Draftversion February1,2008 PreprinttypesetusingLATEXstyleemulateapjv.10/09/06 RADIAL ALIGNMENT IN SIMULATED CLUSTERS Maria J. Pereira, Greg L. Bryan and Stuart P. D. Gill ColumbiaUniversity,DepartmentofAstronomy,NewYork,NY,10025 Draft versionFebruary 1, 2008 ABSTRACT Observational evidence for the radial alignment of satellites with their dark matter host has been accumulating steadily in the past few years. The effect is seen over a wide range of scales, from massiveclustersofgalaxiesdownto galaxy-sizedsystems, yetthe underlying physicalmechanismhas 8 still not been established. To this end, we have carried out a detailed analysis of the shapes and 0 orientations of dark matter substructures in high-resolution N-body cosmological simulations. We 0 find a strong tendency for radial alignment of the substructure with its host halo: the distribution 2 of halo major axes is very anisotropic, with the majority pointing towards the center of mass of the n host. Thealignmentpeaksoncethesub-halohaspassedthevirialradiusofthehostforthefirsttime, a but is not subsequently diluted, even after the halos have gone through as many as four pericentric J passages. This evidence points to the existence of a very rapid dynamical mechanism acting on these 3 systems and we argue that tidal torquing throughout their orbits is the most likely candidate. 2 Subjectheadings: methods: N-bodysimulations,galaxies: kinematicsanddynamics,galaxies: clusters ] h 1. INTRODUCTION ments between galaxies can be dealt with easily: e.g. p downweightingclosepairsreadilyremovescontamination - Anisotropy in galaxy orientations has been a matter o by alignments induced in interacting systems. However, of debate for several decades, and many conflicting re- r as Hirata & Seljak (2003) pointed out, if galaxy orienta- t ports have been published. Past studies have found ev- s tions are affected by their surrounding density field (e.g. idence for three different types of alignment: alignment a a galaxy cluster), then they will also be correlated with [ between clusters (Binggeli 1982; Plionis & Basilakos 2002), between the brightest cluster galaxy (BCG) the orientations of the background population of galax- 2 ies that is being lensed by that field. This correlation and the satellite distribution (e.g., Yang et al. 2006) v between widely separated redshift bins cannot trivially and between the orientation of satellites and their 2 be removed. host (Hawley & Peebles 1975; Pereira & Kuhn 2005; 0 Given the growing body of evidence suggesting that Agustsson & Brainerd 2006). This last type of align- 7 galaxyorientationsareanisotropic,andthepressingneed ment, which we will refer to as radial alignment and is 1 for an accurate quantification of intrinsic alignments for the focus of this paper, has been the hardest to confirm . 7 (Trevese et al.1992;Torlina et al.2007),sinceitrequires weak lensing, it seems crucial that we try and find the 0 physical cause behind these anisotropies. There are two high quality data on small scales. In recent years, this 7 commonly proposed explanations. The first, initially field has seen a resurgence, largely due to the arrival of 0 developed by Peebles (1969) in his tidal torque theory the Sloan Digital Sky Survey (SDSS) (Abazajian et al. : (TTT), explains the anisotropy as a left-over primor- v 2005). The SDSS provides accurate measurements of dial effect. TTT ascribes the orientation and rotation i isophotal shapes for millions of galaxies, and this has X of galaxies to torquing during their formation. It there- finally allowed large statistical studies of galaxy align- r mentsto be performed. Pereira & Kuhn(2005)targeted fore follows that the signal should be stronger on the a outskirts of the cluster, and that it wanes with time, galaxies in massive X-ray selected clusters and found suchthatolder,morerelaxedclustersshouldexhibitless a significant tendency for their radial alignment. This tendency foralignment. The other alternative,proposed result has since been confirmed by Faltenbacher et al. by Pereira & Kuhn (2005), is a dynamical mechanism, (2007) for a larger sample of groups optically selected i.e. an interaction with the tidal field of the host clus- fromtheSDSS.Onsmallerscales,Agustsson & Brainerd ter that gets progressively stronger during infall and is (2006)foundatendencyforsatellitegalaxiesintheSDSS noterasedbysubsequentorbitalmotions. Observational to be radiallyaligned with their hostgalaxy,whereason studies have so far been unable to distinguish between largescales,Mandelbaum et al.(2006a)foundaverysig- the two, due to difficulties in constraining galaxy orbits nificant correlation between the orientations of galaxies and in measuring galaxy shapes accurately out to large and the surrounding density field traced by galaxy over- redshifts. densities. A different approach is needed, and a few numeri- Initiallymotivatedbytheprospectofusinggalaxyori- cal studies have recently been published on this sub- entationstoprobetheirformationhistories,thesestudies ject. Studies of simulated halo shapes and orientations are now also driven by the need to calibrate weak lens- havebeenperformedaroundvoids(Brunino et al.2007), ing and cosmic shear measurements. A key assumption along filaments and sheets (Aragón-Calvo et al. 2007; for lensing techniques is that the population of galaxies Altay et al. 2006; Hahn et al. 2007) and in a Milky-Way being lensed is randomly oriented. Some intrinsic align- typehalo(Kuhlen et al.2007). Anisotropiesarereported Electronicaddress: pereira@astro.columbia.edu in all three environments. The advantages of working 2 with simulated clusters are obvious - 3D spatial infor- elapsedsince their formation, whichis defined, following mation means we do not suffer dilution from projection Lacey & Cole(1993), atthe redshift wherethe halofirst effects. Also, with enough temporal and spatial reso- contains half of its present-day mass. lution, we can follow the galaxies as they fall into the cluster along filaments, and beyond, as they orbit inside Halo Rvir Mvir zform age Nsat( bvesc, ticles (Np) and intermediate-to-major axis ratios (b/a) where b=1.5 is the bound factor, and the only free pa- and fed them through our pipeline. For each value of rameter in our algorithm. We repeat the process until N and b/a we performed 100 random realizations of an p no further particles are removed or a minimum number NFW halo and calculated the angle between the major (Np =200,c.f. 2.3)ofparticleshasbeenreached. Parti- axis direction measured and that which was input. The § clesthataredeterminedtobeunboundaresubsequently dispersioninthesevalues,θ ,isthenagoodestimateof acc ignored. This is a completely effective way of removing the accuracy of our measurement. The minor-to-major theclusterbackground,asparticlesthatdonotbelongto axis ratio (c/a) does not appear to affect the determina- the substructure halo will be quickly left behind. It also tionofthemajoraxisdirection,andtheresultspresented allows us to track debris being stripped off the subhalos infigure1arethereforeonlyforprolatehaloswithb=c. as they orbit inside the cluster. As expected, our accuracy depends very strongly on When all unbound particles have been removed, we the number of particles sampled - the points on the left fit an NFW distribution to the radial profile of the re- panelarewellfitbyarelationoftheform: θ N−0.54. acc maining particles. We define the halo’s radius as the Wewantacompromisebetweenindividualhalo∝accuracy distance at which the average halo density drops below and sample size - at values of N < 200, θ increases p acc ρhalo(rvir) = ∆vir(z)ρb(z), where ∆vir(z) is the virial rapidly, and we pick this, somewhat arbitrarily, for our overdensity at that redshift, and discard any particles lower limit on N . If b/a = 0.8, our measurements of p thatlie outsidethis limit. However,this radiusisalmost these halos would be accurate by θ 10◦. However, acc never reached in the case of substructure, in which case θ also depends strongly on b/a. W≈hen N = 200, acc p the radius of the halo is defined as the distance to the b/a< 0.8 is required to maintain the 10◦ error, with an furthestboundparticle. Oncewehavedeterminedwhich increase in b/a leading to a rapid decrease in accuracy. particles belong to which halo at each timestep, we are Figure 1 refers to the input values of b/a. In fact, the ready to measure their shapes. measuredellipticities are much higher, although the two are tightly correlated: (b/a) = (b/a)0.45 . We 2.3. Shape Measurements input measured place an upper limit of 0.8 on the intrinsic axis ratios, Howcanwecondense athree dimensionalparticledis- which translates to a limit on the measured values of tribution into a few simple parameters describing its b/a<0.9. shape? With no prior knowledge of how the particles With our limits in place for the minimum number of are distributed this is a difficult task. However, ha- particlesandmaximumaxisratios,wearereadytostart los produced in dark matter cosmological simulations analyzing our results. It is worth noting, however, that seem to follow a universal density profile (Navarro et al. boththeseerrorsourceswouldbiasourshapesrandomly: 1996), and are generally well fit by triaxial ellipsoids thereis no preferreddirectionthatwill be selectedif the 4 halos are under-sampled or too spherical. This in turn be radiallyalignedwithrespectto their nearestclusters. implies that the results on alignment presented in the If there is a primordial alignment of halos with respect next section are, if anything, conservative. to the filaments in which they form, then even at large distances this will appear as a radial alignment in our 3. RESULTS analysis. Thistypeofprimordialalignmentatlargeradii 3.1. Alignment at z =0 was seen by Aragón-Calvoet al. (2007) in their study of filamentary structures, where they found similar values The quantity we will focus on is the angle, φ, between for cosφ (their figure 2e). the major axis of each halo and the vector connecting h i The main focus of this paper, however, is what hap- the halo to the center of the host. If halos are oriented pens closer to the host. As the halo falls in, the am- randomly in space, the cosine of φ will be uniformly dis- plitude of the alignment increases dramatically, reach- tributed between 0 and 1, with a mean value, cosφ , ing a peak of cosφ = 0.72 at about one-half of the h i of 0.5. When cosφ 1 the halo is pointing toward the h i virialradiusofthe cluster,before decreasingagaingrad- ≈ hostcenter,whereaswhencosφ 0itisalignedtangen- ually inside the core. The increase of the alignment ≈ tially to it, so that a value of cosφ > 0.5 implies an withdecreasingdistancematchesthebehaviourfoundby h i overall tendency for radial alignment. The standard er- Faltenbacher et al.(2007)intheirstudyofSDSSgroups, roron cosφ isσhcosφi =σ/√N, whereN is the sample and is to be expected if the effect is caused by the tidal h i size and σ is its standard deviation. We show in Figure field of the host, but the dip at small radii, r < 0.3r , vir 2 a histogram of cosφ for all halos within 2rvir of each has not yet been observed. This is most likely due to of the eight hosts. It is immediately apparent that our the severe projection effects that dominate the cores of distribution is inconsistent with isotropy at a very high observed clusters. significance level: cosφ =0.66 0.01, with most halos What causes this behavior? It appears that the align- h i ± pointing toward the center of the host halo. mentthatisset-upintheinfallregionsisbeingdisrupted Whileitisclearthattheresultsoffigure2confirmpre- in the inner regions of the cluster. What causes the dis- viousobservationalreportsofradialalignment,aprecise ruption? Is this primarily a spatial effect caused by the quantitative comparison is rather difficult, and we de- environmentoftheclustercore,oratemporalone,given fer this discussion to 4.2. Nevertheless, much can be thatgalaxiesclosesttothecenterhavebeeninthecluster § learned from a qualitative study of the effect’s behavior environment for longer? And what produced the align- and correlation with individual (and host) halo proper- ment in the first place? The best way to answer these ties. Figure 3 shows the same histogram as in Figure 2 questionsistotakeadvantageoftheextradimensionpro- but now for two separate halo populations, segregated vided by simulations, and explore the evolution of this by mass. There does not appear to be a significant dis- effect with time. tinction between the two populations. This tells us not only that the alignment effect is mass independent, but 3.3. Evolution with Redshift alsoconfirmstheexperimentsin 2.3thatshowthatres- olution effects are unimportant in§ the lowest mass halos The evolution of the alignment with redshift is plot- considered in our analysis (N >200). ted in figure 5 for each of the eight clusters indepen- p We can also study how the effect depends on extrin- dently. Perhaps the most striking feature of this plot sic characteristics of the halo, e.g. the distance to the is the self-similarity of the different curves. Every clus- center of the host, or the host mass. We searched for ter appears to go through exactly the same evolution, correlationswith different global host properties such as regardless of size or formation time, such that at z = 0 mass and age, and found none. The alignment mecha- theyarepracticallyindistinguishable,asdescribedinthe nism appears to be universal, in that it is present with previous section. Figure 5 also reveals that the clusters approximately the same strength in hosts with widely evolve monotonically, with the strength of the effect in- varying mass, formation times and assembly histories. creasingsteadilysincetheformationtime ofeachcluster This surprising result is also seen in observational stud- to the present day. ies: Pereira & Kuhn (2005) found no correlation of the Whatever the source of the disruption at the cluster alignmentstrengthwith the dynamicalstate of the clus- cores,itisseeminglynotstrongenoughtodilutetheover- ters inferred from their x-ray morphologies. allalignmentsignal. Therearetwopossibleexplanations: Itcouldbethat,eventhoughalignmentisdisruptedonce 3.2. Dependence on Distance to Cluster Center the halo reaches the core of the host, the constant infall ofpristinelyalignedhalosresultsinanoverallincreaseof Figure 4 shows the dependence of the effect on the the average alignment per host. Alternatively, the mis- distance from the cluster center. All halos at redshifts alignment seen at the cores could be short-lived - a fea- z < z are included in this analysis, in order to form ture of each halo’s orbital motion through the potential enhance the overall signal. The behavior appears very of the host. smooth: cosφ risesgraduallyasthehostisapproached, h i Distinguishing between these two alternativesrequires peaks slightly past its virial radius, and then decreases adifferentapproach: weneedtotrackhalosontheirway again toward the center. towardthe cluster, andthen trace their orbits inside the It is striking that already at a distance of three virial virial radius of the host. radii there is a small, consistent, tendency for radial alignment. At this distance, how can the halo already 3.4. Evolution with Orbital Phase “feel” the presence of the host? This is easily under- stood once we consider that clusters form at the inter- Figure 6 shows the alignment evolution stacked for all section of filaments, and hence that most filaments will halos throughout their orbits. Initially halos are tracked 5 relative to the amount of time (in Gyrs) remaining un- ter center, in a figure rotation that is co-planar with its til they cross the virial radius of the host for the first orbital rotation and in the same direction. The radial time. Once they cross this threshold, halo orbital times alignment is quickly reinstated, but orbital alignment is are normalized at each passage through pericenter and lost as the halo progresses towards apocenter. Steady apocenter. torquing throughout the orbit keeps halos oriented to- We again detect a small alignment at large distances ward the cluster center and away from the direction of from the cluster , which we believe is evidence for a pri- their orbits until after the apocentric passage,where or- mordial alignment along filaments as discussed in 3.2. bitalalignmentincreasessteadilytowardspericenter,and § As the host is approached the signal increases signifi- a new cycle begins. Figure 8 illustrates this behaviour cantly, peaking just before the first pericentric passage, with a sketch of a halo’s rotation as it orbits around the and then a periodic oscillation ensues, which follows the cluster. halo’s orbital period closely. On average, the tendency Ifhaloorbitswerecircular,haloswouldquicklybecome foralignmentismuchlargerwithinthehostthanbefore, tidally lockedandmaintainradialalignmentthroughout although the alignment tendency changes dramatically their orbits. In reality, their orbits are quite eccentric, with orbitalphase. It follows that the dip observednear and their orbital speed varies significantly. Halos do not the cluster cores in figure 4 is in fact a result of the mis- react to the tidal torquing quickly enough through the alignmentobservedatpericenter,and,mostimportantly, pericentric passage, and the narrow dips observed are that it is not disruptive, since the alignment tendency is the result. In fact, idealized numerical experiments in- restored well before the next apocenter is reached. In volving a single halo in a circular orbit around a static fact, the alignmentis quite constantthroughoutthe rest hostinvariablyleadtotidallockingofthehalo,although of the orbit and seems to increase slightly at each pas- thetimerequiredforlockingvariessignificantlywiththe sage. This evidence points to a stable dynamical effect original orientation of the halo (C. M. Simpson & K. V. that is set-up as the halo orbits around the cluster. Johnston,private communication). Interestingly,for ha- Further insights can be obtained by exploring the ori- los that start out already pointing toward the host cen- entations of the halos with respect to their orbits. We ter, the time required is rather short, of the order of an define a new angle, β, as the angle between each halo’s orbital period or less. major axis and the halo’s velocity, and plot the mean Further support for this tidal torquing hypothesis is valueofitscosineforallhalosvs. orbitalphaseinFigure shown in figure 9. Although we believe our shape mea- 7. Thesimilaritiesinbehaviorbetweenradialandorbital surements to be robust to random outliers, it is possible alignmentatlargedistancesare simply a consequenceof thatstronglydistortedoutershells,caused,e.g.,bytidal the radial nature of the orbits themselves - halos form stripping, could significantly bias the result. As a test, and travelalong filaments towardthe intersecting nodes we apply four different particle cuts to each of our halos where clusters reside. In fact, even inside the hosts, or- by varying the boundedness criteria on the particle ve- bits are quite eccentric, with an average apocentric to locities: instead of throwing out all particles for which pericentric distance ratio of 4:1. v >bv ,whereb=1.5,weexcludealternatelyparticles esc Coulditbe,then,thattheradialalignmentweobserve thathavevelocitiesgreaterthan1,0.75and0.5timesthe within the virial radius is just a tendency for halos to escapevelocity. Forthemostconservativecriteria,which be aligned along their orbits coupled with the fact that only retains particles that have velocities v < 0.5v , esc orbits are, on average, quite radial? Figure 7 tells us more than 70% of the particles are discarded, and we that this is not the case: once inside the cluster, we find are only probing the very bound cores of the halos. Fig- that the orbital alignment is also correlatedwith orbital ure 9 makes clear that stripping cannot possibly be the phase, but whereas the radial alignment is almost in- sole cause of the alignment effect, since even the most stantly recovered after pericenter, the orbital alignment conservative cut shows significant alignment. increases again much more slowly, and only after reach- Nevertheless, a trend is observed, in that the most ing the next apocenter. This asymmetry around peri- boundparticlesshowslightlylesstendencyforalignment center seems, at first, surprising, but, as will be shown overall. This could be the result of tidal stripping in the inthefollowingsection,followsasanaturalconsequence outer layers, but more likely it is a simple statistical ef- of tidal torquing by the cluster potential throughoutthe fect: Because we only consider halos with N > 200 in p halo’s orbit. this analysis, as we progressively exclude more particles from the halo with decreasing b, some halos fall below 4. DISCUSSION thislimitandareconsequentlyignored. Henceadecrease in b implies a smaller number of halos in each sampled 4.1. Tidal Torquing as a Mechanism for Alignment bin,whichreducesthesignal-to-noise,andbrings cosφ h i Once radialand orbitalalignment information is com- closer to 0.5. Despite this trend, the conclusion remains bined, a clearer picture emerges of what is going on in- that halo shapes are not significantly warped by tidal side these clusters. As the halo approaches pericenter stripping, and that tidal torquing of the entire halo is a along an eccentric orbit, it is continually torqued along better explanation for the effect. the direction of the potential gradient, i.e. halos tend to A number of early numerical and analytical studies point toward the host center, and, because their orbits supportthe importance oftidal torques within clusters . are fairly eccentric, also along their orbitaldirection. At Miller & Smith (1982) performed a set of numerical ex- pericenter, the halo is moving too fast for the torquing perimentsonarotatingbarinanexternalforcefieldand to be completely effective, whichcausesthe dip inradial observed tidal braking of the rotation, with a rate that alignment. It is nevertheless enough to torque the halo wasinverselyrelatedtothesquareoftheclustercrossing awayfromitsorbitaldirectionandbacktowardtheclus- time. More recently, numerical N-body experiments by 6 Ciotti & Dutta (1994)showedthatthe time requiredfor tween light and dark matter relatively unimportant. the alignment of a prolate galaxy with the tidal field of We therefore compare the dark matter alignment di- a cluster is much shorter than the Hubble time, and on rectly with the galaxy observations of Pereira & Kuhn the order of a few times the galaxy’s intrinsic dynami- (2005). We project each halo’s dark matter particles cal time. Using a different approach, Usami & Fujimoto alongthe three spatialdimensions in our simulationand (1997) studiedtidal effects ongaseousellipsoids orbiting computethe2Dinertiatensoroftheirprojecteddistribu- in a centralpotential analytically, predicting that galax- tion. Theanglebetweenthehalo’s2Dmajoraxisandits iesineccentricorbitsshouldhavetheirlong-axistrapped projectedseparationfrom the cluster center canthen be toward the direction of the radius vector of the cluster. measured. We include in this sample all galaxies within While this paper was being written, two studies were 2 virial radii of the cluster center - interlopers are not published on halo alignments that describe similar re- accountedfor,sincetheSDSSgalaxieswearecomparing sults. Kuhlen et al. (2007) studied the alignment of our results to are all spectroscopically confirmed cluster substructure around a Milky Way type halo using the members. Figure 10 shows the results of this 2D analy- Via Lactea simulation, and observed a radial alignment sis and compares them with the SDSS observations. We tendency that is preserved throughout the halos’ or- plot all three independent projections and note that the bits. Faltenbacher et al. (2007) looked at several differ- dispersionintheirvaluesshouldgiveusafairestimateof ent types of alignment in a set of dark matter hosts at the error introduced by the projection procedure itself. z = 0, finding similar levels of radial alignment that in- The dark matter alignment is much stronger than crease with decreasing distance to the host. that observed: θ = 34◦.5 0◦.9 whereas θ = h ihalo ± h igal 42◦.79 0◦.55. This mustbe in someparta reflectionof 4.2. A Comparison with Observations ± how much harder it is to measure accurate galaxy posi- Theresultsof 3certainlyseemtosubstantiatetheob- tion angles on an survey image than for a well-resolved § servationalevidenceforradialalignmentofclustergalax- halo in a cosmological simulation, where dynamical in- ies. A quantitative comparison, however, is not easily formationallowsforamuchcleanerbackgroundremoval. made. In order to properly “observe” these simulations, Nonetheless, the dilution caused by this measurement semi-analyticmodelsofgalaxyformationarerequiredto noisecannotwhollyaccountforthe significantdifference extrapolate from the dark matter halos to the luminous in radial alignment between the two components. Given components embedded within. These then need to be the nature of the alignment mechanism established in projected, interlopers and survey limits accounted for, 4.1,itisperhapsnottoosurprisingthatdarkmatterha- and the resulting image fed through traditional source §los are more strongly aligned. One wouldnaively expect extraction and isophotal analysis pipelines. This is a the dark matter halos to be more easily torqued, given laborious procedure and it cannot yet provide accurate that they are much more extended (providing a longer results, since galaxy formation models are still largely lever)andhavegenerallylowerspins ( andthereforeless unconstrained in a crucial parameter: the alignment be- gyroscopicresistance)than their luminous counterparts. tween luminous and dark matter. 4.3. Possible Consequences of Tidal Torquing in Observationally, studies of the alignment and relative Clusters ellipticity of the two components are currently only possible for gravitational lens galaxies, a very rare class of Halo alignments have traditionally been studied ei- objects. Keeton et al. (1998) analysed a sample of 17 ther as a probe of their formation history, or as a con- lenses, mostly isolated early-types, and found that the taminant to weak lensing studies. Now that we have luminous componentof the lens generally aligns with its established that the leading mechanism behind halo inner halo to 10◦. In order to probe the shapes of the alignments within clusters is a dynamical effect present ≤ halos to larger radii, stackedgalaxy-galaxyweak lensing throughouttheirlifetime,itisinterestingtospeculateon studiesareneeded. Thesearejustnowbecomingfeasible, whatpossibleevolutionaryconsequencesthismechanism and preliminary results appear somewhat contradictory might have for the halos affected. (Hoekstra et al. 2004; Mandelbaum et al. 2006b). Figure 8 shows us that at each point in the orbit, the Most theoretical studies have concentratedon the for- torque acts to rotate the halo away from its orbital di- mation of disk galaxies and their angular momentum, rection,whichnecessarilyresults in a decelerationof the where some misalignment between baryonic and dark halo’s orbital motion, inducing orbital decay. The ha- matter spin is commonly seen (e.g. van den Bosch et al. losanalysedin this study do indeed show a tendency for (2002)). Ontheotherhand,Bailin et al.(2005)findthat orbitalcircularization: Gill et al.(2004)showedthatha- the orientations of simulated halos and their embedded los with more pericentric passages have smaller orbital disks are largely uncorrelated at large radii, and almost eccentricites. They argued that dynamical friction was perfectly aligned at small (r <0.1r ). not a likely cause, and tentatively ascribed the effect to vir The current uncertainty in this parameter makes it the growth of the host halo instead. While the velocity impossible to accurately predict the orientation of the dispersion of the satellites is seen to depend on the host galaxies that would populate our halos. However, the halo mass, it seems possible that at least part of the or- results presented in this paper suggest a gravitational bital decay observed is a natural result of the constant origin for the alignment mechanism, and it is therefore torquingthroughoutthehalo’sorbit. Thisisaninterest- reasonable to expect that the two components should ingprospect,sinceanextrasourceoforbitaldecaycould react similarly to it. Furthermore, the tidal torquing potentiallyhelpsolvetheoutstandingproblemofcDfor- within clusters is so effective that the halos appear to mation in massive clusters, as well as alleviate some un- “forget” their original orientations before a single orbit resolveddiscrepanciesbetweenobservedsatellitepopula- is completed, which renders the original alignment be- tionsandthe generallylowefficacyofdynamicalfriction 7 predicted by numerical studies (e.g. Hashimoto et al. tion of radius, with a small but significant effect (2003); Taffoni et al. (2003)). We are currently investi- extending out to many virial radii from the clus- gating the importance of this induced orbital decay,and ter. This signal, which has been seen in previous this will be the subject of a future paper. work(Aragón-Calvo et al.2007), ismostlikelyleft Anotherpossibleconsequenceofthestrongtorquingof overfromtheprimordialimprintofthesurrounding dark matter halos within hosts is the possibility of disk large-scale structure and can be ascribed to tidal warping. Becauseoftheirhighangularmomentum,disks torques exerted at early times, when the cluster- will naturally resist tidal torquing more effectively than size perturbations were just turning around (e.g., the surrounding dark matter halo, which will introduce Peebles 1969). a misalignment between the halo and the disk. Even though recent studies of (isolated) disk-halo alignments Closer to the cluster center, within 1-2 virial radii, show that their orientations are largely uncorrelated at • the amplitude of the alignment increases dramati- large radii (Bailin et al. 2005), the same is not true for cally to a peak of cosφ = 0.72 at about one-half theinnerhalos(r <0.1r ),wheretherotationalaxisof h i vir of the virial radius, and then falls slowly closer to the disk is seen to lie very close to the minor axis of the the cluster center. innerhalo. We haveshownthattidaltorquingaffectsall particles in the halos, even the most bound, so it is not Whenexaminedasafunctionoforbitalphasefora unreasonable to expect that the inner shells should also • givensatellite,wefindthatthealignmentincreases feel these torques. The question then remains whether rapidly as the satellite falls into the cluster for the the disk within will align itself accordingly, or whether first time and remains high after that, except for themisalignmentcouldbeapossiblecauseofwarpingof a short period during pericenter passage, when it the disk, but this will also require further study. dips precipitously. It is this short-lived dip which 5. CONCLUSIONS gives rise to the decrease in cosφ close to the h i cluster center. There is growing observational evidence that a satellite’s major axis is preferentially aligned with the radial vector linking the satellite to its host. This ten- Based on these results, we conclude that the strong dency for satellites to point at their hosts has been seen alignment seen at small radius — within two virial radii on both cluster and group scales (Pereira & Kuhn 2005; — is due to tidal torquing by the cluster halo. The idea Agustsson & Brainerd 2006). Motivated by this result, isverysimple–thegalaxyisonlyinastableequilibrium we haveuseda suite of cosmologicalN-body simulations ifit is pointing atthe cluster center;otherwise there is a to investigate the alignment between satellite and host net torque which acts to rotate the galaxy towards this dark matter halos. equilibriumpoint. Wedemonstratethatthealignmentis Wetakeparticularcaretoseparatesatelliteandcluster seenbothintheouterandinnerpartsofthesatellite,in- particles using a combined halo finder plus tracker. In dicating that it is not due to some process (such as tidal this method, an adaptive halo finder (Gill et al. 2004) is stripping) which impacts only the outer, poorly bound, used to initially identify a set of satellite sub-halos that part of the sub-halo. We also briefly review previous lit- we subsequently track as they enter and orbit the clus- eraturewhichhasinvestigatedtheimpactoftidaltorques ter, removing particles as they become unbound. The oncollisionlesssystemsusinganalyticapproximationsor advantage of this approach is that we can be sure to idealized simulations, and find that the expected ampli- use only genuine sub-halo particles and exclude “back- tudeandtimescaleissufficienttoproducethealignments ground”clusterparticlesthatmightbiasourshapemea- we see. surements. We then use the reduced inertia tensor to Although we study only dark-matter halos, we expect measure the shapes and orientations of all sub-halos this effect to extend to the luminous part of galaxies, as which end up inside the virial radii of a set of eight observations seem to indicate. This will have an obser- simulated clusters. We highlight here the main results vational impact on weak lensing studies and may also obtained from this analysis: modify the distribution of stars in a satellite, as well as the satellite’s orbital properties. We will investigate Thesatellitesinthesimulationsshowastrongten- these possibilities in future work. • dency to point toward the cluster center. The mean cosine of the angle between the major axis of each halo and the cluster center is cosφ = The simulations presented in this paper were carried 0.66 0.01, where an isotropic distributihon woiuld outontheBeowulfclusterattheCentreforAstrophysics have±cosφ = 0.5. This tendency for alignment &Supercomputing,SwinburneUniversity. Wewouldlike is fouhnd fori all clusters at all redshifts analyzed, to thank Jeff Kuhn, Kathryn Johnston and Christine and does not appear to depend on the mass of the Simpson for helpful discussions. Greg Bryan acknowl- cluster or the satellite. edges support from NSF grants AST-05-07161,AST-05- 47823,andAST-06-06959,aswellastheNationalCenter The amplitude of the alignment is a strong func- for Supercomputing Applications. • REFERENCES Agustsson,I.,&Brainerd,T.G.2006,ApJ,644,L25 Allgood, B., Flores, R. A., Primack, J. R., Kravtsov, A. V., Wechsler, R. H., Faltenbacher, A., & Bullock, J. S. 2006, MNRAS,367,1781 8 Altay, G., Colberg, J. M., & Croft, R. A. C. 2006, MNRAS, 370, Hoekstra,H.,Yee,H.K.C.,&Gladders,M.D.2004,ApJ,606,67 1422 Keeton,C.R.,Kochanek,C.S.,&Falco,E.E.1998,ApJ,509,561 Aragoń-Calvo,M.A.,vandeWeygaert,R.,Jones,B.J.T.,&van Klypin, A., & Holtzman, J. 1997, ArXiv Astrophysics e-prints, derHulst,J.M.2007,ApJ,655,L5 arXiv:astro-ph/9712217 Abazajian,K.,etal.2005, AJ,129,1755 Knebe,A.,Green,A.,&Binney,J.2001, MNRAS,325,845 Bailin,J.,etal.2005,ApJ,627,L17 Kuhlen,M.,Diemand,J.,&Madau,P.2007,ArXive-prints,705, Bertschinger,E.,&Gelb,J.M.1991,ComputersinPhysics,5,164 arXiv:0705.2037 Binggeli,B.1982,A&A,107,338 Lacey,C.,&Cole,S.1993,MNRAS,262,627 Brunino, R., Trujillo, I., Pearce, F. R., & Thomas, P. A. 2007, Mandelbaum, R., Hirata, C. M., Ishak, M., Seljak, U., & MNRAS,375,184 Brinkmann,J.2006,MNRAS,367,611 Ciotti,L.,&Dutta,S.N.1994,MNRAS,270,390 Mandelbaum, R., Hirata, C. M., Broderick, T., Seljak, U., & Davis, M., Efstathiou, G., Frenk, C. S., & White, S. D. M. 1985, Brinkmann,J.2006,MNRAS,370,1008 ApJ,292,371 Miller,R.H.,&Smith,B.F.1982,ApJ,253,58 Djorgovski,S.1983,ApJ,274,L7 Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, Faltenbacher, A.,Li,C.,Mao,S.,vandenBosch,F.C.,Yang,X., 563 Jing,Y.P.,Pasquali,A.,&Mo,H.J.2007,ArXive-prints,704, Peebles,P.J.E.1969,ApJ,155,393 arXiv:0704.0674 Pereira,M.J.,&Kuhn,J.R.2005, ApJ,627,L21 Faltenbacher, A., Jing, Y. P., Li, C., Mao, S., Mo, H. J., Plionis,M.,&Basilakos,S.2002,MNRAS,329,L47 Pasquali,A.,&vandenBosch,F.C.2007,ArXive-prints,706, Suto,Y.,Cen,R.,&Ostriker,J.P.1992, ApJ,395,1 arXiv:0706.0262 Taffoni,G.,Mayer,L.,Colpi,M.,&Governato,F.2003,MNRAS, Frenk, C. S., White, S. D. M., Davis, M., & Efstathiou, G. 1988, 341,434 ApJ,327,507 Trevese,D.,Cirimele,G.,&Flin,P.1992, AJ,104,935 Gerhard,O.E.1983,MNRAS,202,1159 Torlina,L.,DePropris,R.,&West,M.J.2007, ApJ,660,L97 Gill,S.P.D.,Knebe,A.,&Gibson,B.K.2004,MNRAS,351,399 Usami,M.,&Fujimoto,M.1997,ApJ,487,489 Gill, S. P. D., Knebe, A., Gibson, B. K., & Dopita, M. A. 2004, van den Bosch, F. C.,Abel, T., Croft, R. A.C., Hernquist, L., & MNRAS,351,410 White,S.D.M.2002, ApJ,576,21 Hahn, O., Carollo, C. M., Porciani, C., & Dekel, A. 2007, ArXiv Weinberg,D.H.,Hernquist,L.,&Katz,N.1997,ApJ,477,8 e-prints,704,arXiv:0704.2595 Wesson,P.S.1984, A&A,138,253 Hahn, O., Carollo, C. M., Porciani, C., & Dekel, A. 2007, ArXiv Yang, X., van den Bosch, F. C., Mo, H. J., Mao, S., Kang, X., e-prints,704,arXiv:0704.2595 Weinmann, S. M., Guo, Y., & Jing, Y. P. 2006, MNRAS, 369, Hashimoto,Y.,Funato, Y.,&Makino,J.2003,ApJ,582,196 1293 Hawley,D.L.,&Peebles,P.J.E.1975, AJ,80,477 Hirata,C.,&Seljak,U.2003, MNRAS,343,459 9 Fig. 1.— Results for “fake” NFW halo analysis. Left: Error in major axis orientation vs. number of particles in halo. The vertical dashedlinerepresents thelowerlimitonNforthehalos analysedinthispaper,whereas thehorizontal linesshow theminimumaccuracy that will be tolerated. Right: The error in major axis orientation vs. the intermediate-to-major axis ratio. Errors are shown for halos with200particles(asdots)andwith1000particles(ascrosses). Fig. 2.—Angledistributionatz=0. Anisotropicdistributionwouldfollowthedashedline,withhcosφi=0.5 10 Fig. 3.— Angle distribution at z = 0 for high mass and low mass halos. An isotropic distribution would follow the dashed line, with hcosφi=0.5. MasslimitsareinunitsofM⊙. Fig. 4.—Radialalignmentvs. distancetoclustercenter forallhaloswithz

Radial Alignment in Simulated Clusters

Similar Radial Alignment in Simulated Clusters