Astrophysics (Index)About


(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.

zVelocity Mpc GyearsVelocity Mpc Gyearsexcess
0.012998km/s 43Mpc 0.1Gy2983km/s 43Mpc 0.1Gy0.50%
0.025996km/s 86Mpc 0.3Gy5936km/s 85Mpc 0.3Gy1.01%
0.038994km/s 128Mpc 0.4Gy8859km/s 127Mpc 0.4Gy1.52%
0.0411992km/s 171Mpc 0.6Gy11752km/s 168Mpc 0.5Gy2.04%
0.0514990km/s 214Mpc 0.7Gy14615km/s 209Mpc 0.7Gy2.56%
0.0617988km/s 257Mpc 0.8Gy17449km/s 249Mpc 0.8Gy3.09%
0.0720985km/s 300Mpc 1.0Gy20253km/s 289Mpc 0.9Gy3.62%
0.0823983km/s 343Mpc 1.1Gy23027km/s 329Mpc 1.1Gy4.15%
0.0926981km/s 385Mpc 1.3Gy25772km/s 368Mpc 1.2Gy4.69%
0.129979km/s 428Mpc 1.4Gy28487km/s 407Mpc 1.3Gy5.24%
0.259958km/s 857Mpc 2.8Gy54061km/s 772Mpc 2.5Gy10.91%
0.389938km/s 1285Mpc 4.2Gy76898km/s 1099Mpc 3.6Gy16.96%
0.4119917km/s 1713Mpc 5.6Gy97230km/s 1389Mpc 4.5Gy23.33%
0.5149896km/s 2141Mpc 7.0Gy115305km/s 1647Mpc 5.4Gy30.00%
0.6179875km/s 2570Mpc 8.4Gy131370km/s 1877Mpc 6.1Gy36.92%
0.7209855km/s 2998Mpc 9.8Gy145658km/s 2081Mpc 6.8Gy44.07%
0.8239834km/s 3426Mpc 11.2Gy158381km/s 2263Mpc 7.4Gy51.43%
0.9269813km/s 3854Mpc 12.6Gy169731km/s 2425Mpc 7.9Gy58.97%
1299792km/s 4283Mpc 14.0Gy179875km/s 2570Mpc 8.4Gy66.67%
1.5449689km/s 6424Mpc 21.0Gy217091km/s 3101Mpc 10.1Gy107.14%
2599585km/s 8565Mpc 27.9Gy239834km/s 3426Mpc 11.2Gy150.00%
3899377km/s 12848Mpc 41.9Gy264523km/s 3779Mpc 12.3Gy240.00%
41199170km/s 17131Mpc 55.9Gy276731km/s 3953Mpc 12.9Gy333.33%
51498962km/s 21414Mpc 69.8Gy283587km/s 4051Mpc 13.2Gy428.57%
61798755km/s 25696Mpc 83.8Gy287801km/s 4111Mpc 13.4Gy525.00%
72098547km/s 29979Mpc 97.8Gy290568km/s 4151Mpc 13.5Gy622.22%
82398340km/s 34262Mpc 111.7Gy292480km/s 4178Mpc 13.6Gy720.00%
92698132km/s 38545Mpc 125.7Gy293856km/s 4198Mpc 13.7Gy818.18%
102997925km/s 42827Mpc 139.7Gy294878km/s 4213Mpc 13.7Gy916.67%
113297717km/s 47110Mpc 153.7Gy295657km/s 4224Mpc 13.8Gy1015.38%
123597509km/s 51393Mpc 167.6Gy296265km/s 4232Mpc 13.8Gy1114.29%
133897302km/s 55676Mpc 181.6Gy296749km/s 4239Mpc 13.8Gy1213.33%
144197094km/s 59958Mpc 195.6Gy297139km/s 4245Mpc 13.8Gy1312.50%
154496887km/s 64241Mpc 209.5Gy297459km/s 4249Mpc 13.9Gy1411.76%
10029979246km/s 428275Mpc 1396.8Gy299734km/s 4282Mpc 14.0Gy9901.96%
1090326773779km/s 4668197Mpc 15225.6Gy299792km/s 4283Mpc 14.0Gy108900.18%

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

Further reading:

Referenced by pages:
Akaike information criterion (AIC)
Alcock-Paczyński effect (AP effect)
astronomical quantities
Balmer jump (BJ)
Balmer series (H)
band shifting
baryon acoustic oscillations (BAO)
Balmer-break galaxy (BBG)
brightest cluster galaxy (BCG)
black hole shadow
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)
cosmic background radiation (CBR)
Fred Young Submillimeter Telescope (FYST)
Canadian Cluster Comparison Project (CCCP)
Cepheid variable (CEP)
CfA Redshift Survey
Canada-France Redshift Survey (CFRS)
Canadian Hydrogen Intensity Mapping Experiment (CHIME)
cosmic infrared background (CIB)
ionized carbon fine structure line ([CII])
cluster radius
cosmic microwave background (CMB)
cosmic neutrino background (CNB)
carbon monoxide (CO)
Carbon Monoxide Mapping Array (COMA)
cosmic distance ladder
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)
deep field (DF)
deep survey
Dark Energy Survey (DES)
Dark Energy Spectroscopic Instrument (DESI)
distance modulus (μ)
damped Lyman alpha absorber (DLA)
Deep Multicolor Survey (DMS)
Doppler shift
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)
Faber-Jackson relation (FJR)
faint blue galaxy (FBG)
Faint Infrared Grism Survey (FIGS)
first galaxies
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
Giant Metrewave Radio Telescope (GMRT)
gravitational redshift
Great Attractor
Great Debate
Great Wall
Gunn-Peterson trough
Hα survey
Hamburg/ESO Survey (HE)
Hercules-Corona Borealis Great Wall (Her-CrB GW)
Herschel Redshift Survey (HeRS)
Hoag's Object
hot DOG
Hubble constant (H0)
Hubble diagram
Hubble expansion
Hubble time (tH)
Hubble Ultra-Deep Field (HUDF)
infrared (IR)
intensity mapping
IRAC Shallow Survey (ISS)
K correction
Lyman-alpha emitter (LAE)
Lambda-CDM model (ΛCDM)
Lyman-break galaxy (LBG)
Las Campanas Redshift Survey (LCRS)
line broadening
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)
Molecular Deep Field
Murchison Widefield Array (MWA)
near infrared (NIR)
observable universe
Origins Space Telescope (OST)
Palomar Four-filter Survey (PC)
P Cygni profile
peak star-formation epoch
photometric redshift (photo-z)
quasar (QSO)
redshift-angular size relation
redshift-magnitude relation
redshift space
redshift survey
rest wavelength
Rossiter-McLaughlin effect (RM effect)
Supernova Cosmology Project (SCP)
Sloan Digital Sky Survey (SDSS)
star formation history (SFH)
star formation rate (SFR)
star-formation rate stellar-mass ratio
Spitzer HETDEX Exploratory Large Area Survey (SHELA)
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
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)
X-ray luminosity function (XLF)
X-ray luminous galaxy cluster
FourStar Galaxy Evolution Survey (ZFOURGE)