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December 19, 2006 (Revised 3/9/07)

Does the Universe Have a Handedness?

Michael J. Longo University of Michigan, Ann Arbor, MI 48109

In this article I study the distribution of spiral galaxies in the Sloan Digital Sky Survey (SDSS) to investigate whether the universe has an overall handedness. A pref-erence for spiral galaxies in one sector of the sky to be left-handed or right-handed spirals would indicate an asymmetry in the overall universe and a preferred axis. The SDSS data show a strong signal for such an asymme-try. Its axis seems to be strongly correlated with that of the quadrupole and octopole moments in the WMAP mi-crowave sky survey, an unlikely alignment that has been dubbed "the axis of Evil".

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The Sloan Digital Sky Survey

The SDSS DR5 database contains ~40000

galaxies with spectra for redshifts <0.04

with a wide coverage in right ascensions

(RA) and a more limited range of declina-

tions ( ). A few percent of these are spiral

galaxies that can be used in a search for a

preferred handedness.

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A few "typical" Galaxies from the Sloan Survey

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A universe with a well-defined handedness is illustrated very sche-matically below. This shows a polar plot of spiral galaxies in RA and redshift (z) or distance. Note that to us, galaxies in one hemisphere would be right-handed while they would be left-handed in the oppo-site hemisphere. (If a predominance of left- or right-handedness were seen in all directions it would be an indication of a bias or sys-tematic error preferring that handedness.)

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(A) Polar plot of right ascensions vs. redshifts for all declinations

(B) Plot of declinations vs. redshifts. The left and right hemispheres in (A)are plotted on their respective sidesin (B). Declinations between -19° and +60° were used in this analysis.

The SDSS sky coverage is, ofcourse, far from complete.

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The Analysis (1)First select galaxies from the SDSS with the SQL command:

select p.objid, p.ra, p.dec, p.u, p.g, p.r, p.i, p.z, s.z as redshiftfrom galaxy p, specobj swhere p.objid=s.bestobjid and p.g < 17 and s.z BETWEEN 0.001 AND .04

which translates as "Select galaxies (with spectra) with green magnitude <17 and with redshifts between 0.001 and 0.04."

This yielded 22,768 galaxies.

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The Analysis (2)These were then scanned "by hand" and galaxies with fairly clearspiral structure were selected.

No Yes No No

Galaxies that were seen too "edge-on" forspiral structure to be apparent were not used.

No

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The Analysis (2-cont'd)

This scanning was done randomly in right ascension and declination, so that any bias would not give a false signal.

Selected spirals were scaled appropriately and down-loaded from the SDSS web site as JPEG files for further analysis. Each JPEG had separate red, green, and blue images.

After some months of effort, this yielded approx. 2835 spirals.

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The Analysis (3)The spiral candidates were then analyzed by an IDL program todetermine their handedness. The red, green, and blue componentsof the JPEG files were analyzed separately.

"Right-handed"

"Left-handed"

The conventions for right- and left-handedspirals are shown.

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The JPEG file for each spiral galaxy was submitted to an IDL program to determine its handedness. The algorithm used for this analysis was based on a rotat-ing one-armed spiral mask similar in shape to half of the spiral in Fig. 1(c). The spiral mask was rotated in 64 steps through the galaxy, and the convolution of the mask and galaxy was determined at each step. The 64 convolutions were then subjected to a Fourier analysis to determine the power in each harmonic term of order n. Two masks were used; one was the mirror image of the other (thus representing right- and left-handed spirals that were otherwise identical).

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I spent many months experimenting with different spiral masks to find the best shape. The diversity of galactic shapes and peculiari-ties is daunting. I varied many parameters including the pitch of the spiral, its width, theweighting vs. radius, and the possibility of a central bar, as well as the use of multiple masks. Each of these was tested against a random sample of galaxies whose handedness was determined "by hand". In the end a rather simple mask turned out to be as good as any, and it had the very distinct advantage that the mirror image was generated by changing one sign in the term describing its pitch. This made the possibility of some built-in asymmetry extremely unlikely. This was my main concern. A more complicated mask or a combination of several masks might have increased the efficiency in finding spirals slightly at the expense of greater complication and the increased possibilityof a subtle flaw. In the end, the efficiency of the mask can only bejudged by comparing it with "eyeball" determinations of thehandedness. Judging by eye, the mask used was probably >95% efficient for 2-arm spirals and ~85% for multi-arm ones.

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QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

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Fourier Power vs. Order

Red is positive handedness maskBlue is negative

Fourier Power vs. Order for previous example

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Spiral galaxies that have recently been disruptedby collisions or close encounters with other galaxies are likely to have lost their primordial spin orientation. These tend to be blueish due tonew star formation, while old, sedate spirals are more yellowish.

A selection on the spectrum requiring 1.9 < |U-Z| <3.7 was made to removethe bluest ones. Here U is the magnitude in the ultraviolet band and Z is the far infrared.

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Red are positivespins; blue arenegative. Thereseems to be somepatchy structure,but hard to tell.

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Net asymmetries <A> by sector in RA and segments in z. Segments with positive <A> are indicated in red and negative <A> in blue. The <A> for segments with <10 galaxies are not shown. The larger numbers near the periphery give the overall asymmetry for that sector; the black num-bers in parentheses are the total number of spiral galaxies in the sector.

RA=0 °

RA= 90°

z = 0 .02

z = 0.0 4

(58)

(65)

(3)

(31)

(65)

0 .23

0.0046

0.082

0.0009

-0 .0046

0.0138

0.0164

0.249

0.0504

0.175

0.0648

0.0959

0.0258

RA=180°

(33)

(284)

(366)

(297)

(258)

(190)

0.0022

0.0064

-0.050

-0.021

-0.068

-0.051

0.0308

0.0381

0.145

0.195

0.259

0.1130.0986

0.02380.0179

0.04060.0657

0.08620.0986

0.0101

0.198

0.0690

0.01780.0982

0.0121

0.0401

0.152

0.0266

0.0653

0.152

0.0780

0.0159

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The are determined from standard normal distribution

statistics, , which gives

The 3rd row shows the difference in number counts between the

first two rows. The combined asymmetry differs from zero by

2.89 . The nominal probability for exceeding 2.89 is 0.39%.

(N ) = N

Table I. Number counts and net asymmetries for the RA ranges indicated. The 3rd row gives the combined numbers for the first two rows. The last column gives the number of standard deviations for the asymmetries.

RA Range N+ N– NTot (N+– N–)/NTot ± A/

( )R 80°to–80° 118 104 222 0.063±0.067 +0.94(L)150°to210° 296 368 664 –0.108±0.039 –2.79

(R-L)Combined 178 264 886 –0.0971±0.0336 –2.89

( A ) = 1 / N + + N −

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An asymmetry in the distribution of spiral galaxies im-plies that the universe has an axis or unique direction. The data suggest that the axis lies generally along the line RA=180° (or 0°) with a declination ~10° where most of the SDSS galaxies lie.

The Wilkinson Microwave Anisotropy Probe (WMAP) studied the cosmic background radiation. Their results for the angular power spectra showed anomalies in the low- l moments. The axis of the dipole, the normal to the quadrupole, two of the octopole axes nearly coincided with each other and with the ecliptic, the plane of the Earth's orbit. This bizarre alignment has been dubbed "the axis of evil".

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On the basis of the 3-year WMAP data (ILC123), Copi et al. find the normal to the plane defined by the quadrupole moments to be at l = –128.3°, b = 63.0° in Galactic polar coordinates. In the equatorial coordinates used here, this corresponds to RA = 166.3°,=16.0°

whichi s consistentwiththeaxisoftheasymmetryseenher .eTheSDSScoverageindeclinationfortunatelyextendsto ~60° in theRA=180°hemispher .eThus the

WMAP quadrupole/octopoleax is reinforcesthefindingofanasymmetryinspiralgalaxyhandednes .sOntheoth er

,hand thespiralgalaxyhandedne ,ssifverifi ,edreprese ntsa uniqueandcompletelyindependentconfirmationthat

thisaxisreallyisaresultoflarge-scalestructureoftheuniver ,se andnot an artifactintheWMA P dat .a

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Quadrupole

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Octupole

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Several anomalous features in the WMAP data have been reported, pointing toward a preferred direction in the sky, the so-called "axis of evil." The origin of this effect remains mysterious, and it could well be that it is due to foreground contamination or unsubtracted systematic errors. Unlike point reflections, mirror reflections select a preferred direction in the sky, that of the normal to the symmetry plane. Hence the search for mirror handedness entails the search for a preferred axis in the CMB fluctuations (although the converse need not be true). The first purpose of this paper is to investigate whether mirror parity could shed light upon the observed statistical anisotropy of CMB fluctuations.

Is the Universe odd? Kate Land and Joao Magueijo Phys. Rev. D 72, 101302(R) (2005)

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Mon. Not. R. Astron. Soc. 000, 1–6 (2006) Printed 16 November 2006

The Axis of Evil revisited Kate Land and Joao Magueijo

ABSTRACT

In light of the three-year data release from WMAP we re-examine the evidence for the “Axis of Evil”. We discover that previous frequentist methods are not robust with respect to the data-sets available and different treatments of the galactic plane. We identify the cause of the instability and show that this result is not a weakness of the data. This is further confirmed by exhibiting an alternative approach, Bayesian in flavour, and based on a likelihood method and the information criteria. We find strong (and sometimes decisive) evidence for the “Axis of Evil” in almost all renditions of the WMAP data. However some significant differences between data-sets remain, and the quantitative aspects of the result depend on the particular information criteria used.

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The Uncorrelated Universe: Statistical Anisotropy and the Vanishing Angular Correlation Function in WMAP Years 1-3

Craig J. Copi, Dragan Huterer, Dominik J. Schwarz, and Glenn D. Starkman astro-ph/0605135 v2 31 May 2006

"We find it hard to believe that these correlations are just statistical fluctuations around standard inflationary cosmology’s prediction of statistically isotropic Gaussian random a m [with a nearly scale-free primordial spectrum]. What are the consequences and possible explanations of these correlations? There are several options — they are statistical flukes, they are cosmological in origin, they are due to improper subtraction of known foregrounds, they are due to a previously unexpected foreground, or they are due to WMAP systematics. As remarked above it is difficult for us to accept the occurrence of a 10-8 unlikely event as a scientific explanation. A cosmological mechanism could possibly explain the weakness of large angle correlations, and the alignment of the quadrupole and octopole to each other. A cosmological explanation must ignore the observed correlations to the solar system, as there is no chance that the universe knows about the orientation of the solar system nor vice-versa. These latter correlations are unlikely at the level of less than 1 in 200 (plus an additional independent ≈ 1/10 unlikely correlation with the dipole which we have ignored). This possibility seems to us contrived and suggests to us that explanations which do not account for the connection to solar system geometry should be viewed with considerable skepticism."

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D. Huterer – "Mysteries of the Large-Angle Microwave Sky"

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PRL 97, 131302 (2006)

Ellipsoidal Universe Can Solve the Cosmic Microwave Background Quadrupole Problem

L. Campanelli, P. Cea and L. Tedesco The recent 3 yr Wilkinson Microwave Anisotropy Probe data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit –cold dark matter prediction. We show that by allowing the large-scale spatial geometry of our universe to be plane symmetric with eccentricity at decoupling or order 10-2, the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.

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Campanelli et al., cont'd

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Campanelli et al. suggest that the eccentricity is produced by a cosmic magnetic field ~5 x 10-9 G. *

This model can also account for the alignment of the dipole with the "axis of Evil", if we tweak it a bit. All we need is to allow a small asymmetry between the poles of the ellipsoid. The conventional wisdom is that the dipole is associated with our motion through the rest system of the CMB.

However, a flattened ellipse could easily produce a dipole term which overwhelms that due to our motion.

_________________* Earlier suggested by Ya. Zeldovich, 1965, Zh. Eksperim. I Teor. Fiz 48, 986.

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A "uniform" primordial cosmic magnetic field would naturally lead to ahandedness in the orientation of spiral galaxies. Matter condensing from primordial cosmic plasma would spiral around the magnetic field lines,losing energy and eventually forming spiral galaxies, whose handednessaxis is along the direction of the magnetic field and the direction of the normal to the plane defined by the quadrupole axes.

My interpretation of all this is that there is indeed a large-scale cosmicmagnetic field that extends at least out to distance scales correspondingto the last scattering surface, ~100,000 yrs after the Big Bang. This explainsthe spiral galaxy spin axis, the CMB quadrupole (and maybe dipole) orientations, and probably the other peculiarities of the low-ℓ moments of the CMB. [It, of course, can't explain the alignment with the equinoxes!]

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When I first saw the apparent spin alignment of the spiral galaxies, I thought that if was fortuitous that the axis of the alignment was so well lined up with the axis about which the Sloan Survey covered.

However, it turns out this seems not to be a matter of luck at all! Astro-nomical surveys prefer to look along the poles of our Galaxy where the Milky Way and dust don't interfere. The North Galactic Pole is at RA =192.9°, = 27.1°, which is right along the axis of the asymmetry. Furthermore, the handedness (direction) of our Galaxy is aligned in the same direction as the preferred spin alignment (right-handed as seen from the direction of the North Galactic Pole).

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Our Galaxy as seen fromthe NGP. Our Galaxy is apparently oriented withthe same spin direction asthe majority of the spirals,i.e., right-handed as seenfrom RA ~180°.

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We can't say too much about the agree-ment of all these axes in declination. Asexplained previously, all lie near the NorthGalactic Pole, including the region coveredby the Sloan Survey.

NGP

NGP

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• The ecliptic (plane of the Earth around the Sun) and the equinoxes.

The thing I can't explain--

In summary, the spiral galaxy spin alignment seems to coincide within an uncertainty ~10° with:

• The normal to the 2 quadrupole axes

• Two of the octopole axes• The dipole axes (which is supposed to be due to Sun's motion through rest system of the microwave background).

• The North Galactic pole and the coverage of the astronomical surveys.• The general direction of the dark matter filaments in the COSMOSanalysis (generally along RA=150°, =2.3°).