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what is the criterion for a group of galaxies to be considered a cluster?

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© ESO, 2015

1. Introduction

Superclusters are the largest prominent density enhancements in our Universe. In the framework of hierarchical structure formation, superclusters are the adjacent objects up from clusters, but unlike clusters, they are not virialised. They are generally divers every bit groups of two or more galaxy clusters above a sure spatial density enhancement (Bahcall, 1988). In this sense superclusters take more often than not been treated just as a drove of clusters. Without a articulate definition, we are left with structures with heterogeneous backdrop. Unlike clusters, superclusters have non reached a quasi-equilibrium configuration that defines their construction. Equally we observe them today, they are transition objects that largely reflect their initial weather. In contrast, clusters can be approximately described past their equilibrium configuration, as given by, for example, the NFW model (Navarro et al., 1995). Fifty-fifty disturbed and merging clusters are characterised by their deviations from this model.

For transition objects similar superclusters, such a description is not possible. One solution to this problem is to include the future evolution in the definition of the object, selecting only those superclusters that will collapse in the hereafter in a more than homogeneous class of objects. There have been attempts to explore this definition in simulations (Dünner et al., 2006). We have been exploring a similar approach observationally in our structure of an X-ray supercluster catalogue (Chon et al., 2013, 2014). We selected the superclusters from the 10-ray galaxy cluster distribution by means of a friends-of-friends (FoF) algorithm in such a way that we expect the superclusters to have their major parts gravitationally leap and to collapse in the futurity. We institute that we obtain a practiced understanding of the properties of our supercluster sample, and we can recover many of the known superclusters described in the literature in our survey volume.

This selection is institute to be slightly more conservative by not linking all the surrounding structure to the superclusters, which are linked to these objects in some other works. In other cases, such as for the Shapley supercluster, big structures are carve up into substructures. But overall the sample has adept backdrop. Thus we find our method not only physically well motivated, but also appealing in selecting the structures that appear observationally distinct and prominent. To distinguish objects selected by our definition from the general usage of the word superclusters, nosotros suggest that those systems be called "superstes-clusters", relating to the Latin word superstes, which ways survivor. Because origins, superclusters were start studied at the time when near cosmologists favoured a marginally airtight Universe in which all overdense regions would eventually plummet. It came with the full general acceptance of a re-accelerating Universe that this concept of future collapse needed to be revised. We prefer using a new term over redefining the word supercluster, out of respect for the previous studies that were done with a less strict definition.

It is our goal with this paper to explore this definition of superclusters and its consequences in some more detail. In item, we provide numerical values for the selection criteria for diverse cosmologies. And then far, nosotros accept based our selection criterion on the matter overdensity, which is motivated by our X-ray cluster observations. In theory, on large scales where the dynamics is dominated by gravity, observations of velocity fields should closely reverberate the dynamical evolution of structures and the underlying mass distribution. The velocity field also does not suffer from the bias that clusters and, to an extent, galaxies have. As a result, the dynamical information may provide a better basis for predicting the future development of the large-scale structure (Zel'dovich, 1970; Shandarin & Zeldovich, 1989; Dekel, 1994; Zaroubi et al., 1999). Therefore we also explore the selection criteria in terms of the infall velocity. In our example we await a close correspondence between the overdensity and the streaming motions, since the large-calibration structure at the calibration of superclusters is yet in the quasi-linear regime of construction formation. Nevertheless, we test the correspondence between the ii descriptions in the paper.

We lay out our concept and explain the benchmark in Sect. ii. In Sect. 3 nosotros illustrate the concept by three applications and Sect. 4 provides discussion and summary.

two. Theoretical concept

To study which primordial overdensities volition finally plummet, we approximate the overdense regions past spheres with homogeneous density. This approximation has been successfully used for many like investigations. Nosotros tin can and so model the evolution of the overdensity with respect to the expansion of the background cosmology with reference to Birkhoff's theorem. This allows the states to describe the evolution of both regions, overdensity and background, by the respective values of the local and global parameters of Hubble constant, H, affair density, Ωm , and the parameter respective to the cosmological constant, ΩΛ .

We calculate the evolution of the local and the global regions by integrating the Friedmann equation for their dynamical evolution. We use z = 500 every bit the starting point of our integration, since nosotros have found that with this starting redshift, the final results take an accuracy well below 1%. To notice the starting values, nosotros find the relevant cosmological parameters mentioned above for the groundwork cosmology at z = 500. We and so define an overdense region by increasing Ωgrand and then that we observe a collapsed region in the future, which is solved iteratively.

In comparing with the structures seen today, nosotros are interested in the post-obit properties of these marginally collapsing objects, which should be observable. What are their typical matter overdensities in the current epoch? What is the Hubble parameter that characterises their current, local dynamical evolution? These parameters will depend on the characteristics of the background cosmology. We have therefore calculated the density and expansion parameters for collapsing overdensities in a ready of relevant cosmologies. We assumed a apartment cosmology, with Ωm + ΩΛ = 1 for near models with the exception of 1 example for an open cosmology. Among the models shown are the best-fit results from the Planck (Planck Collaboration Sixteen, 2014) and WMAP (Hinshaw et al., 2013) missions.

The parameters shown in Table A.ane are the density ratio of the overdensity to the background density, R = ρ ov/ρ grand , the parameter characterising the homogeneous expansion of the overdense sphere given in form of a Hubble parameter, H ov , and the overdensity of the local region with respect to the critical density, ρ c , of the Universe, Δc = (ρ ov − ρ c) /ρ c . The results testify that while the density ratio varies with the matter density in the groundwork universe, the overdensity parameter with respect to critical density inappreciably changes. Changing the Hubble abiding does non alter the nature of the solution. The parameters, R and Δc , stay constant, while the local expansion parameter, H ov , merely scales with the Hubble parameter of the background cosmology. Therefore we evidence only one instance for the change in the parameters with the Hubble constant.

Some other interesting characterisation for superclusters are those structures that are at turn-around now. These structures have decoupled from the Hubble menstruation already and are at rest in the Eulerian reference frame then are only starting to collapse now. Hither the local Hubble parameter is zero by definition. The Einstein-de Sitter (EdS) model with the parameter, Ωm = 1.0, yields a value of Δc = (3π/ 4)2−ane ~ 4.55, which can also be calculated analytically.

2.i. Comparison of overdensity and dynamical criteria

The threshold parameters for collapse given in Table A.1 are merely valid for spherically symmetric overdensities, which are reasonable approximations for realistic overdensities. As described in the previous section, the velocity field provides a ameliorate footing for predicting the future development of a big-scale construction than does the density distribution (Dekel, 1994; Zaroubi et al., 1999). Too in observations, the density distribution of objects has to be corrected for their large-scale structure bias, which is not necessary for evaluating the velocity field. Withal, in current astronomical observations, peculiar velocity data are only available for the very local region of the Universe, and for most other applications, nosotros only accept estimates of overdensity. Therefore it is important to exam how well our criteria that are based on the overdensity argument correspond to those on the velocity information for realistic supercluster morphologies.

For this reason we used the cosmological N -torso simulations (Springel et al., 2005) to compare the radius within which the structure is predicted to collapse based on the overdensity, r Δ , to that of the infall velocity, r v for 570 superstes-clusters. For the details of the construction of the superclusters in simulations, we refer the readers to Chon et al. (2014). The value of r Δ was taken at the radius where the density ratio reaches the threshold value for plummet, and r v is defined as the radius where the required infall velocity is reached. The latter radius marks the largest distance within which, on average, the infall velocities of all haloes are discrete from the Hubble flow with the local expansion parameter prescribed in the previous section. The very close correspondence between the two predictions are shown in Fig. A.1.

We but have five pathological cases, where the collapse overdensity is simply reached once away from the centre, while the infall blueprint never reaches the required threshold. These are the cases where the virtually massive structures are concentrated not at the eye of the supercluster, but near the radius, r five , and beyond. In these cases the velocity design is very different from a smoothen radial infall, and the supercluster is most probably fragmented into two or more than massive substructures near the supercluster boundary in the future. We find it as a very strong encouragement for our approach, where the two alternative criteria commonly give very similar results. The good correspondence is likewise a confirmation that structure development on the scale of superclusters is withal in the quasi-linear regime.

3. Applications

In this section we illustrate the implications of our superstes-cluster definition with respect to some of the known superclusters. The homogeneous sphere approximation but gives a rough approximate of the plummet situation. More detailed solutions have to take the morphology and substructure of the systems into account, which has actually been done for some of the cases below. Both criteria listed in Table A.ane, the overdensity and the peculiar infall velocity, can exist used for such a beginning approximate. The aim of the post-obit discussion is therefore only an approximate application of the suggested criteria for illustration. We employ parameters for the cosmological model with Ωone thousand = 0.3 and H 0 = 70 km s -one  Mpc -1 for the considerations below.

three.ane. Local supercluster and Virgo infall

The Local supercluster is a high concentration of matter roughly centred on the Virgo cluster, which includes the Milky Way and the Local Group in the outskirts. It was first described by de Vaucouleurs (1953, 1958). Detailed studies constitute the system to exist mostly concentrated in an elongated filament that extends about 40 h -one Mpc, e.g. Tully & Fisher (1978), Karachentsev & Makarov (1996), Lahav et al. (2000), Klypin et al. (2003). The Local Group is at a distance of about xvi to 17 Mpc from Virgo, and it shows a peculiar infall velocity towards the Virgo cluster of near 220 ± xxx km s -1 (Sandage et al., 2010) or ~ 250 km s -ane (Klypin et al., 2003).

Applying the peculiar velocity criterion for future plummet, we find the post-obit. The necessary peculiar infall velocity at a sure distance from the middle of the supercluster is given by the difference of the local to the background Hubble parameters multiplied by the altitude, in our example d × 49.5 km south -1  Mpc -1 . Thus at the altitude of the Local Group, a peculiar infall velocity of almost 800 km s -one would exist required. Therefore the Local Group will recede from the Local supercluster in the afar future. This has been concluded in several previous works, and it has been shown, for example, by N -body simulations by Nagamine & Loeb (2003) based on a numerical constraint reconstruction of the local Universe by Mathis et al. (2002). Inspecting the velocity menstruum patterns of the Local supercluster shown in Klypin et al. (2003); Tully & Mohayaee (2004), and Courtois & Tully (2012), we find that only inside 10 Mpc infall velocities up to 500 km s -1 seem to occur, reaching the lower limit for a collapse. Nosotros can also use the gauge of the infall velocity profile from the constraint reconstruction of the Local supercluster by Klypin et al. (2003) to discover the outermost collapsing shell of the supercluster. They judge the mean infall pattern by v = 145 (thirteen h -1 Mpc /r)ane/two km due south -one . With this prescription we observe that just the regions inside about 5.5 Mpc will collapse in the time to come.

We can besides utilize the spherical collapse model to obtain a mass estimate of the Virgo cluster and its surroundings from the peculiar velocity of the Milky way towards the Virgo cluster of ~250 km s -1 . When assuming a Virgo distance of 16 Mpc (Tonry, 1991), the infall peculiar velocity corresponds to a local Hubble parameter of ~54.five km south -1  Mpc -i for a homogeneous sphere with its centre at the Virgo distance. An integration of the Friedmann equations for our fiducial cosmology infers a ratio of the local overdensity to the cosmic mean of nigh 2.6. This translates into a mass of Virgo and surroundings inside a radius of xvi Mpc of 1.8 × tenfifteen M ⊙ . Tully & Mohayaee (2004) get a mass of one.2 × 1015 M ⊙ from fitting the infall pattern, which probably gives virtually weight to the measurement at a slightly smaller radius. Klypin et al. (2003) obtain a mass of ~ x15 M ⊙ for Virgo and the fundamental filament of the Local supercluster from a constrained reconstruction of the Local supercluster. Karachentsev et al. (2014) studied the infall blueprint of tracers with good distance estimates from the HST observations, and find a mass of 8 × 10xiv M ⊙ inside a radius of 7.two Mpc which they estimate to be the plow-around radius at the electric current epoch. The fair agreement of the different methods shows that the spherical infall models provide an splendid get-go estimate of the fate of such a supercluster.

3.2. Laniakea

Based on the compilation of peculiar velocities of galaxies out to z = 0.one in Tully et al. (2013, 2014) presented a new supercluster, which they call Laniakea. We refer the readers to Tully et al. (2013) for the detailed methodology, simply in essence they rely on the absolute distance measures estimated from half-dozen methods including the Tully-Fisher relation to summate peculiar velocities of galaxies within 400 h -one Mpc, where the coverage is sparse beyond 100 h -1 Mpc. In total they written report altitude measures for more than 8000 galaxies in the whole survey region. To reconstruct the underlying velocity field, they used the Wiener filter algorithm (Zaroubi et al., 1995). They conclude from the reconstructed velocity field that in that location is a coherent flow within a sphere of radius, 80 h -i Mpc, which contains an estimated mass of 1017 h -1 Thousand ⊙ , and they define this region as a supercluster. Their mass guess implies that the ratio of Laniakea density to the mean density is about 0.94. Thus Laniakea does non even constitute a region with a significant overdensity and does not fulfil our criteria in Table A.1 for a supercluster. As a result, Laniakea is far from existence a jump system, and as a whole, it will disperse in the future, while only several dense regions will plummet within.

Nosotros tin can also look at Laniakea from some other point of view by applying the peculiar velocity statement. If Laniakea was a bound structure with a radius of lxxx h -1 Mpc, nosotros would estimate the required infall velocity at the boundary to be about 5700 km s -i based on the local Hubble parameter gauge given in Table A.1 for time to come collapse. However, typical peculiar velocities in their catalogue hardly exceed 500−700 km due south -one in the survey. This emphasises again that Laniakea as a whole is not a bound structure.

We too note that their value of the Hubble abiding obtained past minimising the velocity monopole is 75.2 ± iii.0 km south -i  Mpc -1 . At that place are also other local measurements of H 0 , notably by Riess et al. (2011) based on 253 Type Ia supernovae data from the HST and past Freedman et al. (2012) based on an additional mid-infrared observation of Cepheids. The former gives H 0 of 74.viii ± 3.1, and the latter 74.3 ± two.one km s -i  Mpc -one , both with less than 3% uncertainty. Inside their respective errors, the 3 measurements concord, which is also pointed out by Tully et al. (2014). It is interesting to compare these values to H 0 measured by the cosmic microwave background (CMB) experiments, WMAP, and Planck, where H 0 is more sensitive to very large scales. The best-fit H 0 values are 70.0 ± 2.2 (Hinshaw et al., 2013) and 68.0 ± 1.iv km s -1  Mpc -ane (Planck Collaboration 16, 2014), so local measurements of H 0 are always greater than those from the CMB measurements, although they would agree within their respective electric current 1 σ uncertainty. With this information technology is interesting to note that Turner et al. (1992) pointed out that a locally underdense Universe would yield a Hubble constant larger than the cosmic mean. In reference to our work (Böhringer et al., 2015), nosotros find a local region within a radius of 170 h -ane Mpc in the southern sky, which is nether-dense by ≈xx% with respect to the mean density resulting from the cluster number density that is under-dumbo by twoscore% with a cluster bias of about two. Since the REFLEX survey has a high completeness up to a redshift of z ~ 0.3, we take a good handle for tracing the thing density out to a very large radius, containing the volume of Laniakea. The amplitude of the local under-density traced by REFLEX II of ≈twenty%, which implies that the locally measured H 0 would be iii ± i.v% more than for the catholic one. Information technology therefore indicates that the H 0 value obtained by Tully et al. (2014) is consistent with the example where H 0 is measured in an under-dense region.

3.3. Shapley supercluster

The Shapley supercluster is known to have the highest concentration of galaxies in the nearby Universe, at a redshift around 0.046 (Scaramella et al., 1989; Raychaudhury, 1989). X-ray emission in the key region of Shapley was showtime mapped by Kull & Böhringer (1999), and information technology even traces the intra-cluster gas. Nosotros also study three X-ray superclusters in the area of the Shapley supercluster, constructed with a cluster overdensity parameter, f = 10, from the REFLEX Ii cluster catalogue (Chon et al., 2013). Here, f is related to the density ratio R past, f = (R − 1)b CL + one where b CL is a cluster bias factor. Even with a generous option of f = 10, this already indicates that Shapley will be broken into smaller concentrations of thing, rather than collapsing into ane big object. To get deeper insight, we calculated density ratios with data taken from the literature and from our X-ray work described below.

Reisenegger et al. (2000) used velocity caustics from 3000 galaxies to define a central region of Shapley and estimated the upper bound mass in a spherical radius of 8 h -1 Mpc to be 1.iii × 1016 h -1 1000 ⊙ . In this example the density ratio, R, is 20.7. Ragone et al. (2006) established a mass function of about 180 systems with redshifts in the Shapley region and requite a lower mass limit of one.i × 10sixteen h -1 G ⊙ within the same volume as above. In this instance, R is nigh 17.five. Both results indicate that the cardinal eight h -1 Mpc of the Shapley supercluster is probable to collapse into a more massive arrangement. In fact, the density ratios are higher than required for a turn-around, which now implies that the very fundamental region of Shapley supercluster has already started to collapse. To evaluate the total mass of Shapley with the REFLEX Ii clusters, we likewise considered the total cluster mass as a function of a radius for the same volume. Nosotros converted the full cluster mass to the full supercluster mass by adopting a scaling relation establish with cosmological N -trunk simulations in Chon et al. (2014). We find that the required density ratio for collapse is satisfied out to about 12.4 h -1 Mpc. The derived total mass of Shapley inside this distance is one.34 × 10sixteen h -1 Chiliad ⊙ . In fact, the turn-around density ratio is already reached at 11.1 h -1 Mpc, which is consistent with the density ratios estimated from previous work. We too note that the filamentary Ten-ray emission shown in Fig. 2 of Kull & Böhringer (1999) coincides with the cadre of an already collapsing office of Shapley. The estimates of the density ratios of Shapley therefore provide a consistent pic that the central eleven h -one Mpc is undergoing a collapse meaning that only a central part of Shapley supercluster volition class a supercluster in the future even if the outskirts of Shapley are likewise rich in clusters.

4. Discussion and summary

In this paper we have emphasised the need for a clearer, more physically motivated definition of superclusters. We have shown that defining superstes-clusters as those objects that volition collapse in the time to come leads to a conservative selection criterion that does not accept all objects that accept been called superclusters in the literature, but it leads to a more homogeneous class of objects as seen in our previous piece of work on supercluster construction.

Our superstes-cluster definition is also interesting for some other reason. With this definition, we are selecting the most massive virialised objects that will form in the future. In Fig. A.1 nosotros tin, for example, place the near massive structure in the Millennium simulation that will form a virialised dark affair halo in the hereafter with the uppermost point in the plot. It has a collapse radius, r v of 17.three h -one Mpc and a respective mass of ane.94 × 1016 M ⊙ . This tin be compared to the collapsing fraction of the Shapley supercluster estimated in Sect. 3.3, which is quite comparable. Shapley is the highest mass concentration found in the nearby Universe in a volume that is quite similar to that of the Millennium simulation.

We observe it very encouraging that like mass estimates are obtained for the nigh massive structure in the ascertainment and and in the simulation with our criteria for selecting superclusters. We have been applying this criterion in the construction of superstes-clusters using a FoF algorithm with a linking length tuned to select overdense regions that are close to collapse in the hereafter. In our previous study (Chon et al., 2014) we found a close correspondence of the results of this method with the desired overdensity. Information technology is, all the same, not i-to-ane, and in particular, nosotros find outliers for very large supercluster sizes, which are selected by the FoF algorithm but do not reach the overdensity threshold. In these extreme cases, superclusters appear as rather elongated filements, and the region that is bound to collapse is overestimated by the FoF-based method.

Nosotros studied the application of our definition to the Local supercluster and Shapley supercluster, likewise as Laniakea. We detect that the commencement two superclusters will plummet in the cardinal regions while their outskirts are not gravitationally leap. For Laniakea, nosotros find that this structure does non plant a region with a significant overdensity and thus it cannot collapse as a whole. While the velocity construction described by Tully et al. (2014) highlights an impressively large structure in the local Universe, we feel that its labelling as a supercluster is non advisable given that the region is non even overdense. It is interesting that Tully et al. (2014) and other surveys find a local Hubble parameter in this region that tends to exist higher than the Hubble parameter measured on a more global scale (Planck Collaboration XVI, 2014; Hinshaw et al., 2013). This can be taken as an indication that this region in the local Universe may be rather under-dumbo. This conclusion is supported past our recent studies with Ten-ray galaxy clusters and studies of the galaxy distribution (run across Böhringer et al. 2015; Whitbourn & Shanks 2014).

Appendix A

thumbnail Fig. A.i

Comparison of the two radii that define the collapsing region of a supercluster. r Δ is determined past the required density ratio criteria, and r v by the infall velocity criteria. The dashed line indicates the one-to-one line.

Table A.1

Present-epoch parameters characterising marginally collapsing objects in comparison to those at turn-around for various cosmological models. See text for an explanation of the listed parameters.

Acknowledgments

We give thanks the referee for the useful comments. H.B. acknowledges back up from the DfG Transregio Plan TR33 and the DFG cluster of excellence "Origin and Construction of the Universe" (www.universe-cluster.de). G.C. acknowledges the support from the Deutsches Zentrum für Luft- und Raumfahrt (DLR) with the programme 50 OR 1403. S.Z. would like to acknowledge the support of Kingdom of the netherlands Organisation for Scientific Enquiry (NWO) VICI grant and Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence.

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All Tables

Table A.1

Present-epoch parameters characterising marginally collapsing objects in comparing to those at turn-effectually for various cosmological models. See text for an explanation of the listed parameters.

All Figures

thumbnail Fig. A.1

Comparison of the two radii that define the collapsing region of a supercluster. r Δ is determined by the required density ratio criteria, and r five past the infall velocity criteria. The dashed line indicates the one-to-one line.

In the text

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