galaxy redshift abundance periodicity

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arXiv:0711.4885v3[astro-ph]11Sep2008

Galaxy redshift abundance periodicity from Fourier analysis of

number counts N(z) using SDSS and 2dF GRS galaxy surveys

J.G. HartnettSchool of Physics, the University of Western Australia

35 Stirling Hwy, Crawley 6009 WA Australia; [email protected]

K. HiranoDepartment of Physics, Tokyo University of Science

1-3 Kagurazaka Shinjuku-ku, Tokyo 162-8601, Japan; [email protected]

ABSTRACT

A Fourier analysis on galaxy number counts from redshift data of both the Sloan DigitalSky Survey and the 2dF Galaxy Redshift Survey indicates that galaxies have preferred periodicredshift spacings of z = 0.0102, 0.0246, and 0.0448 in the SDSS and strong agreement withthe results from the 2dF GRS. The redshift spacings are confirmed by the mass density fluctua-tions, the power spectrum P(z) and Npairs calculations. Application of the Hubble law results ingalaxies preferentially located on co-moving concentric shells with periodic spacings. The com-bined results from both surveys indicate regular co-moving radial distance spacings of 31.7 1.8h1M pc, 73.4 5.8 h1Mpc and 127 21 h1M pc. The results are consistent with oscillationsin the expansion rate of the universe over past epochs.

Subject headings: galaxies:distances and redshiftslarge-scale structure of universe

1. Introduction

When modeling the large scale structure ofthe cosmos the cosmological principle is assumed,therefore what we see must be biased by our view-point. The assumption is that the universe hasexpanded over time and any observer at any placeat the same epoch would see essentially the samepicture of the large scale distribution of galaxiesin the universe.

However evidence has emerged from both the2dF Galaxy Redshift Survey (2dF GRS) (see fig.

17 of Colless et al (2001)) and also the Sloan Dig-ital Sky Survey (SDSS) (see fig. 2 of Tegmark etal (2004)) that seem to indicate that there is peri-odicity in the abundances of measured galaxy red-shifts. This has emerged from the galaxy numbercounts (N) within a small redshift interval (z) asa function of redshift (z).

What has been found is the so-called picket-

fence structure of the N-z relation, first noticedin one dimension by Broadhurst et al (1990) froma pencil-beam survey of field galaxies. In this pa-per the galaxy surveys are analysed on 2D and3D scales. The usual interpretation is that thisis evidence of the Cosmic Web, including voidsand long filaments of galaxies. An alternative in-terpretation is suggested in this paper; galaxiesare preferentially found in redshift space at cer-tain redshifts with higher number densities thanat other redshifts. Of course, this does not ruleout cosmic web structures in addition to this ef-fect.

However the concept that this represents realspace galaxy distances is incompatible with thecosmological principle, which assumes the unifor-mity of space at all epochs on sufficiently largeenough scales. And it has been demonstrated(Yoshida et al 2001), from a large number of nu-merical simulations using the Einstein-de Sitter

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and CDM models, that the probability of get-ting such a periodic spatial structure from cluster-ing and Cosmic Web filaments is less than 103.

This allows for an alternate explanation, namelythat the redshift periodicity is evidence for pastoscillations in the expansion rate of the universe.

The only information that has been sought fromlarge scale galaxy surveys is the spatial powerspectrum that describes the random yet uniformdistribution of galaxies in the universe, where theonly departure expected from the random distri-bution is some characteristic scale for the cluster-ing of galaxies. Certainly very few expect to findevidence consistent with a periodic redshift distri-bution.

However Hirano et al (2008) have attempted toexplain galaxy redshift abundance periodicity asa real effect resulting from the universe having anon-minimally coupled scalar field that manifests,in later cosmological times. The effect producedoscillations in the expansion rate as a function oftime. They model not only the redshift space ob-servations but also the effect their cosmology hason the CMB power spectrum and the type Ia su-pernova Hubble diagram.

In the usual analysis the spatial two-point orautocorrelation function is used to define the ex-cess probability, compared to that expected for a

random distribution, of finding a pair of galax-ies at a given separation (Baugh 2006). As aresult the power spectrum P(k) is derived fromthe two-point correlation function (Peebles 1980).The power spectrum is predicted by theories forthe formation of large scale structure in the uni-verse and compared with that measured, or moreprecisely calculated from the available data.

The power spectrum for the SDSS has beencalculated using a set of basis functions definedin (Hamilton et al. 2000). Three power spec-tra (galaxy-galaxy, galaxy-velocity, and velocity-velocity) were determined. Local motions of

galaxies only contribute a radial component of agalaxys total redshift, hence only affect the radialcomponent of the power spectrum. Because theangular power spectrum is unaffected the assump-tion is also made that galaxy-galaxy spectrum isequal to the redshift-space power spectrum in thetransverse direction. In this paper we analyzethe redshift hence radial component of the powerspectrum P(z), calculated in redshift space not

k-space, and find periodicity consistent with thatobserved in N(z). Also an Npairs analysis is car-ried out on both survey data sets with confirming

results.The Bulls-eye effect has been studied (Praton et al. 1997

Melott et al. 1998; Thomas et al 2004) via N-body simulations to result from large-scale in-fall plus small-scale virial motion of galaxies. Itis believed that these two effects can bias mea-surements of large scale real space galaxy dis-tributions. One is the so-called fingers-of-God(FOG) effect, which results from random peculiarmotions of galaxies at the same distance from theobserver. The second acts on much larger scalesand where overdensities of galaxies occur, like atthe Great Wall for instance. See Fig. 1.

Galaxies tend to have local motions towardthe center of such structures. These motions arenot random but coherent and add or subtractto the observers line-of-sight redshift determina-tion. These effects preferentially distort the mapin redshift space toward the observer due to thevelocities of galaxies within clusters, i.e. non-cosmological redshift contributions. However thelatter can only enhance in redshift space existingweak real space structures, it cannot create con-centric structures centered on the Galaxy. Andthe FOG effect tends to smooth out finer detailed

or higher Fourier frequency structures in redshiftspace and is not very relevant to this discussion.

In the maps, fig. 18 of Colless et al (2001))and fig. 4 of Tegmark et al (2004), there appearsto the eye to be concentric structure in the ar-rangement of galaxies. See the left hand side ofthe Fig. 1, the SDSS data with declinations be-tween 0 and 6 mapped in Cartesian coordinates.Could it be that we inhabit a region of the Uni-verse that is a bubble, part of a background ofmany such bubbles? But because redshift onlygives us one dimensional information the conclu-sion could be drawn that if the galaxies in the

Universe are evenly distributed throughout thenredshift periodicity is indicative of oscillations inthe expansion at past epochs. All observers wouldsee the same shell structure in redshift space re-gardless of their location.

In this analysis we take a heuristic approachand look for periodicity in the redshift spacing be-tween galaxies, in 2D in the case of slices and in3D in case of the whole SDSS data set. In practice

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the discrete Fourier Transform (s) is calculatedfrom the N-z relations, which are histograms de-termined by binning (counting) the observed red-

shifts of the survey galaxies between z z/2 andz + z/2, as a function of redshift z. Within theith bin there are Ni galaxies. Discrete Fourieramplitudes s are generated for each integer s > 1from

s =1n

ni=1

use2j(i1)(s1)/n, (1)

where us = Ni, j =1, n is the total number

of Ni bins. Because s are complex their abso-lute value is taken in the analysis. The Fourierfrequencies are calculated from

F= nzs

= z. (2)

where z is the periodic redshift interval.

The results suggest that there are redshifts, onthe scale size discussed here, which is not primar-ily the result of clustering or the FOG and infalleffects resulting in distortion of the redshift spacemaps. Both the SDSS and 2dF GRS redshift datawhere the redshifts are known with 95% confidenceor greater are used. Fourier analysis can find pe-riodic structure even where it may not be so ap-

parent to the eye.Data for 427,513 galaxies from the SDSS FifthData Release (DR5) were obtained where the dataare primarily sampled from within about -10 to70 degrees of the celestial equator. Also data for229,193 galaxies were obtained from the 2dFGRSwhere the data are confined to within 2 degreesnear the celestial equator and balanced betweenthe Northern and Southern hemispheres. In theSDSS case the data are not so well balanced, yetthere are nearly twice as many usable data.

2. Fourier analysis of N-z relations

2.1. 2D slices of SDSS data

From the SDSS data three 6 slices were takenin declination (Dec) angle for examination andcomparison. They were taken from 0 < Dec < 6

, 40 < Dec < 46 and 52 < Dec < 58. A realspace Cartesian plot (with aspect ratio of unity)of the data from the first slice near the equato-rial plane is shown in Fig. 1. The redshifts have

been converted to co-moving radial distance withHubble constant H0 = 100 kms

1Mpc1 wherethe parameter h = H0/100. The Great Wall is

shown in the second and third quadrants as indi-cated. In those two quadrants it is evident to theeye that there is general concentric structure witha spacing of about 75 h1 M pc.

Polar coordinate maps of these regions, pro-jected onto the equatorial plane, are shown in Figs2, 3 and 4, respectively. Most of the SDSS datacome from two declination bands on the sky. Thefirst slice is taken from the lower band near thecelestial equator and the latter two from higherdeclinations. Polar maps can tend to distort a realspace image but a comparison of Figs 1 and 2 in-dicates that these polar plots would be very close

in appearance to real space maps if converted toco-moving coordinates.

From simple inspection concentric structure isapparent in both Figs 2 and 4 but not as apparentin Fig. 3. To the eye this seems too coinciden-tal and deserves further investigation. At least atsome declinations the case can be made for red-shift periodicity.

These data were binned with a bin size z =103 resulting in a N-z relation. The redshift res-olution of most, but not all, of the SDSS datais only 103. This bin size essentially counts all

galaxies of the same redshift regardless of theirposition on the sky.

Using (1) the discrete Fourier spectra were cal-culated for N(z) of each data slice, and are shownin Fig. 5. The Fourier frequency axis in Fig. 5,and all subsequent figures, has been converted toa redshift interval (z). For the lowest angle slice(solid black curve) from the data of Fig. 2 andthe highest angle slice (solid gray curve) from thedata of Fig. 4 the peaks at numbers 1 and 2 co-incide. For the data from the 40 < Dec < 46

slice of Fig. 3 the peaks are not strong nor dothey coincide with the others except at peak num-

ber 1. The fact that the maps in Figs 1 through 3are visually different and that the resulting Fourierspectra dont all have coincidental peaks indicatesthat the peaks that do coincide are not the resultof some selection effect resulting from the choiceof filters or otherwise. Therefore it is evident thatthe peaks are the result of real redshift structurethat varies in different directions. The underlyingcause must be common to all, since all three slices

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Fig. 1. Real space Cartesian coordinate plotin units ofh1 Mpc: co-moving (Hubble) distancederived from SDSS redshift data from 0 < Dec

galaxy redshift abundance periodicity

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