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Mem.S.A.It.Vol.,1 (cid:13)c SAIt 2008 Memoriedella Modeling the Outskirts of Galaxy Clusters with Cosmological Simulations DaisukeNagai 1 1 0 DepartmentofPhysics,YaleUniversity,NewHaven,CT06520,U.S.A. 2 e-mail:[email protected] n a J Abstract. Wepresentcosmologicalsimulationsofgalaxyclusters,withfocusontheclus- ter outskirts. We show that large-scale cosmic accretion and mergers produce significant 6 internalgasmotionsandinhomogeneousgasdistribution(”clumpiness”)intheintracluster ] medium(ICM)andintroducebiasesinmeasurementsoftheICMprofilesandthecluster O mass. Wealsoshow that non-thermal pressureprovided bythegasmotions isoneof the dominantsourcesoftheoreticaluncertaintiesincosmicmicrowavebackgroundsecondary C anisotropies. We briefly discuss implications for cluster cosmology and future prospects . h for understanding the physics of cluster outskirts using computer simulations and multi- p wavelengthclustersurveys. - o r t 1. Introduction as radiative gas cooling, star formation, and s a energy injection from active galactic nuclei. In recent years, galaxy clusters have emerged [ Dominant physical processes in the outskirts as one of the most unique and power- are limited to the gravity-driven collisionless 1 ful laboratories for cosmology and astro- dynamics of dark matter and hydrodynamics v physics. Being the largest and most mag- 2 of the intracluster medium (ICM). In the hi- nificent structures in the Universe, clusters 2 erarchical structure formation model, galaxy 3 of galaxies serve as excellent tracers of the clustersgrowby accretingclumpsanddiffuse growth of cosmic structures. Current genera- 1 gas from the surrounding large-scale struc- tion of X-ray cluster surveys have provided . ture in their outer envelope. Numerical simu- 1 independent confirmation of cosmic acceler- 0 lations predict that the large-scale cosmic ac- ation and significantly tighten constraints on 1 cretion and mergers give rise to internal gas the nature of dark energy (Allenetal., 2008; 1 motions and inhomogeneous gas distribution Vikhlininetal., 2009) and alternative theories : in the ICM. However, until very recently, ob- v of gravity (e.g., Schmidtetal., 2009). Several servationalstudiesofthe ICM havebeenlim- i X ongoing and new X-ray (e.g., eROSITA) and itedtoradiiconsiderablysmallerthanthevirial Sunyaev-Zel’dovich effect (SZE) cluster sur- r radiusofclusters. a veys(e.g.,SPT,ACT,Planck)areunderwayto improvecurrentcosmologicalconstraints. Recently, Suzaku X-ray observations have Outskirts of galaxy clusters have special extendedX-raymeasurementsoftheICMpro- importance for cluster cosmology, because fileouttoandbeyondthevirialradiusforsev- they are believed to be much less suscepti- eral clusters (Bautzetal., 2009; Georgeetal., ble to complicated cluster astrophysics, such 2009; Reiprichetal., 2009; Hoshinoetal., 2 D.Nagai:SimulatingtheClusterOutskirts 2010; Kawaharadaetal., 2010). While these measurements are still quite uncertain, initial results suggested that the observed ICM pro- files may deviate significantly from the prediction of hydrodynamicalcluster simulations (e.g., Georgeetal., 2009). In addition to test- ing models of structure formation, these new measurementswillbeimportantforcontrolling systematic uncertainties in cluster-based cos- mologicalmeasurements. In this work, I will present theoretical modeling of the outskirts of galaxy clusters basedoncosmologicalsimulations,withhigh- lights onimplicationsforthe interpretationof forthcomingmulti-wavelengthobservationsof galaxy clusters. The simulations we present here are described in Nagaietal. (2007a) and Nagaietal. (2007b), and we refer the readers tothesepapersformoredetails. 2. GasMotionsinClusterOutskirts Gasmotionsinducedbycosmicaccretionand mergersprovidenon-thermalpressuresupport in galaxy clusters. The top panel of Fig. 2 shows that results of hydrodynamical cluster simulations, illustrating that the non-thermal Fig.1. Top panel: Ratio of pressure from random pressure contributesto 10-20% at r = r of 500 gasmotionstototalpressureasafunctionofradius. thetotalpressure.Thefractionofnon-thermal Relaxedclustersarerepresentedbysolidlineswhile pressure support increases with radius, and it unrelaxed clustersarerepresented bydashed lines. islargerformoredynamicallyactivesystems. Bottompanel:AveragedmassprofilesM(<r)ofthe The bottom panel of Fig. 2 shows that the relaxedclusters,normalizedbyM .Thesolidline 500 cluster mass profile based on hydrostatic as- shows the actual mass profilefromsimulation, the sumption is biased low. We further demon- longdashedlineshowsthemassprofilefromhydro- strate that it is possible correctthe bias in the staticequilibriumincludingrandomgasandthermal hydrostatic mass, if one could measure gas pressure,andtheshortdashedlineshowsthemass profilefromhydrostaticequilibriumincludingther- motions in clusters and hence correct for the malpressureonly.Hashedregionshowsthe1-σer- bias. Upcoming Astro-H X-ray satellite mis- rorofthemean.FromLauetal.(2009). sion (scheduled to be launched in 2014) will providea first directmeasurementof gas mo- tionsinclustersviadopplerbroadeningofiron a major source of systematic bias in X-ray lines(Inogamov&Sunyaev,2003). measurementsofICMprofilesintheenvelope of galaxy clusters (r & r ) (Nagai&Lau, 200 2011). Using hydrodynamical simulations of 3. GasClumpinginClusterOutskirts cluster formation,we show that gas clumping Recently, Suzaku X-ray observations revealed introducestheoverestimateoftheobservedgas thattheobservedentropyprofileoftheICMis density and causes flattening of the entropy significantly offset from the prediction of hy- profile at large radius. This is illustrated in drodynamical simulations of galaxy clusters. Fig.2.Thetoppanelshowsthattheclumping Here,we pointoutthatgasclumpingislikely factor of the X-ray emitting gas (T & 106 K) D.Nagai:SimulatingtheClusterOutskirts 3 8 εf, εDM Ac 2K] 6 µ [ 4 Dℓ 2 08 α0 β 2K] 6 µ [ 4 Dℓ 2 0 103 104 103 104 ℓ ℓ Fig.3.AstrophysicaluncertaintiesintheSZpower spectrum.Differentlinesindicatetheoreticaluncer- taintiesassociatedwith(1)heatingofgasbyenergy injectionfromstarsandAGN(indicatedwithsolid lines)andmergerdynamics(indicatedwithdashed lines in top-left panel), (2) dark matter structures (top-right),and(3)non-thermalpressurebygasmo- tions (bottom-left) and its time evolution (bottom- right).Ineachcase,thethickredlinerepresentsour fiducialmodel.FromShawetal.(2010). C(r)1/3. Results of our analyses indicate that Fig.2. Top panel: Median clumping factor pro- filesofgaswithdifferentminimumtemperaturefor gas clumping causes the flattening of the ob- servedentropyprofilesatr & r .Whilecur- the simulations with gas cooling and star forma- 200 tion. Bottom panel: Impact of gas clumping on X- rent Suzaku measurements are still uncertain, raymeasurements of theICMentropy profile.The our results indicate that gas clumping is im- dashedlineindicatesthetrueentropyprofileofthe portantforreducingthetensionbetweenrecent simulatedclusters,whilethesolidlineindicatesthe Suzakuobservationsandtheoreticalprediction observed entropy profile,obtained by assuming no oftheΛCDMmodel. clumping(C=1).BlackpointsareSuzakuobserva- tionsofPKS0745-191(circles),A1689(triangles), A1413(stars),andA1795(blackdot-dashedlines). 4. ImpactontheSZpowerspectrum FromNagai&Lau(2011). Recent measurements of the SZ power spectrum by SPT and ACT telescopes revealed that the SZ power is significantly below the signal predicted by the current cosmic struc- is C ≡ hρ2gasi/hρgasi2 ∼ 1.3 at r = r200, ture formation model (Luekeretal., 2010; and it increases with radius, reaching C ∼ 5 Shirokoffetal.,2010;Dunkleyetal.,2010). at r = 2r200. In the bottom panel, the solid Inourrecentwork,wearguedthatthecur- line indicates the true entropy profile, which rent SZ power spectrum template is overesti- is consistent with the self-similar prediction, mated by 50-100%, due to lack of important K ≡ T/n2/3 ∝ r1.1 (Voitetal., 2005). From astrophysical process in theoretical modeling e the definition of entropy, the overestimate of oftheSZpowerspectrum(Shawetal.,2010). gas density due to clumping causes an under- Fig. 3 illustrates theoretical uncertainties in estimate of the observed entropy profile by the thermal SZ power spectrum. Our model 4 D.Nagai:SimulatingtheClusterOutskirts accounts for star formation and energy feed- clusterswithdeepimagingdataextendingout back(fromsupernovaeandactivegalacticnu- to large radii. Theoretical modeling based on clei)aswellasradiallydependentnon-thermal detailed numerical simulations is also under- pressure support due to random gas motions, way. A plethora of activities (in both theory the latter calibrated by recent hydrodynami- andobservation)willadvanceourunderstand- calsimulations.Varyingthelevelsoffeedback ing of cluster physics and provide foundation and non-thermal pressure support can signif- fortheuseofgalaxyclustersaslaboratoriesfor icantly change both the amplitude and shape cosmologyandastrophysics. of thethermalSZpowerspectrum.Increasing the feedbacksuppressespowerat small angu- Acknowledgements. I would like to thank my col- larscales,shiftingthepeakofthepowerspec- laborators Andrey Kravtsov, Erwin Lau, Laurie Shawforrewardingcollaborationswhichproduced trum to lower l. On the other hand, increas- resultsdescribedhere.Thisresearchwascarriedout ing the non-thermal pressure support signifi- attheYaleUniversityandwassupportedinpartby cantly reduces power at large angular scales. NSFundergrantAST-1009811. In general, including non-thermal pressure at the level measured in simulations has a large effectonthepowerspectrum,reducingtheam- References plitudeby&60%atangularscalesofafewar- Allen, S. W., Rapetti, D. A., Schmidt, R. W., cminutescomparedtoamodelwithoutanon- Ebeling,H.,Morris,R.G.,&Fabian,A.C. thermal component. Comparing with the re- 2008,MNRAS,383,879 cent measurements of the small-scale cosmic Bautz,M.W.etal.2009,PASJ,61,1117 microwave background power spectrum, our Dunkley, J. et al. 2010, ArXiv e-prints, modelreducesthe tension between the values 1009.0866 of σ measured from the SZ power spectrum 8 George, M. R., Fabian, A. C., Sanders, J. S., andfromclusterabundances. Young, A. J., & Russell, H. R. 2009, MNRAS,395,657 5. FutureProspects Hoshino,A.etal.2010,PASJ,62,371 Inogamov, N. A., & Sunyaev, R. 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