Spatial Orientation of Spin Vectors of Blue-shifted Galaxies
aa r X i v : . [ a s t r o - ph . GA ] J un Astrophysics and Space Science manuscript No. (will be inserted by the editor)
S. N. Yadav , · B. Aryal · W. Saurer Spatial Orientation of Spin Vectors of Blue-shiftedGalaxies
Received: 12 Dec 2015 / Accepted: .........
Abstract
We present the analysis of the spin vectororientation of 5 987 SDSS galaxies having negative red-shift from − − − . Two dimensional ob-served parameters are used to compute three dimen-sional galaxy rotation axes by applying ‘position angle–inclination’ method. We aim to examine the non-randomeffects in the spatial orientation of blue-shifted galax-ies. We generate 5 × virtual galaxies to find expectedisotropic distributions by performing numerical simula-tions. We have written MATLAB program to facilitatethe simulation process and eliminate the manual errors inthe process. Chi-square, auto-correlation, and the Fouriertests are used to examine non-random effects in the polarand azimuthal angle distributions of the galaxy rotationaxes. In general, blue-shifted galaxies show no preferredalignments of galaxy rotation axes. Our results supportHierarchy model, which suggests a random orientation ofangular momentum vectors of galaxies. However, local ef-fects are noted suggesting gravitational tidal interactionbetween neighboring galaxies. Keywords galaxies: evolution – galaxies: formation –galaxies: statistics – galaxies: blue shift
It is commonly believed that the blue-shifted galaxiesare relatively nearby ones whose peculiar motion over-comes the Hubble flow. All of the most distant galax-ies (and indeed the overwhelming majority of all galax-
First Author: S. N. Yadav Central Department of Physics, Tribhuvan University, NepalE-mail: [email protected]. Aryal Central Department of Physics, Tribhuvan University, NepalE-mail: [email protected]. Saurer Institute of Astro- and Particle physics, Innsbruck Univer-sity, Technikstrasse 25/8, A-6020 Innsbruck, AustriaE-mail: [email protected] ies) are red-shifted. According to the conventional defi-nition, the redshift of galaxies is the sum of two terms:the isotropic cosmic expansion velocity and the peculiarvelocity owning to gravitational attraction by the sur-rounding matter. In practice, determining the peculiarvelocity of a galaxy requires knowledge of both its ob-servable radial velocity relative to some reference systemand the distance to the galaxy determined independentlyof the radial velocity. According to the linear theory ofgravitational instability, the peculiar velocities of galax-ies are related to fluctuations in the mass (Peebles 1980).Burbidge & Demoulin (1969) first observed IC 3258with a blueshift of −
490 km s − . They give three possi-ble interpretations of their observations. First, IC 3258is a member of the Virgo cluster and has a very high ve-locity relative to the average for the cluster. Second, IC3258 is a field galaxy closer to the Virgo cluster and itslarge velocity is just a random motion. Third, IC 3258has velocity because it has been ejected in an outburstinvolving one of the radio galaxies in the Virgo cluster.Several other blue-shifted galaxies appear in the direc-tion of the Virgo cluster.By measuring the distance d of a galaxy, one can ob-tain the peculiar velocity of a galaxy V pec = V obs − H o d ,here H o d is Hubble expansion velocity, V obs is observedvelocity of the galaxy. Since the Hubble expansion ve-locity is small for nearby galaxies, the peculiar velocitycould be negative. Negative peculiar velocities are seenall over the region around the Virgo cluster and this havelong been seen as a reflex of the pull of the cluster on us(Aaronson et al. 1982). We live in the Local Superclus-ter, which is overdense part of the Universe. So there ispossibly the a local retardation of the cosmic expansionor a net infall within this region. In another example, anobserver living on the outskirts of a large concentrationis also pulled towards the overdense part of the clusters.When the radiation propagates inside the collapsingbody it is blue-shifted. If this blueshift is greater thanthe redshift caused by the propagation of the radiationthrough expanding universe, distant observer can detectthe gravitational blueshift from the collapsing object. S. N. Yadav , et al. Also the AGNs have blue-shifted spectrum. Bian et al.(2005) studied the radial velocity difference between thenarrow emission-line components and of [O III] λ and H β in a sample of 150 SDSS narrow-line Seyfert 1 galaxies.They found seven ‘blue outliers’ with [O III] blueshiftedby more than 250 km s − . They interpreted the blueshiftas possible result of the outflowing gas from the nucleusand the obscuration of the receding part of the flow by anoptically thick accretion disk and on the viewing angle.Spatial orientation of angular momentum of blue-shifted galaxies (SDSS) has not been studied, so we areinterested to carry out the spatial orientation of blue-shifted galaxies. An idea of the origin of angular mo-mentum of galaxies is very important to understand theevolution of large scale structures of the universe. Thispaper is organized as follows: in Sect. 2 we describe thesample used and the method of data reduction. In Sect. 3we describe the methods, statistical tools and the selec-tion effects. Finally, a discussion of the statistical resultsand the conclusions are presented in Sects. 4 and 5. We compiled a database of 5 987 blue-shifted galaxiesfrom The Sloan Digital Sky Survey seventh Data Re-lease (SDSS DR7). All sky distribution of blue-shiftedgalaxies is shown in Fig. 1a. The inhomogeneous distri-bution of galaxies is because of the nature of the survey.The distribution of blue-shifted galaxies is shown in Fig.1b. We found a linear relationship between the blue-shiftand logarithm of the number of galaxies ( − z ∝ log( N )).We have retained only those galaxies that have blue-shift( − z ) data at 95% level of significance. This removed 569galaxies form the original data. Since blue-shift is foundto be decreases lineally with number (Fig. 1b), the re-maining 4 595 galaxies were classified into three bins byconsidering the bin size of 1 × − . This resulted inthree bins with number of galaxies roughly in the ratioof 3 : 2 : 1 in the largest, medium and the smallest binsrespectively. In the binning process, galaxies that havevery low and high blue-shift values were also removed.Since our galaxies are blue-shifted, their apparentmagnitude increases with time. In order to check the ef-fect of blue-shift on preferred alignments, we have chosentwo extreme filters: infrared ( i ) and ultraviolet ( u ). Thewavelengths of SDSS i and u filters are 7 625 ˚ A and 3 543˚ A , respectively. The true magnitudes of i filter lies in thefar-infrared and u in the visual bands. The study of far-infrared and optical activity in the galaxy gives informa-tion regarding the early star formation activity and theHII region, respectively. Fig. 1c,d shows the magnitudedistribution of near infrared and ultraviolet galaxies. Forboth, Gaussian distribution fits well with the observeddistribution.In order to find angular momentum vectors (or spinvectors, SV hereafter), the diameters, position angles and Fig. 2
Schematic illustration of θ (polar angle between theSV of the galaxy and the reference plane) and φ (azimuthalangle between the projection of SV and the X-axis of thereference plane). The galactic longitude ( l ) and latitude ( b )are shown. For details: Flin & Godlowski (1986) and Aryalet al. (2008). positions of galaxies should be known. We have compiledthe database of diameters and position angle of galaxiesusing SDSS survey. We follow the method suggested by Flin & Godlowski(1986) to convert two dimensional parameters (positions,diameters, position angles of the DR7 SDSS blue shiftedgalaxies) into three dimensional parameters (galaxy ro-tation axes in spherical polar coordinates). The expectedisotropic distribution for angular momentum vectors orSVs of galaxies are determined by using the method pro-posed by Aryal & Saurer (2000). The observed and ex-pected distributions are compared with the help of threestatistical tests namely chi-square, auto-correlation andthe Fourier.3.1 Observed distribution: SVs of galaxiesThe two-dimensional SDSS parameters (positions, posi-tion angles and diameters) are converted into polar ( θ )and azimuthal ( φ ) angles of galaxies using Flin & God-lowski (1986). Our blue-shifted galaxies have negativeradial velocities probably due to their larger peculiar ve-locity. These galaxies are mostly nearby galaxies. Thus,it is convenient to use galactic coordinate system as aphysical reference plane. The formulae to obtain θ and φ in are as follows (Flin & Godlowski, 1986):sin θ = − cos i sin b ± sin i sin p cos b (1) patial Orientation of Spin Vectors of Blue-shifted Galaxies 3 Fig. 1 (a) All sky distribution of blue-shifted galaxies in the galactic coordinate system. The grey-shaded region representsplane of the Milky Way. The symbols solid circle, hollow circle and cross represent small, moderate and strongly blue-shiftedgalaxies (description in the text) (b) Blue-shift (c) i -magnitude and (d) u -magnitude distribution of galaxies. The solid linein (b) is the linear fit. The Gaussian fits are shown by solid curves in (c) and (d). sin φ = (cos θ ) − [ − cos i cos b sin l + sin i ( ∓ sin p sin b sin l ∓ cos p cos l ) (2)where l , b and p are the galactic longitude, latitude andposition angle, respectively. The i represents the incli-nation angle, obtained using Holmberg’s (1946) formula:cos i = [( b/a ) – q ]/(1– q ) where b/a is the measuredaxial ratio and q is the intrinsic flatness of disk galax-ies. The method of determination of intrinsic flatness ofgalaxies is the same as in Aryal et al. (2013).The above formulae show that there are two possiblesolutions for a given galaxy. The normals ( N , N , N , N ) shown in Fig. 2 can not be determined unambigu-ously, because we do not know the side of the galaxywhich is nearer/far to us, and the direction of rotation.Thus, there are four solutions of the SV orientation fora galaxy. We count all four possibilities independently inour analysis.3.2 Expected distribution: numerical simulationAryal & Saurer (2000) studied the effects of various typesof selections in the database and concluded that such se-lections may cause severe changes in the shapes of theexpected isotropic distribution curves in the galaxy ori-entation study. Their method has been applied by sev-eral authors in galaxy orientation studies (Hu et al. 2006,Aryal et al. 2013 and the references therein). Two kinds of selection effects are noticed in our database: (1) inho-mogeneous distribution of positions of galaxies, and (3)less number of high inclination (edge-on) galaxies. Theseselection effects are removed and the expected isotropicdistribution curves ( θ and φ ) are determined using thenumerical simulation method as proposed by Aryal &Saurer (2000). For this, a true spatial distribution of Sof galaxies is assumed to be isotropic. Then, due to theprojection effects, i can be distributed ∝ sin i , latitudecan be distributed ∝ cos b , the variables longitude ( l )and PA can be distributed randomly, and formulae (1)and (2) can be used to simulate (numerically) the corre-sponding distribution of θ and φ . The isotropic distribu-tion curves are based on simulations including 10 virtualgalaxies. The simulation procedure is described in Aryal& Saurer (2004). We perform numerical simulation withrespect to galactic coordinate system systems. These ex-pected isotropic distribution curves are compared withthe observed distribution.3.3 Statistical testsOur observed θ and φ -distributions are compared withexpected isotropic distribution curves. For this compari-son we applied chi-square, autocorrelation and the Fourier(Godlowski 1993) tests. These tests are described in theappendix of Aryal et al. (2007). These statistical testsare a proper method in our case, because θ and φ are S. N. Yadav , et al. independent data. The significance level is chosen to be95%, the null hypothesis is established to be an equidis-tribution for the θ and φ . We have classified our database into six subsamples onthe basis of their redshift values and u & i -magnitudes.Here we discuss the distribution of the polar ( θ ) andazimuthal ( φ ) angles of galaxy rotation axes in eachsubsamples. We study the spatial orientation of SVs ofgalaxies with respect to the galactic coordinate system.Any deviation from the expected isotropic distributionwill be tested using four statistical parameters, namelythe chi-square probability ((P > χ )), auto-correlationcoefficient ((C/C( σ ))), first order Fourier coefficient ( ∆ /σ ( ∆ )), and first order Fourier probability ((P > ∆ )).The conditions for anisotropy are the following: P( > χ ) < σ ) and ∆ / σ ( ∆ ) >
1, and P( > ∆ ) < θ -distribution, a positive (neg-ative) ∆ suggests that the SVs of galaxies tend to ori-ent parallel (perpendicular) with respect to plane of theMilky Way. In the φ -distribution, a positive (negative) ∆ suggests that the SV projections of galaxies tendto point radially (tangentially) with respect to center ofthe Milky Way. Any ‘humps’ or ‘dips’ in the histogramwill be discussed. Here ‘hump’ and ‘dip’ are defined ashaving more or less observed solutions than expected re-spectively.4.1 Polar angle distributionAll three statistical tests suggest isotropy in the θ dis-tribution of subsample i
01 (Table 1). The galaxies inthis subsample are nearby blue-shifted (RV < − − ) having i -magnitude in the range 12.45 and 32.08.In the histogram, no significant humps or dips can beseen (Fig. 3a). Thus, a random orientation of angularmomentum vectors of galaxies is found, suggesting hier-archy model of the structure formation as suggested byPeebles (1969).The galaxies in the subsample i
02 are moderatelyblue shifted (RV: 28.5-58.5 km s − and m i : 10.46 - 36.10).The chi-square and the correlation tests show anisotropy(Table 1). However, the first order Fourier probabilityand the first order Fourier coefficient suggest isotropy.Since the observed distribution follow the expected, weregard the Fourier test as more reliable. There are smalldips at 5 ◦ , ∼ ◦ , and a hump at 15 ◦ (Fig.3b). These arepossibly due to the binning effect.Strong blue-shifted (RV: ≥ − ) SDSS galax-ies (m i : 10.82 - 42.23) are grouped in the subsample i Fig. 3
The polar ( θ ) angle distributions of blue shifted SDSSgalaxies in 6 subsamples. The solid circles with ± σ errorbars represent the observed distribution. The solid line rep-resents the expected isotropic distributions. The cosine dis-tributions (dashed) are shown for the comparison. observed and expected distributions can be seen. Simi-lar to the subsample i
03, chi-square probability and cor-relation coefficient show anisotropy, whereas first-orderFourier probability and the first-order Fourier coefficientsuggests isotropy (Table 1). Several humps (0 ◦ , 45 ◦ , 60 ◦ )and dips (30 ◦ , 35 ◦ , 60 ◦ ) suggests the local effect. Thus,the strong blue-shifted infrared galaxies are in the pro-cess of grouping or subclustering because of the tidal orgravitational shearing effect.All three statistical tests support isotropy in θ distri-bution of u -magnitude low blue-shifted (RV < − ) galaxies. In Fig. 3d, no significant humps or dipsare found. A small hump at 20 ◦ and a dip at 60 ◦ are be-cause of the binning effects. These effects do not changethe statistics of the subsample u
01. Hence, no preferredalignments of SVs of galaxies in subsample u
01 is no-ticed. patial Orientation of Spin Vectors of Blue-shifted Galaxies 5
Table 1
Statistics of the polar ( θ ) and azimuthal angle ( φ ) distributions of galaxies in the six subsamples. The first columnlists the subsamples. The second and third columns give the number of galaxies (N) in the subsample and their blue-shift (- z ,in km s − ). The fourth and fifth columns list the values of chi-square probability (P( > χ )) and auto-correlation coefficient(C/C( σ )). The last three columns gives the first order Fourier coefficient ( ∆ /σ ( ∆ )), the first order Fourier probability(P( > ∆ )), and standard deviation of Fourier amplitude ( σ ( ∆ )) respectively.subsample N − z P( > χ ) C/C( σ ) ∆ /σ ( ∆ ) P( > ∆ ) σ ( ∆ )polar angle i
01 1813 < − − i
02 1144 28.5-58.5 0.025 +1.9 − i
03 569 ≥ − − u
01 1297 < − u
02 839 28.5-58.5 0.896 − − u
03 438 ≥ − i
01 1813 < − i
02 1144 28.5-58.5 0.107 − − i
03 569 ≥ − u
01 1297 < − u
02 839 28.5-58.5 0.433 +0.5 − u
03 438 ≥ In subsample u
02, all three statistics show isotropy inpolar angle ( θ ) distribution. A small dip at 10 ◦ is becauseof the binning effect (Fig. 3e). A random orientation ofSVs of galaxies is noticed in this subsample.All statistics except correlation coefficient showed isotropyin the polar angle distribution of high blue-shifted (RV ≥ − ) u -magnitude galaxies (subsample u > σ level).This is because of the humps at 10 ◦ , 45 ◦ , 55 ◦ and dipsat 15 ◦ , 20 ◦ . These humps and dips suggests the possibil-ity of grouping or subclustering because of the tidal orgravitational shearing effects between comoving galaxies.To sum up, the spatial orientation of blue-shiftedgalaxies is found to be random, supporting hierarchymodel (Peebles 1969) of structure formation. It is foundthat the rapidly moving blue shifted galaxies are in theprocess of large structure (galaxy groups, subclusters,clusters, etc) formation. In addition, magnitude is foundto be independent of the preferred alignments.4.2 Azimuthal angle distributionAll three statistics support isotropy in the azimuthal an-gle distribution of low blue-shifted high magnitude in-frared (subsample i
01) galaxies (Table 2). There is ahump at +65 ◦ and dips at − ◦ and − ◦ (Fig.4a). Theseare due to the binning effect and hence do not change thestatistics. Thus, no preference is noticed for spin vectorprojections of low blue-shifted infrared galaxies.All statistics except χ -test suggest anisotropy in the φ distribution of the subsample i
02. In the histograms forthe φ -distribution of the subsample i
02 (Fig.4b), humpsat − ◦ , +30 ◦ and +90 ◦ , and dips at − ◦ to +20 ◦ canbe seen. These humps and dips lead this subsample toshow anisotropy. The spin vector projection of i
02 galax-ies is found to be directed tangentially outwards with re-spect to the center of the Milky Way. Fig. 4c shows the distribution of the spin vector projections of high blue-shifted galaxies (subsample i i
02, all statistical parameters except P( > χ ) showanisotropy. There is a significant hump at +90 ◦ and dipsat − ◦ and 0 ◦ . The SV projections of high blue-shiftedgalaxies is found to be oriented tangentially with respectto the center of the Milky Way.All statistics except C/C( σ ) show anisotropy in the φ -distribution for subsample u
01. In the histogram, severalhumps and dips can be seen: humps at − ◦ and +80 ◦ ,and dips in the region from − ◦ to +50 ◦ (Fig. 4d). Thissubsample showed isotropy in the polar and anisotropyin the azimuthal angle distribution. This inconsistencyis because of the inappropriate reference coordinate sys-tem. A physical reference system should be identified inthe future.Fourier test suggests isotropy in the subsample u − ◦ , +20 ◦ and a hump at +90 ◦ (Fig.4e). We observe weak anisotropy in the spin vec-tor projection of u
02 galaxies with respect to galacticcoordinate system.Interestingly, all statistics show isotropy in the dis-tribution of SV projections of high blue-shifted galaxies( u ◦ and 40 ◦ , not signifi-cant to alter the statistics of the subsample. There is avery good agreement between the observed and expecteddistributions (Fig. 4f) Thus, a random orientation of spinvector projections is found.4.3 DiscussionIn the numerous past literatures authors have studiedthe spatial orientation of red-shifted galaxies in the field,clusters and Superclusters and found mixed result: (1)noticed anisotropy supporting either ‘pancake model’ (Flin& Godlowski 1986; Godlowski 1993, 1994; Godlowski,Baier & MacGillivray 1998, Flin 2001) as suggested by S. N. Yadav , et al. Fig. 4
The azimuthal ( φ ) angle distributions of blue shiftedSDSS galaxies in 6 subsamples. The solid circles with ± σ error bars represent the observed distribution. The solid linerepresents the expected isotropic distributions. The averagedistributions (dashed) are shown for the comparison. Doroshkevich (1973) or ‘primordial vorticity model’ (Baier,Godlowski & MacGillivray 2003) as proposed by Ozer-noy (1978)(2) found isotropy suggesting a random orien-tation of spin vectors of galaxies supporting ‘hierarchymodel’ (Bukhari & Cram 2003; Aryal & Saurer 2005a,Aryal et al. 2006, 2012, 2013) as recommended by Pee-bles (1969). In addition to these scenarios a bimodal tendency(Kashikawa & Okamura 1992), local anisotropy (Flin1995, Djorgovski 1983, Aryal & Saurer 2004, 2005b),global anisotropy (Parnovsky, Karachentsev & Karachent-seva 1994) are noticed. Godlowski & Ostrowski (1999)noticed a strong systematic effect, generated by the pro-cess of deprojection of a galactic axis from its opticalimage. In isolated Abell clusters, only brightest galax-ies are preferentially aligned (Trevese, Cirimele & Flin1992). Panko et al. (2013), Godlowski (2012) and God-lowski et al. (2010) noticed a dependence of alignmentwith respect to cluster richness.The anisotropy is found mostly for those sampleswhich is taken from a limited region of the sky (e.g.,clusters, sub-clusters, groups, etc). For the field galaxiesand superclusters, i.e., the database taken from the largescale structure, authors notice a random orientation sup-porting hierarchy model. In both the cases (isotropy oranisotropy), a local effect is noticed. This effect mightarises due to the tidal connections between the neigh-boring galaxies or because of the gravitational shearingeffect. Interestingly, blue-shifted galaxies support hierar-chy model. Thus, it can be concluded that the blue-shiftis not different cosmological effect, it is because of thepeculiar velocity as suggested by Aaronson et al. (1982).
We studied the spatial orientation of spin vectors of 5 987blue-shifted galaxies ( − − − ) observedthrough i - and u -filter. These database were taken bySDSS (7 th data release). We classified our data into 6subsamples based upon their blue-shift. We have usedthe ‘PA-inclination’ method proposed by Flin & God-lowski (1986) to convert two dimensional observed pa-rameters to three dimensional galaxy rotation axes (po-lar and azimuthal angles) and carried out random simu-lation by creating 5 × virtual galaxies in order to re-move selection effects from the database (Aryal & Saurer2000). To check for anisotropy or isotropy, we have car-ried out three statistical tests: chi-square, auto-correlationand the Fourier.Since our observed distributions do not vary signifi-cantly from the expected distribution, we have regardedthe Fourier test as more reliable. The local effects areexamined by the correlation test. We have taken χ testin order to check the binning effect. In general, we foundisotropic distribution of the spin vector of galaxies in allsix subsamples with respect to the galactic coordinatesystem. There are humps and dips in the polar angledistributions, and these humps and dips alter the cor-relation test showing anisotropy in subsamples i i u
03. Hence, local effect was observed in these sub-samples suggesting a local tidal connection between therotation axes of neighboring galaxies or the gravitationalshearing effect. However, in the rest of the subsamples patial Orientation of Spin Vectors of Blue-shifted Galaxies 7 ( i u
01, and u
02) small humps and dips do not alterthe statistics of the total subsample, so we suppose theseas binning effects. In general, we observe that there is nopreferred alignment of spin vectors of galaxies. Our re-sults of θ -distribution support the hierarchical clusteringscenario (Peebles 1969), which predicts the random ori-entation of the directions of the spin vectors of galaxies.On the other hand, we found interesting results forthe φ -distribution. As mentioned above, we have regardedthe Fourier test as more reliable. Out of six subsamplesonly two subsamples ( i
01 and u
03) show isotropy in alltests. Rest of the subsamples ( i i u
01, and u u
03) havenegative value of the first order Fourier coefficient ∆ .Therefore, in general the spin vector projection of thegalaxies tend to be orientated perpendicular to the equa-torial plane. However, this result needs to be examinedby using other reference system such as Supergalacticcoordinate system in the future. Acknowledgements
References
1. Aaronson, M., Huchra J., Mould, J., Schechter P. L., TullyR. B.:
Astrophys. J. , 64 (1982)2. Bian, W., Yuan, Q., Zhao, Y.,
Monthly Notices Royal As-tron. Soc.
187 (2005)3. Aryal, B., Bhattarai, H., Dhakal, S., Rajbahak, C., Saurer,W.:
Monthly Notices Royal Astron. Soc. , 1939 (2013)4. Aryal, B., Paudel, R. R.; Saurer, W.:
Astrophys. Space Sci. , 313 (2012)5. Aryal, B., Kafle, P., Saurer, W.:
Monthly Notices RoyalAstron. Soc. , 741 (2008)6. Aryal, B., Paudel, S., Saurer, W.:
Monthly Notices RoyalAstron. Soc. , 1011 (2007)7. Aryal, B., Saurer, W.:
Monthly Notices Royal Astron. Soc. , 438 (2006)8. Aryal, B., Saurer, W.:
Astronom. Astrophys. , 841(2005b)9. Aryal, B., Saurer, W.:
Astronom. Astrophys. , 431(2005a)10. Aryal, B., Saurer, W.:
Astronom. Astrophys. , 871(2004)11. Aryal, B., Saurer, W.:
Astronom. Astrophys. lett. ,L97 (2000)12. Baier, F.W., Godlowski, W., MacGillivray, H.T.:
As-troph. Space Sci. , 847 (2003)13. Burbidge, E. M., Demoulin, M. H.:
Astrophys. J. ,155 (1969)14. Bukhari, F.A., Cram, L.E.:
Astrophys. Space Sci. ,173 (2003)15. Doroshkevich, A.G.:
Astrophys. J. , L11 (1973) 16. Flin, P.: Comments Astrophys.
Overseas Publishers As-sociation, Amsterdam B.V., Vol. , No. 2, p.81 (1995)17. Flin, P., Godlowski, W.: Monthly Notices Royal Astron.Soc. , 525 (1986)18. Flin, P.:
Monthly Notices Royal Astron. Soc. , 49(2001)19. Godlowski, W.:
Astrophys. J. , 1, 7 (2012)20. Godlowski, W., Piwowarska, P., Panko, E., Flin, P.:
As-trophys. J. , 985 (2010)21. Godlowski, W., Ostrowski, M.:
Monthly Notices RoyalAstron. Soc. , , 50 (1999)22. Godlowski, W., Baier, F.W., MacGillivray, H.T.: As-tronom. Astrophys. , 709 (1998)23. Godlowski, W.:
Monthly Notices Royal Astron. Soc. ,19 (1994)24. Godlowski, W.:
Monthly Notices Royal Astron. Soc. ,874 (1993)25. Holmberg, E.:
Medd. Lund. Astron. Obs. , Ser VI, No. 117(1946)26. Kashikawa, N., Okamura, S.: pasj , , 493 (1992)27. Ozernoy, L.M.: in: Longair M.S., Einasto J., eds, Proc.IAU Symp. 79, The Large Scale Structure of the Universe.
Reidel, Dordrecht, p.427 (1978)28. Panko, E., Piwowarska, P., Godlowska, J., Godlowski,W., Flin, P.:
Astrophysics , 3, 322 (2013)29. Parnovsky, S.L., Karachentsev, I.D., Karachentseva,V.E.: Monthly Notices Royal Astron. Soc. , 665 (1994)30. Peebles, P.J.E.:
Astrophys. J. , 393 (1969)31. Trevese, D., Cirimele, G., Flin, P.:
Astronom. J.104