New Astronomy 28 (2014) 1–8

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New Astronomy

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Quantitative analysis of spirality in elliptical galaxies

1384-1076/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.newast.2013.09.006

⇑ Corresponding author.E-mail address: lshamir@mtu.edu (L. Shamir).

Levente Dojcsak a, Lior Shamir b,⇑a Department of Physics, George Washington University, St. Louis, MO, USAb Department of Math and Computer Science, Lawrence Technological University, 21000 W Ten Mile Rd., Southfield, MI 48075, USA

h i g h l i g h t s

� Computer image analysis was applied to galaxies classified as elliptical by human observers.� The analysis shows that many galaxies classified manually as elliptical have a certain slope in their arms.� The radial intensity plot of the galaxy provides a more detailed view for detecting and measuring galaxy spirality.

a r t i c l e i n f o

Article history:Received 14 November 2012Received in revised form 15 August 2013Accepted 25 September 2013Available online 4 October 2013

Communicated by J. Makino

Keywords:Galaxies: elliptical and lenticularTechniques: image processing

a b s t r a c t

We use an automated galaxy morphology analysis method to quantitatively measure the spirality ofgalaxies classified manually as elliptical. The data set used for the analysis consists of 60,518 galaxyimages with redshift obtained by the Sloan Digital Sky Survey (SDSS) and classified manually by GalaxyZoo, as well as the RC3 and NA10 catalogues. We measure the spirality of the galaxies by using theGanalyzer method, which transforms the galaxy image to its radial intensity plot to detect galaxyspirality that is in many cases difficult to notice by manual observation of the raw galaxy image.Experimental results using manually classified elliptical and S0 galaxies with redshift <0.3 suggest thatgalaxies classified manually as elliptical and S0 exhibit a nonzero signal for the spirality. These resultssuggest that the human eye observing the raw galaxy image might not always be the most effectiveway of detecting spirality and curves in the arms of galaxies.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Galaxy morphology is studied for the purpose of classificationand analysis of the physical structures exhibited by galaxies inwide redshift ranges in order to get a better understanding of thestructure and development of galaxies. While significant researchhas been done to study the morphology of galaxies with spiralarms (Loveday, 1996; Ball et al., 2008; Nair, 2009; Nair andAbraham, 2010), research efforts have been focused also on theanalysis of elliptical and S0 galaxies using photometric measure-ment of the electromagnetic radiation, ellipticity, position angle,shape, and colour (Djorgovski and Davis, 1987; Dressler et al.,1987; Scorza and Bender, 1990; van den Bergh, 2009; Kormendyet al., 2009; Kormendy and Bender, 2012). These analyses weresuccessful in acquiring information regarding the structure anddevelopment of some of these galaxies. However, these studieshave done little analysis of the spirality of galaxies that wereclassified as elliptical.

Studying the morphology of large datasets of galaxies have at-tracted significant attention in the past decade (Conselice, 2003;

Abraham et al., 2003; Ball et al., 2008; Shamir, 2009; Banerjiet al., 2010; Huertas-Company et al., 2011), and was driven bythe increasing availability of automatically acquired datasets suchas the data releases of the Sloan Digital Sky Survey (York et al.,2000). However, attempts to automatically classify faint galaxyimages along the Hubble sequence have been limited by the accu-racy and capability of computer learning classification systems,and did not provide results that met the needs of practical research(Thorsten, 2008; Lintott et al., 2008). This contention led to the Gal-axy Zoo (Lintott et al., 2008) project, which successfully used aweb-based system to allow amateur astronomers to manually clas-sify galaxies acquired by SDSS (Lintott et al., 2011), and was fol-lowed by other citizen science ventures based on the sameplatform such as Galaxy Zoo 2 (Masters et al., 2011), Moon Zoo(Joy et al., 2011), and Galaxy Zoo Mergers (Wallin et al., 2010).

While it has been shown that amateurs can classify galaxies totheir basic morphological types with accuracy comparable to pro-fessional astronomers (Lintott et al., 2008), manual classificationmay still be limited to what the human eye can sense and the hu-man brain can perceive. For instance, the human eye can senseonly 15 to 25 different levels of gray, while machines can identify256 gray levels in a simple image with eight bits of dynamic range.The inability of the human eye to differentiate between gray levels

2 L. Dojcsak, L. Shamir / New Astronomy 28 (2014) 1–8

can make it difficult to sense spirality in cases where the arms arejust slightly brighter than their background, but not bright enoughto allow detection by casual inspection of the galaxy image. In fact,this limitation might affect professional astronomers as much as itaffects citizen scientists.

Since the human eye can only sense the crude morphology ofgalaxies along the Hubble sequence, and since the classificationof galaxies is normally done manually, morphological classificationschemes of galaxies are based on few basic morphological types.However, as these schemes are merely an abstraction of galaxymorphology, some galaxies can be difficult to associate with onespecific shape, and many in-between cases can exist.

Here we use the Ganalyzer method to transform the galaxyimages into their radial intensity plots (Shamir, 2011a), and ana-lyze the spirality of galaxies classified manually as elliptical andS0 by the Galaxy Zoo, RC3, and NA10 catalogues.

2. Image analysis method

The method that was used to measure the spirality of the galax-ies in the dataset is the Ganalyzer method (Shamir, 2011a,b). Un-like other methods that aim at classifying a galaxy into one ofseveral classes of broad morphological types (Abraham et al.,2003; Conselice, 2003; Ball et al., 2008; Shamir, 2009; Banerjiet al., 2010; Huertas-Company et al., 2011), Ganalyzer measuresthe slopes of the arms to determine the spirality of a galaxy. Gan-alyzer is a model-driven method that analyzes galaxy images byfirst separating the object pixels from the background pixels usingthe Otsu graylevel threshold (Otsu, 1979). The centre coordinatesof the object are determined by the largest median value of the5 � 5 shifted window with a distance less than 0:1=

ffiffiffiSp

qfrom the

mass centre, where S is the surface area (Shamir, 2011a, 2012).This method allows the program to determine the maximum radialdistance from the centre to the outermost point, as well as the ma-jor and minor axes by finding the longest distance between twopoints which pass through the centre for the major axis, and thenassigning the perpendicular line as the minor axis (Shamir, 2011a).The ellipticity is defined as the ratio of the lengths of the minor axisto the major axis (Shamir, 2011a). Comparison of the ellipticity of1000 galaxies to the ellipticity computed by SDSS (using isoA andisoB) shows a high Pearson correlation of �0.93 between the twomeasurements.

After the centre coordinates of the galaxy Ox; Oy and the radiusr are determined, the galaxy is transformed into its radial intensityplot such that the intensity value of the pixel ðx; yÞ in the radialintensity plot is the intensity of the pixel at coordinatesðOx þ r sin h;Oy � r cos hÞ in the original galaxy image, such that h

Fig. 1. Galaxy images and their transformation to radial intensity plots such

is a polar angel of [0,360], and r is the radial distance that rangesfrom 0.4 to 0.75 of the galaxy radius, producing an image of dimen-sionality of 360 � 35 (Shamir, 2011a, 2012). Fig. 1 shows an exam-ple of two galaxies and their transformation such that the Y axis isthe pixel intensity and the X axis is the polar angle.

As the figure shows, in the case of the elliptical galaxy the peaksare aligned on the same vertical line, while in the case of the spiralgalaxy the peaks shift. The spirality is then measured by the slopeof the groups peaks as described in Shamir (2011a), such that thepeak in radial distance r is grouped with the peak in radial distancer + 1 if the difference between their polar angles is less than 5�. Thistransformation makes it easier for machines to detect and measurethe spirality, but can also detect spirality in galaxies that mightlook to the human observer as elliptical since the human eye canonly recognise 15–25 gray levels, making it difficult to notice sub-tle spirality when looking at a raw galaxy image. For instance,Tables 1 and 2 show several SDSS galaxy images classified manu-ally by Galaxy Zoo participants as elliptical, with their radial inten-sity plot transformation and their spirality as measured byGanalyzer. To test how the method analyzes tidally disrupted ellip-tical galaxies (van Dokkum, 2005), we used several tidally dis-rupted galaxies from the NA10 catalogue, displayed in Table 3.

If the radial intensity plot does not feature peaks the galaxy isdefined as pure elliptical. Elliptical and lenticular galaxies in somecases can also have peaks in their radial intensity plot due to theposition angle, but in these cases all peaks will be aligned on thesame vertical line so that the slope will be very close to zero, andtherefore the galaxy will be identified as elliptical. An exceptioncan be in cases of S0 galaxies in which the position angle of the diskis different from the position angle of the galaxy, but the differenceis not greater than 5�. In that case Ganalyzer might consider thedisk and the galaxy as the same arm, but the difference in the posi-tion angles will lead to a certain slope in that arm. Therefore, thearms of the galaxy will have a certain slope when measured usingGanalyzer.

The radial intensity plot can allow the detection of subtle curvesin the arms that might not be easily detected by manual observa-tion of the raw galaxy image, but becomes noticeable in its radialintensity plot. Therefore, it is possible that many galaxies that wereclassified manually as elliptical might in fact feature a certain spi-rality (Shamir, 2011a). As the table shows, while the galaxies seemelliptical to the unaided human eye, the radial intensity plot trans-formations of the galaxies show that the peaks of maximal inten-sity shift, meaning that these galaxies feature certain curves inthe arms.

By defining spirality and ellipticity thresholds Ganalyzer canalso be used for classifying galaxies into their broad morphologicaltypes of elliptical, spiral and edge-on, and a thorough discussion

that the Y axis is the pixel intensity and the X axis is the polar angle.

Table 1Sample SDSS galaxy images with the Otsu binary transform, radial intensity plot transforms and the measured spirality.

Galaxy image Otsu transform Radial Intensity Plot Spirality0

0

0

0.06

0.14

0.21

L. Dojcsak, L. Shamir / New Astronomy 28 (2014) 1–8 3

and experimental results about galaxy classification with Ganalyz-er are described in Shamir (2011a). In previous experiments withGanalyzer (Shamir, 2011a,b, 2012) thresholds were applied to theslopes in the radial intensity plots so that the decision whether agalaxy is spiral or not is in agreement with the perception of a per-son observing the raw galaxy image. However, as described above,

in this study Ganalyzer is not used as a classifier, but as a tool tomeasure and detect the existence of galaxy spirality. Since theradial intensity plot provides a more sensitive view of galaxy spi-rality than the non-transformed raw image, no thresholds are usedin this study in order to utilise the ability of the radial intensityplots to detect subtle slopes in the galaxy arms and to test whether

Table 2Sample SDSS galaxy images with the Otsu binary transform, radial intensity plot transforms, and the measured spirality.

Galaxy image Otsu transform Radial Intensity Plot Spirality0.44

0.53

0.60

0.77

1.54

4 L. Dojcsak, L. Shamir / New Astronomy 28 (2014) 1–8

galaxies that seem elliptical to the human eye are indeed ellip-ticals, or have a subtle spirality that is difficult to measure usingthe unaided eye. That is, the purpose of the method described inthis section is not to mimic the human eye, but test whether thehuman eye observing the raw galaxy image is indeed the mostaccurate tool to determine whether a galaxy is spiral or elliptical.

3. Data

The data used in the experiment are galaxies acquired by SloanDigital Sky Survey, and were classified manually by theparticipants of the Galaxy Zoo project (Lintott et al., 2008, 2011).All galaxies in the dataset have redshift, and the classification re-

sults were based on the corrected super clean dataset describedin Lintott et al. (2011). For the study, only galaxies that wereclassified by Galaxy Zoo participants as ellipticals were used, andthe dataset consisted of 60,518 galaxies. The images were down-loaded automatically by using the CAS server. The galaxies werealso divided into six bins based on their redshift, ranges from 0to 0.3, such that each bin had a redshift range of 0.05. The numberof galaxies in each redshift is specified in Table 4.

The efficiency of Ganalyzer can be affected by two or moregalaxies that appear very close to each other in the image, eitherdue to merging or superpositioning. Since one galaxy can besegmented with part or all of the other galaxy, Ganalyzer mightdetect the other galaxy as an arm. In most cases such ‘‘arm’’ isnot expected to be mistakenly identified as sharp spirality because

Table 3Sample of tidally disrupted galaxy images taken from NA10 catalogue.

Galaxy image Otsu transform Radial Intensity Plot Spirality0.12

1.05

0

0

0

1.14

Table 4Percent of galaxies with spirality greater than zero,based on redshift.

Redshift # Of galaxies

0.00 to 0.05 77670.05 to 0.10 12,2480.10 to 0.15 12,1070.15 to 0.20 14,4510.20 to 0.25 10,0880.25 to 0.30 2858

L. Dojcsak, L. Shamir / New Astronomy 28 (2014) 1–8 5

the angle of the brightest point compared to the center is notexpected to shift, but it can lead to the false detection of mildspirality that is not based on the morphology of the target galaxy.To avoid analyzing overlapping galaxies each image was scannedfor PSFs as done in Shamir and Nemiroff (2005,), and when morethan one PSF is detected the image is ignored. Out of the galaxiesclassified by Galaxy Zoo as elliptical �12.05% were detected asgalaxies with more than one nucleus and were therefore rejectedfrom the analysis.

6 L. Dojcsak, L. Shamir / New Astronomy 28 (2014) 1–8

Other catalogues that were used in this study were the RC3 cat-alogue (Corwin et al., 1994), of which 261 galaxies classified asellipticals and 640 galaxies classified as S0 were used, and theNA10 catalogue (Nair and Abraham, 2010), of which 2705 galaxiesthat were classified as ellipticals, and 1964 galaxies that were clas-sified as S0 were used in the experiment. Additionally, 7638 galax-ies of the NA10 catalogue classified as spirals were also used in theanalysis.

4. Results

Fig. 2 shows the distribution of the slopes of the arms of the gal-axies classified manually as elliptical. As the figure shows, �24% ofthe galaxies exhibit nonzero signal for spirality, and �10% of thegalaxies had a slope of the arms greater than 0.4, indicating thatmany of the Galaxy Zoo galaxies that were classified manually asellipticals actually have some spirality. Expectedly, the fraction ofgalaxies that meet the spirality threshold decreases as the slopeof the arms gets larger, and just less than 2% of the galaxies thatwere classified manually as ellipticals were detected to have ameasured slope greater than 1. As the graph shows, the measuredslope of the arms of most galaxies is close to 0.

Fig. 3 shows the distribution of the slopes of the arms in a gal-axy population of different redshifts. As can be learned from the

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 to 0.05 0.05 to 0.10 0.10 to 0.15

0.15 to 0.20 0.20 to 0.25 0.25 to 0.30

Slopes of the arms (x)

Fig. 2. Slope of the arms of the entire galaxy population of �60,000 galaxiesclassified as ellipticals.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00 0.20 0.40 0.60 0.80

Slope of the A

Fig. 3. The distribution of the slopes of the arms in galaxies of dif

Figure, the slope of the arms increases with the redshift, showingthat at higher redshifts human readers find it more difficult to de-tect spirality by eye and tend to classify more galaxies as ellipticals.Correlating the apparent magnitude of these galaxies with theslope of the arms provided a weak Pearson correlation value of�0.036, showing that the analysis is merely weakly dependenton apparent magnitude in the redshift range used in this study.

While the experiments above show that human readers can insome cases fail to notice mild spirality, we also tested the error rateof human readers when they determine that the galaxy that theyobserve is spiral. Fig. 4 shows the distribution of the measuredslope of the arms among galaxies that were classified by GalaxyZoo participants as spiral. As the figure shows, when the humaneye is able to detect spirality, spirality does exist, and galaxies clas-sified by human observers as spirals are rarely galaxies that do nothave any spirality in them. The reason could be the limited sensi-tivity of the human eye in detecting spirality, so that once spiralitycan be detected by the human eye it is above a certain spiralitythreshold that can be sensed by applying the analysis of the radialintensity plot of the galaxy as described in Section 2.

The results obtained with the Galaxy Zoo data were comparedalso to the analysis using data taken by the RC3 catalogue (Corwinet al., 1994) and the NA10 catalogue (Nair and Abraham, 2010).Unlike Galaxy Zoo that was classified by amateurs, RC3 and NA10were both classified by professional astronomers. Fig. 5 showsthe slopes of the arms of galaxies classified as ellipticals and S0by RC3.

As the graph shows, galaxies classified as S0 have a higher armslopes compared to galaxies classified as ellipticals. The figure alsoshows that like the Galaxy Zoo catalogue, the arms of many of thegalaxies classified by professional astronomers as ellipticals alsohas a certain slope. These results are in agreement with the obser-vation of Lintott et al. (2008), according which professional astron-omers do not outperform amateur astronomers in classification ofgalaxies into their broad morphological types.

Fig. 6 shows the slopes of the arms of galaxies classified as ellip-ticals and S0 in the NA10 catalogue. These results are in agreementwith the results of the RC3 catalogue, showing higher arm slopes ingalaxies classified manually as S0.

The distribution of the slopes of the arms was also analyzed fordifferent redshifts, as displayed by Figs. 7 and 8, showing galaxiesclassified as ellipticals and S0, respectively. As the figures show,thefraction of galaxies with non-zero slope classified as ellipticals andS0 by the NA10 catalogue does not change significantly with theredshift in the tested redshift ranges. A slight increase in the armslopes can be noticed when the redshift of the S0 galaxies getshigher. This can be explained by the ability of the computer meth-od to identify subtle differences in pixel intensities, and therefore

1.00 1.20 1.40

rms (x)

0-0.02

0.02-0.04

0.04-0.06

0.06-0.08

0.08-0.1

ferent redshifts ranges classified by Galaxy Zoo as ellipticals.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40Slope of the Arms (x)

0-0.02

0.02-0.04

0.04-0.06

0.06-0.08

Fig. 4. The distribution of the slopes of the arms in galaxies classified by Galaxy Zoo participants as spiral galaxies.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60Slope of the Arms (x)

Fig. 5. The distribution of the slopes of the arms in galaxies that were classified byRC3 as ellipticals and S0 galaxies.

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40Slope of the arm (X)

Fig. 6. The distribution of the slopes of the arms in galaxies that were classified byNA10 as ellipticals and S0 galaxies.

00.10.20.30.40.50.60.70.80.9

1

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40Slope of the arms (X)

S0

Fig. 7. The distribution of the slopes of the arms of galaxies that were classified byNA10 as ellipticals for different redshift ranges.

0.000.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40Slope of the arms (X)

All S0

Fig. 8. The distribution of the slopes of the arms of galaxies that were classified byNA10 as S0 for different redshift ranges.

Table 5Photometric differences between galaxies classified manually as ellipticals.

Measured spirality u–g g–r r–i

No arms detected 1.9260 ± 0.0016 1.064 ± 0.0009 0.4296 ± 0.00040.0–0.7 1.9070 ± 0.0023 1.017 ± 0.0019 0.4195 ± 0.001>0.7 1.8945 ± 0.006 1.026 ± 0.0056 0.4223 ± 0.002

L. Dojcsak, L. Shamir / New Astronomy 28 (2014) 1–8 7

can detect the spirality in many galaxies that a human observerwould classify as S0. At higher redshift the galaxies are normallyfainter and therefore more spiral galaxies are classified manuallyas S0, while the computer analysis can still detect their spirality.

Table 5 shows the mean and standard error of u–g, g–r, r–i ofthe galaxies in which no peaks were detected (no arms), galaxieswith mild arm slope <0.7, and galaxies with a higher arm slopeof >0.7. All galaxies were classified manually as ellipticals. As the

table shows, photometric differences exist between galaxies classi-fied manually as ellipticals that have no detected arms, and galax-ies classified manually as ellipticals that have a measured armslope greater than zero.

8 L. Dojcsak, L. Shamir / New Astronomy 28 (2014) 1–8

5. Conclusions

In this study we used computer-aided analysis based on theradial intensity plots of SDSS galaxy images to examine spiralityin galaxies that were classified manually as elliptical. While theunaided human eye provides a limited tool for analyzing ellipticalgalaxy images due to the limited sensitivity of the human vision todifferent gray levels, transforming the images to their radial inten-sity plots allows much easier detection of the spirality.

The results suggest that more than a third of the galaxies thatwere classified manually by Galaxy Zoo participants as ellipticalactually have a certain spirality. Although in most cases the spiral-ity was low, 10% of the galaxies classified as elliptical had a slopegreater than 0.5, suggesting that computer-aided analysis can insome cases be more sensitive to galaxy spirality compared to thehuman eye. These conclusions are also true for galaxies classifiedby professional astronomers, as was shown by using the RC3 andNA10 catalogues.

The results also exhibit redshift bias. This bias can be attributedto the quality of the images, as images of nearby galaxies providehigher image quality and therefore manual inspection of theseimages can be easier compared to images of galaxies with higherredshift, in which the ability of computer-aided analysis to detectsubtle differences between gray levels can provide an advantageover the unaided human eye.

Acknowledgments

Funding for the SDSS and SDSS-II has been provided by theAlfred P. Sloan Foundation, the Participating Institutions, theNational Science Foundation, the US Department of Energy, theNational Aeronautics and Space Administration, the JapaneseMonbukagakusho, the Max Planck Society, and the Higher Educa-tion Funding Council for England. The SDSS Web Site is http://www.sdss.org/.

The SDSS is managed by the Astrophysical Research Consortiumfor the Participating Institutions. The Participating Institutions arethe American Museum of Natural History, Astrophysical InstitutePotsdam, University of Basel, University of Cambridge, Case’Western Reserve University, University of Chicago, Drexel Univer-

sity, Fermilab, the Institute for Advanced Study, the Japan Partici-pation Group, Johns Hopkins University, the Joint Institute forNuclear Astrophysics, the Kavli Institute for Particle Astrophysicsand Cosmology, the Korean Scientist Group, the Chinese Academyof Sciences (LAMOST), Los Alamos National Laboratory, the MaxPlanck Institute for Astronomy (MPIA), the Max Planck Institutefor Astrophysics (MPA), New Mexico State University, Ohio StateUniversity, University of Pittsburgh, University of Portsmouth,Princeton University, the United States Naval Observatory andthe University of Washington.

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