Abstract: When looking at large scale maps of the distribution of galaxies around our position is space it may be noticed that there seem to be finger like structures of these galaxies pointing back at the earth. This is called the Fingers of God (FOG) effect. Some creationists have attempted to use this as an argument for an absolute geocentric universe. But the FOG effect can be simply explained by reasonable assumptions on the dynamics of galaxies within their clusters. Therefore it would be very naïve to use it as evidence in support of a galactocentric universe or an absolute geocentric universe. (This article is somewhat technical. First published in the Journal of Creation 22(2):75-78, 2008; edited here.)
On occasion I have heard discussed among creationists, that considered the Fingers of God (FOG) effect as evidence for a galactocentric1 universe and some foolishly even considered it evidence in favour of a geocentric2 universe. The phenomenon is well known and in Wikipedia it is reported.
“Redshift-space distortions are an effect in observational cosmology where the spatial distribution of galaxies appears squashed and distorted when their positions are plotted in redshift-space (i.e. as a function of their redshift) rather than in real-space (as a function of their actual distance). The effect is due to the peculiar velocities of the galaxies causing a Doppler shift in addition to the redshift caused by the cosmological expansion.”3
From this it would seem that the FOG effect results from Doppler motion of galaxies within their clusters causing a line of sight effect in redshift space4 (explained below), which produces the effect of fingers of galaxies all pointing towards the observer if plotted on a map. But if one realizes that we cannot definitively know how galaxies in the Universe are distributed without making certain assumptions, then how can one use this effect as evidence for a galactocentric universe or even a geocentric universe?
Galaxies clusters are observed with constituent galaxies numbering in the thousands. It does not seem to be unreasonable to assume that within those clusters the galaxies have random orbit trajectories, meaning they orbit around their common centre with different trajectories. Generally clusters appear to be approximately spheroidal or elliptical in shape. And they are believed to be viralised.5 If the mass of the cluster, which includes large quantities of hot intercluster gas comprising about 3 to 4 times the mass of the constituent galaxies, is in hydrodynamic equilibrium then the galaxies are mutually bound to each other. This means on the Hubble timescale or the usually stated age of the universe,6 more than ten billion of years, the cluster will not break up. Using this fact, astrophysicists estimate the dynamical mass of the cluster by either measuring the temperature of the x-ray emitting gas or calculating the dispersion7 of a number of constituent galaxies, which act as tracers. This makes the implicit assumption that the galaxy clusters have had sufficient time in the Universe to come into dynamical equilibrium.
From the Virial Theorem Fritz Zwicky,8 in 1933, first deduced the existence of alleged unseen dark matter. The total mass deduced from the dynamics of galaxy clusters is much greater than the luminous matter seen in the clusters and hence it is said there is a lot of unseen, therefore dark, matter present. See Why is dark matter everywhere in the cosmos?
However if one introduces new physics, hence a new degree of freedom into the calculations, which is the velocity of the expansion of the Universe, which is what I did using Carmelian physics, then one gets almost exactly the measured temperature for massive elliptical and dwarf spheroidal galaxy clusters.9 No dark matter need be assumed. That is one possibility but it highlights the possibility that new physics may be all that is needed.
In astronomy, the real-space positions of galaxies are determined by measuring their redshifts, z, and then applying in the Hubble law,
r = (cH0-1) z, (1)
where r is the radial distance to the galaxy, H0 is the Hubble constant and c the vacuum speed of light.
For redshifts z < 0.2 it is generally assumed that the Hubble Law is essentially independent of the details of any particular cosmological model. So for a redshift-distance relation only the Hubble Law (Eq. (1)) need be assumed. No other assumptions from any particular cosmology is necessary to be assumed. Thus galaxy redshifts (z) may converted into real-space Hubble distances (r) using the natural scale length cH0-1 = 4154 Mpc,10 assuming H0 = 72 km s-1 Mpc-1. (This implicitly assumes the Hubble Law to be valid, which in an expanding universe follows from General Relativity. Some static universe models also assume its validity but without knowing an underlying cause.)
Fingers of God
In redshift-space galaxy clusters tend to be elongated towards the observer at Earth. But in every direction in the sky you look you see galaxy clusters pointing towards Earth. So does that mean we are at the center of the Universe? No!
Though it cannot be definitively proven, the evidence supports the idea that what we see in redshift space is not the same as in real space. And in real space, once we understand what the sources of galaxy redshifts are, we don’t see this effect at all. However it must be added that there is no independent way to verify this, if redshifts are the only method to determine the distance to the cluster members.
There are a number of possible contributions to the observed redshift of a galaxy and the two contributions that are considered in relation to the FOG effect are cosmological redshift–believed to result from the expansion of the Universe itself (space expansion)–and Doppler redshift–resulting from the motion of the source galaxy through space but within its cluster. Doppler motion is expected for all members of a galaxy cluster. Besides this, it is expected, if the cluster is a single gravitationally bound virialized group,11 that there will be center of mass motion of the cluster and this is due cosmological expansion of the Universe. However, even if cosmological expansion is not valid but a simple Hubble law distance rule is (cause unknown) then the following analysis still applies.
In Fig. 1 I have drawn a hypothetical galaxy cluster in real space, but have used units of redshift. In other words, convert to real space distance multiply each axis by cH0-1. The arrow indicates the observer at the origin of coordinates. I have simulated a very large spherical cluster of 1000 galaxies, represented by black dots, about 42 Mpc in diameter assuming our scale length above. The central galaxy in the cluster is at z = 0.05 or about 207 Mpc. This means, in an expanding universe, the center of mass motion has the cluster moving away from us at 5% the speed of light. This is reproduced in Fig. 2a.
Figs 2b and 2c then illustrate what happens if we give each galaxy in the cluster a Doppler redshift due to its orbital speed but with random trajectories around their mutual center of mass. The best way to model the effect is by adding a random redshift component to the individual redshifts of these galaxies, which has the effect of introducing a random radial velocity component. Since we can only see the radial component of any Doppler velocity arising from real motion within the galaxy cluster, this additional component will be either positive—a redshift (motion away from the observer) or negative—a blueshift (motion toward the observer). If the motion is transverse to the observer’s line of sight then the additional component is zero.
Figs 2b and 2c are effectively redshift space maps but plotted in rectangular coordinates with redshift. Because the Doppler velocities add to the total redshift of the source galaxy but not to its cosmological distance it helpful to view these figures as redshift space. We would incorrectly conclude this is real space if the additional component was not corrected for.
In the case of Fig. 2b I have added an orbital velocity of 1,500 km/s, which is very large for a cluster. They typically have x-ray temperatures of 4 to 7 keV or dispersion12 velocities of around 700 km/s. In redshift space you can see this addition of a Doppler component distorts the map—elongates the cluster like a finger pointing towards the observer at the origin. In real space the cluster would still look like it does in Fig. 1. Only the galaxies have motion around their mutual center of mass.
To really exaggerate this in Fig. 2c I have added an orbital velocity of 15,000 km/s, which is more typical of cosmological expansion redshifts (expressed in recession speeds) than peculiar Doppler motion within clusters. In this case the FOG points back and meets the origin. Of course this is deliberately exaggerated for effect. This is what is seen in redshift space but if the interpretation is correct, all that would be seen in real space is as shown in Figs 1 and 2a.
Halton Arp has contended that there is evidence for an excess of redshift within cluster members when compared to the redshift of the massive central (usually elliptical) galaxy.13 He has suggested that there is an additional redshift component involved, not due to Doppler motion, but due to some intrinsic as-yet-unknown effect. He shows a FOG effect that would result in his figure 3-11, when a spherical galaxy cluster is assumed. Based on this assumption the fingers that stretch out, in redshift space, both blue-ward and red-ward of the center of the cluster in Figs 2b and 2c, would instead only stretch out red-ward or out away from the observer. If the central galaxy is correctly identified, with the least redshift of all those in the cluster, then, in redshift space, a FOG would also point to towards the observer with the massive central galaxy at the tip of the finger. Nevertheless with Arp’s interpretation there is no suggestion that the FOG would be seen in real space. It also is purely a redshift-space effect.
From the Fifth Data Release (DR5) of the Sloan Digital Sky Survey14 I sampled the data within ±2° declination of the celestial equator, and plotted each galaxy in redshift space. This resulted in about 49 thousand galaxies, as shown in Fig. 3, plotted as a function of Right Ascension (RA), in degrees around the circle. In this map one can see large continuous clusters arcing around the center, particularly on the left hand side. In the middle there is clearly visible the ‘Great Wall’—a filament of thousands of galaxies. This map suggests concentric structure with us the observer at the center. This appears as a “Bull’s eye” if viewed from a distance. Because it is shown as a polar plot spherical clusters would be stretched out along great circles. These maps need to viewed in real space with rectangular coordinates to see the shape of the clusters.
This so-called “Bull’s-eye” effect15 has been analysed16 using N-body simulations, and suggested that it results from large-scale infall plus small-scale virial motion of galaxies. It is believed that these two effects can bias such determinations. It is a combination of the FOG effect acting on small scales in addition to a much larger effect. The latter acts on much larger scales and where overdensities of galaxies occur, like at the “Great Wall” for instance. Galaxies tend to have local motions toward the center of such structures. These motions are not random but coherent and add or subtract to the observer’s line-of-sight redshift determination. These effects preferentially distort the map in redshift space toward the observer due to the velocities of galaxies within clusters, i.e. non-cosmological redshift contributions. However the latter can only enhance, in redshift space, existing weak real space structures, it cannot create concentric structures centered on the Galaxy. And the FOG effect tends to smooth out the finer detailed structures in redshift space.
In order to model this on different scales, to the observed redshift data, I added additional orbital velocities for the galaxies in Fig. 3, by adding random redshift components ≤ 1 × 10-3 (Fig. 4) and ≤ 5 × 10-3 (Fig. 5). These additional components represent maximum local orbital velocities of 300 km s-1 and 1200 km s-1, with respect to the centers of mass of their particular cluster. By comparing Fig. 4 with Fig. 3 one can see a slight FOG effect—the additional random redshift causes clusters to be elongated toward the origin of the map. And in Fig. 5 the effect is very strongly seen. However the very large scale bull’s-eye pattern still appears to be present. To the eye the FOG effect smooths out the concentric arcs of the original—reducing the fine detail.
If we bin the redshifts between z – δz/2 and z + δz/2 and calculate the resulting number density as a function of redshift, we get N(z), known as the N-z relation. This was done with a redshift bin size δz = 10-3 and the result is shown in Fig. 6 by the black curve. The peaks possibly show periodic structure above or below the expected initial increase due to increasing surface area sampled, then later a fall off as the galaxies become too dim to see.
Again after a random redshift component ≤ 5 × 10-3 was added N(z) was calculated again and is shown in Fig. 6, as the dotted (pink) curve overlaid on the original. It is evident from this that the addition of random velocities has the effect of eliminating or smoothing out the finer detail in the number density. But in Fig. 5 it gives a striking impression when all the fingers point back to the origin.
From the above, we may conclude that the FOG effect cannot be used to justify a unique position for our galaxy in the Universe, or a unique absolute position for planet Earth (at the centre of the Universe) if either the Doppler motion or intrinsic excess redshift interpretations are valid. And there is good evidence for both.
The heating of hydrogen gas within clusters is good evidence for virialised motion and that gives us reasonable Doppler motions of many hundreds km s-1 within clusters.
Arp has explored a number of lines of evidence for excess redshifts—including shifting of abundance histograms—indicating there are more redshifts than blueshifts in a cluster. If the difference were totally from Doppler motion we should see equal red and blueshifts.
I believe that it is most probable that Doppler motion effects are the dominant cause of the FOG effect. There possibly is an additional intrinsic redshift component, as suggested by Arp, that also needs to be considered, but the FOG effect cannot be used to support either a galactocentric or an absolute geocentric universe.
References and Notes
- The Universe with our Milky Way galaxy near the physical centre. There are other larger scale structure evidence that may be in support of near galactocentric Universe. See Our galaxy near the centre of concentric spherical shells of galaxies?
- The Universe with the Earth at the absolute physical centre. Absolute geocentrism is not a biblically sound position. See Cosmological principle and geocentrism.
- Fingers of God effect, Wikipedia, accessed 18-01-2017.
- Redshift space is the space where redshift is the unit of ‘distance’. The real-space distances are determined from the Hubble law. If the redshift measured is not all due to the expansion of the Universe then the redshift-space picture would not simply be a scaling of the real-space picture.
- Given sufficient time a group of objects under mutual gravitation interchange kinetic and potential energy such that twice the total averaged kinetic energy equals the total averaged potential energy of the system. If true, it is a test that the system is gravitationally bound. For more details see Virial Theorem, Wikipedia, accessed 18-01-2017.
- Currently about 13.8 Gyr = 13.8 billion years.
- If the galaxies have peculiar or Doppler motions, the observer can only measure the radial or line of sight component. By sampling many galaxies in a cluster the variance in these line of sight velocities can be calculated. This is used in the Virial theorem to get a figure on the cluster mass.
- Fritz Zwicky, Wikipedia, accessed 18-01-2017.
- A full explanation can be found in J.G. Hartnett, “Spheroidal and elliptical galaxy radial velocity dispersion determined from Cosmological General Relativity,” Int. J. Theor. Phys. DOI 10.1007/s10773-007-9558-0, 2007. ArXiv preprint available as a pdf.
- Mpc = megaparsecs. 1 Mpc = 3.26 million light-years.
- Of course the argument could be made that clusters are not virialised because there has been insufficient time in the universe, when considered against the biblical time line. Still in time dilation creationist cosmologies hundreds of millions if not billions of astronomical years are needed just to grow the spiral galaxies that we see, so I would not assume that astronomical time scales are so very short.
- This is a thermodynamic concept. The line of sight radial velocities are measured and there is a variance among them. If galaxies are treated as particles this can be viewed as measure of the random component of their velocities.
- See chapter 3 of Arp, H., Seeing Red: Redshift s, Cosmology and Academic Science (Apeiron, Montreal, 1998)
- Astrophysical Research Consortium (ARC) and the Sloan Digital Sky Survey (SDSS) Collaboration. Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org.
- Also known as the Kaiser effect.
- E.A. Praton, A.L. Melott, and M.Q. McKee, “The bull’s-eye effect: Are galaxy walls observationally enhanced?” Ap. J.479:L15–L18, 1997; A.L. Melott, P. Coles, H.A. Feldman, and B. Wilhite, “The bull’s-eye effect as a probe of W,” Ap. J.496:L85–L88, 1998; B.C. Thomas, A.L. Melott, H.A. Feldman, and S.F. Shandarin, “Quantifying the bull’s-eye effect,” Ap. J. 601:28–36, 2004
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