Redshift periodicity papers

Few years ago I compiled a list of papers relating to the quantized redshifts (or periodic redshifts, or preferred redshift peaks, or redshift bands, or…). I have previously posted it to a BAUT forum thread, but I decided to post it here as well. The list is not complete. It is probably quite thorough for older papers but there’s no papers that have been published after 2005. “Paper not available” in the list means that I couldn’t access the full text online (back then, I haven’t checked the situation currently). At some point, I might update this list to contain the newer papers as well. Note also that the subject is tied to a mainstream astronomy subject of large scale distribution of galaxies. There is a huge amount of papers on that subject, and only some of them are included to this list (those that seemed to concentreate on the periodicity issues), starting from Broadhurst et al. (1990). Here goes:

On the Wavelengths of the Absorption Lines in Quasi-Stellar Objects – Burbidge, Geoffrey (1967)

Limits to the Distance of the Quasi-Stellar Objects Deduced from Their Absorption Line Spectra – Burbidge, G. R.; Burbidge, E. M. (1967)

On the Nature of "standard" Absorption Spectrum of the Quasi-Stellar Objects – Shklovsky, J. (1967)

Concerning Redshifts in the Spectra of Quasi-Stellar Objects – Cowan, Clyde L. (1968)

The Distribution of Redshifts in Quasi-Stellar Objects, N-Systems and Some Radio and Compact Galaxies – Burbidge, Geoffrey (1968)

– Cowan, Clyde L. (1969) Nature, 224, 665

– Plagemann, S. H., Feldman, P. A. and Gribben, J. R. (1969) Nature, 224, 875

– Deeming, T. J. (1970) Nature, 225, 620

– Coles, W. A. (1970) unpublished

– Wesselink, A. J. (1970) Nature, 225, 927

QSO redshifts-Possible selection effect – Roeder, R. C. (1971) (paper not available)

Possible Discretization of Quasar Redshifts – Karlsson, K. G. (1971)

Some Trends in the Red-Shift Distribution of Quasi-Stellar Objects and Related Peculiar Galaxies – Basu, D.; Abdu, M. A. (1972)

An Analysis of the Distribution of Redshifts of Quasars and Emission-Line Objects – Lake, R. G.; Roeder, R. C. (1972)

Quasars-Effects of Earth’s atmosphere on redshift measurements – Roeder, R. C.; Dyer, C. C. (1972) (paper not available)

The Correlation of Redshift with Magnitude and Morphology in the Coma Cluster – Tifft, W. G. (1972)

The Distribution of Redshifts of Quasi-Stellar Objects and Related Emission-Line Objects – Burbidge, G. R.; O’dell, S. L. (1972)

Quasars-Selection effects and the nature of redshifts – Karlsson, K. G. (1973) (paper not available)

Properties of the redshift-magnitude bands in the Coma cluster – Tifft, W. G. (1973)

Redshift-Magnitude Bands, Quasi-Stellar Sources, and Systems of Redshift – Tifft, W. G. (1973)

QSOs-Selection in redshift measurement – Basu, D. (1973) (paper not available)

A Quantitative Alternative to the Cosmological Hypothesis for Quasars – Bell, Morley B.; Fort, David N. (1973)

The Distribution of Redshifts of Radio Galaxies with Different Optical Spectra and Forms – Burbidge, G. R.; O’dell, S. L. (1973)

Redshift Magnitude Bands for Quasistellar Sources – Veron, P.; Veron, M. P. (1974)

Remarks on the Magnitude-Redshift Bands in the Coma Cluster – Barnothy, Jeno M.; Barnothy, Madeleine F. (1974)

Fine Structure Within the Redshift-Magnitude Correlation for Galaxies – Tifft, W. G. (1974)

The definition, visibility, and significance of redshift-magnitude bands – Tifft, W. G. (1974)

Distribution of quasars in the universe – Schmidt, M. (1974) (paper not available)

On the Significance of Periodicities in the Observed Quasar Redshifts and in the Intrinsic Redshift Components as Computed from Bell and Fort’s Quasar Model – Corso, G. J.; Barnothy, J. M. (1975)

Possible effect of misidentification of QSOs on the redshift distribution – Basu, D. (1975) (paper not available)

The NGC 507 cluster of galaxies – Tifft, W. G.; Hilsman, K. A.; Corrado, L. C. (1975)

The distribution of redshifts of quasars and related objects – Knight, J. W.; Sturrock, P. A.; Switzer, P. (1976)

Critique of Bell and Fort’s quasar model – Barnothy, J. M.; Corso, G. J. (1976)

Discrete states of redshift and galaxy dynamics. I – Internal motions in single galaxies – Tifft, W. G. (1976)

On the redshift distribution of quasi-stellar objects – Wills, D.; Ricklefs, R. L. (1976)

The ln(l+z) Periodicity in the Redshifts of Quasars – Barnothy, M. F.; Barnothy, J. M. (1976)

Periodicity in the ln/1+z/ distribution of quasars – Barnothy, J. M.; Barnothy, M. F. (1976)

On the reality of periodicities in the redshift distribution of emission-line objects – Green, R. F.; Richstone, D. O. (1976)

Redshift-magnitude bands in clusters of galaxies – Tifft, W. G. (1977) (paper not available)

Discrete states of redshift and galaxy dynamics. II – Systems of galaxies – Tifft, W. G. (1977)

Discrete states of redshift and Galaxy dynamics. III – Abnormal galaxies and stars – Tifft, W. G. (1977)

Distortion of Galaxy Radial Velocity Measurements by the Night Sky Spectrum – Simkin, S. M. (1977)

On the existence of significant peaks in the quasar redshift distribution – Karlsson, K. G. (1977)

Gaps in the emission line redshift distribution of QSOs – Basu, D. (1977)

On the In (I + z) Periodicity in QSO Redshifts – Wills, D. (1977)

A trend in the gaps in redshift distribution of QSOs – Basu, D. (1978)

On the periodicity in the distribution of quasar redshifts – Kjaergaard, P. (1978) (paper not available)

The Simkin effect – Tifft, W. G. (1978)

The discrete redshift and asymmetry in H I profiles – Tifft, W. G. (1978)

The absolute solar motion and the discrete redshift – Tifft, W. G. (1978)

Redshift-magnitude bands and the evolution of galaxies. I – New observations – Tifft, W. G. (1978)

Redshift-magnitude bands and the evolution of galaxies. II – Data analysis – Tifft, W. G. (1978)

Band theory applied to the Coma/A1367 supercluster – Tifft, W. G.; Gregory, S. A. (1979)

Structure within redshift-magnitude bands – Morphological evolution – Tifft, W. G. (1979)

Periodicity in the redshift intervals for double galaxies – Tifft, W. G. (1980)

Absorption line redshift distribution of QSOs – Basu, D. (1980)

An analysis of the redshift-magnitude band phenomenon in the Coma Cluster – Nanni, D.; Pittella, G.; Trevese, D.; Vignato, A. (1981)

The periodicity in the distribution of quasar redshifts and the density perturbations in the early universe – Fang, L.-Z.; Chu, Y.-Q.; Liu, Y.; Cao, C. (1982)

Quantum effects in the redshift intervals for double galaxies – Tifft, W. G. (1982)

Double galaxy investigations. II – The redshift periodicity in optically observed pairs – Tifft, W. G. (1982)

The cosmic density wave and its observable vestige – Liu, Y.-Z. (1982)

Effect of search lines on emission and absorption redshift distribution of QSOs – Basu, D. (1983)

Distribution of gaps in emission line redshifts of QSOs – Basu, D. (1983)

Redshift quantization in compact groups of galaxies – Cocke, W. J.; Tifft, W. G. (1983)

The effects of emission line identification on the redshift distribution of QSO’s – Zhou, Y.-Y.; Deng, Z.-G.; Zhou, Z.-L. (1983)

The distribution of quasar emission-line redshifts – Box, T. C.; Roeder, R. C. (1984)

The distribution of absorption line redshifts of quasars and its origin – Chu, Y.; Fang, L.; Liu, Y. (1984) (paper not available)

Status of Quantized Extragalactic Redshifts – Tifft, W. G.; Cocke, W. J. (1984)

Double galaxy redshifts and dynamical analyses – Sharp, N. A. (1984)

Global redshift quantization – Tifft, W. G.; Cocke, W. J. (1984)

Double galaxy investigations. III – The differential redshift distribution and emission-line correlations – Tifft, W. G. (1985)

Theory and interpretation of quantized extragalactic redshifts – Cocke, W. J. (1985)

The redshift distribution law of quasars revisited – Depaquit, S.; Pecker, J.-C.; Vigier, J.-P. (1985)

Emission line redshift distribution of QSOs – Zhou, Y.-Y.; Deng, Z.-G.; Dai, H.-J. (1985)

The distribution of emission line redshift of QSOs – Basu, D. (1985)

Relativistic realization of a proposed model of quantized redshift – Nieto, M. M. (1986) (paper not available)

Results from high precision 21-cm redshift measurements – Cocke, W. J.; Tifft, William G. (1987) (paper not available)

Quantized galaxy redshifts – Tifft, William G.; Cocke, W. John (1987) (paper not available)

Additional members of the Local Group of galaxies and quantized redshifts within the two nearest groups – Arp, Halton (1987)

Quantized Redshifts are Real – Tifft, W. G. (1987) (paper not available)

A different approach to the cosmological quantized redshift problem – Buitrago, J. (1988) (paper not available)

Quantization of redshift differences in isolated galaxy pairs – Tifft, W. G.; Cocke, W. J. (1989)

The periodicity in the redshift distribution of the Lyman-alpha forest – Chu, Yaoquan; Zhu, Xingfen (1989)

Double galaxy redshifts and the statistics of small numbers – Newman, William I.; Haynes, Martha P.; Terzian, Yervant (1989)

Redshift quantization in the Ly-alpha forest and the measurement of q(0) – Cocke, W. J.; Tifft, W. G. (1989)

Periodicities in galaxy redshifts – Croasdale, Martin R. (1989)

Periodicity of quasar redshifts – Arp, H.; Bi, H. G.; Chu, Y.; Zhu, X. (1990)

Deviation from periodicity in the large-scale distribution of galaxies – Kurki-Suonio, H.; Mathews, G. J.; Fuller, G. M. (1990)

Large-scale distribution of galaxies at the Galactic poles – Broadhurst, T. J.; Ellis, R. S.; Koo, D. C.; Szalay, A. S. (1990) (paper not available)

The Virgo cluster as a test for quantization of extragalactic redshifts – Guthrie, B. N. G.; Napier, W. M. (1990)

Double galaxy redshifts and dynamical analyses. II – Sample comparisons – Sharp, N. A. (1990)

A large-scale periodic clustering of galaxies as a result of hydromagnetic ringing of gas in a recombination ERA of the expanding universe – Fujimoto, Mitsuaki (1990)

The redshift peak at Z = 0.06 – Burbidge, G.; Hewitt, A. (1990)

Periodicity of redshift distribution in a T-3 universe – Fang, Li-Zhi (1990)

Oscillating universe – The periodic redshift distribution of galaxies with a scale 128/h megaparsecs at the galactic poles – Morikawa, Masahiro (1990)

Quasar redshifts and nearby galaxies – Karlsson, K. G. (1990)

Can oscillating physics explain an apparently periodic universe? – Hill, Christopher T.; Steinhardt, Paul J.; Turner, Michael S. (1990) (paper not available)

Claims for periodicity in quasar redshifts – Scott, Douglas (1991)

Statistical procedure and the significance of periodicities in double-galaxy redshifts – Cocke, W. J.; Tifft, W. G. (1991)

Coherent peculiar velocities and periodic redshifts – Hill, Christopher T.; Steinhardt, Paul J.; Turner, Michael S. (1991)

Universe with oscillating expansion rate – Morikawa, Masahiro (1991)

Quasi-periodicity in deep redshift surveys – van de Weygaert, Rien (1991)

Against the Delta-ln(1 + z) of about 0.205 periodicity in quasar redshifts – Scott, D. (1991)

Large-scale structure in the Lyman-alpha forest – Fang, L. Z. (1991)

Periodic universe and condensate of pseudo-Goldstone field – Anselm, A. A. (1991)

Quasi-periodic structures in the large-scale galaxy distribution and three-dimensional Voronoi tessellation – Ikeuchi, Satoru; Turner, Edwin L. (1991)

Evidence for redshift periodicity in nearby field galaxies – Guthrie, B. N. G.; Napier, W. M. (1991)

Power-spectrum analysis of one-dimensional redshift surveys – Kaiser, N.; Peacock, J. A. (1991)

Superclusters and pencil-beam surveys – The origin of large-scale periodicity – Bahcall, Neta A. (1991)

Large-scale periodicity – Problems with cellular models – Williams, B. G.; Heavens, A. F.; Peacock, J. A. (1991)

Properties of the redshift. III – Temporal variation – Tifft, W. G. (1991)

Velocity differences in binary galaxies. I – Suggestions for a nonmonotonic, two-component distribution – Schneider, Stephen E.; Salpeter, Edwin E. (1992)

Statistical tests of peaks and periodicities in the observed redshift distribution of quasi-stellar objects – Duari, Debiprosad; Gupta, Patrick D.; Narlikar, Jayant V. (1992)

Possible geometric patterns in 0.1c scale structure – Tully, R. B.; Scaramella, Roberto; Vettolani, Giampaolo; Zamorani, Giovanni (1992)

Statistical methods for investigating periodicities in double-galaxy redshifts – Cocke, W. J. (1992)

Statistical properties of the sky distribution of extragalactic infrared sources – Source-number fluctuations and density peaks – Fabbri, R. (1992)

The distribution of rich clusters of galaxies in the south Galactic pole region – Guzzo, Luigi; Collins, Chris A.; Nichol, Robert C.; Lumsden, Stuart L. (1992)

Large-scale periodicity and Gaussian fluctuations – Dekel, Avishai; Blumenthal, George R.; Primack, Joel R.; Stanhill, David (1992)

The peaks and gaps in the redshift distributions of active galactic nuclei and quasars – Kruogovenko, Andrei A.; Orlov, Viktor V. (1992)

A new method for the detection of a periodic signal of unknown shape and period – Gregory, P. C.; Loredo, Thomas J. (1992)

Cosmological parameters and redshift periodicity – Holba, Agnes; Horvath, I.; Lukacs, B.; Paal, G. (1992)

Redshift quantization in the cosmic background rest frame – Tifft, W. G.; Cocke, W. J. (1993)

The clustering of QSOs at low redshift – Boyle, B. J.; Mo, H. J. (1993)

Upper limit on periodicity in the three-dimensional large-scale distribution of matter – Tytler, David; Sandoval, John; Fan, Xiao-Ming (1993)

High-resolution simulation of deep pencil beam surveys – analysis of quasi-periodicity – Weiss, A. G.; Buchert, T. (1993)

Can Extra Power Explain Periodicity on Large Scales? – Luo, Shan; Vishniac, Ethan T. (1993)

Quasi-periodical structures in the galaxy populations – Mass and luminosity functions for the cluster galaxies – Litvin, V. F.; Holzmann, F. M.; Smirnov, A. V.; Taibin, B. S.; Orlov, V. V.; Baryshnikov, V. N. (1993)

Apparently periodic Universe – Busarello, G.; Capozziello, S.; de Ritis, R.; Longo, G.; Rifatto, A.; Rubano, C.; Scudellaro, P. (1994)

Redshift data and statistical inference – Newman, William I.; Haynes, Martha P.; Terzian, Yervant (1994)

Once more on quasar periodicities – Holba, Agnes; Horvath, I.; Lukacs, B.; Paal, G. (1994) (paper not available)

Redshift Quantization – A Review – Tifft, W. G. (1995) (paper not available)

The Spontaneous Violation of the Cosmological Principle and the Possible Wave Structures of the Universe – Budinich, P.; Nurowski, P.; Raczka, R.; Ramella, M. (1995)

Global Redshift Periodicities: Association with the Cosmic Background Radiation – Cocke, W. J.; Tifft, W. G. (1996) (paper not available)

Evidence for quantized and variable redshifts in the cosmic backgroung rest frame – Tifft, W. G. (1996) (paper not available)

Statiscal analysis of the occurrence of periodicities in galaxy redshift data – Cocke, W.; Devito, C.; Pitucco, A. (1996) (paper not available)

Redshift periodicity in the Local Supercluster – Guthrie, B. N. G.; Napier, W. M. (1996)

Testing for quantized redshifts. I. The project – Napier, W. M.; Guthrie, B. N. G. (1996) (paper not available)

Testing for quantized redshifts. II. The Local Supercluster – Napier, W. M.; Guthrie, B. N. G. (1996) (paper not available)

The 37.5 km s-1 redshift periodicity of galaxies as the machion frequency – Arp, Halton (1996)

Galactic periodicity and the oscillating G model – Salgado, Marcelo; Sudarsky, Daniel; Quevedo, Hernando (1996)

Global Redshift Periodicities and Periodicity Structure – Tifft, W. G. (1996)

The Periodic Distribution of Redshifts – Carvalho, J. C. (1997) (paper not available)

Global Redshift Periodicities and Periodicity Variability – Tifft, W. G. (1997)

The redshift periodicity of galaxies as a probe of the correctness of general relativity – Valerio Faraoni (1997)

A 120 MPC Periodicity in the Three-Dimensional Distribution of Galaxy Superclusters – Einasto, J.; Einasto, M.; Gottloeber, S.; Mueller, V.; Saar, V.; Starobinsky, A. A.; Tago, E.; Tucker, D.; Andernach, H.; Frisch, P. (1997)

A study of the large-scale distribution of galaxies in the South Galactic Pole region – II. Further evidence for a preferential clustering scale? – Ettori, S.; Guzzo, L.; Tarenghi, M. (1997)

Redshift Quantization in the Cosmic Background Rest Frame – Tifft, W. G. (1997)

The Possible Redshift Clumping of Damped Lyman-alpha Absorbers – Gal, R.; Djorgovski, S. G. (1997)

Quantized Redshifts: A Status Report – Napier, W. M.; Guthrie, B. N. G. (1997)

The supercluster-void network – II. an oscillating cluster correlation function – Einasto, J.; Einasto, M.; Frisch, P.; Gottlober, S.; Muller, V.; Saar, V.; Starobinsky, A. A.; Tago, E.; Tucker, D.; Andernach, H. (1997)

Periodicity in the Redshift Distribution of Quasi Stellar Objects – Duari, Debiprosad (1997)

Periodicity revealed by statistics of the absorption-line redshifts of quasars – Liu, Yong-Zhen; Hu, Fu-Xing (1998)

The spatial and temporal distribution of matter in the redshift interval z = 1.2-3.2 – Ryabinkov, A. I.; Varshalovich, D. A.; Kaminker, A. D. (1998) (paper not available)

Periodicity in quasar redshifts or selection effects? – Basu, D. (1999) (paper not available)

Clustering Properties of Low-Redshift QSO Absorption Systems Toward the Galactic Poles – vanden Berk, Daniel E.; Lauroesch, James T.; Stoughton, Chris; Szalay, Alexander S.; Koo, David C.; Crotts, Arlin P. S.; Blades, J. Chris; Melott, Adrian L.; Boyle, Brian J.; Broadhurst, Thomas J.; York, Donald G. (1999)

Galaxy Clustering and Large-Scale Structure from z=0.2 to z=0.5 in Two Norris Redshift Surveys – Small, Todd A.; Ma, Chung-Pei; Sargent, Wallace L. W.; Hamilton, Donald (1999)

Space-time distributions of QSO absorption systems – Kaminker, A. D.; Ryabinkov, A. I.; Varshalovich, D. A. (2000)

Spatial structure and periodicity in the Universe – González, J. A.; Quevedo, H.; Salgado, M.; Sudarsky, D. (2000)

The Distribution of Redshifts in New Samples of Quasi-stellar Objects – Burbidge, G.; Napier, W. M. (2001)

Periodicity versus selection effects in the redshift distribution of QSOs – Basu, D. (2001) (paper not available)

Electrostatic interaction energy and factor 1.23 – Rubcic, A.; Arp, H.; Rubcic, J. (2002)

No Periodicities in 2dF Redshift Survey Data – E. Hawkins, S.J. Maddox, M.R. Merrifield (2002)

Quantum Perturbative Approach to Discrete Redshift – Mark D. Roberts (2002)

The supercluster-void network V.. The regularity periodogram – Saar, E.; Einasto, J.; Toomet, O.; Starobinsky, A. A.; Andernach, H.; Einasto, M.; Kasak, E.; Tago, E. (2002) (paper not available)

Redshift periodicities, The Galaxy-Quasar Connection – Tifft, W. G. (2003) (paper not available)

The Sources of Gamma-Ray Bursts and Their Connections with QSOs and Active Galaxies – Burbidge, G. R. (2003) (paper not available)

Is the Redshift Clustering of Long-Duration Gamma-Ray Bursts Significant?
– J. S. Bloom (2003)

The detection of periodicity in QSO data sets – Napier, W. M.; Burbidge, G. (2003) (paper not available)

Discrete Components in the Radial Velocities of ScI Galaxies – M.B. Bell, S.P. Comeau, D.G. Russell (2004)

Large Scale Periodicity in Redshift Distribution – K. Bajan, M. Biernacka, P. Flin, W. Godlowski, V. Pervushin, A. Zorin (2004)

Distances of Quasars and Quasar-Like Galaxies: Further Evidence that QSOs may be Ejected from Active Galaxies – M. B. Bell (2004)

Selection Effects in the Redshift Distribution of Gamma-Ray Bursts and Associated Quasi-stellar Objects and Active Galaxies – Basu, D. (2005) (paper not available)

Periodicities of Quasar Redshifts in Large Area Surveys – H. Arp, C. Fulton, D. Roscoe (2005)

Evidence for Cosmological Oscillations in the Gold SnIa Dataset – R. Lazkoz, S. Nesseris, L. Perivolaropoulos (2005)

Critical Examinations of QSO Redshift Periodicities and Associations with Galaxies in Sloan Digital Sky Survey Data – Su Min Tang, Shuang Nan Zhang (2005)

Intrinsic redshift component

Some time ago, I wrote about anomalous redshifts ending that to a mention of intrinsic redshift component. I followed that post by explaining how redshift components are generally calculated. There I gave the basic equation used for that:

1 + zM = (1 + zC) * (1 + zK) [eq. 1]

where zM is the measured redshift of the object in question, zC is the cosmological redshift component, and zK is kinematical redshift component, which is my own term, it is generally called as redshift caused by peculiar velocity of the object.

In discordant redshift systems, the kinematical redshift component tends to be too large to be explained by peculiar velocity in traditional thinking. Too large is rather subjective concept but there is no generally accepted limit for that. 1000 km/s is largely used but in tight galaxy cluster conditions even few thousand km/s might be accepted. When the kinematical redshift component is too large, we need another redshift component, the intrinsic redshift component. The “intrinsic” comes from the assumption that the additional redshift comes from within the object in question. I’m not particularly keen on this term because it assumes a rather specific cause for the additional redshift, but as it is commonly used, I’ll do so too. Here I will deal only with the mechanics of the addition of intrinsic redshift component to the equations described in above mentioned posts, I will not discuss the possible causes of the component.

This additional redshift component is added to the equation 1 like this:

1 + zM = (1 + zC) * (1 + zK)* (1 + zi) [eq. 2]

where zi is the intrinsic redshift component. Problem we usually are facing is that we don’t know how large the kinematical redshift component is, so we cannot use this equation as such. As a solution, common method is to assume that there is no kinematical redshift component, so the equation 2 reduces to:

1 + zM = (1 + zC) * (1 + zi) [eq. 3]

Basically it is the same equation as equation 1 but we just call the second redshift component by different name. It is important to remember that the assumption of no kinematical redshift is not necessarily a good assumption. When we are dealing with large redshift differences between objects, then the assumption does not distort our results much, but when the redshift differences are small, the unknown kinematical redshift component introduces a large uncertainty to our calculations, as we shall see later.

Let us now calculate the redshift components of an example system. We’ll use the famous NGC 7603 system. There are four relevant objects in this system; NGC 7603, NGC 7603B, and the two high redshift galaxies ([LG2002] 3 and [LG2002] 2) within the bridge area. Redshift of NGC 7603 (according to NED) is z = 0.029524, redshift of NGC 7603B is z = 0.055742, redshift of [LG2002] 3 is z = 0.391000, and redshift of [LG2002] 2 is z = 0.243000.

Let us now use equation 3 to calculate the intrinsic redshift of NGC 7603B. To calculate that we need to know the cosmological redshift of NGC 7603B. For that, we assume that it is at same physical distance from us than NGC 7603, and we also assume that NGC 7603 itself doesn’t have intrinsic redshift or peculiar velocity (lot of assumptions here). With these assumptions, we can use the redshift of NGC 7603 as cosmological redshift. Before we can calculate the values, we need to solve the equation 3 for intrinsic redshift like this:

1 + zM = (1 + zC) * (1 + zi) | /(1 + zC)
=> 1 + zi = (1 + zM)/(1 + zC) | -1
=> zi = (1 + zM)/(1 + zC) – 1

Now we can insert the values and calculate:

zi = (1 + 0.055742)/(1 + 0.029524) – 1 = 0.025466138

Using relativistic Doppler redshift equation to convert that to velocity yields 7537 km/s. We can use exactly the same equation for the other two objects, and we find out that intrinsic redshift of [LG2002] 3 is zi = 0.35111 (87600 km/s) and intrinsic redshift of [LG2002] 2 is zi = 0.207354 (55800 km/s).

What if NGC 7603B would have peculiar velocity? Let us assume that it does have a peculiar velocity of 1000 km/s. That corresponds to zK = 0.00334. Now we have to use equation 2. Solving it for intrinsic redshift gives:

zi = (1 + zM)/{(1 + zC) * (1 + zK)} – 1

Then we’ll put the numbers in:

zi = (1 + 0.055742)/{(1 + 0.029524) * (1 + 0.00334)} – 1 = 0.022052

When large peculiar velocity was involved, the intrinsic redshift changed from 0.025466138 to 0.022052, a change of 13 %. From this we can see that high precision studies relating to this are very difficult, remembering also the many assumptions that were needed to come this far. However, because of the large redshift difference between NGC 7603 and [LG2002] 3, a similar peculiar velocity in [LG2002] 3 would change the intrinsic redshift only by 1 %, so this approach can be used to cases that have high redshift difference between the object in question and the main galaxy.

Redshift components

In an earlier post, I briefly described the redshift components of an extragalactic object. It turns out that generally an extragalactic object has two redshift components; kinematical and cosmological. In this post I’m going to describe how the different components are handled, when calculating things relating to redshifts of galaxies and their associated objects. When combining different redshift components, they are not simply added together. Redshift is a curious quantity in that sense. Let us consider a simple example of one galaxy having a cosmological and kinematical redshift components.

The galaxy we observe has a peculiar velocity with respect to a reference frame that is non-moving frame local to the galaxy. For example, the Earth moves around the Sun, Sun is in motion around the Milky Way center, and the Milky Way is in motion with respect to Local Group, and so on. All this makes the Earth to have a peculiar velocity with respect to non-moving space at location of the Earth. So, when the galaxy we are observing emits light, the first thing the light experiences is the kinematical redshift that occurs between the galaxy’s rest frame and the galaxy’s local non-moving reference frame. After that, the light starts moving through space towards us. In the space it encounters something that causes redshift also. That is the cosmological redshift component. In Big Bang cosmology, cosmological redshift component is caused by expanding space. Many alternative cosmologies have different explanations.

In the receiving end, there is the Earth’s peculiar velocity that also causes redshifting, but that is usually not kept in these analyses. Instead, the measured redshift is corrected for the Earth’s motion. Usually redshifts have been given in heliocentric reference frame, but galactocentric and Local Group -centric redshifts have also been used. Lately, the redshifts have been increasingly given in CMBR reference frame. However, it is quite common to just use the heliocentric reference frame. That contains some error in the redshift, but when dealing with objects close to each other, such as a galaxy and an object near it, then the correction due to Earth’s complex motion is approximately the same for both objects, so in practice there’s no effect for the Earth’s motion to the results in that kind of situations. Therefore it is OK for us to use heliocentric redshifts here, which is still most common frame where redshifts are given.

Now, let us derive the equation that can be used to calculate the redshift components. This derivation is given in Davis et al. (2003). We start with the basic redshift equation:

1 + z = Lobs/Lem [eq. 1]

where z is the measured redshift (the heliocentric redshift), Lobs is the wavelength of the light we observe, and Lem is the wavelength of the light when it was emitted. The peculiar velocity of the galaxy causes the wavelength to change. We will call this wavelength Lnm, the wavelength of the light in non-moving reference frame local to the galaxy. We will do a mathematical trick next. We will multiply the basic redshift equation by one (which doesn’t change the result so it’s a valid thing to do), but we just write 1 = Lnm/Lnm. So we have:

1 + z = Lobs/Lem * Lnm/Lnm

Then we move Lnm’s a bit:

1 + z = Lobs/Lnm * Lnm/Lem [eq. 2]

This equation now contains both redshift components. I’ll demonstrate that next. If we would be in the non-moving reference frame local to the galaxy, we would observe the wavelength of the galaxy to be Lobs = Lnm, and putting that to equation 2 we would get kinematical redshift zK:

1 + zK = Lnm/Lnm * Lnm/Lem = Lnm/Lem

=> 1 + zK = Lnm/Lem [eq. 3]

If the galaxy wouldn’t have any peculiar velocity, there wouldn’t be any kinematical redshift component, so wavelength in the non-moving reference frame would be the same as emitted wavelength, i.e. Lnm = Lem. Again from equation 2 we would then get cosmological redshift component zC:

1 + zC = Lobs/Lnm * Lnm/Lnm

1 + zC = Lobs/Lnm [eq. 4]

Now we have seen that equation 2 contains both redshift components, but it still has wavelengths in it. We would want redshifts there explicitly. We can do it by replacing wavelengths in equation 2 with redshift components from equations 3 and 4, and it becomes:

1 + zM = (1 + zC) * (1 + zK) [eq. 5]

Where zM is the measured redshift of an object. So, as you can see, when adding up redshift components, it is not done simply by zM = zC + zK. Let’s try the equation 5 with an example galaxy. Let us assume that we have measured a redshift of zM = 0.01 to a galaxy, but let’s also assume that the galaxy has a peculiar velocity of 500 km/s away from us. First thing we need to do is to convert the peculiar velocity to redshift. There is a simple equation for that: z = v/c. Speed of light, c, is 299792.458 km/s, so our kinematical redshift component is:

zK = 500 km/s / (299792.458 km/s) = 0.001668

Now we know the kinematical redshift component and the measured redshift, so only unknown in equation 5 is the cosmological redshift component. Let’s calculate it:

1 + zM = (1 + zC) * (1 + zK)
=> zC = (1 + zM)/(1 + zK) – 1 = (1 + 0.01)/(1 + 0.001668) – 1 = 0.008318

In practice it is very difficult to determine the redshift components. The kinematical and cosmological redshift components look the same in the spectra of objects. If we are only observing a single galaxy, it is practically impossible to determine the components. Situation gets better if we have two objects physically associated with each other, pair of interacting galaxies for example. Easiest situation is when there is a large galaxy interacting with a clearly smaller galaxy, and we wish to calculate the redshift components of the smaller galaxy. In that situation, we can assume that the smaller galaxy follows the motion of the large galaxy similarily as the Earth follows the motion of the Sun around the Milky Way nucleus, even if the Earth also has its own motion around the Sun. So, the smaller galaxy has its own motion around the large galaxy, but it still follows the path of the large galaxy. This means we can calculate the system so that we ignore any peculiar velocity the large galaxy has because the smaller galaxy also has the same peculiar velocity in addition to its own motion around the large galaxy. Or, to put in other words, we can calculate the redshift component that the smaller galaxy has in addition to large galaxy redshift components. So, the thorough equation for the redshift components of the smaller galaxy would be:

1 + zS = (1 + zC) * (1 + zKlarge) * (1 + zKsmall)

Where zS is the measured redshift of the smaller galaxy, zKlarge is the kinematical redshift component, or the peculiar velocity of the large galaxy, and zKsmall is the additional peculiar velocity of the smaller galaxy. zKlarge is included here because we assume that the smaller galaxy follows the motion of the large galaxy, as discussed above. Also following the discussion above, especially the equation 5, we can now just put all large galaxy components under one heading to derive an equation that we can use to calculate the kinematical redshift component of the smaller galaxy:

1 + zS = (1 + zL) * (1 + zKsmall) [eq. 6]

Where zL is the combined redshift components of the large galaxy, i.e. the measured redshift of the large galaxy. Note that equation 6 is exactly the same as equation 5, only the names of the components have changed. How can we use this equation then? In practice, we should have redshifts measured both for the large and the smaller galaxy. The measured redshift of the large galaxy is the zL, and the measured redshift of the smaller galaxy is the zM. So, let’s assume that we have a large galaxy with measured redshift of zL = 0.010, and we have a smaller galaxy right beside the large one with measured redshift of zS = 0.011. We assume that these galaxies are interacting (sometimes there are some visible signs suggesting that, but not always), and we therefore decide we can use equation 6. First, we’ll solve the equation 6 for zKsmall, because that is what we want to calculate:

zKsmall = (1 + zS)/(1 + zL) – 1 [eq. 7]

And then we will just put the numbers in:

zKsmall = (1 + 0.011)/(1 + 0.010) – 1 = 0.00099

Peculiar velocity of the smaller galaxy with reference to the large galaxy is then:

v = cz = 299792.458 * 0.00099 = 297 km/s

The kinematical redshift component of the smaller galaxy is the only redshift component that we can calculate from the system when we only know redshifts of both galaxies. In order to determine other components, we need additionally a redshift independent distance measurement for the galaxy pair. If we know the distance between us and the galaxy pair, we can calculate how big kinematical redshift component the large galaxy has, and the size of the cosmological redshift component. However, problem here is that distance measurements to galaxies are still quite inaccurate, so this calculation will have lot of uncertainty.

Let’s take NGC 289 as an example. NGC 289 has a redshift of c * zL = 1629 km/s (zL = 0.005434) in NED, and a distance of 23.4 Mpc. NGC 289 has a companion, LSBG F411-024, which has a redshift of cz = 1510 km/s (zS = 0.005037). If you look at the distance measurement section for NGC 289 in NED, you will notice that there’s two measurements, from which the NED value is derived; 19.4 Mpc and 27.4 Mpc, quite a difference, which reflects the above mentioned inaccuracy in distance measurements.

To convert the measured distance to redshift, we will use Hubble law (there are more distinguished methods to do that, but it will serve the purpose for us in this example). From Hubble law we get (using Hubble constant of 72 (km/s)/Mpc):

vDIST = H0 * d = 72 (km/s)/Mpc * 23.4 Mpc = 1684.8 km/s

If we assume that this is accurate value, it would mean that NGC 289 has a peculiar velocity of:

vKlarge = c * zL – vDIST = 1629 km/s – 1684.8 km/s = -55.8 km/s

Minus sign indicates that the velocity is towards us (redshift is positive when velocity is directed away from us). From the peculiar velocity we then get the kinematical redshift component of the large galaxy:

zKlarge = vKlarge / c = -55.8 km/s / (299792.458 km/s) = -0.000186

Cosmological redshift component is (from equation 5 applied to the large galaxy):

1 + zL = (1 + zC) * (1 + zKlarge)

zC = (1 + zL) / (1 + zKlarge) – 1 = (1 + 0.005434) / (1 + -0.000186) – 1 = 0.00562

We could also have derived the cosmological redshift component directly from the redshift independent distance measurement (if we multiply the above calculated zC by c, we get 1685.2 km/s which is quite close to vDIST calculated above). Finally we will also have to calculate the kinematical redshift component of the companion galaxy using the equation 7:

zKsmall = (1 + zS)/(1 + zL) – 1 = (1 + 0.005037)/(1 + 0.005434) – 1 = -0.000395

vKsmall = c * zKsmall = 299792.458 km/s * -0.000395 = -118 km/s

Kinematical redshift component of the companion galaxy turns out to be negative too, but that was expected because the redshift velocity cz was smaller in the companion galaxy suggesting that it has a peculiar velocity towards us. Notice that the calculated value here is almost exactly the value from the measured cz’s = 1510 – 1629 = 119 km/s, so we could have calculated the kinematical redshift component also from measured cz’s directly by:

zKsmall = c * zS – c * zL / c = (zS – zL) * c / c = zS – zL

Now you might notice that this goes exactly against what I said in the beginning, that redshifts are not simply added together. It is true, it goes against what I said, and the reason is this: the equation v = cz is only an approximation that works quite well for velocities far lower than the speed of light. If we would use more precise calculation methods, we would use the relativistic doppler line of sight equation instead of v = cz:

1 + z = sqrt[(1 + v/c)/(1 – v/c)]

Using that equation, the companion redshift component calculation wouldn’t reduce back to zS – zL anymore, and our world makes sense again. 🙂

References

Davis et al., 2003, AmJPh, 71, 358, “Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects”

Introduction to anomalous redshifts

It is very difficult to determine the exact meaning of the term “redshift anomaly”. It can be lot of things. It can be said that redshift is anomalous if it doesn’t somehow fit in our current descriptions of the things in the universe. Basically any strange thing studied by redshifts is a redshift anomaly. Redshift anomalies could be found within one object, or within a group of objects, or then a group of objects could exhibit a redshift anomaly as a whole.

In traditional view, redshift of an object is composed of three components; kinematical, gravitational, and cosmological. Local and nearby objects don’t have any cosmological redshift, and gravitational redshift is so small that it can usually be ignored (although in the context of redshift anomalies, gravitational redshift is often mentioned, and sometimes with a good reason), so in those objects we are generally only interested in kinematical redshift, which is caused by peculiar velocity differences between the source of light and the receiving end. On the other hand, objects that are far away have so large cosmological redshift that all other redshift components can be ignored. Generally an extragalactic object has cosmological redshift component that is proportional to its distance from us, and kinematical redshift component which usually is considered to be smaller than cz ~ 1000 km/s (although in some extreme cases even 3000 km/s has been accepted, NGC 1275 system is an example of that). In some cases there are also other redshift components from scattering processes (Compton scattering for example), but they are not usually considered in average extragalactic objects. If there are some redshift observations that don’t fit to this traditional view, then those redshifts are anomalous.

Through the history of spectroscopy there has been redshift anomaly candidates. There is an apparent solar limb effect, where the redshifts at the limb of the Sun don’t quite match the expected values (Mikhail et al., 2002, and references therein). Within Milky Way, there is so called K-effect, where certain types of stars have a small excess redshift component (Arp, 1992). Outside Milky Way lot of redshift anomaly candidates have been found. Companion galaxies might have an excess redshift component (Arp, 1994). Some higher redshift objects might be associated with lower redshift objects, as suggested by their apparent nearness, or by their geometrical alignment, or by apparent connecting bridges (Lopez-Corredoira, 2009). Supporting these, some strange coincidences in redshift values have been cited, such as redshifts of higher redshift objects decreasing when their location being further out from the lower redshift object (Arp, 1999), or redshift values clustering around certain values (Tifft, 1995). Redshift anomalies relating to associations of objects with differing redshifts are usually called discordant redshifts.

Other type of redshift anomaly candidates are already mentioned redshift clustering around certain values (which is known as redshift quantization or periodic redshifts), excess redshift in certain galaxy types, unexpected redshift behaviour across galaxy disks (Jaakkola et al., 1975), and multitude of other suggested anomalous redshift issues (Pioneer anomalies, blueshifted quasars, etc.).

Solutions for redshift anomalies are usually sought from observational problems and from traditional science. Often it is the case that traditional physics are performing some unexpected tricks, and we see them as redshift anomalies. Those occasions give us an opportunity to extend our knowledge and polish our theories. Such seems to be the case with the solar limb effect, which has been a problem for a long time, and now seems to be getting solved mainly by gravitational redshift component revision (Mikhail et al., 2002). Another example of redshift anomaly that got solved, and is now part of mainstream science is the redshift anomaly found in 1920’s that most galaxies seemed to have “velocity shift” towards the red color in the spectrum. This was solved by Hubble (1929) by showing that there is a redshift-luminosity relation in galaxies which was interpreted as redshift-distance relation.

One interesting aspect of anomalous redshifts is the possibility to find something remarkably unexpected, perhaps something that doesn’t fit to our current theories at all. A whole new redshift component, perhaps intrinsic to the object itself (as has been suggested in many papers dealing with some redshift anomaly candidate)? We’ll see…

References

Arp, 1992, MNRAS, 258, 800, “Redshifts of high-luminosity stars – The K effect, the Trumpler effect and mass-loss corrections”

Arp, 1994, ApJ, 430, 74, “Companion galaxies: A test of the assumption that velocities can be inferred from redshifts”

Arp, 1999, A&A, 341L, 5, “A QSO 2.4 arcsec from a dwarf galaxy – the rest of the story”

Hubble, 1929, PNAS, 15, 168, “A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae”

Jaakkola et al., 1975, A&A, 40, 257, “On possible systematic redshifts across the disks of galaxies”

Lopez-Corredoira, 2009, arXiv, 0901.4534, “Apparent discordant redshift QSO-galaxy associations”

Mikhail et al., 2002, Ap&SS, 280, 223, “Application of Theorems on Null-Geodesics on The Solar Limb Effect”

Russell, 2005, Ap&SS, 298, 577, “Evidence for Intrinsic Redshifts in Normal Spiral Galaxies”

Tifft, 1995, Ap&SS, 227, 25, “Redshift Quantization – A Review”