Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed27January2011 (MNLATEXstylefilev2.2) Clustering of HI galaxies in HIPASS and ALFALFA S. S. Passmoor1⋆, C. M. Cress1,2, A. Faltenbacher1 1 1Physics Department, Universityof the WesternCape , Bellville 7535, South Africa 1 2Centre for HighPerformance Computing, 15 Lower Hope St, Cape Town 7700, South Africa 0 2 n 27January2011 a J 6 ABSTRACT 2 WeinvestigatetheclusteringofHI-selectedgalaxiesintheALFALFAsurveyandcom- pareresultswiththoseobtainedforHIPASS.Measurementsoftheangularcorrelation ] functionandthe inferred3D-clusteringarecomparedwith resultsfromdirectspatial- O correlationmeasurements.Weareabletomeasureclusteringonsmallerangularscales C and for galaxies with lower HI masses than was previously possible. We calculate the . expected clustering of dark matter using the redshift distributions of HIPASS and h ALFALFA and show that the ALFALFA sample is somewhat more anti-biased with p - respect to dark matter than the HIPASS sample. o r Key words: large-scale structure of the universe - radio lines: galaxies t s a [ 1 1 INTRODUCTION latter work also measures thebiasof HIPASSgalaxies rela- v tiveto theexpected dark matterdistribution. 7 Measurementsoftheclusteringofgalaxies allows onetoin- In this paper we measure the clustering of HI-selected 0 vestigate the relationship between dark and luminous mat- galaxies detected with the Arecibo L-band Feed Array 0 ter. By comparing galaxies selected in different ways one (ALFA) and compiled in the partially completed AL- 5 gains understanding of how different galaxies trace the un- . FALFA survey (the Arecibo Legacy Fast ALFA survey, 1 derlyingdarkmatterandalsoofprocessesatworkingalaxy Giovanelli et al.2005).Theresultsarecomparedwiththose 0 evolution. This information is important when using galax- obtained for HIPASS.Clustering measurements in HIPASS 1 ies as probes of cosmological parameters. are limited to large angular scales where the beam-size of 1 A number of new radio telescopes, such as the ∼15arcminsdoes notcauseconfusion. TheALFALFAres- : MeerKAT1 ,ASKAP2 andtheSKA,areinthepipelineand v olution is more than four times better allowing us to probe i they will detect huge numbers of galaxies using HI. A reli- clustering on smaller scales. The rms noise per ALFALFA X able measure of the bias of HI-selected galaxies and insight beam is about six times smaller, providing a catalogue of r intotheevolutionofthebiasisimportantforforecastingthe a sources which spansa wider range of redshifts and includes capabilities of telescopes which will probe HI at intermedi- galaxies withlowerHImasses. Wearethusabletomeasure ate or high-redshifts. The clustering of HI-selected galax- clustering of HI-selected galaxies in regimes that have not ieshasbeenstudiedbyMeyeret al.(2007),Basilakos et al. yetbeenexploredandtoinvestigatetrendsseeninHIPASS, (2007) and Ryan-Weber (2006). They used data from the using an independent survey. HI Parkes All Sky Survey (HIPASS, Meyer et al. 2004), a The outline of the paper is as follows: In § 2 we give a blind survey for HI of the southern sky which generated short introduction to the HIPASS and ALFALFA surveys. a catalogue of 4315 sources, the bulk of which have red- Thecomputationoftheangularandspatialtwo-pointcorre- shifts below z ∼0.02. They showed that HI-selected galax- lationfunctionsisdescribedin§3.Theresultsarepresented, ies are less clustered than galaxies selected in other ways. discussedandcomparedwithearlierworkin§4.Finally,§5 Meyer et al. (2007) investigated clustering of various sub- concludes with a short summary. samplesofHIPASSgalaxies,showingthatgalaxieswithhigh rotation velocities are moreclusteredthan thosewith lower rotationvelocities.Therewereindicationsthatgalaxiescon- taining more HI are also more clustered but the differences 2 DATA were not as pronounced as in Basilakos et al. (2007). The HIPASScovers all the southern sky with δ <+2◦ and and can detect HI with velocities in the range 300 kms−1 − 12700 kms−1. The rms noise per beam is ∼ 13 mJy ⋆ E-mail:sean.passmoor@gmail.com (Meyeret al. 2004). To exclude structure associated with 1 www.ska.ac.za theMilky-Way,likehigh-velocitycloudsandlowmasssatel- 2 www.atnf.csiro.au/SKA/ lites, we only use sources with recessional velocities larger 2 S. S. Passmoor et al. 0.1 struction of the random samples. We do not employ the ALFALFA weighted correlation functions used in Meyeret al. (2007) 0.09 HIPASS Virgo 1 asweareinterestedincomparingtheresultsofthetwosur- 0.08 Anti-Virgo veys and in comparing our results with those predicted for er 0.07 Virgo 2 mb dark matter within a ΛCDM model. The unweighted mea- Nu 0.06 surementssufficeforthisworkandweareabletocheckour ed 0.05 unweighted results against those of Meyeret al. (2007). s ali 0.04 m or 0.03 N 3.1 The Angular Two-Point Correlation Function 0.02 0.01 The angular correlation function, ω, is a simple measure of 0 theclusteringofgalaxiesasafunctionofangularseparation 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 on the sky, θ, which does not require redshift information. Redshift It is calculated by counting galaxy pairs within a given an- Figure 1. Plot of the normalised redshift distribution of the gularseparation binandcomparingthisnumbertoacorre- HIPASSandALFALFAsurveysaswellasthedistributionofthe sponding figure derived from a random catalogue with the ALFALFAsourcesinthethree,spatiallyseparatedstrips. same area and shape. The angular correlation, ω(θ), gives the excess probability, over random, of finding two galaxies separated by angle θ. than600kms−1.TheaveragemassofHIinHIPASSgalaxies If we assume a redshift-dependent power law de- is 3.24×109M . scribes the 3-D real-space correlation function, ξ(r,z) = ⊙ When completed, the ALFALFA Survey (r/r0)−γ(1+z)γ−(3+ǫ) (as in Peebles 1980 and Loan et al. (Giovanelli et al. 2005) will cover 7000deg2 of sky with 1997)thentheangularcorrelation functionisrelatedtothe high galactic latitude and to a depth of cz ∼18000kms−1. spatial correlation function by the Limber equation (Rubin Thermsnoiseofthesurveyis∼2.2mJyandthebeam-size 1954; Limber 1954): is ∼ 3.6 arcminutes. Currently the ALFALFA survey Tcohnetsaeinsartehrteheesttrwipos sctorvipersincgenatrteodtalonaretaheofV∼irg4o00redgeigo2n. θ 1−γ = R0∞ N2(z)(1+z)γd−′((z3+)rǫ0−)√γπ(d(z)θ)1−γ Γ(−Γ(1221+γ12)γ) , and the anti-Virgo strip. They contain 1796 sources with (cid:18)θ0(cid:19) ∞N(z)dz 2 0 cz >600kms−1. The first completed Virgo strip is defined (cid:0)R (cid:1) (1) by 11h44m < α<14h00m and 12◦ <δ <16◦ and contains whered(z)isthecomovingdistanceandN(z)istheredshift 708 sources. The second Virgo strip contains 556 galaxies number density distribution of the sources (cf. Figure 1). within11h36m <α<13h52mand8◦ <δ<12◦(Kent et al. We use ǫ=0.8, consistent with the expected clustering be- 2008). The anti-Virgo strip contains 488 sources within haviourinlineartheory,althoughthesurveysaresoshallow 22h00m <α<03h04m and 26◦ <δ<28◦ (Saintonge et al. thattheevolutionofξ couldbeignored. Themeasured val- 2008). A circular region, with radius of 1◦ centred on uesforthelogarithmic slope aθ =1−γ andthecorrelation M 87, has been removed from the survey area due to the lengthθ0(ω(θ0)=1)canthenbeusedtodeterminethe3-D interference of M 87 (Giovanelli et al. 2007). The average parameters r0 and γ. ALFALFA HI mass is 2.48×109M . The source density of The errors for ω are calculated using jack-knife re- the ALFALFA catalogue is approx⊙imately 20 times higher sampling(Lupton1993).Forthispurposethedataaresplit than that of theHIPASSsurvey. up into N RA-bins and the correlation function is recalcu- Figure 1 displays the normalised redshift distributions latedrepeatedlyeachtimeleavingoutadifferentbin.Thusa of the HIPASS and ALFALFA surveys as well as the red- setofN values{ωi,i=1,...,N}forthecorrelationfunction shift distributions in the three separate ALFALFA regions. are obtained and the jack-knife error of the mean, σωmean, A redshift of z = 0.02 corresponds to ∼ 70h−1Mpc which is given by is roughly the distance to the Coma supercluster. The high N galaxy density near theComa cluster and Virgo cluster are σ =v(N−1) (ω −ω)2/N . (2) evident in the redshift distributions shown for the Virgo ωmean u i regions. In the anti-Virgo region the effect of the Perseus- ut Xi=1 Piscessuperclustercanalsobeseenasaslightenhancement The HIPASSsample has been divided into 24 RA bins of galaxies at a redshift of about z ≈0.025. Below, we will while for the ALFALFA catalogue we use 12 binssuch that discusstheimpactoftheseinhomogeneitiesonthedetermi- each bin contains approximately thesame area of thesky. nation of the two-point correlation function. 3.2 The Projected Two-Point Correlation Function 3 TWO-POINT CORRELATION FUNCTIONS The projected correlation function, Ξ(σ), is determined by Herewereviewsomebasicpropertiesoftheangularandpro- the number of pairs at given radial and projected separa- jectedtwo-pointcorrelationfunctions(ωandΞrespectively) tions, π and σ, and a subsequent integration along the ra- and indicate their relations to the three dimensional (3-D) dialdirection.Forthatpurposetheabsoluteradialdistance real-space two-point correlation function, ξ. Subsequently, betweenapairofgalaxies, π=|(v −v )/H |,andtheiran- i j 0 we introduce the estimator used here and discuss the con- gularseparation,θ,areconvertedintoaprojecteddistance, Clustering of HI galaxies 3 σ=[(vi+vj)/H0]tan(θ/2). Thus, 10 Dark matter prediction for ALFALFA Ξ(σ) 2 Dlimit Dark matter prediction for HIPASS = ξ(σ,π)dπ (3) ALFALFA σ σ Z HIPASS 0 1 whereD isthelimit wheretheintegral converges.Here limit we set Dlimit = 25h−1Mpc ≈ 2500kms−1. The projected θ) correlation function is related to the real-space correlation ω( function by(e.g., Davis & Peebles 1983): 0.1 Ξ(σ) 2 ∞ rdr = ξ(r) . (4) σ σ Z (r2−σ2)1/2 σ 0.01 Assumingthattheprojectedandreal-spacecorrelationfunc- 0.1 1 10 tions follow power laws within the region of interest (r < θ (deg) 10h−1Mpc), the parameter for the real-space correlation Figure 2. Angular correlation functions for HIPASS and AL- function can be derived from the projected one by the fol- FALFA.Errorbarswerecalculatedusingjack-knifesampling.The lowing expression: solidredlineandthesmall-dashedbluelineshowthecorrespond- Ξ(σ) = r0 γ Γ(1/2)Γ((γ−1)/2) (5) ingpowerlawfitsforanglesbetween0.1and8◦forALFALFAand σ (cid:16)σ(cid:17) Γ(γ/2) between1and10◦fortheHIPASSdata.Theprojectedclustering ofdarkmatter(inaΛCDMmodel)withredshiftdistributionsof More specifically, we calculate r0 and γ by fitting a power HIPASSandALFALFA areshownbythe greendashed lineand law, Ξ(σ)/σ = (σ/σ0)−aσ, using the Levenberg-Marquardt themagentadotted linerespectively nonlinearleast-squaresmethod.Theparametersofthereal- space correlation function are then given by We repeat the random catalogue generation 20 times and 1 r =σ Γ(1/2)Γ((aσ−1)/2) −aσ (6) thecalculation of random pairs in order to reduce the vari- 0 0(cid:20) Γ(aσ/2) (cid:21) ance from therandom sampling. γ =a . (7) σ 3.4 The angular correlation function of dark Therefore, similar to the angular correlation function the matter projected correlation functioncanbeusedtodeterminethe real-space clustering. We apply both methods to determine Based on Limber’s equation, the redshift distributions of thereal-spaceclusteringstrengthbasedontheHIPASSand HIPASS and ALFALFA and the expression for the non- theALFALFA surveysand compare the results. linearpowerspectrumdiscussedinPeacock & Dodds(1996) we predict the angular correlation function of dark matter using the cosmological parameters given in Komatsu et al. 3.3 Estimator and random sampling (2009). The bias parameter, b, at various angles is then de- Threedifferent estimators are commonly used todetermine termined by the two-point correlation function (Davis & Huchra 1982; ω Hamilton 1993; Landy & Szalay 1993). In this work we use b= HI . (9) the Landy& Szalay (1993) estimator as it reduces errors rωdarkmatter caused byedgesand holes within agiven catalogue. Inpar- ticular this is important for the ALFALFA survey with the hole caused by M 87 (Giovanelli et al. 2007) and the large 4 RESULTS edge effects due to the three strips. The estimator is of the 4.1 The full HIPASS and ALFALFA samples form: DD(r)−2DR(r)+RR(r) 4.1.1 Angular correlation functions ξ(r)= , (8) RR(r) Figure2showstheangularcorrelationfunctionsforHIPASS whereristheseparationdistancewhichhasdifferentmean- andALFALFAdataaswellasthepredictedcorrelationfunc- ings for the different correlation functions. For the angular tions of cold dark matter weighted with the redshift distri- correlation it denotes the separation angle, θ, for the pro- butionsof thesurveys.Thestraight lines are powerlaw fits jected correlation function it is the projected distance, σ, forpairseparationsintherangebetween0.1and8◦ forAL- and for thereal-space correlation it indicates thereal-space FALFA and between 1 and 10◦ for HIPASS. The effect of distancer.DD(r)isthenumberofdata-datapairs,DR(r)is source confusion in HIPASS is evident at smaller angular thenumberofdata-randompairs,andRR(r)isthenumber scales. The corresponding parameters, θ and a , are given 0 θ of random-random pairs all with separations r. in Table 1. The random catalogues were generated with uniform The measured slopes in the two surveys agree reason- distributionsontheskyandredshiftdistributionswhichre- ablywell.Asexpected,thevalueofθ islowerforALFALFA 0 semblethedistributionofrecessionalvelocitiesinthesurvey since it is deeper than HIPASS and the clustering in 3-D smoothed using kernel density estimation (Wand & Jones iswashed outinthe2-Dprojection. ALFALFAalso detects 1995). Throughout this work we use random samples that galaxieswithlowerHImasseswhicharepotentiallylessclus- are equal in size compared to the corresponding data set. tered. 4 S. S. Passmoor et al. HIPASS ALFALFA 10000 ALFALFA regions with clusters removed θa0θ 00..65063±±00.0.024◦ 00..50944±±0.00.6013◦ 1000 AnVVti-iiVrrggiroog 12o -1c) 100 Table 1.Theangularclusteringfittedparameters,θ0 andaθ. 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Clustering of HI galaxies in HIPASS and ALFALFA

Similar Clustering of HI galaxies in HIPASS and ALFALFA