Detection of the large scale alignment of massive galaxies at z~0.6
aa r X i v : . [ a s t r o - ph . C O ] M a y To appear in ApJ Letters
Preprint typeset using L A TEX style emulateapj v. 5/2/11
DETECTION OF THE LARGE SCALE ALIGNMENT OF MASSIVE GALAXIES AT Z ∼ . Cheng Li , Y. P. Jing , A. Faltenbacher , and Jie Wang To appear in ApJ Letters
ABSTRACTWe report on the detection of the alignment between galaxies and large-scale structure at z ∼ . θ p ) between the orientation of galaxies and the line connecting to other galaxies, and2) the cos(2 θ ) − statistic which estimates the average of cos(2 θ p ) for all correlated pairs at given sepa-ration s . We find significant alignment signal out to about 70 h − Mpc in both statistics. Applicationsof the same statistics to dark matter halos of mass above 10 h − M ⊙ in a large cosmological simu-lation show similar scale-dependent alignment signals to the observation, but with higher amplitudesat all scales probed. We show that this discrepancy may be partially explained by a misalignmentangle between central galaxies and their host halos, though detailed modeling is needed in order tobetter understand the link between the orientations of galaxies and host halos. In addition, we findsystematic trends of the alignment statistics with the stellar mass of the CMASS galaxies, in the sensethat more massive galaxies are more strongly aligned with the large-scale structure. Subject headings: dark matter — large-scale structure of universe — galaxies: halos — galaxies:formation — methods: statistical INTRODUCTIONGalaxies are not oriented at random, but show vari-ous forms of spatial alignment (Carter & Metcalfe 1980;Binggeli 1982; Dekel 1985; West 1989; Struble 1990;Plionis 1994; Plionis et al. 2003; Hashimoto et al. 2008).In particular, recent studies of galaxies in the Sloan Dig-ital Sky Survey (SDSS; York et al. 2000) have revealedthat satellite galaxies are preferentially distributed alongthe major axis of the central galaxies (Brainerd 2005;Yang et al. 2006; Azzaro et al. 2007; Faltenbacher et al.2007, 2009), and tend to be preferentially orientedtoward the central galaxy (Pereira & Kuhn 2005;Agustsson & Brainerd 2006; Faltenbacher et al. 2007).These studies were mostly limited to the local universeand intermediate-to-small scales (less than a few tensof Mpc). Similar alignment signals have been detectedfor galaxies at intermediate redshifts (0 . < z < . . < z < .
44 out to 100 h − Mpc in the SDSS clustercatalogs. There have also been many observational stud-ies which include galaxy ellipticity and measure both thegalaxy orientation-density correlation and the intrinsicshear-density correlation (e.g. Mandelbaum et al. 2006;Hirata et al. 2007; Blazek et al. 2011; Joachimi et al. [email protected] Partner Group of the Max Planck Institute for Astrophysicsat the Shanghai Astronomical Observatory and Key Laboratoryfor Research in Galaxies and Cosmology of Chinese Academy ofSciences, Nandan Road 80, Shanghai 200030, China Center for Astronomy and Astrophysics, Department ofPhysics, Shanghai Jiao Tong University, Shanghai 200240, China School of Physics, University of the Witwatersrand, PO BoxWits, Johannesburg 2050, South Africa National Astronomical Observatories, Chinese Academy ofSciences, Beijing 100012, China . < z < .
7) and largerscales ( < h − Mpc). For this we use the recently-released CMASS galaxy sample from the ninth datarelease (DR9; Ahn et al. 2012) of the Baryon Oscilla-tion Spectroscopic Survey (BOSS; Schlegel et al. 2009;Dawson et al. 2013), which is a part of the SDSS-III(Eisenstein et al. 2011). We apply two different statisticssuitable for quantifying the spatial alignment of galax-ies to the CMASS sample, and show that the align-ment between the orientation of the CMASS galaxiesand the large-scale galaxy distribution extends out to120 h − Mpc. Applying the same statistics to dark mat-ter halos in a large cosmological simulation, we detectsimilar alignment signals for the halos. This indicatesthat the observed large-scale alignment of galaxies canbe explained by the anisotropy in the large-scale matterdistribution, as we have recently found from a theoreticalanalysis of dark matter halos (Faltenbacher et al. 2012). C. Li et al. METHODOLOGYWe use two different statistics to quantify the align-ment between the orientation of galaxies and their large-scale spatial distribution: the alignment correlation func-tion (ACF) and the cos(2 θ ) − statistic, which were origi-nally introduced in Faltenbacher et al. (2009). Here webriefly describe the statistics and refer the reader to thatpaper for details.2.1. Alignment correlation function
The ACF extends the conventional two-point correla-tion function (2PCF) by including the angle between themajor axis of a galaxy and the line connecting to an-other galaxy ( θ p , projected on the sky for a survey sam-ple) as an additional property of galaxy pairs. For a pairof galaxies with one member in the sample in question(called Sample Q hereafter) and another member in thereference sample (called Sample G hereafter), we con-sider θ p as a secondary property of the pair, in additionto the separation of the paired galaxies. The estimatorfor the conventional 2PCF is then easily modified to givea measure of the ACF: ξ ( θ p , s ) = N R N G QG ( θ p , s ) QR ( θ p , s ) − , (1)where s is the redshift-space pair separation, N G and N R are the number of galaxies in the reference and randomsamples. QG ( θ p , s ) and QR ( θ p , s ) are the counts of crosspairs between the given samples for given θ p and s . Thevalue of θ p ranges from zero (parallel to the major axisof the main galaxy) to 90 degrees (perpenticular). Thus,higher amplitudes of ξ ( θ p , s ) at small (large) θ p indicatethe galaxies in G are preferentially aligned along the ma-jor (minor) axis of the galaxies in Q. Sample Q is eitherthe same as, or a subset of Sample G. In the former casethe ACF is actually the alignment auto -correlation func-tion, thus probing the alignment between galaxies withinthe same sample.2.2. The cos(2 θ ) − statistic The cos(2 θ ) − statistic measures the average value ofcos(2 θ ) over all correlated pairs for a given spatial sepa-ration. This statistic is related to the ACF by h cos(2 θ p )cor i ( s ) = R π/ cos(2 θ p ) ξ ( θ p , s ) dθ p R π/ ξ ( θ p , s ) dθ p , (2)and estimated by h cos(2 θ p )cor i ( s ) = QG θ p ( s ) QG ( s ) − ( N G /N R ) · QR ( s ) , (3)where QG θ p ( s ) is the sum of cos(2 θ p ) for all the crosspairs between samples Q and G at separation s : QG θ p ( s ) = X ( i,j ) ∈ QG ( s ) cos(2 θ i,jp ) . (4)The statistic so-defined ranges between -1 and 1, withpositive and negative values indicating a preference forsmall ( < ◦ ) and large ( > ◦ ) angles. Values of zeromeans isotropy. DATA3.1.
The BOSS/CMASS galaxy sample
By selection the CMASS is a roughly volume-limitedsample of massive galaxies in the redshift range of 0 . The MultiDark Run 1 Simulation In addition to analyzing the CMASS galaxy sample, wealso apply our alignment statistics to dark matter halosin the MultiDark Run 1 simulation (MDR1; Prada et al.2012) . Assuming the WMAP7 concordant ΛCDM cos-mology, the simulation uses 2048 particles to followthe dark matter distribution in a cubic region with 1 h − Gpc on a side, which corresponds to a particle massof 8 . × h − M ⊙ . Dark matter halos are identifiedby means of a friends-of-friends (Davis et al. 1985) algo-rithm with a linking length of 0.17 times the mean par-ticle separation. For the comparison with the CMASSgalaxy sample we use snapshot 60 which corresponds toa redshift of z ∼ . z -axis. We limit our analysis todark matter halos with masses above 10 h − M ⊙ , i.e.,the aforementioned lower limit of the host halo mass forCMASS galaxies as found by White et al. (2011). Halosof this mass are identified with a number of 115 par-ticles. In this case an uncertainty of 10% is expectedfor the halo orientation determination (Bett et al. 2007;Joachimi et al. 2013), which we expect not to introducesignificant bias into our result in the next section. RESULTSWe have obtained the alignment correlation function ξ ( θ p , s ) from the CMASS galaxy sample for three succes-sive angular intervals: 0 ◦ ≤ θ p < ◦ , 30 ◦ ≤ θ p < ◦ ,and 60 ◦ ≤ θ p < ◦ , as well as the conventional two-point correlation function, ξ ( s ), which is a function of http://data.sdss3.org/datamodel/fiels/BOSS LSS REDUX/ arge scale alignment of massive galaxies at z ∼ . Fig. 1.— Left: difference between the alignment correlation function at given projected angle ξ ( θ p , s ) and the conventional correlationfunction ξ ( s ), obtained from the CMASS galaxy sample. Results at the small and large θ p bins are plotted in grey and black symbolsseparately. The hatched regions plotted in red/green/blue represent the 1 σ variance between 100 random samples in which the positionangles are randomly shuffled among the galaxies, measured for the three angle bins separately. The solid and dashed lines show the resultsfor dark matter halos with mass above 10 h − M ⊙ . The solid lines are for the halos with no misalignment, and the dashed lines are resultswith the misalignment parameter of σ θ = 35 ◦ . Right: the cos(2 θ ) − statistic measured for the same galaxy sample and dark matter halocatalog. Symbols and lines are the same as in the left-hand panel. only the redshift-space separation and can be regardedas an average of the alignment correlation function overthe full range of θ p .In Figure 1 (left panel) we plot the difference in thealignment correlation function at small/large angles withrespect to the conventional correlation function ξ ( s ).The error bars plotted in the figure and in what followsare estimated using the bootstrap resampling technique(Barrow et al. 1984). We have constructed 100 bootstrapsamples based on the real sample, and we estimate thedifference between ξ ( θ, s ) and ξ ( s ) for each sample. Theerror at given scale is then estimated from the 1 σ vari-ance between the bootstrap samples.As can be seen, ξ ( θ p , s ) differ from ξ ( s ) at both smalland large angles, with stronger clustering at smaller an-gles and weaker clustering at larger angles, consistentwith the picture that the major axis of the galaxies ispreferentially aligned with their spatial distribution.It is essential to perform systematics tests on anyclustering measurements (e.g. Mandelbaum et al. 2005;Sanchez et al. 2012). As one of such tests, we have re-peated the same analysis as above for a set of 100 ran-dom samples in which the position angles are shuffledat random among the main galaxies (Sample Q). Thehatched regions plotted in red/green/blue in Figure 1show the 1 σ variance of the alignment correlation func-tion between the random samples, measured for the threeangle bins separately. It is interesting that the alignmentsignal detected in the real sample is significantly seen fora wide range of scales, from the smallest scales probed( ∼ h − Mpc) out to ∼ h − Mpc according to both thebootstrap errors of the measurements and the 1 σ regionsof the random samples.The right-hand panel of Figure 1 shows the cos(2 θ ) − statistic, plotted in solid circles for the CMASSsample and in green hatched region for the 100 randomlyshuffled samples. The statistic for the real sample showspositive values on all scales probed, while its differencefrom the random samples is significantly seen only forscales below ∼ h − Mpc, consistent with what the left-hand panel reveals. As mentioned above, a positive valuein the cos(2 θ ) − statistic indicates a preference for anglessmaller than 45 ◦ , thus implying that the major axis ofthe galaxies tends to be aligned with the large-scale dis-tribution of galaxies. The cos(2 θ ) − statistic of the ran-dom samples shows a systematic positive bias at scalesabove ∼ h − Mpc, implying that the position angle ofthe CMASS galaxies is not randomly distributed on thesky, a cosmic variance effect due to the limited surveyarea and probably also the quite irregular shape of thesurvey geometry. This can be tested in future with mockcatalogs or later data releases of the BOSS survey.For comparison the same statistics obtained for darkmatter halos of mass M h > h − M ⊙ in the MDR1simulation are shown in Figure 1 as solid lines. Align-ment signal is seen in both statistics and on all thescales up to 120 h − Mpc. Both statistics show strongdependence on the spatial scale, which is very simi-lar to what is seen for the CMASS galaxies. At fixedscale, however, the alignment of the halos is system-atically stronger than that of the galaxies. This dis-crepancy might be partially (if not totally) due to themisalignment between the orientation of central galaxiesand that of their host halos. A previous study done byOkumura et al. (2009) on the alignment of luminous redgalaxies (LRGs) at 0 . < z < . 47 in the SDSS/DR6suggested that the misalignment angle between a centralLRG and its host halo follows a Gaussian distribution C. Li et al. Fig. 2.— Alignment correlation function and the cos(2 θ ) − statistic for a subset of the CMASS galaxies with fracDev > . R deV > ′′ and ellipticity 1 − b/a > . 2. Symbols and lines are the same as in Figure 1, except that the red/blue lines in the left panel and the redlines in the right panel show the results for a set of 51 jacknife samples. See the text for detailed description. Fig. 3.— Alignment correlation function for the CMASS galaxies with stellar masses either below (left panel) or above (right panel)10 . M ⊙ . The result for the full sample is repeated for reference in both panels as the red/blue solid lines. with a zero mean and a typical width σ θ = 35 . σ θ = 35 ◦ for the misalignment angle. Theresults are plotted as dashed lines in Figure 1. As ex-pected, the amplitude of both statistics decreases con-siderably, becoming comparable with the data on scalesbelow ∼ h − Mpc. This simple experiment implies thatthe observed large-scale alignment signal for the massivegalaxies at z ∼ . z ∼ . ∼ , 000 galaxies with the weightof the de Vaucouleurs model component fracDev > . R deV > ′′ , andellipticity 1 − b/a > . 2. The results are shown in Fig-ure 2, with the grey/black symbols for the real sampleand the hatched regions for the randomly shuffled sam-ples. In addition, we have constructed 51 jacknife sam-ples by dividing the CMASS/North area into 51 non-overlapping subregions and dropping one of the subre-gions from each of the 51 samples. The results of thesesamples are plotted in the red/blue lines in the same fig-ure. These tests demonstrate that the alignment signalis reliably detected in the CMASS sample, at least to ∼ h − Mpc, and is robust to the position angle mea-surements and the statistical error estimation.Finally, we focus on the CMASS galaxies and exam-ine the dependence of the alignment statistics on thestellar mass of the galaxies. For this we take the stel-lar mass esimates from the Wisconsin group derivedby Chen et al. (2012) from a BOSS spectrum princi-pal component analysis (PCA) using the stellar popu-lation models of Bruzual & Charlot (2003). We dividethe CMASS galaxies into two subsamples, with stellarmass either below or above 10 . M ⊙ . We take each ofthe subsamples as Sample Q, and we measure the align-ment cross-correlation function with respect to the fullCMASS galaxy sample (Sample G) in the same way asabove. The results are shown in Figure 3, with the twopanels for the two subsamples separately. The result ofthe full sample is repeated in both panels as red/bluesolid lines, for reference. Both subsamples show system-atic differences from the full sample, in the sense that thehigh-mass subsample shows stronger-than-average align-ment signals and the low-mass subsample shows weaker-than-average signals. SUMMARYWe have applied two statistics, that are defined to besuitable for quantifying the spatial alignment of galaxies,to the CMASS galaxy sample from the SDSS-III/BOSSDR9, which consist of about 2 × massive galaxieswith mass above ∼ M ⊙ and redshift in the range0 . < z < .