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arXiv:1001.0006v2 [astro-ph.CO] 4 May 2010Draft version November 2, 2018 Preprint typeset using L ATEX style emulateapj v. 11/10/09 COMPARISON OF HECTOSPEC VIRIAL MASSES WITH SZE MEASUREMENT S Kenneth Rines1,2, Margaret J. Geller2, and Antonaldo Diaferio3,4 Draft version November 2, 2018 ABSTRACT We present the first comparison of virial masses of galaxy clusters with their Sunyaev-Zel’dovich Effect (SZE) signals. We study 15 clusters from the Hectospec Clus ter Survey (HeCS) with MMT/Hectospec spectroscopy and published SZE signals. We measu re virial masses of these clusters from an average of 90 member redshifts inside the radius r100. The virial masses of the clusters are strongly correlated with their SZE signals (at the 99% confidence lev el using a Spearman rank-sum test). This correlation suggests that YSZcan be used as a measure of virial mass. Simulations predict a powerlaw scaling of YSZ∝Mα 200withα≈1.6. Observationally, we find α=1.11±0.16, significantly shallower (given the formal uncertainty) than the theoretical pr ediction. However, the selection func- tion of our sample is unknown and a bias against less massive clusters c annot be excluded (such a selection bias could artificially flatten the slope). Moreover, our sam ple indicates that the relation between velocity dispersion (or virial mass estimate) and SZE signal has significant intrinsic scatter, comparable to the range of our current sample. More detailed stud ies of scaling relations are therefore needed to derive a robust determination of the relation between clu ster mass and SZE. Subject headings: galaxies: clusters: individual — galaxies: kinematics and dynamics — co smology: observations 1.INTRODUCTION Clusters of galaxies are the most massive virialized systems in the universe. The normalization and evo- lution of the cluster mass function is therefore a sen- sitive probe of the growth of structure and thus cos- mology (e.g., Rines et al. 2007, 2008; Vikhlinin et al. 2009; Henry et al. 2009; Mantz et al. 2008; Rozo et al. 2008, and references therein). Many methods exist to estimate cluster masses, including dynamical masses from either galaxies (Zwicky 1937) or intracluster gas (e.g., Fabricant et al. 1980), gravitational lensing (e.g., Smith et al.2005;Richard et al.2010), andthe Sunyaev- Zel’dovich effect (SZE Sunyaev & Zeldovich 1972). In practice, these estimates are often made using simple observables, such as velocity dispersion for galaxy dy- namics or X-ray temperature for the intracluster gas. If one of these observable properties of clusters has a well-defined relation to the cluster mass, a large survey can yield tight constraints on cosmological parameters (e.g., Majumdar & Mohr 2004). There is thus much interest in identifying cluster observables that exhibit tight scaling relations with mass (Kravtsov et al. 2006; Rozo et al. 2008). Numerical simulations indicate that X-ray gas observables (Nagai et al. 2007) and SZE sig- nals (Motl et al. 2005) are both candidates for tight scal- ing relations. Both methods are beginning to gain ob- servational support (e.g., Henry et al. 2009; Lopes et al. 2009; Mantz et al. 2009; Locutus Huang et al. 2009). Dynamical masses from galaxy velocities are unbiased kenneth.rines@wwu.edu 1Department of Physics & Astronomy, Western Washington University, Bellingham, WA 98225; kenneth.rines@wwu.edu 2Smithsonian Astrophysical Observatory, 60 Garden St, Cam- bridge, MA 02138 3Universit` a degli Studi di Torino, Dipartimento di Fisica G en- erale “Amedeo Avogadro”, Torino, Italy 4Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Torino, Italyin numerical simulations (Diaferio 1999; Evrard et al. 2008), and recent results from hydrodynamical simula- tions indicate that virial masses may have scatter as small as ∼5% (Lau et al. 2010). Previous studies have compared SZE signals to hydro- staticX-raymasses(Bonamente et al.2008;Plagge et al. 2010) and gravitational lensing masses (Marrone et al. 2009, hereafter M09). Here, we make the first compar- ison between virial masses of galaxy clusters and their SZE signals. We use SZE measurements from the lit- erature and newly-measured virial masses of 15 clus- ters from extensive MMT/Hectospec spectroscopy. This comparison tests the robustness of the SZE as a proxy for cluster mass and the physical relationship between the SZE signal and cluster mass. Large SZ cluster sur- veys are underway and are beginning to yield cosmologi- calconstraints(Carlstrom et al.2010;Hincks et al.2010; Staniszewski et al. 2009). We assume a cosmology of Ω m=0.3, Ω Λ=0.7, and H0=70 km s−1Mpc−1for all calculations. 2.OBSERVATIONS 2.1.Optical Photometry and Spectroscopy We are completing the Hectospec Cluster Survey (HeCS), a study of an X-ray flux-limited sample of 53 galaxy clusters at moderate redshift with extensive spec- troscopy from MMT/Hectospec. HeCS includes all clus- ters with ROSAT X-ray fluxes of fX>5×10−12erg s−1at [0.5-2.0]keVfrom the Bright Cluster Survey (BCS Ebeling et al.1998)orREFLEXsurvey(B¨ ohringer et al. 2004) with optical imaging in the Sixth Data Release (DR6) of SDSS (Adelman-McCarthy et al. 2008). We use DR6 photometry to select Hectospec targets. The HeCS targets are all brighter than r=20.8 (SDSS cata- logs are 95% complete for point sources to r≈22.2). Out of the HeCS sample, 15 clusters have published SZ mea- surements.2 Rines, Geller, & Diaferio 2.1.1.Spectroscopy: MMT/Hectospec and SDSS HeCS is a spectroscopic survey of clusters in the red- shift range 0.10 ≤z≤0.30. We measure spectra with the Hectospec instrument (Fabricant et al. 2005) on the MMT 6.5m telescope. Hectospec provides simultaneous spectroscopy of up to 300 objects across a diameter of 1◦. This telescope and instrument combination is ideal for studying the virial regions and outskirts of clusters at these redshifts. We use the red sequence to preselect likely cluster members as primary targets, and we fill fibers with bluer targets (Rines et al. in prep. describes the details of target selection). We eliminate all targets withexistingSDSSspectroscopyfromourtargetlistsbut include these in our final redshift catalogs. Ofthe15clustersstudiedhere,onewasobservedwitha single Hectospec pointing and the remaining 14 were ob- served with two pointings. Using multiple pointings and incorporatingSDSS redshifts of brighterobjectsmitigate fiber collision issues. Because the galaxy targets are rel- atively bright ( r≤20.8), the spectra were obtained with relativelyshortexposuretimes of3x600sto 4x900sunder a variety of observing conditions. Figure 1 shows the redshifts of galaxies versus their projected clustrocentric radii for the 15 clusters stud- ied here. The infall patterns are clearly present in all clusters. We use the caustic technique (Diaferio 1999) to determine cluster membership. Briefly, the caustic technique uses a redshift-radius diagram to isolate clus- ter members in phase space by using an adaptive ker- nel estimator to smooth out the galaxies in phase space, and then determining the edges of this distribution (see Diaferio 2009, for a recent review). This technique has been successfully applied to optical studies of X-ray clus- ters, and yields cluster mass estimates in agreement with estimatesfromX-rayobservationsandgravitational lensing (e.g., Rines et al. 2003; Biviano & Girardi 2003; Diaferio et al. 2005; Rines & Diaferio 2006; Rines et al. 2007, and references therein). We apply the prescription of Danese et al. (1980) to determine the mean redshift cz⊙and projected velocity dispersion σpof each cluster from all galaxies within the caustics. We calculate σpusing only the cluster members projected within r100estimated from the caustic mass profile. 2.2.SZE Measurements The SZE detections are primarily from Bonamente et al. (2008, hereafter B08), supplemented by three measurements from Marrone et al. (2009, hereafter M09). Most of the SZ data were obtained with the OVRO/BIMA arrays; the additional clusters from M09 were observed with the Sunyaev-Zel’dovich Array (SZA; e.g., Muchovej et al. 2007). Numerical simulations indicate that the integrated Compton y-parameter YSZhas smaller scatter than the peak y-decrement ypeak(Motl et al. 2005), so B08 and M09 report only YSZ. Although ypeakshould be nearly independent of redshift, YSZdepends on the angular size of the cluster. The quantity YSZD2 Aremoves this depen- dence. Thus, we compare our dynamical mass estimates to this quantity rather than ypeakorYSZ. Table 1 sum- marizes the SZ data and optical spectroscopy. It is also critical to determine the radius within whichYSZis determined. B08 use r2500, the radius that en- closes an average density of 2500 times the critical den- sity at the cluster’s redshift; r2500has physical values of 300-700kpc forthe massiveclustersstudied by B08(470- 670kpcforthesubsamplestudiedhere). M09useaphys- ical radius of 350 kpc because this radius best matches their lensing data. To use both sets of data, we must estimate the con- version between YSZ(r2500) measured within r2500and YSZ(r= 350 kpc) measured within the smaller radius r=350 kpc. There are 8 clusters analyzed in both B08 and M09 (5 of which are in HeCS). We perform a least- squaresfit to YSZ(r2500)−YSZ(r= 350kpc) to determine an approximate aperture correction for the M09 clusters. We list both quantities in Table 1. 3.RESULTS We examine two issues: (1) the strength of the corre- lation between SZE signal and the dynamical mass and (2) the slope of the relationship between them. Figure 2 shows the YSZ−σprelation. Here, we compute σpfor all galaxies inside both the caustics and the radius r100,cde- fined by the caustic mass profile [ rδis the radius within which the enclosed density is δtimes the critical density ρc(z)]. Because we make the first comparison of dynami- cal properties and SZE signals, we first confirm that these two variables are well correlated. A nonparametric Spearman rank-sum test (one-tailed) rejects the hypoth- esis of uncorrelated data at the 98.4% confidence level. The strong correlation in the data suggests that both σp andYSZD2 Aincrease with increasing cluster mass. Hydrodynamic numerical simulations indicate that YSZ(integrated to r500) scales with cluster mass as YSZ∝Mα 500, whereα=1.60 with radiative cooling and star formation, and 1.61 for simulations with radiative cooling, star formation, and AGN feedback ( α=1.70 for non-radiative simulations, Motl et al. 2005). Combin- ing this result with the virial scaling relation of dark matter particles, σp∝M0.336±0.003 200 (Evrard et al. 2008), the expected scaling is YSZ∝σ4.76(we assume that M100∝M500). The right panels of Figure 2 shows this predicted slope (dashed lines). The bisector of the least-squares fits to the data has a slope of 2 .94±0.74, significantly shallower than the predicted slope of 4.8. We recompute the velocity dispersions σp,Afor all galaxies within one Abell radius (2.14 Mpc) and in- side the caustics. Surprisingly, the correlation is slightly stronger (99.4% confidence level). This result supports the idea that velocity dispersions computed within a fixedphysicalradiusretainstrongcorrelationswith other cluster observables, even though we measure the velocity dispersion inside different fractions of the virial radius for clusters of different masses. Because cluster veloc- ity dispersions decline with radius (e.g. Rines et al. 2003; Rines & Diaferio 2006), σp,Amay be smaller than σp,100 (measured within r100,c) for low-mass clusters, perhaps exaggerating the difference in measured velocity disper- sionsrelativeto the differences in virialmass(i.e., σp,Aof a low-mass cluster may be measured within 2 r100while σp,Aof a high-mass cluster may be measured within r100; the ratio σp,Aof these clusters would be exaggerated rel-Hectospec Virial Masses and SZE 3 Fig. 1.— Redshift versus projected clustrocentric radius for the 15 HeCS clusters studied here. Clusters are ordered left-to-r ight and top-to-bottom by decreasing values of YSZD2 A(r2500). The solid lines show the locations of the caustics, which w e use to identify cluster members. The Hectospec data extend out to ∼8 Mpc; the figure shows only the inner 4 Mpc to focus on the viria l regions. ative to the ratio σp,100). Future cluster surveys with enough redshifts to estimate velocity dispersions but too few to perform a caustic analysis should still be sufficient for analyzing scaling relations. Because of random errors in the mass estimation, the virial mass and the caustic mass within a given radius do not necessarily coincide. Therefore, the radius r100 depends on the mass estimator used. Figure 2 shows the scaling relationsfor two estimated masses M100,cand M100,v;M100,cis the mass estimated within r100,c(where bothquantitiesaredefinedfromthecausticmassprofile), andM100,vis the mass estimated within r100,v(both quantities are estimated with the virial theorem, e.g., Rines & Diaferio 2006). including galaxies projected in- sider100,v. Similar to σp, there is a clear correlation between M100,vandYSZD2 A(99.0% confidence with a Spearman test). The strong correlation of dynamical mass with SZE also holds for M100,cestimated directlyfrom the caustic technique (99.8% confidence). The bisector of the least-squares fits has a slope of 1.11±0.16, again significantly shallower than the pre- dicted slope of 1.6. This discrepancy has two distinct origins. By looking at the distribution of the SZE sig- nals in Figure 2, we see that, at a given velocity disper- sion or mass, the SZE signals have a scatter which is a factor of ∼2. Alternatively, at fixed SZE signal, there is a scatter of a factor of ∼2 in estimated virial mass. Unless the observational uncertainties are significantly underestimated, the data show substantial intrinsic scat- ter. Moreover, this scatter is comparable to the range of our sample and, therefore, the error on the slope derived from our least-squares fit to the data is likely to be un- derestimated (see Andreon & Hurn 2010, for a detailed discussionofaBayesianapproachtofittingrelationswith measurement uncertainties and intrinsic scatter in both quantities).4 Rines, Geller, & Diaferio TABLE 1 HeCS Dynamical Masses and SZE Signals Cluster z σ p M100,vM100,c YSZD2 AYSZD2 ASZE (350 kpc) ( r2500) km s−11014M⊙1014M⊙10−5Mpc−210−4Mpc2Ref. A267 0.2288 743+81 −616.86±0.82 4.26 ±0.14 3.08 ±0.34 0.42 ±0.06 1 A697 0.2812 784+77 −596.11±0.69 5.96 ±3.51 – 1.29 ±0.15 1 A773 0.2174 1066+77 −6318.4±1.7 16.3 ±0.7 5.40 ±0.57 0.90 ±0.10 1 Zw2701 0.2160 564+63 −473.47±0.42 2.69 ±0.30 1.46 ±0.016 0.17 ±0.02a2 Zw3146 0.2895 752+92 −676.87±0.89 4.96 ±0.91 – 0.71 ±0.09 1 A1413 0.1419 674+81 −606.60±0.85 3.49 ±0.15 3.47 ±0.24 0.81 ±0.12 1 A1689 0.1844 886+63 −5215.3±1.4 9.44 ±5.66 7.51 ±0.60 1.50 ±0.14 1 A1763 0.2315 1042+79 −6416.9±1.6 12.6 ±1.5 3.10 ±0.32 0.46 ±0.05a2 A1835 0.2507 1046+66 −5519.6±1.6 20.6 ±0.3 6.82 ±0.48 1.37 ±0.11 1 A1914 0.1659 698+46 −386.70±0.57 6.21 ±0.21 – 1.08 ±0.09 1 A2111 0.2290 661+57 −454.01±0.41 4.77 ±1.23 – 0.55 ±0.12 1 A2219 0.2256 915+53 −4512.8±1.0 12.0 ±4.7 6.27 ±0.26 1.19 ±0.05a2 A2259 0.1606 735+67 −535.59±0.60 4.90 ±1.69 – 0.27 ±0.10 1 A2261 0.2249 725+75 −577.13±0.83 5.10 ±2.07 – 0.71 ±0.09 1 RXJ2129 0.2338 684+88 −644.31±0.57 2.94 ±0.13 – 0.40 ±0.07 1 Note. —aExtrapolated to r2500using the best-fit relation between YSZD2 A(350kpc) and YSZD2 A(r2500) for eight clusters in common between B08 and M09. Note. — Redshift zand velocity dispersion σpare computed for galaxies defined as members using the causti cs. Masses M100,vand M100,care evaluated using the virial mass profile and caustic mass p rofile respectively. Note. — REFERENCES: SZE data are from (1) Bonamente et al. 2008 and (2) Marrone et al. 2009. Our shallow slopes may also arise in part from the fact that our sample, which has been assembled from the lit- erature and whose selection function is difficult to deter- mine, is likely to be biased against clusters with small mass and low SZE signal. Larger samples should deter- mine whether unknown observational biases or issues in the physical understanding of the relation account for this discrepancy. 4.DISCUSSION Thestrongcorrelationbetweenmassesfromgalaxydy- namics and SZE signals indicates that the SZE is a rea- sonableproxyforcluster mass. B08compareSZEsignals toX-rayobservables,inparticularthetemperature TXof the intracluster medium and YX=MgasTX, whereMgas isthemassoftheICM(seealsoPlagge et al.2010). Both of these quantities are measured within r500, a signifi- cantly smaller radius than r100where we measure virial mass. M09 compare SZE signals to masses estimated from gravitational lensing measurements. The lensing masses are measured within a radius of 350 kpc. For the clusters studied here, this radius is smaller than r2500 and much smaller than r100. Numerical simulations indi- cate that the scatter in masses measured within an over- densityδdecreases as δdecreases (White 2002), largely because variations in cluster cores are averaged out at larger radii. Thus, the dynamical measurement reaching to larger radius may provide a more robust indication of the relationship between the SZE measurements and cluster mass. TheYSZD2 A−Mlensdata presented in M09 show a weakercorrelationthanouropticaldynamicalproperties. A Spearman test rejects the hypothesis of uncorrelated data for the M09 data at only the 94.8% confidence level, compared to the 98.4-99.8% confidence levels for our op- tical dynamical properties. One possibility is that Mlensis more strongly affected by substructure in cluster cores and by line-of-sight structures than are the virial masses and velocity dispersions we derive. Few measurements of SZE at large radii ( > r500) are currently available. Hopefully, future SZ data will allow a comparisonbetween virialmass and YSZwithin similar apertures. 5.CONCLUSIONS Our first direct comparison of virial masses, velocity dispersions, and SZ measurements for a sizable clus- ter sample demonstrates a strong correlation between these observables (98.4-99.8% confidence). The SZE sig- nal increases with cluster mass. However, the slopes of both the YSZ−σrelation ( YSZ∝σ2.94±0.74 p) and the YSZ−M100relation ( YSZ∝M1.11±0.16 100) are significantly shallower(giventheformaluncertainties)thantheslopes predictedbynumericalsimulations(4.76and1.60respec- tively). This result may be partly explained by a bias against less massive clusters that could artificially flatten our measured slopes. Unfortunately, the selection function of our sample is unknown and we are unable to quan- tify the size of this effect. More importantly, our sample indicates that the relation between SZE and virial mass estimates (or velocity dispersion) has a non-negligible in- trinsicscatter. Acomplete, representativeclustersample is required to robustly determine the size of this scatter, its origin, and its possible effect on the SZE as a mass proxy. Curiously, YSZis more strongly correlated with both σpandM100than with Mlens(M09). Comparison of lensingmassesandclustervelocitydispersions(andvirial masses)forlarger,complete, objectivelyselected samples of clusters may resolve these differences. Thefull HeCS sampleof53clusterswill providealargeHectospec Virial Masses and SZE 5 Fig. 2.— Integrated S-Z Compton parameter YSZD2 Aversus dynamical properties for 15 clusters from HeCS. Left panels: SZE data versus virial mass M100estimated from the virial mass profile (top) and the caustic m ass profile (bottom). Solid and open points indicate SZ measurements from B08 and M09 respectively. The dashed li ne shows the slope of the scaling predicted from numerical si mulations: YSZ∝M1.6(Motl et al. 2005), while the solid line shows the ordinary le ast-squares bisector. Arrows show the aperture correction s to the SZE measurements (see text). Right panels: SZE data versus projected velocity dispersions measured fo r galaxies inside the caustics and (top) inside r100,cestimated from the caustic mass profile and (bottom) inside t he Abell radius 2.14 Mpc. The dashed line shows the scaling predicted from simulations: YSZ∝M1.6(Motl et al. 2005) and σ∝M0.33(Evrard et al. 2008). The solid line shows the ordinary least-squares bisector. Data points and arrows are defined a s in the left panels. sample of clusters with robustly measured velocity dis- persions and virial masses as a partial foundation for these comparisons. We thank Stefano Andreon for fruitful discussions about fitting scaling relations with measurement errorsand intrinsic scatter in both quantities. AD gratefully acknowledges partial support from INFN grant PD51. We thank Susan Tokarz for reducing the spectroscopic data and Perry Berlind and Mike Calkins for assisting with the observations. Facilities: MMT (Hectospec) REFERENCES Adelman-McCarthy, J. 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