VII. Unexpected Galactic Redshifts


Expected Hubble distance-velocity relation

1930: H0 = 558 km s−1 Mpc−1
Intervening years: H0 = 30-100 km s−1 Mpc−1
 Today, although narrowed, we still have a range of values: H0 = ~63-75 km s−1 Mpc−1

The Hubble-Lemaître distance relation, which was discovered by at least 1929 if not before, is considered perhaps the central discovery of modern cosmology. However, the H0 relation has a long history of alterations. In 2004, Kirshner reviewed the history and status of H0 in a paper discussing the SN Ia data about the putative acceleration of the cosmic expansion. From Hubble and Humason's 1929 paper through 2004.

Kirshner (2004) f1
Kirshner f1 legend
Kirshner (2004) f2_H0 from 1929 to 2004
Kirshner f2 legend
Kirshner f3
Kirshner, f3 legend

Krshner f4
Krshner f4 legend
Kirshner f6_SN1 redshift data
Kirshner f6 legend

Above, we see the 2004 estimates of the SN1a acceleration data compared with various HBBC models with chosen proportions of 'dark energy' and 'dark matter' (Kirshner, 2004; link). Their review was in many ways far too simplistic to fully consider the magnitude and complications of the ad hoc free-parameter fitting required in HBBC models.

In the NASA website of the Lambda working group, they attempted to provide a summary of the many estimated values of the Hubble constant H0 from a series of major studies done from 2001 to 2021. This serves to highlight the difficulties of nailing down this supposed constant:

H0 values


H0 2nd table
Hubble Constant (NASA / LAMBDA Archive Team; link)

PNG (480 x 697 px) 38Kb    PNG (1024 x 1488 px) 39kb    PNG (2048 x 2975 px) 194kb
PDF 77kb (Vector Art)    SVG 57kb (Vector Art)   EPS 41kb (Vector Art).(https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.cfm).


Over recent years, there has been a growing disagreement between estimating the Hubble constant, H0, using more local distance measures with (often a very few) 'standard candles' such as Cepheid variables and red giants (~72-73 or even 75 +/- 2.3, &c., km s−1 Mpc−1 ) and those estimated by supposedly early universe parameters of the CMB which are model-derived by the CDM and ΛCDM versions of the HBBC (~67-69 km s−1 Mpc−1 ; see citations on the disconnect controversy link, link, and link). Despite the above claims of approaching resolution between 'standard candle' and model-dependent estimates of H0, as of 2022, the discrepancies are gaping, as indicated in a selection of recent papers.

Since JWST. Since becoming fully operational in July of 2022, JWST has not resolved the questions. Just within the arXiv database, a non-quote restricted query for 'measuring the Hubble constant' continues to illustrate the ongoing tensions within and beyond the >CDM paradigm for determining H0 (1,927 results by 30 May 2024: arXiv query; 1,920 results without 'the': arXiv query). In the more restricted case of the quote-restricted phrase "Hubble tension" query we have 612 results (30 May 2024: arXiv query), whereas for the non-quote-restricted phrase 'Hubble constant' we have 1,386 results (30 May 2024: arXiv query). There is a large burgeoning of attempts to resolve this tension.

Questions: Is the Hubble tension caused by artifacts of instrumentation in different data cohorts? Or is there a paradigmatic reason why such a tension exists? On 28 May 2024, physicist / physics (sometimes cosmology) popular commentator, Sabine Hossenfelder on her YouTube channel suggested that "A huge cosmology problem just might have disappeared" (videolink) citing the November of 2023 paper, which we discuss further by Freedman, W. L. & Madore, B. F. (2023). Progress in direct measurements of the Hubble constant. Journal of Cosmology and Astroparticle Physics (JCAP) 2023, 1-35. JCAP11(2023)050. https://iopscience.iop.org/article/10.1088/1475-7516/2023/11/050/pdf. https://doi.org/10.1088/1475-7516/11/050. Hossenfelder frames the issues succinctly by noting that the Hubble tension is caused by one (any) of the following:

In chapter V, we discuss the Freedman & Madore (2023) paper, the data, analyses, results, and the implications for cosmology.

Question for JWST: Has the James Webb Space Telescope (JWST), which became operational in July of 2022, helped this 'tense' situation any? According to a report from November of 2022, Yuan et al. [including 'dark energy' Nobel laureate Adam Riess] (2022. A first look at Cepheids in Type Ia supernova host with JWST. ApJ Letters 940, L17. https://doi.org/10.3847/2041-8213/ac9b27), they found that although not fully optimized for Cepheid observation, with JWST's higher sensitivity in the near-IR part of the spectrum, they were able to mitigate host dust-dimming effects on distance estimates from Cepheid variables in NGC 1365 the host galaxy for distance calibration of SNIa 2012fr for the Hubble constant (H0). Using a standard star, they did photometry on 31 previously-assayed Cepheids with JWST spanning the period (P) interval from 1.15 < log P < 1.75 including 24 Cepheids with longer P range of 1.35 < log P < 1.75. The period-luminosity (P-L) relations of this cohort was compared to the HST photometry results from 49 Cepheids in the full period range as well as 38 in the longer-period interval. HST and JWST results respectively show good agreement on P-L relations with intercepts (at log P = 1) of magnitudes of 25.74 +/- 0.04 and 25.72 +/- 0.05. The HST-JWST Cepheid photometric consistency shows that there's no HST-'biased-bright' error at the ~0.2 magnitude level which was suggested as a resolution to the 'Hubble tension.' See Yuan et al.'s Figures 1 and 3 below. 






Answer: No. The 'Hubble tension' is left unresolved because it is not an artifact of method or instrumentation, but a real feature of the data sets, which again suggests the need for a paradigmatic shift in cosmological theory. The data collected from the world's next generation space observatory, the JWST, is helping in that direction. 

Back in 2021, Di Valentino et al. (with an author line including 'dark energy' Nobel Laureate Adam Riess and grand master astronomer Joseph Silk) published a 110 page monograph reviewing >1000 peer-reviewed papers with a title parroting Edwin Hubble's famous 1936 book title, "In the realm of the Hubble tension—a review of solutions" in Class. Quantum Grav. 38, 153001 (https://doi.org/10.1088/1361-6382/ac086d). For their comparison standards, Di Valentino et al. compared this multitude of papers to the Planck 2018 cosmic microwave background power spectrum data with baryonic acoustic oscillations (already loaded with adjustable ΛCDM parameters and yielding an H0 value centered on 67.36 +/- 0.54 km s−1 Mpc−1, according to Hart & Chluba, 2019) and the combined Pantheon SN1e and latest R20 data from the SH0ES Team Riess et al. (2021, Astrophys. J. 908, L6) with an extrapolation of the Hubble constant, H0 = 73.2 +/- 1.3 km s−1 Mpc−1 at the 68% confidence level (CL). Like the Planck 2018 data, the SH0ES data set is itself heavily parametrized as indicated in the mere meaning of the acronym itself, "Supernova, H0, for the Equation of State of Dark Energy" (ESA press release on the 2001-2021 SN data). Excerpted from the many figures of the H0 values in studies cited in the monograph, one can see the vast degree of parameter-fitting or epicycles-upon-epicycles inserted to try to resolve this supposed constant considered a holy grail of modern cosmology. Even with all of the multitude of attempts to adjust parameters or create epicycles, create complex new models, some appealing to unknown physics, there still is a 4 σ discrepancy between these two standards, or euphemistically we can call it a mere 'tension':

In the excerpted whisker plots from select figures (di Valentino et al. 2021): The vertical pink band equates with the H0 value reported by the Planck 2018 team "within a ΛCDM scenario," while the vertical cyan band equates with the 68% CL estimation of the value based the SH0ES R20 data
Fig. 1 (di Valentinto et al. 2021).


Fig. 2 (di Valentinto et al. 2021).


Fig. 4 (di Valentinto et al. 2021).


Fig. 6 (di Valentinto et al. 2021).


Fig. 8 (di Valentinto et al. 2021).


Fig. 10 (di Valentinto et al. 2021).


Fig. 12 (di Valentinto et al. 2021).


Fig. 14 (di Valentinto et al. 2021).



Fig. 16 (di Valentinto et al. 2021).

In the spring of 2021, in a blog entitled, "What is the Hubble tension, really? A SH0ES-centric view of the problem," fellow at the Kavli Institute of Cosmology (University of Cambridge), Sunny Vagnozzi posted a humorous "10 commandments for Hubble hunters" satirizing the parameter-fitting required for those seeking to resolve the Hubble "tension." Here is the original version, before he softened and euphemized the "4th commandment" for a visiting lecture:


(https://www.sunnyvagnozzi.com/blog/what-is-the-hubble-tension-really).

What's with the Hubble Constant determination Indeterminacy? What is going on with the notorious difficulty of nailing down a consistent, across the galactic constituent population and across cosmic time value of H0? Is it because H0? varies over cosmological time? Or is it because too narrow a sample of 'standard candle' bodies and the heavily cosmological model-dependent CMB-based calculations of H0. What are they missing in the cosmological data?

This following diagram from Risaliti & Luzzo (2019; DOI:10.1038/s41550-018-0657-z) further illustrates the actual diversity of redshift / estimated distance modulus with error bars in the data (including ~1600 quasars marked in yellow just with 1σ uncertainties, or the new [blue-starred marked] quasars with z > 3 from the JLA survey), all illustrating much more redshift-diverse populations of extragalactic objects. When set distance ladder 'standard candle' are not the only objects included, then it becomes obvious that the H0 relation values are not nearly so tightly constrained as the HBBC model suggests, let alone the highly-parameter-fitted CDM versions.

Hubble diagram of several types of objecs
Figure legend
Figure legend

And that does not even include the whole sample size of ~7,300 quasars (marked in grey) with available X-ray and UV measurements, shown in this UV and X-ray luminosity relation diagram:

UV / X-ray monocromatic luminosities of larg sample of quasars
Figure legend (link).

In actuality, the so-called Hubble 'tension' is far too circumscribed by various parameters of the Big Bang ΛCDM model to even come close to the state of the data regarding the trends in galactic and galactic object redshifts in the Universe. In a lecture a couple weeks later commenting on the early data after the release of the JWST inaugural images in July of 2022, astronomer and plasma cosmologist Eric Lerner with colleague Ricardo Scarpa summarized the the tension between the SH0ES and the model-driven CMB estimates of the H0 constant, which have now diverged while each being were refined into a ~5σ spread of significance.

Image from Lerner lecture (26 July 2022): "Panic and censorship in cosmology" (link) as well as a link to the 3 papers.

On 22 November 2023, Licia Verde, Nils Schöneberg, & Héctor Gil-Marín released a review paper on the status and meaning of the 'Hubble tension' and attempts to measure and account for it in the quest for a precision cosmology: Verde et al. 2023. A tale of many H0. https://arxiv.org/abs/2311.13305; https://doi.org/10.48550/arXiv.2311.13305. The authors point out that there are two values around with the measurements cluster: (a) the model-independent determinations from nearby galaxies with standard candles like Cepheid variables and SNIa distance ladder data of H0 = ~68 km s–1 Mpc–1 and (b) the ΛCDM model-dependent determination of H0 = ~73 km s–1 Mpc–1 based on the CMB (for a discussion of the CMB and its interpretation in cosmology, see the yet-to-be-published Chapter IV. The Cosmic Microwave Background (CMB) radiation: From Where and Whence? "As far as the eye can see?"). They suggest that there are three ways to resolve the 'tension' none of which bring consensus to the research community:
 The authors opine, "The research community has been actively looking for deviations from ΛCDM for two decades; the one we might have found makes us wish we could put the genie back in the bottle."




TT = temperature power..., TE = temperature-polarization cross..., & EE = polarisation power spectra, respectively.

BAO = baryonic acoustic oscillation.


Verde et al. (2023).
It is hardly necessary to say: The 'Hubble tension' crisis in cosmology continues on.

Redshift anomalies: Long before the current 'Hubble tension'

Long before the ongoing 'Hubble tension' crisis in cosmology, in fact decades before a series of unexpected, non-HBBC-canonical galactic redshift anomalies began to surface, quite prior to the various 'fixes' of added epicycles to the ΛCDM version of the HBB cosmology, suggesting that something is going on which not only does not fit the HBBC in general, but has never been directly dealt with in dominant ΛCDM hot Big Bang cosmology (HBBC).  We will be returning in several chapters (VIII, IX, and X, as well as possible remote JWST-discovered redshift associations in chapter V) to the subject of anomalous redshifts.

Unexpected redshifts: The complicated nature of galactic redshifts. The early start of the real problem arose when the proponents of the HBBC paradigm narrowed their focus and research to simply trying to determine and then refine "the value H0" by selected from the diversity of object-specific redshifts or z-values in any given cluster or supercluster of galaxies, rather than examining all the redshifts in any clusters and superclusters under survey to see if there are perchance any issues affecting the H0 redshift relation.

Continuing the history from chapter III. The Hubble relation and the expanding Universe: 'The war of the world-views' & a new Ptolemaic system (1929-2013), although observed by radio frequencies as radio sources since the 1950s, what came to be called quasi-stellar objects (QSOs) or quasars (Chiu, 1964), that is, the radio sources were identified with optical objects in 1962 (Schmidt, 1963; link). These unusual star-like objects with a radio-loud signatures and found to have very unexpectedly high red-shifts, and so according to the Hubble relation were thought to be very remotely distant in the Universe, given the Hubble relation. They are now associated with active galactic nuclei (AGN) in more than one cosmological model.

In the mid-1960s, a series of discussions stirred up by CSSC-associated cosmologists questioned whether the QSOs and their redshifts fit well into the distance-luminosity H0 models. In a pitched 'battle' between: Hoyle, F. & Burbidge, G. R. 1966. Nature 210, 1846; Hoyle. F. & Burbidge, G. R. 1966. ApJ 144, 634; and Hoyle, F., Burbidge, G. & Sargent, W. 1966. On the nature of the Quasi-stellar Sources. Nature 209, 751. https://doi.org/10.1038/209751a0, and their Big Bang interlocutors, Longair, M. 1966. Evidence on the evolutionary character of the Universe derived from recent redshift measurements. Nature 211, 949. https://doi.org/10.1038/211949a0; Sciama, D. & Rees, M. 1966. Cosmological significance of the relation between red-shift and flux density for quasars. Nature 211, 1283. https://doi.org/10.1038/2111283a0; Roeder, R. O. & Mitchell, G. F. 1966. Nature 212, 166; and Bolton, J. 1966. Identification of radio galaxies and Quasi-Stellar Objects. Nature 211, 917. https://doi.org/10.1038/211917a0. In their letter to Nature, Hoyle, F. & Burbidge, G. 1966. Relation between the red-shifts of Quasi-stellar Objects and their radio magnitudes. Nature 212, 1334. https://doi.org/10.1038/2121334a0, pointed out that these critics had misrepresented them, and jumped the gun to conclude that the QSO redshifts supported an evolutionary model (short hand for Big Bang cosmology). Sciama & Rees (1966) had gone so far as to say that the QSO redshift data ruled out the steady state (CSSC) cosmologies. As with Martin Ryle's early claims in the late 1950s about an evolving cosmos based on radiosources (see chapter III), Hoyle & Burbidge (1966) pointed out that in fact their interlocutors had jumped the gun, as it were, and that their own goals had been modest, balanced, writing:
     "While one can certainly express a personal preference for this latter form of argument. it is overstating the case to claim support from it for one cosmology or another. It appears to us that all these discussions are predicated on the cosmological interpretation of the red-shifts of the quasi-stellar objects, in the sense that this interpretation is taken as axiomatic. Conclusions following from it are accepted, essentially whatever they may be, because a non-cosmological interpretation [non-BB] is taken to be out of the question. In fact, the issue is an open one. The difficulties of the problem, both observational and theoretical, lie in deciding between the cosmological and the 'local' interpretation, not in seeing the implications of either one of them by itself. Throughout our work on this subject, we have been concerned to cover both sides of the problem, rather than to concentrate on one half. By doing so we have been able to place limitations on the kind of model required in the cosmological case, as well as in the local case."
—Hoyle & Burbidge (1966). Nature 212, 1334 [emphasis added].
(One of the pivotal creative papers from the 1960s, to be discussed further).

So below, we begin to  discuss the data which show that in fact there are other causal factors which effect the observed redshifts of various kinds of galaxies and galactic objects which do not conform to the simple Hubble relation. Specific types of galaxies which do not neatly conform to the expected redshifts of the 'standard candles' even if they are apparently in comparable distances. Some of these extragalactic sources include quasars (QSOs), BL Lacertae objects (BL Lac), Seyfert galaxies, blue stellar x-ray objects, ultra-luminous infrared galaxies (ULIRGs), and other types of active galactic nuclei (AGNs) within the clusters and superclusters in which they occur. These associated objects with different redshifts indicate that some component(s) of z may not be Hubble-distance related. Some of the first phenomena we would expect to notice then, starting with canonical Hubble relation data, are
The evidence for these three phenomena is developed in brief as follows. First, we note that the canonical account of the Hubble redshift relation follows a straightforward distance-(Doppler) velocity relation, which was graphed in the early years after Hubble's 1929 discovery of the distance-redshift relation (Hubble, 1929; Hubble & Humason, 1931; Tolman, 1934). 


(0) Early canonical redshifts in the Hubble distance-redshift relationship:


Hubble relation (Hubble, 1929; from Hoyle et al. 2000).

Log velocity plotted against photographic magnitude (mpg) indicative of the Hubble relation (Hubble & Humason, 1931; plot taken from Tolman, 1934; from Hoyle et al. 2000).

By 1934, the distance-velocity redshift relation had been extended >10x farther than in Hubble (1929).

Hubble relation (Tolman, 1934; from Hoyle et al. 2000).


(i) Unusual scatters in the redshift-distance relationships of large aggregates of galaxies and galactic objects.

Some early (but not-understood) observations of this non-canonical or unexpected redshift scatter phenomena were compiled in the study of Lang et al. 1975 by plotting of galactic redshifts taken from the de Vaucouleurs, G. & de Vaucouleurs, A. 1964. Bright Galaxy Catalogue (Austin, TX: University of Texas Press; and since updated to a 3rd edition, 1994: https://heasarc.gsfc.nasa.gov/W3Browse/all/rc3.html). Among the 'bright' galaxies since the early 1960s there emerged a scatter of even the standard 'bright galaxies' in the de Vaucouleurs Catalogue.


Galaxy Radial Velocity (z in km s–1) versus Apparent Magnitude (m). The data for this plot is taken from Lang et al. (1975), from the 'Reference Catalogue of Bright Galaxies' (de Vaucouleurs et al. 1964). There is a high resolution PostScript version of this plot, and the specific plot was created with Cat's eye (http://tarantella.gsfc.nasa.gov/viewer/example/catseye_intro.html).

In standard, canonical, HBBC-compliant terms the scatter of redshifts was interpreted as the peculiar velocities of the galaxies in a cluster superimposed on the Hubble relation. However, that effect is expected to dampen out and vanish with distance in a standard interpretation. It does not.


Compiled by Allan Sandage, Palomar Observatories: Dashed lines are supposed to represent the effect of peculiar velocities of 1000 - 2000 km/s (cited in Arp, 1998).

It began to be noticed by some astronomers that active extragalactic objects like Seyfert galaxies or quasars showed higher than expected redshift (z) values, and thus seemed to depart from the Hubble correlation, to which we will return below.


Compiled by Halton Arp (1968, cited in 1998), Max Planck Institute: Solid circles = nearby Seyfert galaxies (gen. spiral with very bright, rapidly varying nuclei); 'x's = compact Seyfert-like galaxies; open triangles = QSOs; dashed line represents predicted Hubble relation.


Redshift (v0) versus distance (Mpc): Ascending Hubble relation according to Arp (1998).

By the early 2000s, the results were showing a scatter where the Cepheid distance ladder calculations showed galaxies nearer than indicated by their redshift (z) values. What was the meaning of these excess redshift values?


Based on data from the Hubble Space Telescope (www.haltonarp.org).

Those are just a taste of the looming redshift complications for the HBBC paradigm.


About a decade after the HBBC-CSSC controversy over QSOs, near the end of 1975, Lang, K. R. et al. published, The composite Hubble diagram. ApJ 202 (3), 583-590. https://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1975ApJ...202..583, and sought to settle the issue in favor of evolutionary or HBB cosmologies by their analyses of the redshift situation among known QSOs as the situation stood nearly 10 years after the CSSC-HBBC-related arguments above. While they found showed an evolutionary sequence, it was not so much about the rival HBBC-CSSC models, but about the possible rival cosmogonies of galaxy evolution, as we shall see.

It is important to note that Lang et al. (1975) assumed the old Sandage and colleagues determined H0 = 50 km–1 Mpc–1 and a q0 = 1.0, when later H0 had jumped to nearly 70 km–1 Mpc–1 or higher (given the 'Hubble tension') and by 1998, the q0 parameter had switched sign to q0 = ~ –1, as discussed in chapter III and above, regarding the so-called 'accelerating Universe' or 'dark energy' discoveries.







Lang et al. (1975).


Lang et al. (1975) had indeed found an evolutionary sequence, but with the actual distances of the quasars not yet well-established, it was illusory as support for the HBBC, and as mentioned, it actually suggested something quite revolutionary as far as galactic cosmogony and evolution is concerned.
 
We turn to summaries of these emerging data showing a QSO scatter of redshifts.

 

(http://chandra.harvard.edu/xray_sources/3c273/xray_opt.html).

Scatters in redshifts appear not only in linear size vs luminosity but also in redshift vs spectral index (Condon, 1991).

Condon (1991):
Linear Size versus Luminosity

For 1.4 Ghz radio sources brighter that 2 jansky, the distribution of linear size versus luminosity is a scatter diagram (Condon, 1991).
Redshift versus Spectral Index

The distribution of redshift versus spectral index at 1.4 GHz is also a scatter diagram (Condon, 1991).

Greer (in a 1999 presentation at a science & religion conference in Gallup, NM) presented these quasar (QSO) redshift scatters in redshift (raw z as well as log z) vs apparent magnitude (m) data from Hewett, P. C., Foltz, C. B., & Chaffee, F. H. 1995. The large bright quasar survey [LBQS]. 6: Quasar catalogue and survey parameters. AJ 109 (4), 1498. https://articles.adsabs.harvard.edu/full/1995AJ....109.1498H; LBQS home: https://heasarc.gsfc.nasa.gov/W3Browse/all/lbqs.html).

Greer (1999) plotting of Hewitt et al. (1995) Large Bright QSO redshift data:

Compiled & graphed by L. Greer (1999) from the LBQS data (Hewett et al. 1995).


Compiled & graphed by L. Greer (1999) from the LBQS data (Hewett et al. 1995).

Scatter apparent with both z raw and log z data.

Excess z in QSOs
Excess QSO redshifts beyond the Hubble relation for large galaxies (Joseph, 2010b).

With a much larger data set Hoyle, Burbidge, & Narlikar (2000) in their volume presenting the QSSC the following year, quasars were shown to have a scatter instead of a good correlation with the Hubble distance relation:

The empirical relation: m = 5 log (z) + H0 (km s–1 Mpc–1)


Redshift (log z) versus apparent magnitude for 7315 QSOs showing a wide scatter [& possible periodicity along the m axis] (Hewitt & Burbidge, 1993; cit. in Hoyle et al. 2000).


Angular locations of the then-known 7315 QSOs projected on Milky Way Galactic coordinates
(Hewitt & Burbidge, 1993; cit. in Hoyle et al. 2000).

Further studies confirmed an intrinsic excess of redshifts in certain AGNs, such as QSOs and even radio galaxies. In pursuit of insights from the Ambartsumian-Vorontsov-Vel'yaminov-Arp (AVVA) cosmogony of ejection of higher redshift compact galactic objects from lower redshift AGNs (see chapter IX), Bell, M. B. 2007. Further evidence that the redshifts of AGN galaxies may contain intrinsic components. arXiv release (v1 12 Apr 2007; v2 21 Aug 2007): https://arxiv.org/abs/0704.1631. ApJ 667 (2), L129. https://doi.org/10.1086/522337, referring to the DIR (declining intrinsic redshifts) post-ejection evolving with increasing luminosity. According to the DIR deductions from the Ambartsumian-Vorontsov-Vel'yaminov-Arp (AVVA) cosmogony young AGNs or QSOs evolve into BL Lac objects, Seyfert galaxies, and in the penultimate stage into radio galaxies before losing the rest of their intrinsic redshift and becoming quiescent mature galaxies. Because of low redshift galaxies and high redshift compact sources, we can now infer that the evolutionary pattern Lang et al. espied in 1974 does not show the evolutionary BB cosmology, but the stages of the Ambartsumian-Vorontsov-Vel'yaminov-Arp (AVVA) cosmogony of galaxies (see chapter IX), and a brief introduction below.  



The triangle at the lower right pf Figure 1 represents where the QSOs would be if the intrinsic component were absent.

The intrinsic redshifts of AGNs suggest that we should expect increased departures from the ordinary H0 redshift relation perhaps with the degree of the energetic activity of AGNs.

Although the QSOs and other types of AGNs attracted more attention, some little noticed papers showed evidence for intrinsic (non-canonical) redshifts in regular spiral galaxies: Russell, D. G. arXiv: v1 19 Aug 2004; v2 26 Sep 2004: https://arxiv.org/abs/astro-ph/0408348); 2005. Evidence for intrinsic redshifts in normal spiral galaxies. Astrophys Space Sci 298, 577. https://doi.org/10.1007/s10509-005-2317-x. Russell summarized data showing that even ordinary spiral galaxies have some excess redshift component, above the Hubble constant redshift-distance relation expectations. In his 2004 arXiv manuscript, Russell had diagrams to show this, including some intrinsic additional redshift seemingly dependent in part on morphology, calibrated by the commonly-used Tully-Fisher relation (link) between mass / intrinsic luminosity (of spiral galaxies) vs. asymptotic rotation velocity (expressed as emission line width). 

Russell (2004) data with supplementary data











In Table VI in the next two cells below, the barred spiral ScI data are of especial interest since they include the largest cohort of the barred spiral galaxies in the study.

Table VI: ScI sample (cont.).



Table VIII. Excess redshifts of small groups (cont.).

Excess or intrinsic redshifts associated with small groups of galaxies.



Russell (2004) data and supplementary data.

Next, we turn to divergent redshift associations and the early hypothesis of galactic ejection phenomena, which will be discussed in depth in later chapters.

(iii) Unexpected divergent redshift associations and apparent ejection phenomena

Furthermore, quasars began to be found in close apparent connection with nearby, lower redshift galaxies. Low redshift, barred spiral galaxy NGC 1073 with three putatively associated, high redshift QSOs (discovered by H. Arp; cited in Burbidge et al. 1999). Note the alignment of the quasars with the spiral arms. We will return to this and similar associations. These ejection phenomena data will be explored further in Chapters IX (Vast jets and galactic ejection phenomena: Mass origin-ejection?) and X (Multiple galactic alignments: Ejections and galaxy clusters?). 


(Arrows added to image from http://www.astronomy.com/asy/default.aspx?c=a&id=3430).



Another local, low redshift galaxy, NGC 3842, with three putatively-associated, more high redshift QSOs in juxtaposition (discovered by H. Arp; cited in Burbidge et al. 1999).



Higher redshift with nearly identical z-values, blue stellar objects in paired-alignment across the minor axis of the Seyfert galaxy NGC 4258 (cited by Arp, 1998 and Burbidge et al. 1999).


Another galaxy-QSO pair 0248 + 430 with an x-ray contour map superimposed (Borgeest et al. 1991. A&A 243, 93). The differing redshifts are zG = 0.051 for the galaxy and the much higher zQ = 1.311 for the quasar, both of which are only separated by about ~14" arcseconds. S1 is a foreground star (from Hoyle et al. 2000, citing Arp, 1998). The juxtaposition and the x-ray contours are suggestive of ejection. 


Another association is found in NGC 7603, where the main galaxy has a redshift equivalent of 8,700 km/s if interpreted as a Doppler shift, while the apparently physically-associated by a seeming jet with a compact companion galaxy has a redshift equivalent of ~17,000 km/s (cited Arp, 1987; 1998).



In 2002, two more high z objects were discovered in the NGC 7603 system, apparently associated with the same seeming ejection filament (Lopez-Corredoira & Gutierrez, 2002; https://doi.org/10.1051/0004-6361:20020476) indicating a decrease in z with distance from 'parent' galaxy (z = 0.391, 0.243, 0.057).

NGC 7603 & companions

(Images courtesy of www.haltonarp.org).

What this resembles is an apparent physically-connected ejection of high redshift objects from NGC 7603 with descending z values as distance increases from the main galaxy. Such potential ejection phenomena will be examined in much greater detail in upcoming sections.

Later, we'll be exploring the differing redshift associations of 'host' galaxies and apparently associated quasars and other higher z objects.

There is an observed pattern as illustrated in the redshift vs. angular separation for 392 galaxy-QSO pairs plotted on a logarithmic scale (Left figure in the following table), indicating an inverse relation between (ascending) angular measure and (descending) redshift, strongly indicative of ejection and at least some connection between higher z values and proximity to putative ejections / angular distance 'associations.'
Hatched regions indicate areas excluded by selection effect, i.e., determining whether a galaxy-QSO 'pair' is actually observed.

In another study, about 300 galaxy-QSO pairs were plotted by angular separation (modified from Burbidge et al. 1990; Narlikar 1993). The dotted line indicates what would be expected from a random background distribution of QSOs without any pairing or galaxy-QSO associations.


 In yet another study, 197 galaxy-QSO pairs were plotted by angular separation, and again, the non-random pattern of association was assayed (Burbidge et al., 1990; Hoyle et al. 2000).
(Images from studies cited in the table).

We will return to the recurring anomalous associations of low redshift galaxies, often with active galactic nuclei (AGNs), with higher redshift companion galaxies and galactic objects. These are often associated in ways which strongly suggest ejection and recurring ejection events. See Chapter IX. Vast jets and Galactic Ejection Phenomena: Mass origin-ejection?.

Another anomalous redshift phenomenon?
STIS 123627STIS 123627
A distant galaxy, STIS 123627, apparently had a changing redshift interpreted as 12.1 Gly distant down to a nearer 9 Gly (Joseph, 2010a). If this is real, it is again more evidence of a non-distance related z values.

(iv) Unusual redshift periodicities which won't go away.

Another non-Hubble relation redshift phenomenon which we now explore in some detail are the patterns observed starting in the late 1960s that redshifts tend to cluster in a periodic way around certain preferred values of z at least in our cosmic neighborhood. In Burbidge, G. R. & Burbidge, E. M. 1967. Limits to the distance of the Quasi-Stellar Objects deduced from their absorption line spectra. ApJ 148, L107. https://ui.adsabs.harvard.edu/abs/1967ApJ...148L.107B/abstract, a clustering around these values for z was pointed out:

[Image from Burbidge, G. 2003. NGC 6212, 3C 345, and other Quasi-stellar Objects associated with them.
ApJ 586, L119. https://iopscience.iop.org/article/10.1086/374793/fulltext/16874.text.html#crf14].
In 1973, Bell, M. B. & Fort, D. N. A quantitative alternative to the cosmological [Hubble relation] hypothesis for quasars. ApJ, 186, 1. https://articles.adsabs.harvard.edu//full/1973, published a quantitative equation to summarize the data for quantized or periodic redshifts departing from a simple, linear Hubble relation: (1 + z) = (1 + zc)(l + zx), where they divided z into a cosmological or Hubble component, zc, and into a component of unknown origin, zx.


Brief Excursus on the Ambartsumian-Vorontsov-Vel'yaminov-Arp (AVVA) galactic ejection cosmogony hypothesis (for more, see forthcoming Chapter IX). Cf. Arp, 2003. Catalogue of Discordant Redshift Associations; pp. 13-16. The clustering of redshift quantities around certain "preferred values" was discovered by Burbidge & Burbidge (1967. Limits to the distance of the Quasi-Stellar Objects deduced from their absorption line spectra. ApJ 148, L107. https://www.adsabs.harvard.edu/full/1967ApJ). K. G. Karlsson (1971. Possible discretization of quasar redshifts. Astron. Astrophys. 13, 333. https://adsabs.harvard.edu/pdf/1971) showed that these discrete values follow an empirical relationship, (1 + z2) / (1 + z1) = 1.23, where z1 = the lower redshift and z2 = the next higher redshift up (Arp, 1998. Seeing Red: Redshifts, Cosmology, and Academic Science. Apeiron Press; p. 203) yielding preferred redshift peaks or periodicities in a geometric series or Karlsson series, where z1 = or corresponds to zi and z2 = or corresponds to zi + 1, with terms reordered thus:


Karlsson showed that the first six elements of the series were observed in the available redshift data, and further he predicted the existence of the next higher peaks with values of z = 2.64 and 3.48. So, given that we repeatedly observe pairs of quasars or other higher redshift compact objects juxtaposed across the minor axis of lower redshift active galaxies as if ejected in pairs from the putative parent galaxy with its lower redshift (zG), suppose that we consider the putatively ejected pair of quasars with their measured redshifts (z1, z2) for example across NGC 4258 (in the figure above from Burbidge & Burbidge, 1997. Ejection of matter and energy from NGC 4258. ApJ 477, L13-L15. https://doi.org/10.1086/310517, which is discussed in greater detail in chapter V), we can relate them to the parent galaxy redshift (zG) by correcting their redshifts to be in the reference frame or rest frame of the active center of the parent galaxy (zG), i.e., zQ, related by (1 + zQ) = (1 + z1) / (1 + zG). The difference between zQ and the next Karlsson peak in the series is assumed to predict the actual velocity of ejection, vej in units of c, that is, (1 + vej) = (1 + zQ) / (1 + zp), where zp = the redshift of that nearest Karlsson periodicity peak. For more details see forthcoming Chapter IX.

In 1989, Jayant Narlikar was invited to review the issue of 'noncosmological' or non-Hubble relation associated redshifts, and he also covered some of the hypotheses and a few theories put forward to explain these 'anomalous' data. Narlikar, J. V. 1989. Noncosmological redshifts (Invited Review). Sp. Sc. Rev. 50, 523. https://articles.adsabs.harvard.edu//full/1989SSRv...50..523N/0000538.000.html. Narlikar reviewed the history of the discovery of cosmological redshifts, which abide by the 'cosmological hypothesis' (CH) of an expanding Universe, as well as of the non-Hubble relation or 'anomalous' redshifts, and the attempts to interpret these data. Already multiple examples were known then (1989), and much more has been found since. We turn aside to consider this historic review from late in the 20th century. A forerunner of this review was a lecture given by Prof. Narlikar in 1986 at an IAU symposium, followed by a revealing discussion about how the subject was received at the meeting (Narlikar, J. V. 1986. Noncosmological Redshifts. Symposium - International Astronomical Union 119, 463-473; also In Swarup, G. & Kapahi, V. K. (eds.). Quasars, pp. 463-473. https://doi.org/10.1017/S0074180900153215).

Narlikar (1989) review title page, historical prologue & quotes, figures, and tables.













Then about 2 decades, and now many decades, of data collection show that QSOs do not have a linear Hubble relation, but remain an anomalous scatter diagram.











Now, recognized as an unusually low value for the H0 constant in a sample of bright 3C galaxies.

 Non-CH consistent clustering of redshifts around certain periodic values.




These following images, cited in the review, are not the astronomical images in their original quality. For the original, higher quality images, see the original publications cited in Prof. Narlikar's review.



Companion galaxies exhibit consistently higher redshifts than the main galaxies in these groups. Under the CH this should be more randomized.







Under the CH, QSOs should be randomly positioned in the background, however they exhibit excess clustering around near, bright galaxies.


Under CH, there should be no such correlation.
Juxtaposition of higher redshift QSOs along the axis of NGC 3384, as if ejected along that axis. Under CH, we would expect random background juxtaposition.

 Although the quality of this image is poor, the three QSOs are juxtaposed with the spiral arms, and exhibit location of their z values at Karlsson peaks.

See larger version above as well:

(Arrows added to image from http://www.astronomy.com/asy/default.aspx?c=a&id=3430).

AGN galaxy M82, we now know, not only has the 4 juxtaposed higher redshift QSOs but up to 15 as discussed in chapter IX. Vast Jets, juxtapositioning referenced in chapter V. JWST v ΛCDM.



According to the CH view of redshifts, these galaxies are this discordant in size.

 Redshift values weirdly in excess with certain galactic morphologies, namly S0 and Sbc and Sc.

In the HN Machian gravity-cosmology, less massive particles closer to their origin are more highly redshifted.


Narlikar (1989).
 
We note that the empirical preferential clustering of redshifts around certain values began to be observed after 1970, and these were noted in the Narlikar review (1989) just cited.
 

Modified from figure 8-4 in H. Arp, 1998. Seeing Red: Redshifts, Cosmology, and Academic Science. Montreal, Quebec, Canada: Apeiron Press.

Representation of preferential clustering of redshift values (cited Arp, 1998) showing a preferential clustering around increments of 37.5 km s–1. In the case of QSOs / BSOs, a possible empirical relation which was pointed out early is 1 + z0 = (1 + zg)(1 + ze)(1 + zi), where z0 is the observed redshift, zg is the Doppler shift of the parent galaxy, ze is the QSO's Doppler shift (+ or -) from its putative ejection from the parent galaxy, and zi is an intrinsic redshift component-associated Machian age-mass scale in a matter creation process (Burbidge et al. 1999). That is one of the models of galactic cosmogony we will explore further. 


Power spectrum of the redshifts of 97 spiral galaxies (Guthrie & Napier, 1996; cit. in Hoyle et al. 2000. A Different Approach to Cosmology: From a Static Universe through the Big Bang Towards Reality. Cambridge, UK: Cambridge University Press).


Frequencies of the redshifts of all 7315 then known QSOs with peaks at z ~ 0.3, 1.4, 1.9-2.0. From Hoyle et al. 2000. A Different Approach to Cosmology: From a Static Universe through the Big Bang Towards Reality. Cambridge, UK: Cambridge University Press).


In 2003, a volume was published to honor the late Sir Fred Hoyle (1915-2001) by C. Wickramasinghe, G. Burbidge, & J. Narlikar. (eds.). 2003. Fred Hoyle's Universe. Dordrecht, The Netherlands: Kluwer Academic Publishers, with lots of invited scientists, astronomers, and astrophysicists, on subjects as varied as Hoyle's contributions to people's personal reminiscences, stellar structures and evolution, cosmology, interstellar matter, and panspermia. Among the chapters, two were devoted to redshift periodicities: W. M. Napier on p. 139, republished from A statistical evaluation of anomalous redshifts. Astrophysics and Space Science 285 (2), 419. https://doi.org/10.1023/A:1025452813441.

The hypotheses Napier tested statistically were observations in the light of so-called class of 'anomalous' redshifts for pairs of galaxies and QSOs with widely different z-values, often displaying bridges of luminosity between them. These tests are critical tests of the universality of the Hubble distance relation and whether the HBBC fails the test.

(a) The first claim was that in the galactocentric frame of reference, the Virgo cluster spiral galaxies have a distribution with a periodicity of 71 km s–1, which is similar to an early claim of 72 km s–1 in the Coma cluster of galaxies by Tifft, W. C. 1976. Discrete states of redshift and galaxy dynamics. I. Internal motions in single galaxies. ApJ 206, 308. https://ui.adsabs.harvard.edu/abs/1976. Napier (2003) figure 1 shows part of the periodicty / redshift frequency data.

The significance of the 71 km s–1, periodicity was determined by synthetic simulations of Virgo clusters. The statistical tests were searches of 3-d spaces to find a single Imax, that is, the highest power to be found anywhere in the parameter space of the study. The test results for the real data set of the actual Virgo Cluster are very robust indeed (Napier, 2003; Figure 2). 

(b) The second claim was that there is a galactocentric periodicity among "wide-profile field [spiral] galaxies" of 36 km s–1 in the Local Super Cluster (LSC) as reported by Tifft & Cocke. 1984. Properties of the redshift. ApJ 287, 492. https://doi.org/10.1017/S0252921100005546. Napier's more accurate tests showed a 37.5 km s–1 periodicity in the LSC, as portrayed in Napier, Fig. 3.

And in Figure 4, which shows a persisting and robust 37.5 km s–1 periodicity out to 40 cycles, but detectable out to at least 90 cycles, Napier found. This is shown by Arp in 1998 as indicated above, including by a power spectrum test (see figure cited by Hoyle et al. 2000 on the power spectrum of a periodicity of 37.6 km s–1).

 

As Tifft and Cocke (1984) had suggested, a robust 37.5 km s–1 redshift periodicity, in a galactocentric frame of reference, has been found within the Local Super Cluster (LSC). A J statistical test with simulations for artificial LSCs was used to test whether the periodicity is a local or a global effect.

 


It is indeed a global effect, although more strongly or prominently visible in local groups and associations. The global periodicity of 37.5 km s–1 was found to be strongly significant statistically, contrary to the predictions of a smooth Hubble relation.


(c) The third claim was that quasars or QSOs clustered around bright local galaxies exhibit a redshift periodicity of 0.89 in log10 (1 + z), although it is not clear whether this is within the galactocentric frame of reference or local periodicities from discrete velocity residuals with respect to the variable solar apex used in assessing the periodicity found in the study of the Virgo Cluster done by Guthrie, B. N. G. & Napier, W. M. 1991. Evidence for redshift periodicity in nearby field galaxies, MNRAS 253 (3), 533. https://doi.org/10.1093/mnras/253.3.533. See also Napier, 1999. Quantized redshifts - New physics or old muddle? Symposium - International Astronomical Union, Volume 194: Activity in Galaxies and Related Phenomena, pp. 290-294. https://doi.org/10.1017/S0074180900162126. What they found was that there is indeed such a periodicity in the distribution of the QSOs appearing around local galaxies.

The work of Karlsson (1990. Astronom. Astrophys. 239, 50) and and that of Burbidge & Napier, 2001; The distribution of redshifts in new samples of quasi-stellar objects. Astrophys. J. 121 (1), 21. https://doi.org/10.1086/318018, was confirmed.

Napier concluded that if all of the above periodicities (a), (b),and (c) are real, then they must be the effects of some single underlying phenomenon and must be connected with the linearity of the local Hubble flow. Again, a cosmology other than the standard HBBC was indicated. We will return to this Burbidge & Napier (2001) paper below, after discussion of Tifft's modeling.


Another paper from the same memorial volume for Fred Hoyle was Tifft, W. 2003. Redshift periodicities, the galaxy-quasar connection. Astrophysics and Space Science 285 (2), 429. https://doi.org/10.1023/A:1025457030279. This paper develops the consequences of a particular decay model for predicting the periodicities in redshift found in various data sets, including the Hubbled Deep Field (HDF) and Hubble Southern Deep Field (SDF), tackling three classes of observations of intrinsic redshifts departing from the linear Hubble redshift relation, (α) characteristic peaks in QSO redshift distributions, (β) associated objects with very discordant redshifts, and (γ) normal galaxy redshift quantization.

Tifft (2003) Figure 1 illustrates the periodic quantized redshift distribution for double glaxies (Tifft & Cocke, 1989).


Figure 2 shows the characteristic redshift periods observed globally using concepts which predict the discrete values (Tifft, 1996).

A first principles Planck decay process & the Lehto-Tifft quantization model equations. Although previous work (before 1992) had focused on empirical periodic intervals observed differentially or globally in a galactocentric frame of reference, the emphasis shifted thereafter to the cosmic background frame of reference. Finnish physicist Ari Lehto put forward a mechanism for predicting redshift periodicities (1990. Chinese J. Phys. 28, 15), which Tifft (1996; 1997) tested, confirmed, and developed into the Lehto-Tifft quantization model with a set of equations: Tifft, W. G. 1996. Global redshift periodicities and periodicity structure. ApJ 468, 491. http://dx.doi.org/10.1086/177710; and Tifft, 1997. Global redshift periodicities and variablility. ApJ 485, 465. https://iopscience.iop.org/article/10.1086/304443. In what follows, we closely follow Tifft (2003): 

Lehto (1990) planned to describe fundamental particle properties using first principles, namely beginning with the original Planck units of Max himself (link), listed here with their modern values all calculated using 3 fundamental constants in modern values, the velocity of light in vacuo, or c = 2.99792458 x 108 m s–1 (link), the reduced (divided by 2π, i.e., it's Dirac formulation) Planck constant ħ = 6.582119569 x 10–16 eV⋅s (link), and the gravitational constant G = 6.674 x 10–11 m3⋅kg–1⋅s–2 (link):

Thus, the observed properties of atomic particles, including the redshift, are assumed to emerge from a decay process beginning at the Planck scale in Planck units. Taking this explicit assumption, Lehto hypothesized that the Planck units decay via a period doubling action in factors of 2, commonly observed in chaotic systems. Exploring this, he found apparent ratios involving cube-root powers of 2. Lehto suggested that his hypothetical doubling may happen in a 3-dimensional or 3-parameter space, perceived as 1-dimensional via a cube-root transformation. He predicted that the redshift periods (P) would follow from this doubling under this transformation, such that

(1)     P = c2–N/3,

where N is an integer ≥ 0. In applying this to particle physics, we replace c with the Planck mass (M) or energy (L2MT-2). The above equation is significant in being a general form comparable to Kepler's Third Law in ordinary space, where "a spatial distance relates to the 2/3 power of a time interval,... a unique property of 3-d spaces." This suggests "the possibility that temporal/frequency/energy space is actually 3-dimensional." If such a "3-d temporal space" flows relative to a "3-d spatial space" then the constancy of c and the applicability of special relativity are preserved. "Temporal space" is quantized into a stepwise decay process from the fixed units indicated. In a dynamic 4-space with 3-space and flowing 1-time, there are no such restrictions, so according to Tifft (2003), quantum physics and continuous, infinitesimal classical physics can co-exist.

At this point, Tifft argued that one may re-write equation (1) to distinguish cube-root doubling families thus
(2)     P = c–N/3 = c2–[(3D+L)/3],

where D is the number of doublings and L = 0, 1, 2 to specify which root is utilized. Tifft (2003) points out that equation (2) predicts most redshift periodicities, however to account for all of the observed periodicities, one needs a second cube root to produce 9 9th-root famliies distinguished by a n index T:

(3)     P = c2–N/3 = c2–[(9D+T)/9],

Equation (3), claims Tifft (2003), "completely and uniquely describes" all of the periodicities observed as of Tifft (1996, 1997). The index T values are not random, but involve pure doubling, T = L = 0, the dominant relation, followed by a 'Keplerian' T = 6 (L = 2) value, where the odd T values are shifted by 1 as in T = 1, 5, 7 which is less common, and finally the even values of T = 2, 4, 8 are rare or absent entirely. Weirdly, which T family is observed seems to relate to galaxy morphology (Tifft, 1997). Equation (3) seems to describe redshift distributions in local galaxies, whereas at higher redshifts and deeper in space, the T = 0 family "becomes increasingly dominant."

A correction must be made to assess underlying redshift quantization, and that is, redshift intervals "dilate with distance" because of effects both relativistic and geometric, which must be removed. Classically in cosmology, 'curvature' is described by the 'deceleration' parameter q0, while the Hubble 'constant' serves as a function of time, H = H(t) = f(z, q0), which in a flat or Euclidean cosmos would have q0 = 1/2. Removing the z-dependent distortion is called the 'cosmological' correction in redshift. Tifft & Cocke (1984) investigated the 'cosmological' correction for global redshift quantization studies. Tifft (1996) assumed that redshift intervals dilate as √[H(t)] to show a linearization of galaxy redshifts out to >10,000 km s–1 provided that q0 = 1/2. Tifft (2003), whose treatment we are following, showed that this correction works well out to z = 1 or 2, far enough to encompass, as we shall see, the Hubble Deep Fields North and South, taken in the 1990s. Following the classical H(t) formulation to find the function H(t) = f(z, q0), Tifft integrated with a Taylor expansion around q0 = 1/2 to arrive at a closed relation between z(observed) and z(Lehto-Tifft):

(4)     zobs = {[z(LT)/4] + 1}4 – 1        z(LT) = 4[(1 + zobs]1/4 – 1,

a formulation empirically-fitting all of the then available data (Tifft, 1996, 1997). Tifft (2003) uses equation (4) to convert observed redshift to z(LT) to evaluate redshift quantization. Since equation (4) is consistent with the "temporal 3-d space" model discussed above, where energies vary with temporal volumes as t3 so that if photon redshifts are a result of energy densities, which vary as these volumes evolve, the rate of change will be observed as H = H(t) = f(z, q0). The spatial volume will evolve as t2 so that H = H(t) = f(z, q0) depends on t2 redshift periodicities vary as √[H(t)] exactly as observed.

At this point, let's look at the data which Tifft (2003) summarized in light of the doubling decay process postulated in the Lehto-Tifft model:

Tifft's (2003) Table 1 shows that the redshift peak locations match the empirical logarithmic sequence of QSO redshift peaks observed by Karlsson, K. G. 1977. On the existence of significant peaks in the quasar redshift distribution. A&A 58 (1,2), 237. https://articles.adsabs.harvard.edu//full/1977. Tifft (2003) Figure 3 shows the quasars known in 1977.

When one adds the full set of the 3rd Cambridge catalog of quasars, one gets the results in Tifft (2003) Figure 4. In addition, one can add the quasars from studies referenced involving the "south galactic cap field" in Tifft (2003) Figure 5, differentiated by filled and open circles.

The Karlsson empirical peaks and the Lehto-Tifft model-predicted peaks continue to pile higher (Tifft, 2003, Fig. 6) when all of the data from the galactic southern hemisphere south of the initial field are included as found in the QSO and active galaxy catalogue of Veron-Cetty & Veron 1996. 7th ed. A Catalog of Quasars and Active Galaxies. ESO Scientific Report 17. See https://heasarc.gsfc.nasa.gov/W3Browse/all/veroncat.html. Tifft (2003) Figure 7 shows that there may be a c/8 peak also.


The trend is extended not on from the c/8 region but also to the c/16 region of the graph when data from Schmidt, M. & Green, R. F. 1983. Quasar evolution derived from the Palomar bright quasar survey and other complete quasar surveys. ApJ 269, 352. https://articles.adsabs.harvard.edu/full/1983ApJ, as illustrated in Tifft (2003) Figure 8.

The Lehto-Tifft model suggests that ongoing Planck unit decay would also yield less active QSOs and ordinary galaxies, thus linking galaxies and quasars. Decay from the first doubling would show a c/2 associated with z = 0.6 quasar peak. The redshift 'spectrum' would be T = 0 dominant, have various decay product periodicities, and importantly, "discordant redshift associations where physically related objects have decayed into different, but related states" as has been discussed by Halton Arp and a few others for years. Although local decay has gone to D = 12-16, but at z = 0.5, the model predicts periodicities in D = 4-9, i.e., c/16 - c/512 (20,000+ to 500 km s–1) range.

In 1995, the Hubble Space Telescope made a deep and long exposure in a small patch in the celestial northern hemisphere called the Hubble Deep Field (HDF), which provided opportunity to examine redshifts of faint and distant galaxies.

This hypothesis could be tested in 2003 with the Hubble Space Telescope (HST) Hubble Deep Field (HDF) and Southern Deep Field (SDF), in Tifft (2003) Figure 9, as adapted from Cohen et al. 2000. Caltech faint galaxy redshift survey. X. A redshift survey in the region of the Hubble Deep Field north. ApJ 538 (1), 29. https://iopscience.iop.org/article/10.1086/309096/pdf. .
. 



The following Figure 2 from Cohen et al. (2000) superimposes on the HDF the redshifts as well as their color-coded spectral classes, with circles of different colors for redshifts z ≤ 1 and white circles for redshifts z > 1. Cohen and colleagues classified galaxy spectral classes as including galaxies with dominant emission lines (ℰ), galaxies with dominant absorption lines (𝒜), galaxies with intermediate spectra (ℐ), and galaxies with broad emission lines (𝒬). The authors note that starburst galaxies with higher Balmer lines Starburst galaxies with higher Balmer emission lines (Hγ, Hδ, etc.) are classified (ℬ). However, the authors point out, "but for such faint objects, it was not always possible to distinguish them from 'ℰ' galaxies."



Tifft's first study (1997) used the data from Cohen et ai. 1996. Redshift clustering in the Hubble Deep Field. ApJ 471 (1), L5. https://iopscience.iop.org/article/10.1086/310330. That analysis is seen in Tifft (2003) Figure 10. The model predicted T = 1 and T = 6 values are present, especially at the c/2, c/16, and c/32 peaks.

Tifft (2003) Figure 11 showed how precise is the fit to these three peaks, and where the strongest peak was. However, a larger sample was needed and became available with Cohen et al. (2000) as illustrated in Tifft (2003) Figure 12. 

Tifft (2003) Figure 13 shows the main peaks as well as some "satellite peaks ... offset slightly" from the predicted c/32 and c/16 peaks. Note that all of the fractions are odd (not even) fractions.

In Tifft (2003) Figure 14, we find the sky positions of the "extended study" region of the HDF within certain z and magnitude (m) values, designations of galaxy clusters (~1 Mpc), and also marking of the discordant redshift pairs of galaxies. Figure 15 shows where Tifft (2003) asked D. Christein Monte Carlo statistical analysis of the probability of pair association by "angular separation" distribution between pairs of sources with discordant redshifts compared with 1000 random sample displacements (in RA and Dec) of objects in one z peak compared with another. Figure 15 also shows the difference between two peaks separated to the extreme by redshift values equivalent to 25,000 km s–1, showing evidence of clear physical association. 

Tifft's (2003) Figures 16 and 17 show the Monte Carlo association analysis for adjacent peaks with discordant redshift differences equivalent to the moderate 12,000-13,000 km s–1 range.

Just as they had done HDF extensions into the higher redshift values, Tifft (2003) extended the search for redshift peaks into the lower redshift values in Figure 18.

Just as satellite 'phase' peaks have been observed around certain values in the HDF, Tifft (2003) Figure 19 shows 'phase' peaks around the value c/16 for the data range of 0.2 < z < 0.46. Figure 20 shows 'phase' or satellite peaks around c/16 for z < 0.5. 

The last step in analyzing the lower redshift cohort for Tifft (2003) was to locate their positions on the celestial sphere in RA and Dec (Figure 21), in order to assess which 'clumpings' may represent physical associations between sources with discordant redshifts. Again, there are suggested physical associations of galaxies with discordant redshifts.

In 1998, another deep exposure was taken with the HST called the Hubble Deep Field South (HDFS; https://stsci-opo.org/STScI from https://hubblesite.org/contents/media/images/1998/). Cf. full story link. Even under the ideal Earth-based conditions at the Cerro-Telolo Inter American Observatory, this is the Earth-bound view of the HDFS region of the sky:


Credit: J. Gardner (NOAO/GSFC), Cerro Tololo Inter- American Observatory (https://hubblesite.org/contents/media/images/1998/).

The HDF findings were tested on the HDFS. It is no surprise that such periodicities were found there as well in the opposite celestial hemisphere. Tifft (2003) Figure 22 shows sources with redshifts from 0.3 < z < 0.6, and sure enough, there are stark periodicities in the predicted T = 0 around c/64 and c/32, as well as some peaking associated with the T = 6 state. 

Tifft (2003)'s Figure 23 shows the 'phase' peaking around the c/32 periodicity in the HDFS.

Summary on the Lehto-Tifft model. The Tifft (2003) study was presented at a conference of friends, colleagues, and some old rivals honoring the widely-loved and admired, great astronomer and cosmologist Sir Fred Hoyle and the quest to "better understand the cosmos that Fred so loved." Sir Fred would have much enjoyed the presentation, pouring over the data, and a bracing discussion. While the Lehto-Tifft model shows a striking agreement of numerical results with a model of redshift periodicity built up from the use of a double decay process from the Planck state, it still is a pattern-fitting empirical model, which only hints at the processes underneath. We note the importance of the model of these astounding data which are so unexplained in standard HBB cosmology, and as the literature cited above references, mainstream cosmologists have tended to dismiss or pretend that the redshift periodicities are not real phenomena. In what follows, we will explore a little more data bringing us up to more contemporary times, and some other possible cosmological models to explain these data. (Other reading and resources can be found at link & link).


Return to the Karlsson periodicity. We return to the Burbidge & Napier (2001) paper. Ever since 2001 with more complete sets of quasar data, Burbidge, G. & Napier, W. M. [2001. The distribution of redshifts in new samples of Quasi-stellar Objects. AJ 121 (1), 21. https://doi.org/10.1086/318018] found direct observational evidence for the next set of predicted by the Karlsson formula of redshift periodicity peaks, z = 2.63, 3.45, and 4.47, beyond what had been empirically observed up to then. In careful fashion, Burbidge & Napier (consulting with Margaret Burbidge and Sir Fred Hoyle) not only ran statistical tests but laid out the possible interpretations or hypotheses to explain these data.  


















Table 3 continuing with 3C radio sources: z-values in the 4th column:

With the QSO data available in 2001, the Karlsson periodicity continued to appear and extend beyond and confirming previous predictions.

In 2009, Burbidge & Napier published another paper, Associations of high-redshift Quasi-Stellar Objects with active, low-redshift spiral galaxies. ApJ 706 (1), 657. https://iopscience.iop.org/article/10.1088/0004-637X/706/1/657, where they were able to affirm that the statistically-robust associations between higher redshift quasars and lower redshift galaxies in earlier data sets remained, but were unable to reproduce the results with a partial data set from the SDSS at that point. The observations suggesting associations between low redshift active galaxies and higher redshift continued to build on the trend since the 1950s and 1960s, where the Ambartsumian-Vorontsov-Vel'yaminov-Arp (AVVA) ejection cosmogony of galaxies recommends itself as a model (see the discussion in chapter IX. Vast jets and galactic ejection phenomena: Mass origin-ejection?).

A year before the courageous and persistent dissident observational astronomer Halton Arp's death, more results were published on the 2dF survey in Fulton, C. C. & Arp, H. C. 2012. The 2df Redshift Survey. I. Physical association and periodicity in quasar families. ApJ 754 (2), 134. https://doi.org/10.1088/0004-637X/754/2/134. (Some of the curated data has been placed at http://casjobs.sdss.org/CasJobs/ and http://tdc-www.cfa.harvard.edu/2mrs/2mrs_v240.tgz). They examined data from the 2dF Galaxy Redshift Survey (2dFGRS) and from the 2dF Quasar Redshift Survey (2QZ) in the two declination strips at Dec 0o and -30o. In order to avoid a range of mixed redshifts of galaxies and quasars, they filtered out all but quasars z ≥ 0.5. Making no mention of the Lehto-Tifft model, Fulton & Arp searched for Karlsson-type periodicity in quasar redshifts. Around each galaxy, they detected quasars which conform to "empirically derived constraints based on an ejection hypothesis." They "ran Monte Carlo control trials against the pure physical associations by replacing the actual redshifts of the candidate companion quasars with quasar redshifts drawn randomly from each respective ... [R.A.] hour." When properly constrained for quasar z grouping and the Karlsson periodicity, the 2dF data showed that the Karlsson periodicity is statistically significant, and not a selection effect (Fulton & Arp, 2012; Figure 5).

Fulton & Arp (2012) Figure 6 shows that the presence of discordant redshift data between physically connected galaxies and quasars has been shown to be statistically significantly.

One of the more recent papers which has attempted to pull together the data on redshift periodicity and compare theoretic explanations was first submitted for publication in 2016, but only published in 2020, indicating the ongoing difficulty of suggesting alternative hypotheses for unusual phenomena in cosmology, and getting them published. That paper is from an Indian group, Mal et al. 2020. Periodicity of quasar and galaxy redshift. Astron & Astroph. 643, A160. https://doi.org/10.1051/0004-6361/201630164. They briefly and informally review >5 decades of published research on periodic redshift data. As already noted, there have been empirical / numerical formulations of the periodicities observed. And there've been attempts, as seen above, to model the causes of the observed periodicities. For example, Depaquit, S., Pecker, J. C. & Vigier, J. P. 1985. Astron. Nachr. 306 (1), 7. https://adsabs.harvard.edu/full/1985AN, argued that the periodicities were caused by (1) a selection effect from data sampling; (2) the non-randomness of quasar distribution in the Universe, and (3) the presence of Dopplerian / non-Dopplerian contributions to redshift. Lehto (1990. Chin. J. Phys. 28, 215) and Tifft (1997; 2003) proposed their developed explanation, discussed above.

In 2007, Bajan & Flin published a review called, Redshift periodicity. Old New Concepts Phys. IV, 159. http://merlin.phys.uni.lodz.pl/concepts/2007_2/2007_2_159.pdf, in which they reviewed studies published since the late 1960s up to their date on the redshift periodicity issue. In their review they included the famous periodicity paper published by K. G. Karlsson (1971. Possible discretization of quasar redshifts. Astron. Astrophys. 13, 333. https://adsabs.harvard.edu/pdf/1971) who found peaks empirically predicted in a geometric series: z = 0.3, 0.6, 0.96, 1.41, 1.96, and predicted at 2.63 and 3.46 (Bajan & Flin, 2007; Figure 1), as well as the extensive analysis of Hawkins E., Maddox S. J., & Merrifield M. R. 2002. MNRAS 336 (1), L13. No periodicities in 2dF Redshift Survey data. https://doi.org/10.1046/j.1365-8711.2002.05940.x. (Bajan & Flin, 2007; Figure 2), from the SDSS data set.

Bajan & Flin (2007).

Reviewing previous studies and utilizing power spectrum analysis (PSA), as well as a number of possible explanations standard and exotic, Bajan & Flin (2007) concluded that redshift periodicity "among galaxies is not well established" despite there being some effect at the 2σ significance level. See also the review by Bajan, K., Flin, P., Godlowski, W. et al. 2007. On the investigations of galaxy redshift periodicity. Phys. Part. Nuclei Lett. 4, 5. https://doi.org/10.1134/S1547477107010025.

Many years earlier, following in the empirical astronomy trail-blazed path of Viktor Ambartsumian (1954, 1958, 1961, cf. Arp, 1999. Ambartsumian's greatest insight - the origin of galaxies, in Terzian, Y., Weedman, D., Khachikian, E., [eds.], Active Galactic Nuclei and Related Phenomena, IAU Symposium 194, 473; where Arp recounts Jan Oort's privately whispered confession to him in 1973 that 'You know, Ambartsumian was right about absolutely everything'), Narlikar, J. V. & Das, P. K. 1980. Anomalous redshifts of quasi-stellar objects. ApJ 240, 401. https://articles.adsabs.harvard.edu/full/1980ApJ; and Narlikar, J. V. & Arp, H. 1993. ApJ 405 (1), 51. https://adsabs.harvard.edu/full/1993ApJ argue that QSO redshift periodicities are the result of active galactic nuclei (AGN) ejecting quasars, in accord with the even earlier proposal of a conformally-invariant Machian 'variable mass hypothesis' of Hoyle, F. & Narlikar, J. V. 1964f. A new theory of gravitation. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 282, 191. http://dx.doi.org/10.1098/rspa.1964.0227; and 1966. A conformal theory of gravitation. Proc. Royal Soc. London 294 (1437), 138. http://dx.doi.org/10.1098/rspa.1966.0199) developed in the elaborations of the CSSC, post-1948; in their C-field formulations).

Theoretical models aside momentarily, the trail blazed by Viktor Ambartsumian and later championed by Halton Arp in galactic cosmology, we in this history tentatively call the Ambartsumian-Vorontsov-Vel'yaminov-Arp (AVVA) cosmogony. Next we turn aside briefly to an excursus on a Machian accounting for anomalous, discrepant or discordant redshifts and redshift periodicity.


Summary Excursus: An empirical, Machian variable mass hypothetical approach to redshift periodicity
(Exapted from Narlikar et al. 2017 in a volume honoring observational astronomer Halton Arp:
References below are cited in full in the Select Bibliography & Resources in the home page).
In 2017, Narlikar and colleagues published again on the redshift periodicity problem applying the HN Machian theory within a larger collection of essays in honor of Halton Arp (1927-2013): Narlikar, J. V., Vishwakarma, R. G., Banerjee, S. K., Das, P. K., & Fulton, C. C. 2017. An empirical approach to periodic redshifts. In Fulton, C. C. & Kokus, M. (eds.). The Galileo of Palomar: Essays in Memory of Halton Arp. Montreal, Canada: Apeiron; pp. 341-358. http://haltonarp.com/inc/memorial/TheGalileoOfPalomar.pdf.

When QSOs were discovered in 1963, their super high redshifts could either be (a) Doppler shifts, (b) gravitational redshifts, or (c) cosmological redshifts, which is due to the 'expansion' of the Universe, the Hubble-Lemaître law, which was quickly the standard view. If the latter or (c) is true, the QSO redshifts should distribute as (eq 1) z = F(r), where z is the redshift, r is the distance, and the function F(r) would tend toward H0 r/c with H0 being the Hubble's constant and c the velocity of light. Under a simple cosmological Hubble-Lemaître interpretation, the probability of the angular distribution and separation between any distant quasar (Q) and any angularly-juxtaposed foreground galaxy (G) should be (eq 2) p = π.∆2n, where the likelihood of chance near juxtaposition, p should be a small fraction of unity, say p ~ 10−4, consistent with the Hubble-Lemaître law. However, if the near angularly-juxtaposed redshifts zG and zQ are different, then there's an anomalous discrepancy with the Hubble-Lemaître interpretation in those cases. Furthermore, if there are evidences of tidal interaction between or even more 'on the nose' a jet connecting the objects with discrepant redshifts zG and zQ, then we have a class of interacting objects which contradict the Hubble-Lemaître law.

Over the years and now decades, the data for anomalous galactic redshifts now includes not only objects in the optical wavelengths, but also in the radio, x-ray, and gamma ray wavelengths. Furthermore, the range of known anomalous z-values has not expanded in a smooth distribution but are clustered as discussed around discrete values such that for small z, there is an arithmetic progression (Tifft, 1976) and a geometric progression of (1 + z) for larger z-values (Karlsson, 1977). These discrete or periodic values may be designated (Z1, Z2, ... , ZN), where (eq 3) (1 + ZN) = λN × (1 + Z0), where λ ~ 1.228, and Z0 = 0.06, &c. The Hubble-Lemaître law cannot explain such a effect. This persisting problem has been by most cosmologists ignored for the following pretexts (or excuses, if you will). These stubbornly anomalous data....
  • (1) Are comparatively rare and few in number,
  • (2) Involve ex post facto probability computations,
  • (3) Are simply artifacts, artifactual coincidences, or
  • (4) Result from gravitational lensing increasing low probabilities, suggesting that the n density in (2) should amplify and thus increase the number of intrinsically faint QSOs, juxtaposed by chance, thus increasing the p value so that the null hypothesis of p=π.∆2n is rescued.
For years, since J. P. Ostriker (1989) observed in essence that these expedients fail to explain away all the anomalous redshifts. Also, J. V. Narlikar (1989) pointed out that Doppler shifts also fail to explain away the anomalies because they entail blue as well as redshifts, and blueshifted QSOs should be even easier to spot and find in around galaxies, however, no blueshifted QSOs are known. Narlikar further noted that gravitational redshifts also fail to explain these anomalies because under ordinary physical conditions, the surface gravitational redshifts for objects in equilibrium approach an upper limit of z ≤ 0.63 for surface gravitational redshifts of objects in equilibrium (Bondi, 1964). Although it is conceivable for there to be higher gravitational redshifts in light photons from the interior of a massive object, that seems like a 'contrived' scenario (Das, 1976).

So starting with the Hubble-Lemaître flow, there seems to be an excess 'intrinsic' component in systems where any QSO Q with redshift zQ is in apparent physical association with a galaxy G with redshift zG. Applying the Ambartsumian-Vorontsov-Vel'yaminov-Arp (AVVA) cosmogony as a working hypothesis, where higher redshift QSOs originate and are ejected from active galactic nuclei (AGNs) with an intrinsic redshift component, such that zQ >> zG in general and the intrinsic component, zI, is defined in empirical terms with the equation:

(1 + zQ) = (1 + zG)(1 + zI)                                                                  (4)

Narlikar and colleagues now proceed to lay out an alternative theoretic framework to explain these data, in terms of the AVVA cosmogony. The underlying mechanism was proposed during a fruitful period as the Machian theory of gravity by Hoyle & Narlikar (1964f, 1966d) in the C-field context of the Classic Steady State Cosmologies (CSSC). {It is important to note that Stephen Hawking's (1965) famous claim during the HBBC-CSSC controversy about falsifying infinities in the HN theory has long been falsified: See below: Appended Note on Replies to Hawking, 1965}. Narlikar adapted the HN Machian theory to explain the anomalous redshifts within the AVVA cosmogony context thus (cf. Narlikar, 1977; Narlikar & Das, 1980, cf. 1975; Narlikar & Arp, 1993, 1997) and the dynamics of ejection in Narlikar et al. (2002):

The field equations of the Hoyle-Narlikar theory are [eq dim: w = 377 and 392 in honor of Narlikar & Hoyle respectively by date]

where m is the mass of a particle allowed to vary by Mach's Principle-type interaction with the rest of the masses in the Universe. The simplest solution to (5) in Minkowski spacetime is the metric line element (6):


The mass function in the Hoyle-Narlikar field equations is given by

where a is the density of the Universe. A simple 'static cosmos' solution emerges which is non-collapsing because the mass m derivatives in the HN field equation are non-zero. This keeps spacetime from inwardly contracting. So in this simple 'static' solution from where does the redshift come? From the 'variable mass' effect, where in the 'static cosmos' every line element (6) has a start point or 'beginning' at some cosmic epoch τ = 0 Microsoft Word - 2017 Arp Title Page.doc when all particle masses are 0. However, unlike the classical HBBC, there is no spacetime singularity, because at this epoch there exists a zero mass 3-hypersurface m = 0. However, since mass increases with cosmic epoch as m = aτ2 in a Machian cosmos, then when an observer in galaxy (O) sees a galaxy (G) at distance d at some cosmic epoch τ = τO, accounting for lookback time d/c, our O sees G as it was, τG = τO − d/c, The ratio of particle masses, mO and mG, e.g., electrons, protons, and neutrons, in the O and G references frames are

Thus, in the case of the typical hydrogen atom spectrum, the wavelengths λ of the H lines will be proportional to m−1 and so the λ of light from galaxy G will be longer than that from O by the factor
 

The redshift of G observed in O arises from the variable mass effect, an idea known as the Variable Mass Hypothesis or VMH for short. That is in the 'static universe' case.

Expanding universe case. Now, moving to the 'expanding universe' case, as Hoyle & Narlikar (1971) argued, this VMH redshift is precisely what one gets in an 'expanding cosmos' with particle masses, m1, m2, ... , mN, remaining constant. However, since the Hoyle-Narlikar theory is conformally invariant (unlike general relativity), standard relativistic cosmology can be obtained from (6) the simplest line element in Minkowski spacetime by this conformal transformation

where β is a constant, particle masses transform as m ∝ Ω−1, and constant particle masses results with Ω as defined above. The general relativistic metric line element then becomes

and with the substitution and removal of the conformal cosmic epochal time, τ, Microsoft Word - 2017 Arp Title Page.doc the time t-based coordinate transformation,


applied to the general relativistic line element (11), we recover the traditional flat Einstein-de Sitter metric line element:



And then t-time in the traditional line element is simply the standard cosmic time of Friedmann (HBBC) cosmology and the redshift formula gives the same expected result as (9) above. The Friedmann cosmology by insisting that particle masses at all epochs are constant (a) forces spacetime to be non-Euclidean (contrary to observational data), (b) leads to a spacetime singularity (classic Big Bang) / singularities (black holes), and (c) exiles the never-vanishing question of matter creation (non-conservation of baryon number) back to some singular, energetic unification epoch post-t = 0. As Khembavi (1978) showed in his 'Zero mass surfaces and cosmological singularities' study, under general conditions, the zero mass 3-hypersurface at t = 0 forms a singularity under the conformal transformation Ω ∝ m and all the singularities under the singularity theorems expected by Penrose (1965), Hawking & Ellis (1973), and Hawking (1977) are found and explained. As Khembavi notes, contrary to Hawking & Ellis (1973; p. 364) and Hawking (1977), the presence of singularities in general relativity is no virtue, and contrary to the rest of physics—recognizing that conformal invariance is a symmetry of Nature (as Khembavi points out). Within the Hoyle-Narlikar conformally invariant theory, Khembavi showed, there are a number of non-singular cosmological models possible (citing also the Hoyle & Narlikar, 1974 opus).

The Hoyle-Narlikar Machian-based flat cosmology described can be augmented so that rather than assuming that all matter originates at some τ = 0, we allow that matter can also originate repeatedly and episodically wherever and whenever the energetic conditions in the AGN of galaxies reach thresholds to manifest as the creation and ejection of compact objects like QSOs (as in the AVVA cosmogony). So, in the AGN of the galaxy (G), the particles of the new QSO are similar but start with a zero mass 3-hypersurface at τQ, gaining mass by Machian interaction with a growing region of the Universe. The formal mathematics and physics of this proposed process is discussed in Narlikar (1977), building on earlier work done by Hoyle and Narlikar in the 1960s.

Consider, argued Narlikar (1977), that a conformal theory of gravity (e.g., Hoyle-Narlikar, 1964f; 1966d; 1971), modeled similar to action-at-a-distance electrodynamics (cf. Wheeler & Feynman, 1945; 1949), a series of implications may be found. The HN general theory and its applications in the CSSC, QSSC, and possible oscillating cosmologies will be reviewed in Chapters III and XII.

In the same volume, Fulton, C. C. (2017). From Hubble to Arp. In Fulton, C. C. & Kokus, M. (eds.). The Galileo of Palomar: Essays in Memory of Halton Arp. Montreal, Canada: Apeiron; pp. 293-339. http://haltonarp.com/inc/memorial/TheGalileoOfPalomar.pdf, summarized the implications of the general Narlikar (1977) model with the Friedmann (1922) model, both models are special cases of larger theories of interpretation of the Hubble-Lemaître relation (Fig. 39):

Fulton (2017), Figure 39.

The particles in the QSO will grow in mass as

And the redshift of Q will be observed from galaxy O as


Thus, even though parent galaxy G and QSO Q are at the same basic distance from O, there will be a Machian-based intrinsic component to the QSO redshift observed from O with a magnitude calculated by


So if we go to the derived conformal Einstein-de Sitter frame, galaxy mass will have asymptotically approached a constant value consistent with the Hubble-Lemaître distance relation, while the QSO redshift will increase with time smoothly asymptotically approaching the Hubble-Lemaître constant H0. So that's the basic conformal HN theory approach to discrepant redshifts. However, we now have the problem of the quantized or periodic redshifts phenomenon, sometimes called by the authors the Karlsson effect. How do we account for those in this hypothetical paradigm? 


Periodic redshifts. The authors consider the periodic redshift data first in a Minkowski spacetime. Empirically, the authors consider a sample of central galaxies with measured redshifts (zG) with the measured redshifts of paired quasars (z1, z2) in tabular form (Narlikar et al. 2017; Table 1), which are then corrected to the galaxy redshifts to find the putative intrinsic components by (1 + zQ) = (1 + zi) / (1 + zG); i = 1, 2, ... , which are then compared to the nearest periodic peak identified from the sequence Zn given by the Karlsson (1977) formula: Δlog(1 + Zn) = constant = 0.089, Z0 = 0.06, which generates a sequence of redshift values of n = 0, 1, 2, ... , n; where Zn = 0.06, 0.30, 0.60, 0.96, 1.41, 1.96, 2.64, &c. Arp et al. (1990) have claimed that QSO redshifts seem to be distributed preferentially close to the Karlsson sequence values.

 

With respect to the data compiled in Table 1, Narlikar et al. (2017) proposed to test the following hypothesis: The differences between zQ and the nearest peaks are postulated to be the true Doppler velocities of ejection as viewed by the observer (O), i.e., (1 + zej) = (1 + zQ) / (1 + Zp), where Zp is nearest Karlsson peak. These calculated values of ejection velej (columns 7 and 8 of Table 1), show approach toward and recession away from the observer (O) respectively. Except for the first two cases, NGC 4258 and 4235 in the table, which are ambiguous with their low redshifts, zQ values associated with the nearest Karlsson peak yield one QSO approach and the other receding away from the observer (O). It is also possible in the case of galaxy NGC 4235 that the low velocity of approach of one of the ejected QSOs at zQ1 = 0.031 compared with the velocity of recession of zQ2 = −0.128, because it has encountered some resistance slowing down the velocity of ejection.   

These preferred peaks in higher redshift quasar families associated with galaxies have been further confirmed by Fulton & Arp (2012) in the 2df data, and have since 2017 been again even further confirmed by Fulton, Arp, & Hartnett (2018) in the SDSS and 2MRS data. Even in the small sample in Table 1, the conformity of the quasar pairs to the Karlsson peaks is impressive, the authors note. The statistical significance of the peaks here may be summarized thus (Arp method): Column 9 contains the 'accidental probability' that both QSO redshifts (zQ) fall close to the proximal Karlsson peak (Zp) in the reference frame of the galaxy (G) calculated by taking the difference between zQ and Zp and then dividing that by 1/2 of the distance to the nearest Karlsson peak: {| zQ | – | Zp |} ÷ 1/2 = P(Zp), where each pair is an independent trial and their combined probability is computed, the pair being normalized to 0.5, yielding the probability P that the real QSO pair redshifts fall as close to the Karlsson peak as they do.
 
For NGC 1068, the QSO1 is 0.030 away from Karlsson peak Z2 = 0.60 in the Karlsson interval (0.60, 0.96), so the probability for it is 0.030/0.18. Similarly for the QSO2, the ejection velocity −0.034 is negative with respect to Karlsson peak 0.30, so the Karlsson interval is (0.06−0.30) and the probability is 0.034 / 0.12. The combined probability is 2 × (0.030 / 0.18) × (0.034 / 0.12) = 0.09. Thus, the combined probability for the first 5 QSO pairs is P = 9 × 10−6, the combined probability for the last 5 is P = 4 × 10−4, so that the combined probability of all the pairs in Table 1 being randomly close to the Karlsson peak values is P = 7 × 10−9. 

In addition to the periodic intrinsic redshift values, the projected QSO ejection velocities seem well matched in magnitude, even though they might not be because of factors such as (a) initial ejections not being exactly opposite, (b) perturbations or collisions of ejected QSOs modifying their projected velocities, and (c) the speed at which the QSO redshifts transition between Karlsson quantized peak values may catch some quasar z-values between peaks. The projected velocities are graphed in Figure 1, where the intrinsic redshift component declines with increased Machian contact with the rest of the Universe, and also the QSO projected ejection velocities decline as the QSOs separate from the putative parent galaxy.


The important quantified take home from Table 1 would be the average velocity of QSO pair separation from the putative parent galaxy as a function of declining redshift (see Table 2). Empirically, the ejected QSO must slow down from its unknown initial velocity of ejection to about ~28,000 km s−1 when the zQ has evolved to the z = 0.96 Karlsson peak, further to about ~10,000 km s−1 within a few hundred kpc, such that for the QSOs to become gravitationally bound companion galaxies, their velocities of ejection must be dissipated by an apogee of ~500 kpc.


According to calculations in sections 2 and 3 from Arp et al. (2002), the ejected QSOs arrive at their observed angles of separation from the putative parent galaxy with very low velocities of ejection because, given the assumption of a homogeneous Universe, the created and ejected particles take a long time to grow in mass through Machian interactions. However, this prediction conflicts with the estimations in Table 2. How does one reconcile this?

Suppose that the new proto-QSOs are initially held as energetic components in incubative orbits within the active galactic nucleus (AGN), and then later blown out in explosive events at the observed velocities? In the QSSC (Hoyle, Narlikar, & Burbidge, 2000), as in this empirical approach to the VMH, it is argued that creation of matter (baryons) takes place in an increasingly negative energetic region of a negative scalar field (C-field) of Machian origin. As baryon creation proceeds the C-field negative energy builds to a repulsive-explosive threshold overcoming gravity (in the conformally-invariant gravitational field), and the AGN fragments ejecting coherent proto-QSOs, relaxing the C-field energy again below the repulsive-explosive threshold. Assuming that baryogenesis occurs according to the C-field hypothesis and that some as yet unknown quantum process causes the ejection stages, the proto-QSO is explosively expelled from the AGN only exactly when its redshift is at one of the Karlsson peak values.

So periodic Karlsson peak-z data require modifying the original Narlikar-Das hypothetical scenario. Using a t coordinate for convenience instead of the τ coordinate, a QSO originating at tQ is bound in incubative orbit in the AGN and not ejected until time tE when the proto-QSO's intrinsic VMH redshift is decreased through Machian interaction to zE—such that the intrinsic VMH redshift zI —> zE, a member of the Karlsson sequence values Zn, and zE determines the time of ejection, tE., as observed in galaxy O when the QSO's light arrives at time tO:
 

An ejected QSO at velocity ω, within the angle to the line of sight α from O, will travel in that direction. The ejected QSO will then proceed as described in the equation of motion in Narlikar & Das (1980), as worked out in detail in the example in Narlikar et al. (2002). Using this approach, the distance traveled by the QSO is R, where the radial or angular separation observed perpendicular to the line of sight from (20) O is dG × θQG ≈ R sin α, where dG is the redshift distance of the parent galaxy, and θQG is the angular separation of the QSO and the parent AGN.

Integration of the equation of motion from Narlikar et al. (2002) yields the velocity ω of the QSO at that point in time. Using a composite redshift formula combining both Doppler effect as well as VMH, observed redshift zQ can be related to speed ω and the angle to the line of sight α in the local spacetime [R, T] coordinates from Narlikar et al. (2002):


The data from Table 1 can be used to calculate the following. Suppose that two QSOs are born at the same epoch tQ and ejected in opposite directions at the same epoch tE, their ejection angles to line of sight would be (22) α1 = α and α2 = α + π, respectively. Knowing this, can one calculate all the other ejection parameters (tQ, tE, α) for the ejected pair? Yes, via the following procedure:
  1. For each QSO of the pair, assume some time of origin tQ value.
  2. Choose the z-value from the Karlsson peak series lying between the two QSO redshifts for the zE, the redshift of ejection.
  3. Assume some chosen trial value for the velocity of ejection (v).
  4. Use equation (19) to get tE, the time of ejection.
  5. Solve the differential equation of motion to find the distance traveled, R, and the speed of ejection, ω.
  6. The ejection angles, α, can be calculated using both (20) dG × θQG ≈ R sin α and equation (21). Generally these values would not agree with the chosen trial velocity, α....
  7. So, the trial parameter of velocity, v, is varied until a unique value is found when both equations (20) and (21) arrive at the same value for the angle of ejection, α. Thus for our assumed time of origin, tQ value, we can find the α for each QSO.
  8. Where the two curves intersect, the parameters are all determined: Figure 2 illustrates the procedure for one QSO pair from Table 1.

 
The first three QSO pair cases in Table 1 are analyzed using the above procedure, and the results placed in Table 3, where column 1 has the designation of the galaxy and its redshift, and the rest of the parameters in their respective columns, ending with the nearest Karlsson peak (Zp) in the last column, so that Table 3 may be thought of as the beginning of a more refined version of Table 1, on the dynamics of quasar ejection:


The following tentative conclusions from these calculations emerge regarding the dynamics of QSO ejection from AGN galaxies in the VMH, according to the authors:
  1. AGN galaxies eject QSO pairs when their redshifts have decreased in Machian interaction to a value close to one of the Karlsson series peak redshifts.
  2. Ejections are in opposite directions. With momentum conserved, we can predict that the masses of the two quasars ejected should be inversely proportional to these velocities. By examining the morphology of This can be tested by examining the ejected QSOs' morphologies  to estimate their mass ratios.
  3. The three cases analyzed so far support the hypothesis of ‘ejection in opposite directions.’ There's no reason to think this is random. The differences from the Karlsson peak redshift includes both VMH and Doppler effect components.
Correcting for frictional resistance. So far the frictional effects of the interstellar / infragalactic / intergalactic media on ejected QSOs have been neglected. To correct for friction, the authors constructed a model in which friction is proportional to the velocity of the ejected QSO and in the opposite direction of the ejected motion: This frictional force opposite the ejected QSO is ΛṘ (t), where Λ is hand-picked from a series of values to examine the effects of the frictional force. For any Λ, we restore the scale factors in the equation of motion, following Narlikar & Das (1980):
 
where Ṙ is defined as

The gravitational acceleration is approximated by the following in c.g.s. units (centimeter-gram-second variation on the metric system) as

The frictional deceleration is estimated as


where  (in c.g.s. units) is dimensionless and the Hubble time scale is T ~ 2 × H−1. Using ~ 100 and v ~ 104 km s−1, we have (27), Ff ≈ 102 × 109 × 10−18 ~ 10−7. Thus, in this example, the frictional force, Ff < FG, the gravitational acceleration, by an order of magnitude. It is assumed that Ff is significant up to about 1/10th of the galactic radius. When the calculations are modified to correct for frictional force, Ff, the observed QSO velocities ω ~ 28,000 km s−1 are reduced by about half, but never going below ~10,000 km s−1, which the boundary condition of (22) α1 = α and α2 = α + π, in general would likely only allow velocities above that order of magnitude. Ultimately, further numbers of observations will be needed to check the expected velocities of ejected QSOs.

An underlying quantum theory yet to be discovered? Unlike most authors, these authors take the finding of periodic redshift peaks a series first discovered by Karlsson seriously. Using the VMH, they showed that as a new QSO created in an AGN galaxy, its particle masses increase with time through Machian interactions with the Universe. In a classical VMH, the mass has a steady and continuous decline of the QSO intrinsic redshift from infinity in the beginning at tQ = 0 to finite values at the time of QSO ejection. Using mass × (1 + z) = constant from the modified VMH suggests that particle masses in the new QSOs should exhibit the Karlsson periodicity peaks. However according to the modified VMH, the newly created QSO 'hibernates' or remains in the AGN until the QSO particle masses match some discretized or quantized Karlsson peak value before QSO ejection, thus revealing the intrinsic redshift peaks we observe! Why?

Thus they searched for a theory underlying this phenomenon. So they conceived a heuristic quantum mechanical VMH model (they call it a 'toy model') drawing the obvious comparison between the energy levels in the physics of a simple harmonic oscillator and the peak redshift values in the Karlsson series. In this heuristic quantum mechanical VMH, the discrete or quantized sequence values ln(1 +Zn) forms this arithmetic series:
 

where Δ = ln(1.06) = 0.058 and K = ln(1.228) = 0.205; so that Δ − 1⁄2K ≅ −0.044, which can be compared to the simple harmonic oscillator in quantum mechanics. In classical mechanics, the simple harmonic oscillator of any mass M and a rotation frequency ω has the equation of motion,

corresponding to the Hamiltonian

By contrast, in quantum mechanics, the eigen states of the Hamiltonian correspond to the energy levels of the sequence:


Therefore, considering a QSO a quasar created at time τn passing the observer in galaxy G at the epoch τG such that the observer sees a redshift Zn from the QSO. From the modified VMH, the authors conclude that the particle masses in the ejected QSO (Mn) and the observer's galaxy (MG) are related by


Then, using the arithmetic series in equation (28), we can state

Therefore, they authors 'argue that the particle masses through [ln Mn] are quantized with the eigen values of Y rising in the arithmetic sequence very similar to that [of] ... the simple harmonic oscillator.' As in the classical VMH, this suggests the heuristic quantum mechanical VMH 'toy model' to describe the periodic redshift phenomenon:
  1. In the AGN galaxy G, the QSO Q is created at epoch τQ and remains in 'hibernation' near its creative hypersurface....
  2. Until a time τn when the particle masses in Q, via Machian action-at-a-distance interaction with the Universe, increase to some value Mn correlating with a peak redshift Zn within the Karlsson periodic series.
  3. Then Q is ejected out of the AGN at τn,
  4. Where and when the Q particle masses continue to grow in discrete, periodic, or quantized steps with values for Mn falling in the Karlsson series.
  5. In the classical VMH, the mass function was described by equation (14) which is a smooth function, not yielding the discrete values found in the Karlsson effect;
  6. So equation (14) is modified in the heuristic quantum mechanical 'toy model' such that Q particle mass function stays constant but jumps at specific time intervals, τN,
  7. So the authors define mQ as rising by the factor λ from equation (3), so equation (14) is replaced by equation (34), where the function θ(x) is the discrete or quantized step function taking 1 for its positive argument and remains zero otherwise. The time steps τn defined by equation (14) correspond to the discrete mass values of Mn:

The elements of the heuristic quantum mechanical VMH 'toy model' seem arbitrary, but they hint at a deep underlying theory, which we don't yet have, to justify those assumptions. The authors suggest that perhaps there's an analogy to the role of Niels Bohr's heuristic theory of the hydrogen atom. In Bohr's rule, the discretization or quantization of the motions of electrons (e−) in a H atom seemed ad hoc, arbitrary, and weird from a classical physics sense with its designating the angular momentum of the e− of the H atom in the form nħ where n is an integer rather than a continuous angle! However, Bohr's rule correctly predicted the H atom spectral frequencies. The assumptions of Bohr's were only later justified in the deeper quantum mechanical theory. For artistic and historic purposes, we include the physicist-artist George Gamow's representation of the Bohr model from his popular 1966 volume, Thirty Years that Shook Physics (Garden City, NY: Doubleday. https://archive.org/details/thirtyyearsthats0000unse):

Gamov (1966), Figure 12:

Gamov (1966).

The search for that deeper VMH / Machian quantum theory justifying these assumptions and predictions continues.

Microsoft Word - 2017 Arp Title Page.doc Microsoft Word - 2017 Arp Title Page.doc

Appended Note on Replies to Hawking, 1965: In 1965, Stephen Hawking published, On the Hoyle-Narlikar theory of gravitation. Proc. Royal Soc. A 286, 313. https://doi.org/10.1098/rspa.1965.0146, argued that the Machian HN theory in its time-symmetric retarded and advanced (going backwards in time) relativistic wave equations in integration would diverge to infinity because of the infinite future. Hoyle & Narlikar, in 1995. Cosmology and action at a distance electrodynamics. Rev. Mod. Phys. 61, 113. https://doi.org/10.1103/RevModPhys.67.113, pointed out that 'no normalization is necessary' in HN gravity because unlike the Friedmann cosmologies, the CSSC and QSSC with C-fields meet the requirements of the Wheeler-Feynman absorber theory of radiation in the past light-cones of the Universe as well as in the asymptotic future. Further, as H. Fearn (2015) has shown in Mach's Principle, action at a distance, and cosmology. Journal of Modern Physics 2015 (6), 260. http://dx.doi.org/10.4236/jmp.2015.63031; http://www.scirp.org/journal/jmp, because of the Cosmic Event Horizon (CEH, i.e., observer's horizon) in an expanding, accelerating Universe (as predicted by the CSSC), the advanced solutions indeed would not diverge to infinity given the CEH boundary, and hence, Hawking's objection is mistaken. That an ongoing, robust theoretic development can take place along the conformally invariant HN theoretic lines, is evident in Yadav et al. 2016. C-field cosmological models: revisited. Research in Astronomy and Astrophysics 16 (12), 188. https://iopscience.iop.org/article/10.1088/1674-4527/16/12/188, and in Narlikar (2021), Three pathbreaking papers of 1966 revisited: their relevance to certain aspects of cosmological creation today. EPJ H 46, 21. https://doi.org/10.1140/epjh/s13129-021-00025-6. We will return to this arena further in later chapters.

In 2018, Fulton and Hartnett followed up Fulton & Arp (2012) by publishing another paper with Halton Arp as a posthumous author again confirming with even larger databases revealing physical associations of quasars and galaxies, as well as redshift periodicities: Fulton, C. C., Arp, H. C. & Hartnett, J. G. 2018. Physical association and periodicity in quasar families with SDSS and 2MRS. Astrophys Space Sci 363, 134. https://doi.org/10.1007/s10509-018-3355-5.


In light of this rich historical and theoretic background (and because of HBBC-defending referees), a paper written in 2016 was finally published 4 years later: Mal et al. (2020) in Periodicity of quasar and galaxy redshift. A&A 643, A160. https://doi.org/10.1051/0004-6361/201630164, aimed to test for redshift periodicities using singular value decomposition (SVD) on the Sloan Digital Sky Survey (SDSS) 2dF data which includes >10,000 quasars and >100,000 galaxies from the DR10 and DR12 subsets as well as simulated data. Instead of the usual Fourier transforms, to detect fundamental periods of z in redshift distributions, they applied singular value decomposition (SVD) and quite unlike Hawkins et al. (2002), they found a multiplicity of redshift periodicities in the SDSS data. 

Histograms of the periodicities they detected in the SDSS quasar and galaxy redshift data versus the periodicities detected in the mock data, Mal et al. (2020)'s Figures 7 & 8, and Table 3, respectively. 

SVR spectra of redshift periodicities for QSOs and galaxies in the SDSS data in Mal et al. (2020) Figures 9 and 10.



Although it took 4 years to get their paper published, Mal et al. (2020), having reviewed the field of redshift periodicities, made some conclusions on how various theoretical models help explain these phenomena. In the standard HBBC theory, where we have an expanding cosmos which is generally isotropic and homogenous, they point out, the distribution of extragalactic redshifts should be approximately aperiodic and continuous. However, as the data show, they are neither. Since redshift periodicity is really there, Mal et al. in their discussion and conclusions turn to three main theoretical solutions to explain these results:
Mal et al. (2020) suggest that the details of a promising Machian HN theoretic approach remain to be worked out.

In later chapters, we'll also discuss how these phenomena and theoretical considerations are beyond the current New Ptolemaic System paradigm of the ΛCDM Concordance cosmology of the HBBC. We also await the development of the emerging CGC model, by friend and colleague Joe Bakhos, who is taking cognisance of this fascinating and deeply significant class of observations of our Universe. See Bakhos, J. 2022. Chasing Oumuamua: An apology for a cyclic gravity and cosmology, consistent with an adaptation of general relativity. https://vixra.org/pdf/2203.0032v4.pdf, and the further postings at The Taurus Report: https://taurusreport.com/ and its Youtube channel).

What do we do with data which don't fit a prevailing model?

In light of these anomalous redshift phenomena, we turn to the wise words from late last century of three of the pioneers of dissent in modern cosmology: Sir Fred Hoyle, Geoffrey Burbidge, and Jayant Narlikar.


Geoff Burbidge, Sir Fred Hoyle, Jayant Narlikar

"[Because it is outside current theory] most astrophysicists and cosmologists have felt justified in ignoring the evidence for anomalous redshifts, the thought being that what is known to be impossible remains impossible no matter how strong the evidence for it may be. . . [Our] main purpose . . . [in] the present paper is to question this mode of thinking" (Hoyle & Burbidge, 1995).


We will next turn to the phantasmagorical world of radio astronomy and the part it has played in the history of the search for a modern scientific cosmology.