Analysis of the alignment of non-random patterns of spin directions in populations of spiral galaxies
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Analysis of the alignment of non-random patterns of spin directions in populations ofspiral galaxies
Lior Shamir Kansas State UniversityManhattan, KS 66506 (Dated:)
ABSTRACTObservations of non-random distribution of galaxies with opposite spin directionshave recently attracted considerable attention. Here, a method for identifying cosine-dependence in a dataset of galaxies annotated by their spin directions is describedin the light of different aspects that can impact the statistical analysis of the data.These aspects include the presence of duplicate objects in a dataset, errors in thegalaxy annotation process, and non-random distribution of the asymmetry that does notnecessarily form a dipole or quadrupole axes. The results show that duplicate objectsin the dataset can artificially increase the likelihood of cosine dependence detected inthe data, but a very high number of duplicate objects is required to lead to a falsedetection of an axis. Inaccuracy in galaxy annotations has relatively minor impact onthe identification of cosine dependence when the error is randomly distributed betweenclockwise and counterclockwise galaxies. However, when the error is not random, evena small bias of 1% leads to a statistically significant cosine dependence that peaks atthe celestial pole. Experiments with artificial datasets in which the distribution wasnot random showed strong cosine dependence even when the data did not form a fulldipole axis alignment. The analysis when using the unmodified data shows asymmetryprofile similar to the profile shown in multiple previous studies using several differenttelescopes.
Keywords:
Cosmology; galaxies; large-scale structure INTRODUCTION [email protected]
The contention that the spin directions of spi-ral galaxies are distributed in a non-randommanner (Longo 2011; Shamir 2012, 2013, 2016,2019, 2020; Lee et al. a r X i v : . [ a s t r o - ph . C O ] J a n Lior Shamir ered a certain mystery in astronomy in the pastdecade. While early experiments with man-ually annotated galaxies were limited by thesize of the data that can be processed (Land et al. et al. et al. et al. et al. et al. et al. et al. et al. on-random spin patterns ∼ . · SDSS galaxies. ANALYSIS METHODAssuming that the distribution of spin direc-tions of spiral galaxies exhibits a cosmological-scale dipole axis, it is expected that the spin di-rection distribution would have a non-randomcosine dependence. In other words, statisticallysignificant fitness of the spin directions of thespiral galaxies into cosine dependence can bean indication of dipole alignment of the spin di-rections.The cosine dependence between the angle andthe spin directions of the galaxies can be com-puted from each ( α, δ ) coordinates in the sky.For each possible integer ( α, δ ) combination, theangular distance between ( α, δ ) to all galaxiesin the dataset is computed. Then, χ statisticscan be used to fit the spin direction distributionto cosine dependence. That is done by fitting d · | cos( φ ) | to cos( φ ), where φ is the angulardistance between the galaxy and ( α, δ ), and d is a number within the set {− , } , such that d is 1 if the galaxy spins clockwise, and -1 if thegalaxy spins counterclockwise.The χ computed when the d of each galaxy isassigned the actual spin directions of the galax-ies is compared to the average of the χ whencomputed in 10 runs such that the d of eachgalaxy is assigned with a random number within { -1,1 } . After repeating 10 runs, each with adifferent set of random values, the mean andstandard deviation of the χ of all runs can bedetermined. Then, the σ difference between the χ computed with the actual spin directions andthe mean χ computed with the random spin di-rections provide the probability to have a dipoleaxis in that ( α, δ ) combination. Computing theprobability for each possible integer ( α, δ ) in thesky can provide an all-sky analysis of the prob-ability of a dipole axis. The same method canalso be used to fit the distribution to quadrupolealignment, by fitting the distribution of the spindirections to cos(2 φ ). DATAThe dataset used in this study is based on thedataset of photometric objects imaged by SloanDigital Sky Survey, from which duplicate pho-tometric objects were removed. The purpose ofthat dataset was to examine evidence of photo-metric differences between galaxies with oppo-site spin directions observed in a much smallerdataset (Shamir 2016). The dataset contains740,908 relatively bright (g <
19) and large (Pet-rosian radius > Lior Shamir tion methods, Ganalyzer’s main advantage isthat it is not based on machine learning or deeplearning algorithms that rely on complex non-intuitive data-driven rules. As will be discussedlater in this paper, certain noise in the datadoes not have a major impact on the detection.However, even a small but consistent bias in theannotation of the galaxies can lead to a statis-tically significant non-random alignment of thegalaxies. Since such subtle biases are often diffi-cult to identify, the analysis method needs to bea symmetric method. More information aboutGanalyzer is available in (Shamir 2011a), andthe process of the galaxy annotation is describedin (Shamir 2017a,b).Since not all galaxies have identifiable spin di-rections, Ganalyzer does not assign a spin direc-tion to all galaxies, and annotates some galax-ies as “undetermined”. From the dataset of740,908, 172,883 objects were assigned a spindirection. For the removal of photometric ob-jects that are part of the same galaxies, pho-tometric objects that were closer than 0.01 o toanother object in the dataset were removed. Re-moving all duplicate objects provided a datasetof 77,840 galaxies, available at http://people.cs.ksu.edu/ ∼ lshamir/data/assymdup. The distri-bution of the exponential r magnitude is shownin Figure 1, and Figure 2 shows the distributionof the redshift of the galaxies that have spectrain SDSS.Of the 77,840 galaxies in the dataset, 39,187galaxies spin clockwise, and 38,653 had a coun-terclockwise spin, showing a ∼ ∼ <12 12-13 13-14 14-15 15-16 16-17 17-18 >18 g a l a x i e s r (magnitude) Figure 1.
The distribution of the exponential rmagnitude of the galaxies in the dataset. - .
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16 0 . - . > . g a l a x i e s z Figure 2.
The distribution of the redshift of thegalaxies in the dataset that have spectra. clockwise and counterclockwise galaxies changesbased on the direction of observation.Figure 3 shows the asymmetry A between thenumber of clockwise galaxies and the numberof counterclockwise galaxies in different RAranges. The asymmetry A is defined by A = N cw − N ccw N cw + N ccw . Each bar shows the asymmetry be-tween the number of clockwise galaxies andcounterclockwise galaxies in a certain RA range.The declination is not used in this visualiza-tion, but the galaxies are separated by theirRA only. The galaxies are not separated bytheir declination ranges, and therefore each RAslice is averaged by the declination. The fig-ure shows differences in the number of clock- on-random spin patterns α = 160 o ). In that hemisphere there are 24,648galaxies with clockwise spin and just 23,958galaxies with counterclockwise spin. The one-tailed probability of having such a difference orgreater by chance is 0.00086, and the two-tailedprobability is 0.0017. The opposite hemispherehas a higher number of galaxies with counter-clockwise spin direction. Although that asym-metry is not significant, it also does not conflictwith the asymmetry in the other hemisphere forthe assumption that these two hemisphere ex-hibits a dipole. The weaker signal in one hemi-sphere can be because most of the SDSS galax-ies are in the hemisphere toward right ascen-sion 180 o . The uneven distribution of the SDSSgalaxies in the sky can also lead to a bias ofthe real asymmetry compared to the asymme-try shown using SDSS data. -0.015-0.01-0.005 RA (degrees) A Figure 3.
The asymmetry A between the num-ber of galaxies that spin clockwise and the numberof galaxies that spin counterclockwise in different60 o RA ranges. The asymmetry A is defined by A = N cw − N ccw N cw + N ccw . Each bar shows the asymmetry be-tween clockwise and counterclockwise galaxies in adifferent RA range. The error bars are the normaldistribution standard error of √ N , where N is thetotal number of galaxies in the RA range. Applying the analysis to the data described inSection 2 provided a dipole axis with maximumstatistical strength of 2.56 σ . The most likelylocation of the dipole axis was identified as de-scribed in Section 2 at ( α = 165 o , δ = 40 o ).The 1 σ error range is (90 o , o ) for the rightascension, and ( − o , o ) for the declination.Interestingly, the most likely dipole axis is notparticularly far from the location of the mostlikely dipole reported in (Shamir 2012) at ( α =132 o , δ = 32 o ), and well within the 1 σ errorrange.The dataset used in (Shamir 2012) also con-tained galaxies with similar radius and mag-nitude limits as the dataset used here. Fig-ure 4 shows the likelihood of the dipole axisfrom each possible integer ( α, δ ) combination inincrements of five degrees. Figure 5 shows thesame analysis, when the Mollweide projection iscentered around ( α = 165 o , δ = 40 o ). Figure 4.
The χ probability of a dipole axis inspin directions of the galaxies from different ( α, δ )combinations. Figure 6 shows the probability of a quadrupoleaxis from all possible integer ( α, δ ) combina-tions. The most likely axis is identified at( α = 355 o , δ = 45 o ), with 1 σ error range of(305 o , o ) for the RA, and (15 o , o ) for thedeclination.When the galaxies are assigned with randomspin directions, the asymmetry becomes statis-tically insignificant. Figure 7 shows the differ- Lior Shamir
Figure 5.
The χ probability of a dipole axis inspin directions of the galaxies from different ( α, δ )combinations, centered at ( α = 165 o , δ = 40 o ). Figure 6.
The probability of a quatdrupole axisfrom different ( α, δ ). ences in different RA ranges when using thesame dataset, but when the spin directions ofthe galaxies are random. Figure 8 shows thelikelihood of the dipole axis when the galaxiesare assigned with random spin directions. Theprobability of the most likely axis dropped to0.78 σ .The dataset can be separated to galaxies withg magnitude of less than 18, and g magnitudegreater than 18. That separation provides twoorthogonal datasets of galaxies. The number ofgalaxies with exponential g magnitude of lessthan 18 is 46,052, while 31,798 galaxies had ex-ponential g magnitude greater than 18. Fig-ures 9 and 10 show the analysis for galaxies withg magnitude lower than 18, and g magnitudegreater than 18, respectively. -0.02 -0.015-0.01-0.0050 A RA (degrees)
Figure 7.
The asymmetry between the numberof galaxies that spin clockwise and the number ofgalaxies that spin counterclockwise in different RAranges when the galaxies are assigned with randomspin directions.
Figure 8.
The χ probability of the dipole axiswhen the galaxies are assigned with random spindirections. Figure 9.
The χ probability of the dipole axiswhen the dataset in limited to galaxies with expo-nential g magnitude of less than 18. As the figures show, although the two datasetsare completely orthogonal, they provide fairlysimilar profiles. The most likely axis whenthe galaxies are limited to g <
18 is at ( α = on-random spin patterns Figure 10.
The χ probability of the dipole axiswhen the dataset in limited to galaxies with expo-nential g magnitude greater than 18. o , δ = − o ), with probability of 2.43 σ .When the galaxies are limited to g >
18, themost likely axis is at ( α = 150 o , δ = 25 o ), withprobability of 5.57 σ . That shows that while thetwo orthogonal subsets show fairly similar loca-tions of the most likely dipole axis, the statis-tical signal is stronger when the galaxies havehigher g magnitude. Since the magnitude iscorrelated with the redshift, that agrees withthe previous observation that the asymmetrygrows when the redshift gets higher (Shamir2019, 2020). IMPACT OF DUPLICATE OBJECTS INTHE DATASETThe dataset described in Section 3, as wellas the datasets used in (Shamir 2012, 2019,2020), did not contain duplicate objects. How-ever, when working with photometric measure-ments of extended objects, a single galaxy canhave more than one photometric object in thedataset. To test the impact of duplicate objectsseveral experiments were made by artificiallyadding duplicate objects to the dataset. In thefirst experiment, each galaxy in the dataset wasduplicated. Naturally, the right ascension, dec-lination, and spin direction of the duplicatedgalaxy matched the spin direction of the orig-inal galaxy. Figure 11 shows the asymmetry between the number of clockwise and counter-clockwise galaxies in different RA ranges. -0.015 -0.01-0.0050 A RA (degrees)
Figure 11.
The asymmetry between the number ofclockwise and counterclockwise galaxies in differentRA ranges such that each galaxy in the dataset isduplicated.
As expected, the asymmetry in Figure 11 isidentical to the asymmetry in Figure 3. How-ever, the difference is in the error bars, as thestandard error is smaller in the dataset thatcontains duplicate objects. With one dupli-cate object for each galaxy, the probability tohave more clockwise galaxies in the hemispherearound ( α = 160 o ) is < − . That showsthat adding duplicate objects does not changethe distribution of the galaxies or the profile ofthe asymmetry, but it increases the statisticalsignificance by increasing the number of galax-ies. Figure 12 shows the statistical strength ofa dipole axis in different ( α, δ ). The most likelyaxis is identified at the same location as in Fig-ure 4, but the statistical signal of the dipole axisincreased to 3.62 σ .The graph shows that artificial duplicate ob-jects can strengthen the statistical signal whenthe spin directions of the galaxies in the originaldataset form a statistically significant dipole, asshown in Section 3. To test the impact of dupli-cate objects in a dataset that does not have sig-nal of parity violation between galaxies with op-posite spin directions, an experiment was done Lior Shamir
Figure 12.
The χ probability of a dipole axis inspin directions when each galaxy in the dataset isduplicated. with a dataset of galaxies assigned with randomspin directions, but each galaxy was duplicated,providing a dataset twice as large as the originaldataset.Figure 13 shows the statistical significanceof a dipole axis at different ( α, δ ) combina-tions. The maximum dipole axis has statisticalstrength of 1.93 σ . That shows that duplicatesin the dataset can lead to statistically signifi-cant asymmetry in a dataset, even if the origi-nal dataset has no asymmetry between the num-ber of clockwise and counterclockwise galaxies.However, the number of duplicates needs to bevery large, and the dataset needs to be far largerthan the original dataset to have an asymmetrythat becomes statistically significant. Figure 13.
The χ probability of a dipole axis inspin directions when the spin directions are randomand each galaxy in the dataset is duplicated fivetimes. 5. ERROR IN THE GALAXYANNOTATIONSpiral galaxies have complex morphology, andthe identification of the spin direction of agalaxy is therefore not a straightforward task.It has been shown that manual identification isheavily biased by the human perception, andtherefore datasets annotated manually can besystematically biased (Land et al. et al. A in a certain part of the sky can be definedby A = ( N cw + E cw ) − ( N ccw + E ccw ) N cw + E cw + N ccw + E ccw , where E cw is thenumber of counterclockwise galaxies classifiedincorrectly as clockwise, and E ccw is the num-ber of clockwise galaxies classified incorrectlyas counterclockwise. If the galaxy classificationalgorithm is symmetric, the number of counter-clockwise galaxies misclassified as clockwise isexpected to be roughly the same as the numberof clockwise galaxies missclassified as counter-clockwise. Assuming E cw = E ccw , the asymme-try can be defined as A = N cw − N ccw N cw + E cw + N ccw + E ccw .Since E cw and E ccw cannot be negative, a higherrate of misclassified galaxies is expected to makethe asymmetry A lower. Therefore, misclassi- on-random spin patterns ∼ σ . As expected, when 50% of the galax-ies are assigned with random spin directions thestatistical significance of the dipole axis drops to1.44 σ .That shows that inaccuracy in the annotation ofthe galaxies results in weaker statistical signal.However, the experiment was performed suchthat the incorrect annotations were distributedrandomly between clockwise and counterclock-wise galaxies. To test the impact of system-atic bias in the annotations, randomly selected2% of the galaxies were assigned with clockwisespin direction regardless of their actual spin di-rection. That means that ∼
1% of the counter-clockwise galaxies were assigned with clockwisespin direction. Figure 14 shows the statisticalsignal of a dipole axis at different ( α, δ ) coordi-nates. The most likely dipole axis was identifiedat δ = 90 o , with 4.42 σ .Figure 15 shows the same graph created fromthe same dataset such that 2% of the counter-clockwise galaxies were assigned with clockwisespin directions. The statistical significance ofthe dipole axis in that case elevates to 9.21 σ ,and the strongest axis was detected at ( δ =90 o ). These graphs show that while random incorrect annotations have relatively small im-pact and lead to weaker signal, even a small rateof consistently incorrect annotations leads tostrong statistical signal of a dipole axis. Fittingthe spin directions to a quadrupole alignmentprovides statistical signal of 7.12 σ as shown inFigure 16, but does not identify two strong axes. Figure 14.
The χ probability of a dipole axis inthe galaxy spin directions when 1% of the counter-clockwise galaxies are assigned with clockwise spindirection. Figure 15.
The χ probability of a dipole axisin spin directions when 2% of the counterclockwisegalaxies are assigned with clockwise spin direction.6. NON-RANDOM DISTRIBUTION OFTHE ASYMMETRYThe method for profiling cosine dependence inspin direction of galaxies discussed in Section 2can identify the location and statistical strengthof a dipole axis if such exists. However, non-random distribution of the spin directions ofspiral galaxies that does not necessarily forma dipole axis can also exhibit itself as a sta-tistically significant dipole axis. To test the0
Lior Shamir
Figure 16.
The χ probability of a quadrupoleaxis in spin directions when 2% of the counterclock-wise galaxies are assigned with clockwise spin direc-tion. identification of a dipole, all galaxies in thedataset were assigned random spin directions.The only exception was galaxies in the sky re-gion of (120 o < α < o , o < δ < o ), inwhich all 2,558 in that sky region galaxies wereassigned with clockwise spin direction. Fig-ures 17 and 18 show the probability of dipoleand quadrupole axes in that dataset, respec-tively. As the figures show, the non-random dis-tribution of these 2,558 galaxies among the restof the galaxies that were assigned random spindirections show strong statistical signal. Themost likely dipole axis was identified with sta-tistical strength of 15 . σ , while quadrupolefitness showed a slightly weaker statistical sig-nificance of 14 . σ . The strong signal is ex-pected due to the very low probability of a largenumber of galaxies to have the same spin di-rection. But despite the fact that the rest ofthe sky showed no dipole axis, the small regionof non-random spin directions was sufficient tolead to dipole and quadrupole axes with highstatistical significance.Figures 19 and 20 show a similar experiment,such that in addition to the galaxies in (120 o <α < o , o < δ < o ), the 2,336 galaxies inthe sky region (180 o < α < o , o < δ < o )were also assigned with clockwise spin direc-tions. That leads to a distribution of the galaxyspin directions that is not random, but also Figure 17.
The χ probability of a dipole axissuch that the galaxies are assigned with randomspin directions, except for a certain sky region. Figure 18.
The χ probability of a quadrupoleaxis such that the galaxies are assigned with ran-dom spin directions, except for a certain sky region. does not form a perfect dipole alignment. Fig-ures 19 and 20 show the statistical significanceof a dipole and quadrupole alignment in thatdataset. The dipole axis had a statistical signalof 21.51 σ , and the quadrupole axis had 22.14 σ .That shows that non-random distribution of thegalaxy spin directions can exhibit itself in theform of a dipole or quadrupole axes, also in casethat the distribution of the spin directions ofmost galaxies in the dataset do not fit cosinedependence. CONCLUSIONSIf the spin directions of spiral galaxies arealigned in the form of a dipole axis, the spindirections are expected to exhibit cosine depen-dence with the direction of observation com-pared to the location of the most likely axis.Here, a method that can identify the location on-random spin patterns Figure 19.
The χ probability of a dipole axissuch that the galaxies are assigned with randomspin directions, except for two sky regions that donot necessarily form a dipole. Figure 20.
The χ probability of a quadrupoleaxis such that the galaxies are assigned with ran-dom spin directions, except for two different skyregions. of the most likely dipole axis by analyzing thespin directions of spiral galaxies is discussed.The method is tested in the light of potentialanomalies in the data that can lead to a falsedetection of such dipole, or change its statisticalsignal.The experiments show that duplicate objects inthe dataset can increase the statistical signalof the detection of a dipole alignment of thedistribution of spin directions of spiral galaxies.However, if the galaxy spin directions are dis-tributed randomly, the duplicate objects needto make the dataset far larger than the origi-nal dataset. In the case of the dataset of SDSSgalaxies tested here, each galaxy needed to havefive duplicate objects to reach statistical signifi-cance when the galaxies were assigned with ran- dom spin directions. However, since duplicateobject can artificially change the statistical sig-nal, the analysis of cosine dependence or anyother non-random distribution of spin directionsof galaxies should be done in a dataset in whichduplicate objects are removed.Inaccuracy of the galaxy annotations does nothave a substantial impact on the analysis ofa dipole axis. Even if 25% of the galaxiesare annotated randomly the statistical signal ofthe asymmetric distribution can still be iden-tified. In any case, inaccurate annotations ofthe galaxy spin directions reduces the statisti-cal signal of a possible dipole axis rather thanincreasing it.The relatively weak impact of inaccuracy of theannotation of the spin directions is true onlywhen the inaccurate annotations are distributedrandomly between clockwise and counterclock-wise galaxies. When the inaccurate annotationsof the galaxies are not random, but have a sys-tematic bias toward a certain spin direction,even a relatively small bias can lead to a sta-tistically significant dipole axis detected in thedataset. For instance, even a small consistentbias of 1% of the annotations leads to a statisti-cally significant dipole axis. That artificial axispeaks at the celestial pole, which is expectedsince SDSS contains galaxies mostly from theNorthern hemisphere. In general, dipole axesthat peak at the celestial pole should be exam-ined with caution, as many catalogs are createdby using ground-based instruments that cannotcover more than one hemisphere. When com-bining data from different hemispheres into asingle catalog, a dipole of asymmetry that isaligned with the celestial pole might indicateon differences between the instrument that col-lected the data from the Northern hemisphereand the instrument that collected the data fromthe Southern hemisphere. Such difference is ex-2 Lior Shamir pected to exhibit itself in the form of a dipoleaxis that peaks at the celestial pole, but doesnot necessarily indicate on an astronomical orcosmological phenomenon.The analysis used here is also sensitive to non-random distribution of galaxy spin directionseven if the spin directions are not aligned inthe form of a dipole axis. For instance, a singlespot in the sky with very strong asymmetry ingalaxy spin directions can lead to the identifi-cation of a dipole axis in that spot with verystrong statistical signal, even if the spin direc-tions of all other galaxies in the dataset are dis-tributed randomly. While a cosmological dipoleaxis of asymmetry in galaxy spin directions isexpected to exhibit itself in the form of cosinedependence, other anomalies in the distributionof spin directions of spiral galaxies can also beidentified in the form of a statistically signifi-cant cosine dependence. Therefore, full identi-fication of a possible dipole or quadrupole axeswill require the analysis of a very high numberof galaxies covering a large part of the sky tofully profile the nature of a possible asymmetryin the spin directions of spiral galaxies.The dataset that was used in this study isa dataset of SDSS galaxies designed for ex-periments related to photometry of galaxies(Shamir 2017a). Here the dataset is tested forthe identification of non-random distribution ofgalaxy spin directions, and for that purposephotometric objects that are part of the samegalaxies were removed. The statistical signalafter removing the duplicate objects is 2.56 σ for a dipole axis, and 3.0 σ for a quadrupoleaxis. The statistical signal does not meet the5 σ discovery threshold, but it is still consider-able, and comparable to the statistical signal ofother provocative observations of primary scien-tific interest such as the CMB cold spot (Cruz et al. α = 165 o , δ = 40 o ), with 1 σ error range of(90 o , o ) for the RA and ( − o , o ) for thedeclination. The most likely dipole axis re-ported with a dataset of spectorscopic objectsreported in (Shamir 2012) is ( α = 132 o , δ =32 o ), close to the dipole axis shown here, andwithin 1 σ error. The axis reported by Longo(Longo 2011) at ( α = 217 o , δ = 32 o ), whichsomewhat more distant, but also within the1 σ error from the dipole axis reported here.The dipole axis shown with Galaxy Zoo dataat (161 o , o ) is also within close distance tothe dipole axis shown here, although it shouldbe noted that the asymmetry between clock-wise and counterclockwise galaxies in GalaxyZoo data was determined to be driven by per-ceptional bias of the volunteers who annotatedthe data, and not statistically significant whenthe perceptual bias was corrected (Land et al. et al. et al. et al. et al. et al. on-random spin patterns et al. et al. et al. et al. et al. et al. et al. et al. et al. Lior Shamir
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