Galaxy Filaments As Pearl Necklaces⋆

A&A 572, A8 (2014) Astronomy DOI: 10.1051/0004-6361/201424418 & c ESO 2014 Astrophysics Galaxy filaments as pearl necklaces? E. Tempel1;2, R. Kipper1;3, E. Saar1;4, M. Bussov1;5, A. Hektor2, and J. Pelt1 1 Tartu Observatory, Observatooriumi 1, 61602 Tõravere, Estonia e-mail: [email protected] 2 National Institute of Chemical Physics and Biophysics, Rävala pst 10, 10143 Tallinn, Estonia 3 Institute of Physics, University of Tartu, 51010 Tartu, Estonia 4 Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn, Estonia 5 Institute of Mathematical Statistics, University of Tartu, 50409 Tartu, Estonia Received 17 June 2014 / Accepted 19 September 2014 ABSTRACT Context. Galaxies in the Universe form chains (filaments) that connect groups and clusters of galaxies. The filamentary network includes nearly half of the galaxies and is visually the most striking feature in cosmological maps. Aims. We study the distribution of galaxies along the filamentary network, trying to find specific patterns and regularities. Methods. Galaxy filaments are defined by the Bisous model, a marked point process with interactions. We use the two-point correlation function and the Rayleigh Z-squared statistic to study how galaxies and galaxy groups are distributed along the filaments. Results. We show that galaxies and groups are not uniformly distributed along filaments, but tend to form a regular pattern. The characteristic length of the pattern is around 7 h−1 Mpc. A slightly smaller characteristic length 4 h−1 Mpc can also be found, using the Z-squared statistic. Conclusions. We find that galaxy filaments in the Universe are like pearl necklaces, where the pearls are galaxy groups distributed more or less regularly along the filaments. We propose that this well-defined characteristic scale could be used to test various cosmological models and to probe environmental effects on the formation and evolution of galaxies. Key words. methods: numerical – methods: observational – large-scale structure of Universe 1. Introduction that filaments extracted from the spatial distribution of galaxies/haloes are also dynamical structures that are well connected Many cosmological probes have been developed and used to with the underlying velocity field. Galaxy filaments that connect estimate the parameters of the cosmological models describ- groups and clusters of galaxies also affect the evolution of galax- ing our Universe. Most of them rely on some aspects of the ies (e.g. Tempel & Libeskind 2013; Tempel et al. 2013; Zhang large-scale structure. The most common probe used to quantify et al. 2013) and the distribution of satellites around galaxies galaxy clustering is the two-point correlation function which was (Guo et al. 2014b). first used decades ago (Davis & Geller 1976; Groth & Peebles In this paper we study the distribution of galaxies along 1977; Davis et al. 1988; Hamilton 1988; White et al. 1988; galaxy filaments to search for regularities in galaxy and group Boerner et al. 1989; Einasto 1991). Some recent examples in- distributions. As was shown decades ago (e.g. Jõeveer et al. clude Connolly et al.(2002), Zehavi et al.(2005), Contreras 1978; Einasto et al. 1980), this clustering pattern is present in et al.(2013), de Simoni et al.(2013), Wang et al.(2013), and some filaments. In the current study, we use the two-point cor- the references in these papers. Other examples of cosmological relation function (see Peebles 1980) and the Rayleigh Z-squared probes are the three-point correlation functions (e.g. McBride statistics (see Buccheri 1992) to look for the regularity in the et al. 2011; Marín et al. 2013; Guo et al. 2014a) and the galaxy distribution. We suggest that the regularities we find in power spectrum analysis (Hütsi 2006, 2010; Blake et al. 2010; the galaxy distribution could be used as cosmological probes for Balaguera-Antolínez et al. 2011). dark energy and dark matter, the mysterious components in the It is well known that galaxy filaments are visually the most dark energy dominated cold dark matter (ΛCDM) cosmological dominant structures in the galaxy distribution, being part of the models. so-called cosmic network (Jõeveer et al. 1978; Bond et al. 1996). Throughout this paper we assume the Wilkinson Microwave Presumably, nearly half (∼40%) of the galaxies (or mass in sim- Anisotropy Probe (WMAP) cosmology: the Hubble constant −1 −1 ulations) are located in filaments. This number is based on mor- H0 = 100 h km s Mpc , with h = 0:697, the matter density phological or dynamical classification of the cosmic web (e.g. Ωm = 0:27 and the dark energy density ΩΛ = 0:73 (Komatsu Jasche et al. 2010; Tempel et al. 2014b; Cautun et al. 2014). et al. 2011). Properties of the three-point correlation function also indicate that galaxies tend to populate filamentary structures (Guo et al. 2. Data and methods 2014a) and, indeed, filaments have been found between galaxy clusters (e.g. Dietrich et al. 2012). Tempel et al.(2014a) show 2.1. Galaxy and group samples for the SDSS data The present work is based on the Sloan Digital Sky Survey ? Appendices are available in electronic form at (SDSS, York et al. 2000) data release 10 (DR10; Ahn et al. http://www.aanda.org 2014). We use the galaxy and group samples as compiled in Article published by EDP Sciences A8, page 1 of8 A&A 572, A8 (2014) Tempel et al.(2014c) that cover the main contiguous area of where the Bisous model was applied to the SDSS DR8 (Aihara the survey (the Legacy Survey, approximately 17.5% from the et al. 2011) data. Since the datasets in the SDSS DR8 and DR10 full sky). The flux-limited catalogue extends to the redshift 0.2 are basically the same, the extracted filaments in DR10 are statis- (574 h−1 Mpc) and includes 588 193 galaxies and 82 458 groups tically the same as those presented in Tempel et al.(2014b). The with two or more members. assumed scale (radius) for the extracted filaments is 0.5 h−1 Mpc. In Tempel et al.(2014c) the redshift-space distortions, the Because the survey is flux-limited, the sample is very diluted so-called finger-of-god (FoG) effects, are suppressed using the farther away. Hence, we were only able to detect filaments in rms sizes of galaxy groups in the plane of the sky and their rms this scale up to the redshift 0.15 (≈450 h−1 Mpc). The longest radial velocities as described in Liivamägi et al.(2012). We cal- filaments in our sample are up to 70 h−1 Mpc long. culate the new radial distances for galaxies in groups in order The filaments are extracted from a flux-limited galaxy sam- to make the galaxy distribution in groups approximately spher- ple, hence, the completeness of extracted filaments decreases ical. We note that such a compression will remove the artificial with distance. In Tempel et al.(2014b) we showed that the line-of-sight filament-like structures as shown in Tempel et al. volume filling fraction of filaments is roughly constant with (2012). distance if filaments longer than 15 h−1 Mpc are considered. Therefore, in the current study we only used filaments longer than this limit. In addition, this choice is justified, since longer 2.2. Bisous model: extracting filaments from galaxy filaments allow us to study the distribution of galaxies along the distribution filaments, which is the purpose of this paper. The remaining in- The detection of filaments is performed by applying an ob- completeness of filaments in our sample is not a problem, be- ject/marked point process with interactions (the Bisous process; cause we analysed single filaments. The filaments we used are Stoica et al. 2005) to the distribution of galaxies. This algorithm the strongest filaments (or segments of filaments) in the sample. provides a quantitative classification which agrees with the vi- To suppress the flux-limited sample effect, we volume-limit sual impression of the cosmic web and is based on a robust the galaxy content for single filaments. To this end, we find for and well-defined mathematical scheme. A detailed description every filament the maximum distance (from the observer) of its of the Bisous model is given in Stoica et al.(2007, 2010) and galaxies and the corresponding magnitude limit and use only Tempel et al.(2014b); for convenience, a brief description is galaxies brighter than this value. Since the majority of filaments given below. extend over a relatively narrow distance interval (always nar- rower than the length of the filament), the number of excluded The marked point process we propose for filament detection galaxies in every filament is small. is different from the ones already used in cosmology. In fact, To study the galaxy spacing along the filaments, we project we do not model galaxies, but the structure outlined by galaxy every galaxy to the filament spine. Hence, the distance is mea- positions. sured along the filament spine. Figure1 illustrates extracted This model approximates the filamentary network by a ran- galaxy filaments and their spines in the field of galaxies. dom configuration of small segments (thin cylinders). We as- For our analysis, we use only filaments that contain at least sume that locally galaxies may be grouped together inside a ten galaxies. When studying galaxy groups, we use only fila- rather small cylinder, and such cylinders may combine to form ments where the number of groups per filament is at least five. a filament if neighbouring cylinders are aligned in similar direc- We use the groups from the catalogue by Tempel et al.(2014c). tions. This approach has the advantage that it uses only posi- The upper panel in Fig.2 shows the cumulative filament length tions of galaxies and does not require any additional smoothing and the cumulative number of galaxies in filaments as a function to create a continuous density field.

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