Clusters and Superclusters in the Las Campanas Redshift Surv

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a r X i v :a s t r o -p h /0304546v 1 30 A p r 2003Astronomy &Astrophysics manuscript no.lcrs10s

February 2,2008

(DOI:will be inserted by hand later)Clusters and Superclusters in the Las Campanas Redshift Survey J.Einasto 1,M.Einasto 1,G.H¨u tsi 1,E.Saar 1,D.L.Tucker 2,E.Tago 1,V.M¨u ller 3,P.Hein¨a m¨a ki 1,4,S.S.Allam 2,5

Tartu Observatory,EE-61602T?o ravere,Estonia 2

Fermi National Accelerator Laboratory,MS 127,PO Box 500,Batavia,IL 60510,USA 3

Astrophysical Institute Potsdam,An der Sternwarte 16,D-14482Potsdam,Germany 4

Tuorla Observatory,V¨a is¨a l¨a ntie 20,Piikki¨o ,Finland 5

Dept.of Astronomy,New Mexico State University,Las Cruces,NM 88003-8001,USA Received 2003/Accepted ...Abstract.We use a 2-dimensional high-resolution density ?eld of galaxies of the Las Campanas Redshift Survey (LCRS)with a smoothing length 0.8h ?1Mpc to extract clusters and groups of galaxies,and a low-resolution ?eld with a smoothing length 10h ?1Mpc to ?nd superclusters of galaxies.We study the properties of these density ?eld (DF)clusters and superclusters,and compare the properties of the DF-clusters and superclusters with those of Abell clusters and superclusters and LCRS groups.We show that among the cluster samples studied the DF-cluster sample best describes the large-scale distribution of matter and the ?ne structure of superclusters.We calculate the DF-cluster luminosity function and ?nd that clusters in high-density environments are about ten times more luminous than those in low-density environments.We show that the DF-superclusters that contain Abell clusters are richer and more luminous than the DF-superclusters without Abell clusters.The distribution of DF-clusters and superclusters shows the hierarchy of systems in the universe.Key words.cosmology:observations –cosmology:large-scale structure of the Universe;clusters of galaxies 1.Introduction The basic tasks of observational cosmology are to describe the distribution of various objects in the universe and to understand the formation and evolution of these struc-tures.One means for describing the structure is the den-sity ?eld method.In this method the distribution of dis-crete objects (galaxies and clusters of galaxies)is substi-

tuted by the density ?eld calculated by smoothing the dis-

crete distribution.This method has the advantage that it

is easy to take into account various selection e?ects which

distort the distribution of inpidual objects.The density

?eld can be applied to calculate the gravitational ?eld as

done in the pioneering study by Davis &Huchra (1982),

to investigate topological properties of the universe (Gott

et al.1986),and to map the universe and to ?nd super-

clusters and voids (Saunders et al.1991,Marinoni et al.

1999,Hoyle et al.2002,Basilakos et al.2001).

In this paper we use the density ?eld of galaxies to ?nd

clusters and superclusters of galaxies.This method was in-

troduced by Einasto et al.(2003b,hereafter Paper I)and

applied to the Early Data Release of the Sloan Digital Sky

Survey.Here we apply the density ?eld method to the Las

Campanas Redshift Survey (LCRS).The LCRS is essen-

2J.Einasto et al.:LCRS clusters and superclusters

al2000,hereafter TUC),and of Abell clusters and of su-perclusters traced by Abell clusters(Abell superclusters) (Einasto et al.2001,hereafter E01).This study is car-ried out in the framework of preparation for the analysis of results of the Planck mission to observe the Cosmic Microwave Background radiation.

In Sect.2we give an overview of observational data. In Sect.3we identify the DF-clusters,discuss selec-tion e?ects in the LCRS,analyse properties of DF-clusters,and derive the luminosity function of DF-clusters. Similarly,in Sect.4we compose a catalogue of DF-superclusters and analyse these systems as tracers of the structure of the universe.Sect.5brings our conclusions. In Tables4and5we list the DF-superclusters and their identi?cation with conventional superclusters.The three-dimensional distribution of clusters and superclusters,as well as colour versions of the?gures with density?eld maps,are available on the Tartu Observatory website (www.aai.ee/～maret/cosmoweb.htm).

2.Observational data

2.1.LCRS galaxies and loose groups

The LCRS(Shectman et al.1996)is an optically selected galaxy redshift survey that extends to a redshift of0.2 and covers six1.5×80degree slices containing a total of23,697galaxies with redshifts.Three slices are located in the Northern Galactic cap centred at the declinations δ=?3?,?6?,?12?,and three slices are located in the Southern Galactic cap centred at the declinationsδ=?39?,?42?,?45?.The thickness of the survey slices at the mean redshift of the survey(z≈0.1)is approximately

7.5h?1Mpc.Throughout this paper,the Hubble constant

h is expressed in units of100km s?1Mpc?1.

The spectroscopy of the survey was carried out via a50or a112?bre multi-object spectrograph;therefore the selection criteria varied from?eld to?eld.The nomi-nal apparent magnitude limits for the50?bre?elds were m1=16.0≤R≤m2=17.3,and for the112?bre?elds m1=15≤R≤m2=17.7.The general properties of the 50?bre and the112?bre groups agree well with group properties found from other surveys.We note that in the case of one slice,δ=?6?,all observations were carried out with the50-?bre spectrograph only.On the basis of the LCRS galaxies TUC extracted a catalogue of loose groups of galaxies;a group had to contain at least3galaxies to be included in the catalogue(for more details on the com-pilation of the group catalogue see TUC).Data on the LCRS slices are given in Table1:RA–the mean right ascension of the slice,?RA–the width of the slice(both in degrees),N gal–the number of galaxies,N DF–the number of DF-clusters,N LC–the number of loose groups by TUC,N A–the number of Abell clusters,and N scl–the number of DF-superclusters.Table1.Data on LCRS galaxies,clusters and superclus-ters

?3?191.481.0406512032891819?6?189.877.923239521471317?12?191.481.1448212662761115?39?12.1113.8392212852562818?42?12.2112.5415812162651914?45?12.3114.1375311822632017

J.Einasto et al.:LCRS clusters and superclusters

3 Fig.1.The left panel shows the absolute magnitudes of galaxies,as well as magnitudes of the luminosity window, M1and M2,for the?3?slice.The right panel gives the luminosities(weights)of galaxies as a function of distance for the same slice.In the left panel black symbols mark the absolute magnitudes of observed galaxies,the upper and lower strips with grey symbols show the absolute magnitude limit M1and M2.In the right panel grey symbols show the observed luminosities of galaxies,black symbols are for total luminosities corrected for the unobserved part of the luminosity range.

sity enhancement is actually a halo,consisting of one or

more bright galaxies in the visibility window,and galax-

ies fainter or brighter than seen in the visibility window.

In calculating the total luminosity of the DF-cluster we

assume that luminosities of galaxies are distributed ac-

cording to the Schechter(1976)luminosity function.The

estimated total luminosity per a visible galaxy is

L tot=L obs W L,(1)

where L obs=L⊙100.4×(M⊙?M)is the luminosity of the

visible galaxy of absolute magnitude M,and

W L= ∞0Lφ(L)dL

N50?(20.33±0.12)?(0.40±0.18)

S50?(20.64±0.18)?(0.74±0.21)

N112?(20.40±0.05)?(0.76±0.07)

S112?(20.40±0.05)?(0.70±0.07)

NS112?(20.38±0.04)?(0.70±0.04)

TOTAL?(20.40±0.03)?(0.69±0.04)

4J.Einasto et al.:LCRS clusters and superclusters

Fig.2.The luminosity density?eld of the LCRS slices smoothed with aσ=0.8h?1Mpc Gaussian?lter.Open circles denote positions of Abell clusters located within boundaries of slices.In some cases an Abell cluster consists of several subclusters,in these cases only rich subclusters are marked.The observer is located at the coordinates(x,y)=(0,0).

resolution density?eld found using a10h?1Mpc smooth-ing length.We used this?eld to?nd DF-superclusters and to de?ne the global density,characterising the en-vironment of DF-clusters(see Sect.3.3below).The high-

J.Einasto et al.:LCRS clusters and superclusters

5 Fig.3.The density?eld of the LCRS slices smoothed with aσ=10h?1Mpc Gaussian?lter.Panels are located as in Fig.2.

resolution maps show the density distribution in wedges of increasing thickness as the distance from the observer in-creases.The low-resolution density maps are converted to sheets of constant thickness by piding the surface den-sity to the thickness of the sheet at particular distance from the observer.

To identify DF-clusters,every cell of the?eld was ex-amined to see whether its density exceeds the density of all neighbouring cells.If the density of the cell was higher

6J.Einasto et al.:LCRS clusters and superclusters

Fig.4.The luminosity density of the LCRS slices as a function of distance.The left panel shows Northern slices,the right panel shows Southern slices.010*******

400500d [h ?1 Mpc]0123

D L

?03

?06

?120100200300400500

d [h ?1 Mpc]01

3D L ?39?42?45

than that of all its neighbours,then the cell was consid-

ered to be the centre of a DF-cluster.The total luminosity

of the DF-cluster was determined by summing luminosity

densities of cells within a box of size ?2≤?x ≤2,and

?2≤?y ≤2in cell size units.This range corresponds

to the smoothing length 0.8h ?1Mpc which distributes

the luminosity of every galaxy between the central and 24

neighbouring cells.The luminosities were calculated in so-

lar luminosity units.At large distances the LCRS sample

is rather diluted,and there are only a few galaxies in the

nearby region of the LCRS slices.Thus we included into

our catalogue of DF-clusters only objects within the dis-

tance interval 100...450h ?1Mpc.The DF-cluster sample

has only a few low-luminosity clusters;thus we included in

our catalogue only clusters having total luminosities over

L 0≥0.5×1010L ⊙.The number of DF-clusters found in

the inpidual slices is given in Table 1.

According to the general cosmological principle the

mean density of luminous matter (smoothed over super-

clusters and voids)should be the same everywhere.A weak

dependence on distance may be due to evolutionary ef-

fects:luminosities of non-interacting galaxies decrease as

stars age.If we ignore this e?ect we may expect that the

total corrected luminosity density should not depend on

the distance from the observer,in contrast to the num-

ber of galaxies which is strongly a?ected by selection (for

large distances we do not see absolutely faint galaxies).

This di?erence in observed and total luminosity is clearly

seen in Fig.1:with increasing distance total luminosities

exceed observed ones by a factor of ten or more.We can

use the mean luminosity density as a test of our weighting

procedure.In Fig.4we show the mean luminosity density

in spherical shells of thickness 5h ?1Mpc for all 6slices

of the LCRS.We see strong ?uctuations of the luminos-

ity density,caused by superclusters and voids.The overall mean density is,however,almost independent of the dis-tance from the observer.The mean density is a very sensi-tive test for the parameters of the luminosity function.It shows that the presently accepted set of parameters of the luminosity function compensates correctly the absence of faint galaxies in our sample.3.2.Selection e?ects The main selection e?ects in the LCRS (as in the SDSS)are due to the ?nite width of the apparent magnitude window,m 1...m 2,which excludes galaxies outside this window from the redshift survey.This e?ect reduces the number of galaxies observed for a given structure element (cluster)of the universe.If the cluster contains at least one galaxy within the visibility window of the survey,then the contribution of the remaining galaxies to the expected total luminosity of the cluster can be restored using the weighting scheme discussed above.However,if the cluster has no galaxies in the visibility window,it is lost.For this reason,with increasing distance from the observer,more and more mostly poor clusters disappear from our survey.This e?ect is clearly seen in Fig.5,which shows the total luminosities of DF-clusters as a function of the distance from the observer,d .For comparison we also show the relationship between the luminosities and distances of the LCRS loose groups of galaxies.We see that low-luminosity clusters are seen only at distances d ≤250h ?1Mpc.This limit is the same for the DF-clusters and the LCRS loose groups,with the di?erence that there are practically no LCRS loose groups with luminosities less than 2×1010L ⊙,whereas the lower limit of the DF-clusters is 0.5×1010L ⊙,i.e.4times lower.There exists a well-de?ned lower limit of cluster lumi-nosities at larger distances;this limit is practically linear

J.Einasto et al.:LCRS clusters and superclusters

Fig.5.The luminosities of DF-clusters as a function of distance.The upper panels show the distribution for the DF-clusters,the lower panels for the LCRS loose groups;the left panels show Northern slices,the right panels show Southern

slices.

Fig.6.Total luminosities of the DF-clusters(upper panels)and the LCRS loose groups(lower panels)as a function of the global relative densityδ.The left panels show Northern slices,the right panels show Southern slices.

in the log L?d plot.Within random?uctuations the lower

luminosity limit is identical for most LCRS slices:at200

and400h?1Mpc it is0.5and4.8×1010L⊙,respectively;

only the slice?6?has a factor of2higher limit.This slice

was observed with50?bres only,and has a narrower ap-

parent magnitude window.The LCRS loose group sample

has at200and400h?1Mpc a completeness limit of2and

16×1010L⊙,respectively,i.e.a factor of～3.3higher

than that for the DF-cluster sample.The absence of low-

luminosity clusters at large distances can be taken into

account statistically in the calculation of the cluster lumi-

nosity function(see below).The location of these missing

8J.Einasto et al.:LCRS clusters and

superclusters

Fig.7.Total luminosities of DF-clusters as a function of the global relative densityδ;clusters are pided into3distance classes:100...250,250...350,and350...450h?1Mpc,shown in the lower,middle and upper panels,respectively. The left panels show Northern slices,the right panels show Southern slices.

clusters is not known.Thus with increasing distance there are fewer poor clusters to trace the large-scale structure.

The more luminous DF-clusters and the LCRS loose groups form volume-limited cluster samples;the num-ber of clusters in these samples is,however,considerably smaller than in the full samples.Moreover,the exclusion of poorer clusters would make the investigation of the de-pendence of cluster richness on environment di?cult.The study of the internal structure of superclusters and voids would also be di?cult.Thus we have not used volume-limited subsamples of clusters.

In addition to the above selection e?ect the LCRS has one more problem:due to relatively small number of?-bres used in measuring redshifts of galaxies the samples were diluted,i.e.not all galaxies within the observational window m1...m2were observed for redshifts.This e?ect is strong in the?6?slice,which was observed only with the50-?bre spectrograph.For this reason,the number of loose groups detected by TUC in this slice is only about half that of any of the other slices.Similarly,the number of detected DF-clusters is smaller.In calculating the total luminosity of superclusters this additional selection e?ect is taken into account,so supercluster properties are not a?ected.The properties of luminous DF-clusters of this slice are similar to the properties of DF-clusters in other slices,and we can conclude that our procedure worked properly.

3.3.Luminosities of DF-clusters in various environment In Paper I we used the density found with a10h?1Mpc smoothing as a parameter to describe the environment in the vicinity of clusters of galaxies.Here we analyse the LCRS DF-clusters and loose groups to investigate the de-pendence of cluster luminosities on the density of their environment.We calculated the global relative densityδ(in units of the mean density of the low-resolution den-sity?eld)for all DF-clusters and LCRS loose groups;the results are shown in Fig.6.As expected from analogy with the SDSS analysis,there is a clear correlation be-tween the luminosity of clusters/groups and the density of their environment.In all LCRS slices the relation be-tween the DF-cluster luminosity and the environmental density is statistically similar.Only in the?6?slice are low-luminosity clusters absent due to this slice’s higher luminosity completeness limit.

There exists a well-de?ned upper limit for the luminos-ity of the most luminous clusters.DF-clusters in the high-est density environments have luminosities up to about 1012L⊙.Most luminous loose groups are even brighter–their luminosity in high-density environments goes up to 2.5×1012L⊙.The most luminous DF-clusters in the low-est density environment have luminosities about1011L⊙, i.e.they are almost one-tenth as luminous.A similar dif-ference was also found for the SDSS clusters.The upper envelope of the luminosity-density relation is statistically identical for all LCRS slices;for the LCRS loose groups this upper envelope is also observed,but over a smaller range of enviromental densities.

Comparing the relationship for the DF-clusters and the LCRS loose groups shows two important di?erences. First of all,there are very few loose groups in low-density environments,δ≤0.5(we recall that in this plot the en-vironmental density is expressed in the units of the mean

J.Einasto et al.:LCRS clusters and superclusters9

density for the whole slice);there are also very few low-luminosity groups.This comparison shows that the LCRS loose groups are much less suitable for studying the struc-ture of the universe in low-density regions.The other dif-ference is observed in the regions of high environmental density.Here the dispersion of luminosities of loose groups is larger than that of DF-clusters.In other words,in high-density environments there are both high-luminosity as well as low-luminosity loose groups,whereas most DF-clusters in high-density environments tend to be quite lu-minous.The reason for this disagreement between the DF-clusters and the LCRS loose groups is not yet understood.

One may ask whether the cluster luminosity-density dependence could be explained by selection e?ects,i.e. by the relationship between cluster luminosities and dis-tances shown in Fig.5.To clarify this problem we pided the DF-clusters into three distance classes and derived the luminosity-density relationship separately for each dis-tance class.The results are shown in Fig.7.Here the dependence of the cluster luminosity on the density of the environment is seen quite clearly,so this e?ect must be an intrinsic property of clusters of galaxies.Luminous clusters are predominantly located in high-density regions, poor clusters in low-density regions.

The luminosity-density relation can also be inverted, telling us that we obtain a higher environmental(lumi-nosity)density in a given region if the DF-clusters there are more luminous.As the environmental luminosity den-sity comes mainly from summing up the luminosities of inpidual DF-clusters,this conclusion is trivial.Fitting a power-law density-luminosity relationship to the data in Fig.6,we obtain a simple linear law,δ～L;this means that this simplest model may indeed be correct.Of course, this fact does not exclude other,more complicated models of the luminosity-density dependence.

The most luminous DF-clusters in high-density en-vironments exceed in luminosity the most-luminous DF-clusters in low-density environments by a factor of10,as also found for the SDSS clusters in Paper I.The upper envelope of the cluster luminosity-density distribution is very well de?ned,as seen in Figs.6and7.The lower en-velope is not so sharp as the upper one,and it is de?ned best for nearby clusters(see the lower panels of Fig.7).

This tendency is seen also in Fig. 2. In the colour-coded version of this?gure (http://www.aai.ee/～maret/cosmoweb),we see that clusters in low-density regions appear blue,which indi-cates medium and small densities,whereas rich clusters, which appear red in this?gure,dominate the central high-density regions of superclusters.This di?erence is very clear in nearby regions up to a distance～300h?1Mpc. At large distances from the observer poor clusters cannot be observed.Thus,at these distances,all clusters in our appear red in our colour-coded map.3.4.The luminosity function of DF-clusters

As in Paper I we calculated the integrated luminosity func-tion of DF-clusters,i.e.the number of DF-clusters per unit volume exceeding the luminosity L.As we have seen in previous sections,only the brightest DF-clusters can be observed over the whole depth of our samples.We used two methods to calculate the luminosity function: the nonparametric histogram method,and the maximum likelihood method.In the?rst method we corrected for the incompleteness of less luminous clusters by multiply-ing the number of observed clusters at each luminosity step by the ratio(d lim/d L)3,where d lim=450h?1Mpc is the limiting distance of the total sample,and d L is the maximum distance where DF-clusters of luminosity L can be observed.The limiting distance for every L value can be extracted from Fig.5;we used here a linear relation between d L and log L.

The luminosity function for all6slices is shown in Fig.8.It spans almost3orders of magnitude in lumi-nosity and4orders of magnitude in spatial density.The di?erence between inpidual slices is very small.Only the slice?3?has a slightly higher density at low luminosities than the other slices.Here the data have probably been over-corrected for non-observed poor clusters.For com-parison we plot the cluster luminosity function for the SDSS Northern slice(Paper I).As we see there is excel-lent agreement between the LCRS and the SDSS Northern slice data.

We also calculated the luminosity function of the LCRS loose groups of galaxies;this function is shown in the right panel of Fig.8.Here we used group lumi-nosities as given by TUC.The comparison with the DF-cluster luminosity function shows that the luminosity of the most luminous groups is higher than in the case of the DF-clusters(this is seen also in Figs.5and6).Another di?erence is in the range of poor clusters.The number of the LCRS loose groups of a given luminosity is much lower than the number of the DF-clusters for the same luminosity.At L=2×1010L⊙the mean integrated densities of the LCRS DF-clusters and loose groups are 4.0×10?4(h?1Mpc)?3and1.9×10?4(h?1Mpc)?3,re-spectively.For comparison we note that the densities of the SDSS DF-clusters at the same luminosity level are 3.5×10?4(h?1Mpc)?3and2.9×10?4(h?1Mpc)?3for the Northern and Southern slice,respectively.The lower spatial density of the LCRS loose groups may be explained by a selection e?ect inherent in the de?nition of a loose group:here at least3galaxies must be present in the group within the observational window,whereas in the case of DF-clusters only one galaxy is needed.Hein¨a m¨a ki et al. (2003)has calculated the mass function of LCRS loose groups.This function also shows a lower spatial density of loose groups in the poor cluster range.

As a second method,we describe the observed lumi-nosity function by the gamma-distribution,suggested by Schechter(1976):

Φ(L)dL=Axαexp(?x)dx,(3)

10J.Einasto et al.:LCRS clusters and superclusters

Fig.8.The left panel shows the distribution of luminosities of DF-clusters(the cluster luminosity function)in the LCRS slices.The right panel shows the LCRS loose group luminosity functions.For comparison we show the cluster luminosity function for the SDSS Northern slice(Paper I).

where x=L/L?is the luminosity in dimensionless units,

L?is the characteristic luminosity of clusters,A is the

normalisation amplitude,andαis the shape parameter.

We?nd the estimates of the parameters L?andαby the

maximum likelihood method(Yahil et al.1996),minimis-

ing the log-likelihood function

L=?

log(p i),

where N is the number of DF-clusters and p i is the prob-ability density for observing the cluster i:

p i=

Φ(L i)

J.Einasto et al.:LCRS clusters and superclusters11

Table3.Shape parameters of the Schechter luminosity function for the DF-clusters of the LCRS slices.The slices are marked by their central declinationδ(the?rst column in the table).The last row gives the luminosity function parameters for the full LCRS DF-cluster sample.

?0315.8±1.2-0.55±0.07

?0615.2±1.3-0.52±0.07

?1214.4±1.1-0.70±0.06

?3916.1±1.1-0.51±0.06

?4213.4±0.9-0.42±0.06

?4519.1±1.5-0.71±0.06

total14.4±0.2-0.43±0.01

∞L0Φ(L)LdL,

(4)Fig.10.The cluster luminosity selection function,deter-mined by two methods.The solid line

shows the selection function found in this paper using Eq.(4).Dots give the selection function as found in Paper I using two sets of parameters of the Schechter function.

where L0=0.5×1010L⊙is the lower limit of luminosi-ties of our cluster a2542e2f2af90242a895e558ing the set of Schechter pa-rameters for the SDSS Northern sample(which approxi-mates well the mean of the LCRS samples)we calculated the selection function F sel(L);the results are shown in Fig.10.For comparison we show also the selection func-tion as found in Paper I using two sets of parameters of the Schechter function,by piding the luminosity func-tions for both parameter sets at a given luminosity L.The overall agreement of the selection functions calculated by di?erent methods is satisfactory.The method used in this paper is more physically motivated.The correction factor to calculate the unbiased values of cluster luminosities is 1/F sel(L);here the luminosity L is distance dependent and should be calculated from the lower threshold of the lumi-nosities of the DF-clusters at a given distance,as shown in Fig.5.At the limiting distance d lim=450h?1Mpc the threshold luminosity is L=8×1010L⊙,and here F sel=0.72(i.e.the luminosities of DF-clusters at this distance must be decreased by a factor of1.4).We see that this selection e?ect is rather modest.

Presently we have no data for the masses of DF-clusters.Thus we are unable to convert the luminosity function to the cluster mass function.Even so,the lu-minosity function is interesting in and of itself.It is less distorted by random errors(which in?uence masses of in-pidual clusters)and it can be easily determined for all clusters independently of the number of galaxies observed in the a2542e2f2af90242a895e558parison with the SDSS data shows ex-cellent agreement.

12J.Einasto et al.:LCRS clusters and superclusters 4.Density?eld superclusters

4.1.The DF-supercluster catalogue

We de?ne superclusters of galaxies as the largest non-

percolating density enhancements in the universe(Einasto

et al.1997).Superclusters can be identi?ed using either

galaxy or cluster data.Here we use the low-resolution den-

sity?eld to?nd large overdensity regions which we call

density?eld superclusters(DF-superclusters).This?eld

was calculated using the galaxy data and corrected to ac-

count for galaxies outside the visibility window.The den-

sity?eld was Gaussian-smoothed,using the smoothing

lengthσsm=10h?1Mpc,which eliminates small-scale

irregularities and the’?nger-of-god’e?ect.To reduce the

conical volume of slices(wedges)to an identical thickness

we pided densities by the thickness of the slice at the

particular distance.In this way the surface density of the

?eld is in the mean constant.This reduced density?eld

for all6LCRS slices is shown in Fig.3.

In the density?eld approach superclusters can be iden-

ti?ed as connected,high-density regions.The remaining

low-density regions can be considered voids.To pide the

density?eld into superclusters and voids we need to?x

the threshold density,δ,which pides the high-and low-

density regions.This threshold density plays the same role

as the neighbourhood radius used in the friends-of-friends

(FoF)method to?nd clusters in galaxy samples or super-

clusters in cluster samples(for a more detailed discussion

see Paper I).To make a proper choice of the threshold

density we plot in Fig.11the number of superclusters,

N,the area of the largest supercluster P(in units of the

total area covered by superclusters),and the maximum size of the largest supercluster(either in the x or y di-rection),as a function of the threshold densityδ(we use relative densities as above).The data are given for all 6slices.We see that the number of superclusters has a maximum atδ=1.3...1.8.The diameters of superclus-ters decrease with increasing threshold density.At a low threshold density the largest superclusters have several concentration centres(local density peaks),their diame-ters exceed100h?1Mpc,and their area forms a large frac-tion of the total area of superclusters.We have accepted the threshold densityδ=1.8;the same value was also used in Paper I for the density?eld of the Sloan Digital Sky Survey.This threshold density de?nes compact and rather rich superclusters.If we want to get a sample of poor or medium rich superclusters then we would need to use a lower threshold density,with the price of getting su-percluster complexes instead of inpidual superclusters in regions of higher density.Superclusters were identi?ed in the distance interval100...450h?1Mpc.We include only the superclusters with areas greater than100(h?1Mpc)2; the remaining maxima are tiny spots of diameter less than 10h?1Mpc.

The number of superclusters is given in Table1.In the Tables4and5we provide data on inpidual superclus-ters;the columns are as follows:Column(1):the identi-Fig.11.Properties of the LCRS density?eld superclus-ters as a function of the threshold density,δ,that sepa-rates superclusters(high-density regions)and voids(low-density regions).The upper panel shows the number of superclusters,N,the middle panel shows the area of the largest supercluster(in units of the total area covered by superclusters),and the lower panel shows the size(either in the x or y direction,whatever is larger)of the largest supercluster.

?cation number No;column(2):the peak densityδmax (the peak density of the low-resolution density?eld,ex-pressed in units of the mean density);column(3):L tot–the estimated total luminosity of the supercluster,found from the sum of observed luminosities of the DF-clusters located within the boundaries of the supercluster;column (4):L D–the estimated total luminosity of the superclus-ter calculated by integration of the low-resolution density ?eld inside the boundaries of the supercluster(both in units of1010L⊙);column(5):D–the diameter of the supercluster(the diameter of a circular area equal to the area of the supercluster);column(6):?=max(dx,dy)–the maximal size of the supercluster either in the horizon-tal or vertical directions(both in h?1Mpc);column(7): RA–the right ascension of the centre;columns(8)–(10):

J.Einasto et al.:LCRS clusters and superclusters13 Table4.The list of Northern superclusters

-03.01 3.71565259531391561841061510.029********D

-03.02 2.1161379141815611465940.0057430D

-03.03 2.6666141826371583822113190.0196900F

-03.04 2.848591920231603281692820.01191300M

-03.05 2.72679820113892121723481073310.2306124294100M

-03.05a 2.9582100820281683971553650.01791000C

-03.05b 2.788229526591061713151052970.151664203100D

-03.05c 4.91498369534431734301304100.05111200M

-03.05d 3.062515372437177383953720.0267911265M

-03.06 3.995724803036183329423260.02691740M

-03.07 2.11853071215189394183940.0046400F

-03.08 2.452710792333193404-144040.0155500D

-03.09 2.22685231622196420-414180.0077500F

-03.10 5.4326658714475197249-262480.0572*******M

-03.11 2.01142141015199397-553930.0033200F

-03.12 3.4399450734568199328-413260.06064131M

-03.13 2.0982311114205438-1034260.0036200C

-03.14 2.11213511317207226-642170.0053410F

-03.15 2.01733031216208432-1224150.0046500F

-03.16 2.7197932063751211404-1353810.04172830M

-03.17 2.22105751725216240-1032170.0084620C

-03.18 2.11573211216220173-841510.0048550F

-03.19 2.842210002124228330-1972640.0129900155M

-06.01 2.219739818171544272423520.0064200D

-06.02 4.3169727454053156160881340.0318188188M

-06.03 6.53911678754511573842003280.05962322M

-06.04 1.9882521419166192761760.0044500D

-06.05 6.5572876506276179379733720.0774*******M

-06.06 4.6363251975563179244422400.061634101M

-06.07 3.699320273635190401-34010.0257600F

-06.08 2.0953631718191304-93040.0062300D

-06.09 3.4141225544139194264-232630.03362330D

-06.10 2.66249842729202439-974290.0144700F

-06.11 2.941811142825202372-863620.0154600D

-06.12 3.4244634024865204332-853210.04612310D

-06.13 2.01393291618204278-692690.0056500D

-06.14 2.22836172227210222-792080.0101810F

-06.15 3.4379754946185211419-1573890.07531810D

-06.16 4.0219839244750224327-1852700.04492031M

-06.17 3.062212882928226395-2393140.0177700F

-12.01 2.9711257643491534552743630.0352800D

-12.02 2.230066423231564072283380.0100710D

-12.03 4.02077362546451613521733070.04002640D

-12.04 2.542865822201624171993670.0093700C

-12.05 2.51412246743631622241071970.035415110M

-12.06 3.11578612738911231733411043250.155699213105M

-12.07 3.6131223543939174228652190.028220100M

-12.08 3.59329918773107197271-262700.0994********M

-12.09 2.46553621968142198418-504150.08704200M

-12.10 2.7243328204557207186-491800.038220191141M

-12.11 2.83778472423211358-1183380.0114700C

-12.12 2.13836022228211299-1012810.00931100F

-12.13 2.1161326274361222314-1582710.0353*******M

-12.14 2.851710112725226371-2073080.0135700D

-12.15 2.577614183333227427-2463490.02021701D

14J.Einasto et al.:LCRS clusters and superclusters

Table5.The list of Southern superclusters

-39.01 2.115338017163163081992350.0062310F -39.02 2.120230315143162631702000.0049310C -39.03 2.136332816153194102603170.0053600C -39.04 2.450075424253251951091620.0114830F -39.05 3.79818965274843354301933840.10864001M -39.06 2.02142531414337215941930.0042410F -39.07 2.353467323233413581383310.0104900M -39.08 3.2295533474748355423844150.04352201D -39.09 2.698614983335356300582950.021712239M -39.10 2.51740260943536332203320.037316425M -39.11 2.16077662537719981990.0126741M -39.12 2.127032816158396143960.0054400D -39.13 2.39201154303719352-373500.01791100M -39.14 2.4618754242448417-1953690.0116600M -39.15 2.1296403181949384-1793400.0065611F -39.16 2.951623960547951276-1362400.0578*******M -39.17 3.647024455557653172-921450.05893328348M -39.18 3.948934296545964412-2533260.05843201D -42.01 2.013124114133213101792540.0042300M -42.02 2.441561322213214012333270.0098801M -42.03 2.4688102228343212141221760.016311101182F -42.04 3.01975271543463363321363030.03882130M -42.05 2.453899327333413691333450.0156701F -42.06 3.6814266696693353269602630.0886********M -42.07 3.44840477557684376293750.06573131M -42.08 2.710391437323220356-453540.02131700M -42.09 1.8139281152522267-412640.0050310F -42.10 2.0200328162030365-913530.0056311F -42.11 3.554545404577547188-811700.06803621148M -42.12 2.0180369171850427-1973790.0064300F -42.13 2.4648848252552382-1883320.0132800D -42.14 3.417672362394365394-2363160.03081901M -45.01 2.71193139132343172911702360.020********F -45.02 3.2822149931303254012043450.01991002D -45.03 2.578910442827327181891580.01591151182D -45.04 2.14707632532340262922450.0125911197M -45.05 5.06838692665803423661213450.08464723206M -45.06 2.23215602122343149481410.0089440C -45.07 3.02220259543451387423850.03662430D -45.08 2.951844863597116365-233640.06873941M -45.09 2.813191577333520434-534310.02261300D -45.10 3.427103635485224261-442580.047123140M -45.11 2.1256628222436283-872690.0104510F -45.12 3.113101867353738408-1323870.02491500D -45.13 2.7556885252446384-1593500.0129601F -45.14 2.5544709232247337-1413060.0107301C -45.15 4.765055971576148205-911840.06433720448M -45.16 2.7505766232158284-1472430.0110300C -45.17 4.8114969387719464388-2203190.10195361M

J.Einasto et al.:LCRS clusters and superclusters15 the distance d and the coordinates,x,y,of the centre of

the supercluster(in h?1Mpc);column(11):f–the frac-

tion of the area of the supercluster(in units of the total

area of superclusters in the particular slice);columns(12)

–(14):the number of the DF-clusters N DF,the LCRS

loose groups,N LC,and the Abell clusters,N A,within the

boundaries of the supercluster;column(15):identi?cation

with known superclusters based on the Abell supercluster

sample by E01;column(16):the type of the supercluster,

estimated by visual inspection of the density?eld.

The total luminosity L tot was calculated as described

in Paper I:

L tot=

16J.Einasto et al.:LCRS clusters and superclusters

Fig.14.The total luminosities of the DF-superclusters in the LCRS slices at di?erent distances from the observer.0

100

200300

400

500

d [h ?1

Mpc]

L t o t [1010

L S u n ]

?03?06?12

0100

200300

400500

d [h ?1

Mpc]

L t o t [1010

L S u n ]

?39?42?45

peak density.For small DF-superclusters the di?erence lies within the accuracy of the determination of both po-sitions,±1h ?1Mpc.For large DF-superclusters with sev-eral concentration centres the di?erence between various determinations of the centre is larger (in some cases over 10h ?1Mpc).In Tables 4and 5we give the position of the centre as found from the mean of the extreme coordinates.To check our weighting scheme we show in Fig.14the luminosities of the DF-superclusters as a function of the distance from the observer,d .We see that luminous DF-superclusters are observed at various distances and that there is no obvious dependence of supercluster luminosity on distance.This is indirect evidence suggesting that the luminosities of the DF-superclusters are not in?uenced by large selection e?ects.As with the SDSS DF-superclusters,the luminosities span an interval of over 2orders of mag-nitude.

4.3.DF-superclusters and superclusters of Abell

clusters

Let us now discuss the structure of some prominent su-perclusters.The high-resolution map shows ?ne details of the structure,and the low-resolution map shows the over-all shapes and densities of the high-density regions.The gap between adjacent slices is rather thin,so by compar-ing neighbouring slices we get some information on the 3-dimensional structure of superclusters.Further,the gap between the ?03?slice and the Northern slice of the SDSS survey is only about 1degree wide,so we have a chance here to compare the structures using both the SDSS and LCRS data.

The positions of superclusters identi?ed from the dis-tribution of Abell clusters depend on a small number of objects (Abell clusters),and no luminosity weighting is used as in the density ?eld method.On the other hand,the positions of the Abell superclusters were found using a

full 3-dimensional data set,whereas the DF-superclusters were extracted from a 2-dimensional data set.For this rea-son alone we cannot expect a good coincidence in positions for the Abell and density ?eld superclusters.In spite of these di?erences,in 19cases the DF-superclusters can be identi?ed with superclusters of Abell clusters catalogued by E01;all identi?cations are given in the Tables 4and 5.

The most prominent supercluster,seen both in the LCRS ?03?and the SDSS Northern slices,is the SCL126from the catalogue by E01;in Table 4it is the ?03.10;in the SDSS supercluster catalogue the N13.Within the ?03?slice this supercluster has 3Abell clusters;in the SDSS survey 1Abell cluster.These clusters are also X-ray sources.In both slices the supercluster has a multi-branch appearance;in the LCRS slice the ?laments form a cross,in the SDSS slice there is a strong ?lament in the tangen-tial direction (in the y ?direction)and a weaker ?lament away from the observer.According to the calculations of the density ?eld the density in the region of this superclus-ter is one of the highest in the whole LCRS survey.The same can be found by the distribution of Abell clusters in this supercluster (Einasto et al.2003c).

Another supercluster common to both the LCRS ?03?and SDSS Northern slices is the SCL155in the catalogue by E01,the ?03.19in the present catalogue,and the N23in the SDSS catalogue (Paper I).The main ?lament of this supercluster is very thin and directed almost exactly toward the observer;inpidual density enhancements can,however,be clearly distinguished.This supercluster has also a multi-branch appearance.

An interesting supercluster is the SCL82(N02).It con-sists of two strong almost perpendicular ?laments in the SDSS slice.In the LCRS slice this supercluster is not vis-ible at all.This example shows us that ?laments in super-clusters are truly thin.

The largest and most luminous supercluster in the LCRS ?03?slice is the SCL100in the Abell superclus-

J.Einasto et al.:LCRS clusters and superclusters17

ter catalogue(the?03.5in the present catalogue).At the1.8threshold density level its length is over200 h?1Mpc;at the2.1level it splits into4sub-superclusters. The overall form is multi-branching.The forms of the sub-superclusters are di?erent,with compact,di?use and multi-branch appearances.

The Sextans supercluster(SCL88in the E01catalogue,?03.01and?06.02in the present catalogue)is clearly seen in two LCRS slices,a weak extension(not included as a supercluster)is seen also in the?12?slice.In the?03?slice it has a di?use form,but in the?06?slice it shows a clear multi-branching character.

In the?12?slice we see two large under-dense re-gions centred at x=20,y=250and x=20,y= 350h?1Mpc,surrounded by two rings of rich superclus-ters:the?12.05,?12.06,?12.07,?12.08,?12.09,?12.10,?12.11,?12.12,?12.13.Within both supervoids (we use this term for voids surrounded by superclusters, see Lindner et al.1995)we see numerous small?laments of DF-clusters,but all these clusters are poor.This exam-ple alone shows how much more information we get using the high-resolution density?eld map.

The most prominent supercluster crossed by the Southern LCRS slices(and one of the most prominent superclusters known)is the Horologium-Reticulum super-cluster(the SCL48in E01,and the?39.16,?39.17,?42.11,?45.15in the present catalogue).This superclus-ter contains9Abell clusters within the LCRS slices,2of which are X-ray clusters,and a number of clusters from the APM cluster catalogue.This supercluster has in all slices a multi-branch shape.In the?39?slice it is split into2separate superclusters.The location of?laments in di?erent slices is di?erent,thus the multi-?lamentary character is seen extremely clearly.

Another very rich supercluster crossed by all Southern LCRS slices is the?39.18,?42.14,?45.17.This su-percluster is located at a mean distance of400h?1Mpc and is too distant to be included into the E01supercluster catalogue.In the?45?slice it consists of a very rich DF-cluster?lament,slightly inclined to the line of sight,in the ?42?slice it has also a rich DF-cluster?lament,which is directed at almost right angle in respect to the previous one.In the?39?slice the supercluster has a di?use shape.

Einasto et al.(1997)have shown that about75%of very rich superclusters are concentrated in a so-called Dominant Supercluster Plane(DSP),consisting of chains of superclusters and voids between them.The Southern slice?39?goes almost through the DSP,due to this the number of Abell clusters is the largest in this slice(28). Also the sliceδ=?42?is very close to the DSP.The?45?slice crosses a region of extended voids between superclus-ters;as elsewhere in voids this region is not completely empty but contains numerous poor DF-cluster?laments.

Now let us compare the properties of the DF-superclusters that belong to superclusters of Abell clus-ters(the Abell sample)with those of the DF-superclusters that cannot be identi?ed with Abell superclusters(the non-Abell sample).Since the data for Abell superclus-Table6.Properties of the DF superclusters Abell2434503150050.05 non-Abell4412102815050.02

18J.Einasto et al.:LCRS clusters and superclusters

that are also the Abell superclusters are more luminous and richer than the non-Abell DF-superclusters.Einasto et al.(2003a,2003c)showed using the data on the Las Campanas loose groups(TUC)that loose groups in super-clusters of Abell clusters are richer,more luminous,and more massive than loose groups in systems that do not belong to Abell superclusters.Fig.15extends this rela-tion to larger systems–superclusters.This?nding shows that the presence of rich(Abell)clusters is closely related to properties of superclusters themselves.

4.4.DF-clusters and superclusters,and the hierarchy

of systems in the universe

Abell clusters were originally identi?ed by visual inspec-tion of the Palomar plates.In spite of the subjective char-acter of their identi?cation they have served for decades as the basic source of information on high-density regions in the universe.Now we have redshifts and magnitudes for thousands of galaxies,which allow us to use objective methods for cluster identi?cation.It is interesting to com-pare the3sets of clusters used in this study as tracers of the structure of the universe.

A glance at the Tables1,4and5shows that the num-bers of the DF-clusters,the LCRS loose groups,and the Abell clusters per slice and per supercluster are very di?er-ent.Almost all Abell superclusters are seen as density en-hancements in our low-resolution density map.In contrast, there exist many DF-superclusters and other density en-hancements in the low-resolution density?eld which con-tain no rich clusters from the Abell catalogue within the slice boundaries.This di?erence has an easy explanation: the Abell clusters are relatively rare enhancements of the high-resolution density?eld,not represented in all large-scale density enhancements;the total number of Abell clusters within the LCRS boundaries is about one-?ftieth the number of DF-clusters.

The sample of loose groups of galaxies by TUC con-tains galaxy systems which are poorer than the Abell clus-ters,so the number of these groups per DF-supercluster is much larger than the number of Abell clusters per DF-supercluster.However,there exist a number of superclus-ters with a very small number of LCRS loose groups in it –in some cases there are no LCRS groups at all.This oc-curs in more distant superclusters where the LCRS groups were not searched for.Most luminous DF-clusters can be identi?ed with the LCRS loose groups.This comparison shows that among presently available cluster samples the DF-clusters are the best tracers of structure.

Tables4and5show that in about two-thirds of cases superclusters have a?lamentary or multi-?lamentary mor-phology.A careful inspection of Figs.2and3indicates that small density enhancements of the low-resolution density?eld have a?ne structure in the high-resolution map,similar to the DF-superclusters.Most of these sys-tems also consist of weak?laments of DF-clusters in large voids.This shows the hierarchy of galaxy systems:the morphology of galaxy systems is similar,only in superclus-ters the clusters are richer,and superclusters containing very rich clusters are themselves also richer.

5.Conclusions

We have used the LCRS galaxy data to construct high-and low-resolution2-dimensional density?elds for all6 slices of the survey.In calculating the density?eld the expected luminosity of galaxies outside the observational window of apparent magnitudes was estimated using the Schechter luminosity function.The high-resolution density ?eld was found using a smoothing length0.8h?1Mpc, which corresponds to the characteristic scale of clusters and groups of galaxies.This?eld was used to construct a catalogue of clusters of galaxies(DF-clusters).The low-resolution?eld was found using a smoothing length 10h?1Mpc and was employed to construct a catalogue of superclusters of galaxies given in Tables4and4.

The DF-cluster catalogue contains about5times more clusters/groups than the catalogue of loose groups of galaxies compiled by TUC,and about50times more than the Abell catalogue of rich clusters.Thus,this new sample is best suited for the investigation of the distribution of matter in superclusters and low-density regions between superclusters.The?ne distribution of the DF-clusters in superclusters shows that luminous superclusters preferen-tially have a multi-branching structure,whereas poor su-perclusters as well as galaxy systems outside superclusters have in most cases a?lamentary or compact morphology.

The density of the low-resolution?eld was used as an environmental parameter to characterise the supercluster environment of the DF-clusters.Cluster properties depend strongly on the density of the large-scale environment:the clusters located in high-density environments are a factor of5±2more luminous than the clusters in low-density environments.This?nding con?rms the results obtained from the study of clusters in the Sloan Survey.

We calculated the luminosity function of the DF-clusters for all LCRS slices,as well as for the SDSS Early Data Release samples.These functions can be ap-proximated by a Schechter function with the parameters L?=(14±3)×1010L⊙andα=?0.44±0.15(the er-rors are estimated from the scatter of values for inpidual slices).

We found also that the DF-superclusters,which con-tain Abell clusters,are more luminous and richer than the DF-superclusters without Abell clusters. Acknowledgements.We thank Heinz Andernach for the per-mission to use the new unpublished compilation of redshifts of the Abell clusters.The present study was supported by the Estonian Science Foundation grants ETF2625,ETF4695,and by the Estonian Research and Development Council grant TO 0060058S98.P.H.was supported by the Finnish Academy of Sciences.J.E.thanks Fermilab and Astrophysikalisches Institut Potsdam(using DFG-grant436EST17/2/01)for hospitality where part of this study was performed.

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