Multipole alignment in the large-scale distribution of spin

direction of spiral galaxies

Lior ShamirKansas State University, Manhattan, KS 66502

Abstract

Previous observations have suggested non-randomdistribution of spin directions of galaxies at scalesfar larger than the size of a supercluster. Here I use∼ 1.7 · 105 spiral galaxies from SDSS and 3.3 · 104

spiral galaxies from Pan-STARRS to analyze thedistribution of galaxy spin patterns of spiral galax-ies as observed from Earth. The analysis showsin both SDSS and Pan-STARRS that the distribu-tion of galaxy spin directions forms a non-randompattern, and can be fitted to a dipole axis in proba-bility much higher than mere chance. These obser-vations agree with previous findings, but are basedon more data and two different telescopes. Theanalysis also shows that the distribution of galaxyspin directions fits a large-scale multipole align-ment, with best fit to quadrupole alignment withprobability of ∼ 6.9σ to have such distribution bychance. Comparison of two separate datasets fromSDSS and Pan-STARRS such that the galaxies inboth datasets have similar redshift distribution pro-vides nearly identical quadrupole patterns.

1 Introduction

Because the spin direction of a spiral galaxy de-pends on the perspective of the observer, the dis-tribution of the spin directions of spiral galaxiesis expected to be randomly distributed in the skyto an Earth-based observer. However, several pre-vious studies showed evidence of non-random pat-terns of the distribution of spin directions of spiralgalaxies [25, 36, 37, 15, 38, 39, 41, 40, 23, 24, 42, 43].

First experiments were done with manually an-notated galaxies [18, 22, 25], and showed evidenceof asymmetry between the number of galaxies withopposite spin directions. However, manual an-

notation of galaxies is impractical for analyzingvery large datasets of galaxies, and can also bebiased by the human perception [22, 14]. Theability to automate the galaxy annotation led tofar larger datasets, that are less vulnerable to hu-man bias due to the machine-based nature of theannotation. Automatically annotated datasets ofgalaxy images showed clear and statistically sig-nificant asymmetry between clockwise and coun-terclockwise galaxies in Sloan Digital Sky Survey[39, 41, 43]. While the first experiments were basedon SDSS alone, more recent work using several tele-scopes showed very good agreement between SDSSand data collected by other telescopes such as Pan-STARRS [40], and Hubble Space Telescope [42].Other experiments used smaller manually anno-tated datasets to show patterns of spin directionsof galaxies [44], including galaxies that are too farfrom each other to have gravitational interactions[24]. Alignment of spin directions has also beenshown with quasars [17].

Although the observations might be difficult toexplain without violating the basic cosmologicalfoundations, explanations to the observations thatdo not necessarily require the violation of the foun-dational cosmology have been proposed [46, 4].Here I use a large dataset of ∼ 1.7 ·105 SDSS galax-ies that were annotated automatically by their spindirections to show a possible multipole alignment ofthe distribution of galaxy spin directions. The pat-terns identified in SDSS galaxies are also comparedto the patterns of galaxy spin directions in a com-pletely separate dataset of Pan-STARRS galaxies.

2 Data

Data from two different digital sky surveys wereused in this experiment, to allow a comparison be-

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tween data collected by different telescopes and re-duce the probability that the results are driven byan unknown instrumental flaw in a certain tele-scope system. The first dataset is ∼ 1.7 · 105 spi-ral galaxies from SDSS annotated by their spindirections, and it is the same dataset used in[39, 41, 40, 43]. The galaxies are spiral galaxiestaken from the catalog of ∼ 3 · 106 SDSS galax-ies classified automatically into spiral and ellipticalgalaxies [21]. These galaxies are relatively brightand large, with i magnitude < 18 and Petrosianradius larger than 5.5”. The 740,908 galaxies iden-tified as spiral galaxies were used, while the galax-ies that were identified as elliptical galaxies wereremoved from the experiment.

In addition to the SDSS dataset, a separatedataset of Pan-STARRS galaxies was used to al-low comparisons between the results produced bythe two sky surveys. For that purpose, a dataset of2,394,452 Pan-STARRS galaxies that were labeledby Pan-STARRS photometric pipeline as extendedsources in all bands [45] was used.

The galaxy images from both datasets were re-trieved using the Cutout service, which both SDSSand Pan-STARRS provide. The images were re-trieved in the form of 120×120 JPG images. Toensure that the galaxy fits inside the image, if morethan 25% of the pixels on the edge of the imagehad grayscale value greater than 125, the imagewas downscaled by 0.01” and downloaded again un-til the number of bright pixels on the edge of theframe was less than 25% of the total number of edgepixels [21].

After the images were downloaded, they wereseparated into galaxies with clockwise spin direc-tion and galaxies with counterclockwise spin direc-tion. That was done by using the Ganalyzer algo-rithm [34, 35], as was done in [36, 37, 15, 9, 38, 39,41, 40]. In summary, Ganalyzer computes the ra-dial intensity plot of each galaxy images, which isa simple transform of the raw galaxy image into animage of dimensionality of 360×35, such that the Xaxis is the polar angle (in degrees) and the Y axisis the radial distance (in percents of the galaxy ra-dius). The value of the pixel at coordinates (x, y)in the radial intensity plot is the median of the 5×5pixels around (Ox + sin(θ) · r,Oy − cos(θ) · r) in thegalaxy image, such that θ is the polar angle and r isthe radial distance. The radial distance is measuredin terms of percent of the radius of the galaxy.

Figure 1: Original galaxy images (left), the radialintensity plots (middle), and the peaks detected inthe radial intensity plots (right). The sign of the re-gression of the vertical lines of the peaks determinesthe curve of the arms of the galaxy, and thereforealso the spin direction.

After the radial intensity plot is computed, peakdetection is applied to identify groups of peaksacross the horizontal lines of the radial intensityplot [34]. Since arm pixels are brighter than thesky background, the groups of peaks in the radialintensity plot are the arms of the galaxy. Con-necting the peaks detected in different horizontallines creates vertical lines that correspond to thecurve of the arm. Therefore, a linear regression ap-plied to the peaks can reflect the shape of the arm,and the sign of the regression coefficient indicateswhether the galaxy has clockwise or counterclock-wise spin direction. Figure 1 shows examples oforiginal galaxy images, the transforms into radialintensity plots, and the peaks detected in the radialintensity plots. A through description of the algo-rithm as well as analysis of its performance can befound in [34], as well as in [15, 36].

To use galaxies which their spin direction canbe determined, only galaxies that had at least 10identifiable peaks in the radial intensity plot wereused, and galaxies that did not have at least 10peaks were ignored. Of the peaks that were de-tected, at least 75% were expected to be orientedtowards the same direction. Galaxies that did notmeet these criteria were rejected, and were not usedin the analysis. Manual inspection of 200 galaxieswith clockwise spin direction and 200 randomly se-lected galaxies with counterclockwise spin directionshowed that 10 galaxies classified as clockwise and

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RA cw−ccwcw+ccw # galaxies

0o-30o -0.005 27,12830o-60o 0.068 18,02360o-90o -0.031 3,47790o-120o 0.011 5,302120o-150o 0.022 20,820150o-180o 0.005 19,585180o-210o 0.012 18,466210o-240o 0.021 18,894240o-270o -0.001 14,245270o-300o 0.019 873300o-330o -0.04 8,351330o-360o 0.016 19,184

Table 1: The number of galaxies and the asymme-try between clockwise and counterclockwise galax-ies in different RA ranges in SDSS.

13 galaxies classified as counterclockwise did nothave identifiable spin patterns, but none of thesegalaxies was missclassified.

An important feature of Ganalyzer is that itis a model-driven algorithm that follows definedrules that are driven by the features of the galaxy.As deep neural networks are commonly used forthe task of image classification, these methods arebased on complex and unintuitive data-driven rulesthat make it extremely difficult to understand howthe classification is performed. Such methods cancapture subtle biases in the training set or in thedata collection process, and lead to unexplainedbias or asymmetry that is difficult to understanddue to the complex classification process.

Annotating the dataset of SDSS galaxies by theirspin direction using Ganalyzer as described aboveprovided a dataset of 88,273 galaxies with clock-wise spin patterns and 86,075 galaxies with coun-terclockwise patterns. Assuming mere chance prob-ability of 0.5 of a galaxy to be associated with oneof the two possible spin directions, the probabil-ity to have such separation by chance can be com-puted using cumulative binomial distribution, suchthat the number of tests is 174,348 and the suc-cess probability is 0.5. The two-tailed probabilityto have 88,273 or more successes is P < 10−7. Re-peating the experiment after mirroring the galaxiesled to identical results, which is expected due to thedeterministic and symmetric nature of Galanyzer.Table 1 shows the number of SDSS galaxies in each30o redshift range.

Figure 2 shows the distribution of the exponen-tial r magnitude, Petrosian radius measured in ther band, and the redshift of the galaxies that were

RA cw−ccwcw+ccw # galaxies

0o-30o -0.009 3,55930o-60o -0.031 2,67660o-90o -0.015 1,69890o-120o 0.041 1,099120o-150o 0.025 3,473150o-180o -0.022 5,064180o-210o -0.001 5,195210o-240o 0.023 4,088240o-270o 0.013 1,874270o-300o 0.082 429300o-330o -0.024 1,074330o-360o -0.007 2,799

Table 2: The number of galaxies and the asymme-try between clockwise and counterclockwise galax-ies in different RA ranges in Pan-STARRS.

classified as clockwise, counterclockwise, or couldnot be classified and were therefore rejected fromthe analysis. Most SDSS galaxies do not have spec-tra, and therefore just the subset of 10,281 SDSSDR8 galaxies that had spectra were used for deduc-ing the redshift distribution.

The application of Ganalyzer to the Pan-STARRS galaxies provided a dataset of 33,028,of which 16,508 had clockwise spin direction and16,520 had counterclockwise spin. Figure 3 showsthe distribution of the Petrosian radius measure inthe r band and the r Kron magnitude of the galax-ies. The redshift distribution of the Pan-STARRSgalaxies is shown in Figure 4. The redshift distribu-tion is important for making a comparison betweenthe Pan-STARRS and SDSS data, and will be usedin Section 3. In the case of Pan-STARRS, Gana-lyzer was applied to all galaxies that met the crite-ria described above, and not just to galaxies identi-fied as spiral as was done in SDSS, since no catalogof Pan-STARRS spiral galaxies exists yet. There-fore, the number of Pan-STARRS galaxies withidentifiable spin directions is much smaller relativeto the size of the initial dataset of Pan-STARRSgalaxies.

The distribution of these galaxies and the differ-ence between clockwise and counterclockwise galax-ies in the different RA ranges is shown in Table 2.The table also shows the asymmetry in each 30o RArange measured by cw−ccw

cw+ccw . Consistency betweenthe asymmetries in Tables 1 and 2 is not expected,due to differences in the declination and redshift ofthe galaxies, as will be discussed in Section 3.

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Figure 2: Distribution of the exponential r magnitude, Petrosian radius measured in the r band, and thedistribution of redshift.

3 Results

To test for the existence of an axis of asymmetry inthe distribution of galaxy spin directions, for eachpossible (α, δ) combination the cos(φ) of the galax-ies were fitted using χ2 to d · | cos(φ)|, such that φ isthe angular distance between (α, δ) and the galaxy,and d is the spin direction of the galaxy (1 clockwiseand -1 counterclockwise). To deduce the statisticalsignificance of the axis, each galaxy was assigneda random number within {-1,1}, and the χ2 of fit-ting the cos(φ) of the galaxies to d · | cos(φ)| wascomputed such that d was the randomly assignedspin direction (1 or -1). The χ2 was computed 1000times for each (α, δ). The mean and standard de-viation of the 1000 runs were computed for each(α, δ) combination. Then, the mean χ2 computedwith the random spin patterns was compared tothe χ2 computed with the actual spin directions ofthe galaxies. The σ difference between the meanχ2 of the random spin directions and the χ2 of theactual spin directions is the statistical probabilityof a dipole axis at (α, δ).

Figure 5 shows the σ of the axis of spin directionasymmetry of all possible (α, δ) combinations [43].The most likely axis was identified at (α = 88o, δ =36o), with σ of ∼4.34 (P < 0.000014). The 1σ errorof the right ascension of the axis is (62o, 124o), andthe error range of the declination is (7o, 69o).

Figure 6 shows the probability of an axis whenthe spin directions of the galaxies are determinedrandomly. The random spin directions shows nostatistically significant pattern, and the maximumprobability of the axis is 1.04σ. The much lowerstatistical significance indicates that the asymme-try profile is not driven by certain statistical noise.

Previous observations in the context of CMB

anisotropy as observed by COBE, WMAP, andPlanck showed evidence of quadrupole alignment[7, 13, 28, 47]. Figure 7 shows the χ2 of fittingthe galaxies to cosine 2φ dependence in each possi-ble (α, δ) combinations. The axis with the high-est probability of 6.88σ was identified at (α =333o, δ = 56o). The 1σ error range of the RA is(292o, 7o), and on the declination the error rangeis (36o, 81o). The other axis peaks at (212o, 17o).Repeating the same experiment when the galaxiesare assigned with random spin directions is shownin Figure 8, exhibiting no statistically significantpattern with maximum probability of 1.18σ.

An attempt to fit the galaxy spin directions tooctopole alignment is displayed in Figure 9. Themost likely axis is identified at (α = 11o, δ = −22o)with probability of 6.41σ.

The patterns of spin direction asymmetry iden-tified by SDSS was compared to the asymmetriesidentified with the dataset of Pan-STARRS galax-ies described in Section 2. Figure 10 shows theprobability (in σ) of a dipole axis to happen bychance in each possible (α, δ) combination. Themost likely axis was identified at (49o,−3o), withσ=1.86. The 1σ error range is (3o, 112o) on theright ascension and (−81o, 52o) on the declina-tion. The figure shows some differences betweenthe large-scale patterns of spin direction asymme-try identified in Pan-STARRS and the patternsidentified in SDSS as shown by Figure 5, althoughthe differences are well within 1σ error.

The experiments described above with SDSSdata showed that the probability of quadrupolealignment of the galaxy spin directions is muchhigher than the probability of a dipole alignment.Figure 11 shows the σ probability of quadrupoleaxis in each possible (α, δ) combination. The most

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Figure 3: The distribution of the Petrosian radiusand the r Kron magnitude of the Pan-STARRSgalaxies used in the experiment.

likely axes are at (198o, 9o) and (305o, 40o), withσ of 1.65. These locations are very close to thequadrupole axis identified with the SDSS galaxies.

To further compare the large-scale alignment ofgalaxy spin patterns in SDSS and Pan-STARRS,another dataset of SDSS galaxies was prepared suchthat the redshift distribution of the galaxies in bothdatasets was similar. That was done by select-ing SDSS galaxies with redshift such that the red-shift distribution of the galaxies follows the red-shift distribution of Pan-STARRS as shown in Fig-ure 4. SDSS DR14 had spectra for 63,693 galax-ies, and 38,998 of these galaxies were selected suchthat the redshift distribution of the galaxies wassimilar to the redshift distribution of the galaxiesin Pan-STARRS as shown in Figure 4. Table 3shows the number of galaxies and asymmetry be-tween clockwise and counterclockwise galaxies ineach RA range. As the table shows, the asymme-try in the different redshift ranges is more similar to

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Figure 4: The redshift distribution of the Pan-STARRS galaxies. Pan-STARRS is an optical skysurvey that does not provide spectroscopy for theobjects. Therefore, the redshift distribution wasdetermined by using 12,186 objects that have cor-responding spectroscopic objects in SDSS DR8.

Figure 5: The σ of possible dipole axes in all com-binations of (α, δ) coordinates using the spin direc-tions of SDSS galaxies.

the asymmetry shown in the same RA ranges in Ta-ble 2, with Pearson correlation between the asym-metries in the two sky surveys of ∼0.55 (P ' 0.05).The σ of quadrupole alignment in the spin direc-tions of these galaxies is shown in Figure 12.

Although the two datasets were collected inde-pendently by two different telescopes, both datasetsshow very similar patterns of quadrupole alignmentof the spin directions of the galaxies. The probabil-ity of the axis is ∼ 1.81σ and ∼ 1.66σ for the SDSSdata and Pan-STARRS data, respectively. Due tothe overlap in the footprint of the two telescopes itis expected that some galaxies would be includedin both datasets. The number of galaxies includedin both the SDSS and the Pan-STARRS datasetsis 4,426. Excluding those galaxies such that the

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Figure 6: The σ of the dipole axes in all combina-tion of (α, δ) coordinates when the SDSS galaxieswere assigned with random spin directions.

Figure 7: The probability of a quadrupole axis indifferent (α, δ) combinations.

two datasets are completely orthogonal has minorimpacts on the distribution of the galaxies, andthe graph practically does not change when thesegalaxies are excluded.

4 Conclusion

The distribution of galaxy spin directions in SDSSand Pan-STARRS shows patterns in the asymme-try between galaxies with opposite spin directions.Assuming that the asymmetry observed by the twotelescopes reflects the real sky rather than a flawin the telescope systems, the observation can beconsidered as evidence for large-scale anisotropy.The highest probability was achieved when fit-ting the distribution of galaxy spin directions toquadrupole, with probability greater than 6σ. As-signing the galaxies with random spin directionsprovides no statistically significant patterns.

The method used to annotate the galaxies is adeterministic model-driven algorithm that follows

Figure 8: The probability of a quadrupole axis indifferent (α, δ) combinations when the galaxies areassigned with random spin directions.

Figure 9: The probability of an octopole axis indifferent (α, δ) combinations.

defined rules. It is not based on complex data-driven non-intuitive rules determined during thetraining process of a deep neural networks, whichare very difficult to understand and can capturebackground noise or subtle biases in the trainingset. Using randomly assigned spin patterns leadsto no statistically significant patterns in the data.Using mirrored images of the galaxies expectedlyflips the numbers of clockwise and counterclock-wise galaxies, providing also experimental evidencethat the algorithm is symmetric. The observationthat the asymmetry changes with the direction ofobservation also shows that a bias in the algorithmis unlikely, since a bias in the annotation algorithmis expected to be consistent in all directions of ob-servation.

The analysis is based on data acquired by theSloan Digital Sky Survey and Pan-STARRS, andunder the assumption that these telescopes andtheir photometric pipelines are not biased in someunexplained manner that leads to differences be-tween galaxies based on their spin direction. It is

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Figure 10: The σ of the probability of a dipole axisin different (α, δ) combinations in Pan-STARRSdata.

Figure 11: The σ probability of quadruple align-ment to happen by chance in different (α, δ) com-binations in Pan-STARRS data.

difficult, however, to think of a bias that would leadto asymmetry between clockwise and counterclock-wise galaxies, as SDSS and Pan-STARRS are notexpected to be affected by the spin direction of thegalaxy.

The observations reported in this paper agreewith previous observations that show asymme-try between galaxies with opposite spin direc-tions [25, 36, 37, 15, 38, 39, 41, 40, 42, 43], orpatterns between spin directions of galaxies thatare too far to have gravitational interactions [24].Cosmological-scale anisotropy was also observed inradio sources [? ] and short gamma ray bursts[26], providing evidence of non-uniform distributionthat could violate the isotropy assumption of thecosmological principle, although long gamma raybursts show no statistically significant anisotropy[1]. Luminosity-temperature ratio of 313 galaxyclusters also showed violation of the isotropy as-sumption [27].

Cosmic Microwave Background (CMB) data also

RA cw−ccwcw+ccw # galaxies

0o-30o -0.049 259630o-60o -0.001 149760o-90o -0.115 6190o-120o 0.024 1152120o-150o 0.001 8550150o-180o -0.020 10482180o-210o -0.001 7676210o-240o 0.014 5892240o-270o -0.004 1018270o-300o - 0300o-330o -0.081 74330o-360o - 0

Table 3: The number of galaxies asymmetry be-tween clockwise and counterclockwise galaxies inSDSS, such that the galaxies have redshift distri-bution similar to the redshift distribution of thePan-STARRS galaxies.

Figure 12: The σ probability of a quadruple align-ment to happen by chance in different (α, δ) combi-nations in SDSS galaxies such that the redshift dis-tribution of these galaxies is similar to the redshiftdistribution of the galaxies in the Pan-STARRSdataset.

shows evidence of possible cosmological-scale polar-ization [2, 16, 8, 3, 10], and was fitted to quadrupolealignment [7, 13, 47]. These observations led totheories that shift from the standard cosmologi-cal models [11, 32, 33, 31, 20, 5]. Since the spinpatterns of a galaxy as visible from Earth is alsoan indication of the actual spin direction of thegalaxy [19], the large-scale patterns in the distri-bution of the spin directions can be an indicationof a rotating universe [12, 29, 30, 6]. Other expla-nations that do not violate the basic cosmologicalassumptions have also been proposed, such as pos-sible primordial subtle chiral violation exhibited inthe current epoch by the asymmetry of the distri-bution of galaxy spin directions [46], or to parity-breaking gravitational waves [4]. As future space-

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based telescopes such as Euclid and ground-basedtelescopes such as the Vera Rubin Telescope will al-low much more powerful data collection, the asym-metry of the distribution of the spin directions ofspiral galaxies can be studied in higher resolutionto provide more accurate profiling.

Acknowledgments

Funding for the Sloan Digital Sky Survey IV hasbeen provided by the Alfred P. Sloan Foundation,the U.S. Department of Energy Office of Science,and the Participating Institutions. SDSS-IV ac-knowledges support and resources from the Centerfor High-Performance Computing at the Universityof Utah. The SDSS web site is www.sdss.org.

SDSS-IV is managed by the Astrophysical Re-search Consortium for the Participating Institu-tions of the SDSS Collaboration including theBrazilian Participation Group, the Carnegie In-stitution for Science, Carnegie Mellon Univer-sity, the Chilean Participation Group, the FrenchParticipation Group, Harvard-Smithsonian Centerfor Astrophysics, Instituto de Astrofısica de Ca-narias, The Johns Hopkins University, Kavli Insti-tute for the Physics and Mathematics of the Uni-verse (IPMU) / University of Tokyo, the KoreanParticipation Group, Lawrence Berkeley NationalLaboratory, Leibniz Institut fur Astrophysik Pots-dam (AIP), Max-Planck-Institut fur Astronomie(MPIA Heidelberg), Max-Planck-Institut fur As-trophysik (MPA Garching), Max-Planck-Institutfur Extraterrestrische Physik (MPE), National As-tronomical Observatories of China, New MexicoState University, New York University, Universityof Notre Dame, Observatario Nacional / MCTI,The Ohio State University, Pennsylvania StateUniversity, Shanghai Astronomical Observatory,United Kingdom Participation Group, UniversidadNacional Autonoma de Mexico, University of Ari-zona, University of Colorado Boulder, Universityof Oxford, University of Portsmouth, University ofUtah, University of Virginia, University of Wash-ington, University of Wisconsin, Vanderbilt Uni-versity, and Yale University.

The Pan-STARRS1 Surveys (PS1) and the PS1public science archive have been made possiblethrough contributions by the Institute for Astron-omy, the University of Hawaii, the Pan-STARRS

Project Office, the Max-Planck Society and its par-ticipating institutes, the Max Planck Institute forAstronomy, Heidelberg and the Max Planck In-stitute for Extraterrestrial Physics, Garching, TheJohns Hopkins University, Durham University, theUniversity of Edinburgh, the Queen’s UniversityBelfast, the Harvard-Smithsonian Center for Astro-physics, the Las Cumbres Observatory Global Tele-scope Network Incorporated, the National CentralUniversity of Taiwan, the Space Telescope ScienceInstitute, the National Aeronautics and Space Ad-ministration under Grant No. NNX08AR22G is-sued through the Planetary Science Division of theNASA Science Mission Directorate, the NationalScience Foundation Grant No. AST-1238877, theUniversity of Maryland, Eotvos Lorand University(ELTE), the Los Alamos National Laboratory, andthe Gordon and Betty Moore Foundation.

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