Absorption lines in thevisible spectrum of asupercluster of distant galaxies (right), as compared to absorption lines in the visible spectrum of theSun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases).
All redshifts can be understood under the umbrella offrame transformation laws.Gravitational waves, which also travel atthe speed of light, are subject to the same redshift phenomena.[1] The value of a redshift is often denoted by the letterz, corresponding to the fractional change in wavelength (positive for redshifts, negative for blueshifts), and by the wavelength ratio1 +z (which is greater than 1 for redshifts and less than 1 for blueshifts).
Other physical processes exist that can lead to a shift in the frequency of electromagnetic radiation, includingscattering andoptical effects; however, the resulting changes are distinguishable from (astronomical) redshift and are not generally referred to as such (see section onphysical optics and radiative transfer).
The history of the subject began in the 19th century, with the development of classicalwave mechanics and the exploration of phenomena which are associated with theDoppler effect. The effect is named after theAustrian mathematician,Christian Doppler, who offered the first known physical explanation for the phenomenon in 1842.[2][3]: 107 In 1845, the hypothesis was tested and confirmed forsound waves by theDutch scientistChristophorus Buys Ballot.[4] Doppler correctly predicted that the phenomenon would apply to all waves and, in particular, suggested that the varyingcolors ofstars could be attributed to their motion with respect to the Earth.[5]
Unaware of Doppler's work, French physicistHippolyte Fizeau in 1848, suggested that a shift inspectral lines from stars might be used to measure their motion relative to Earth.[3]: 109 In 1850François-Napoléon-Marie Moigno analyzed about both Doppler's and Fizeau's ideas in a publication read byJames Clerk Maxwell who subsequently with British astronomerWilliam Huggins. While Huggins initially stuck to the idea that the color of stars related to their chemistry, by 1868, he was the first to determine the velocity of a star moving away from the Earth by the analysis of spectral shifts.[6][3]: 111
In 1871, optical redshift was confirmed when the phenomenon was observed inFraunhofer lines, using solar rotation, about 0.1 Å in the red.[7] In 1887, Vogel and Scheiner discovered the "annual Doppler effect", the yearly change in the Doppler shift of stars located near the ecliptic, due to the orbital velocity of the Earth.[8] In 1901,Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors.[9][7]
Beginning with observations in 1912,Vesto Slipher discovered that theAndromeda Galaxy had a blue shift, indicating that it was moving towards the Earth.[10] Slipher first reported on his measurement in the inaugural volume of theLowell Observatory Bulletin.[11] Three years later, he wrote a review in the journalPopular Astronomy.[12] In it he stated that "the early discovery that the great Andromeda spiral had the quite exceptional velocity of –300 km(/s) showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well."[13] Slipher reported the velocities for 15 spiral nebulae spread across the entirecelestial sphere, all but three having observable "positive" (that is recessional) velocities.[10]
Until 1923 the nature of the nebulae was unclear. By that yearEdwin Hubble had established that these weregalaxies and worked out a procedure to measure distance based on the period-luminosity relation of variableCepheids stars. This make it possible to test a prediction byWillem de Sitter in 1917 that redshift would be correlated with distance.In 1929 Hubble combined his distance estimates with redshift data from Slipher's reports and measurements byMilton Humason to report an approximate relationship between the redshift anddistance, a result now calledHubble's law.[10]: 64 [14][15]
Theories relating to the redshift-distance relation also evolved during the decade of the 1920s.The solution to the equations of general relativity described by de Sitter contained no matter, but in 1922Alexander Friedmann's derived dynamic solutions, now called theFriedmann–equations, based on frictionless fluid models.[16] IndependentlyGeorges Lemaître derived similar equations in 1927 and his analysis became widely known around the time of Hubble's key publication.[10]: 77
By early 1930 the combination of the redshift measurements and theoretical models established a major breakthrough in the new science of cosmology: the universe had a history and its expansion could be investigated with physical models backed up with observational astronomy.[10]: 99
In the 1960s the discovery ofquasars, which appear as very blue point sources and thus were initially thought to be unusual stars, lead to the idea that they were as bright as they were because they were closer than their redshift data indicated. A flurry of theoretical and observational work concluded that these objects were very powerful but distant astronomical objects.[10]: 261
Thespectrum of light that comes from a source (see idealized spectrum illustration top-right) can be measured. To determine the redshift, one searches for features in the spectrum such asabsorption lines,emission lines, or other variations in light intensity. If found, these features can be compared with known features in the spectrum of various chemical compounds found in experiments where that compound is located on Earth. A very commonatomic element in space ishydrogen.
The spectrum of originally featureless light shone through hydrogen will show asignature spectrum specific to hydrogen that has features at known positions. If restricted to absorption lines it would look similar to the illustration (top right). If the same pattern of intervals is seen in an observed spectrum from a distant source but occurring at shifted wavelengths, it can be identified as hydrogen too. If the same spectral line is identified in both spectra—but at different wavelengths—then the redshift can be calculated using the table below.
Determining the redshift of an object in this way requires a frequency or wavelength range. In order to calculate the redshift, one has to know the wavelength of the emitted light in the rest frame of the source: in other words, the wavelength that would be measured by an observer located adjacent to and comoving with the source. Since in astronomical applications this measurement cannot be done directly, because that would require traveling to the distant star of interest, the method using spectral lines described here is used instead. Redshifts cannot be calculated by looking at unidentified features whose rest-frame frequency is unknown, or with a spectrum that is featureless orwhite noise (random fluctuations in a spectrum).[21]
Redshift (and blueshift) may be characterized by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy, it is customary to refer to this change using adimensionless quantity calledz. Ifλ represents wavelength andf represents frequency (note,λf =c wherec is thespeed of light), thenz is defined by the equations:[22]
Calculation of redshift,
Based on wavelength
Based on frequency
Afterz is measured, the distinction between redshift and blueshift is simply a matter of whetherz is positive or negative. For example,Doppler effect blueshifts (z < 0) are associated with objects approaching (moving closer to) the observer with the light shifting to greaterenergies. Conversely, Doppler effect redshifts (z > 0) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, gravitational blueshifts are associated with light emitted from a source residing within a weakergravitational field as observed from within a stronger gravitational field, while gravitational redshifting implies the opposite conditions.
Redshifts are commonly attributed to relative motion between the source and the observer, to the expansion of the universe, and to gravity. These origins are fundamentally all equivalent,[23] but they refer to different contexts. The following sections explain these origins.
Doppler effect, yellow (~575nm wavelength) ball appears greenish (blueshift to ~565 nm wavelength) approaching observer, turnsorange (redshift to ~585 nm wavelength) as it passes, and returns to yellow when motion stops. To observe such a change in color, the object would have to be traveling at approximately 5,200km/s, or about 32 times faster than the speed record for thefastest space probe.Redshift and blueshift
If a source of the light is moving away from an observer, then redshift (z > 0) occurs; if the source moves towards the observer, thenblueshift (z < 0) occurs. This is true for all electromagnetic waves and is explained by theDoppler effect. Consequently, this type of redshift is called theDoppler redshift. If the source moves away from the observer withvelocityv, which is much less than the speed of light (v ≪c), the redshift is given by
(since)
wherec is thespeed of light. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.
A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on therelativistic Doppler effect. In brief, objects moving close to the speed of light will experience deviations from the above formula due to thetime dilation ofspecial relativity which can be corrected for by introducing theLorentz factorγ into the classical Doppler formula as follows (for motion solely in the line of sight):
This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called theIves–Stilwell experiment.[24]
Since the Lorentz factor is dependent only on themagnitude of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on theprojection of the movement of the source into theline-of-sight which yields different results for different orientations. Ifθ is the angle between the direction of relative motion and the direction of emission in the observer's frame[25] (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:
and for motion solely in the line of sight (θ = 0°), this equation reduces to:
For the special case that the light is moving atright angle (θ = 90°) to the direction of relative motion in the observer's frame,[26] the relativistic redshift is known as thetransverse redshift, and a redshift:
is measured, even though the object is not moving away from the observer. Even when the source is moving towards the observer, if there is a transverse component to the motion then there is some speed at which the dilation just cancels the expected blueshift and at higher speed the approaching source will be redshifted.[27]
The observations of increasing redshifts from more and more distant galaxies can be modeled assuming ahomogeneous and isotropic universe combined withgeneral relativity. This cosmological redshift can be written as a function ofa, the time-dependent cosmicscale factor:[28]: 72
The scale factor ismonotonically increasing as time passes. Thusz is positive, close to zero for local stars, and increasing for distant galaxies that appear redshifted.
Using aFriedmann-Robertson-Walker model of the expansion of the universe, redshift can be related to the age of an observed object, the so-calledcosmic time–redshift relation. Denote a density ratio asΩ0:
withρcrit the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per cubic meter of space.[29] At large redshifts,1 + z > Ω0−1, one finds:
Thecosmological redshift is commonly attributed to stretching of the wavelengths of photons due to the stretching of space. This interpretation can be misleading. As required bygeneral relativity, the cosmological expansion of space has no effect on local physics. There is no term related to expansion inMaxwell's equations that govern light propagation. The cosmological redshift can be interpreted as an accumulation of infinitesimal Doppler shifts along the trajectory of the light.[32]
There are several websites for calculating various times and distances from redshift, as the precise calculations require numerical integrals for most values of the parameters.[33][34][35][36]
Distinguishing between cosmological and local effects
The redshift of a galaxy includes both a component related torecessional velocity from expansion of the universe, and a component related to thepeculiar motion of the galaxy with respect to its local universe.[37] The redshift due to expansion of the universe depends upon the recessional velocity in a fashion determined by the cosmological model chosen to describe the expansion of the universe, which is very different from how Doppler redshift depends upon local velocity.[38] Describing the cosmological expansion origin of redshift, cosmologistEdward Robert Harrison said, "Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and the observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space. It is as simple as that..."[39]Steven Weinberg clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change ofa(t) [thescale factor] at the times of emission or absorption, but on the increase ofa(t) in the whole period from emission to absorption."[40]
If the universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted.[41]
M is themass of the object creating the gravitational field,
r is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually aSchwarzschild coordinate), and
This gravitational redshift result can be derived from the assumptions ofspecial relativity and theequivalence principle; the full theory of general relativity is not required.[43]
Several important special-case formulae for redshift in certain special spacetime geometries, as summarized in the following table. In all cases the magnitude of the shift (the value ofz) is independent of the wavelength.[46]
Thelookback time of extragalactic observations by their redshift up to z=20.[48] There are websites for calculating many such physical measures from redshift.[33][34][35][36]
The redshift observed in astronomy can be measured because theemission andabsorption spectra foratoms are distinctive and well known, calibrated fromspectroscopic experiments inlaboratories on Earth. When the redshifts of various absorption and emission lines from a single astronomical object are measured,z is found to be remarkably constant. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained bythermal or mechanicalmotion of the source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts. Alternative hypotheses and explanations for redshift such astired light are not generally considered plausible.[49]
Spectroscopy, as a measurement, is considerably more difficult than simplephotometry, which measures thebrightness of astronomical objects through certainfilters.[50] When photometric data is all that is available (for example, theHubble Deep Field and theHubble Ultra Deep Field), astronomers rely on a technique for measuringphotometric redshifts.[51] Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source,errors for these sorts of measurements can range up toδz = 0.5, and are much less reliable than spectroscopic determinations.[52]
However, photometry does at least allow a qualitative characterization of a redshift. For example, if a Sun-like spectrum had a redshift ofz = 1, it would be brightest in theinfrared (1000nm) rather than at the blue-green (500nm) color associated with the peak of itsblackbody spectrum, and the light intensity will be reduced in the filter by a factor of four,(1 +z)2. Both the photon count rate and the photon energy are redshifted. (SeeK correction for more details on the photometric consequences of redshift.)[53]
In nearby objects (within ourMilky Way galaxy) observed redshifts are almost always related to theline-of-sight velocities associated with the objects being observed. Observations of such redshifts and blueshifts enable astronomers to measurevelocities and parametrize themasses of theorbitingstars inspectroscopic binaries. Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able todiagnose and measure the presence and characteristics ofplanetary systems around other stars and have even made verydetailed differential measurements of redshifts duringplanetary transits to determine precise orbital parameters. Some approaches are able to track the redshift variations in multiple objects at once.[54]
The most distant objects exhibit larger redshifts corresponding to theHubble flow of theuniverse. The largest-observed redshift, corresponding to the greatest distance and furthest back in time, is that of thecosmic microwave background radiation; thenumerical value of its redshift is aboutz = 1089 (z = 0 corresponds to present time), and it shows the state of the universe about 13.8 billion years ago,[60] and 379,000 years after the initial moments of theBig Bang.[61]
The luminous point-like cores ofquasars were the first "high-redshift" (z > 0.1) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.[62]
For galaxies more distant than theLocal Group and the nearbyVirgo Cluster, but within a thousand megaparsecs or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed byEdwin Hubble and has come to be known asHubble's law.Vesto Slipher was the first to discover galactic redshifts, in about 1912, while Hubble correlated Slipher's measurements with distances hemeasured by other means to formulate his Law.[63] Hubble's law follows in part from theCopernican principle.[63] Because it is usually not known howluminous objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law.[64]
Gravitational interactions of galaxies with each other and clusters cause a significantscatter in the normal plot of the Hubble diagram. Thepeculiar velocities associated with galaxies superimpose a rough trace of themass ofvirialized objects in the universe. This effect leads to such phenomena as nearby galaxies (such as theAndromeda Galaxy) exhibiting blueshifts as we fall towards a commonbarycenter, and redshift maps of clusters showing afingers of god effect due to the scatter of peculiar velocities in a roughly spherical distribution.[63] This added component gives cosmologists a chance to measure the masses of objects independent of themass-to-light ratio (the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuringdark matter.[65][page needed]
The Hubble law's linear relationship between distance and redshift assumes that the rate of expansion of the universe is constant. However, when the universe was much younger, the expansion rate, and thus the Hubble "constant", was larger than it is today. For more distant galaxies, then, whose light has been travelling to us for much longer times, the approximation of constant expansion rate fails, and the Hubble law becomes a non-linear integral relationship and dependent on the history of the expansion rate since the emission of the light from the galaxy in question. Observations of the redshift-distance relationship can be used, then, to determine the expansion history of the universe and thus the matter and energy content.[66]
While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, observations beginning in 1988 of the redshift-distance relationship usingType Ia supernovae have suggested that in comparatively recent times the expansion rate of the universe hasbegun to accelerate.[67]
Comoving distance andlookback time for the Planck 2018 cosmology parameters, from redshift 0 to 15, with distance (blue solid line) on the left axis, and time (orange dashed line) on the right. Note that the time that has passed (in giga years) from a given redshift until now is not the same as the distance (in giga light years) light would have traveled from that redshift, due to the expansion of the universe over the intervening period.
The most reliable redshifts are fromspectroscopic data,[68] and the highest-confirmed spectroscopic redshift of a galaxy is that ofJADES-GS-z14-0 with a redshift ofz = 14.32, corresponding to 290 million years after the Big Bang.[69] The previous record was held byGN-z11,[70] with a redshift ofz = 11.1, corresponding to 400 million years after the Big Bang, and byUDFy-38135539[71] at a redshift ofz = 8.6, corresponding to 600 million years after the Big Bang.
Slightly less reliable areLyman-break redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshiftz = 7.5[72][73] and the next highest beingz = 7.0.[74] The most distant-observedgamma-ray burst with a spectroscopic redshift measurement wasGRB 090423, which had a redshift ofz = 8.2.[75] The most distant-known quasar,ULAS J1342+0928, is atz = 7.54.[76][77] The highest-known redshift radio galaxy (TGSS1530) is at a redshiftz = 5.72[78] and the highest-known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 atz = 6.42.[79]
Extremely red objects (EROs) areastronomical sources of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population.[80] Objects that are even redder than EROs are termedhyper extremely red objects (HEROs).[81]
Thecosmic microwave background has a redshift ofz = 1089, corresponding to an age of approximately 379,000 years after the Big Bang and aproper distance of more than 46 billion light-years.[82] The yet-to-be-observed first light from the oldestPopulation III stars, not long after atoms first formed and the CMB ceased to be absorbed almost completely, may have redshifts in the range of20 <z < 100.[83] Other high-redshift events predicted by physics but not presently observable are thecosmic neutrino background from about two seconds after the Big Bang (and a redshift in excess ofz > 1010)[84] and the cosmicgravitational wave background emitted directly frominflation at a redshift in excess ofz > 1025.[85]
In June 2015, astronomers reported evidence forPopulation III stars in theCosmos Redshift 7galaxy atz = 6.60. Such stars are likely to have existed in the very early universe (i.e., at high redshift), and may have started the production ofchemical elements heavier thanhydrogen that are needed for the later formation ofplanets andlife as we know it.[86][87]
With advent of automatedtelescopes and improvements inspectroscopes, a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of thelarge-scale structure of the universe. TheGreat Wall, a vastsupercluster of galaxies over 500 millionlight-years wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.[88]
The first redshift survey was theCfA Redshift Survey, started in 1977 with the initial data collection completed in 1982.[89] More recently, the2dF Galaxy Redshift Survey determined the large-scale structure of one section of the universe, measuring redshifts for over 220,000 galaxies; data collection was completed in 2002, and the finaldata set was released 30 June 2003.[90] TheSloan Digital Sky Survey (SDSS), is ongoing as of 2013 and aims to measure the redshifts of around 3 million objects.[91] SDSS has recorded redshifts for galaxies as high as 0.8, and has been involved in the detection ofquasars beyondz = 6. TheDEEP2 Redshift Survey uses theKeck telescopes with the new "DEIMOS"spectrograph; a follow-up to the pilot program DEEP1, DEEP2 is designed to measure faint galaxies with redshifts 0.7 and above, and it is therefore planned to provide a high-redshift complement to SDSS and 2dF.[92]
Effects from physical optics or radiative transfer
The interactions and phenomena summarized in the subjects ofradiative transfer andphysical optics can result in shifts in the wavelength and frequency of electromagnetic radiation. In such cases, the shifts correspond to a physical energy transfer to matter or other photons rather than being by a transformation between reference frames. Such shifts can be from such physical phenomena ascoherence effects or thescattering ofelectromagnetic radiation whether fromchargedelementary particles, fromparticulates, or from fluctuations of theindex of refraction in adielectric medium as occurs in the radio phenomenon ofradio whistlers.[46] While such phenomena are sometimes referred to as "redshifts" and "blueshifts", in astrophysics light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for theeffects discussed above.[46]
In many circumstances scattering causes radiation to redden becauseentropy results in the predominance of many low-energy photons over few high-energy ones (whileconserving total energy).[46] Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculatedz is generally afunction of wavelength. Furthermore, scattering fromrandommedia generally occurs at manyangles, andz is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion ofspectral lines as well.[46]
Ininterstellar astronomy,visible spectra can appear redder due to scattering processes in a phenomenon referred to asinterstellar reddening[46]—similarlyRayleigh scattering causes theatmospheric reddening of the Sun seen in the sunrise or sunset and causes the rest of the sky to have a blue color. This phenomenon is distinct from redshifting because thespectroscopic lines are not shifted to other wavelengths in reddened objects and there is an additionaldimming and distortion associated with the phenomenon due to photons being scattered in and out of theline of sight.[93]
The opposite of a redshift is ablueshift. A blueshift is any decrease inwavelength (increase inenergy), with a corresponding increase in frequency, of anelectromagnetic wave. Invisible light, this shifts a color towards the blue end of the spectrum.
Doppler blueshift is caused by movement of a source towards the observer. The term applies to any decrease in wavelength and increase in frequency caused by relative motion, even outside thevisible spectrum. Only objects moving at near-relativistic speeds toward the observer are noticeably bluer to thenaked eye, but the wavelength of any reflected or emitted photon or other particle is shortened in the direction of travel.[94]
Doppler blueshift is used inastronomy to determine relative motion:
Components of abinary star system will be blueshifted when moving towards Earth
When observing spiral galaxies, the side spinning toward us will have a slight blueshiftrelative to the side spinning away from us (seeTully–Fisher relation).
Matter waves (protons, electrons, photons, etc.) falling into agravity well become more energetic and undergo observer-independent blueshifting.
Unlike therelative Doppler blueshift, caused by movement of a source towards the observer and thus dependent on the received angle of the photon, gravitational blueshift isabsolute and does not depend on the received angle of the photon:
Photons climbing out of a gravitating object become less energetic. This loss of energy is known as a "redshifting", as photons in the visible spectrum would appear more red. Similarly, photons falling into a gravitational field become more energetic and exhibit a blueshifting. ... Note that the magnitude of the redshifting (blueshifting) effect is not a function of the emitted angle or the received angle of the photon—it depends only on how far radially the photon had to climb out of (fall into) the potential well.[98][99]
There are farawayactive galaxies that show a blueshift in their[O III] emissionlines. One of the largest blueshifts is found in the narrow-linequasar,PG 1543+489, which has a relative velocity of −1150 km/s.[97] These types of galaxies are called "blue outliers".[97]
In a hypothetical universe undergoing a runawayBig Crunch contraction, a cosmological blueshift would be observed, with galaxies further away being increasingly blueshifted—the exact opposite of the actually observedcosmological redshift in the presentexpanding universe.[101]
^abcdefRobert, Smith (2019). "Observations and the universe". In Kragh, Helge; Longair, Malcolm S. (eds.).The Oxford handbook of the history of modern cosmology. Oxford University Press.ISBN978-0-19-881766-6.OCLC1052868704.
^Slipher, Vesto (1912). "The radial velocity of the Andromeda Nebula".Lowell Observatory Bulletin.1 (8):2.56 –2.57.Bibcode:1913LowOB...2...56S.The magnitude of this velocity, which is the greatest hitherto observed, raises the question whether the velocity-like displacement might not be due to some other cause, but I believe we have at present no other interpretation for it
^de Sitter, W. (1934). "On distance, magnitude, and related quantities in an expanding universe".Bulletin of the Astronomical Institutes of the Netherlands.7: 205.Bibcode:1934BAN.....7..205D.It thus becomes urgent to investigate the effect of the redshift and of the metric of the universe on the apparent magnitude and observed numbers of nebulae of given magnitude
^See, for example, this 25 May 2004press release fromNASA'sSwiftspace telescope that is researchinggamma-ray bursts: "Measurements of the gamma-ray spectra obtained during the main outburst of the GRB have found little value as redshift indicators, due to the lack of well-defined features. However, optical observations of GRB afterglows have produced spectra with identifiable lines, leading to precise redshift measurements."
^For a tutorial on how to define and interpret large redshift measurements, see: Huchra, John."Extragalactic Redshifts".NASA/IPAC Extragalactic Database. Harvard-Smithsonian Center for Astrophysics. Archived fromthe original on 2013-12-22. Retrieved2023-03-16.
^abStaff (2015)."UCLA Cosmological Calculator".UCLA. Retrieved6 August 2022. Light travel distance was calculated from redshift value using the UCLA Cosmological Calculator, with parameters values as of 2015: H0=67.74 and OmegaM=0.3089 (see Table/Planck2015 at "Lambda-CDM model#Parameters" )
^abStaff (2018)."UCLA Cosmological Calculator".UCLA. Retrieved6 August 2022. Light travel distance was calculated from redshift value using the UCLA Cosmological Calculator, with parameters values as of 2018: H0=67.4 and OmegaM=0.315 (see Table/Planck2018 at "Lambda-CDM model#Parameters" )
^This is only true in a universe where there are nopeculiar velocities. Otherwise, redshifts combine as
which yields solutions where certain objects that "recede" are blueshifted and other objects that "approach" are redshifted. For more on this bizarre result see:Davis, T. M.; Lineweaver, C. H.; Webb, J. K. (April 2003). "Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects".American Journal of Physics.71 (4):358–364.arXiv:astro-ph/0104349.Bibcode:2003AmJPh..71..358D.doi:10.1119/1.1528916.S2CID3219383.
^Einstein, A. (1907). "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen".Jahrbuch der Radioaktivität und Elektronik.4:411–462.Bibcode:1908JRE.....4..411E. See p. 458The influence of a gravitational field on clocks
^For a review of the subject of photometry, consider:Budding, E. (September 24, 1993).Introduction to Astronomical Photometry. Cambridge University Press.ISBN0-521-41867-4.
^The technique was first described by:Baum, W. A. (1962). McVittie, G. C. (ed.).Problems of extra-galactic research. IAU Symposium No. 15. p. 390.
^Bolzonella, M.; Miralles, J.-M.; Pelló, R. (2000). "Photometric redshifts based on standard SED fitting procedures".Astronomy and Astrophysics.363:476–492.arXiv:astro-ph/0003380.Bibcode:2000A&A...363..476B.
^A pedagogical overview of the K-correction by David Hogg and other members of theSDSS collaboration can be found at:Hogg, David W.; et al. (October 2002). "The K correction".arXiv:astro-ph/0210394.
^In 1871Hermann Carl Vogel measured the rotation rate ofVenus.Vesto Slipher was working on such measurements when he turned his attention to spiral nebulae.
^Asaoka, Ikuko (1989). "X-ray spectra at infinity from a relativistic accretion disk around a Kerr black hole".Publications of the Astronomical Society of Japan.41 (4):763–778.Bibcode:1989PASJ...41..763A.
^Rybicki, G. B.; Lightman, A. R. (1979).Radiative Processes in Astrophysics. John Wiley & Sons. p. 288.ISBN0-471-82759-2.
^"Cosmic Detectives". The European Space Agency (ESA). 2013-04-02. Retrieved2013-04-25.
^An accurate measurement of the cosmic microwave background was achieved by theCOBE experiment. The final published temperature of 2.73 K was reported in this paper:Fixsen, D. J.; Cheng, E. S.; Cottingham, D. A.; Eplee, R. E. Jr.; Isaacman, R. B.; Mather, J. C.; Meyer, S. S.; Noerdlinger, P. D.; Shafer, R. A.; Weiss, R.; Wright, E. L.; Bennett, C. L.;Boggess, N. W.; Kelsall, T.; Moseley, S. H.; Silverberg, R. F.; Smoot, G. F.; Wilkinson, D. T. (January 1994). "Cosmic microwave background dipole spectrum measured by the COBE FIRAS instrument".Astrophysical Journal.420: 445.Bibcode:1994ApJ...420..445F.doi:10.1086/173575.. The most accurate measurement as of 2006 was achieved by theWMAP experiment.
^Totani, Tomonori; Yoshii, Yuzuru; Iwamuro, Fumihide; Maihara, Toshinori; et al. (2001). "Hyper Extremely Red Objects in the Subaru Deep Field: Evidence for Primordial Elliptical Galaxies in the Dusty Starburst Phase".The Astrophysical Journal.558 (2):L87 –L91.arXiv:astro-ph/0108145.Bibcode:2001ApJ...558L..87T.doi:10.1086/323619.S2CID119511017.
^Davis, Marc; et al. (DEEP2 collaboration) (2002).Science objectives and early results of the DEEP2 redshift survey. Conference on Astronomical Telescopes and Instrumentation, Waikoloa, Hawaii, 22–28 Aug 2002.arXiv:astro-ph/0209419.Bibcode:2003SPIE.4834..161D.doi:10.1117/12.457897.
^Impey, Chris. Gay, Pamela (ed.)."Dust Extinction and Reddening".Teach Astronomy - Dust Extinction and Reddening. Teach Astronomy. Retrieved2025-03-06.
Odenwald, S. & Fienberg, RT. 1993; "Galaxy Redshifts Reconsidered" inSky & Telescope Feb. 2003; pp31–35 (This article is useful further reading in distinguishing between the 3 types of redshift and their causes.)
Lineweaver, Charles H. and Tamara M. Davis, "Misconceptions about the Big Bang",Scientific American, March 2005. (This article is useful for explaining the cosmological redshift mechanism as well as clearing up misconceptions regarding the physics of the expansion of space.)
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