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The PSCz Dipole Revisited

The PSCz Dipole Revisited
The PSCz Dipole Revisited

a r X i v :a s t r o -p h /0609476v 1 18 S e p 2006

Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 5February 2008

(MN L A T E X style ?le v1.4)

The PSCz Dipole Revisited

Spyros Basilakos 1,2&Manolis Plionis 1,3

1Institute

of Astronomy &Astrophysics,National Observatory of Athens,I.Metaxa &B.Pavlou,P.Penteli 15236,Athens,Greece

2Academy of Athens,Research Center for Astronomy &Applied Mathematics,Soranou Efessiou 4,11-527,Athens,Greece

3

Instituto Nacional de Astrof′?sica,′Optica y Electronica (INAOE)Apartado Postal 51y 216,72000,Puebla,Pue.,M′e xico

5February 2008

ABSTRACT

We re-examine the gravitational acceleration (dipole)induced on the Local Group of galaxies by the Infrared Astronomical Satellite (IRAS)galaxy dis-tribution of the Point Source Catalogue redshift survey (PSCz).We treat the cirrus-a?ected low galactic latitudes by utilizing a spherical harmonic expan-sion of the galaxy surface density ?eld up to the octapole order.We ?nd strong indications for signi?cant contributions to the Local Group motion from depths up to ~185h ?1Mpc and possible contribution even from ~210h ?1Mpc,in agreement with the recent analysis of Kocevski &Ebeling of a whole sky X-ray cluster survey.What changes with respect to the previous PSCz dipole analyses is:(a)the large-scale dipole contributions and (b)an increase of the overall dipole amplitude due to the important contribution of the local volume

(~<4h ?1

Mpc),which we now take into account.This results in a lower value

of the β(≡?0.6

m /b )parameter,which we ?nd to be βIRAS ?0.49in real space.Therefore,for the concordance cosmological model (?m =1??Λ=0.3)the IRAS galaxies bias factor is b IRAS ?1which means that IRAS galaxies are good traces of the underlying matter distribution.

Keywords :galaxies:clusters:general -large-scale structure of universe -in-frared:galaxies

1

INTRODUCTION

It is well known that the peculiar velocity of the Lo-cal Group of galaxies is accurately determined from the CMB temperature dipole (Kogut et al.1996;Ben-nett et al.2003),being u LG =622km/sec towards (l,b )=(277?,30?).Under the framework of linear the-ory,the most probable cause for this motion as well as for the observed peculiar motions of other galaxies and clusters is gravitational instability (see Peebles 1980).The latter is supported by the fact that the gravitational acceleration of the Local Group of galaxies,as traced by many di?erent samples of extra-galactic mass trac-ers is well aligned with the general direction of the CMB dipole (eg.Yahil,Walker &Rowan-Robinson 1986;La-hav 1987;Plionis 1988;Lynden-Bell et al.1988;Miyaji &Boldt 1990;Rowan-Robinson et al.1990;Strauss et al.1992;Hudson 1993;Scaramella et al.1991;Plionis &

Valdarnini 1991;Branchini &Plionis 1996;Basilakos &Plionis 1998;Schmoldt et al.1999;Rowan-Robinson et al.2000;Kocevski,Mullis &Ebeling 2004;Erdogdˇu et al.2006;Kocevski &Ebeling 2006).

However,what has been debated over the last decades,is the largest depth from which density ?uctu-ations contribute signi?cantly to the gravitational ?eld that shapes the Local Group motion,which is called dipole convergence depth,D conv .

The outcome of many studies in the past,using di?erent ?ux or magnitude limited galaxy and cluster samples,was that the apparent value of the dipole con-vergence depth di?ered from sample to sample,in the range from 40to 160h ?1Mpc,with a strong depen-dence to the sample’s characteristic depth.For exam-ple,the dipole of the IRAS Point Source Catalogue for redshifts (hereafter PSCz)was claimed to mostly con-

2S.Basilakos&M.Plionis

verge within a depth of~100h?1Mpc with negligible, if any,contributions beyond~140h?1Mpc(Rowan-Robinson et al.2000;Schmoldt et al.1999),while that of the optical Abell/ACO cluster sample,which is vol-ume limited out to a large depth(~>200h?1Mpc),was claimed to converge at~>160h?1Mpc but with signi?-

cant contributions beyond~140h?1Mpc(Scaramella et al.1991;Plionis&Valdarnini1991;Branchini&Plio-nis1996).The latter result has been con?rmed using X-ray cluster samples,which are free of the various sys-tematic e?ects from which the optical catalogues suf-fer(Plionis&Kolokotronis1998;Kocevski et al.2004; Kocevski&Ebeling2006).Of course,under the as-sumption that there is a linear bias relation between the cluster,the galaxy and the underlying matter den-sity?uctuations,as proposed by Kaiser(1987),then the galaxy dipole should also show similarly deep con-tributions.This hinted that the shallower galaxy dipole convergence was spurious,and it could be attributed to the lack of adequately sampling of the distant density ?uctuations.

This discussion was recently re-opened by two im-portant papers,that of Erdogdˇu et al.(2006)who anal-ysed the2Micron All-Sky Redshift Survey(hereafter 2MRS)and found D conv~60h?1Mpc,and of Ko-cevski&Ebeling(2006)who analysed a complete whole-sky survey of X-ray clusters and found D conv~>200h?1 Mpc.

Due to the fact that the Erdogdˇu et al.(2006) analysis accounted for the dipole contribution of local galaxies with known true distances and due to the po-tential importance of such contributions,especially on the light of the apparent di?erence between the original PSCz and2MRS dipole results(see section5in Er-dogdˇu et al.2006),we decided to re-analyse the PSCz catalogue along the same lines.In particular,we esti-mate the PSCz dipole using an approach which is based on(a)a spherical harmonic expansion of the galaxy sur-face density up to the octapole order in order to mask the“zone of avoidance”and(b)accounting for contri-butions to the PSCz dipole from the nearby galaxies.

2DATA AND METHOD

In this analysis we utilize the IRAS?ux-limited60-μm redshift survey(PSCz)which is described in Saunders et al.(2000).It is based on the IRAS Point Source Cat-alogue and contains~15000galaxies with?ux>0.6 Jy.The subsample we use,de?ned by|b|≥8?and lim-iting galaxy distance of240h?1Mpc,contains~12300 galaxies and covers~85%of the sky.

We remind the reader that using linear perturba-tion theory one can relate the gravitational acceleration of an observer,induced by the surrounding mass distri-bution,to her/his peculiar velocity,according to:

v(r)=

H0β

|x|3d r=βD(r),(1) whereβ=?0.6m/b and n is the mean number density. The dipole moment,D,is estimated by weighting the unit directional vector pointing to the position of each galaxy,with its gravitational weight and summing over the galaxy distribution:

D=

H0

φ(r)r2

.(2) In order to estimate the dipole using observational data, it is necessary to recover the true galaxy density?eld from the observed?ux-limited samples.This is done by weighting each galaxy byφ?1(r),whereφ(r)is the se-lection function,de?ned by:

φ(r)=

1

3.(4) 2.1Treatment of the Masked regions

Firstly,we need to model the excluded,due to cirrus emission,galactic plane and correct accordingly our raw dipole.We do so by extrapolating to these regions the galaxy distribution from the rest of the unit sphere with the help of a spherical harmonic expansion of the galaxy surface density?eld(e.g.,Yahil,Walker,Rowan-Robinson1986;Lahav1987;Plionis1988;Tadros et al. 1999).For the purpose of the present analysis we expand

The PSCz Dipole Revisited3

the PSCz surface density?eld,Σ(θ,φ),in spherical har-

monics up to the octapole order:

Σ(θ,φ)=

3

l=0A0l P l(x)+l m=1P m l(x)[A m l cos(mφ)+

B m l sin(mφ)]

where0≤θ≤π(θ=90??b),0≤φ≤2πand P m l(x)the associated Legendre functions(x=cosθ). The observed surface density is related to the intrinsic one,σ(θ,φ),by:Σ(θ,φ)=M(θ)σ(θ,φ),where M(θ)is a mask to account for the excluded galactic plane:

M(θ)= 1for|b|≥b lim

0for|b|

with b lim=8?.Thus the overall problem is reduced to the inversion of a16×16matrix,T,which then pro-vides the values for the whole sky components of the

galaxy distribution:C=T?1A,where A is a16×1ma-trix which contains the observed components(A m l,B m l) from the incomplete data and C is a1×16matrix containing the model corrected(αm l,b m l)components. Then the di?erential dipole components,at each spher-ical shell in r,are corrected according to this expansion.

Secondly,about~4%of the sky was unobserved by IRAS and we therefore apply to these areas a ho-mogeneous distribution of galaxies following the PSCz redshift selection function.

2.2Determining distances from redshifts

All heliocentric redshifts are?rst transformed to the Local Group frame using cz?cz⊙+300sin(l)cos(b). We then derive the distance of each tracer by using:

r=

2c

c

[u(r)?u(0)]·?r

the non-linear term that takes into account the con-tribution of galaxy peculiar velocities,u(r),to the galaxy redshift[u(0)the peculiar velocity of the Lo-cal Group].Instead of using3D reconstruction schemes (e.g.,Schmoldt et al.1999;Branchini&Plionis1996; Branchini et al.1999;Rowan-Robinson et al.2000)to estimate this term,we use a rather crude but adequate for the purpose of this work model velocity?eld(see Basilakos&Plionis1998),the main assumptions of which are:

(a)The tracer peculiar velocities can be split in two vectorial components;that of a bulk?ow and of a local non-linear term:u(r)=V bulk(r)+u nl(r)

(b)The?rst component dominates and thus u(r)·?r

Figure https://www.wendangku.net/doc/f15219662.html,parison of our PSCz(solid line)and the 2MRS(dashed line)number-weighted dipoles in redshift space,corrected for their respective shot-noise according to eq.(4).The insert panel shows the misalignment angles(ours -solid line and Erdogdˇu et al.2006-dashed line)between the galaxy and CMB dipoles as a function of distance from the Local Group.

V bulk(r)·?r.As for the observed bulk?ow direction and pro?le we use that given by Dekel(1997)and combined with that of Branchini,Plionis&Sciama(1996).The zero-point,V bulk(0),and the direction of the bulk?ow is estimated assuming,due to the“coldness”of the local velocity?eld(eg.Peebles1988),by V bulk(0)=u(0)?u inf(where u inf=200km/s is the LG in-fall velocity to the Virgo Cluster).

2.3Treatment of the Local Volume

As in Erdogdˇu et al.(2006)we use the true distances for all possible nearby PSCz galaxy.To this end we cross correlate the PSCz catalogue(|b|≥8?)with two literature datasets of neighbouring galaxies with mea-sured distances(Freedman et al.2001;Karachentsev et al.2004),which revealed56common galaxies up to cz≤1000km/s,out of which three are blue-shifted galaxies.Two of these belong to the Virgo cluster area and thus we put them to the center of Virgo(15.4Mpc), while the other one is assigned to the zero velocity sur-face~1.18h?1Mpc(see Courteau&van den Bergh 1999;Erdogdˇu et al.2006).

4S.Basilakos&M.Plionis

3RESULTS

3.1Redshift-Space

In?gure1we present a comparison in redshift space

of our PSCz(solid line)and the2MRS(dashed line;

Erdogdˇu et al.2006)number-weighted galaxy dipoles,

out to210h?1Mpc,both corrected for their respec-

tive shot-noise(eq.4).The corresponding galaxy-CMB

dipole misalignment angle is shown in the insert of?g-

ure1.The shape and amplitude of the two pro?les are

in very good agreement but only within~<100?120h?1 Mpc.The2MRS dipole seemingly reaches a plateau at

60h?1Mpc while the corresponding PSCz dipole contin-

ues to grow.

Beyond~140h?1Mpc,however,the2MRS dipole

drops dramatically,a behaviour not seen in the?ux-

weighted2MRS dipole(see Erdogdˇu et al.2006),while

the PSCz dipole appears to increase by5%up to~170h?1Mpc.Despite,the fact that the2MRS catalogue samples the volume within~140h?1Mpc better than the PSCz survey,the opposite is observed at greater dis-tances,as revealed by comparing the two redshift distri-butions(see?gure3of Erdogdˇu et al.2006).Therefore, the PSCz catalogue samples the distant matter?uctu-ations better than the2MRS survey.This can also be appreciated when comparing the corresponding PSCz and2MRS dipole misalignment angles with the CMB (see the insert panel of?gure1).

3.2Real-Space

We concentrate now on the real space dipoles.Due to the fact that Erdogdˇu et al.(2006)did not present the 2MRS dipole in real space,we will compare our results only with previous PSCz analyses(Schmoldt et al.1999; and Rowan-Robinson et al.2000).These studies,how-ever,utilize di?erent techniques in order to correct for the redshift space distortions while they also practically exclude the local volume(galaxies with r≤4h?1Mpc), an important contributor of the local velocity?eld.

In?gure2we present our PSCz dipole(solid line) in real space taking into account the contributions from the local volume.Apparently,there are three ampli-tude dipole bumps.The?rst one,at~40h?1Mpc, is caused by the Great Attractor(Lynden-Bell et al. 1988).The second one is caused by the Shapley con-centration(Scaramella et al.1989;Raychaudhury1989; Bardelli et al.1994),a huge mass overdensity located beyond~130h?1Mpc in the general direction of the Hydra-Centaurus supercluster(e.g.,Plionis&Val-darnini1991;Scaramella et al.1991;Branchini&Plionis 1996;Plionis&Kolokotronis1998;Kocevski et al.

2004;

Figure2.The cumulative PSCz dipole in real space(a)tak-ing into account contributions from the local volume(solid line)and(b)excluding the local volume,r≤4h?1Mpc(dot dashed line).The open and the solid points show the Rowan-Robinson et al.(2000)and Schmoldt et al.(1999)dipole,re-spectively.The insert panel shows the misalignment angles (ours-solid line and Schmoldt et al.1999-solid points)be-tween the PSCz and CMB dipoles as a function of distance from the Local Group.

Kocevski&Ebeling2006and references therein).Fi-

nally,from our analysis there appears to be also a third

bump,at r~>210h?1Mpc.However,due to sparse sam-pling such deep contributions cannot be accurately de-

termined by the present galaxy sample(e.g.,Kolokotro-

nis et al.1996).

If we now exclude the local volume(r~<4h?1Mpc), we can directly compare our estimated PSCz dipole (dot dashed line)with those derived by Schmoldt et al.(1999)and Rowan-Robinson et al.(2000)(solid and open circles respectively).The three dipoles compare very well,although they are based on a di?erent treat-ment of the masked regions and of the method used to translate redshift to real space,to which we should attribute the small di?erences in the Local Universe (r≤60h?1Mpc)and between140and200h?1Mpc(in which distance range we slightly di?er only with Rowan-Robinson et al.results).The insert panel of?gure2 shows the PSCz-CMB dipole misalignment angle as a function of distance from the Local group for our(line) and Schmoldt et al.(dots)results.Evidently,they al-most coincide at large distances.The further decrease of our PSCz-CMB dipole misalignment angle out to~240

The PSCz Dipole Revisited

5

Figure 3.Fluctuations of the real-space PSCz dipole ampli-tude around its value at r =200h ?1Mpc as a function of the limiting value of the galactic latitude de?ning the masked re-gion.Insert Panel:The corresponding dipole misalignment angles as a function of b lim .

h ?1

Mpc supports the existence of possible dipole con-tributions from very large depths.

3.3Robustness of Spherical Harmonic Mask

As we discussed in section 2.1we have decided to use the mathematically elegant spherical harmonic apporach in order to deal with the so-called “zone of avoidance”.For concistency we have decided to use the same galactic latitude limit (b lim =8?)as in Schmoldt et al.(1999),who however used a cloning technique (see Lynden-Bell,Lahav &Burstein 1989)to extrapolate the galaxy dis-tribution of two strips,above and below the “zone of avoidance”,to the masked region.Rowan-Robinson et al.(2000)used a slightly di?erent technique although of the same philosophy.They divided the sky into 413areas,each approximately 100deg 2.The areas a?ected by the mask where arti?scially ?lled,at random posi-tions,with ?ux-velocity pairs either randomly selected from the whole data set or from two neighboring bins that were at least 75%full.However,the resulting dipole direction and amplitude was found,especially at large distances,to be distinctly di?erent.

Therefore it appears imperative to test the robust-ness of our approach,to variations of the galactic lat-itude limit.In Fig.3we present the ?uctuation of the real-space dipole amplitude,?,around its value at r =200h ?1Mpc for the di?erent b lim values.The ro-busteness of the dipole amplitude is evident (variations <3%).As for the dipole misalignment angle with re-spect to the CMB (see insert of Fig.3)it is always

lower than ~16?.However,there is a small increase of the misalignment angle as a function of increasing b lim which should be expected from the important structures located near the galactic plane (eg.Radburn-Smith et al.2006and references threin).

We conclude that our dipole results are robust to small variations of the considered size of the “zone-of -avoidance”.

3.4Deep Contributions

In order to further investigate the probable deeper PSCz dipole contributions we estimate the di?erential dipole in equal volume shells of di?erent sizes (see Plio-nis,Coles &Catelan 1993;Basilakos &Plionis 1998).In table 1,we present results for the case of δV ?1.4×105h ?3Mpc 3.A measure of the signi?cance of the di?erential dipole of the individual shells,is given by:S

σ3D

cos(δθcmb ).

(5)

We observe that two local shells (<129h ?1Mpc)and four distance shells reaching up to 228h ?1Mpc have signal to noise ratios >5and relatively small misalignment angles between the di?erential and CMB

dipoles:δθcmb ~<24?and 24?~<δθcmb ~<56?

for the in-ner and outer shells,respectively.The joint probabil-ity to have random alignments within the above mis-alignment limits is extremely low.Indeed,the formal probability that two vectors are aligned within δθcmb is given by the ratio of the solid angle which corresponds to δθcmb ,to the solid angle of the whole sphere,ie.,p f (δθcmb )=sin 2(δθcmb /2).

We can now estimate the random joint prob-ability of alignment,within the observed δθcmb ,of N independent vectors,which is given by:P N ≈ N

i =1p i

(δθ)/p i (90?).Due to (a)the fact that galaxies are correlated spatially and (b)the vicinity of some of the shells,we consider the joint probability of the ?rst (1-103h ?1Mpc),the eighth (187-196h ?1Mpc)and the tenth (214-221h ?1Mpc)shells,for which we ?nd

P 3~<5×10?4

.This should be considered as a conserva-tive upper limit since we have not taken into account the other four,S/N >5,shells.As a further test we also use a Monte-Carlo procedure (see Basilakos &Plionis 1998)to test whether the dipole-CMB alignments could be in-duced due to our frame transformation procedure.We ?nd that the probability to have random alignments due to the frame transformation is low and comparable to p f .As a result,we conclude that the di?erential dipole directions are not randomly oriented with respect to the

6S.Basilakos&M.Plionis

Table1.Di?erential PSCz dipole directions,misalignment angles with respect to the CMB dipole,di?erential dipole signal to noise ratio and probabilities of alignment within δθcmb(see text for complete de?nition).

1-1038238141.7290.740.3150.017 103-129139013.1249.839.3240.043 129-148662 1.8191.415.7780.400 148-163480 3.1324.9-14.2640.280 163-176375-3.8147.7-34.91370.868 176-1872600.2304.9-54.4880.480 187-196201 5.2300.644.8240.042 196-205164-5.9132.8-25.81480.925 205-214165 5.1254.8-21.5560.219 214-2211429.3297.3 1.5340.088 221-2281079.8269.8-10.5410.123 228-235100 1.6325.6-36.1800.416

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