Redshift-space distortions

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Redshift-space distortions are an effect in observational cosmology where the spatial distribution of galaxies appears squashed and distorted when their positions are plotted as a function of their redshift rather than as a function of their distance. The effect is due to the peculiar velocities of the galaxies causing a Doppler shift in addition to the redshift caused by the cosmological expansion.

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Redshift-space distortions (RSDs) manifest in two particular ways. The Fingers of God effect is where the galaxy distribution is elongated in redshift space, with an axis of elongation pointed toward the observer. [1] It is caused by a Doppler shift associated with the random peculiar velocities of galaxies bound in structures such as clusters. The large velocities that lead to this effect are associated with the gravity of the cluster by means of the virial theorem; they change the observed redshifts of the galaxies in the cluster. The deviation from the Hubble's law relationship between distance and redshift is altered, and this leads to inaccurate distance measurements.

A closely related effect is the Kaiser effect, in which the distortion is caused by the coherent motions of galaxies as they fall inwards towards the cluster center as the cluster assembles. [2] Depending on the particular dynamics of the situation, the Kaiser effect usually leads not to an elongation, but an apparent flattening ("pancakes of God"), of the structure. It is a much smaller effect than the fingers of God, and can be distinguished by the fact that it occurs on larger scales.

The previous effects are a consequence of special relativity, and have been observed in real data. There are additional effects that arise from general relativity. One is gravitational redshift distortion, which arises from the net gravitational redshift, or blueshift, that is acquired when the photon climbs out of the gravitational potential well of the distant galaxy and then falls into the potential well of the Milky Way galaxy. [3] This effect will make galaxies at a higher gravitational potential than Earth appear slightly closer, and galaxies at lower potential will appear farther away.

The other effects of general relativity on clustering statistics are observed when the light from a background galaxy passes near, or through, a closer galaxy or cluster. These two effects are the integrated Sachs-Wolfe effect (ISW) and gravitational lensing. [4] In ISW, when a photon passes through a low area of gravitational potential it is shielded from the cosmological expansion of space, making the background galaxy appear closer. Gravitational lensing, unlike all of the previous effects, distorts the apparent position, and number, of background galaxies.

The RSDs measured in galaxy redshift surveys can be used as a cosmological probe in their own right, providing information on how structure formed in the Universe, [5] and how gravity behaves on large scales. [6]

See also

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<span class="mw-page-title-main">Galaxy groups and clusters</span> Largest known gravitationally bound object in universe; aggregation of galaxies

Galaxy groups and clusters are the largest known gravitationally bound objects to have arisen thus far in the process of cosmic structure formation. They form the densest part of the large-scale structure of the Universe. In models for the gravitational formation of structure with cold dark matter, the smallest structures collapse first and eventually build the largest structures, clusters of galaxies. Clusters are then formed relatively recently between 10 billion years ago and now. Groups and clusters may contain ten to thousands of individual galaxies. The clusters themselves are often associated with larger, non-gravitationally bound, groups called superclusters.

<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 blueshift, or negative redshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect, and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth, a fact known as Hubble's law that implies the universe is expanding.

<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.

<span class="mw-page-title-main">Gravitational lens</span> Light bending by mass between source and observer

A gravitational lens is matter, such as a cluster of galaxies or a point particle, that bends light from a distant source as it travels toward an observer. The amount of gravitational lensing is described by Albert Einstein's general theory of relativity with much greater accuracy than Newtonian physics, which treats light as corpuscles travelling at the speed of light.

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Peculiar motion or peculiar velocity refers to the velocity of an object relative to a rest frame — usually a frame in which the average velocity of some objects is zero.

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  1. a cosmological constant denoted by lambda (Λ) associated with dark energy,
  2. the postulated cold dark matter, and
  3. ordinary matter.

Redshift quantization, also referred to as redshift periodicity, redshift discretization, preferred redshifts and redshift-magnitude bands, is the hypothesis that the redshifts of cosmologically distant objects tend to cluster around multiples of some particular value.

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<span class="mw-page-title-main">Weak gravitational lensing</span>

While the presence of any mass bends the path of light passing near it, this effect rarely produces the giant arcs and multiple images associated with strong gravitational lensing. Most lines of sight in the universe are thoroughly in the weak lensing regime, in which the deflection is impossible to detect in a single background source. However, even in these cases, the presence of the foreground mass can be detected, by way of a systematic alignment of background sources around the lensing mass. Weak gravitational lensing is thus an intrinsically statistical measurement, but it provides a way to measure the masses of astronomical objects without requiring assumptions about their composition or dynamical state.

<span class="mw-page-title-main">Strong gravitational lensing</span>

Strong gravitational lensing is a gravitational lensing effect that is strong enough to produce multiple images, arcs, or even Einstein rings. Generally, for strong lensing to occur, the projected lens mass density must be greater than the critical density, that is . For point-like background sources, there will be multiple images; for extended background emissions, there can be arcs or rings. Topologically, multiple image production is governed by the odd number theorem.

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<span class="mw-page-title-main">Ofer Lahav</span>

Ofer Lahav is Perren Chair of Astronomy at University College London (UCL), Vice-Dean (International) of the UCL Faculty of Mathematical and Physical Sciences (MAPS) and Co-Director of the STFC Centre for Doctoral Training in Data Intensive Science. His research area is Observational Cosmology, in particular probing Dark Matter and Dark Energy. His work involves Machine Learning for Big Data.

<span class="mw-page-title-main">Extended theories of gravity</span> Theories

Extended theories of gravity are alternative theories of gravity developed from the exact starting points investigated first by Albert Einstein and Hilbert. These are theories describing gravity, which are metric theory, "a linear connection" or related affine theories, or metric-affine gravitation theory. Rather than trying to discover correct calculations for the matter side of the Einstein field equations; which include inflation, dark energy, dark matter, large-scale structure, and possibly quantum gravity; it is proposed, instead, to change the gravitational side of the equation.

<span class="mw-page-title-main">Void (astronomy)</span> Vast empty spaces between filaments with few or no galaxies

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References

Specific citations:

  1. Jackson, J. C. (1972). "A Critique of Rees's Theory of Primordial Gravitational Radiation". Monthly Notices of the Royal Astronomical Society. 156: 1P–5P. arXiv: 0810.3908 . Bibcode:1972MNRAS.156P...1J. doi:10.1093/mnras/156.1.1p.
  2. Kaiser, Nick (1987). "Clustering in real space and in redshift space". Monthly Notices of the Royal Astronomical Society. 227: 1–21. Bibcode:1987MNRAS.227....1K. doi: 10.1093/mnras/227.1.1 .
  3. McDonald, Patrick (2009). "Gravitational redshift and other redshift-space distortions of the imaginary part of the power spectrum". Journal of Cosmology and Astroparticle Physics. 2009 (11): 026. arXiv: 0907.5220 . Bibcode:2009JCAP...11..026M. doi:10.1088/1475-7516/2009/11/026. S2CID   119188837.
  4. Yoo, Jaiyul (2009). "Complete treatment of galaxy two-point statistics: Gravitational lensing effects and redshift-space distortions". Physical Review D. 79 (2): 023517. arXiv: 0808.3138 . Bibcode:2009PhRvD..79b3517Y. doi:10.1103/physrevd.79.023517. S2CID   73543566.
  5. Percival, Will J.; White, Martin (11 February 2009). "Testing cosmological structure formation using redshift-space distortions". Monthly Notices of the Royal Astronomical Society. 393 (1): 297–308. arXiv: 0808.0003 . Bibcode:2009MNRAS.393..297P. doi:10.1111/j.1365-2966.2008.14211.x. S2CID   15066577.
  6. Raccanelli, A.; Bertacca, D.; Pietrobon, D.; Schmidt, F.; Samushia, L.; Bartolo, N.; Dore, O.; Matarrese, S.; Percival, W. J. (25 September 2013). "Testing gravity using large-scale redshift-space distortions". Monthly Notices of the Royal Astronomical Society. 436 (1): 89–100. arXiv: 1207.0500 . Bibcode:2013MNRAS.436...89R. doi:10.1093/mnras/stt1517. S2CID   9570774.

General references: