Planck Intermediate Results. XI: The gas content of dark matter halos: the Sunyaev-Zeldovich-stellar mass relation for locally brightest galaxies
Planck Collaboration, P. A. R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, F. Atrio-Barandela, J. Aumont, C. Baccigalupi, A. J. Banday, R. B. Barreiro, R. Barrena, J. G. Bartlett, E. Battaner, K. Benabed, J.-P. Bernard, M. Bersanelli, I. Bikmaev, H. Böhringer, A. Bonaldi, J. R. Bond, J. Borrill, F. R. Bouchet, H. Bourdin, R. Burenin, C. Burigana, R. C. Butler, A. Chamballu, R.-R. Chary, L.-Y Chiang, G. Chon, P. R. Christensen, D. L. Clements, S. Colafrancesco, S. Colombi, L. P. L. Colombo, B. Comis, A. Coulais, B. P. Crill, F. Cuttaia, A. Da Silva, H. Dahle, R. J. Davis, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, J. Démoclès, J. M. Diego, H. Dole, S. Donzelli, O. Doré, M. Douspis, X. Dupac, T. A. Enßlin, F. Finelli, I. Flores-Cacho, M. Frailis, E. Franceschi, M. Frommert, S. Galeotta, K. Ganga, R. T. Génova-Santos, M. Giard, Y. Giraud-Héraud, J. González-Nuevo, K. M. Górski, A. Gregorio, A. Gruppuso, F. K. Hansen, D. Harrison, C. Hernández-Monteagudo, D. Herranz, S. R. Hildebrandt, E. Hivon, M. Hobson, W. A. Holmes, A. Hornstrup, W. Hovest, K. M. Huffenberger, G. Hurier, T. R. Jaffe, A. H. Jaffe, W. C. Jones, M. Juvela, E. Keihänen, R. Keskitalo, I. Khamitov, T. S. Kisner, R. Kneissl, J. Knoche, M. Kunz, H. Kurki-Suonio, A. Lähteenmäki, J.-M. Lamarre, A. Lasenby, C. R. Lawrence, M. Le Jeune, R. Leonardi, P. B. Lilje, M. Linden-Vørnle, et al. (97 additional authors not shown)
aa r X i v : . [ a s t r o - ph . C O ] D ec Astronomy&Astrophysicsmanuscript no. PIP18 c (cid:13)
ESO 2018October 31, 2018
Planck Intermediate Results. XI: The gas content of dark matterhalos: the Sunyaev-Zeldovich-stellar mass relation for locallybrightest galaxies
Planck Collaboration: P. A. R. Ade , N. Aghanim , M. Arnaud , M. Ashdown , , F. Atrio-Barandela , J. Aumont , C. Baccigalupi ,A. J. Banday , , R. B. Barreiro , R. Barrena , J. G. Bartlett , , E. Battaner , K. Benabed , , J.-P. Bernard , M. Bersanelli , ,I. Bikmaev , , H. B¨ohringer , A. Bonaldi , J. R. Bond , J. Borrill , , F. R. Bouchet , , H. Bourdin , R. Burenin , C. Burigana , ,R. C. Butler , A. Chamballu , R.-R. Chary , L.-Y Chiang , G. Chon , P. R. Christensen , , D. L. Clements , S. Colafrancesco ,S. Colombi , , L. P. L. Colombo , , B. Comis , A. Coulais , B. P. Crill , , F. Cuttaia , A. Da Silva , H. Dahle , , R. J. Davis , P. deBernardis , A. de Rosa , G. de Zotti , , J. Delabrouille , J. D´emocl`es , J. M. Diego , H. Dole , , S. Donzelli , O. Dor´e , , M. Douspis ,X. Dupac , T. A. Enßlin , F. Finelli , I. Flores-Cacho , , M. Frailis , E. Franceschi , M. Frommert , S. Galeotta , K. Ganga ,R. T. G´enova-Santos , M. Giard , , Y. Giraud-H´eraud , J. Gonz´alez-Nuevo , , K. M. G´orski , , A. Gregorio , , A. Gruppuso ,F. K. Hansen , D. Harrison , , C. Hern´andez-Monteagudo , , D. Herranz , S. R. Hildebrandt , E. Hivon , , M. Hobson , W. A. Holmes ,A. Hornstrup , W. Hovest , K. M. Hu ff enberger , G. Hurier , T. R. Ja ff e , , A. H. Ja ff e , W. C. Jones , M. Juvela , E. Keih¨anen ,R. Keskitalo , , I. Khamitov , T. S. Kisner , R. Kneissl , , J. Knoche , M. Kunz , , , H. Kurki-Suonio , , A. L¨ahteenm¨aki , ,J.-M. Lamarre , A. Lasenby , , C. R. Lawrence , M. Le Jeune , R. Leonardi , P. B. Lilje , , M. Linden-Vørnle , M. L´opez-Caniego ,P. M. Lubin , G. Luzzi , J. F. Mac´ıas-P´erez , C. J. MacTavish , B. Ma ff ei , D. Maino , , N. Mandolesi , , , M. Maris , F. Marleau ,D. J. Marshall , E. Mart´ınez-Gonz´alez , S. Masi , M. Massardi , S. Matarrese , P. Mazzotta , S. Mei , , , A. Melchiorri , , J.-B. Melin ,L. Mendes , A. Mennella , , S. Mitra , , M.-A. Miville-Deschˆenes , , A. Moneti , L. Montier , , G. Morgante , D. Mortlock ,D. Munshi , J. A. Murphy , P. Naselsky , , F. Nati , P. Natoli , , , H. U. Nørgaard-Nielsen , F. Noviello , D. Novikov , I. Novikov ,S. Osborne , C. A. Oxborrow , F. Pajot , D. Paoletti , L. Perotto , F. Perrotta , F. Piacentini , M. Piat , E. Pierpaoli , R. Pi ff aretti , ,S. Plaszczynski , E. Pointecouteau , , G. Polenta , , L. Popa , T. Poutanen , , , G. W. Pratt , S. Prunet , , J.-L. Puget , J. P. Rachen , ,R. Rebolo , , , M. Reinecke , M. Remazeilles , , C. Renault , S. Ricciardi , I. Ristorcelli , , G. Rocha , , M. Roman , C. Rosset ,M. Rossetti , , J. A. Rubi˜no-Mart´ın , ∗ , B. Rusholme , M. Sandri , G. Savini , D. Scott , L. Spencer , J.-L. Starck , V. Stolyarov , , ,R. Sudiwala , R. Sunyaev , , D. Sutton , , A.-S. Suur-Uski , , J.-F. Sygnet , J. A. Tauber , L. Terenzi , L. To ff olatti , , M. Tomasi ,M. Tristram , L. Valenziano , B. Van Tent , P. Vielva , F. Villa , N. Vittorio , L. A. Wade , B. D. Wandelt , , , W. Wang , N. Welikala ,J. Weller , S. D. M. White , M. White , A. Zacchei , and A. Zonca (A ffi liations can be found after the references) Received XXXX; accepted YYYY
ABSTRACT
We present the scaling relation between Sunyaev-Zeldovich (SZ) signal and stellar mass for almost 260,000 locally brightest galaxies (LBGs)selected from the Sloan Digital Sky Survey (SDSS). These are predominantly the central galaxies of their dark matter halos. We calibrate thestellar-to-halo mass conversion using realistic mock catalogues based on the Millennium Simulation. Applying a multi-frequency matched filter tothe
Planck data for each LBG, and averaging the results in bins of stellar mass, we measure the mean SZ signal down to M ∗ ∼ × M ⊙ , with aclear indication of signal at even lower stellar mass. We derive the scaling relation between SZ signal and halo mass by assigning halo propertiesfrom our mock catalogues to the real LBGs and simulating the Planck observation process. This relation shows no evidence for deviation froma power law over a halo mass range extending from rich clusters down to M ∼ × M ⊙ , and there is a clear indication of signal down to M ∼ × M ⊙ . Planck ’s SZ detections in such low-mass halos imply that about a quarter of all baryons have now been seen in the form of hothalo gas, and that this gas must be less concentrated than the dark matter in such halos in order to remain consistent with X-ray observations. Atthe high-mass end, the measured SZ signal is 20 % lower than found from observations of X-ray clusters, a di ff erence consistent with Malmquistbias e ff ects in the X-ray sample. Key words. cosmology: observations — cosmic microwave background — large-scale structure of the Universe — galaxies: clusters: general
1. Introduction
Galaxy evolution is currently understood to reflect a thermal cy-cle operating between baryonic components confined in darkmatter halos. Gas cools radiatively during the hierarchical build-up of the halo population and condenses to form galaxies in halocores. Left unchecked, cooling results in more massive galaxiesthan observed (Balogh et al. 2001; Lin & Mohr 2004; Tornatore ∗ Corresponding author: J. A. Rubi˜no-Mart´ın, [email protected] et al. 2003), and one must invoke an additional source of non-gravitational heating to prevent a “cooling crisis” (White & Rees1978; Cole 1991; White & Frenk 1991; Blanchard et al. 1992).Feedback from star formation and supernovae appears insu ffi -cient to halt cooling in massive halos (Borgani et al. 2004), sosome modelers have invoked additional heating by active galac-tic nuclei (AGN, Churazov et al. 2002; Springel et al. 2005a;McNamara & Nulsen 2007). Such models show substantiallyimproved agreement with the luminosity-temperature relationof X-ray clusters (Valageas & Silk 1999; Bower et al. 2001; Cavaliere et al. 2002) and the luminosity function of galaxies(Croton et al. 2006; Bower et al. 2006; Somerville et al. 2008).The energetics of AGN feedback imply that it should have es-pecially strong e ff ects on low-mass clusters, heating gas in thecentral regions and pushing it to larger radii, thereby reducingboth gas fractions and X-ray luminosities (Puchwein et al. 2008;McCarthy et al. 2010).Relationships between the gas, stellar, and dark matter prop-erties of halos are important to our understanding of galaxy for-mation. Measurements of these relationships over a wide rangeof halo mass, from rich clusters down to individual galaxies, aretherefore a primary objective of a number of current observa-tional campaigns. Recent studies have probed the relationshipbetween the mass of a halo and the stellar mass of its centralgalaxy (the SHM relation) using “abundance matching” tech-niques, the dynamics of satellite galaxy populations, and gravita-tional lensing (Guo et al. 2010; Moster et al. 2010; Mandelbaumet al. 2006; Leauthaud et al. 2011).Corresponding constraints on the gas content of halos overa similar mass range are not yet available. Although there aremany detailed X-ray studies of the intracluster medium, thesemostly concern massive clusters; lower mass groups are faintand so are di ffi cult to study individually. The Sunyaev-Zeldovich(SZ) e ff ect (Sunyaev & Zeldovich 1972; Birkinshaw 1999) of-fers a fresh means to address this problem. Large-area SZ sur-veys are just beginning to be amassed by ground-based instru-ments such as the Atacama Cosmology Telescope (ACT, Swetzet al. 2008; Marriage et al. 2010; Sehgal et al. 2010; Hand et al.2011), the South Pole Telescope (SPT, Carlstrom et al. 2009;Staniszewski et al. 2009; Vanderlinde et al. 2010; Williamsonet al. 2011) and APEX-SZ (Dobbs et al. 2006), as well as bythe Planck satellite mission, (Planck Collaboration VIII 2011;Planck Collaboration IX 2011; Planck Collaboration X 2011;Planck Collaboration XI 2011; Planck Collaboration XII 2011).High S / N observations of individual objects are not currentlypossible over the full mass range from galaxy clusters down toindividual bright galaxies. The SHM relation can only be esti-mated for lower mass objects through statistical methods appliedto large catalogues. In this context, the SZ e ff ect presents excit-ing new opportunities. First steps in this direction were taken byPlanck Collaboration XII (2011) and Hand et al. (2011), withmore recent work by Draper et al. (2012) and Sehgal et al.(2012). In our first study (Planck Collaboration XII 2011), webinned large numbers of maxBCG (Koester et al. 2007) clustersby richness to measure the relation between mean SZ signal andrichness. In a similar manner, Hand et al. (2011) binned ACTmeasurements of luminous red galaxies to determine the meanrelation between SZ signal and LRG luminosity.Here, we extend our previous work with Planck multi-frequency observations of a large sample of locally brightestgalaxies (LBGs). These were selected from the Sloan DigitalSky Survey (SDSS) using criteria designed to maximize the frac-tion of objects that are the central galaxies of their dark matterhalos. We stack the
Planck data in order to estimate the meanSZ signal for LBGs in a series of stellar mass bins. We thenuse mock galaxy catalogues based on the Millennium Simulationand tuned to fit the observed abundance and clustering of SDSS Planck ( ) is a project of theEuropean Space Agency (ESA) with instruments provided by two sci-entific consortia funded by ESA member states (in particular the leadcountries France and Italy), with contributions from NASA (USA) andtelescope reflectors provided by a collaboration between ESA and a sci-entific consortium led and funded by Denmark. galaxies to establish the relation between stellar and halo mass. Planck is a unique SZ instrument for this purpose because of itslarge frequency coverage and the fact that it observes the entireSDSS survey area, allowing study of large samples of galaxysystems with extensive multi-wavelength data.We unambiguously ( > σ ) detect the SZ signal down to stel-lar masses of 2 × M ⊙ , corresponding to an e ff ective halomass M of 2 × M ⊙ (see Sect. 2) and we find clear indica-tions of signal down to 10 M ⊙ ( M = × M ⊙ ). Detailedsimulation both of the galaxy sample and of the Planck mea-surement process allows us to correct the e ff ects of halo mis-centering and of the scatter in halo mass at fixed stellar masswhen estimating the SZ signal-halo mass relation. We find thatthe relation is well described by a single power law within itsstatistical uncertainties. At the high end, our results overlap themass range probed by X-ray clusters, where we find a 20% lowerSZ signal than obtained from fits to X-ray selected cluster sam-ples. This di ff erence is consistent with possible Malmquist biase ff ects in the X-ray sample. The gas properties of dark matterhalos display a remarkable regularity from the poorest groups tothe richest clusters.Throughout this paper, we adopt a fiducial Λ CDM cosmol-ogy consistent with the WMAP7 results (Komatsu et al. 2011).In particular, we use Ω m = . Ω Λ = . n s = . σ = . z as H ( z ) = H E ( z ), with H = h ×
100 km s − Mpc − and h = . z < ∼ E ( z ) = Ω m (1 + z ) + Ω Λ . The virial radius of a halois defined here as R , the radius enclosing a mean density 200times the critical density at that redshift, i.e., 200 × ρ c ( z ), where ρ c ( z ) = H ( z ) / (8 π G ). The virial mass is then defined as M ≡ π/ R ρ c , which we also refer to as M h . Similarly, we quote the conven-tional masses M and radii, R , when presenting the SZ scal-ings. For stellar mass, we use the symbol M ∗ .The SZ signal is characterized by Y , the Comptonizationparameter integrated over a sphere of radius R , expressed insquare arcminutes. Specifically, Y ≡ ( σ T / ( m e c )) Z R PdV / D ( z ) , where D A ( z ) is the angular-diameter distance, σ T is the Thomsoncross-section, c is the speed of light, m e is the electron restmass, and P = n e kT e is the pressure, obtained as the productof the electron number density and the electron temperature.Throughout this paper, we use the quantity˜ Y ≡ Y E − / ( z )( D A ( z ) /
500 Mpc) , also expressed in square arcminutes, as the intrinsic SZ signal,scaled to redshift z = Planck maps used in our analysis, and our reference catalogueof locally brightest galaxies, based on SDSS data. Sect. 3 de-scribes our methodology. Sects. 4 and 5 gives our main resultsand the tests made to demonstrate their robustness. Sections 6and 7 contain discussion and conclusions, respectively.
2. Data
Planck (Tauber et al. 2010; Planck Collaboration I 2011) is thethird generation space mission to measure the anisotropy of the cosmic microwave background (CMB). It observes the sky innine frequency bands covering 30–857 GHz with high sensitiv-ity and angular resolution from 31 ′ to 5 ′ . The Low FrequencyInstrument (LFI; Mandolesi et al. 2010; Bersanelli et al. 2010;Mennella et al. 2011) covers the 30, 44, and 70 GHz bands withamplifiers cooled to 20 K. The High Frequency Instrument (HFI;Lamarre et al. 2010; Planck HFI Core Team 2011a) covers the100, 143, 217, 353, 545, and 857 GHz bands with bolometerscooled to 0.1 K. Polarisation is measured in all but the highesttwo bands (Leahy et al. 2010; Rosset et al. 2010). A combina-tion of radiative cooling and three mechanical coolers producesthe temperatures needed for the detectors and optics (PlanckCollaboration II 2011). Two data processing centres (DPCs)check and calibrate the data and make maps of the sky (PlanckHFI Core Team 2011b; Zacchei et al. 2011). Planck ’s sensitivity,angular resolution, and frequency coverage make it a powerfulinstrument for Galactic and extragalactic astrophysics as wellas for cosmology. Early astrophysics results are given in PlanckCollaboration VIII–XXVI 2011, based on data taken between13 August 2009 and 7 June 2010. Intermediate astrophysics re-sults are now being presented in a series of papers based on datataken between 13 August 2009 and 27 November 2010.
To select a sample of central galaxies, we first define a par-ent population with r < . r -band, extinction-corrected,Petrosian magnitude) from the spectroscopic galaxy catalogueof the New York University Value Added Galaxy Catalogue .This was built by Blanton et al. (2005) based on the seventh datarelease of the Sloan Digital Sky Survey (SDSS / DR7 Abazajianet al. 2009). This parent catalogue contains 602,251 galaxies.We then define “locally brightest galaxies” to be the set of allgalaxies with z > .
03 that are brighter in r than all other samplegalaxies projected within 1.0 Mpc and with redshift di ff ering byless than 1,000 km s − . After this cut 347,486 locally brightestgalaxies remain.The SDSS spectroscopic sample is incomplete because itproved impossible to place a fibre on every object satisfying thephotometric selection criteria, and because some spectra failedto give acceptable redshifts. The completeness to our chosenmagnitude limit varies with position, with a mean of 91.5 % overthe survey as a whole. To ensure that galaxies without SDSSspectroscopy do not violate our sample selection criteria, wehave used SDSS photometry to eliminate all objects with a com-panion that is close and bright enough that it might violate theabove criteria. Specifically, we have used the “photometric red-shift 2” catalogue (photoz2 Cunha et al. 2009) from the SDSSDR7 website to search for additional companions. This cata-logue tabulates a redshift probability distribution in bins of width ∆ z = . r -magnitudeand projected within 1.0 Mpc, unless the photometric redshiftdistribution of the “companion” is inconsistent with the spectro-scopic redshift of the candidate. (Our definition of “inconsistent”is that the total probability for the companion to have a redshiftequal to or less than that of the candidate is less than 0.1; inpractice this eliminates “companions” that are too red to be at aredshift as low as that of the candidate.) This procedure leavesus with a cleaned sample of 259,579 locally brightest galaxies. NYU-VAGC, http://sdss.physics.nyu.edu/vagc/
The NYU-VAGC provides a variety of data for each galaxy.In addition to the positions, magnitudes, and redshifts used tocreate our sample, we will make use of rest-frame colours andstellar masses. The latter are based on stellar population fits tothe five-band SDSS photometry and on the measured redshifts,assuming a Chabrier (2003) stellar initial mass function (Blanton& Roweis 2007). In Fig. 1 we compare the colour and redshiftdistributions of our final sample of locally brightest galaxies tothose of the parent sample for five disjoint ranges of stellar mass.For log M ∗ / M ⊙ ≥ .
8, the distributions are similar for thetwo populations. At lower stellar mass, locally brightest galaxiesare a small fraction of the parent sample and are biased to bluercolours and to slightly larger redshifts. In our stacking analysisbelow, we obtain significant SZ signals only for galaxies withlog M ∗ / M ⊙ ≥ .
0. Our sample contains 81,392 galaxies sat-isfying this bound, the great majority of them on or near the redsequence.
We expect the majority of our locally brightest galaxies to bethe central galaxies of their dark matter halos, just as bright fieldgalaxies lie at the centres of their satellite systems and cD galax-ies lie near the centres of their clusters and are normally theirbrightest galaxies. For our later analysis, it is important to knowboth the reliability of our galaxy sample, i.e., the fraction ofgalaxies that are indeed the central galaxies of their halos, andthe relation between the observable stellar masses of the galax-ies and the unobservable masses of their halos. In this section weinvestigate both issues using an update of the publicly available semi-analytic galaxy formation simulation of Guo et al. (2011).The update uses the technique of Angulo & White (2010) torescale the Millennium Simulation (Springel et al. 2005b) to theWMAP7 cosmology, then readjusts the galaxy formation param-eters to produce a z = r within 1.0 Mpc projected distanceand 1,000 km s − in redshift. We divide galaxies into “centrals”,defined as those lying at the minimum of the gravitational poten-tial of the dark matter friends-of-friends (FoF) group with whichthey are associated, and “satellites”, defined as all other galaxies.With these definitions we can assess the fraction of our lo-cally brightest galaxies that are truly central galaxies. The blackline in Fig. 2 shows, as a function of stellar mass, the fraction of all galaxies in the simulation that are centrals. At stellar massesjust above 10 M ⊙ this fraction is about one half, but it increaseswith stellar mass, reaching two thirds by log M ∗ / M ⊙ = . M ∗ / M ⊙ = .
8. In contrast, the fraction oflocally brightest galaxies that are centrals is much higher, witha minimum of just over 83 % at stellar masses somewhat above Fig. 1.
Distributions in colour ( left ) and redshift ( right ) of our locally brightest galaxies and of the SDSS / DR7 population fromwhich they were drawn. Black histograms refer to the parent sample and red histograms to the locally brightest galaxies. The panelsin each set correspond to five disjoint ranges of log M ∗ / M ⊙ , as indicated in the labels. In the left-hand set, additional labels givethe number of galaxies contributing to the parent (black) and locally brightest (red) histograms. Dashed vertical lines in these samepanels indicate the colour we use to separate red and blue galaxies in Fig. 3 below. Fig. 2.
Fraction of locally brightest galaxies that are the centralobjects in their dark halos, based on the simulations of Guo et al.(2011). The solid line traces the fraction of all simulated galaxiesthat are central galaxies as a function of stellar mass. This frac-tion increases with stellar mass, reaching 90 % at the high massend. The dashed line presents the central galaxy fraction for lo-cally brightest galaxies selected from the simulation accordingto the criteria applied to the SDSS data. This yields a samplethat is over 83 % reliable at all stellar masses.10 M ⊙ . We have checked those locally brightest galaxies thatare satellites, finding that for log M ∗ / M ⊙ >
11, about two-thirds are brighter than the true central galaxies of their halos.The remainder are fainter than their centrals, and are consideredlocally brightest because they are more than 1 Mpc (projected)from their centrals (60 %) or have redshifts di ff ering by morethan 1,000 km s − (40 %). We can assign a halo mass, M , to every galaxy in our sim-ulation. For both satellite galaxies and central galaxies, we take M to be the current M of the FoF dark matter halo withwhich the object is associated, i.e., the mass contained withinits R . Figure 3 shows a scatter plot of M against M ∗ for arandom subset (one out of every 80) of our sample of simulatedlocally brightest galaxies. We indicate central galaxies with redor blue points according to their rest-frame g − r colour (withthe two distinct regions separated by the vertical dashed lines inthe left panel of Fig. 1) while satellite galaxies are indicated byblack points. Clearly, red (passive) and blue (star-forming) cen-tral galaxies lie on di ff erent M - M ∗ relations. That for passivegalaxies is steeper, and is o ff set to larger halo mass in the stellarmass range where both types of central galaxy are present.Satellite galaxies lie in halos in the massive tail of the dis-tribution for central galaxies of the same stellar mass. Satellitesmisidentified as centrals in our catalogue are usually outlyingmembers projected at relatively large separation (from a fewhundred kiloparsecs to 2 Mpc). Their presence bias high both themean halo mass (the high black points in Fig. 3) and the spatialextent of the stacked SZ signals we measure below. However,since two thirds of the satellites that we misidentify as centralgalaxies are in fact brighter than the true central galaxies of theirhalos (i.e., they are not typical satellites), this bias is not extreme.In any case, we correct for these e ff ects explicitly in our analysisusing the simulation.The lower of the two continuous curves in Fig. 3 shows themedian M as a function of M ∗ . We will take this as an esti-mate of the typical halo mass associated with a central galaxy ofknown M ∗ , and will use it to set the angular size of the matchedfilter for each observed galaxy when stacking SZ signal as afunction of stellar mass. The upper continuous curve shows themean M as a function of M ∗ . The substantial shift between the Fig. 3.
Scatter plot of M against M ∗ for a random subset (oneout of 80) of our sample of simulated locally brightest galaxies.Central galaxies are shown as red or blue points according totheir g − r colour, using the cuts indicated in Fig. 1. Satellitegalaxies are shown as black points. The lower and upper curvesgive the median and mean values of halo mass as a function ofstellar mass.two is a measure of the skewness induced by the di ff ering rela-tions for passive and star-forming centrals and by the presenceof the tail of cluster satellite galaxies (see Appendix B).
3. Analysis
Our analysis closely follows that presented in PlanckCollaboration X (2011), Planck Collaboration XI (2011), andPlanck Collaboration XII (2011), employing as primary methoda multi-frequency matched filter (hereafter MMF) optimized inboth frequency and angular space to extract the thermal SZ sig-nal (Herranz et al. 2002; Melin et al. 2006). We find that dustemission from our target sources a ff ects the MMF measurementsnoticeably at low stellar mass, and that an e ff ective mitigation isto restrict our final measurements to the three lowest HFI fre-quencies (100, 143, and 217 GHz). This is detailed in Sect. 5.Our primary scientific results are hence all based on this three-band MMF.For the SZ model template, we employ, as in earlier work(Planck Collaboration X 2011; Planck Collaboration XI 2011;Planck Collaboration XII 2011), the so-called “universal pres-sure profile” (Arnaud et al. 2010) deduced from X-ray observa-tions of the REXCESS cluster sample (B¨ohringer et al. 2007).The R value associated with the halo of each central galaxyis obtained as follows. We first use the SHM relation giving themedian halo M as a function of central galaxy stellar mass, aspresented in Sect. 2.2.1. Then, using an NFW profile (Navarroet al. 1997) and the concentration parameter c given by Netoet al. (2007), we convert M to M and derive R for eachhalo. The angular scale for the filter is finally given by projecting R at the redshift of the target LBG.In addition to the MMF, and in order to test the robustness ofthe results, the impact of foreground contamination and possible systematic e ff ects, we have also implemented aperture photome-try (hereafter AP). For the AP, given an object of certain angularsize R , the method evaluates the mean temperature in a circleof radius r = R and subtracts from it the average found in asurrounding ring of inner and outer radii r = R and r = f R ,respectively, with f > R , f ) = (FWHM , √ + exp( − − exp( − − for the above choice of R and f . For extended objects (e.g., those objects with R larger thanthe beam size, and which are modeled here using the “universalpressure profile”), the conversion factor can be evaluated numer-ically.Using one of these methods (MMF or AP), we obtain ameasure of the intrinsic SZ signal strength ˜ Y ( i ) and the as-sociated measurement uncertainty ˜ σ θ ( i ) for the halo of eachgalaxy i . The majority of these individual SZ measurementshave low signal-to-noise ratio. Following the approach in PlanckCollaboration X (2011) and Planck Collaboration XII (2011),we bin them by stellar mass, calculating the bin-average signal h ˜ Y i b = [ P / ˜ σ θ ( i )] − P N b i = ˜ Y ( i ) / ˜ σ θ ( i ), with uncertainty σ − b = P N b i = / ˜ σ θ ( i ), where N b is the number of galaxies in bin b .
4. Results
Our main observational result is given in Fig. 4 and Table 1,showing the mean SZ signal measured using the three-bandMMF for locally brightest galaxies binned according to stel-lar mass. In the plot, the thick error bars show the uncertaintypropagated from the individual measurement errors as describedabove, while the thin bars with large terminators give the vari-ance of the weighted bin-average signal found by a bootstrapresampling. For the latter, we constructed 1,000 bootstrap real-izations of the original LBG catalogue and performed the fullanalysis on each.The inset uses a linear scale to better display the significanceof our detections. We have a clear signal down to the bin at11 . < log ( M ∗ / M ⊙ ) < .
3, centred at M ∗ = . × M ⊙ .The next three bins provide evidence that the signal continues tolower mass with “detections” significant at the 1 . σ , 1 . σ and2 . σ levels, from high to low mass, respectively. The last binis centered at M ∗ = × M ⊙ , corresponding to a mean halomass of M ∼ . × M ⊙ . These last three bins, however,are more seriously a ff ected by dust contamination, as discussedbelow, and for this reason may be more uncertain than these sta-tistical measures suggest.
5. Systematic errors
In this section, we present a number of tests of the robustnessof our principal result against systematic error. In the follow-
Fig. 4.
Mean SZ signal vs. stellar mass for locally brightestgalaxies. Thick error bars trace the uncertainty on the bin av-erage due purely to measurement error, while thin bars withlarge terminators show the variance calculated by bootstrap re-sampling and so also include the intrinsic scatter in the sig-nal. The inset provides a view on a linear scale to better eval-uate the significance of the detections. We observe a clear re-lation between the mean SZ signal and stellar mass down tolog ( M ∗ / M ⊙ ) = .
25 (the detection in this bin is at 3 . σ ),with a suggestion of signal to lower mass: the next three binsshow signal at 1 . σ , 1 . σ and 2 . σ , respectively. Table 1.
Planck
SZ signal measurements ˜ Y binned by stellarmass (adopting a WMAP7 cosmology). These data are displayedin Fig. 4. E rrors [10 − arcm ]˜ Y log (cid:16) M ∗ M ⊙ (cid:17) [10 − arcm ] Statistical Bootstrap10.05 . . . . . . . 0.47 ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . − ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± . ± ± ± ± ± ± ± ± ing, unless otherwise stated, all results use data at 100, 143, and217 GHz only. According to Fig. 4, the lowest bin at which we have a > σ detection is the one at log ( M ∗ / M ⊙ ) = .
25. As a consistency check, and also as an illustration of the fre-quency dependence of the detected SZ signal, Fig. 5 showsstacked images of central galaxies in six di ff erent mass binsof width ∆ log M ∗ = . ( M ∗ / M ⊙ ) = . , . , . , . , . , and 11 . Planck
Planck
Intermediate Papers (e.g., Planck Collaboration V2012; Planck Collaboration X 2012). The well-known internallinear combination approach (e.g., Eriksen et al. 2004) searchesfor the linear combination of the input maps that minimises thevariance of the final reconstructed map while imposing spectralconstraints. This preserves the thermal SZ signal and removesthe CMB contamination (using the known spectral signatures ofthe two components) in the final SZ map. The resulting map usedfor this analysis has an angular resolution (FWHM) of 10 ′ . Wehave checked that almost identical maps are obtained with othermethods.The SZ signal is clearly visible in all panels withlog ( M ∗ / M ⊙ ) ≥ .
25. The stacked maps show no sign of agradient in the residual signal in the vertical direction, showingthat the MILCA method is very e ff ective in removing Galacticemission. Below the mass limit of 11.25, there is also some ev-idence of SZ signal, although here the contrast relative to thenoise is lower. Finally, we note that the signal in the lower stellarmass panels is extended. This is mainly due to the larger satellitefraction at these masses that results in a significant contributionto the stack from relatively massive halos with centres signifi-cantly o ff set from the locally brightest galaxy (see Figs. 2, 3 andAppendix C). We also discuss in Appendix C the impact of dustcontamination on these maps. Null tests used to check for systematic errors are shown in Fig. 6.Taking the set of MMF filters adapted to each target galaxy, weshift their positions on the sky, either with a random displace-ment (i.e., by generating a random distribution of new positionsisotropically distributed outside our Galactic mask) or by shift-ing all coordinates one degree in declination, and rerunning ouranalysis. In both cases the result should be zero. The shifted fil-ter sets indeed have bin-average SZ signals consistent with zeroover the entire mass range.
Although most of the halos traced by our locally brightestgalaxies are, according to their inferred R values, at mostmarginally resolved by the Planck beams, size e ff ects are notnegligible, and the full pressure profile has to be used for the fluxdetermination. If instead the objects are (incorrectly) assumed tobe point-like, we find that the flux is underestimated by roughly20–30 %, although the slope of the ˜ Y - M ∗ scaling relation ispractically una ff ected. Figure 7 compares the SZ signal extracted for our LBG sam-ple by the two photometry methods described above, namelyMMF and AP. Here, we compare the total SZ flux from MMF(computed as ˜ Y R ) with the total flux recovered from the Fig. 5.
Equal-weighted stacks of reconstructed SZ maps (i.e., Comptonization parameter maps) for objects in six mass bins centred,from left to right and top to bottom, at log ( M ∗ / M ⊙ ) = [11 . , . , . , . , . , . .
2, so the galaxies in two consecutive panels partially overlap. Maps are 2 ◦ on a side, with Galactic north at the top. The SZsignal traced by the central galaxies is clearly detected in all bins above log ( M ∗ / M ⊙ ) = .
25. In all panels, the circles indicatethe FWHM of the data, which corresponds to 10 ′ .AP method, after applying the correction factors described inSect. 3. For simplicity, we assume point-like objects for the fluxextraction in this analysis. This is why the MMF data pointsdi ff er from the corresponding points in Fig. 4. For the AP, wealso compare the nominal four-band analysis with a three-bandcase to illustrate the impact of residual foregrounds on our fluxestimates. When the 353 GHz channel is included, the AP fluxestimates at low stellar-mass are biased towards high SZ val-ues. This indicates contaminating high-frequency emission as-sociated with the sources, presumably dust in the LBGs or theirsatellites. We discuss this issue further in Sect. 5.5.The main conclusion is that the two methods, despite theirdi ff erent data processing approaches, produce fully consistentresults for log ( M ∗ / M ⊙ ) > ∼ .
25, while the results start to showa dependence on the method for stellar masses below that limit.
The analysis of the last section suggests that our SZ signal es-timates may be contaminated by residual dust emission that in- creases with frequency and could bias our primary results. Toevaluate the potential e ff ects, we have performed measurementsusing three di ff erent MMFs, as shown in Fig. 8. The green trian-gles and red diamonds represent the results of using all six HFIchannels or only the lowest three (100, 143, 217 GHz), respec-tively. In both cases there is no explicit allowance for a possibledust contribution. The blue crosses show results for a modifiedsix-band MMF that includes amplitude fits not only to the SZspectrum, but also to a fiducial thermal dust spectrum.The three sets of measurements fully agree for the stel-lar masses for which we unambiguously detect the SZ signal,log M ∗ / M ⊙ ≥ .
25. This indicates that dust emission doesnot significantly a ff ect our results for these stellar mass bins.At lower mass the three-band results and the dust-corrected six-band results remain consistent, but the six-band results withoutexplicit dust correction are systematically di ff erent. Dust emis-sion is clearly su ffi cient to contaminate our six-band filter esti-mates of SZ signal if uncorrected, but it does not appear to be amajor problem when only the lower three frequency bands areused. The residual dust contribution estimated from the scatter Fig. 6.
Null tests performed on the locally brightest galaxy sam-ple. Red points correspond to placing the filter one degree in dec-lination away from the position of each LBG, while green pointscorrespond to random high latitude filter positions. Both sets areconsistent with zero. The black points show our measurementswith filters centred on the LBG sample, demonstrating highlysignificant detections.
Fig. 7.
Comparison of the SZ measurements on the full locallybrightest galaxy sample for two di ff erent photometry methods:the matched multi-filter (MMF) and the aperture photometry(AP) approach. For this figure and only for this figure, we as-sume point-like objects for both methods and plot the derivedtotal SZ flux (or the flux within 5 R for MMF). The signaldetected by the two methods is consistent at all stellar masseswhen only three frequencies are used, but when four frequen-cies are used, the AP results are contaminated by high frequencyemission at stellar masses below ∼ × M ⊙ .and o ff set of the red and blue points for log M ∗ / M ⊙ < . ∼ − arcmin and so lies comfortably below our mea-sured signal.There is a clear indication of signal in the three bins just be-low log M ∗ / M ⊙ = .
25 both for the three-band MMF and forthe dust-corrected six-band MMF. However, the dust-correctedresults appear systematically lower than the (uncorrected) three-band results by an amount similar to that seen at lower masseswhere the SZ signal is undetected. Further, the six-band MMFmeasurements without dust correction (the green triangles) dif-fer substantially for these (and all lower) bins. This suggests that
Fig. 8.
Impact of dust contamination on our SZ measurements.Three cases are shown: a 6-band MMF (all
Planck
HFI frequen-cies) with no explicit allowance for a dust contribution (greentriangles), a 3-band MMF also with no explicit dust modelling(red diamonds); and a modified 6-band MMF that includes anamplitude fit to a fiducial dust spectrum (blue crosses). The errorbars include measurement uncertainties only. For stellar masseswhere we clearly detect the signal (i.e., at log M ∗ / M ⊙ > . ff ect those measurements. At lowermasses the 3-band results are consistent with the 6-band resultswhen dust is explicitly included in the modelling, but not other-wise.dust emission a ff ects these stellar mass bins noticeably even forthe three-band MMF, so the corresponding points in Fig. 4 maybe more uncertain than indicated by their statistical error bars.Although formally the dust-corrected six-band MMF would ap-pear to give our most accurate estimates of stacked SZ signal,we are uncertain whether the fiducial dust spectrum it assumesis appropriate for these specific sources. Therefore we conser-vatively quote results based on the three-band MMF, using thedust-corrected six-band results to give an estimate of remainingdust-related systematics.Finally, we note that residual dust contamination bi-ases the (uncorrected) six-band MMF signal estimates forlog M ∗ / M ⊙ <
11 (Fig. 8) in the opposite direction to the APsignal estimates (see Fig. 7). The agreement of the two meth-ods for log M ∗ / M ⊙ > .
25 is thus a further indication of therobustness of our primary results.
We have also checked that the SZ signal is stable against split-ting the
Planck data into complementary subsets. For instance,the signal obtained from the maps of the first 6 months of ob-serving time is fully consistent with that obtained from maps ofthe second 6 months and the last 3.5 months (of course the latterhas larger error bars due to its smaller sky coverage).
6. The Y - M relation We now turn to the interpretation of our measurements in termsof the SZ signal-halo mass scaling relation: Y - M . Our con-clusions are summarised in Fig. 9.From our simulation of the locally brightest galaxy cata-logue, we expect a large range of halo masses within a given Fig. 9.
Left:
Comparison of the measured mean SZ signal as a function of LBG stellar mass (red points) to simulated observations(blue points). The simulations assign to each observed LBG the halo mass and positional o ff set of a randomly chosen simulatedLBG of the same stellar mass (compare Fig. 3). Our best fit Y - M scaling relation is then used, together with the universalpressure profile, to inject a simulated signal into the Planck maps (see text). An “observed” signal is obtained by applying the MMFexactly as for the real data. The inset gives the ratio of the bin-averaged injected and actual signals.
Right:
Mean SZ signal as afunction of e ff ective halo mass. The bin-averaged SZ signal measurements of the left panel have been translated to this plane usingthe simulations as described in the text (the red points). The dot-dashed line is our best fit relation between halo mass and SZ signal,i.e., the one leading to the simulated measurements in the left panel. The green points give the mean SZ signal of MCXC clustersbinned by a halo mass estimated from their X-ray luminosity using the REXCESS relation without correction for Malmquist bias(line 3 in Table 2 of Planck Collaboration X 2011). The dashed blue line shows the self-similar model calibrated on the REXCESSsample as given by Arnaud et al. (2010). The inset gives the ratio of all measurements to this model’s predictions. As in previousfigures, the thick error bars account only for measurement uncertainties, while thin bars with large terminators result from a bootstrapanalysis and so include intrinsic scatter e ff ects.bin of stellar mass and, in addition, a fraction of galaxies thatare, in fact, satellites, with significant positional o ff sets relativeto their host halo (see Fig. 3). These e ff ects impact our measure-ments of the SZ signal-stellar mass relation in two ways. First,the MMF is not perfectly matched to each individual object be-cause we fix the filter scale to the median halo size. This causesan aperture-induced bias in the flux measurement. Second, ourfilter is miscentred for those systems where the LBG is, in fact,a satellite. These galaxies are often associated with substantiallymore massive dark halos than typical LBGs of the same stel-lar mass, leading to an increase in the mean signal in the bin,mitigated by the substantial angular o ff sets of most such satel-lites from the true centres of their rich clusters. This increasesthe apparent extent of the signal in stacked maps like Fig. 5, butdecreases the contribution to the signal through a matched filtercentred on the galaxy (see Appendix C).Using our simulation of the LBG catalogue, we can accountfully for these e ff ects and extract the underlying Y - M rela-tion in an unbiased way. Within each stellar mass bin, we iden-tify each observed LBG with a randomly chosen simulated LBGof the same stellar mass, assigning it the halo mass and positionalo ff set from halo centre of its partner, but retaining its observedredshift. We give each halo a SZ signal distributed according tothe “universal pressure profile” and normalized using a specificmodel Y - M scaling relation. Each synthesised object is thenobserved with the three-band MMF centred on the galaxy’s posi-tion, and the measurements are binned and weighted in the sameway as the real data to obtain h Y i s .This procedure enables us to translate a model Y - M re-lation to our observational plane, Y - M ∗ , and thus to fit for the underlying scaling relation with halo mass M . We model thisrelation as˜ Y = Y M M × M ⊙ ! α M , (1)fixing the mass exponent to its self-similar value, α M = / Y M . Restricting the fit tolog ( M ∗ / M ⊙ ) > ∼ .
5, for direct comparison to X-ray samplesin the discussion below, we find Y M = (0 . ± . × − arcmin . (2)In the left-hand panel of Fig. 9, the red points reproduce the mea-surements given in Fig. 4, while the blue points show the simu-lated observations for this best-fit Y - M scaling relation.The best-fit is, however, formally unacceptable, with a re-duced χ ν of 3, which we can more readily appreciate from theinset showing the ratio of the actual observations to the simu-lated bin averages on a linear scale. The data prefer a shallowerslope than the self-similar α M = / Y - M relation. The blue dashed line is the self-similar re-lation derived from X-ray cluster studies (Arnaud et al. 2010),while the green points present binned SZ measurements for theapproximately 1,600 clusters in the Meta-Catalogue of X-ray de-tected Clusters (MCXC) (Pi ff aretti et al. 2010). The latter mea-surements are as reported in Planck Collaboration X (2011), withone minor change: in Planck Collaboration X (2011) we used an empirical slope for the Y - M relation taken from X-raystudies; for the points in Fig. 9, we repeated the same analy-sis fixing the slope instead to its self-similar value, as was donefor the LBG sample. This change moves the green points onlyvery slightly relative to those shown in Planck CollaborationX (2011). For the mass estimates of the MCXC objects, weapplied the X-ray luminosity-mass relation from Pratt et al.(2009), corresponding to the case of line 3 of Table 2 in PlanckCollaboration X (2011). The mass is calculated for each MCXCcluster and then binned. We plot the point at the median value ofthe mass in each bin.To transcribe our central galaxy catalogue measurementsonto this figure, we must first find the e ff ective halo mass corre-sponding to each stellar mass bin. This e ff ective mass is a com-plicated average over the halo masses within the bin, weight-ing by the fraction of SZ signal actually observed, i.e., after ac-counting for aperture and miscentering e ff ects. The bin-averagedmean SZ signals we estimate for our mock LBG catalogue in-clude all these e ff ects, and so can be used to calculate an e ff ectivemass as M e ff = × M ⊙ ( h Y i s / Y M ) /α M , where h Y i s is calcu-lated for each bin as described above, and Y M and α M = / Y M .) We do this for asuite of simulated catalogues and take the ensemble average ef-fective mass for each bin, plotting the results as the red points inthe right-hand panel of the figure.These LBG results extend the SZ-halo mass scaling relationdown in mass by at least a factor of 3, to M = × M ⊙ (the stellar mass bin at log M ∗ / M ⊙ = . . σ ) correspondsto e ff ective halo mass log M / M ⊙ = .
6. Our power-law fitadequately describes the data points over more than two ordersof magnitude in halo mass down to this remarkably low valuewith no hint of a significant deviation.The inset in the right panel of Fig. 9 shows the ratio of ourmeasured mean SZ signal to that predicted by the self-similarscaling relation deduced from X-ray observations of clusters(the dashed blue line (Arnaud et al. 2010)). Direct measure-ments obtained by binning the MCXC clusters (the green points)agree with this relation. This was the principal result of PlanckCollaboration X (2011). The SZ measurements for our LBGsfall below the relation, however. The horizontal dot-dashed linegives the ratio our LBG fit to the X-ray model (this is the o ff setbetween the two blue lines in the main figure). Recall that the fitto the LBG catalogue was restricted to masses overlapping theX-ray sample, log M / M ⊙ > .
8. Over this range, the meanSZ signals associated with LBG halos are about 20 % lower thanfound for X-ray clusters with the same halo mass, a di ff erencethat is significant at the 2 . σ level.A number of e ff ects could contribute to an o ff set of thissize. The masses plotted for the MCXC were calculated using aluminosity-mass relation derived from the REXCESS sample as-suming that halo mass scales self-similarly with the mass-proxy Y X and without correction for Malmquist bias (Pratt et al. 2009).Using the Malmquist-corrected relation would remove much ofthe o ff set and bring the two Y - M scaling relations into ac-ceptable agreement. In this sense, the o ff set is consistent withthe estimated e ff ects of Malmquist bias on the X-ray sample.However, such biases depend on the detailed selection proce-dure of the stacked and calibrating cluster samples, on the way in which the calibration relation is derived, and on the (corre-lated) intrinsic scatter of clusters around the L x - M and Y - M relations. Thus they can only be corrected through detailedmodelling both of the cluster population itself and of the defi-nition and analysis of the specific cluster surveys involved (e.g.,Angulo et al. 2012). Furthermore, halo masses are estimated invery di ff erent ways in our two samples — from X-ray luminosi-ties calibrated against individual hydrostatic mass measurementsfor the MCXC, and through an abundance matching argumentbased on the WMAP7 cosmology for the LBG catalogue. Anyo ff set between these two halo mass scales will result in o ff setsin Fig. 9. For example, a number of recent papers have arguedthat failure of some of the assumptions underlying the standardmethods for estimating cluster masses from X-ray data (e.g., de-tailed hydrostatic equilibrium or the unimportance of turbulentand nonthermal pressure) could produce a systematic bias in theX-ray cluster mass scale (Planck Collaboration XII 2011; Rozoet al. 2012; Sehgal et al. 2012). Finally, as for the LBG sam-ple, each luminosity bin of the MCXC contains a distribution ofhalo properties that are averaged in complicated fashion by ourstacked SZ measurement. Understanding the relative importanceof these various e ff ects at a precision better than 20% wouldagain require detailed modeling of the heterogeneous MCXCcatalogue.
7. Conclusions
Using
Planck data, we have measured the scaling relation be-tween Sunyaev-Zeldovich signal and stellar mass for locallybrightest galaxies ( Y - M ∗ ). This is the first time such a rela-tion has been determined, and it demonstrates the presence ofhot, di ff use gas in halos hosting central galaxies of stellar massas low as M ∗ = × M ⊙ , with a strong indication of signal ateven lower masses. We have constructed a large mock catalogueof locally brightest galaxies from the Millennium Simulationand used it to model the Planck observational process in detailin order to extract from our measurements the underlying SZsignal-halo mass relation ( Y - M ). This new relation spansa large range in halo mass, reaching from rich clusters down to M = . × M ⊙ , with a clear indication of continuation to M ∼ × M ⊙ . This is the lowest mass scale to which anSZ scaling relation has so far been measured. The fact that thesignal is close to the self-similar prediction implies that Planck -detected hot gas represents roughly the mean cosmic fractionof the mass even in such low-mass systems. Consistency withtheir low observed X-ray luminosities then requires the gas to beless concentrated than in more massive systems. Integration ofthe halo mass function down to M = × M ⊙ shows that Planck has now seen about a quarter of all cosmic baryons in theform of hot gas, about four times as many as are inferred fromX-ray data in clusters with M > M ⊙ .At the high mass end, the scaling relation we derive fromour LBG data shows reasonable agreement with X-ray clusterresults. The 20% lower normalisation that we find (significantat the 2 . σ level) can be explained in principle by a number ofpossible e ff ects related to the di ff ering selection and mass esti-mation methods of the two samples. Agreement at this level ofprecision is remarkable, and understanding the remaining di ff er-ence would require detailed modeling of the selection and cali-bration of the X-ray samples. The fact that plausible Malmquistcorrections can eliminate most of the di ff erence shows that clus-ter studies are now reaching the ∼
10% precision level.We find that the Y - M scaling law is described by apower law with no evidence of deviation over more than two orders of magnitude in halo mass. The gas properties of darkmatter halos appear remarkably regular over a mass range wherecooling and feedback processes are expected to vary strongly.In particular, we find no change in behaviour in the low-masssystems for which substantial feedback e ff ects are invoked incurrent galaxy formation models (e.g., from AGN). Statisticalstudies of large galaxy and cluster samples, such as those pre-sented here, can clearly shed new light on the thermal cycle atthe heart of the galaxy formation process. Acknowledgements.
The authors from the consortia funded principally byCNES, CNRS, ASI, NASA, and Danish Natural Research Council acknowl-edge the use of the pipeline-running infrastructures Magique3 at Institutd’Astrophysique de Paris (France), CPAC at Cambridge (UK), and USPDCat IPAC (USA). The development of
Planck has been supported by: ESA;CNES and CNRS / INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy);NASA and DoE (USA); STFC and UKSA (UK); CSIC, MICINN, JA andRES (Spain); Tekes, AoF and CSC (Finland); DLR and MPG (Germany); CSA(Canada); DTU Space (Denmark); SER / SSO (Switzerland); RCN (Norway);SFI (Ireland); FCT / MCTES (Portugal); and PRACE (EU). A description ofthe Planck Collaboration and a list of its members, including the technicalor scientific activities in which they have been involved, can be found at . We acknowl-edge the use of the HEALPix package (G´orski et al. 2005).
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Appendix A: Robustness of our results tovariations in isolation criteria
As explained in Sect. 2.2, our locally brightest galaxy cataloguewas built starting from a parent population with r < . r magnitude vio-lating certain isolation criteria. In particular, we defined locallybrightest galaxies to be the set of all objects with z > .
03 thatare brighter than all other sample galaxies projected within a ra-dius of R iso = . ff ering in redshift by less than1,000 km s − . Hereafter, we refer to these criteria as the “1 Mpccase”.To test the robustness of our results against changes in theseisolation criteria, we compared them to a case with stricter iso-lation criteria, R iso = . − in redshift, here-after the “2 Mpc case”.Applying the isolation criteria to the parent spectroscopiccatalogue as before, but with these new values, we end up witha first sample of 206,562 locally brightest galaxes. Again, in asecond step we use SDSS photometry to further eliminate ob-jects with companions that might violate the isolation criteria.After removing any candidate with a (photometric) companionof equal or brighter r magnitude and projected within 2.0 Mpc, we end up with a cleaned sample of 110,437 locally brightestgalaxies. In particular, this sample contains 58,105 galaxies sat-isfying the bound log M ∗ / M ⊙ ≥ .
0, which is the regimewhere we find significant SZ signal. Thus, 23,287 galaxies inthis mass range are eliminated from the sample studied in themain body of this paper by the stricter isolation criteria.To evaluate the reliability of the new R iso = . R iso = . R iso = . M ⊙ . Theimprovement is less than might have been anticipated because,as noted in Sect. 2.2.1, the majority of the satellite galaxies in oursimulated 1 Mpc sample were included because they are brighterthan the central galaxies of their own halos, rather than becausethe isolation criteria failed to eliminate them.Finally, Fig. A.1 compares the SZ signal-halo mass relations( Y - M ) derived for the two cases (1 Mpc and 2 Mpc). Halomasses for the 2 Mpc case are computed as explained in Sect. 6(see Table B.1 for the numerical values). The main conclusion isthat the SZ signal-halo mass scaling relation is not sensitive tothe isolation criteria. Appendix B: Predicted properties of the stellarmass-halo mass relation
Using our mock catalogues based on the semi-analytic galaxyformation simulation of Guo et al. (2011), we provide here ad-ditional information on the predicted properties of the stellarmass-halo mass relation. Figure B.1 shows the distribution ofhalo mass ( M h ) predicted for nine of the stellar mass bins con-sidered in this paper, and for two sets of isolation criteria: the1 Mpc and 2 Mpc cases (see Sect. 2.2 and Appendix A). Verticallines correspond to the mean (red), median (green), and the “ef-fective” (blue) values of halo mass in each bin. The correspond-ing numbers are listed in Table B.1, which also gives the RMSof the posterior M h distribution. The e ff ective halo masses arecomputed as described in Sect. 6. Appendix C: Impact of miscentering and scatter onthe binned SZ signal and stacked SZ maps
As discussed in Sec. 6, we used the semi-analytic galaxy forma-tion simulation of Guo et al. (2011) to account for the e ff ects ofmiscentering and scatter in halo mass at fixed stellar mass wheninterpreting our measurement (see Figs. 4 and 9). Figure C.1isolates the impact of each e ff ect on the binned SZ measure-ments, using the procedure outlined in that section. The greenpoints represent the ideal case with no miscentering and SZ filterperfectly matched to the size of each individual object. The redcrosses add miscentering o ff sets taken from the o ff set distribu-tion in the simulations for each stellar mass bin. The drop in SZamplitude is expected because we now miss SZ signal from themiscentered objects. Additionally fixing the filter size accord-ing to the median halo mass in each stellar mass bin, as donethroughout this paper, we recover our previous results, shown asthe blue triangles here and as the red diamonds in the left-handpanel of Fig. 9.Using the same simulations, we can also estimate the im-pact of miscentering on the stacked SZ maps of locally brightest galaxies (see Fig. 5). Here, we use the full simulation to com-pute r p , the projected distance of each locally brightest galaxyfrom the gravitational potential minimum of its halo. Averageand RMS values for r p for all the stellar mass bins consideredin this paper and for the 1 Mpc and 2 Mpc samples are given inTable C.1. Histograms of these r p values are shown in Fig. C.2.Note that the median value of r p , which is not listed in the table,is zero for all bins.These values can be used to predict the impact of miscenter-ing of the locally brightest galaxy with respect to its halo (andthus, with respect to the centre of the associated SZ emission).Figure C.3 illustrates the broadening of the SZ stacked profilecaused by this e ff ect. For this computation, we assume point-likeobjects and a Gaussian beam profile of 10 ′ for easier compari-son with Fig. 5. For each stellar mass bin, the M h value from thesimulation is used to predict the total SZ flux using Eqs. 1 and 2,and the r p value is used to o ff set the position of the SZ signal. Inorder to convert r p values (in physical units) into angular o ff sets,a redshift for each simulated object is drawn from the observeddistribution for locally brightest galaxies of similar stellar mass.Miscentering broadens the stacked SZ profile, yielding typicalFWHM of ∼ ′ for log M ∗ / M ⊙ ≤ .
25, and also modifiesthe shape of the profile, by increasing the amount of SZ flux inthe tails of the distribution. These values are slightly smaller (butcomparable) to the observed widths of the SZ emission in Fig. 5.Finally, Fig. C.4 shows equal-weighted stacks of SZ mapscentred on the real central galaxy sample, similar to those ofFig. 5, but now using all six HFI frequency channels in theMILCA algorithm, rather than just the lowest four. For all sixstellar mass bins the noise in these new maps, as measured bythe RMS fluctuation about the mean in pixels more than 20 ′ frommap centre, is lower than in the maps of Fig. 5. This shows thatthe addition of high frequency information has improved the ac-curacy with which non-SZ signals, primarily dust emission, areremoved. Almost all this improvement comes from the inclu-sion of the 545 GHz channel; maps made with and without the857 GHz channel are almost identical. As a result of this im-provement, the signal-to-noise ratio of the peaks near the mapcentre is higher in all the panels of Fig. C.4 than in the corre-sponding panels of Fig. 5. This strengthens our conclusion thatthe apparent SZ signals near the centres of the two lowest stellarmass panels are, in fact, real, despite their apparent breadth andirregularity. The breadth is likely due to the miscentering e ff ectsexplored above while the irregularity looks consistent with theoverall noise level of the maps. APC, AstroParticule et Cosmologie, Universit´e Paris Diderot,CNRS / IN2P3, CEA / lrfu, Observatoire de Paris, Sorbonne ParisCit´e, 10, rue Alice Domon et L´eonie Duquet, 75205 Paris Cedex13, France Aalto University Mets¨ahovi Radio Observatory, Mets¨ahovintie 114,FIN-02540 Kylm¨al¨a, Finland Academy of Sciences of Tatarstan, Bauman Str., 20, Kazan,420111, Republic of Tatarstan, Russia African Institute for Mathematical Sciences, 6-8 Melrose Road,Muizenberg, Cape Town, South Africa Agenzia Spaziale Italiana Science Data Center, c / o ESRIN, viaGalileo Galilei, Frascati, Italy Agenzia Spaziale Italiana, Viale Liegi 26, Roma, Italy Astrophysics Group, Cavendish Laboratory, University ofCambridge, J J Thomson Avenue, Cambridge CB3 0HE, U.K. Atacama Large Millimeter / submillimeter Array, ALMA SantiagoCentral O ffi ces, Alonso de Cordova 3107, Vitacura, Casilla 7630355, Santiago, Chile12lanck Collaboration: Gas content of dark matter halos Fig. A.1.
Left: Comparison of the SZ signal-halo mass scaling relation for two di ff erent sets of isolation criteria. The triple-dotdashed line is our best fit model (see Eq. 1 and 2). Right: Same as above, but now showing the ratio of the previous data points tothe Arnaud et al. (2010) Y - M relation. Fig. B.1.
Probability distribution function of halo mass, M h , for nine of the stellar mass bins considered in this paper. Solid linescorrespond to the sample isolated according to the 1 Mpc criteria, while dashed lines show the distributions for the 2 Mpc sample.Vertical colored lines show three di ff erent characteristic masses (the mean, median, and “e ff ective” halo masses) for the 1 Mpcsample (see Table B.1 for numerical values). Table B.1.
Statistics of halo mass for various stellar mass bins, for the 1 Mpc and 2 Mpc isolation criteria. The first three columnsfor each case (mean, median, and RMS values for the halo mass) are derived from the simulation only, while the e ff ective halo mass M e ff h uses the redshifts and stellar masses of the observed galaxies, as described in Sect. 6. All masses ( M ) in this table are decimallogarithms of the value in units of M ⊙ . log (cid:16) M h M ⊙ (cid:17) R iso = R iso = (cid:16) M ∗ M ⊙ (cid:17) Mean Median RMS E ff ective Mean Median RMS E ff ective11.0–11.1 . . . . . . 13.22 12.70 13.86 12.71 12.92 12.61 13.39 12.7911.1–11.2 . . . . . . 13.38 12.93 13.94 12.97 13.14 12.85 13.67 12.8111.2–11.3 . . . . . . 13.55 13.17 14.04 13.21 13.37 13.12 13.79 13.0511.3–11.4 . . . . . . 13.72 13.43 14.03 13.41 13.60 13.40 13.87 13.3511.4–11.5 . . . . . . 13.90 13.67 14.15 13.63 13.81 13.65 13.92 13.6011.5–11.6 . . . . . . 14.06 13.89 14.19 13.84 14.01 13.87 14.10 13.7911.6–11.7 . . . . . . 14.21 14.09 14.19 13.99 14.19 14.08 14.13 13.9911.7–11.8 . . . . . . 14.41 14.29 14.39 14.20 14.39 14.29 14.25 14.2011.8–11.9 . . . . . . 14.52 14.42 14.49 14.34 14.49 14.42 14.30 14.3311.9–12.0 . . . . . . 14.71 14.60 14.56 14.54 14.69 14.60 14.52 14.51 Fig. C.1.
Impact of miscentering and scatter on the binned SZmeasurements. The green points give results in an ideal situationwith no miscentering and SZ filter perfectly matched to each in-dividual object in a given stellar mass bin. The red crosses addthe e ff ect of miscentering, with o ff sets drawn from the distribu-tions given by the simulations for each stellar mass bin. The bluetriangles additionally include the aperture e ff ect caused by fixingthe filter size according to the median value of the halo mass ineach bin. CITA, University of Toronto, 60 St. George St., Toronto, ON M5S3H8, Canada CNRS, IRAP, 9 Av. colonel Roche, BP 44346, F-31028 Toulousecedex 4, France California Institute of Technology, Pasadena, California, U.S.A. Centre of Mathematics for Applications, University of Oslo,Blindern, Oslo, Norway Centro de Astrof´ısica, Universidade do Porto, Rua das Estrelas,4150-762 Porto, Portugal Centro de Estudios de F´ısica del Cosmos de Arag´on (CEFCA),Plaza San Juan, 1, planta 2, E-44001, Teruel, Spain Computational Cosmology Center, Lawrence Berkeley NationalLaboratory, Berkeley, California, U.S.A. Consejo Superior de Investigaciones Cient´ıficas (CSIC), Madrid,Spain
Table C.1.
Statistics of the distribution of distances r p of the lo-cally brightest galaxies from the gravitational potential minimaof their parent halos, for the 1 Mpc and 2 Mpc isolation criteria. r p [kpc]R iso = iso = (cid:16) M ∗ M ⊙ (cid:17) Mean RMS Mean RMS11.0–11.1 . . . . . . 140.2 469.6 75.8 322.111.1–11.2 . . . . . . 165.7 533.1 94.9 373.311.2–11.3 . . . . . . 195.6 636.1 121.8 501.811.3–11.4 . . . . . . 202.4 682.1 143.6 579.111.4–11.5 . . . . . . 217.8 720.3 165.1 659.811.5–11.6 . . . . . . 239.8 852.8 205.7 812.111.6–11.7 . . . . . . 193.4 775.2 171.5 758.511.7–11.8 . . . . . . 213.4 896.7 200.4 892.011.8–11.9 . . . . . . 145.1 726.2 128.5 720.911.9–12.0 . . . . . . 342.5 1062.6 332.2 1065.1 DSM / Irfu / SPP, CEA-Saclay, F-91191 Gif-sur-Yvette Cedex,France DTU Space, National Space Institute, Technical University ofDenmark, Elektrovej 327, DK-2800 Kgs. Lyngby, Denmark D´epartement de Physique Th´eorique, Universit´e de Gen`eve, 24,Quai E. Ansermet,1211 Gen`eve 4, Switzerland Departamento de F´ısica Fundamental, Facultad de Ciencias,Universidad de Salamanca, 37008 Salamanca, Spain Departamento de F´ısica, Universidad de Oviedo, Avda. CalvoSotelo s / n, Oviedo, Spain Department of Astronomy and Geodesy, Kazan Federal University,Kremlevskaya Str., 18, Kazan, 420008, Russia Department of Astrophysics / IMAPP, Radboud UniversityNijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands Department of Physics & Astronomy, University of BritishColumbia, 6224 Agricultural Road, Vancouver, British Columbia,Canada Department of Physics and Astronomy, Dana and David DornsifeCollege of Letter, Arts and Sciences, University of SouthernCalifornia, Los Angeles, CA 90089, U.S.A. Department of Physics, Gustaf H¨allstr¨omin katu 2a, University ofHelsinki, Helsinki, Finland14lanck Collaboration: Gas content of dark matter halos
Fig. C.2.
Distribution of o ff sets of locally brightest galaxies from the gravitational potential minima of their parent halos, both forthe 1 Mpc (black) and for the 2 Mpc (green) isolation criteria. Table C.1 gives mean and RMS values for these distributions. Fig. C.3.
Impact of miscentering on stacked SZ maps. See the text for details of the simulation shown here. For an original resolutionof FWHM = ′ , miscentering broadens the stacked profiles to a FWHM ∼ ′ for log M ∗ / M ⊙ ≤ . Fig. C.4.
Similar to Fig. 5, but using a reconstructed SZ map that now uses all six HFI frequency channels. The noise in all maps isreduced by the inclusion of the two highest frequencies. Stacked images in the stellar-mass bins above log ( M ∗ / M ⊙ ) = .
25 arenot significantly a ff ected, but for the low stellar-mass panels, the extended signal near map centre is larger and has higher signal tonoise than in Fig. 5, suggesting that it may be real SZ signal broadened by miscentering e ff ects. Department of Physics, Princeton University, Princeton, NewJersey, U.S.A. Department of Physics, University of California, Berkeley,California, U.S.A. Department of Physics, University of California, Santa Barbara,California, U.S.A. Department of Physics, University of Illinois atUrbana-Champaign, 1110 West Green Street, Urbana, Illinois,U.S.A. Dipartimento di Fisica e Astronomia G. Galilei, Universit`a degliStudi di Padova, via Marzolo 8, 35131 Padova, Italy Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara,Via Saragat 1, 44122 Ferrara, Italy Dipartimento di Fisica, Universit`a La Sapienza, P. le A. Moro 2,Roma, Italy Dipartimento di Fisica, Universit`a degli Studi di Milano, ViaCeloria, 16, Milano, Italy Dipartimento di Fisica, Universit`a degli Studi di Trieste, via A.Valerio 2, Trieste, Italy Dipartimento di Fisica, Universit`a di Roma Tor Vergata, Via dellaRicerca Scientifica, 1, Roma, Italy Discovery Center, Niels Bohr Institute, Blegdamsvej 17,Copenhagen, Denmark Dpto. Astrof´ısica, Universidad de La Laguna (ULL), E-38206 LaLaguna, Tenerife, Spain European Southern Observatory, ESO Vitacura, Alonso de Cordova3107, Vitacura, Casilla 19001, Santiago, Chile European Space Agency, ESAC, Planck Science O ffi ce, Caminobajo del Castillo, s / n, Urbanizaci´on Villafranca del Castillo,Villanueva de la Ca˜nada, Madrid, Spain European Space Agency, ESTEC, Keplerlaan 1, 2201 AZNoordwijk, The Netherlands GEPI, Observatoire de Paris, Section de Meudon, 5 Place J.Janssen, 92195 Meudon Cedex, France Helsinki Institute of Physics, Gustaf H¨allstr¨omin katu 2, Universityof Helsinki, Helsinki, Finland INAF - Osservatorio Astronomico di Padova, Vicolodell’Osservatorio 5, Padova, Italy INAF - Osservatorio Astronomico di Roma, via di Frascati 33,Monte Porzio Catone, Italy INAF - Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11,Trieste, Italy INAF Istituto di Radioastronomia, Via P. Gobetti 101, 40129Bologna, Italy INAF / IASF Bologna, Via Gobetti 101, Bologna, Italy INAF / IASF Milano, Via E. Bassini 15, Milano, Italy INFN, Sezione di Roma 1, Universit‘a di Roma Sapienza, PiazzaleAldo Moro 2, 00185, Roma, Italy IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, Pune411 007, India Imperial College London, Astrophysics group, BlackettLaboratory, Prince Consort Road, London, SW7 2AZ, U.K. Infrared Processing and Analysis Center, California Institute ofTechnology, Pasadena, CA 91125, U.S.A. Institut Universitaire de France, 103, bd Saint-Michel, 75005,Paris, France Institut d’Astrophysique Spatiale, CNRS (UMR8617) Universit´eParis-Sud 11, Bˆatiment 121, Orsay, France Institut d’Astrophysique de Paris, CNRS (UMR7095), 98 bisBoulevard Arago, F-75014, Paris, France Institute for Space Sciences, Bucharest-Magurale, Romania16lanck Collaboration: Gas content of dark matter halos Institute of Astro and Particle Physics, Technikerstrasse 25 / Institute of Astronomy and Astrophysics, Academia Sinica, Taipei,Taiwan Institute of Astronomy, University of Cambridge, Madingley Road,Cambridge CB3 0HA, U.K. Institute of Theoretical Astrophysics, University of Oslo, Blindern,Oslo, Norway Instituto de Astrof´ısica de Canarias, C / V´ıa L´actea s / n, La Laguna,Tenerife, Spain Instituto de F´ısica de Cantabria (CSIC-Universidad de Cantabria),Avda. de los Castros s / n, Santander, Spain Jet Propulsion Laboratory, California Institute of Technology, 4800Oak Grove Drive, Pasadena, California, U.S.A. Jodrell Bank Centre for Astrophysics, Alan Turing Building,School of Physics and Astronomy, The University of Manchester,Oxford Road, Manchester, M13 9PL, U.K. Kavli Institute for Cosmology Cambridge, Madingley Road,Cambridge, CB3 0HA, U.K. LAL, Universit´e Paris-Sud, CNRS / IN2P3, Orsay, France LERMA, CNRS, Observatoire de Paris, 61 Avenue del’Observatoire, Paris, France Laboratoire AIM, IRFU / Service d’Astrophysique - CEA / DSM -CNRS - Universit´e Paris Diderot, Bˆat. 709, CEA-Saclay, F-91191Gif-sur-Yvette Cedex, France Laboratoire de Physique Subatomique et de Cosmologie,Universit´e Joseph Fourier Grenoble I, CNRS / IN2P3, InstitutNational Polytechnique de Grenoble, 53 rue des Martyrs, 38026Grenoble cedex, France Laboratoire de Physique Th´eorique, Universit´e Paris-Sud 11 &CNRS, Bˆatiment 210, 91405 Orsay, France Lawrence Berkeley National Laboratory, Berkeley, California,U.S.A. Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild-Str. 1,85741 Garching, Germany Max-Planck-Institut f¨ur Extraterrestrische Physik,Giessenbachstraße, 85748 Garching, Germany National University of Ireland, Department of ExperimentalPhysics, Maynooth, Co. Kildare, Ireland Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark Observational Cosmology, Mail Stop 367-17, California Instituteof Technology, Pasadena, CA, 91125, U.S.A. Optical Science Laboratory, University College London, GowerStreet, London, U.K. SISSA, Astrophysics Sector, via Bonomea 265, 34136, Trieste,Italy School of Physics and Astronomy, Cardi ff University, QueensBuildings, The Parade, Cardi ff , CF24 3AA, U.K. Space Research Institute (IKI), Profsoyuznaya 84 /
32, Moscow,Russia Space Research Institute (IKI), Russian Academy of Sciences,Profsoyuznaya Str, 84 /
32, Moscow, 117997, Russia Space Sciences Laboratory, University of California, Berkeley,California, U.S.A. Special Astrophysical Observatory, Russian Academy of Sciences,Nizhnij Arkhyz, Zelenchukskiy region, Karachai-CherkessianRepublic, 369167, Russia Stanford University, Dept of Physics, Varian Physics Bldg, 382 ViaPueblo Mall, Stanford, California, U.S.A. T ¨UB˙ITAK National Observatory, Akdeniz University Campus,07058, Antalya, Turkey UPMC Univ Paris 06, UMR7095, 98 bis Boulevard Arago,F-75014, Paris, France Universit´e Denis Diderot (Paris 7), 75205 Paris Cedex 13, France Universit´e de Toulouse, UPS-OMP, IRAP, F-31028 Toulouse cedex4, France University Observatory, Ludwig Maximilian University of Munich,Scheinerstrasse 1, 81679 Munich, Germany University of Granada, Departamento de F´ısica Te´orica y delCosmos, Facultad de Ciencias, Granada, Spain University of Miami, Knight Physics Building, 1320 Campo SanoDr., Coral Gables, Florida, U.S.A.93