Sam LaRoque, The Integrated Sachs–Wolfe Effect. University of Chicago, IL.
- Aguiar, Paulo, and Paulo Crawford, Sachs–Wolfe effect in some anisotropic models. (PDFPortable Document FormatPortable Document Format is an open standard for document exchange. This file format, created by Adobe Systems in 1993, is used for representing documents in a manner independent of application software, hardware, and operating systems....
format) - White, Martin, and Wayne Hu, The Sachs–Wolfe effect. Astronomy and Astrophysics 321, 89. 1997. Enrico Fermi Institute, University of Chicago. (PDFPortable Document FormatPortable Document Format is an open standard for document exchange. This file format, created by Adobe Systems in 1993, is used for representing documents in a manner independent of application software, hardware, and operating systems....
format) - Sachs–Wolfe effect Level 5.
- "Dark Energy and the Imprint of Super-Structures on the Microwave Background", a webpage by Granett, Neyrinck & Szapudi.