Abell 1201: The anatomy of a cold front cluster from combined optical and X-ray data
Matt S. Owers, Paul E.J. Nulsen, Warrick J. Couch, Maxim Markevitch, Gregory B. Poole
aa r X i v : . [ a s t r o - ph ] O c t Draft version November 1, 2018
Preprint typeset using L A TEX style emulateapj v. 03/07/07
ABELL 1201: THE ANATOMY OF A COLD FRONT CLUSTER FROM COMBINED OPTICAL AND X-RAYDATA
Matt S. Owers , Paul E.J. Nulsen , Warrick J. Couch , Maxim Markevitch and Gregory B. Poole Draft version November 1, 2018
ABSTRACTWe present a combined X-ray and optical analysis of the cold front cluster Abell 1201 using archival
Chandra data and multi-object spectroscopy taken with the 3.9m Anglo Australian and 6.5m MultipleMirror Telescopes. This paper represents the first in a series presenting a study of a sample of cold frontclusters selected from the
Chandra archives with the aim of relating cold fronts to merger activity,understanding the dynamics of mergers and their effect on the cluster constituents. The
Chandra
X-ray imagery of Abell 1201 reveals two conspicuous surface brightness discontinuities, which areshown to be cold fronts, and a remnant core structure. Temperature maps reveal a complex multi-phase temperature structure with regions of hot gas interspersed with fingers of cold gas. Our opticalanalysis is based on a sample of 321 confirmed members, whose mean redshift is z = 0 . ± . ±
36 km s − . We search for dynamical substructure and find clear evidence formultiple localized velocity substructures coincident with over-densities in the galaxy surface density.Most notably, we find structure coincident with the remnant X-ray core. Despite the clear evidencefor dynamical activity, we find the peculiar velocity distribution does not deviate significantly fromGaussian. We apply two-body dynamical analyses in order to assess which of the substructures arebound, and thus dynamically important in terms of the cluster merger history. We propose that thecold fronts in Abell 1201 are a consequence of its merger with a smaller subunit, which has inducedgas motions that gave rise to ‘sloshing’ cold fronts. Abell 1201 illustrates the value of combiningmulti-wavelength data and multiple substructure detection techniques when attempting to ascertainthe dynamical state of a cluster. Subject headings: galaxies: clusters: individual (Abell 1201) — X-rays: galaxies: clusters INTRODUCTION
Within the current cosmological paradigm, large scalestructure in the Universe is expected to form in a hierar-chical manner. This “bottom up” formation scenario cul-minates with the formation of clusters of galaxies, whichare the largest and most massive virialized objects in theUniverse. At the current epoch, a high fraction of clus-ters are still growing through the infall of matter, muchof which is funneled through the surrounding spider-weblike filamentary structures. The most extreme growthevent occurs when two clusters of roughly equal massmerge, the merging process being one of the most ener-getic in the Universe, releasing around 10 ergs of grav-itational binding energy. Some 10% of this is dissipatedvia mechanisms such as shock and adiabatic heating ofthe intracluster medium (ICM), acceleration of relativis-tic particles, and generation of peculiar velocities andturbulence in the ICM (for a review of these physicalprocesses see Sarazin 2002).In this context, the new generation of X-ray obser-vatories (XMM-Newton and Chandra ) have provided awealth of new information on the ICM and hence newinsights into this cluster merger phenomenon. One ofthe first interesting discoveries – attributed to the ex-cellent spatial resolution and sensitivity of
Chandra –was the observation of extended ‘edge’ features in the School of Physics, University of New South Wales, Sydney,NSW 2052, Australia; [email protected] Harvard Smithsonian Center for Astrophysics, 60 GardenStreet, Cambridge, MA 02138, USA Center for Astrophysics and Supercomputing, Swinburne Uni-versity of Technology, Hawthorn, VIC 3122, Australia
X-ray surface brightness maps obtained for Abell 2142(Markevitch et al. 2000) and Abell 3667 (Vikhlinin et al.2001). The sharp discontinuity in surface brightness seenin Abell 3667 had been observed previously with
ROSAT ,and was interpreted as a shock front (Markevitch et al.1999). However, the
Chandra observations showed thatin both Abell 2142 and Abell 3667, the temperature ofthe gas on the brighter (denser) side of the discontinuitywas colder than the temperature of the less dense down-stream gas – opposite to expectations for a shock. Fur-thermore, the temperature and density profiles across thediscontinuities showed, in combination, that the pressureis roughly continuous, again inconsistent with a shockfront. Thus, the observed edges appear to be contactdiscontinuities between cool, dense, low entropy gas andhotter, diffuse ambient ICM, leading them to be dubbed“cold fronts”. Initial explanations attributed the low en-tropy gas to the remnant cooling core of a merging sub-cluster (Markevitch et al. 2000).As the number of clusters observed to have cold frontfeatures has increased, it has become clear that the rem-nant core scenario is not the correct interpretation inall cases, since a number of cold fronts are observedto exist in clusters with an otherwise relaxed X-raymorphology (Mazzotta et al. 2001a,b; Markevitch et al.2001; Markevitch & Vikhlinin 2007). One such ex-ample is Abell 1795, the observations of which ledMarkevitch et al. (2001) to propose an alternative sce-nario whereby the ‘sloshing’ of the cooling core withinthe stationary gravitational potential well causes coolcentral gas to be displaced and a cold front formed whereit comes into contact with higher entropy gas at larger Owers et al.radii.Hydrodynamic simulations have an integral role in aid-ing the interpretation of these cluster X-ray observationsand further understanding the underlying physics. BothAscasibar & Markevitch (2006) and Poole et al. (2006)found a plethora of transient cold-front like phenom-ena associated with sub-cluster gas arising during theirsimulated mergers, including the classic ram-pressurestripped remnant sub-cluster core preceded by a mergershock. Tittley & Henriksen (2005) explored the possi-bility of forming a cold front through gas sloshing, find-ing it is possible to produce similar edges to those ob-served through core oscillations, although in their modelthey find the gravitational potential well oscillates dueto the motion of the dark matter, inducing motion inthe gas. Churazov et al. (2003) and Fujita et al. (2004)also showed that gas oscillations can be induced whenthe cluster core is displaced from the potential well by aweak shock or acoustic wave which has passed throughthe cluster center. Ascasibar & Markevitch (2006) foundthat oscillation of the central gas and dark matter caneasily be induced by infalling sub-clusters, and can evenbe induced due to the infall of a dark matter only sub-cluster. The gas core decouples from the dark matterwhen a rapid change in the direction of oscillation dueto the core passage of the dark matter sub-cluster causesa change in the ram pressure felt by the gas, displacingit from the dark matter. The gas sloshing then occurswhen the displaced gas falls back toward the potentialminimum, generating edges at the turn-around point ofeach oscillation.Whatever the mechanism, it appears the existence ofa cold front can generally be interpreted as strong ev-idence of a system which is in the process of, or hasrecently undergone a merger. What has been lackingto date is a systematic study of the relationship be-tween cold fronts and other dynamical indicators of clus-ter merger activity using multi-wavelength observations,which can be incorporated into detailed models in or-der to garner a complete understanding of how a ma-jor merger impacts the different cluster mass compo-nents. To address this issue, we have conducted a searchof the
Chandra archives and selected a sample of clus-ters exhibiting robust examples of cold fronts (the se-lection criteria and sample will be presented in a forth-coming paper; Owers et al. 2008, in prep.) for opticalmultiple-object spectra (MOS) and radio follow up obser-vations. This paper represents the first of a series wherewe aim to show a relationship between cold fronts andmerger activity through detection of substructure at op-tical wavelengths. Subsequent papers will relate the starformation/radio properties of the galaxies and large scalediffuse radio halo/relic emission associated with clustermergers (Giovannini & Feretti 2002).Detection of substructure within clusters using opticaldata has a long history. Initially, galaxy surface densitycontours were used to search for projected galaxy con-centrations within clusters (Geller & Beers 1982). Ad-vances in multi-object spectroscopy have allowed simul-taneous observations of tens, and now hundreds of galaxyspectra within a field, meaning large samples of spectro-scopically confirmed cluster members can now be com-piled. Radial velocity information aids in eliminatingthe projection effects inherent in galaxy surface density contour methods, and a number of methods have beenproposed which use the combination of galaxy radial ve-locity and spatial information to develop a statistic forthe robust detection of substructures within a cluster (eg.see Dressler & Shectman 1988; West & Bothun 1990;Colless & Dunn 1996; Girardi & Biviano 2002). Sincedifferent statistics are sensitive to different types of sub-structure (Pinkney et al. 1996), the use of a combinationof a number of different statistical methods is essentialin diagnosing the dynamical activity in a cluster. Com-bining these substructure detection methods with data atX-ray wavelengths has proven to be a powerful tool in di-agnosing cluster merger scenarios and is essential for dis-entangling the complex histories of merging systems (eg.Boschin et al. 2004; Girardi et al. 2006; Barrena et al.2007; Carrasco et al. 2007; Maurogordato et al. 2008).Here, in this first paper, we present a detailed opticaland X-ray analysis of the cluster Abell 1201. The (previ-ously unpublished)
Chandra observations of this clusterreveal two sharp surface brightness discontinuities, bothof which are cold fronts, and also an offset core of X-rayemission. Based on comparisons of the simulations ofPoole et al. (2006) and Ascasibar & Markevitch (2006)and these observations, Abell 1201 appears to be an ex-cellent example of cold fronts generated by core gas mo-tions caused by a gravitational perturbation in the formof a merging subcluster. Thus, Abell 1201 provides aunique opportunity to test this scenario using combinedoptical and X-ray analyses.Abell 1201 is a richness class 2 cluster (Abell et al.1989) at moderate redshift z=0.168 (Struble & Rood1999) with an X-ray luminosity L x = 2 . × ergs s − (B¨ohringer et al. 2000). The analysis presented is basedon comprehensive optical spectroscopy obtained us-ing both AAOmega on the Anglo-Australian Telescope(AAT) and Hectospec on the Multiple-Mirror Telescope(MMT) combined with Chandra archival X-ray data.The structure of the paper is as follows: In § Chandra data. In § § § H = 70 km s − , Ω m = 0 . Λ =0 .
7. For this cosmology and at the redshift of the cluster1 ′′ = 2 .
88 kpc. X-RAY OBSERVATIONS AND ANALYSIS
Our X-ray analysis of Abell 1201 uses
Chandra archivaldata that were taken on 2004 November 3 (ObsId 4216).The observations were made with the ACIS-S array withthe cluster centered on the back illuminated S3 chip, fora total exposure time of 40 ksec.
Data preparation
The data were reprocessed using the CIAO softwarepackage (version 3.4) starting from the standard
Chandra pipeline processed level-1 event list. Observation specificbad pixel files containing hot pixel and cosmic ray af-terglow information were produced and applied, the lat-est gain files and calibrations were applied and VFAINTmode cleaning was used for improved rejection of cosmicray events. The data were then filtered to include onlynatomy of Abell 1201 3events with
ASCA grades 0, 2, 3, 4 and 6.Since the backside illuminated chips are prone to flarecontamination, we filtered the data for periods of anoma-lously high background. We followed standard proce-dure and extracted lightcurves from source-free regionsto search for flares. Cluster emission covers much ofthe S3 chip, so we extracted a lightcurve in the 2.5-6 keV range using the S1 chip which has very similarflare properties to the S3 chip. The observation sufferedfrom a strong flare, and approximately half the expo-sure time was affected, leaving a useful exposure time of21.5 ks. During the spectral analyses presented below,this cleaned data is used. For the imaging analyses, in-cluding the fitting of surface brightness profiles, the full40ks uncleaned exposure is used.Background data were taken from the blank sky obser-vations appropriate for the epoch of observation . Thebackgrounds are taken from observations with low Galac-tic foregrounds and soft X-ray brightness, so we checkthe soft X-ray flux in the vicinity of Abell 1201 usingthe ROSAT all sky R45 count rates and confirm theyare consistent with the blank sky background rates. Thebackground and source data were processed using thesame calibration files, bad pixel files and background fil-tering, with the backgrounds being reprojected to matchthe observations.We check for residual backgrounds in the cleaned databy extracting spectra from the S1 chip and after sub-tracting backgrounds from the blank sky observations,find a small residual background. This residual was mod-eled by a soft thermal MEKAL component with solarabundance and kT=0.27 keV (similar to that found inMarkevitch et al. 2003) plus a cutoff power law, which isnot folded through the instrument response, with pho-ton index of -0.15 and exponential cutoff at 5.6 keV(Markevitch et al. 2003). Including these components,scaled for region size, in the spectral fits performed in § X-ray images and Surface Brightness Modeling
The raw 0.5–7.0 keV
Chandra image, uncorrected forexposure and showing the entire ACIS-S3 chip, is pre-sented in the left panel of Figure 1. The right panelof Figure 1 shows the corresponding exposure corrected,adaptively smoothed
Chandra image. The cluster has abright core, and appears elongated along an axis point-ing to the north-west. Along this axis, there are threedistinct features apart from the cool core: There are twosurface brightness discontinuities, one to the south-east ∼
300 kpc from the core running from position angle (PA;measured from due west) 240 ◦ to 267 ◦ and one ∼
50 kpcnorth-west of the core (PA 8 ◦ to 120 ◦ ) and ∼
430 kpcto the north-west there is a faint, diffuse excess clump ofemission. We discuss the discontinuities further in § Chandra
X-raycontours overlaid. The X-ray peak is offset by ∼ . ′′ from the brightest cluster galaxy (BCG) and the excessclump of emission approximately coincides with a secondconcentration of galaxies, which will be discussed furtherin § § See http://cxc.harvard.edu/contrib/maxim/acisbg/ See http://heasarc.gsfc.nasa.gov/docs/tools.html
Beta model
In order to emphasize the structures seen in Figure 1,we use the method of Neumann & Bohringer (1997).The surface brightness distribution is fitted with an az-imuthally symmetric model and the residuals are in-spected for significant deviations. We use the
Sherpa fitting package to fit a background subtracted double-Beta model of the form S ( r ) = X i =1 S ,i " (cid:18) rr ,i (cid:19) − β +1 / + B, (1)where r is the radius, measured from an adjustable ori-gin. One Beta model accounts for the excess emissionwithin the central 100 kpc and the second models theremaining cluster emission. For fitting, the model is mul-tiplied by the exposure map to account for instrumentaleffects. The best fitting model parameters are presentedin Table 1.We obtain residual maps by subtracting the smoothmodel described above from the entire cluster image.This residual map is smoothed with a Gaussian kernelwith σ = 5 . ′′ and residual significance is determined us-ing the method of Neumann & Bohringer (1997), whereGaussian smoothing and Poissonian statistics are usedto determine an error map for the X-ray image, and thesignificance map is the ratio of the residual to error map.Figure 3 shows the residual significance map, with thenorth-west clump detected at greater than 10 σ signifi-cance while an excess plume is detected in the directionof the south-east discontinuity. There appears to be a sig-nificant excess detected in the south-west at the bottomof the chip. This can be attributed to excess emissiondue to the background flare, since the excess is much lesssignificant when the same analysis is performed on thecleaned 21.5 ks exposure. Also apparent are the signifi-cant negative residuals surrounding the south-east plumeand in the outer parts of the chip to the west, artifactsof the azimuthally symmetric model. Global spectral properties and the nature of thesurface brightness discontinuities
In this section we derive global properties forAbell 1201, and also analyze the properties of the sharpsurface brightness discontinuities seen in Figure 1 withthe aim of determining the nature of the fronts. Table 2summarizes the various best fitting spectral parametersmeasured in the following sections.
Global Temperature
We derived a global temperature and metallicity forAbell 1201 within an elliptical region covering the major-ity of the cluster emission (see Figure 4). The spectrumwas extracted using the CIAO dmextract tool, and pointsources detected with wavdetect excised. The CIAO tool mkwarf was used to create the auxiliary response file(ARF), which accounts for spatial variations in quan-tum efficiency (QE), effective area and the buildup ofcontaminant on the filter windows. The observation wasperformed at − ◦ C, so the CIAO tool mkacisrmf wasused to create redistribution matrix files (RMF). TheARF and RMF calculated within a region are weightedby the number of events in the 0.5-2 keV range withinthe region. Owers et al. D E C ( J2000 )
300 kpc
Fig. 1.—
Left:
Raw
Chandra
ACIS-S3 X-ray image of Abell 1201 in the 0.5-7.0 keV energy range, binned to 4 ′′ pixels, including only theS3 chip, using the full 40ks exposure and displayed on a logarithmic scale to enhance the diffuse, low surface brightness emission. North isup and east is to the left. Right:
Adaptively smoothed, exposure corrected close up version of the left image with point sources removed.The emission appears elongated on an axis from the south-east to north-west, and there is a bright central X-ray core. To the north-westthere is a clump of excess emission and there are two surface brightness discontinuities, one to the south-east and one near the core.
TABLE 1Beta model parameters derived from fitting the surface brightness distributionwith a double beta model (see text). x , y S , S , β r , r , B (deg, J2000) (10 − ) (10 − ) (kpc) (kpc) (10 − )11 h m . s , +13 ◦ ′ . ′′ . +0 . − . . +0 . − . . +0 . − . +4 − +22 − . +0 . − . Note . — Units of S , , S , and B are photons/cm /s/arcsec . Errors on x and y are ∼ . ′′ . TABLE 2Summary of best fitting spectral parametersfor several regions.
Region kT Abundance(keV) ( Z )Global 5 . ± . . ± . . +1 . − . · · · Outside south-east front 5 . +3 . − . · · · Inside north-west front 3 . +1 . − . · · · Outside north-west front 5 . +1 . − . · · · The unbinned spectra were fitted in the 0.5-9.8 keVrange using the MEKAL (Kaastra 1992; Liedahl et al.1995) and WABS models within the XSPEC package(Arnaud 1996), minimizing the Cash statistic. TheMEKAL component models a hot, diffuse, single tem-perature plasma, and is multiplied by WABS, a pho-toelectric absorption model accounting for Galactic ab-sorption, where the neutral hydrogen column densityis fixed to the Galactic value of N H = 1 . × (Dickey & Lockman 1990). The best fitting values forthe temperatures and abundance are kT = 5 . +0 . − . and Z = 0 . +0 . − . where the errors are 90% confidence lim-its. We used the LUMIN function to determine theintegrated unabsorbed X-ray luminosity from the best fitting model in the energy range 0.5-7.0 keV, and ob-tained L X (0 . − . . × erg s − within the r ≃
550 kpc elliptical aperture shown in Figure 4.
Surface Brightness Discontinuities
To characterize the surface brightness discontinuitiesas either shock or cold fronts, we fitted the surface bright-ness profiles across them with a density model, and alsomeasured the temperature difference across the discon-tinuities. The density model consists of a broken powerlaw function such that n e ( r ) = n e, (cid:16) rR f (cid:17) − α , r < R f ,n e, (cid:16) rR f (cid:17) − α , r > R f , (2)where R f is the radius at which the discontinuity occurs, n e, and n e, are the densities of the inner and outergas at R f , respectively, and the spheroidal radius, r , isdefined by r = ̟ + ǫ ζ ζ . Here ζ is the coordinatealong our line of sight and the elliptical radius, ̟ , isdefined by ̟ = ǫ [ x cos θ + y sin θ ] + [ y cos θ − x sin θ )] ǫ , (3)where x and y are cartesian coordinates centered at thecenter of curvature of the discontinuity and θ determinesnatomy of Abell 1201 5 Fig. 2.—
SDSS r-band image of the central region of Abell 1201.The red contours are the
Chandra
X-ray contours logarithmicallyspaced by a factor of 1.3 in the interval 1 . × − − . × − pho-tons cm − s − pixel − , the black squares identify galaxies whichare cluster members, the green squares show galaxies allocated toKMM1, and the green ellipse shows the 1 σ region for KMM1 fromthe KMM analysis (see § whitesquare appears to be associated with the bright X-ray core, al-though is offset by ∼ . ′′ . Fig. 3.—
Residual significance map derived from subtracting asmooth double Beta model from the X-ray image and calculatingthe significance (see text). Grey scales show the negative residuals,whilst color scales show the positive residuals. The black contoursrange from 1 − σ with linear increments of 1 σ . the orientation of the front on the plane of the sky. Weassumed the gas density distributions inside and outsidethe front have the same ellipticities and have rotationalsymmetry so that ǫ ζ = 1 /ǫ . The model is incorporatedinto Sherpa where we fitted the surface brightness across
Fig. 4.—
Close up of the raw
Chandra image with regions show-ing where surface brightness profiles were fitted, and where spectrawere extracted for temperature measurements. The large greenellipse shows the region where spectra were extracted for globaltemperature and abundance measurements. The surface brightnessprofiles shown in Figure 5 are taken from the solid red and whitesectors. The boundaries indicate the fronts, and delineate regionswhere the temperature inside and outside the fronts are measured.The dashed red sector indicates the slightly larger opening angleused in measuring the temperature outside the south-east front. the discontinuity in the sectors shown in Figure 4 usingthe full 40 ks exposure, in the energy range 0.5-7 keV, andalso add to the model a constant background componentwhich was measured in § A and A , we deriveda density jump of p A /A = n e, /n e, = 2 . +0 . − . forthe south-east discontinuity and n e, /n e, = 1 . +0 . − . for the north-west discontinuity. The confidence rangefor the density jump was computed from the extremesof the 90% confidence ranges for A and A , assuming asingle parameter of interest. We note that if the densityjump is the only parameter of interest, this overestimatesits confidence range.The temperature profile across the front is an essentialdiagnostic tool. Ideally, to minimize projection effects wewould like to measure the deprojected temperature pro-file across the fronts, however the limited number of pho-tons available do not allow this. Instead, we extractedspectra from two regions for each front, one on the brightside of the front (inside) and one on the faint side (out-side). The regions from which we extracted spectra forboth the south-east and north-west fronts are shown inFigure 4. For the north-west front, we extracted spectrafrom one sector centered at RA=168.2268, DEC=13.4344with PA from 7 ◦ − ◦ and radii 0 − . ′′ and one withthe same center and PA, but with radii 18 . − . ′′ , cor-responding to the sector in which we fit the density modelabove. For the south-east front, we extracted spectrain one sector centered at RA=168.2197, DEC=13.45094with PA from 240 ◦ − ◦ and radii 127 . − . ′′ , and Owers et al. Fig. 5.—
Left:
Surface brightness profile across the north-west discontinuity measured in a sector from PA 7 ◦ − ◦ centered at the centerof curvature of the front (RA=168.2268, DEC=13.4344). Right:
Surface brightness profile across the south-east discontinuity measured ina sector from PA 240 ◦ − ◦ centered at the center of curvature of the front (RA=168.2197, DEC=13.4509). The red curves show thesurface brightness profile for the best fitting density model. one with the same center, but PA from 234 ◦ − ◦ andradii 175 . − . ′′ . Note that the region from which weextracted a spectrum for outside the south-east front hasa slightly larger opening angle compared to the region inwhich the surface brightness profile was fitted. The sec-tor is wider for better statistical accuracy. Spectra andresponses for these regions were extracted as describedin § § § . +3 . − . keV outside the front and 3 . +1 . − . keV inside thefront, and for the north-west front we measured a tem-perature of 5 . +1 . − . keV outside the front and 3 . +1 . − . keVinside the front.The pressure should be continuous at a cold front. Thepressure jump across a front can be measured by tak-ing the ratio ( n e, kT ) / ( n e, kT ). We measured pressurejumps of 1 . +1 . − . and 1 . +1 . − . for the south-east and north-west fronts, respectively, consistent with the pressure be-ing continuous across both fronts. A shock interpreta-tion for the fronts can be also ruled out by applying theRankine-Hugoniot shock jump conditions for the mea-sured density jumps and post-shock temperatures (i.e. the temperature on the dense side of the front) and com-paring with the values observed. For shock fronts, wewould expect to observe pre-shock gas temperatures of1 . + . − . keV and 2 . +1 . − . keV for the south-east and north-west fronts, respectively, significantly different from ourmeasured temperatures. With continuous pressure and atemperature increase, these discontinuities have the hall-marks of cold fronts. Temperature Map
Temperature maps provide extremely useful tools forsearching for multi-phase temperature structure dueto the effects of an ongoing merger. To search forevidence of merger induced temperature structure inthe ICM of Abell 1201, we generated a temperaturemap using the broad energy band method described inMarkevitch et al. (2000). Briefly, we produced sourceand background images, binned in 7.8 ′′ pixels, inthe energy bands 0.5-1.0-2.0-5.0-10keV, excluding pointsources. Exposure maps that corrected for mirror vi-gnetting relative to the on-axis position, QEU (includ-ing low energy contamination) and exposure time wereproduced for each energy band. The background im-ages, which were taken from the blank sky observationsdescribed above, were normalized by the ratio of thesource to background 9-12 keV counts, subtracted fromthe source images and the resulting image divided by itscorresponding exposure map. Each image was smoothedusing the same variable width Gaussian, where σ var-ied from 8.6-39.4 ′′ , with it being smallest in the bright-est regions and chosen such that statistically significanttemperatures could be measured whilst maximum spatialinformation was retained. The noise in each pixel was de-termined from the raw, uncorrected images and weightedaccordingly to allow for the effects of the smoothing.Each pixel was fitted with an absorbed single temper-ature MEKAL model with the absorption column set atthe Galactic value. The metal abundance was set tothe best fitting average cluster value derived in § Fig. 6.—
Temperature map with 0.5–7.0 keV brightness contoursoverlaid (same as Figure 2). The 68% temperature uncertaintiesrange from ± . < ± − > large cluster region, and was binned to match the chosenenergy bands. The temperature map is presented in Fig-ure 6, where we have excluded pixels where the 1 σ erroris greater than 30% of the best fit temperature value.The cold fronts described above are clearly visible inFigure 6 and the temperature map values are consistentwith the temperatures measured spectroscopically in theabove sections. Interestingly, there is a finger of cool gasextending from the south-east cold front to the core ofthe cluster. This finger is coincident with the residualobserved after subtraction of the Beta model in § ∼ . σ ≃ ′′ here). Thus the temper-ature measurement is averaged over a large region andis heavily contaminated by ambient gas projected ontothis region, thus the temperature of the excess remainsuncertain. OPTICAL SPECTROSCOPY - REDUCTION ANDANALYSIS
In this section we present our optical analysis which in-cludes selection of photometric samples for spectroscopicfollow up, spectroscopic observations and data analysis,determination of cluster membership and substructuredetection. The purpose of this optical analysis is tosearch for substructures and use them in correlation withthe X-ray observations to develop a scenario for the for-mation of the cold fronts observed above, and also forthe merger history of Abell 1201.
Data Reduction and Selection Criteria
The multi-object spectroscopic (MOS) data presentedin this paper were taken from two sets of observations,one set at the 3.9m Anglo-Australian Telescope (AAT)on 2006 April 2-5, and the second at the 6.5m Multi-ple Mirror Telescope (MMT) in queue schedule mode inthe months of February and April 2007. The observa-tion details are listed in Table 3 where we list the dates,magnitude limits, frame exposures and the seeing.
Parent Photometric Catalog
The initial target catalog was taken from the SloanDigital Sky Survey (SDSS) sky server , with all objectswithin an 18 arcmin radius of the center of Abell 1201(RA=11 h m . s , DEC=+13 ◦ ′ . ′′ ) included. Thiscatalog was then filtered to include only those objectsclassified by the SDSS pipeline as galaxies (SDSS class 3).The SDSS r and g magnitudes for the remaining objectswere then converted to Johnson B and R magnitudesvia equations A5 and A7 of Cross et al. (2004) and onlythose galaxies with R < . green stars ), foreground galaxies ( blue squares ) andbackground galaxies ( red circles ). Also plotted is the line B − R = 3 . − . R which was used to distinguishthose galaxies which we define to be lying on or belowthe red sequence from those redward of the red sequence.The slope of the line is calculated from the best fit to theCM slope versus redshift diagram of L´opez-Cruz et al.(2004) and the constant is estimated by eye such thatthe line lies just above the red sequence. AAT AAOmega Observations
The AAT observations were taken using the AAOmegafiber-fed spectrograph (Saunders et al. 2004; Smith et al.2004; Sharp et al. 2006), which is a bench mounted dual-beam spectrograph, which is fed by 400 fibers robotically-placed within the two degree field at the telescope’s primefocus. A total of 392 fibers, each 2 ′′ in diameter, areavailable for the simultaneous observation of scientifictargets (with the remaining 8 fibers being used for ac-quisition and guiding). All our observations were takenusing the medium resolution ( R ≃ See: http://cas.sdss.org/dr5/en/
Owers et al.
TABLE 3Summary of the observations.
Telescope/Instrument Date Magnitude Frames SeeingAAT/AAOmega 2006 Apr 2 19 . < R < . × ′′ × · · · . < R < . × ′′ · · · R < . × ′′ · · · R < . × ′′ · · · R < . × ′′ MMT/Hectospec 2007 Feb 21 20 . < R < . × ′′ · · · < R < . × ′′ · · · R < . × ′′ · · · R < . × ′′ Fig. 7.—
Color-magnitude diagram for all galaxies within ourobserved field (black dots). The green stars represent cluster mem-bers, the blue squares foreground galaxies, and the red circles back-ground galaxies. The pink line is the line used to delineate galaxieson and blueward of the red sequence from those redward of the redsequence for the purpose of ranking galaxies during fiber configu-ration. the 15 µ m pixel 2k ×
4k E2V CCD detectors produce aspectral resolution of 3 . . ∼ ′′ dueto the physical size of the fiber buttons) and the factour input catalog contained ∼ CONFIGURE software . A totalof 5 configurations were required for Abell 1201: threefor galaxies with R < .
5, and two for galaxies in therange 19 . < R < . posures being taken through thin cloud cover, with somebeing interrupted by thicker clouds. In commencing theobservations for each new configuration, a 4 s dome flatand 60 s FeAr arc lamp exposure were taken for flat field-ing and wavelength calibration of the data, respectively.The data were reduced with the AAO pipelinesoftware with a patch included to fix fiber to slit positionmapping errors present in AAOmega data taken beforeAugust 2006.Redshift identification and measurement for each spec-trum was carried out using the RUNZ code written byWill Sutherland for the 2dF Galaxy Redshift Survey(2dFGRS; Colless et al. 2001). This program utilizes thecross-correlation method of Tonry & Davis (1979), basedon a library of galaxy template spectra that are rep-resentative of all the different observed spectral types.Each spectrum was inspected visually and given a red-shift quality classification, Q. Here we used the samescheme as adopted for the 2dFGRS, with each spectrumbeing assigned a Q value on a six-point integer scale, withQ=1 indicating that no redshift could be estimated, Q=2a possible but unreliable redshift, Q=3 a probable red-shift (with ∼
90% confidence), Q=4 a reliable redshift,Q=5 a reliable redshift with high-quality spectrum, andQ=6 indicating a star or non-extragalactic object. Weobtained spectra for 917 galaxies during the run, whichyielded reliable (Q=3, 4, or 5) redshift measurements for580 single galaxies.
MMT Hectospec Observations
The MMT observations were taken using the Hec-tospec multi-object spectrograph (Fabricant et al. 2005).This is also a bench-mounted spectrograph, which is fedby 300 1.5 ′′ diameter fibers that cover a 1 degree fieldof view. The observations were taken using the mediumresolution (R=1000-2000) 270 groove mm − grating andthe data were captured on a single array of two E2VCCDs with 13.5 µm pixels, resulting in spectra with aresolution of 6.2˚A and covering the wavelength range3500 − , with a total of four being required for galaxieswith R < .
5, and one being required for galaxies with20 . < R < .
5. Typically 150 fibers were allocatedto galaxies, with around 100 fibers allocated to blanksky areas. The details of each observed configurationare listed in Table 3. The seeing during the observationsranged from 0.61-1.2 ′′ , and the observations performed inthe worst seeing conditions were somewhat affected witha number of galaxies requiring re-observation since thespectra were inadequate for determining redshifts. Thedata were reduced at the Telescope Data Center (TDC) using the TDC pipeline. The data were also redshiftedat the TDC using the IRAF cross-correlation XCSAOsoftware (Kurtz et al. 1992) and spectra were assigneda redshift quality of “Q” for reliable, “?” for question-able and “X” for bad redshift measurements. We usein our analysis only those galaxies with reliable redshiftmeasurements (quality=Q). A subsample of the data wasvisually inspected and the redshifts and quality assign-ments were found to be robust. We obtained spectrafor 742 galaxies during the run, which yielded reliableredshift measurements for 534 single galaxies. Redshift completeness and measurement errors
A number of galaxies were observed multiple times inthe two observing runs. There were also 67 galaxieswith independently measured redshifts within 20 arcminof the cluster center in the NASA Extragalactic Database(NED) . To check the accuracy of our measured red-shifts, we compared the redshifts of all multiply-observedgalaxies by determining the mean of the differences aswell as their standard deviation. The MMT observationshad a mean intrinsic uncertainty of 42 ± − for 534redshifts. There were 19 repeat observations made withthe MMT, and the mean difference was 1 ±
25 km s − after removing a spurious result where the difference was cz = 44894 km s − . From these repeat observations, wecalculate an RMS of 105 km s − implying an uncertaintyof 74 km s − for the MMT observations, higher than themean of the individual redshift measurements. An ex-ternal test of these redshift uncertainty measurementscomes from the 12 redshifts in common between theNED and MMT catalogs which have a mean differenceof − ±
20 km s − with an RMS scatter of 74 km s − .The NED redshifts come primarily from the SDSS andthe catalog of Miller et al. (2002) which have redshift un-certainties ∼
30 km s − . Taking this into account givesan external uncertainty measurement of 43 km s − , con-sistent with the mean of the individual uncertainty mea-surements. The high uncertainty value given by the re-peat MMT observations can be understood by consider-ing that these objects were re-observed due to the lowquality of their initial redshift measurements.There were no repeat observations taken at the AAT,which have a mean internal uncertainty for the individ-ual redshift measurements of 109 ± − from 580redshifts. An external check of this value comes from31 galaxies re-observed with the MMT which had bothQ=3 redshifts from the AAT data set and quality=Qfrom the MMT. The mean difference in the measured N E D r ed s h i ft ( O r ange , D a r k B l ue ) o r MM T r ed s h i ft ( P i n k , L i gh t B l ue ) AAT redshift (Orange, Light Blue) or MMT redshift (Pink, Dark blue)
Fig. 8.—
Redshift comparison for Abell 1201 using our MMT andAAT redshifts, and also a sample of NED redshifts. The compari-son of different measurements are plotted with the following colorcodes: MMT/MMT = pink, AAT/MMT = light blue, AAT/NED= orange, MMT/NED = dark blue. The black line represents theone-to-one relationship; the general scatter of the data about thisline indicates the absence of any gross systematic errors in our mea-surements, and indicates our AAT and MMT measurements havea precision of 159 km s − and 74 km s − , respectively. We assumean uncertainty of 30 km s − for the NED measurements. redshifts of these was 50 ±
44 km s − . Two galaxieswith obviously spurious redshift differences of ∆( cz ) =53417 km s − and ∆( cz ) = 119800 km s − were excludedfrom this calculation. The RMS scatter in the differ-ence was 248 km s − , and taking into account the uncer-tainty derived above for the MMT redshifts (74 km s − ),we calculate an uncertainty of 159 km s − . This valueis higher than the mean of the individual redshift un-certainties, however again it is noted that these objectswere re-observed due to their poor initial redshift mea-surements (all had Q=3), thus the measured uncertaintyis expected to be higher. This value can be checked us-ing the 45 measurements in common with the NED cat-alog, where the mean difference was 33 ±
29 km s − , andan RMS scatter in the differences of 191 km s − , aftertwo spurious results where the redshift differences were∆( cz ) = 3480 km s − and ∆( cz ) = 10472 km s − were ex-cluded. Based on these redshift differences, we measurean uncertainty of 132 km s − , again after accounting forthe ∼
30 km s − uncertainty associated with the NEDredshifts.Figure 8 shows the comparison of redshift measure-ments using different instruments in the redshift range ofthe cluster. The figure, in combination with the redshiftdifferences above, show that there are no gross systematicerrors in our measurements and the scatter about a 1-to-1 relationship is well encompassed by the uncertaintiesof 159 km s − and 74 km s − for AAT and MMT, respec-tively, which we take from the more conservative highervalues derived above from the double observations, andthese values indicate the precision of our measurements.For galaxies which had multiple redshift measure-ments, the following approach was taken to determiningwhat their final adopted redshift would be: If a galaxywas observed with both the MMT and AAT, we used theMMT redshift since the MMT redshifts were in generalmore precise with lower errors (as expected since the re-observed galaxies were ones with AAT quality Q=3). If agalaxy was observed more than once with the MMT, we0 Owers et al.took the redshift based on the highest cross-correlationcoefficient. If a galaxy was observed more than once withthe AAT, we took the redshift with the highest Q value.Note that in no cases did we ever use the NED redshiftif that galaxy had been observed on either the AAT orMMT. When added to our single redshift measurements,this yielded a total of 560, 534 and 10 redshifts mea-sured with the AAT, MMT and sourced from NED, re-spectively, giving an overall total of 1104 robust redshiftsacquired within the cluster field.We determined the spectroscopic completeness of thesample by measuring the ratio of galaxies in the parentphotometric catalog which have reliable redshifts (as de-fined previously) to those which have no reliable redshiftmeasurement. The spectroscopic completeness as a func-tion of cluster-centric radius for the R magnitude inter-vals 0-18, 18-19.5, 19.5-20.5, and 20.5-21.5 is plotted inFigure 9 where we also plot the spectroscopic complete-ness within 3.5 Mpc as a function of R magnitude. Weachieve &
80% spectroscopic completeness at all radii,apart from within the 3-3.5 Mpc range, for magnitudesbrighter than 19.5, whilst we obtain ∼
60% spectroscopiccompleteness at all radii for magnitudes between 19.5 and20.5 and ∼
20% spectroscopic completeness for magni-tudes between 20.5 and 21.5 within a radius of ∼ . R magnitudes brighter than 20.5, which corresponds to ∼ . M ∗ R = − . Cluster member selection
Identification of cluster members from our spectro-scopic redshifts was achieved through the eliminationof foreground and background galaxies along the lineof sight to Abell 1201. An initial rejection was per-formed using the “velocity gap” method outlined byDe Propris et al. (2002), where the galaxies are sortedin redshift space and the velocity ( cz ) gap between eachone determined. Here the velocity gap for the nth galaxyis ∆ v n = cz n +1 − cz n . Clusters appear as well populatedpeaks in redshift space which are separated by velocitygaps of greater than 1000 km s − from the nearest fore-ground and background galaxies, and Figure 10 showsthat Abell 1201 is readily identified on this basis.Due to the filamentary structures which surround clus-ters, it is necessary to further refine this rejection pro-cess. For this refinement, we used a slightly different ver-sion of the “shifting gapper” method first implementedby Fadda et al. (1996) where both cluster-centric radiusand peculiar velocity information are used and the gapmethod outlined above is applied as a function of radius.The galaxies were binned radially such that each bin con-tained 35 galaxies, and were then sorted by v pec , with thevelocity gaps determined as before (but in peculiar ve-locity, not cz ). Peculiar velocities were determined withrespect to the central cluster redshift using the followingprocedure: We estimated the mean cluster redshift usingthe biweight location estimator (Beers et al. 1990) whichwe assume represents the cosmological redshift of thecluster. The peculiar redshift, z pec , was derived underthe assumption that the observed redshift of the galaxy, z gal , is comprised of only two components, the cosmologi-cal component, z cos , and the component due to the pecu- liar motion within the cluster, z pec . Hence, the peculiarredshift is z pec = ( z gal − z cos ) / (1 + z cos ) and the peculiarvelocity was derived using the standard special relativis-tic formula v pec = c ((1 + z pec ) − / ((1 + z pec ) + 1),where c is the speed of light.We used the “f pseudosigma” (Beers et al. 1990), de-rived from the first and third quartiles of the peculiarvelocity distribution, as the fixed gap to separate thecluster from interlopers. The f pseudo-sigma is an esti-mator of the scale of the velocity distribution which isrobust to the presence of velocity interlopers in the tailsof the cluster distribution. The above procedure wasiterated until the number of members was stable andthe results are shown in Figure 11 where it can be seenthat the cluster is clearly separated from the filamentarystructure surrounding it, and the interlopers are cleanlyrejected. The advantage of this method is that it doesnot assume a particular mass model or velocity distribu-tion which both rely on the cluster being relaxed.The final cluster sample contains 321 members out toa cluster-centric radius of ∼ . z cos = 0 . ± . ±
36 km s − . The errors for the redshift and velocitydispersion are 1 σ and are estimated using the jackkniferesampling technique. Substructure Detection
Now that we have separated our cluster members fromforeground and background interlopers, we can applysubstructure detection tests to the cluster member sam-ple. Substructure in a cluster can present itself in a num-ber of different ways, and generally no single statisticaltest is capable of revealing all such manifestations. Henceit is essential that the full range of statistical tests are ap-plied if the search for substructure is to be an exhaustiveone. In general, statistics using the maximum amount ofinformation (eg., the radial velocity and spatial dimen-sions) are the most effective at revealing substructure,however these can fail if, for example, roughly equal massclusters are merging along the line of sight such thatthe cores are spatially coincident (see eg. Girardi et al.2006; Pinkney et al. 1996). The use of velocity infor-mation by itself can be successful, although there aredocumented cases where the velocity distribution mim-ics that of a relaxed cluster where other methods haveclearly shown it to be disturbed (Maurogordato et al.2000; Johnston-Hollitt et al. 2008). The use of 2-D spa-tial information alone suffers from foreground and back-ground contamination. In this section, we apply a num-ber of statistical methods to the detection of substructurein Abell 1201.
Deviations from Gaussianity
The velocity distribution of a relaxed cluster is wellapproximated by a single Gaussian, with velocity dis-persion related to the cluster mass via the virial the-orem. Departures from Gaussianity can be attributedto a dynamically active cluster where substructures maycause symmetric and asymmetric distortions in the veloc-ity distribution. As a first test of Gaussianity, we usedthe standard Kolmogorov-Smirnov (K-S) test. At the90% confidence level, the observed velocity distributionnatomy of Abell 1201 11
Fig. 9.—
Spectroscopic completeness as a function of cluster-centric radius ( left panel) for the R -band magnitude intervals 0-18 ( solid line), 18-19.5 ( dashed line), 19.5-20.5 ( dot-dashed line), and 20.5-21.5 ( dotted line). This shows we have both good completeness and radialcoverage for magnitudes brighter than R = 20 .
5. The spectroscopic completeness as a function of magnitude is shown in the right panel.
Fig. 10.—
A histogram of all the reliable redshifts measuredwithin the Abell 1201 field. The Abell 1201 cluster clearly standsout against the foreground and background galaxies. The insetpanel shows the distribution of peculiar velocities for the clustermembers, with a Gaussian with mean zero and standard deviationof 778 km s − overplotted. is consistent with being drawn from a Gaussian distribu-tion with v pec = 0 and σ vpec = 778 km s − . On the basisof this test, therefore, it appears unlikely Abell 1201’svelocity distribution is significantly non-Gaussian.The disadvantage of using the K-S test is that it ismost sensitive to the behavior of the distribution near itsmedian, but is relatively insensitive to differences in thetails of the distribution. Also, the K-S test does not givequantitative information about the way in which two dis-tributions differ. Quantifying these deviations is impera-tive in determining the state of the cluster, and a numberof different methods can be used to quantify asymmetricand symmetric distortions (Pinkney et al. 1996). Herewe choose to use the method outlined in Zabludoff et al.(1993), where the velocity distribution, L , is approxi-mated by a series of Gauss-Hermite functions L = X j =0 h j H j ( x ) , (4)where h j are the Gauss-Hermite moments defined by Fig. 11.—
A plot of deviations in peculiar velocities as a func-tion of cluster-centric radius, illustrating the efficacy of our refinedrejection method whereby foreground and background interlopersare identified and eliminated using a shifting gapper technique (seetext). The black crosses represent galaxies allocated as clustermembers while the orange asterisks are rejected foreground andbackground galaxies lying close to the cluster in redshift space.
Zabludoff et al. (1993) as h j = 2 √ πN S N X i =1 H j ( x i ) , (5)where x i = v pec,i − VS , H j ( x ) = e − x / √ π H j ( x ) , (6)and H j ( x ) are the Hermite polynomials given byvan der Marel & Franx (1993). In principle, the veloc-ity distribution can be described by equations 4 and5 and a wide variety of S and V values, where thereis significant degeneracy in the choices of S and V and the j = 1 , S and V so that the zeroth-order term, H , de-scribes the best fit Gaussian to the data. This is achievedby choosing S and V such that h = h = 0. We iterated2 Owers et al.with different values of S and V until these criteria weremet. The terms h and h describe, respectively, theasymmetric and symmetric deviations from Gaussianity,much like the higher order Gaussian skewness and kurto-sis terms, but have the advantage of being less sensitiveto outliers in the tails of the distribution. Applying thismethod to the velocity distribution for Abell 1201, weobtain values of values of h = − .
016 and h = 0 . σ = S and µ = V to determinethe probability of detecting our h and h terms. Valuesof | h | ≥ .
016 occur in 70% of the realizations, while val-ues of | h | ≥ .
023 occur in 50% of the realizations. Weconclude there is no significant evidence for asymmetricor symmetric deviations from Gaussianity.
Velocity Distribution Profiles
Figure 12 shows integral and differential projected ra-dial profiles of the biweight location, µ ( R ) and scale, σ ( R ), estimators. The differential profiles are binned us-ing the same radial intervals as used for the shift gap-per in § µ ( R ) are constant withradius within the 1 σ error bars. This is expected for anisotropic distribution of radial velocities. The differential σ ( R ) profile is flat out to r = 1 Mpc, and smoothly de-clines at larger radii. den Hartog & Katgert (1996) clas-sified σ ( R ) profiles as flat, inverted or peaked, dependingon the shape of the profile within ∼ σ ( R ) profileswhich have the highest σ ( R ) value measured between0.5 and 1.0 Mpc, all of which show signs of recent mergeractivity. While this is by no means a definitive sign ofmerger activity, it is interesting to note that Abell 1201also exhibits its highest value of σ ( R ) at ∼ σ ( R ) profile increases gradually to its max-imum value at ∼ ∼ . σ measured at this radius is no longer affected by velocityanisotropy, and is representative of the cluster potential(Fadda et al. 1996).We include the estimate of the velocity dispersion de-rived from the cluster X-ray temperature measured in § β = µm p σ /kT = 1 (i.e., assumingthe same specific kinetic energy in the gas and galaxies),where σ is the galaxy velocity dispersion, µ is the meanmolecular weight of the gas particles, m p is the protonmass and kT is the gas temperature within R ≃
500 kpc.The integral and differential σ ( R ) profiles appear, towithin the errors, to be consistent with the value es-timated from the X-ray temperature when consideringregions within 1 Mpc. Fig. 12.—
Differential velocity dispersion profile ( top panel)and mean peculiar velocity ( bottom panel) profiles as a functionof projected radius. The solid lines show the total cluster values,while the dashed lines and error bars show the 1 σ confidence limitsderived using the jackknife technique. The dot-dashed line showsthe velocity dispersion derived from the mean X-ray temperature(see text), with the dotted lines showing the upper and lower limitsbased on the errors in the temperature (see § The most efficient way to detect real physical substruc-tures is to use a combination of the 2-D spatial and 1-Dvelocity information to search for local variations in thevelocity distribution (Pinkney et al. 1996). The mostcommon method here is to utilize the ∆ statistic de-veloped by Dressler & Shectman (1988), which tests fordifferences in the local mean and dispersion comparedto the global mean and dispersion. The downfall of thismethod is that it assumes the global and local peculiarvelocity distributions are Gaussian, which may not betrue for dynamically active systems. Here we prefer thek-statistic, κ , employed by Colless & Dunn (1996), whichis very similar to the ∆ statistic but does not require theassumption of Gaussianity to be made. To determine κ ,the n = √ N nearest neighbors in projection are selectedfor each cluster member, where N is the total clustermember sample size, and the local velocity distributionof the n nearest neighbors is compared to the global clus-ter velocity distribution (minus the n nearest-neighborvelocities). Local departures from the global velocity dis-tribution are quantified using the K-S D statistic, withthe null hypothesis that the local distribution is drawnfrom the global one and the significance determined bymeasuring the probability that the D statistic is largerthan the observed D statistic for the observed samplesize, P KS ( D > D obs ). Then, κ n is defined as κ n = N X i =1 − log P KS ( D > D obs ) , (7)giving a global measure of the substructure present in thecluster by summing the individual κ values. The signifi-cance of κ n was determined by performing 10,000 MonteCarlo realizations with the peculiar velocities randomlyshuffled, whilst maintaining the positional information,and remeasuring κ n .The observed value of κ n = 379, is larger than anyvalue obtained in our 10,000 realizations, which fol-low a log-normal distribution with a mean value ofnatomy of Abell 1201 13 Fig. 13.—
Bubble plot outputs from the κ test. The bold bub-bles are those deemed to be significant insomuch as they only occurin 5% of 10,000 realizations. The blue bubbles are those galaxieswhich have negative v pec , and the red bubbles have positive v pec .The contours are galaxy density contours generated from applyinga variable width Gaussian filter to the spatial distribution of spec-troscopically confirmed members. The contours are linearly spacedby 10 in the interval 10-150 gals Mpc − . Note the four clumpingsof significant bubbles are coincident with overdensities in the pro-jected galaxy density. The center of the cluster is located at 0,0Mpc. µ (ln κ sim ) = 4 . σ (ln κ sim ) =0 .
2. Thus, the observed κ n lies 6 σ from the meanof the realizations, and we can put an upper limit onthe probability of observing this κ n value by chanceat less than 10 − . We conclude, therefore, that thereis velocity substructure present in Abell 1201 at highsignificance.
The results of the κ test are best pre-sented using “bubble plots” showing a circle with radius r ∝ − log P KS ( D > D obs ) at each galaxy position, suchthat clustered large bubbles reveal local departures fromthe global velocity distribution. We show these bubblesin Figure 13 and color code them based on the sign ofthe peculiar velocity, with blue and red having negativeand positive v pec , respectively. Overplotted are contoursof galaxy surface density which have been produced byapplying a variable width Gaussian filter, with σ varyingfrom ∼
100 kpc in the cluster center to ∼
400 kpc in theoutskirts, to the spatial distribution of the spectroscop-ically confirmed members. We define significant valuesof − log P KS ( D > D obs ) as those which occur only 5%of the time in the 10,000 Monte Carlo realizations, andthese are highlighted by the bold bubbles in Figure 13.Visual inspection of the distribution of large clusteredbubbles in Figure 13 confirms the significance of the mea-sured κ n , as there appear to be four conglomerations ofsignificant bubbles, each coincident with an increase inprojected galaxy density.Having verified the existence of substructure withinAbell 1201, we further utilize the spatial and velocityinformation of our cluster galaxies by allocating groupmembership using the Kaye’s Mixture Model (KMM) al- gorithm of Ashman et al. (1994). The algorithm fits auser specified number of N-dimensional Gaussians to thedata and determines the improvement of the fit over thatof a single N-dimensional Gaussian via a maximum likeli-hood test. The major drawbacks of this method are thatthe spatial distribution of the galaxies does not follow aGaussian shape (although the velocity distribution doesfor a relaxed cluster), and the number of Gaussians needsto be known a priori. Visual inspection of the projectedX and Y galaxy distributions reveal they are at leastqualitatively Gaussian, and given the benefit of includ-ing an extra two dimensions in the analysis far outweighsthe false assumption of Gaussianity, we proceed with thefull 3-D KMM analysis. Overcoming the latter drawbackrequires a robust method of estimating the initial numberof Gaussians, and also their parameters. Given the corre-lation between the significant bubbles and galaxy surfacedensity peaks seen in Figure 13, we use it as a guide to es-timate the positions and projected radii of substructures.There appear to be 6 spatially separated substructureswhere the local velocity distribution differs significantlyfrom the global one, along with the main Abell 1201 clus-ter. We inspect the velocity distributions of all galaxieswithin the estimated projected radius for each substruc-ture, excise any obvious interlopers and determine themedian and standard deviation of the X position (kpc),Y position (kpc) and velocity distributions for the re-maining substructure galaxies. These parameters serveas initial estimates for input into the KMM algorithm,and are presented in table 4, along with the outputs fromthe KMM algorithm, where ( x, y, v ) are the means of thedistributions, ( σ x , σ y , σ v ) the standard deviations, N gal is the number of galaxies in the substructure and Rate isthe estimate of the overall rate for correct allocation ofgalaxies to this substructure.Given that the substructures KMM3 and KMM4 areclose both spatially and in velocity, as are KMM5 andKMM6, it is possible that they are part of the same struc-tures. We therefore combined the inputs for the four sub-structures into KMM(3+4) and KMM(5+6) and re-ranthe KMM algorithm on the 5 substructures. The resultsfor KMM1, KMM2 and KMM7 were very similar to thosefound using 7 partitions, with similar galaxies being allo-cated to the combined KMM(3+4) and KMM(5+6) sys-tems as were allocated when considering them as sepa-rate entities, and the overall correct allocation estimatorfor both the 5 and 7 substructure analyses being 98% and97 . MERGER SCENARIO
Both the X-ray and optical analyses give clear indi-cations that Abell 1201 hosts multiple substructures.In this section we first give a qualitative scenario ex-plaining the appearance of the X-ray structure and cold4 Owers et al.
TABLE 4Results of the KMM analysis for partitioning the data into 7 ( top ) and 5 ( bottom ) substructures. SeeFigure 14 for the spatial and velocity distributions of the 5 partition results.
Initial Inputs KMM OutputsGroup ( x, y, v ) ( σ x , σ y , σ v ) N gal ( x, y, v ) ( σ x , σ y , σ v ) N gal Rate (%)7 substructuresKMM1 (138, 388, 444) (103, 64, 175) 9 (150, 383, 432) (145, 121, 167) 12 100KMM2 (-1125, 550, -1816) (320, 283, 318) 11 ( -890, 346, -1887) (419, 224, 254) 14 100KMM3 (-431,-444, -996) (62,134, 221) 7 ( -462, -427, -1008) (44, 139, 160) 6 100KMM4 (-869,-63, -607) (134, 116, 383) 12 ( -924, -58, -672) (146, 120, 257) 12 100KMM5 (1563, 513,-642) (200, 139, 233) 11 (1650, 533, -769) (180, 132, 208) 10 98KMM6 (2150, 1213, -236) (155, 249, 170) 9 (2037, 1429, -317) (401, 459, 220) 15 96KMM7 (0, 0, 2) (1236, 979, 738) 262 ( -96, 93, 133) (1211, 1016, 682) 252 985 substructuresKMM1 (138 388, 444) (103, 64, 175) 9 (151, 382, 432) (145, 121, 166) 12 100KMM2 (-1125, 550, -1816) (320, 283, 318) 11 (-890, 346, -1886) (419, 224, 255) 14 100KMM(3+4) (-720, -200, -777) (239,223, 321) 19 (-684, -249, -867) (304, 264, 211)) 16 94KMM(5+6) (1884, 849, -608) (323, 421, 246) 20 (1831, 900, -753) (348, 452, 328) 17 99KMM7 (0, 0, 2) (1236, 979, 738) 262 (-32, 138, 127) (1250, 1028, 663) 262 98
Note . — The units of x, y, σ x and σ y are kpc, and the units of v and σ v are km s − . fronts through simple interpretations of the optical andX-ray observations combined with hydrodynamic simula-tions of Poole et al. (2006) and Ascasibar & Markevitch(2006). Second we use two-body analytic models to de-termine which of the substructures are bound to the maincluster. KMM1, the north-west X-ray excess and theformation of the cold fronts
Figure 2 shows an SDSS r -band image of the central re-gions of Abell 1201 with X-ray contours overlaid, alongwith regions showing the cluster members and KMM1allocations. Clearly, KMM1 is coincident with the ex-cess X-ray emission which is probably the remnant ofthe gas core of KMM1. The morphology of the X-rayemission indicates the remnant KMM1 core is breakingup, and there appears to be a tail pointing towards themain cluster, although it is difficult to disentangle thecluster and subclump emission. The positioning of thecold fronts on opposite sides of the cluster center, alongthe direction to the north-west clump, suggests motionof the cluster core in this direction. This evidence pointsto a scenario where KMM1 has made its closest approachto the core of Abell 1201 and is traveling outwards to-ward the north-west. Projection effects make it difficultto know on exactly which plane the merger is occurring,although the small radial velocity offset between KMM1and Abell 1201 and the location of the cold fronts sug-gest the majority of the subcluster motion is in the planeof the sky. Since the core of Abell 1201 is not completelydisrupted and is coincident with the dominant clustergalaxy, which presumably lies at the cluster potentialminimum, it is unlikely KMM1 passed directly throughthe cluster core (Poole et al. 2008). The low velocitydispersion and compact galaxy distribution of KMM1suggest we are seeing the surviving central region of aonce larger cluster which has been stripped of its outermembers due to the tidal effects of the main Abell 1201cluster potential.The south-east cold front appears to be connected tothe core of the main cluster, as evidenced by the signifi- cant residuals extending from the core to the cold front,and also by the finger of cold ( ∼ r min = 360 kpc), 3 to1 mass ratio merger simulation of Poole et al. (2006) gen-erated using emission weighted temperatures integratedalong a 3.5 Mpc line-of-sight. There are 3 projectionseach at 0.7 Gyrs after pericentric passage with one pro-jection viewing along an axis perpendicular to the planeof the merger orbit ( x − y ) and two projections orthogo-nal to this. This makes apparent the effect of projection– the spiral type structure produces cold fronts observ-able over a wide range of viewing angles. Qualitatively,the map shown in the middle panel of Figure 15 repro-duces the features of Abell 1201 noted above, althoughthe secondary core appears farther from the cluster cen-ter than that in Abell 1201. If the orbit of the secondarycore is close to our line-of-sight and the core is close toturn around, this might be resolved by projecton effects.However, the simulation illustrated has generic initialconditions, not specific to Abell 1201. In particular, itis possible that a closer core passage could produce thestructure observed in Abell 1201 without appealing tofortuitous viewing conditions. The fact that an ideal-natomy of Abell 1201 15 Fig. 14.—
Top Panel:
The spatial distribution of the differentpartitions assigned by the KMM analysis. The ellipses show the2 σ contours for the Gaussians fitted to the respective spatial distri-butions. We also plot the galaxy surface density contours in pink (same spacing as Fig. 13). Bottom panel:
The velocity distribu-tions of the different partitions; the curved lines represent Gaussianfunctions whose mean and σ are equal to the KMM v and σ v val-ues. The color coding in the bottom panel matches the key in thetop left of the top panel. The bottom right-most velocity distri-bution shows the whole cluster sample with a Gaussian generatedusing the biweight estimators overplotted in pink ; the combinationof all the KMM Gaussians is plotted in black . ized simulation reproduces the majority of the observedfeatures supports the proposed merger scenario. Futuresimulations specific to Abell 1201 will determine whichof these possibilities can better explain its observed fea-tures.It appears Abell 1201 is an excellent example of a“sloshing” type cold front cluster, where the perturber isstill clearly visible in the X-ray and optical observations(in the form of KMM1), similar to Abell 1644 (see Figure17 Markevitch & Vikhlinin 2007). Thus, Abell 1201 is anexcellent candidate for follow up detailed simulations inorder to derive an accurate picture of exactly how the sys-tem has evolved to its current state, and whether it willevolve into a relaxed looking cluster harboring cold frontswith no discernable perturber (eg., RXJ1720.1+2638,MS1455.0+2232 or Abell 2029 Markevitch & Vikhlinin2007; Mazzotta & Giacintucci 2008) Two-body merger dynamics
In this section we apply the two-body dynamical anal-ysis first implemented by Beers et al. (1982) to the sub-structures detected in § R p , the line of sight velocitydifference, V r , and the total mass of the system, returningpossible solutions for α (the angle between the line join-ing the two clusters and the line of sight), the total massrequired to bind the system, and the true 3-D spatialseparation, R , and velocity difference, V . The paramet-ric solutions to the equations of motion for bound radialorbits are V = V R sin α = (cid:18) GMR m (cid:19) / sin χ (1 − cos χ ) , (8) t = (cid:18) R m GM (cid:19) / ( χ − sin χ ) , (9) R = R p cos α = R m − cos χ ) , (10)where R m is the maximum separation of the two clustersat turn around, M is the total mass of the system, and χ is the developmental angle which varies from 0 < χ < π with χ = 0 , π being the stages of the orbit correspondingto zero spatial separation. It is also possible to solve forthe unbound case, where the parametric solutions are V = V r sin α = V ∞ sinh χ (cosh χ − , (11) t = GMV ∞ (sinh χ − χ ) , (12) R = R p cos α = GMV ∞ (cosh χ − , (13)where V ∞ is the asymptotic expansion velocity.6 Owers et al. Fig. 15.—
Snapshot temperature maps of the 3 to 1 mass ratio, offset ( r min = 360 kpc) merger simulation from Poole et al. (2006) taken0.7 Gyrs after pericentric passage. The left panel shows the merger viewed from a vantage point where the line of sight is perpendicularto the merger orbital plane, while for the middle panel the line of sight is along the x-axis and the right panel the line of sight is alongthe y-axis. The vectors on the lower left of each panel show this, and the length of each vector has physical size 500 kpc. The color scaleruns from black to white with black showing the lowest temeperatures, and white the highest (on an arbitrary temperature scale). X-raysurface brightness contours are overlaid and the white crosses show the positions of the peak in the dark matter density for the primaryand secondary clusters. For the bound case, combining equations 8, 9 and 10gives tan α = V r tR p (1 − cos χ ) sin χ ( χ − sin χ ) , (14)and, similarly, we obtaintan α = V r tR p (cosh χ − sinh χ (sinh χ − χ ) . (15)for the unbound case. Assuming t = 11 .
38 Gyrs, i.e. theage of the Universe at z = 0 .
168 in our assumed cosmol-ogy, for values of the parameter χ in the range 0 to 2 π these equations determine possible solutions for α . Giventhat the mass of the system is the least well constrainedof the input parameters, we solved for M as a function of α using as input V r and R p for each group in the KMManalysis. Here R p was calculated as the distance fromthe KMM centroid to the central dominant galaxy, ratherthan the KMM7 center, which is slightly offset from thecentral dominant galaxy position. V r is the radial veloc-ity offset of the KMM partition of interest, taken withrespect to the biweight location of peculiar velocities inKMM7, where either the median (for KMM groups with N gal <
15) or the biweight locator ( N gal >
15) was usedto determine the group’s peculiar velocity. We plot thepossible solutions of M as a function of α in Figure 16.Determination of solutions for the orbits of the systemsrequires knowledge of the total mass of the system. Giventhe velocity dispersions of the substructures in Abell 1201are much smaller than that of the main cluster, it isreasonable to assume that when compared to the massof the main Abell 1201 cluster the contribution of themasses of the subclumps is negligible. Hence we assumedthe total system mass was equivalent to the virial massof Abell 1201. We used the methodology of Girardi et al.(1998) for the determination of the mass M = M vir − C = 3 π σ v R P V G − C, (16)where C is the surface term correction accounting for thelack of coverage for the entire cluster (i.e. out to the turnaround radius). Here we took C = 0 . M vir , which is themedian value derived in Girardi et al. (1998), and σ v =665 ±
32 km s − which is the biweight scale estimator derived for galaxies assigned to KMM7 and R P V = N vir ( N vir − P N vir i = j +1 P i − j =1 R − ij , (17)which was determined within r = 0 . σ v /H ( z ) =1 . N vir = 154 is thenumber of KMM7 members within r , and R ij is theprojected distance between two galaxies. We determined R P V = 1 . ± . M = 5 . ± . × M ⊙ where the error in R P V was determined using the Jack-knife technique, and standard error propagation was usedto derive the error in the mass.The possible solutions for the orbits are given by theintersection of the line representing the Abell 1201 virialmass estimate with the curve for M as a function of α inFigure 16. For each solution, we present the associatedprobability relative to the other solutions by consideringthe range of possible α given by the upper and lowervalues, α U and α L , respectively, derived from the errorbounds on each curve, and assuming that each individualsolution is equally probable. The relative probability is p rel = (cid:16)R α U α L cos α d α (cid:17)P p rel , (18)for the solution of interest, and X p rel = p BO + p UO + p BI a + p BI b , (19)where p BO , p UO , p BI a , p BI b are the R α U α L cos α d α valuesfor the bound outgoing, unbound outgoing, first boundincoming and second bound incoming solutions, respec-tively (Brough et al. 2006). We present the results inTable 5.We also determined the probability the subclumps arebound using the Newtonian binding criterion, where atwo-body system is bound if the kinetic energy is lessthan or equal to the potential energy. The criterion isgiven by Beers et al. (1982) as V r R p ≤ GM sin α cos α. (20)This curve is also plotted in Figure 16, and the prob-ability is P bound = R α U α L cos α d α , where α L and α U aredetermined from the intersections of M vir and the curvenatomy of Abell 1201 17 Fig. 16.—
Binding mass as a function of α ( orange and green curves). The orange curves correspond to bound solutions, while the green curves represent unbound solutions. The dashed curves show the 1 σ errors. The blue line shows the mass derived using galaxies allocatedto KMM7 and the dashed blue lines indicate the upper and lower 1 σ errors. The small black dashed line delineates the bound and unboundregions according to the Newtonian binding criterion. TABLE 5Probabilities that the detected substructures are bound to the Abell 1201 cluster,derived using the two-body dynamical analysis and the Newtonian Criterion (see text).
Subclump V r R P P BI a P BI b P BO P UO P bound ( km s − ) (Mpc) (per cent) (per cent) (per cent) (per cent) (per cent)KMM2 − ±
46 0.95 - - - 100 -KMM(3+4) − ±
72 0.73 62 38 - << − ±
113 2.04 - - << representing the Newtonian criterion. We present theresults in Table 5.Considering the Newtonian criterion and two-bodysolutions, we find that there is a high probability ofKMM(3+4) being bound to Abell 1201, with two solu-tions which are, roughly speaking, as probable as eachother. The most probable solution is KMM(3+4) isbound and incoming with α = 26 degrees, R = 0 . V = − − , whilst the slightly less probablesolution is also bound and incoming with α = 71 degrees, R = 2 . V = − − . If KMM1 is out-bound to the north-west, as proposed in § α = −
88 degrees (i.e. it’s motion is aligned at 2 deg tothe line of sight), R = 24 . V = 1990 km s − .Thus it is likely that KMM2 is a group of galaxies ly-ing in the foreground moving away from Abell 1201, andnot physically associated. KMM(5+6) has a best fit-ting unbound outgoing solution, although within the er-rors this may be bound outgoing, with α = −
81 degrees, R = 12 . V = 808 km s − . Given the Newto-nian criterion allows KMM(5+6) to be bound and that itis possible we have underestimated the mass within theradius at which KMM(5+6) lies, it is entirely plausiblethat we have also underestimated the binding probabilityfor KMM(5+6).The two body analysis presented here has allowed thedetermination of which substructures are most likelybound to the main cluster. This gives an initial under-standing of which substructures are important in under-standing the internal dynamics of Abell 1201, which willbe further modeled in future simulations and presentedin a forthcoming paper. SUMMARY AND CONCLUSIONS
We have presented an analysis of Abell 1201 using both
Chandra
X-ray data and optical spectroscopic data ob-tained using the AAT/AAOmega and MMT/HectospecMOS. The X-ray analysis reveals the following:1. An elliptical morphology with two surface bright-ness discontinuities positioned roughly on an axisjoining the main cluster with a clump of excessemission to the north-west. The density, temper-ature and pressure jumps across these discontinu-ities are consistent with cold fronts.2. A residual map obtained by subtracting a doublebeta model from the surface brightness distributionshows significant residuals at the position of thenorth-west clump. It shows significant residualsextending from the cluster core to the south-eastcold front.3. A temperature map shows that south-east residualis coincident with a finger of cold gas which alsoextends from the cluster core and terminates onthe inner side of the front.4. There is also a significantly hotter region on thenorth-west side of the inner cold front between themain cluster core and the subclump further to thenorth-west.The optical MOS analysis reveal:1. From 321 cluster member spectra the cluster red-shift is z=0.1673 and the velocity dispersion is778 km s − .2. The velocity distribution is not significantly non-Gaussian, despite the clearly disturbed nature ofAbell 1201 evidenced by the X-ray data.3. Combining the peculiar velocity and spatial infor-mation reveals significant localized velocity sub-structure. 4. Using the KMM method of Ashman et al. (1994)the substructure can be partitioned into 5 dis-tinct clumps - the main Abell 1201 cluster with262 members (KMM7), an infalling subgroup ∼
410 kpc to the north-west coincident with the X-ray excess containing 12 members (KMM1), a sub-group ∼
950 kpc to the NE with 14 members(KMM2), a subgroup ∼
730 kpc to the south-eastwith 16 members (KMM3+4) and a group ∼ ACKNOWLEDGMENTS
We thank David Woods for useful discussions and san-ity checks. We are grateful to Will Saunders and thestaff at the Anglo-Australian Observatory for their sup-port during AAT observations. Observations reportedhere were obtained at the MMT Observatory, a joint fa-cility of the Smithsonian Institution and the Universityof Arizona. We thank the MMT operators and queue-schedule mode scientists for their help during observa-tions and the staff at the Harvard-Smithsonian Centerfor Astrophysics Telescope Data Center for reducing theHectospec data.This research has made use of software provided by theChandra X-ray Center (CXC) in the application packagesCIAO, ChIPS, and Sherpa and also of data obtained fromthe Chandra archive at the NASA Chandra X-ray center(http://cxc.harvard.edu/cda/). This research has madeuse of the NASA/IPAC Extragalactic Database (NED)which is operated by the Jet Propulsion Laboratory, Cal-ifornia Institute of Technology, under contract with theNational Aeronautics and Space Administration.MSO was supported by an Australian PostgraduateAward, and acknowledges the hospitality of the Harvard-Smithsonian Center for Astrophysics where a portionof this study was undertaken. We acknowledge the fi-nancial support of the Australian Research Council (vianatomy of Abell 1201 19its Discovery Project Scheme) throughout the course ofthis work. PEJN was supported by NASA grant NAS8- 01130.
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