DOES THE CORONA BOREALIS SUPERCLUSTER FORM A ... - arXiv

DOES THE CORONA BOREALIS SUPERCLUSTER FORM A GIANT BINARY-LIKE SYSTEM? Giovanni C. Baiesi Pillastrini1* 1 U.A.I. c/o Osservatorio Astronomico Fuligni - Via Lazio 14, 00040 Rocca di Papa (RM), Italy

ABSTRACT The distribution of local gravitational potentials generated by a complete volume-limited sample of galaxy groups and clusters filling the Corona Borealis region has been analyzed. Mapping such a distribution as a function of spatial positions, the deepest potential wells trace unambiguously the locations of the densest cluster clumps within the selected sample providing the physical keys to disentangle a still open issue regarding the true extent and cluster membership of the well-known region of the Corona Borealis Supercluster. The two deepest potential wells found at R.A. ~ 230°, Decl. ~ 29° and z ~ .074 and, R.A. ~ 240°, Decl. ~ 28° and z ~ .09 correspond to very close and massive clumps of galaxy groups and clusters similar to a binary-like system lying in the central part of the Corona Borealis region. The first clump matches the location of the supercluster commonly referred to as Corona Borealis, while its more massive companion is centrally dominated by the cluster A2142, one of the richest clusters found by Abell (1961). To a first approximation, this binary-like system seems gravitationally bound favoring the idea that the region apparently dominated by the Corona Borealis Supercluster is more massive and extended than commonly believed in literature.

Keywords: methods: data analysis - galaxies: clusters: individual: Corona Borealis – Cosmology: large scale structures of the Universe

*

permanent address: via Pizzardi, 13 - 40138 Bologna - Italy - email: [email protected]

1

1. INTRODUCTION Stimulated by an old study of Bahcall and Soneira (1984) and a recent one of Luparello et al. (2011) which hypothesized a much more extended and massive structure where the well-known Corona Borealis Supercluster (CBS hereafter) should be only a part of it, we attempt to disentangle that issue applying an exploratory analysis based on the gravitational potential method (GPM hereafter) suggested by Baiesi Pillastrini (2013, BP13). Since the first identification of the CBS by Abell (1961) using his own Catalog of Galaxy Clusters (Abell 1958), that region has been largely investigated using a variety of clustering algorithms generally based on the density field analysis and compared with the Abell cluster distribution (Bahcall and Soneira 1984; Cappi and Maurogordato 1992; Zucca et al. 1993; Kalinkov and Kuneva 1995 Einasto et al. 1994, 1997, 2001, 2011). On the other hand, many other dedicated studies have analyzed its composition, morphology and dynamical state (Postman et al. 1988; Small et al. 1997, 1998; Kopylova and Kopylov 1998; Marini et al. 2004; Génova-Santos et al. 2010; Batiste and Batuski 2013; Pearson et al. 2014). A new generation of Supercluster catalogs constructed with more accurate and complete datasets combined with new methodologies of clustering analysis have provided more insight on the extension and membership of the CBS ( Einasto et al. 2006; Luparello et al. 2011; Liivamagi et al. 2012; Nadathur and Hotchkiss 2013; Chow-Martinez et al. 2014). These studies used quite similar clustering algorithms and methodologies where galaxies are taken as tracers of the velocity field not of mass as well as a common practice of introducing arbitrary parameters as linking lengths, spatial density thresholds, etc. in the selection procedure that provided quite different boundaries and membership for the same structures. Also the assignment of the Abel cluster members belonging to the CBS was subject to many modifications with respect to the firs definition of Abell (1961). In the present study, the GPM has been applied. This clustering algorithm is based on the Newtonian gravity theory and is able to detect clustered structures in a simple, fast and efficient way. It was developed following the prescription of the exploratory data analysis and rests on the basic idea that the gravitational potential is closely connected with the matter density field and that galaxy systems aggregate by following the laws of gravity no matter how different they are. As established by the theory of gravitational instability, the formation (and evolution) of huge scale structures seen in the galaxy distribution is tightly related to the potential field distribution (Madsen et al.1998). It follows that clustered regions arise due to slow matter flows into negative potential wells so that, the detection of huge mass concentrations can be carried out simply observing the regions where the deepest potential wells (DPW hereafter) originate. Its application is becoming now possible after accurate mass estimations are provided by galaxy group/cluster catalogs up to intermediate redshift (see for instance Tempel et al. 2014). The use of large datasets of galaxy systems taken as tracers of mass density field not of velocity is the most relevant difference between the GPM and other methods based on the analysis of space density fields. The GPM is designed to graphically display the isopotential contours originated by the underlying mass distribution from which one can explore and identify the location of a single or more clustered structures simply looking for the deepest negative potential counterparts (see BP13 for details). Specifically, the GPM performs a two-step analysis as follows: i) DPWs are identified either on a graphic plot and/or sorting the numerical output; ii) each DPW location is assumed as the provisory center of mass of the cluster clump and iii) a density contrast criterion is applied in order to quantify their bound part in terms of membership and mass. In the present study we assume: H0 = 100 h km s-1 Mpc-1, Ωm = 0.27 and ΩΛ = 0.73 according to the cosmological parameters of the dataset used hereafter. The paper is organized as follows: in Sect.2 we briefly describe the GPM. In Sect.3 the GPM is applied to a complete volume-limited sample of galaxy groups and clusters filling the CBS region with the purpose to identify the locations of the DPWs. Then, the assumed density contrast criterion to identify the bound part of the underlying cluster clump is described and applied. The results are then compared with other studies and various issues addressed by our study are discussed. In Sect.4, the conclusions are drawn. 2. A BRIEF DESCRIPTION OF THE GRAVITATIONAL POTENTIAL METHOD (GPM) The methodology of investigation adopted for the GPM is essentially based on the exploratory data analysis (Tukey 1977). In this context, BP13 introduced a method based on the determination of the local gravitational potential distribution generated by a complete volume-limited sample of objects which does not depend on arbitrary free parameters except for those of the cosmological model adopted. This property prevents the common arbitrary nature in clustering selection which depends on the specific choice and tuning of a number of free parameters. Now, being gravity a superposable force, the gravitational potential generated by a collection of point masses at a certain location in space is the sum of the potentials generated at that location by each point mass taken in isolation. By measuring the local potential at the position of each object taken one at a time as a test-particle, the map of the local potential distribution generated by the spatial distribution of the whole sample is displayed. The DPWs identify unambiguously the location of the densest clumps in a mass distribution. Hence, given N V j point-masses located at position vectors d i (from the observer) within a spherical volume V j of fixed radius

RV centered on a generic test-particle j at position vector d j from the observer,

2

then the local gravitational potential generated at position vector d j by the N V j point masses is given by the conventional formula  j  G

1

NV j

 m d

i i 1,i  j ,iV j

mi (i  1,...., NV j )

i

dj

where G is the gravitational constant.

Repeating the calculation for each point mass of the selected sample, we provide the whole  j distribution.  j is given in 106 h(km/s)2 unit and is always negative denoting that the force between particles is attractive. The GPM provides many relevant advantages: i) it enables the identification of clustered structures using an algorithm based on gravity theory. Being gravity a long range force, the potential distribution is smoother than the density distribution since the contribution to local potential fields due to small density fluctuations is irrelevant. This is an important property which enables us to constrain overdensities with a clearer physical meaning than, for example, spatial density-based algorithms. By knowing positions in space and individual mass estimations of a complete volume-limited sample of mass tracers, the local gravitational potential distribution can be constructed and mapped by contour plots of the potential projected surface as a function of space positions; ii) it does not require any threshold to be set overcoming the problem of arbitrary density thresholds in the clustering analysis. A property that reduces the complexity of the GPM and enables to build a fast and simple program that can run only once on a commercial notebook with very little computer time consumption. The main disadvantage of the GPM is that its accuracy in detecting superstructures depends largely on the accuracy of mass estimations provided by the used dataset. In other words, the more accurate the mass estimates (as well as the spatial position of the tracers in real space) of the dataset, the more reliable the clustering analysis will be. It follows that the GPM applied to different datasets (obtained by different spatial reconstruction techniques or different selection methods) may give different results. 3. THE GPM APPLIED TO THE CORONA BOREALIS REGION 3.1. The dataset As demonstrated in BP13, the GPM can be an efficient clustering algorithm only if the selected sample of objects under study is volume-limited and free of bias effects (selection effect, redshift distortion and so on). In studies concerning gravitational interactions, the use of cluster samples overcomes some of these problems faced by galaxy samples since clusters are luminous enough for samples to be volume-limited out to large distances, trace the peaks of the density fluctuation and reduce the effect of redshift distortion. Therefore, galaxy clusters emerge as the most convenient mass tracer candidate for our clustering analysis. In particular, the best choice would be a complete volume-limited catalog of galaxy clusters where reliable mass estimations (assumed as point-mass tracers) are available. Recently, Tempel et al. (2014, T14), applied an improved Friends of Friends (FoF) method to flux- and volume-limited samples drawn from the SDSS DR10 survey (Ahn et al. 2013) main contiguous area covering 7221 square degrees in the sky. It has been used to trace groups and clusters of galaxies out to z = .2 involving 588,193 galaxies. Their technique provided a flux-limited catalog of over 82,458 galaxy group/clusters and, seven other catalogs constructed volume-limited with different absolute magnitude limits: from M = -18 to -21. These catalogs provide for each identified cluster the parameters of our interest that are: n° of galaxy of the group/cluster; J2000 equatorial coordinates of the center as the origin; the spectroscopic redshift (CMB-corrected), comoving distance in h-1Mpc and, finally, the estimated dynamical mass (assuming NFW profile) in solar mass unit. For our purpose, the M=-20 volume-limited group/cluster catalog of 24,258 identified objects is selected. From this sample, a subsample filling the Corona Borealis region inbetween equatorial coordinates 200° < R.A. < 260° and -4°< Decl. < 64° and, radially, up to the comoving distance limit for completeness of 322.6 h-1Mpc (T14) has been extracted. Because of the Authors warn of the large error affecting the mass estimation of the galaxy pairs, in order to reduce the bias due to outliers in mass estimations of the T14’s catalog, we excluded all pairs from the sample retaining only 3,942 systems. 3.2. Methodology A two-step exploratory analysis is performed: first, applying the GPM to the selected sample, for each sampled object (group or cluster) taken one at a time as a test point-mass, the local gravitational potential generated by the surrounding mass distribution at that position is computed. Then, the output of the computations provides a list and map of the DPWs as well as their spatial locations within the CBS region. Second, a density contrast criterion is applied in order to constrain membership and mass of the bound part of the group/cluster clump underlying the identified DPW.

3.3. Simplifying assumptions - The GPM measures the local gravitational potential generated by point-masses located in a defined spherical volume centered at the position of a point-mass taken as a test-particle on the assumption that the gravitational potential is time-

3

independent; - The simplest assumption to connect dark and luminous matter is that galaxy clusters trace the peaks of the underlying matter density field even if the galaxy cluster density is linearly biased with respect to the dark matter density. The exact relationship between the cluster power spectrum and the dark matter power spectrum is well understood theoretically (Mo and White 1996), and this relationship or biasing is a function of cluster mass. However, to simplify the calculation a bias factor set equal 1 has been assumed so that fluctuations of the gravitational potential generated by the galaxy cluster distribution also reflect those in the full matter distribution; - There is the well-known problem to find a finite solution of  j for infinite number of gravitating masses. To overcome this problem we need to assume the form of the spatial distribution of these masses. By considering that at the position of each test cluster, the local gravitational potential is mainly influenced by its nearer neighbors and much less by other distant masses i.e.  j  0 when d i  d j   , we may assume the mass distribution within the spherical volume V j of fixed radius

RV is embedded in a uniform background. Such supposed segregation of galaxy groups and

clusters within V j provides the finiteness of the local gravitational potential. Outside V j the potential vanishes that is, at the distance of d i  d j  Rv ,  j

 0 . However, for our purpose (clustering analysis of a large scale structure),

V j should be large enough to enclose a massive cluster of clusters since  computed at the position of its center of mass would include all gravitational contributions provided by its members. The most massive superstructures identified in the local Universe, say, the Sloan Great Wall or the Shapley concentration, fill volumes with 50÷70 h-1Mpc radii; therefore, assuming a value of RV = 80 h-1Mpc it should be large enough to incorporate the major share of the gravitational influence exerted by neighboring masses (for instance, supposing a galaxy supercluster of ~ 1016 Mʘ lying beyond RV as an extreme case, the gravitational potential influence induced by such a massive object is only of ~ -0.5 x 106 h(km/s)2 at the center position) and prevent the so-called shot noise error. - When RV overlaps the volume boundaries of our selected cluster sample,

the measured  j is automatically ig-

nored in order to minimize the edge effect. 3.4. Uncertainties - The volume-limited group/cluster catalogs of T14 do not provide an estimated error for the parameters (mass and comoving distance of each group/cluster) entering in the  determination. Therefore, a direct evaluation of the standard error for  cannot be established. Even if this error is difficult to quantify when the dataset gives not information on the mass estimation uncertainties, we may attempt to evaluate the order of magnitude of the uncertainty on  knowing that errors on spectroscopic redshifts of the SDSS DR10 survey do not exceed a few % (error due to cluster peculiar velocities is not take into account since is smaller than that due to single galaxy ones) and those affecting dynamical mass estimations of galaxy groups and clusters go up to ~ 31% (Liljeblad 2012) which, of course, is very large. However, the uncertainty on  is somewhat smaller, not only because of dynamical mass estimations given in T14 are obtained with an accurate technique based on the assumed density profile, but it is well-known that these estimations strongly depend on the sample size i.e. the error is larger for poor systems rather than rich ones. Note that such a dependence works in favor of our exploratory analysis since the  determination of the most negative potentials (the most important in our study) are due to the richest and massive structures which, in turn, have the most accurate mass estimation. Furthermore, unless the unknown errors in the mass estimates computed by T14 are systematics (all masses are overestimated or underestimated), they should follow a Gaussian distribution. Note that  j is obtained from the summation of N V j point masses

mi (i  1,...., NV j ) within a spherical volume V j then, algebraic summation of the

errors will reduce consistently the total error on

 j . To quantify it, a Monte-Carlo simulation based on the

resampling technique has been applied (Andrae 2010) . Assuming a Gaussian error distribution with σ ~ 3% for spectroscopic redshifts and ~ 31% for cluster mass estimates, we can now randomly sample new data points to estimate the simulated  j . Repeating this resampling task 100 times, we get the distribution of the simulated data from which we can then infer the uncertainty given by the standard deviation. We find that the estimated standard error does not exceed the 7%, which ensures an accurate reconstruction of the local gravitational potential distribution. 3.5. Displaying  j The outputs of the GPM routine are a numerical file where each cluster is identified by its 3D comoving position asso-

4

ciated with the calculated  j and sorted by negative increasing value and, a 2D contour map which displays the  j distribution as a function of Equatorial coordinates integrated along the line of sight. This graphic tool enables to model certain qualitative aspect of the underlying mass distribution through appropriate choices of the number of contour lines. Fig.1 shows 10 contour lines (9 intervals) which is a reasonable compromise between the macro and micro clustering research according to our aim. Note also that the shape of contours may be inaccurate if  j varies too slowly i.e. a function that is almost flat can give irregular contours. However,  j is a rapidly varying function due to the large difference in mass among small galaxy groups and massive clusters as well as in separations which gives a regular pattern of contours.

Fig.1 Contour plot of the  j projected density surface as a function of R.A. - Dec (in degree) plot. The two deepest potential contours of  j are labeled as A and B.

From the visual inspection of the Fig.1, the distribution of  j as a functions of space positions, highlighted by 10 contour levels ranging from -0.612 to -4.347 x 106 h(km/s)2 , reveals a very large, irregular and deep potential well roughly circumscribed in the central region of the map of ~ 100 h-1Mpc diameter. The clustered structure responsible of such a potential well is a giant concentration of galaxy groups and clusters which represent the denser part of the selected sample. We have labeled A and B the locations of the DPWs defined by the deepest contour level  j ≤ -4.346 x 106 h(km/s)2 where A lies at R.A. ~ 230°, Dec. ~ 29° and z ~ .074 and B at R.A. ~ 240°, Dec. ~ 28° and z ~ .09. The map shows a giant potential well dominated by the two deepest potential well spatially separated by less than 60 h-1Mpc. They are generated by two distinct massive clumps of groups and clusters forming a binary-like system embedded in the densest part of the CBS region. In order to verify if the map of Fig. 1 is not due to graphic artifact and, to better investigate the mass distribution around A and B, we extract a subsample from our selected dataset composed of groups (n≥3) and clusters within 223° < R.A.< 245°, 4° < Dec < 33° and .069 < z