How Non-Velocity Redshifts in Galaxies Depend on Epoch of Creation
| Scientific Paper | |
|---|---|
| Title | How Non-Velocity Redshifts in Galaxies Depend on Epoch of Creation |
| Read in full | Link to paper |
| Author(s) | Halton C Arp |
| Keywords | redshifts, evolutionary ages, Hubble constant |
| Published | 1991 |
| Journal | Apeiron |
| Volume | 1 |
| Number | 9-10 |
| No. of pages | 28 |
| Pages | 53-80 |
Read the full paper here
Abstract
Non-velocity redshifts of the brightest OB stars in the Magellanic Clouds are correlated with their evolutionary ages. It is shown that these excess redshifts are quantitatively predicted if the stars are made of matter created only ≤ 3 × 106 yrs. later than the average matter in the Clouds. Intrinsic spectral shifts of galaxies and quasars are produced by relatively small differences in the epochs of their creation, though their average Hertzsprung-Russel diagrams are left essentially unchanged.
The Hubble constant is then quantitatively derived as a predominantly distance-intrinsic redshift effect which is a function of look back time, not as a distance-expansion velocity relation. Present estimates of the age of the oldest stars predict—on the basis of the age-intrinsic redshift law—a Hubble parameter of H0 = 45 ± 7 km s−1 compared to a recently measured value of H0 = 52 ± 2 km s−1 (Sandage and Tamman 1990).
Overview
This 1991 Apeiron paper is the theoretical companion to Halton Arp's observational paper on systematic redshifts in OB stars, written while he was at the Max-Planck-Institut für Astrophysik in Garching. It is one of his most ambitious pieces, because it does not merely report anomalous redshifts — it attempts to derive the Hubble constant itself from them, and gets a number that agrees with the measured value.
The argument runs from small scales to large. Arp starts from the well-documented fact that in groups dominated by a large galaxy the smaller companions are systematically redshifted — 21 out of 21 in the Local Group and the M81 group, a result with a chance probability of about one in two million. If companion galaxies carry excess redshift, and companions are systematically bluer and younger in spectral type, then the youngest stars within a galaxy should show it too. They do: 30 of 34 OB supergiants in the Magellanic Clouds sit above the systemic HI velocity of their host. Arp then plots those excess redshifts against stellar evolutionary ages read off the Hertzsprung–Russell diagram and finds the younger stars are the more redshifted. The mechanism he proposes, taken from the variable-mass conformal gravity of Hoyle and Narlikar, is that a particle's mass depends on how much matter it can exchange gravitons with — hence on the volume of universe inside its light-signal sphere, hence on how long it has existed. Younger matter has lighter electrons, emits lower-energy photons, and is therefore redshifted. Applied over cosmological look-back times, this same law reproduces the Hubble relation without any expansion.
The argument
The observational base
Arp assembles independent lines of evidence for OB excess redshift. In the Magellanic Clouds, with the systemic HI shifts well determined at vSMC = 161 ± 2 km s−1 and vLMC = 270 ± 2 km s−1, 30 of 34 OB stars lie redward: a binomial probability of 2.7 × 10−6. Trumpler (1935) found 9 of 9 O stars in galactic clusters redshifted relative to their clusters; Findlay-Freundlich (1954) found B stars in Orion receding at 10 km s−1 from their gas; and the classical "K term" grows toward earlier spectral types. With a stellar-wind correction of ≥ 15 km s−1 added, Arp puts the residual excess for galactic OB stars at 15 < cΔz < 37 km s−1. Since these samples are independent, the joint probability of accident is, in his phrase, "astonishingly, negligibly small."
What property causes it?
Plotting excess redshift on the H–R diagram for 24 LMC stars shows no correlation with temperature across the range from O (~35,000 K) to A0 (~10,000 K). Arp treats this as a direct falsification of one class of tired-light models — those, such as Marmet's inelastic photon scattering, in which the shift should scale with source temperature. The SMC gives a cleaner test because it has less dust and lower stellar density, hence smaller reddening uncertainties and fewer peculiar velocities; there the correlation is with luminosity, and by laying Maeder (1990) evolutionary tracks for Z = 0.0002 across the diagram Arp reads off ages for ten supergiants spanning 60 to 15 solar masses. Plotted against excess redshift, the younger stars are the more redshifted.
The variable-mass redshift law
The governing relation, taken from Narlikar and Das (1980), is
(1 + z1)/(1 + z0) = t02/t12,
with z0 ≡ 0 for the oldest matter considered. Taking the oldest matter's own age as τ0 = 17 × 109 yr, which in the external t frame is t0 = 3τ0 = 51 × 109 yr, the law gives cz1 = 35 km s−1 for matter created 3 × 106 yr later, 71 km s−1 for 6 × 106 yr, and 106 km s−1 for 9 × 106 yr. Arp emphasizes that both the slope and the zero point of the resulting envelope in the age–redshift plot are fixed within narrow limits by independently known quantities: the age of the oldest stars (13–17 × 109 yr, Sandage and Cacciari 1990) and the evolutionary age of the youngest first-generation SMC stars (~7–8 × 106 yr). The observed points fall roughly along that line.
The scheme nests. A giant Sb such as M31 is created at t0; a companion such as the SMC from matter 8 × 106 yr younger acquires ~94 km s−1 of intrinsic redshift — and the SMC is observed at 94 km s−1. Stars within the SMC formed from matter another ~3 × 106 yr younger acquire ~35 km s−1, as observed. Crucially, Arp shows that mixing in stars 3–8 × 106 yr younger leaves the composite H–R diagram essentially untouched: 1010, 109 and 108 yr tracks are unaffected, and only at the very top of the diagram do the later-generation supergiants separate out. Larger discordances need only modest offsets: the NGC 7603 companion at 8,000 km s−1 requires Δτ ≈ 6.7 × 108 yr, and the NGC 1232 blue companion at 28,000 km s−1 requires 2.2 × 109 yr, or 12% of the parent's age.
Quantization and negative shifts
If matter is created in periodic bursts every ~6 × 106 yr, the 72 km s−1 galaxy periodicity of Tifft follows directly. For quasars the observed spacing is multiplicative, (1 + zi+1)/(1 + zi) = 1.228 (Karlsson), which requires ti+1 = 0.9024 ti; Arp tabulates the corresponding creation epochs for the Karlsson peaks at z = 0.06, 0.30, 0.60, 0.96, 1.41, 1.96, 2.64, 3.47, 4.49. He notes in a footnote that real peculiar velocities of order 72 km s−1 would erase such a pattern, so if quantization is real then genuine velocities must be smaller than assumed — and consequently virial masses of groups and clusters are overestimated, so that "the question of missing mass may well disappear altogether."
The law also predicts negative shifts for matter created earlier. Arp reports that of seven negative-shift candidates outside the Local Group, all seven lie toward the Virgo Cluster centre, five are morphological class Sb or Sab, and the only certain Sb's in Virgo have negative redshifts. Since a single morphological class should not show preferential motion within a cluster, he takes this as evidence against a velocity interpretation. The mean of the four largest negative values, cz = −284 km s−1, corresponds to creation 24 × 106 yr earlier than M31's material, which after allowing 71 × 106 yr of look-back time to Virgo at 21.9 Mpc puts the Virgo Sb's ~95 × 106 yr — 0.6% — ahead of the Local Group.
Deriving the Hubble constant
The key step is arithmetical. Since 3.26 × 106 light years is one megaparsec, and 3 × 106 yr of creation-epoch difference yields ~35 km s−1, look-back time alone imposes cΔzi ≈ 38 km s−1 Mpc−1. Taking the lower limit τ0 = 13 × 109 yr instead gives 51 km s−1 Mpc−1. So the law predicts 38 < H < 51 depending on the age adopted — that is, 44.5 ± 6.5 — against Sandage and Tamman's measured 52 ± 2. Arp checks it on Virgo directly: with τ0 = 15 × 109 yr and d = 21.9 Mpc the law predicts a Virgo redshift of 975 km s−1 against the adopted core value of 976 ± 45. He credits Hoyle (1972) with having produced the Hubble law in one step from an equivalent relation, his own addition being to supply the stellar age that fixes the constant numerically. He also notes that the reported gradient from H ≈ 50 at low redshift to H ≈ 100 at higher redshift follows naturally, since higher-redshift samples include younger matter.
Two times, and the metric
Section XI supplies the machinery. Atomic clock rate R scales with particle mass, so dτ ∝ m(t)dt ∝ t2dt; integrating gives τ = t3/3t02 and hence τ0 = t0/3. Differentiating the redshift law gives dz/dΔt = (2/t0)(1 + z)3/2, so H = 2/t0 at z = 0, matching Section X. For large z the apparent Hubble parameter grows as (1 + z)3/2 — at z = 1.5 it is 3.95 H0, which if misread as an expanding-universe deviation would demand galaxies about 3 magnitudes brighter in the past, "just the order of deviations observed" and conventionally ascribed to luminosity evolution. Arp then stresses that these relations are not new physics: applying Narlikar's conformal transformation τ = t3/3t02 to the Friedmann solutions of the Einstein equations yields exactly the same expressions. "We are simply giving the quantities different interpretations, namely, m(const) → m(t) and z(r) → z(t)." The corresponding cosmology is a low-density, near-Euclidean universe in which the Local Supercluster is a dense island occupying some 4 × 10−7 of the visible volume.
Assessment
The paper's power lies in the tightness of the loop it closes. Arp does not fit a free parameter: the age–redshift law comes from Narlikar and Das, the stellar ages come from Maeder's evolutionary tracks, the ages of the oldest stars come from Sandage and Cacciari, and out the far end comes a Hubble constant of 44.5 ± 6.5 km s−1 Mpc−1 against a then-measured 52 ± 2. That a chain running from OB supergiants in the SMC to the expansion rate of the universe should land within uncertainties is a genuinely striking result, and the internal consistency — the same equation giving 94 km s−1 for the SMC when 94 is observed, 35 km s−1 for its supergiants when 35 is observed, and a Virgo redshift of 975 when 976 is observed — is more than one would expect from a scheme with no explanatory content. The variable-mass framework is also not fringe mathematics: as Arp correctly shows, it is a conformal rewriting of the Friedmann solutions, so nothing in it violates general relativity; the dispute is about interpretation, not about the field equations. And his methodological instincts are sound throughout — he uses the SMC rather than the LMC precisely because dust and stellar density make the LMC less trustworthy, and he explicitly rules out a rival dissident model (temperature-dependent tired light) using his own data.
The difficulties are equally real. The Hubble-constant derivation is arithmetically slighter than it appears: H = 2/t0, so any theory tying the redshift scale to the age of the oldest objects will produce a number of the right order, and the agreement is really the familiar coincidence H0−1 ≈ age of the universe rather than an independent prediction. Since H emerges as 2/t0 and Arp chooses t0 from stellar ages spanning 13–17 × 109 yr, the predicted range 38–51 is wide, and the measured value he compares against, 52 ± 2, lies at or just outside its upper edge. The subsequent history is unkind here: the distance ladder has moved to H0 ≈ 73 and CMB-based inference to ≈ 67, both far above 44.5 ± 6.5, so the prediction that looked successful in 1991 no longer does.
Several of the empirical props have also weakened. The redshift quantizations on which Section VIII depends — Tifft's 72 km s−1 and the Karlsson quasar peaks — have not survived the large redshift surveys; analyses of 2dF and SDSS samples find no significant periodicity, and the Broadhurst pencil-beam result Arp cites was not reproduced in wide-area surveys. The negative-shift Virgo Sb's are drawn from a sample of seven objects in a cluster with a velocity dispersion near 700 km s−1, where a −284 km s−1 mean is entirely ordinary as peculiar motion; Arp's counter-argument, that one morphological type should not show preferential motion, is weakened by the fact that spiral and elliptical populations in Virgo genuinely do have different kinematics and infall histories.
The sharpest test the paper does not face is time dilation. If cosmological redshift is intrinsic rather than kinematic, distant clocks should not be observed to run slow in proportion to (1 + z); yet the light curves of Type Ia supernovae are stretched by exactly (1 + z), a result established from the mid-1990s onward and now measured out to z ≈ 1 and confirmed independently in quasar variability. Arp's own scheme does produce a slowing of atomic clocks in younger matter, so the effect is not simply absent — but the paper never computes the predicted stretch factor and compares it with what is seen, which is the calculation that would decide the matter. Similarly, the blackbody spectrum and acoustic structure of the microwave background receive one dismissive clause ("smoothness of the microwave background") in a list of Big Bang problems, and the COBE FIRAS spectrum, published the previous year, is not addressed at all.
The companion-galaxy statistics with which the paper opens remain its most durable element, and the general point — that a redshift observed is not the same thing as a velocity measured — is a legitimate one that has never been fully answered on Arp's own terms. But the paper argues from a strong local anomaly to a global replacement of the expansion picture, and the intervening steps carry far more weight than the OB-star data can bear.