A Systematic Search for High Surface Brightness Giant Arcs in a Sloan Digital Sky Survey Cluster Sample J. Estrada1, J. Annis1, H.T. Diehl1, P. B. Hall2, T. Las1, H. Lin1, M. Makler3, K. W. Merritt1, V. Scarpine1, S. Allam1 and D. Tucker1. 1 Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510, USA 7 0 2 Department of Physics and Astronomy, York University, 4700 Keele St., Toronto, 0 Ontario, M3J 1P3, Canada 2 3 Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil n a J 2 ABSTRACT 1 1 We present the results of a search for gravitationally-lensed giant arcs con- v 3 ducted on a sample of 825 SDSS galaxy clusters. Both a visual inspection of 8 3 the images and an automated search were performed and no arcs were found. 1 This result is used to set an upper limit on the arc probability per cluster. We 0 7 present selection functions for our survey, in the form of arc detection efficiency 0 curves plotted as functions of arc parameters, both for the visual inspection and / h the automated search. The selection function is such that we are sensitive only p - to long, high surface brightness arcs with g-band surface brightness µ ≤ 24.8 o g r and length-to-width ratio l/w ≥ 10. Our upper limits on the arc probability t s a are compatible with previous arc searches. Lastly, we report on a serendipitous : v discovery of a giant arc in the SDSS data, known inside the SDSS Collaboration i X as Hall’s arc. r a Subject headings: clusters, arcs, SDSS 1. Introduction Clusters of galaxies are the largest gravitationally bound structures in the universe. It has long been recognized that they constitute very usefeul probes for cosmology (see, e.g., Press & Schechter 1974; Mohr et al. 2001; Voit 2005), and therefore understanding them in detail has been a major field of research. Notable progress in the theoretical under- standing of clusters has been achieved in recent years through N-body and hydrodynamical simulations. At present, different simulation schemes converge in reproducing several broad – 2 – properties of clusters (Frenk et al. 1999; Heitman et al. 2005). Furthermore, several prop- erties of the simulated clusters are in agreement with observations (see, e.g., Borgani et al. 2004; Evrard et al. 2002; Eke et al. 1998). The strong gravitational lensing of background galaxies produced by massive clusters is a probe of cluster structure. This effect hasbeen observed in many previous studies, with the most extreme case being the giant gravitational arcs first seen by Lynds & Petrosian (1989) and Soucail et al. (1987). Almost a decade later, spectacular images of these arcs were provided by the excellent resolution of the Hubble Space Telescope (Couch & Ellis 1995; Kneib et al. 1996; Smail et al. 1996). There are now about a hundred clusters with giant arcs imaged by HST (for a recent compilation, see Sand et al. 2005). Several arc searches have been carried out with ground based observations, both for X-ray selected clusters (see, e.g., Luppino et al. 1999; Cypriano 2002; Campusano et al. 2006) as well as for optically identified clusters (Zaritsky & Gonzalez 2003; Gladders et al. 2003). The comparison of the abundance of gravitational arcs with theoretical predictions has been proposed as a toolto constrain cosmology (Grossman & Narayan 1988;Miralda-Escud´e 1993; Wu & Hammer 1993). The early results indicated that the number of strongly-lensed arcsgreatlyexceeded thatexpected fromΛCDMsimulations (Bartelmann et al.1998). More detailedstudiesofthetheoreticaluncertaintiesandsystematiceffectsinvolvedinthisanalysis seem to indicate that the observations do, in fact, agree with the theoretical expectations from the standard cosmology (Hennawi et al. 2005; Dalal et al. 2004; Wambsganss et al. 2004; Oguri et al. 2003), although uncertainties may still remain (Li et al. 2005). The main goal of the work presented here is not in the extraction of cosmological infor- mation from the statistics of gravitational arcs. Instead it is both (a) to locate high surface brightness giant arcs that would prove useful in follow-up imaging and spectroscopy pro- grams, and more directly (b) to understand the probability for a galaxy cluster to produce a giant arc as a function of the cluster mass and redshift. We believe this is an important aspect to be considered before cosmology can be extracted from arc statistics and that it will provide a significant improvement in our understanding of the mass distribution inside galaxy clusters. Adefining characteristic of previous arcsearches isthatthey were donein themost mas- sive clusters. Luppino et al. (1999) searched for arcs in 38 X-ray selected clusters (redshifts 0.15 ≤ z ≤ 0.82) with X-ray luminosity L ≥ 2×1044 ergs/sec and found arcs in a high frac- x tion of clusters with L > 1045 ergs/sec, but no arcs in clusters with L < 4×1044 ergs/sec. x x Zaritsky & Gonzalez (2003) searched for arcs in 44 optically selected clusters (0.5 ≤ z ≤ 0.8) from a list ranked by surface brightness, finding arcs in two clusters. Gladders et al. (2003) searched ≈ 900 optically selected clusters (0.3 ≤ z ≤ 1.4) ranked by a galaxy overdensity – 3 – parameter, finding arcs in 8 clusters, with none at z < 0.64. Sand et al. (2005) used a very different technique, searching for arcs in the heterogeneous sample of clusters that have been observed with HST; out of 128 clusters (0.1 ≤ z ≤ 0.78) 45 had tangential arcs, although it is worth noting that many of the clusters were targeted by HST precisely because of known arcs. It is possible to compute which of the arcs found in high quality images would be found in images of lower quality, and we will perform such a comparison. The results so far suggest looking for arcs in clusters with high X-rayluminosity or high redshift. Luppino et al. (1999) found a higher frequency of arcs in high L clusters, and since the bremstrahlung emission x in clusters is proportional to n2, this result suggests that arcs are found preferentially in the e highest density clusters. Gladders et al. (2003) found a higher frequency of arcs in higher redshift clusters, which suggests either an evolution of cluster structure in a way not fully understood, or perhaps that the sources lensed are predominately at higher redshifts, where the lensing cross section would be much larger for z ∼ 0.7 clusters than for those at z ∼ 0.3 (Ho & White 2005). Observationally, however, it is clear that the dominant variables for successful arc detection are limiting surface brightness and, in particular, seeing. The Sloan Digital Sky Survey (York et al. 2000) to date has produced multiband ugriz imaging of 8000 deg2 of the northern sky, along with an associated catalog of 1,048,496 spectra, of which 674,749 are galaxies (Adelman-McCarthy et al. 2006). It has proven useful as a data set for gravitational lens searches. An example is the multiply-lensed quasar searches of Pindor et al. (2003) and Oguri et al. (2006), which use the imaging data to select quasar-colored objects that are larger than a PSF, or groupings of quasar-colored objects in a small area. A second example of lens searches in the SDSS data uses the large SDSS spectroscopic data set: Bolton et al. (2006) searched red galaxy spectra for indications of a second, higher redshift nebular emission spectrum. This locates strongly-lensed background galaxies, whicharerevealedasarcsafterapplyinggalaxysubtractiontechniques onHSTACS images. Our program is a search for strongly-lensed background galaxies behind clusters; that is, a search for giant arcs. Our ability to locate gravitational arcs in the SDSS images is demonstrated by recovering arcs observed by other surveys and by the discovery of new gravitational arcs (see Fig. 1, Appendix A, and Allam et al. 2006). A similar arc search in a sample of 240 rich SDSS clusters has been carried out by Hennawi et al. (2006) and has found a significant number of new giant arc systems, but relies on deeper imaging data to discover the arcs, whereas we use the original SDSS imaging data itself. Our analysis consists of a search for giant gravitational arcs in a sample of SDSS galaxy clusters sorted by a richness estimator. Our imaging data does not have the depth or seeing available to previous searches, but it does have the twin features of homogenity and large – 4 – sky coverage. This results in our ability to greatly increase the number of clusters searched. The search reported here totals 825 clusters, comparable to the largest previous search. We intend, in a future paper, to decrease the mass threshold down to the poor group range in order to search tens or hundreds of thousands of locations. Furthermore, the redshift range of the cluster catalog we have searched is predominantly 0.1 ≤ z ≤ 0.3, a regime poorly covered by previous searches. – 5 – Fig. 1.— On the left, the SDSS image of the RCS1419.2+5361 cluster. The arc was dis- covered by visual inspection of the RCS cluster sample (Gladders et al. 2003) and is clearly visible in this color image composed of the SDSS g, r, and i data. On the right, Hall’s arc (see Appendix), serendipitously discovered in the SDSS data. It too is clearly visible in the composite gri image. These observations, together with the recent discovery of a new arc system (Allam et al. 2006), demonstrate the ability of the SDSS to detect high surface brightness giant arcs. – 6 – 2. The Data The data set we use is the Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5; Adelman-McCarthy et al. 2006). The SDSS uses a wide-field drift-scanning mosaic CCD camera (Gunn et al. 1998) on a dedicated 2.5m telescope (Gunn et al. 2006) at Apache Point Observatory, New Mexico, to image the sky in the five photometric bandpasses ugriz (Fukugita et al. 1996; Stoughton et al. 2002). The SDSS photometric data are processed using pipelines that address astrometric calibrations (Pier et al. 2003), photometric data re- duction (Lupton et al. 2001), and photometric calibrations (Tucker et al. 2006; Smith et al. 2002; Hogg et al. 2001; Ivezic et al. 2004). Note that the SDSS is a survey that trades rela- tively shallow exposures – 55 seconds on a 2.5m telescope, resulting in point sources detected at 95% confidence level at g = 22.2 and i = 21.3 (AB) – for a very wide area: 8000 deg2 or 20% of the total sky. 2.1. The Cluster Sample The cluster catalog was constructed using the maxBCG algorithm. This is a red- sequence locating technique that has shown completeness levels of 90% at 0.1 ≤ z ≤ 0.3 and down to N = 10, where N is the number of galaxies on the E/S0 red sequence brighter g g than 0.4L⋆ and within 1h−1 Mpc of the brightest cluster galaxy. The correlation of the richness N with mass can be calibrated with independent mass estimators, such as velocity g dispersions or weak lensing shear profiles. A detailed description of the maxBCG technique is discussed in Koester et al. (2006a). Koester et al (2006b) used the SDSS DR5 data to construct a cluster catalog containing 12,875 rich clusters, plus two orders of magnitude more clusters of lower masses. The catalog we used in this work was created using an earlier version of the maxBCG algorithm (see, e.g., Hansen et al. 2005; Sheldon et al. 2001). Oneofthedefining featuresofredsequence methodsisthatprojectioneffectsarepresent only at a minimal level: if the clusters differ by ∆z < 0.05 then they can be confused as a single object. The resulting purity (lack of false positives) is ≈ 95%, and the completeness (lack of false negatives) is ≈ 85% above 1×1014M , as determined by running this algorithm ⊙ on mock catalogs (Koester et al 2006b). We selected a sample of 825 clusters with N ≥ 20, approximately 50% of the N ≥ 20 g g clusters in our sample. The whole sample was not searched due to a variety of technical reasons, but lack of a complete sample is not important for the results of this paper. The distribution of g-band seeing of the cluster images is shown in Fig. 2 and has a mean of 1.44′′; this is important because the seeing is the single dominating factor in our ability to – 7 – detect arcs. The cluster redshift distribution is shown in Fig. 3. The richest clusters in our sample are presented in Table 5, and the table listing our full cluster sample is available electronically. – 8 – Fig. 2.— The g-band seeing distribution for the SDSS images of the 825 clusters inspected in this paper. The distribution is well fit by a gaussian of mean 1.44” and standard deviation 0.20”. – 9 – 100 80 60 40 20 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 z Fig. 3.— The redshift distribution for the 825 clusters inspected for this paper. We have good statistics in the redshift range 0.1 < z < 0.3. – 10 – While we do not use the masses of the clusters directly in this work, we do have a rough mass calibration. Stacked cluster spectroscopic velocity dispersions, plus isothermal sphere fitstostackedclusterweaklensingshearprofiles, bothfromearlyworkintheSDSSEDR(see, e.g. Bahcall et al. 2003; Sheldon et al. 2001), were combined to produce a scaling relation between velocity dispersion σ and N given by σ ≈ 85N0.6 km/s. Modeling the cluster as v g v g a singular isothermal sphere, the mass enclosed within a radius having an overdensity of 200 with respect to the critical density is (see, e.g. Bryan & Norman 1998) σ 3 1 M = v 1015M , (1) 200 (cid:16) (cid:17) ⊙ σ E(z)h 0 where σ = 1148 km/s, E(z) = Ω +Ω (1+z)3 +(1−Ω −Ω )(1+z)3, h is the 0 Λ m Λ m p Hubble constant in units of 100 km/s/Mpc, and Ω and Ω are the energy densities of m Λ cold/presureless normal matter and the cosmological constant, respectively, in units of the critical density. The σ -N relation has a significant scatter. Indirect methods, such as (a) v g running the cluster finding algorithm on mock catalogs based on N-body simulations and (b) measuring the higher moments of the velocity distributions of galaxies in stacked cluster samples, suggest that the scatter is ∆M /M ∼ 40% at high N and increases at lower 200 200 g N . A more sophisticated calibration using weak lensing measurements of the full maxBCG g catalog is given in Sheldon (2006) and Johnston et al. (2006). In future work we expect to use the current maxBCG catalog and mass calibrations.