### redshift

(z, redshift parameter)
(change to longer wavelengths due to Doppler effects)

Redshift is a lengthening of wavelengths, e.g., of spectral lines, due to Doppler effects of radial motion of the radiation-source away from the observer (i.e., its recessional velocity). Given the expansion of the universe, which effectively results in higher recessional velocity at further distances, redshift is used as a measure of distance and time, and a redshift due to this is called a cosmological redshift.

Redshifts and blue shifts (for the analogous shortening of the wavelength from sources moving toward the observer) are also measured to determine radial velocity in studies of peculiar velocity and of objects orbiting stars such as extra-solar planets and binary star companions. Measurements using the highest-precision high resolution spectrography (HRS) can determine radial velocity differences as small as 1 meter per second.

The redshift parameter (often just called redshift) z is:

```     observed wavelength - rest wavelength
z =  —————————————————————————————————————
rest wavelength
```

The relationship between z and the recessional velocity is:

```              1 + v/c
1 + z = sqrt( ——————— )
1 - v/c
```

Transverse motion and gravity also produce/affect redshift.

Redshift derived from absorption lines is termed absorption redshift (zabs) and from emission lines is termed emission redshift (zem). A difference between the two implies distance and/or velocity differences between the emitting and absorbing material, and can motivate some analysis to determine the "true" cosmological redshift.

If a body's redshift is determined, assuming the redshift is cosmological, a distance estimate can be calculated using the redshift and the Hubble constant (70 km/s/Mpc). Below are some calculated values. "Linear" was calculated using a simple linear approximation (workable for z less than 0.1) and "Relativistic" taking special relativity into account (the above formula), suitable for more redshifts (though for the largest redshifts, corresponding distances and times are further affected by the universe's density, calculated to be a little smaller than shown below). "Gyears" (for gigayears) is how far in the past we're viewing the body and is also its distance in billions of light-years.

 z Velocity Mpc Gyears Velocity Mpc Gyears excess 0.01 2998km/s 43Mpc 0.1Gy 2983km/s 43Mpc 0.1Gy 0.50% 0.02 5996km/s 86Mpc 0.3Gy 5936km/s 85Mpc 0.3Gy 1.01% 0.03 8994km/s 128Mpc 0.4Gy 8859km/s 127Mpc 0.4Gy 1.52% 0.04 11992km/s 171Mpc 0.6Gy 11752km/s 168Mpc 0.5Gy 2.04% 0.05 14990km/s 214Mpc 0.7Gy 14615km/s 209Mpc 0.7Gy 2.56% 0.06 17988km/s 257Mpc 0.8Gy 17449km/s 249Mpc 0.8Gy 3.09% 0.07 20985km/s 300Mpc 1.0Gy 20253km/s 289Mpc 0.9Gy 3.62% 0.08 23983km/s 343Mpc 1.1Gy 23027km/s 329Mpc 1.1Gy 4.15% 0.09 26981km/s 385Mpc 1.3Gy 25772km/s 368Mpc 1.2Gy 4.69% 0.1 29979km/s 428Mpc 1.4Gy 28487km/s 407Mpc 1.3Gy 5.24% 0.2 59958km/s 857Mpc 2.8Gy 54061km/s 772Mpc 2.5Gy 10.91% 0.3 89938km/s 1285Mpc 4.2Gy 76898km/s 1099Mpc 3.6Gy 16.96% 0.4 119917km/s 1713Mpc 5.6Gy 97230km/s 1389Mpc 4.5Gy 23.33% 0.5 149896km/s 2141Mpc 7.0Gy 115305km/s 1647Mpc 5.4Gy 30.00% 0.6 179875km/s 2570Mpc 8.4Gy 131370km/s 1877Mpc 6.1Gy 36.92% 0.7 209855km/s 2998Mpc 9.8Gy 145658km/s 2081Mpc 6.8Gy 44.07% 0.8 239834km/s 3426Mpc 11.2Gy 158381km/s 2263Mpc 7.4Gy 51.43% 0.9 269813km/s 3854Mpc 12.6Gy 169731km/s 2425Mpc 7.9Gy 58.97% 1 299792km/s 4283Mpc 14.0Gy 179875km/s 2570Mpc 8.4Gy 66.67% 1.5 449689km/s 6424Mpc 21.0Gy 217091km/s 3101Mpc 10.1Gy 107.14% 2 599585km/s 8565Mpc 27.9Gy 239834km/s 3426Mpc 11.2Gy 150.00% 3 899377km/s 12848Mpc 41.9Gy 264523km/s 3779Mpc 12.3Gy 240.00% 4 1199170km/s 17131Mpc 55.9Gy 276731km/s 3953Mpc 12.9Gy 333.33% 5 1498962km/s 21414Mpc 69.8Gy 283587km/s 4051Mpc 13.2Gy 428.57% 6 1798755km/s 25696Mpc 83.8Gy 287801km/s 4111Mpc 13.4Gy 525.00% 7 2098547km/s 29979Mpc 97.8Gy 290568km/s 4151Mpc 13.5Gy 622.22% 8 2398340km/s 34262Mpc 111.7Gy 292480km/s 4178Mpc 13.6Gy 720.00% 9 2698132km/s 38545Mpc 125.7Gy 293856km/s 4198Mpc 13.7Gy 818.18% 10 2997925km/s 42827Mpc 139.7Gy 294878km/s 4213Mpc 13.7Gy 916.67% 11 3297717km/s 47110Mpc 153.7Gy 295657km/s 4224Mpc 13.8Gy 1015.38% 12 3597509km/s 51393Mpc 167.6Gy 296265km/s 4232Mpc 13.8Gy 1114.29% 13 3897302km/s 55676Mpc 181.6Gy 296749km/s 4239Mpc 13.8Gy 1213.33% 14 4197094km/s 59958Mpc 195.6Gy 297139km/s 4245Mpc 13.8Gy 1312.50% 15 4496887km/s 64241Mpc 209.5Gy 297459km/s 4249Mpc 13.9Gy 1411.76% 100 29979246km/s 428275Mpc 1396.8Gy 299734km/s 4282Mpc 14.0Gy 9901.96% 1090 326773779km/s 4668197Mpc 15225.6Gy 299792km/s 4283Mpc 14.0Gy 108900.18%

See "Distances table" for redshifts/distances to example astronomical objects and times since astronomical events.

(measure,EMR,Doppler)
https://en.wikipedia.org/wiki/Red_shift

Referenced by pages:
AEGIS
Akaike information criterion (AIC)
AIM-CO
Alcock-Paczyński effect (AP effect)
ALFALFA
astronomical quantities
AzTEC-3
Balmer jump (BJ)
Balmer series (H)
band shifting
baryon acoustic oscillations (BAO)
Balmer-break galaxy (BBG)
brightest cluster galaxy (BCG)
BINGO
blind survey
Butcher-Oemler effect (BOE)
Baryon Oscillation Spectroscopic Survey (BOSS)
Calán/Tololo Supernova Survey
Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS)
carbon (C)
Fred Young Submillimeter Telescope (FYST)
Cepheid variable (CEP)
CfA Redshift Survey
Canadian Hydrogen Intensity Mapping Experiment (CHIME)
cosmic infrared background (CIB)
ionized carbon fine structure line ([CII])
cosmic microwave background (CMB)
cosmic neutrino background (CNB)
carbon monoxide (CO)
COMAP
Carbon Monoxide Mapping Array (COMA)
CONCERTO
COPSS
cosmological time dilation
cosmological zoom simulation
Cosmic Evolution Survey (COSMOS)
critical density (ρc)
Carnegie Supernova Project (CSP)
dark age
data cube
direct collapse black hole (DCBH)
DEEP2
deep field (DF)
deep survey
Dark Energy Survey (DES)
Dark Energy Spectroscopic Instrument (DESI)
DEVILS
distance modulus (μ)
damped Lyman alpha absorber (DLA)
Deep Multicolor Survey (DMS)
Doppler shift
dropout
Extended Groth Strip (EGS)
emission line galaxy (ELG)
emission line
ESO Nearby Abell Cluster Survey (ENACS)
epoch of reionization (EOR)
epoch of galaxy formation
extremely red object (ERO)
Euclid
Faber-Jackson relation (FJR)
faint blue galaxy (FBG)
Faint Infrared Grism Survey (FIGS)
first galaxies
FRB121102
galaxy age determination
galaxy cluster (CL)
galaxy merger
galaxy power spectrum
Galaxy Zoo
gas fraction estimation
Green Bank Telescope (GBT)
Gemini Observatory
Giant Gemini GMOS survey (GGG survey)
Giant GRB Ring
GISMO
GLARE
gravitational redshift
Great Attractor
Great Debate
Great Wall
Gunn-Peterson trough
Hα survey
Hamburg/ESO Survey (HE)
HERA
Hercules-Corona Borealis Great Wall (Her-CrB GW)
Herschel Redshift Survey (HeRS)
HFLS3
HIRAX
Hoag's Object
hot DOG
Hubble constant (H0)
Hubble diagram
Hubble expansion
Hubble time (tH)
Hubble Ultra-Deep Field (HUDF)
infrared (IR)
intensity mapping
isotropy
IRAC Shallow Survey (ISS)
K correction
KMOS3D
Lyman-alpha emitter (LAE)
Lambda-CDM model (ΛCDM)
Lyman-break galaxy (LBG)
Las Campanas Redshift Survey (LCRS)
LIGO
Large Millimeter Telescope (LMT)
Low-frequency Array (LOFAR)
large quasar group (LQG)
luminous red galaxy (LRG)
luminosity distance (dL)
luminosity function (LF)
Lyman alpha (Ly-α)
Lyman-alpha forest
Lyman series (L)
Multi-Epoch Nearby Cluster Survey (MENeaCS)
microwave
Molecular Deep Field
Murchison Widefield Array (MWA)
near infrared (NIR)
observable universe
OIR
Origins Space Telescope (OST)
Pantheon
PAPER
Palomar Four-filter Survey (PC)
P Cygni profile
peak star-formation epoch
PHIBSS
photometric redshift (photo-z)
PRIMUS
proto-cluster
protogalaxy
quasar (QSO)
recombination
redshift-angular size relation
redshift-magnitude relation
redshift space
redshift survey
rest wavelength
Rossiter-McLaughlin effect (RM effect)
r-process
Supernova Cosmology Project (SCP)
Sloan Digital Sky Survey (SDSS)
star formation history (SFH)
star formation rate (SFR)
star-formation rate stellar-mass ratio
SHARDS
Spitzer HETDEX Exploratory Large Area Survey (SHELA)
SINS
6dF Galaxy Survey (6dFGS)
supermassive black hole (SMBH)
SMBH formation
submillimeter galaxy (SMG)
Supernova Legacy Survey (SNLS)
spectral feature
spectral line
Swope Supernova Survey (SSS)
standard ruler
survey depth
Sachs-Wolfe effect (SWE)
systemic velocity
templates
3C 273
3C 279
3C 295
3C 48
Tianlai Project
time dilation
Tomographic Ionized-carbon Mapping Experiment (TIME)
tired light
21-cm experiment
21-cm line
2dF Galaxy Redshift Survey (2dFGRS)
ultra-fast outflow (UFO)
ultraluminous infrared galaxy (ULIRG)
USS Sources
VIMOS Public Extragalactic Redshift Survey (VIPERS)
VIMOS-VLT Deep Survey (VVDS)
James Webb Space Telescope (JWST)
WiggleZ
X-ray luminosity function (XLF)
X-ray luminous galaxy cluster
FourStar Galaxy Evolution Survey (ZFOURGE)

Index