Superclusters are the largest prominent density enhancements in our Universe. In the framework of hierarchical structure formation, superclusters are the next objects up from clusters, but unlike clusters, they are not virialised. They are generally defined as groups of two or more galaxy clusters above a certain spatial density enhancement Bahcall, In this sense superclusters have mostly been treated just as a collection of clusters.
Without a clear definition, we are left with structures with heterogeneous properties. Unlike clusters, superclusters have not reached a quasi-equilibrium configuration that defines their structure.
As we observe them today, they are transition objects that largely reflect their initial conditions. In contrast, clusters can be approximately described by their equilibrium configuration, as given by, for example, the NFW model Navarro et al. Even disturbed and merging clusters are characterised by their deviations from this model.
For transition objects like 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 future in a more homogeneous class of objects.
We have been exploring a similar approach observationally in our construction of an X-ray supercluster catalogue Chon et al. We selected the superclusters from the X-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 bound and to collapse in the future.
We found that we obtain a good 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 found 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, large structures are split into substructures.
But overall the sample has good properties. Thus we find our method not only physically well motivated, but also appealing in selecting the structures that appear observationally distinct and prominent. Considering origins, superclusters were first studied at the time when most cosmologists favoured a marginally closed Universe in which all overdense regions would eventually collapse.
It came with the 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 particular, we provide numerical values for the selection criteria for various cosmologies.
So far, we have 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 reflect 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. Therefore we also explore the selection criteria in terms of the infall velocity. In our case we expect a close correspondence between the overdensity and the streaming motions, since the large-scale structure at the scale of superclusters is still in the quasi-linear regime of structure formation. Nevertheless, we test the correspondence between the two descriptions in the paper.
We lay out our concept and explain the criterion in Sect. In Sect. To study which primordial overdensities will finally collapse, we approximate the overdense regions by spheres with homogeneous density. This approximation has been successfully used for many similar investigations. We calculate the evolution of the local and the global regions by integrating the Friedmann equation for their dynamical evolution.
In comparison with the structures seen today, we are interested in the following 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 set of relevant cosmologies. The parameters shown in Table A. The results show that while the density ratio varies with the matter density in the background universe, the overdensity parameter with respect to critical density hardly changes.
Changing the Hubble constant does not alter the nature of the solution. Therefore we show only one example for the change in the parameters with the Hubble constant. Another interesting characterisation for superclusters are those structures that are at turn-around now. These structures have decoupled from the Hubble flow already and are at rest in the Eulerian reference frame so are just starting to collapse now.
Here the local Hubble parameter is zero by definition. The threshold parameters for collapse given in Table A. As described in the previous section, the velocity field provides a better basis for predicting the future evolution of a large-scale structure than does the density distribution Dekel, ; Zaroubi et al.
Also 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. However, in current astronomical observations, peculiar velocity data are only available for the very local region of the Universe, and for most other applications, we only have estimates of overdensity.
Therefore it is important to test 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 -body simulations Springel et al.
For the details of the construction of the superclusters in simulations, we refer the readers to Chon et al. The latter radius marks the largest distance within which, on average, the infall velocities of all haloes are detached 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. We only have five pathological cases, where the collapse overdensity is only reached once away from the centre, while the infall pattern never reaches the required threshold. These are the cases where the most massive structures are concentrated not at the centre of the supercluster, but near the radius, r v , and beyond. In these cases the velocity pattern is very different from a smooth radial infall, and the supercluster is most probably fragmented into two or more 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 usually give very similar results. The good correspondence is also a confirmation that structure evolution on the scale of superclusters is still in the quasi-linear regime. In this section we illustrate the implications of our superstes-cluster definition with respect to some of the known superclusters. The homogeneous sphere approximation only gives a rough estimate of the collapse 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. The aim of the following discussion is therefore only an approximate application of the suggested criteria for illustration.
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 , Detailed studies found the system to be mostly concentrated in an elongated filament that extends about 40 h -1 Mpc, e. Applying the peculiar velocity criterion for future collapse, we find the following.
Thus at the distance of the Local Group, a peculiar infall velocity of about km s -1 would be required. Therefore the Local Group will recede from the Local supercluster in the distant future. Inspecting the velocity flow patterns of the Local supercluster shown in Klypin et al.
We can also use the estimate of the infall velocity profile from the constraint reconstruction of the Local supercluster by Klypin et al. With this prescription we find that only the regions inside about 5. An integration of the Friedmann equations for our fiducial cosmology infers a ratio of the local overdensity to the cosmic mean of about 2.
This translates into a mass of Virgo and surroundings inside a radius of 16 Mpc of 1. Klypin et al. Karachentsev et al. The fair agreement of the different methods shows that the spherical infall models provide an excellent first estimate of the fate of such a supercluster. We refer the readers to Tully et al. In total they report distance measures for more than galaxies in the whole survey region. To reconstruct the underlying velocity field, they used the Wiener filter algorithm Zaroubi et al.
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