IMPLICATIONS FOR COSMIC RAYS, DARK MATTER AND NGC 1275fulir.irb.hr/1407/1/Hrupec2010(433144).pdf · † Send oﬀprint requests to F. Zandanel ([email protected]) & C. Pfrommer ([email protected])

Draft version December 17, 2009Preprint typeset using LATEX style emulateapj v. 04/20/08

MAGIC GAMMA-RAY TELESCOPE OBSERVATION OF THE PERSEUS CLUSTER OF GALAXIES:IMPLICATIONS FOR COSMIC RAYS, DARK MATTER AND NGC 1275

J. Aleksica, L. A. Antonellib, P. Antoranzc, M. Backesd, C. Baixerase, S. Balestrac, J. A. Barrioc,D. Bastierif, J. Becerra Gonzalezg, W. Bednarekh, A. Berdyugini, K. Bergeri, E. Bernardinij, A. Bilandk,

R. K. Bockl,f, G. Bonnolib, P. Bordasm, D. Borla Tridonl, V. Bosch-Ramonm, D. Bosec, I. Braunk, T. Bretzn,D. Britzgerl, M. Camarac, E. Carmonal, A. Carosib, P. Colinl, S. Commichauk, J. L. Contrerasc, J. Cortinaa,

M. T. Costadog,o, S. Covinob, F. Dazzip,*, A. De Angelisp, E. De Cea del Pozoq, R. De los Reyesc,***, B. DeLottop, M. De Mariap, F. De Sabatap, C. Delgado Mendezg,**, M. Doertd, A. Domınguezr, D. Dominis Presters,

D. Dornerk, M. Dorof, D. Elsaessern, M. Errandoa, D. Ferencs, M. V. Fonsecac, L. Fonte, N. Galantel,R. J. Garcıa Lopezg,o, M. Garczarczykg, M. Gaugg, N. Godinovics, D. Hadaschq, A. Herrerog,o, D. Hildebrandk,

D. Hohne-Monchn, J. Hosel, D. Hrupecs, C. C. Hsul, T. Joglerl, S. Klepsera, T. Krahenbuhlk, D. Kranichk,A. La Barberab, A. Laillet, E. Leonardou, E. Lindforsi, S. Lombardif, F. Longop, M. Lopezf, E. Lorenzk,l,P. Majumdarj, G. Manevav, N. Mankuzhiyilp, K. Mannheimn, L. Maraschib, M. Mariottif, M. Martıneza,

D. Mazina, M. Meucciu, J. M. Mirandac, R. Mirzoyanl, H. Miyamotol, J. Moldonm, M. Molesr, A. Moralejoa,D. Nietoc, K. Nilssoni, J. Ninkovicl, R. Oritol, I. Oyac, S. Paianof, R. Paolettiu, J. M. Paredesm, S. Partiniu,M. Pasaneni, D. Pascolif, F. Paussk, R. G. Pegnau, M. A. Perez-Torresr, M. Persicp,w, L. Peruzzof, F. Pradar,E. Prandinif, N. Puchadesa, I. Puljaks, I. Reichardta, W. Rhoded, M. Ribom, J. Ricox,a, M. Rissik, S. Rugamern,

A. Saggionf, T. Y. Saitol, M. Salvatib, M. Sanchez-Conder, K. Sataleckaj, V. Scalzottof, V. Scapinp,C. Schultzf, T. Schweizerl, M. Shaydukl, S. N. Shorey, A. Sierpowska-Bartosikh, A. Sillanpaai, J. Sitarekl,h,

D. Sobczynskah, F. Spaniern, S. Spirob, A. Stamerrau, B. Steinkel, J. C. Struebign, T. Surics, L. Takaloi,F. Tavecchiob, P. Temnikovv, T. Terzics, D. Tescaroa, M. Teshimal, D. F. Torresx,q, H. Vankovv,

R. M. Wagnerl, V. Zabalzam, F. Zandanelr,†, R. Zanina, J. Zapateroe

(The MAGIC Collaboration)

C. Pfrommerz,†, A. Pinzke1, T. A. Enßlin2, S. Inoue3 and G. Ghisellini4

Draft version December 17, 2009

ABSTRACT

The Perseus galaxy cluster was observed by the MAGIC Cherenkov telescope for a total effectivetime of 24.4 hours during November and December 2008. The resulting upper limits on the γ-rayemission above 100 GeV are in the range of 4.6 to 7.5× 10−12cm−2 s−1 for spectral indices from −1.5to −2.5; thereby constraining the emission produced by cosmic rays, dark matter annihilations andthe central radio galaxy NGC 1275. Results are compatible with cosmological cluster simulations forthe cosmic ray induced γ-ray emission, constraining the average cosmic ray-to-thermal pressure to< 4% for the cluster core region (< 8% for the entire cluster). Using simplified assumptions adoptedin earlier work (a power-law spectrum with an index of −2.1, constant cosmic ray-to-thermal pressurefor the peripheral cluster regions while accounting for the adiabatic contraction during the cooling flowformation), we would limit the ratio of cosmic ray-to-thermal energy to ECR/Eth < 3%. Improvingthe sensitivity of this observation by a factor of about seven will enable us to scrutinize the hadronicmodel for the Perseus radio mini halo: a non-detection of γ-ray emission at this level implies cosmicrays fluxes that are too small to produce enough electrons through hadronic interactions with theambient gas protons to explain the observed synchrotron emission. The upper limit also translatesinto a level of γ-ray emission from possible annihilations of the cluster dark matter (the dominantmass component) that is consistent with boost factors of ∼ 104 for the typically expected dark matterannihilation induced emission. Finally, the upper limits obtained for the γ-ray emission of the centralradio galaxy NGC 1275 are consistent with the recent detection by the Fermi-LAT satellite. Due tothe extremely large Doppler factors required for the jet, a one-zone synchrotron self-Compton modelis implausible in this case. We reproduce the observed spectral energy density by using the structuredjet (spine-layer) model which has previously been adopted to explain the high-energy emission of radiogalaxies.Subject headings: gamma-rays: observations, galaxies: clusters: individual (Perseus)

a IFAE, Edifici Cn., Campus UAB, E-08193 Bellaterra, Spainb INAF National Institute for Astrophysics, I-00136 Rome, Italyc Universidad Complutense, E-28040 Madrid, Spaind Technische Universitat Dortmund, D-44221 Dortmund, Ger-

manye Universitat Autonoma de Barcelona, E-08193 Bellaterra, Spainf Universita di Padova and INFN, I-35131 Padova, Italyg Inst. de Astrofısica de Canarias, E-38200 La Laguna, Tenerife,

Spainh University of Lodz, PL-90236 Lodz, Polandi Tuorla Observatory, University of Turku, FI-21500 Piikkio, Fin-

landj Deutsches Elektronen-Synchrotron (DESY), D-15738 Zeuthen,

Germanyk ETH Zurich, CH-8093 Switzerland

2 Aleksic, J. et al.

1. INTRODUCTION

Clusters of galaxies provide us with the opportu-nity to study an “ecosystem”, a volume that is ahigh-density microcosm of the rest of the Universe.Clusters of galaxies are the largest and most massivegravitationally bound systems in the Universe, withradii of few Mpc and total masses M ∼ (1014 −1015)M⊙, of which galaxies, gas and dark matter(DM) contribute roughly for 5, 15 and 80%, respec-tively (see e.g. Sarazin (1988), Kochanek et al. (2003)and Voit (2005) for a general overview). While nocluster has been firmly detected as a γ-ray sourceso far (Reimer et al. 2003; Perkins et al. 2006; Perkins2008; Aharonian et al. 2009a,b; Domainko et al. 2009;Galante et al. 2009; Kiuchi et al. 2009; Acciari et al.2009), they are expected to be significant γ-ray emitterson the following general grounds. (i) Clusters are activelyevolving objects and being assembled today, in the latestand most energetic phase of hierarchical structure forma-tion. (ii) Clusters serve as cosmic energy reservoirs forpowerful sources such as radio galaxies and supernova-driven galactic winds. (iii) Finally, clusters contain largeamounts of gas with embedded magnetic fields, oftenshowing direct evidence for shocks and turbulence aswell as relativistic particles. For recent reviews regard-ing non-thermal processes in clusters as well as numer-ical simulations, see Blasi et al. (2007) and Dolag et al.(2008).

In the cosmological hierarchic clustering model, largescale structures grow hierarchically through mergingand accretion of smaller systems into larger ones, andclusters are the latest and most massive objects toform (e.g. Peebles 1993). Recently, high resolution

l Max-Planck-Institut fur Physik, D-80805 Munchen, Germanym Universitat de Barcelona (ICC/IEEC), E-08028 Barcelona,

Spainn Universitat Wurzburg, D-97074 Wurzburg, Germanyo Depto. de Astrofisica, Universidad, E-38206 La Laguna, Tener-

ife, Spainp Universita di Udine, and INFN Trieste, I-33100 Udine, Italyq Institut de Ciencies de l’Espai (IEEC-CSIC), E-08193 Bel-

laterra, Spainr Inst. de Astrofısica de Andalucıa (CSIC), E-18080 Granada,

Spains Croatian MAGIC Consortium, Institute R. Boskovic, Univer-

sity of Rijeka and University of Split, HR-10000 Zagreb, Croatiat University of California, Davis, CA-95616-8677, USAu Universita di Siena, and INFN Pisa, I-53100 Siena, Italyv Inst. for Nucl. Research and Nucl. Energy, BG-1784 Sofia,

Bulgariaw INAF/Osservatorio Astronomico and INFN, I-34143 Trieste,

Italyx ICREA, E-08010 Barcelona, Spainy Universita di Pisa, and INFN Pisa, I-56126 Pisa, Italyz CITA, University of Toronto, M5S 3H8 Toronto, Canada1 Stockholm University, SE - 106 91 Stockholm, Sweden2 Max-Planck-Institut fur Astrophysik, D-85740 Garching, Ger-

many3 Kyoto University, 606-8502 Kyoto, Japan4 INAF National Institute for Astrophysics, I-23807 Merate,

Italy* supported by INFN Padova** now at: Centro de Investigaciones Energeticas, Medioambien-

tales y Tecnologicas*** now at: Max-Planck-Institut fur Kernphysik, D-69029 Hei-

delberg, Germany† Send offprint requests to F. Zandanel ([email protected]) &

C. Pfrommer ([email protected])

X-ray observations by Chandra and XMM-Newtonorbiting telescopes provided confirmation of this picture(e.g. Rosati et al. 2002; Voit 2005). During the course ofcluster assembly, energies of order of the final gas bindingenergy Eb ∼ 3 × (1061 − 1063) erg should be dissipatedthrough merger and accretion shocks (collectively called“structure formation shocks”) as well as turbulence.The energy is expected to be dissipated on a dynamicaltimescale of τdyn ∼ 1 Gyr. Hence the correspondingrates of energy release are L ∼ (1045 − 1047) erg/s,so even a small fraction of this energy channeledinto non-thermal particles can be of major observ-able consequence. Shocks and turbulence are alsolikely to accelerate non-thermal electrons and protonsto high energies (e.g. Jaffe 1977; Schlickeiser et al.1987; Brunetti et al. 2001; Miniati et al. 2001b,a;Ohno et al. 2002; Miniati 2002, 2003; Sarazin 2002;Brunetti et al. 2004; Inoue et al. 2005; Brunetti et al.2007; Brunetti & Lazarian 2007; Pfrommer et al. 2007,2008; Pfrommer 2008; Falceta-Goncalves et al. 2009).

Clusters are also home to different types of energeticoutflows, and the intra-cluster medium (ICM) can func-tion as an efficient energy reservoir. Most clusters areseen to harbor radio galaxies around their central re-gions, whose large, powerful jets of relativistic plasmaare interacting vigorously with the ICM (Heinz et al.1998; Forman et al. 2003; Fabian et al. 2006). A crudeestimate of the total energy output by a single pow-erful radio galaxy is ERG ∼ (1060 − 1062) erg, tak-ing reasonable values for the kinetic luminosity LRG ∼(1045 − 1046) erg/s and effective duration of activitytRG ∼ (107 − 108) yr (McNamara & Nulsen 2007). Theintegrated output from the whole cluster radio galaxypopulation should be even greater (Enßlin et al. 1997,1998; Inoue & Sasaki 2001). Although rarely seen inpresent-day clusters, another source which should havebeen active in the past are galactic winds, i.e. out-flows driven by the joint action of numerous supernovae(Volk et al. 1996). Taking the observed mass of Fe inthe ICM to be MFe,ICM ∼ 3 × (109 − 1010)M⊙, theenergy and Fe mass ejected by each supernovae to be re-spectively ESN ∼ 1051 erg and MFe,SN ∼ 0.1M⊙, andan outflow efficiency ξGW ∼ 0.1 (Veilleux et al. 2005),we estimate the total galactic wind energy output to beEGW ∼ ξGW ESN/MFe,SNMFe,ICM ∼ 3 × (1060 − 1061)erg. In any case, along with dumping energy, thesesources can inject substantial quantities of non-thermalparticles into the ICM, or could have done so in the past.

Faraday rotation measurements provide a powerfultool to probe the strength of the intra-cluster mag-netic fields (Kim et al. 1991) and even their distribu-tion (Clarke et al. 2001), resulting in the ICM now beingknown to be permeated by magnetic fields with strengthsB ∼ (1 − 10) µG (Carilli & Taylor 2002; Vogt & Enßlin2005), which allow for particle acceleration in shocks upto γ-ray emitting energies. Observations of radio ha-los and radio relics have already established that syn-chrotron emitting electrons with energies reaching ∼10 GeV are present in at least some clusters (Feretti2003; Ferrari et al. 2008), although their precise originis still unclear. Similar populations of electrons but withharder spectra may produce γ-rays efficiently via inverseCompton (IC) up-scattering of the cosmic microwave

MAGIC Observation of the Perseus Galaxy Cluster 3

background (Loeb & Waxman 2000; Totani & Kitayama2000; Miniati 2002, 2003; Petrosian et al. 2008). Obser-vations in the hard X-ray regime may suggest the pres-ence of a non-thermal component due to the IC scat-tering of cosmic microwave photons by relativistic elec-trons (see Rephaeli et al. (2008) for a recent review).However, Ajello et al. (2009) found no evidence of ahard tail above the thermal emission in a Swift/BATsample of clusters. The ICM gas should also provideample target matter for inelastic collisions leading topion-decay γ-rays (Volk et al. 1996; Enßlin et al. 1997;Pfrommer & Enßlin 2003, 2004a; Pfrommer et al. 2008;Pfrommer 2008) as well as secondary electron injection(Dennison 1980; Vestrand 1982; Blasi & Colafrancesco1999; Dolag & Enßlin 2000; Pfrommer & Enßlin 2004a;Fujita et al. 2007; Pfrommer 2008). The magnetic fieldsplay another crucial role by confining non-thermal pro-tons within the cluster volume for longer than a Hub-ble time, i.e. any protons injected into the ICM accu-mulates throughout the cluster history (Volk et al. 1996;Berezinsky et al. 1997).

Galaxy clusters present very large M/L ratios and con-siderable overdensities, which is crucial for indirect DMsearches. Despite the fact that they are not as near asother potential DM candidates, as the dwarf spheroidalgalaxies (Albert et al. 2008d; Aliu et al. 2009a), the largeDM masses of clusters could make them ideal laborato-ries also for the search of a DM annihilation γ-ray signal(Jeltema et al. 2009; Pinzke et al. 2009).

In this paper we report the results of the Perseuscluster observation performed by the MAGIC telescopefor a total effective time of 24.4 hours during Novem-ber and December 2008. In Section 2, we explain thephysical motivations why we chose Perseus over othergalaxy clusters and present its main characteristics. InSection 3, we briefly introduce the MAGIC telescope.We then describe the Perseus data sample, the analy-sis and the obtained flux upper limits. We discuss theimplications for the cosmic ray pressure and the possi-ble DM annihilation induced γ-ray emission in Section 4and 5, respectively. In Section 6, we discuss the impli-cations for the jet emission model of the central radiogalaxy NGC 1275. Finally, in Section 7, we summarizeour conclusions. All cluster masses and luminosities arescaled to the currently favored value of Hubble’s constantH0 = 70 km s−1 Mpc−1.

2. TARGET SELECTION AND PRELIMINARIES

The Perseus cluster, also called A426, is at a dis-tance of 77.7 Mpc (z = 0.018). It is the brightest X-ray cluster (Edge et al. 1992) and hosts a massive cool-ing flow with high central gas densities of 0.05 cm−3

(see Table 1). Perseus furthermore hosts a luminousradio mini-halo – diffuse synchrotron emission that fillsa large fraction of the cluster core region – and showsa source extension of ∼ 200 kpc (Pedlar et al. 1990).This radio mini-halo is well modeled by the hadronic sce-nario where the radio emitting electrons are produced inhadronic cosmic ray (CR) proton interactions with ambi-ent gas protons requiring only a very modest fraction ofa few percent CR pressure relative to thermal pressure(Pfrommer & Enßlin 2004a). In particular the similar-ity of the thermal X-ray emission and that of the ra-dio mini-halo comes about naturally as both processes

scale with the number density squared. An alterna-tive model for the radio emission has been proposedby Gitti et al. (2002) which explains the radio mini-halo by re-acceleration of relativistic electrons throughsecond order interactions with magneto-hydrodynamic(MHD) turbulence. However, it remains to be shownwhether the necessary turbulent energy density can beprovided throughout the entire cooling flow region ofPerseus. These conditions provide high target densitiesfor hadronic CRp-p interactions and enhance the result-ing γ-ray flux.

The Perseus galaxy cluster was carefully chosen overother nearby clusters after considering the expected γ-ray emission from the pion-decay and DM annihilation.Moreover, the central radio galaxy NGC 1275 is expectedto be a promising GeV-TeV target, and hence is anotherstrong motivation to observe this cluster. In the followingsubsections, we detail our considerations.

2.1. Cosmic Ray Induced Emission

In the course of this work, we used cosmological sim-ulations of the formation of galaxy clusters to inform usabout the expected spatial and spectral characteristicsof the CR induced γ-ray emission. A clear detection ofthe IC emission from shock-accelerated CR electrons willbe challenging for Imaging Atmospheric Cherenkov Tele-scopes (IACTs) due to the large angular extent of theseaccretion shocks that subtend solid angles correspondingto up to six virial radii. For these instruments, the spa-tially concentrated pion-decay γ-ray emission resultingfrom hadronic CR interactions that dominates the totalγ-ray luminosity (Pfrommer et al. 2008; Pfrommer 2008)should be more readily detectable than the emission fromthe outer region.

To address the question of universality and predictabil-ity of the expected γ-ray emission we simulated a sampleof 14 galaxy clusters that span one and a half decadesin mass and show a variety of dynamical states rangingfrom relaxed cool core clusters to violent merging clusters(details are given in Sect. 4.1). In order to find the mostpromising target cluster in the local Universe for detect-ing the pion decay emission, we computed the scalingrelations between γ-ray luminosity and cluster mass ofour sample (Pfrommer 2008) and used these to normal-ize the CR induced emission of all clusters in a completesample of the X-ray brightest clusters (the extended HI-FLUGCS catalogue, Reiprich & Bohringer 2002). Thisfavors high-mass, nearby galaxy cluster with a scaling

Mβ200/D2

lum, where M200 is the virial mass1, Dlum theluminosity distance, and β ≃ 1.32 a weakly model de-pendent scaling parameter that provides the rank order-ing according to the brightness of each individual cluster(Pfrommer 2008). As a second criterion, we requiredlow zenith angle observations, i.e below 35 deg, that en-sure the lowest possible energy thresholds and the max-imum sensitivity for the detector. We carefully mod-eled the most promising targets, accounting for the mea-sured gas density and temperatures from thermal X-raymeasurements while assuming a constant CR-to-thermalgas ratio (Pfrommer & Enßlin 2004a). Cluster-wide ex-

1 We define the virial mass M∆ and the virial radius R∆ asthe mass and radius of a sphere enclosing a mean density that is∆ = 200 times the critical density of the Universe.


TABLE 1Properties of the Perseus galaxy cluster

z Dlum [Mpc] R200 [Mpc] M200 [M⊙] LX,0.1−2.4 [erg s−1] TX [keV] Lν=1.4 [erg s−1 Hz−1]

0.0183 77.7 1.9 7.71 × 1014 8.31 × 1044 6.8 3.38 × 1031

Notes. Data taken from Reiprich & Bohringer (2002), Pedlar et al. (1990) and Churazov et al. (2003).

tended radio synchrotron emission that informs aboutpresent high-energy processes were additionally takeninto account before we selected the Perseus cluster as ourmost promising source. Although other clusters showeda somewhat higher γ-ray flux in our simulations (e.g.Ophiuchus), the facts that Perseus is observable at lowzenith angles and that the expected emission is more spa-tially concentrated make it the best suited target for thisobservation.

2.2. Dark Matter Content

Typically up to 80% of the total mass of a galaxy clus-ter is in the form of non-baryonic DM. Since the DMannihilation γ-ray signal is expected to be proportionalto the integrated squared DM density along the line ofsight (Evans et al. 2004; Bergstrom & Hooper 2006), itis obvious that galaxy clusters could be good candidatesto look for DM as well. This is true despite the fact thatthey are located at much larger distances than other po-tential DM candidates, such as dwarf spheroidal galaxiessatellites of the Milky Way or the Galactic Center. Oneobvious reason is the huge amount of DM hosted by clus-ters compared with the rest of candidates. Perseus, forexample, is located ∼1000 times farther than Milky Waydwarfs, but it contains roughly six orders of magnitudemore DM than the Willman 1 dwarf galaxy, one of themost promising DM candidates according to recent work(Strigari et al. 2007; Aliu et al. 2009a). Additionally, thepresence of substructures could be of crucial importance.Substructures in clusters may significantly enhance theDM signal over the smooth halo, while we do not expectthis to be of special relevance for dwarf galaxies sincetheir outer regions are severely affected by tidal strip-ping (Pinzke et al. 2009, Sanchez-Conde et al., in prep.).

Essentially, the annihilation flux is proportional to theproduct of two parameters (see e.g. Evans et al. 2004for details): a first one that captures all the particlephysics (DM particle mass, cross section, etc), that wewill label as fSUSY, and a second one, Jastro, that ac-counts for all the astrophysical considerations (DM dis-tribution, telescope PSF, etc). The particle physics fac-tor just acts as a normalization in the expected anni-hilation flux, so we can neglect it when performing acomparative study – as we are doing in this section.Concerning the astrophysical factor, the DM distribu-tion is commonly modeled with radial density profiles ofthe form ρ(r) = ρs/[(r/rs)

γ (1+ (r/rs)α)(β−γ)/α], where

ρs and rs represent a characteristic density and a scaleradius respectively (Kravtsov et al. 1998). These den-sity profiles are well motivated by high-resolution N-bodycosmological simulations. Here we adopt the Navarro-Frenk-White (Navarro et al. 1997; hereafter NFW) DMdensity profile, with (α,β,γ) = (1,3,1). For an NFW pro-file, 90% of the DM annihilation flux comes from the

region within rs, so that the corresponding integratedluminosity is proportional to r3

sρ2s. We can derive rs

and ρs for Perseus, assuming M200 = 7.7 × 1014 M⊙

(as given in Table 1) and a concentration of ∼6 (as givenby the Bullock et al. 2001 virial mass-concentration scal-ing relation). We obtain rs = 0.384 Mpc and ρs =1.06×1015 M⊙ Mpc−3, which translates into a total valueof Jastro ∼ 1.4× 1016 GeV2 cm−5 for the scale radius re-gion. In the case of Coma, although slightly (∼15%)more massive than Perseus, the fact that it is locatedsignificantly farther (101 Mpc) translates into a slightlylower annihilation flux. Virgo, only 17 Mpc away fromus, gives a larger DM annihilation flux, but here the largeextension of the region from which most of the annihi-lation flux is expected to come compared with Perseus(rs ∼ 1.2 deg and rs ∼ 0.3 deg, respectively) could rep-resent an obstacle from the observational point of view.Source extension is of special relevance for single tele-scope IACTs, for which point-like sources (sources withan angular extension smaller or similar to the telescopePSF) are more readily observable.

2.3. The NGC 1275 Radio Galaxy

The central NGC 1275 radio galaxy is another strongmotivation for γ-ray observations of the Perseus galaxycluster. The detection at TeV energies of the radiogalaxies M 87 (Aharonian et al. 2006) and Centaurus A(Aharonian et al. 2009c) has forced a substantial revisionof the paradigm whereby VHE emission is a characteris-tic property of highly relativistic jets closely aligned withthe line of sight, establishing radio galaxies as a new classof VHE γ-ray emitters. Note that NGC 1275 has variouscharacteristics in common with Centaurus A which hasalso been interpreted as a possible source of ultra-highenergy cosmic rays (Hardcastle et al. 2009).

The NGC 1275 radio galaxy is the brightest radiosource in the northern sky. Its jet inclination angleseems to increase from 10 − 20 deg at milliarcsecondsscales up to 40−60 deg at arcseconds scales (Dunn et al.2006). Note that NGC 1275 was classified as a blazarby Angel & Stockman (1980) because of its optical po-larization, and it has been seen to vary in the opticalon time scales of a day (Geller et al. 1979). All theseelements are promising from the point of view of theTeV detectability, since they suggest that the emissionregion is located at the base of the jet. In these condi-tions, in the scenario based on the structured jet model(Tavecchio & Ghisellini 2008), we expected VHE emis-sion from the layer of the jet at a level detectable byMAGIC.

3. MAGIC OBSERVATION AND RESULTS

The MAGIC (Major Atmospheric Gamma ImagingCherenkov) telescope is located on the Canary Island of


La Palma (2200 m asl, 28.45N, 17.54W). With a pri-mary mirror diameter of 17 m, it is currently the largestIACT. CRs impinging the Earth atmosphere originate at-mospheric showers that in turn produce Cherenkov light.The ultra-violet Cherenkov flashes are reflected in the fo-cal plane of the telescope, where a camera of 577 photo-multipliers records the resulting images. MAGIC recon-structs the incoming γ-ray directions with an accuracyof about 0.1 deg and achieves an energy resolution above150 GeV of about 20% (see Albert et al. (2008c) andAliu et al. (2009b) for details).

3.1. Observation and Analysis

MAGIC observed the Perseus cluster for 33.4 hoursduring November and December 2008, at zenith anglesbetween 12 and 32, which guarantees the lowest energythreshold. The observation was performed in the false-source tracking (wobble) mode (Fomin et al. 1994) point-ing alternatively to two different sky directions, each at0.4 deg distance from the nominal target position.

The main background for Cherenkov telescopes is dueto the hadronic cosmic rays and the night sky back-ground. Our standard analysis procedure is the follow-ing (for a detailed description see Albert et al. 2008c):data calibration and extraction of the number of photo-electrons per pixel is done (Albert et al. 2008a). Thisis followed by an image cleaning procedure using theamplitude and timing information of the calibrated sig-nals. Particularly, the arrival times in pixels contain-ing > 6 photoelectrons (core pixels) are required to bewithin a time window of 4.5 ns and for pixels contain-ing > 3 photoelectrons (boundary pixels) within a timewindow of 1.5 ns from a neighboring core pixel. Forthe surviving pixels of each event, the shower parame-ters are reconstructed using the Hillas parametrizationalgorithm (Hillas 1985). Hadronic background suppres-sion is achieved using a multivariate method called Ran-dom Forest (Breiman 2001; Albert et al. 2008b), thatuses the Hillas parameters to define an estimator calledhadronness (it runs from 0 for gammas to 1 for hadrons)by comparison with Monte Carlo (MC) γ-ray simula-tions. Moreover, the Random Forest method is used forthe energy estimation of a reconstructed shower. Thegamma/hadron (g/h) separation in the analysis was opti-mized on a sample of well understood Crab Nebula data,which is commonly accepted as standard reference sourcefor VHE astronomy.

Part of the data have been rejected mainly due to thebad weather conditions during some observation days.The total data rejected amount to ∼ 27%, resulting in24.4 hours effective observation time of very high dataquality. Independent cross-checks were performed on thedata giving compatible results.

3.2. Results

Given the good data quality and the low zenith an-gles of observation, the analysis energy threshold resultsto be 80 GeV. Beyond this threshold, no significant ex-cess of γ-rays above the background was detected in 24.4hours of observation. In Figure 1, the α-plot for energiesabove 250 GeV, where the best integral sensitivity is ob-tained from a Crab Nebula data sample, is reported. Theα-parameter is defined as the angular distance between

the shower image main axis and the line connecting theobserved source position in the camera and the imagebarycenter. Background events are isotropic in nature,and thus produce randomly oriented shower images. Thisresults in a more or less smooth event distribution in theα-plot. The γ-ray events due to the source, on the otherhand, are predominantly aligned to the observed posi-tion in the camera. For a detected source, this results ina significant excess of events at small α. A fiducial re-gion α < 6 and a hadronness cut of 0.05 are chosen byoptimizing the analysis on a Crab Nebula data sample.

]°| [α|0 10 20 30 40 50 60 70 80 90

En

trie

s0

50

100

150

200

250

300

350

400

95± = -54 exc

= -0.57, Nσ

40± = 55 exc

= 1.35; Nσ

Fig. 1.— Perseus α-plot as seen by MAGIC in 24.4 hours above250 GeV using a hadronness cut of < 0.05. The blue crosses repre-sent the signal, the red shaded region is the background. The ver-tical black dotted line represents the fiducial region α < 6 wherethe signal is expected. Displayed are only events above 250 GeVsince the best integral sensitivity, around 1.6% of Crab, is obtainedfrom a Crab Nebula data sample in this energy range.

In Figure 2, the significance map for events above150 GeV in the observed sky region is shown. The sourceindependent DISP method has been used. This impliesthe rise of the energy threshold from 80 GeV to around150 GeV (see Domingo-Santamaria et al. 2005 for a de-tailed description). The significance distribution in themap is consistent with background fluctuations. In Fig-ure 2, X-ray contours from the XMM-Newton observa-tions (Churazov et al. 2003) are also shown.

The significance was calculated according to Eqn. 17 ofLi & Ma (1983) and upper limit estimation is performedusing the Rolke method (Rolke et al. 2005). The upperlimits in number of excess events are calculated with aconfidence level of 95%. For the upper limit calculation,a systematic uncertainty of 30% in the energy estima-tion and effective area calculation is taken into account.Our systematic error budget is obtained by adding upthe individual contributions in quadrature. The differentsources of systematic uncertainties are mainly related tothe differences between the real experimental conditionsand the simulated ones (see Albert et al. (2008c) for adetailed discussion on the systematic errors). The pho-ton flux upper limit is finally reconstructed for a generalγ-ray spectrum as described in Aliu et al. (2009a).

In sections 4 and 5 we will discuss the implications ofthis observation for the CR and DM annihilation inducedγ-ray flux, respectively. Using the true density profile asobtained by X-ray measurements (Churazov et al. 2003),we will be able to model the spatial characteristics of theCR induced γ-ray signal. Our simulations indicate that


RA [h]3.26 3.28 3.3 3.32 3.34 3.36 3.38 3.4

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deg

]

40.6

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41

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ican

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Fig. 2.— Significance map for events above 150 GeV in the ob-served Perseus cluster sky region. The significance distributionis consistent with background fluctuations. Black contours fromXMM-Newton observations in the X-ray band (Churazov et al.2003) are also shown. The angular extent of the outermost con-tours is approximately 0.45 deg, which corresponds to ∼ 610 kpc.

60% of the total γ-ray flux are contained within a circle ofradius r0.6 = 0.15 deg (this angular scale corresponds toa physical radius of 200 kpc). We then compare the fluxfrom within this region to the upper limits. As the char-acteristics of the considered emission region are close toa point source we use point-like upper limits. The sameconclusion is valid also for the DM annihilation signal.In this case, as explained in section 2.2, the 90% of theexpected emission is coming form the scale radius region.For Perseus, we obtained rs ∼ 0.3 deg which is somewhatextended compared to the telescope angular resolution.However, the fact that the NFW profile is very steep im-plies that the main DM emission comes from the core ofthe source that can be considered approximately point-like compared to our angular resolution.

To compute flux upper limits, we assume specific spec-tral indices that have been motivated by an astrophysicalscenario in mind (see the following sections). This “sce-nario guided” approach allows us to provide the tightestlimits on physically motivated parameters and underly-ing astrophysical models. In the next sections we willconsider flux upper limits computed using a power-lawγ-ray spectrum with spectral indexes Γ of −1.5, −2.2 and−2.5. In Table 2, the corresponding integral flux upperlimits for energies above 100 GeV are listed.

In Section 4, we will use an integral flux upper limitset above given energy thresholds in order to trace theenergy range where we can better constrain the mod-els. In Table 3 the obtained integral flux upper limits forΓ = −2.2 are shown. Note that we do not compute in-tegral upper limits above 80 GeV (as we have not showna cumulative α-plot for energies above this value). Thisis because the g/h separation for events below 100 GeVworks in a substantially different way with respect to thehigher energy events. Therefore, we analyze separatelythe events below 100 GeV and the events of higher en-ergy, with different sets of analysis cuts.

TABLE 2Integral flux upper limits above 100 GeV

Γ FUL [×10−12 cm−2 s−1]

-1.5 4.63-2.2 6.55-2.5 7.52

Notes. Integral flux upper limits are listed for a power-law γ-rayspectrum with spectral index Γ for energies above 100 GeV. Thecorresponding upper limit for the number of excess events is 186.

Finally, for completeness, in Table 4 the differentialflux upper limits for the assumed spectral indexes areshown in different energy intervals. Spectral energy den-sity (SED) upper limits can also be obtained from thosedifferential flux upper limits, as done in Section 6 dis-cussing the observation implications for the radio galaxyNGC 1275.

TABLE 3Integral flux upper limits for a power-law γ-ray

spectrum with spectral index Γ = −2.2 above a givenenergy threshold Eth.

Eth[GeV] FUL [×10−12 cm−2 s−1]

100 6.55130 6.21160 6.17200 5.49250 4.59320 3.36400 1.83500 1.39630 0.72800 0.651000 0.47

3.3. Comparison to Previous Observations

There are few existing IACT observations ofgalaxy clusters (Perkins et al. 2006; Perkins 2008;Aharonian et al. 2009a,b; Domainko et al. 2009;Galante et al. 2009; Kiuchi et al. 2009; Acciari et al.2009). In section 4.3, we will compare the limits onthe cosmic ray-to-thermal pressure obtained by otherIACTs with those derived in this work. However, thereare two observations of the Perseus galaxy cluster madeby WHIPPLE (Perkins et al. 2006) and VERITAS(Acciari et al. 2009) with which we can directly compareour upper limits.

The WHIPPLE collaboration observed the Perseusgalaxy cluster (Perkins et al. 2006) for ∼ 13 hours ob-taining an integral upper limit above 400 GeV of 4.53×10−12 cm−2 s−1 assuming a spectral index Γ = −2.1.We can compare this value with our integral upper limitabove 400 GeV of 1.83× 10−12 cm−2 s−1 with Γ = −2.2(see Table 3). Our upper limit is significantly lowerthan the WHIPPLE one; clearly, this is not a surpriseas the MAGIC telescope belongs to a new generationof IACTs. More recently, the VERITAS collaborationobserved Perseus (Acciari et al. 2009) for ∼ 8 hoursand obtained an integral upper limit above 126 GeV of


TABLE 4Differential flux upper limits

Γ [80-100] [100-160] [160-250] [250-400] [400-630] [630-1000] [1000-10000]

-1.5 130.7 23.6 12.6 4.33 0.865 0.168 0.015-2.2 144.8 25.3 13.2 4.53 0.897 0.174 0.018-2.5 150.6 25.8 13.3 4.57 0.903 0.176 0.018

Notes. Differential flux upper limits are listed in units of 10−11 cm−2 s−1 TeV−1 for a power-law γ-ray spectrum with spectral index Γin energy ranges in units of GeV.

1.27 × 10−11 cm−2 s−1 assuming Γ = −2.5. We cancompare this value with our corresponding integral up-per limit above 100 GeV of 7.52 × 10−12 cm−2 s−1 (seeTable 2). Despite the fact that the VERITAS sensitivityof about 1% of Crab Nebula (Otte et al. 2009) is betterthan the MAGIC one, our upper limit is slightly lowerthan that found by Acciari et al. (2009) as expected fromthe significant difference in observation time.

4. COSMIC RAY INDUCED EMISSION

We use the upper limits on the integrated flux (Table 3)to put constraints on the CR-to-thermal pressure distri-bution and pursue three different approaches. (1) Weperform high-resolution hydrodynamical simulations ofcluster formation and evolution in a cosmological frame-work that include CR physics to predict the γ-ray emis-sion and to obtain limits on the CR-to-thermal pressure.(2) Following Pfrommer & Enßlin (2004a), we use a sim-plified approach that assumes a constant CR-to-thermalenergy density, a power-law spectrum in momentum, andcompare the resulting CR-to-thermal pressure limits tothose obtained by other IACT observations. (3) We usethe observed luminosity of the radio-mini halo to placea lower limit on the expected γ-ray flux in the hadronicmodel of the radio mini-halo. This translates into a min-imum CR pressure that is crucial for disentangling theemission mechanism in the radio and provides a clearprediction for the expected γ-ray flux.

Before doing so, we detail our cosmological simulationsthat we base our main analysis on. To this end we in-vestigated the spatial and spectral properties of γ-rayemission in these simulations and refer the reader to thetheory papers for further details (Pfrommer et al. 2008;Pfrommer 2008, Pinzke & Pfrommer, in prep.).

4.1. Cosmological Simulations

Simulations were performed using the “concordance”cosmological cold DM model with a cosmological con-stant (ΛCDM) motivated by First Year cosmological con-straints of WMAP. The cosmological parameters of ourmodel are: Ωm = Ωdm+Ωb = 0.3, Ωb = 0.039, ΩΛ = 0.7,h = 0.7, n = 1, and σ8 = 0.9. Here, Ωm denotes the totalmatter density in units of the critical density for geomet-rical closure today, ρcrit(z = 0) = 3H2

0/(8πG). Ωb andΩΛ denote the densities of baryons and the cosmologicalconstant at the present day. The spectral index of theprimordial power-spectrum is denoted by n, and σ8 isthe rms linear mass fluctuation within a sphere of radius8 h−1Mpc extrapolated to z = 0.

Our simulations were carried out with an updatedand extended version of the distributed-memory par-allel TreeSPH code GADGET-2 (Springel et al. 2001;Springel 2005). Gravitational forces were computed us-

ing a combination of particle-mesh and tree algorithms.Hydrodynamic forces were computed with a variant ofthe smoothed particle hydrodynamics (SPH) algorithmthat conserves energy and entropy where appropriate,i.e. outside of shocked regions (Springel & Hernquist2002). We have performed high-resolution hydrodynamicsimulations of a sample of galaxy clusters that span overone and a half decades in mass and show a variety ofdynamical states ranging from relaxed cool core clus-ters to violent merging clusters. Our simulated clustershave originally been selected from a low-resolution dark-matter-only simulation (Yoshida et al. 2001). Usingthe ‘zoomed initial conditions’ technique (Katz & White1993), the clusters have been re-simulated with highermass and force resolution. In high-resolution regions, theDM particles had masses of mdm = 1.61 × 109 h−1

70 M⊙

and SPH particles mgas = 2.4×108 h−170 M⊙ so each indi-

vidual cluster is resolved by 8× 104 to 4× 106 particles,depending on its final mass. The SPH densities werecomputed from 48 neighbours, allowing the SPH smooth-ing length to drop at most to half of the value of thegravitational softening length of the gas particles. Thischoice of the SPH smoothing length leads to our mini-mum gas resolution of approximately 1.1× 1010 h−1

70 M⊙.For the initial redshift we chose 1 + zinit = 60. Thegravitational force softening was of a spline form (e.g.Hernquist & Katz 1989) with a Plummer equivalent soft-ening length that is assumed to have a constant comovingscale down to z = 5, and a constant value of 7 h−1

70 kpc inphysical units at later epochs.

These simulations included radiative hydrodynamics,star formation, supernova feedback and followed CRphysics using a novel formulation that followed the mostimportant injection and loss processes self-consistentlywhile accounting for the CR pressure in the equationsof motion (Pfrommer et al. 2006; Enßlin et al. 2007;Jubelgas et al. 2008). To obtain predictions of the GeV-TeV γ-ray emission from clusters, we used an updatedversion of the CR physics in our code. It is capable offollowing the spectral evolution of the CR distributionfunction by tracking multiple CR populations in eachgaseous fluid element; each of these populations is de-scribed by an amplitude, a low-momentum cut-off, anda characteristic power-law distribution in particle mo-mentum with a distinctive slope that is determined bythe acceleration process at formation shocks or super-nova remnants (Pinzke & Pfrommer, in prep.). Adia-batic CR transport processes such as compression andrarefaction, and a number of physical source and sinkterms which modify the CR pressure of each particleare modeled. The most important sources consideredare diffusive shock acceleration at cosmological structure


formation shocks and optionally injection by supernovaewhile the primary sinks are thermalization by Coulombinteractions, and catastrophic losses by hadronic inter-actions. We note that the overall normalization of theCR distribution scales with the maximum accelerationefficiency at structure formation shock waves. Followingrecent observations at supernova remnants (Helder et al.2009) as well as theoretical studies (Kang & Jones 2005),we adopt a realistic value of this parameter and assumethat 50% of the dissipated energy at strong shocks is in-jected into CRs while this efficiency rapidly decreases forweaker shocks (Enßlin et al. 2007).

We computed the γ-ray emission signal and found thatit obeys a universal spectrum and spatial distribution(Pinzke & Pfrommer, in prep.). This is inherited fromthe universal concave spectrum of CRs in galaxy clustersthat is caused by the functional form and redshift de-pendence of the Mach number distribution of structureformation shocks that are responsible for the accelerationof CRs (Pfrommer et al. 2006). The CR distribution hasa spectral index of Γ ≃ −2.5 at GeV energies and expe-riences a flattening towards higher energies resulting inΓ ≃ −2.2 at energies above a few TeV. Hence, the result-ing γ-ray spectrum from CR induced pion-decay showsa characteristic spectral index of Γ ≃ −2.2 in the energyregime ranging from 100 GeV to TeV. The spatial dis-tribution of the CR number density is mainly governedby adiabatic transport processes (Pfrommer et al. 2007)and similarly attains an approximate universal shape rel-ative to that of the gas density. These findings allow usto reliably model the CR signal from nearby galaxy clus-ters using their true density profiles as obtained by X-raymeasurements that we map onto our simulated densityprofiles.

In addition to CR protons, we modeled relativistic elec-trons that have been accelerated at cosmological struc-ture formation shocks (primary CR electrons) and thosethat have been produced in hadronic interactions ofCRs with ambient gas protons (secondary CR electrons).Both populations of CR electrons contribute to the γ-rayemission through Compton up-scattering photons fromthe cosmic microwave background as well as the cumula-tive star light from galaxies. It turns out that the pion-decay emission of the cluster dominates over the con-tribution from both inverse Compton components – inparticular for relaxed systems (Pfrommer 2008).

In our optimistic CR model (radiative physics withgalaxies), we calculated the cluster total γ-ray flux withina given solid angle. In contrast, we cut the emission fromindividual galaxies and compact galactic-sized objects inour more conservative model (radiative physics withoutgalaxies). In short, the ICM is a multiphase medium con-sisting of a hot phase which attained its entropy throughstructure formation shock waves dissipating gravitationalenergy associated with hierarchical clustering into ther-mal energy. The dense, cold phase consists of the trueinterstellar medium (ISM) within galaxies and at thecluster center as well as the ram-pressure stripped ISM.These cold dense gas clumps dissociate incompletely inthe ICM due to insufficient numerical resolution as wellas so far incompletely understood physical properties ofthe cluster plasma. All of these phases contribute to theγ-ray emission from a cluster. To assess the bias asso-ciated with this issue, we performed our analysis with

100 1000E [GeV]

10-14

10-13

10-12

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Fγ (

>E

) [

ph s

-1 c

m-2

]

radiative physics w/o gal. x 2

radiative physics w/ gal.

radiative physics w/o gal.

Fγ, min (B0 = 10 µG, εB < εth / 3)

Fig. 3.— Integral flux upper limits (this work, Table 3) are com-pared with simulated integrated spectra of the γ-ray emission fromdecaying neutral pions that result from hadronic CR interactionswith the ambient gas in the Perseus cluster. Our conservativemodel without galaxies (solid) is contrasted to our model withgalaxies (dashed). We scaled our conservative model with a factorof two so that it is just consistent with the upper limits obtained inthis work (dotted). In our simulations, we assume an observation-ally motivated large value for the maximum CR energy injectionefficiency at structure formation shocks and convert half of thedissipated energy to CRs at strong shocks. Smaller values wouldimply smaller γ-ray fluxes. Additionally shown are minimum γ-rayflux estimates for the hadronic model of the radio mini-halo of thePerseus cluster (dash-dotted with minimum flux arrows, see maintext for details). Note that a non-detection of γ-rays at this levelseriously challenges the hadronic model.

both limiting cases bracketing the realistic case.In Figure 3, we compare the integral flux upper lim-

its obtained in this work (see Table 3) with the sim-ulated flux that is emitted within a circle of radiusr0.6 = 0.15 deg for our two models, with and withoutgalaxies. The upper limits are a factor of two larger thanour conservative model and a factor of 1.5 larger thanour most optimistic model predictions implying consis-tency with our cosmological cluster simulations. We notehowever that our simulated flux represents a theoreticalupper limit of the expected γ-ray flux from structureformation CRs; lowering the maximum acceleration effi-ciency would decrease the CR number density as well asthe resulting γ-ray emission.

4.2. Constraints on the Cosmic Ray Pressure

In Figure 4, we show the simulated γ-ray surfacebrightness map of a cooling flow cluster of mass simi-lar to Perseus. As the CR induced γ-ray flux is a radi-ally declining function so is the CR pressure. A quan-tity that is of great theoretical interest is the CR pres-sure relative to the thermal pressure, XCR = PCR/Pth

as it directly assesses the CR bias of hydrostatic clustermasses since the CR pressure enters in the equation ofmotion. On the right-hand side of Figure 4, we show theprofile of the CR-to-thermal pressure (volume-weighted)of this simulated cluster. Moving from the peripherytowards the center, this quantity is a steadily declin-ing function until we approach the cooling flow regionaround the cD galaxy of this cluster (similar to NGC1275) where the CR pressure rises dramatically rela-tive to that of the thermal gas which cools on a shorttime scale (Pfrommer et al. 2006). The volume average


10-12

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PC

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cosmological shocks

cosmological shocks and by SNRs

Fig. 4.— Left: simulated γ-ray emission at energies E > 100 GeV from a cluster that has twice the mass as Perseus (using the simulationof the cooling flow cluster g51 from Pfrommer et al. 2008). We show the sum of pion-decay induced γ-rays (which dominates the centraland the total flux) and the IC emission of CR electrons accelerated at formation shocks and by hadronic CR interactions. Right: profileof the CR-to-thermal pressure (volume-weighted) of this cluster. We contrast a simulation where we only accelerate CRs at structureformation shocks of the entire cosmic history (solid) with one where we additionally account for CRs that are injected through supernovafeedback within the star forming regions in our simulation (dashed).

is 〈XCR〉 = 〈PCR〉/〈Pth〉 = 0.02, dominated by the re-gion around the virial radius, while the ratio of CR-to-thermal energy is given by ECR/Eth = 0.0322. Perseushas a smaller mass and a corresponding temperature thatis only half of that of our simulated cooling flow cluster.Noting that XCR ∝ 1/Pth ∝ 1/kT ,3 we expect thesevalues to be a factor of ≃ 2 larger in Perseus, yielding〈XCR〉 ≃ 0.04 for the entire cluster and 〈XCR〉 ≃ 0.02 forthe core region that we probe with the present observa-tion.

We have to scale our conservative model prediction bya factor of ∼ 2 to reach the upper limits (cf. Figure 3)which implies that this work constrains the relative pres-sure contained in CRs to < 8% for the entire cluster andto < 4% for the cluster core region. The presence ofdense gas clumps potentially biases the simulated γ-rayflux high and hence the inferred limits on XCR low. An-other source of bias could be unresolved point sourcesinside the cluster such as AGN. In the presented simu-lation of the cool core cluster g51, the bias due to sub-clumps amounts to a factor of 1.5 but it could be as highas 2.4 which is the mean difference between our conser-vative and optimistic model across our scaling relations.We note however that the latter case is already excludedby our upper limits provided the maximum shock accel-eration efficiency is indeed as high as 50%. While thereare indications from supernova remnant observations ofone rim region (Helder et al. 2009) as well as theoreticalstudies (Kang & Jones 2005) that support such high ef-ficiencies, to date it is not clear whether these efficiencies

2 Note that for a CR population in clusters that have beenaccelerated in structure formation shocks the relativistic limitECR/Eth = 2〈PCR〉/〈Pth〉 is not applicable since the CR pressureis dominated by the trans-relativistic regime. This implies a some-what harder equation of state for the CRs with a larger adiabaticindex and yields the relation ECR/Eth = 1.6〈PCR〉/〈Pth〉.

3 This relation should only hold for regions with long thermalcooling times compared to the dynamical time scale. In particularit breaks down towards the center of a cooling flow cluster wherethe thermal gas cools on a shorter time scale such that the formingcooling flow causes adiabatic contraction of the CR population.

apply in an average sense to strong collisionless shocks orwhether they are realized for structure formation shocksat higher redshifts. Improving the sensitivity of the pre-sented type of observations will help in answering theseprofound plasma astrophysics questions.

In Figure 4, we additionally compare a simulationwhere we only accelerate CRs at structure formationshocks with one where we additionally account for CRsthat are injected through supernova feedback within thestar forming regions in our simulation. Outside the cDgalaxy, there is no significant difference visible which sug-gests that the CRs injected into the ICM by supernovadriven winds are negligible compared with those acceler-ated by structure formation shocks. While this is partlyan artifact of our simulations that neglect CR diffusion,we expect this behavior due to the adiabatic losses thatCRs suffer as they expand from their compact galacticISM into the dilute ICM. Assuming a conservative valuefor the density contrast of ∆ = 10−3, the CR pressure isdiluted by PCR ∼ ∆4/3 PCR,ISM ∼ 10−4 PCR,ISM.

4.3. Simplified Approach and Comparison to PreviousResults

As anticipated in section 3.3, there are few existingIACT observations of galaxy clusters; some of whichderived limits on the CR-to-thermal pressure containedin clusters, in particular the WHIPPLE observation ofthe Perseus cluster (Perkins et al. 2006) and the HESSobservations of the Abell 85 (Aharonian et al. 2009a;Domainko et al. 2009) and Coma (Aharonian et al.2009b) clusters. These work used simplifying assump-tions about the spectral and spatial distribution of CRs.They typically assumed a single CR power-law distribu-tion with a spectral index of Γ = −2.1 (that providesoptimistic limits on the CR-to-thermal pressure) and as-sumed that the CR energy density is a constant fractionof the thermal energy density throughout the entire clus-ter. Based on these two assumptions, WHIPPLE andHESS found in Perseus and Abell 85 ECR/Eth < 0.08,respectively, while HESS found ECR/Eth < 0.2 in Coma.


To facilitate comparison with these earlier works,we repeated the data analysis with a spectral indexΓ = −2.1 to obtain an integral upper limit FUL(>100 GeV) = 6.22 × 10−12 cm−2 s−1. Following the for-malism of Pfrommer & Enßlin (2004a), we compute theγ-ray flux of a CR population with Γ = −2.1 within acircular region of radius r0.6 = 0.15 deg or equivalently200 kpc. In our isobaric model of CRs we assume thatthe CR pressure scales exactly as the thermal pressureand constrain ECR/Eth < 0.053 which corresponds toan averaged relative pressure of 〈XCR〉 = 〈PCR〉/〈Pth〉 =0.033. This would be the most stringent upper limit onthe CR energy in a galaxy clusters.

In our adiabatic model of CRs we account for the cen-trally enhanced CR number density due to adiabaticcontraction during the formation of the cooling flow(Pfrommer & Enßlin 2004a). We assume that the CRppopulation scaled originally as the thermal populationbut was compressed adiabatically during the formation ofthe cooling flow without relaxing afterwards (we adoptedtemperature and density proles given by Churazov et al.2003). In this model, we obtain an enhanced γ-ray fluxlevel for virtually the same volume averaged CR pressureor vice versa for a given flux limit, hence we can put atighter constraint on the averaged CR pressure. We con-strain ECR/Eth < 0.03 which corresponds to an averagedrelative pressure of 〈XCR〉 = 〈PCR〉/〈Pth〉 = 0.019.

How can we reconcile these tighter limits with our sim-ulation based slightly weaker limit? We have to compareour simulated CR profile to a CR distribution that doesnot show any enhancement relative to the gas density. Inthe central region for r < 200 kpc, we derive an adiabaticcompression factor of 1.7 that matches that in our sim-plified approach – suggesting that our simple adiabaticmodel captures the underlying physics quite realistically.Secondly, we have then to relate the pressure of a power-law spectrum with Γ = 2.1 to our simulated concavespectrum. Noting that the γ-rays at 100 GeV are pro-duced by CR protons at ≃ 1 TeV, we normalize bothspectra at 1 TeV and find that the simulated spectrumcontains a larger pressure by a factor of 1.8. This factorbrings the limit of our simplified adiabatic model intoagreement with our simulation-based limit of the rela-tive CR pressure 〈XCR〉 < 4% for the cluster core region.Finally, since γ-ray observations are only sensitive to thecluster core regions (the emission is expected to peak inthe center due to the high target gas densities), they can-not constrain the average CR-to-thermal pressure withinthe entire cluster. Hence we have to use cosmologicalcluster simulations to address how much CR-to-thermalpressure could be additionally hidden in the peripheralcluster regions.

4.4. Minimum γ-ray Flux

For clusters that host radio (mini-)halos we are able toderive a minimum γ-ray flux in the hadronic model of CRinteractions. The idea is based on the fact that a steadystate distribution of CR electrons loses all its energy tosynchrotron radiation for strong magnetic fields (B ≫BCMB ≃ 3.2µG) so that the ratio of γ-ray to synchrotronflux becomes independent of the spatial distribution ofCRs and thermal gas (Pfrommer 2008). This can beeasily seen by considering the pion decay induced γ-rayluminosity Lγ and the synchrotron luminosity Lν of a

steady state distribution of CR electrons that has beengenerated by hadronic CR interactions,

Lγ =Aγ

∫dV nCRngas, (1)

Lν =Aν

∫dV nCRngas

ε(αν+1)/2B

εCMB + εB(2)

≃Aν

∫dV nCRngas for εB ≫ εCMB. (3)

Here Aγ and Aν are dimensional constants thatdepend on the hadronic physics of the interaction(Pfrommer et al. 2008; Pfrommer 2008) and αν ≃ 1 isthe observed synchrotron spectral index. Hence we canderive a minimum γ-ray flux in the hadronic model

Fγ,min =Aγ

Aν

Lν

4πD2lum

, (4)

where Lν is the observed luminosity of the radio mini-halo and Dlum denotes the luminosity distance to therespective cluster. Lowering the magnetic field wouldrequire an increase in the energy density of CR electronsto reproduce the observed synchrotron luminosity andthus increase the associated γ-ray flux.

Using the values of Table 1, we obtain a minimum γ-ray flux in the hadronic model of the radio mini-halo ofFγ,min(> 100 GeV) = 6 × 10−13cm−2 s−1, assuming apower-law CR distribution with Γ >

∼ − 2.3. This lowerlimit is independent of the spatial distribution of CRsand magnetic fields. We note that the spectral index isconsistent with the radio data4. It turns out that therequirement of strong magnetic fields violates the energyconditions in clusters as it implies a magnetic energy den-sity that is larger than the thermal energy density – inparticular at the peripheral cluster regions. The min-imum γ-ray flux condition requires a constant (large)magnetic field strength throughout the cluster while thethermal energy density is decreasing by more than a fac-tor of 100 from its central value. This would imply thatthe magnetic field eventually dominates the energy den-sity at the virial regions – a behavior that is unstable asit is subject to Parker-like buoyancy instabilities. Ad-ditionally, such a configuration would be impossible toachieve in first place as the magnetic energy density typ-ically saturates at a fixed fraction of the turbulent energydensity which itself is only a small fraction of the thermalenergy density in clusters (Schuecker et al. 2004). Hencethese considerations call for lowering the assumed clustermagnetic fields which should strengthen the lower limitson the γ-ray flux considerably – however at the expensethat these limits inherit a weak dependence on the spatialdistribution of magnetic fields and CRs.

Estimates of magnetic fields from Faraday rotationmeasures (RMs) have undergone a revision in the last fewyears with more recent estimates typically in the order ofa few µG with slightly higher values up to 10 µG in cool-ing flow clusters (Clarke 2004; Enßlin & Vogt 2006). For

4 The CR protons responsible for the GHz radio emitting elec-trons are ∼ 100 times less energetic than those CR protons that areresponsible for the TeV γ-ray emission. This is consistent with theconcave curvature found in the CR spectrum by Pinzke & Pfrom-mer (in prep).


the Perseus radio mini-halo, Faraday RMs are availableonly on very small scales (Taylor et al. 2006), i.e. few tens

of pc. RM estimates are of the order of ∼ 7000 rad m2

leading to magnetic field values of ∼ 25µG assumingthe Faraday screen is localized in the ICM. This, how-ever, appears to be unlikely as variations of 10% in theRM are observed on pc-scales (Taylor et al. 2002), whileICM magnetic fields are expected to be ordered on sig-nificantly larger scales of a few kpc (Taylor et al. 2006;Vogt & Enßlin 2005; Enßlin & Vogt 2006). Applicationof the classical minimum-energy argument to the Perseusradio mini-halo data leads to estimates for the centralmagnetic field strength of B0 ≃ 7µG or even B0 ≃ 9µGfor the more appropriate hadronic minimum-energy ar-gument (Pfrommer & Enßlin 2004b).

We select a cooling flow cluster of our sample that ismorphologically similar to Perseus with a mass M200 ≃1015 M⊙ (the simulated cluster g51 of Pfrommer et al.2008). We adopt a conservative choice for the centralmagnetic field strength of ∼ 10µG and parametrize themagnetic energy density in terms of the thermal energydensity by εB ∝ ε0.5

th which ensures εB < εth/3 in theentire cluster. This allows us to strengthen the physi-cally motivated lower limit to Fγ,phys.min(> 100 GeV) =8.5 × 10−13 cm−2 s−1 as shown by the dash-dotted linein Figure 3. In the hadronic model, this minimum γ-ray flux implies a minimum CR pressure relative to thethermal pressure. Figure 3 shows that the minimumflux Fγ,phys.min is a factor of 3.6 lower than the sim-ulated flux for Perseus in our conservative model. Asseen in Sect. 4.2, this model corresponds to a relativeCR pressure of 〈XCR〉 = 〈PCR〉/〈Pth〉 = 0.04 wherethe averages represent volume averages across the entirecluster. Hence we obtain a minimum relative CR pres-sure, 〈XCR, min〉 = 〈PCR, min〉/〈Pth〉/3.6 = 0.01. Thisminimum CR pressure corresponds to a minimum to-tal CR energy of ECR min = ECR min/Eth × Eth =1.6 〈XCR, min〉 × Eth = 9 × 1061 erg where we integratedthe temperature and density profiles from X-ray observa-tions (Churazov et al. 2003) to obtain the total thermalenergy of Eth = 5.7×1063 erg. These considerations showthe huge potential of combining future TeV γ-ray and ra-dio observations in constraining physical models of thenon-thermal cluster emission and to obtain importantinsights in the average distribution of cluster magneticfields.

5. DARK MATTER ANNIHILATION

As discussed in Section 2.2, the expected DM annihi-lation flux is proportional to the product of a factor thatencloses all the particle physics and a second one thataccounts for all the involved astrophysics. Therefore, inorder to obtain an estimate of the annihilation flux, weneed to choose a particular particle physics model (thatwas not needed in Section 2.2, since only a comparativestudy was done there) in addition to the modeling of theDM distribution. Although the uncertainties in the par-ticle physics factor fSUSY are very large and spread oversome orders of magnitude (see e.g. Albert et al. 2008d),it is common to use the most optimistic value for a givenenergy threshold of the telescope. This factor just actsas a rescaling factor in the total flux, so we could changeto other particle physics model simply by rescaling for its

new value. Let us assume fSUSY = 10−32 GeV−2 cm3 s−1

above 100 GeV, which corresponds to one of the most op-timistic allowed scenarios at the energies of interest here(Sanchez-Conde et al. 2007), with the neutralino as DMparticle. Then, taking a value of 1.4 × 1016 GeV2 cm−5

for the integrated astrophysical factor inside rs (as givenin Section 2.2), we obtain a maximum DM annihila-tion flux of ∼ 1.4 × 10−16 cm−2 s−1 for energies above100 GeV. The comparison with the derived upper limitsfrom our observations are not very constraining. Assum-ing a generic DM annihilation spectrum without cutoffand spectral index -1.5 as a good approximation (e.g.Albert et al. 2008d; Aliu et al. 2009a), it can be seenfrom Table 2 that we need a boost in flux in the or-der of 104 to reach the predicted DM annihilation fluxvalues, since FUL (>100 GeV) = 4.63× 10−12 cm−2 s−1.

This boost factor could come from different uncertain-ties that may enhance the annihilation γ-ray flux notablyand that were not taken into account in the above cal-culation. One of them, the presence of substructures,could play a crucial role for Perseus, as explained in sec-tion 2.2. Although still uncertain, its effect could en-hance the expected annihilation flux by more than a fac-tor of 10 for Perseus-size halos according to Kuhlen et al.(2008). More recent work have shown that the expectedboost factors could be as high as 200 (Springel et al.2008a,b). However, with IACTs it is challenging tomake use of these large boost factors as their contribu-tion is expected to be more important on large angularscales comparable to the virial extend of the cluster. De-tailed modeling of the substructures is needed in orderto correctly evaluate their impact on the Perseus DMinduced signal. Finally, also recently proposed mecha-nisms in the particle physics side, such as the InternalBremsstrahlung (Bringmann et al. 2008) and the Som-merfeld effect (Lattanzi & Silk 2009; Pinzke et al. 2009),could enhance the DM annihilation flux by more thanone order of magnitude for some particle physics models.

It is worth noting that the result obtained here for theboost factor needed in order to probe the predicted DMannihilation flux is comparable with previous observa-tions of the Milky Way satellite galaxies (Albert et al.2008d; Aliu et al. 2009a).

6. THE NGC 1275 EMISSION

The SED of the NGC 1275 core is shown in Figure 5.The radio and optical data represented with gray filledcircles (Abdo et al. 2009) have been obtained with lowresolution and thus include a large contribution from thelarge scale regions of the jet (radio) and from the hostgalaxy (optical). In the following we model the datacorresponding to the core emission. This is different towhat was done by Abdo et al. (2009) who used the lowresolution data in their models. We calculated our upperlimit, shown in Figure 5 as a red arrow, assuming that thespectrum in the MAGIC energy band is a power law withspectral index Γ = −2.5, as indicated by the extrapola-tion of the last points of the Fermi-LAT spectrum. Note,however, that the level of the differential upper limits isonly weakly dependent on the assumed spectral index(see Table 4).

The data clearly show a double peak SED. The radio-optical data suggest a peak of the emission in the IRband, similarly to the case of other γ-ray emitting ra-


Fig. 5.— SED of the NGC 1275 core (lower two lines and data)and that of the well known blazar S5 0716+714 for comparison (up-per line and data). Gray filled circles are data points in the radioand optical bands from Abdo et al. (2009). Filled black squaresshow, instead, the radio (VLBI, Taylor et al. 1996) and the opti-cal emission (HST, Chiaberge et al. 1999) of the core alone. Thesoft X-ray bow tie is from Chandra (Balmaverde et al. 2006), whilethe red filled circles represent the Fermi-LAT spectrum taken fromAbdo et al. (2009). The red arrow shows the MAGIC upper limitbetween 80 and 100 GeV. The lower blue and red lines show theemission from the spine and the layer of the structured jet. Theupper blue lines is the SED of the spine as observed at a smallangle (see text for details): for comparison we report historicaldata of S5 0716+714 (data from Tavecchio & Ghisellini 2009 andreferences therein).

dio galaxies (Tavecchio & Ghisellini 2008, 2009). Highenergy data constrain the peak frequency of the sec-ond component at about 100 MeV. As discussed inTavecchio & Ghisellini (2008), in these cases a one-zonesynchrotron self-Compton (SSC) model for the entireemission is implausible, since the large separation in fre-quency between the two peaks would require extremelylarge values of the Doppler factor:

δ ≃ 258 Ls,42.8L−1/2C,43.4 ν−2

s,13.5 νC,23 R−116 (5)

where Ls = νsL(νs), LC = νcL(νc), νs and νC are thesynchrotron and SSC peak luminosities and frequenciesand R is the size of the emitting region. Here Q = 10xQx,in cgs units and we use the values derived for NGC 1275.In this estimate we assume the typical size of the emis-sion regions derived in blazars, R = 1016 cm, though theFermi-LAT data does not allow to constrain the radiusof the emission region using the variability (Abdo et al.2009). Such large values of the Doppler factor are ratherunlikely. Typical values found modeling the SED ofblazars are around 10 − 20 (e.g. Celotti & Ghisellini2008), with few extreme TeV BL Lacs requiring largervalues during exceptional states (δ ∼ 50 − 100, e.g.Begelman et al. 2008; Ghisellini & Tavecchio 2008). Ar-guments based on the observation of superluminal mo-tions at VLBI scales (e.g. Kellermann et al. 2004) and on

the unification of blazars with radio galaxies also requirevalues around 10 (e.g. Urry & Padovani 1995).

The most direct way to overcome the problem posedby the large Doppler factor is to assume two emissionregions, as in the spine-layer model of Ghisellini et al.(2005). In this scenario the jet is assumed to be struc-tured, with a fast inner region (the spine) surrounded bya slower sheet (the layer). Both components produce syn-chrotron and inverse Compton radiation and they are inradiative interplay: the synchrotron radiation from onecomponent is seen boosted (by the relative velocity) bythe other one and thus the IC emission of both regionsis enhanced with respect to the standard SSC. In radiogalaxies, in which the jet is observed at relatively largeangles, the emission is expected to be dominated by thelayer, which, due to the lower bulk Lorentz factor, hasa larger emission cone. At smaller angle, instead, theemission is dominated by the spine, as in blazars.

We reproduce the SED with the spine-layer model.The orange line in Figure 5 shows the emission from thelayer, while the spine produces the emission shown by theblue bottom line. The spine is assumed to be a cylinderof radius R = 1.5 × 1016 cm, height HS = 1.5 × 1016 cm(as measured in the spine frame) and in motion withbulk Lorentz factor ΓS = 15. The layer is modeled as anhollow cylinder with internal radius R, external radiusR2 = 1.2 × R, height HL = 4 × 1016 cm (as measured inthe frame of the layer) and bulk Lorentz factor ΓL = 3.Each region contains tangled magnetic field with inten-sity BS = 2.5 G and BL = 1 G and it is filled by relativis-tic electrons assumed to follow a (purely phenomenolog-ical) smoothed broken power-law distribution extendingfrom γmin to γmax and with indices n1, n2 below andabove the break at γb. For the spine we use γmin = 40,γb = 2×104, γmax = 105, n1 = 2, n2 = 3.5. For the layerγmin = 10, γb = 4× 103, γmax = 105, n1 = 2.4, n2 = 4.2.The normalization of these distributions is calculated as-suming that the systems produce an assumed (bolomet-ric) synchrotron luminosity L′

syn,S = 1042 erg s−1 and

L′syn,L = 2.7× 1041 erg s−1 (as measured in the local co-

moving frame of the spine and layer, respectively), whichis an input parameter of the model. As said above, theseed photons for the IC scattering are not only those pro-duced locally in the spine (layer), but we also considerthe photons produced in the layer (spine). We assumea viewing angle of θ = 15 deg. As discussed above, thesame jet observed at smaller angle would be dominatedby the emission from the spine and we expect that itsSED resembles those of typical blazars. We show theSED of the jet when observed at angle of 4.5 degree(blue upper line in Figure 5). The SED is dominatedby the emission of the spine. For comparison we reporthistorical data for the well known blazar S5 0716+714(data from Tavecchio & Ghisellini 2009 and referencestherein).

Note that, as observed, the model naturally predicts avery rapid decrease of the emission level above 10 GeV,due to the decreasing efficiency of the IC scattering inthe Klein-Nishina regime. The position of this breakis tightly constrained by the Fermi-LAT spectrum andMAGIC upper limit. In our model, this is critically de-pendent on the value of the frequency of the target pho-tons for the IC scattering that in the spine-layer scenario


are mainly those coming from the spine (and scatteredby the electrons in the layer). Therefore, the determina-tion of the cut-off frequency between the Fermi-LAT andthe MAGIC band allows us to infer the peak frequencyof the synchrotron component of the spine. For instance,assuming that the peak of the spine is at IR frequen-cies or below (using for the layer the same parametersadopted above), we predict a flux in the MAGIC bandabove the measured upper limit. This argument allowsus to fix the synchrotron peak of the spine at optical-UVfrequencies. This, in turn, assures that the beamed coun-terpart of NGC 1275 is an intermediate BL Lac object,as the chosen S5 0716+714. In conclusion, the knowledgeof the upper limit at the low energy end of the MAGICband offers us the important possibility to have indepen-dent limits on the characteristics of the emission of the(otherwise invisible) spine and thus to constrain the kindof beamed counterpart of this radio galaxy. Future ob-servations can confirm or rule-out our interpretation. Inparticular, the detection of photons above ∼ 100 GeVwould be challenging for the scenario depicted here, re-quiring major changes of the emission properties of thespine.

7. CONCLUSIONS

The Perseus cluster was observed by MAGIC duringNovember and December 2008 resulting in 24.4 hours ef-fective observation time of very high data quality. Nosignificant excess of γ-ray was detected beyond the en-ergy threshold of 80 GeV.

Using simplified assumptions (power-law CR spectra,constant ratio of CR-to-thermal energy density) thathave been adopted in earlier work, we obtain a limiton the CR energy of ECR/Eth < 5%. This limit couldbe tightened furthermore by considering an adiabaticallycontracted CR population during the formation of thecooling flow yielding ECR/Eth < 3%. This would be themost stringent constraint on the CR energy using γ-rayobservations to date. Using cosmological cluster simula-tions, it turns out, that these assumptions are not ful-filled for CR populations that have been accelerated bystructure formation shocks: while the adiabatic modelseems to match the simulated CR profiles towards thecenter very well, the expected ratio of CR-to-thermalpressure is increasing towards the peripheral cluster re-gions causing the volume averaged pressure across theentire cluster to increase by a factor of two. In additionthe CR spectral distribution shows a concave curvaturewith a spectrum that flattens towards high energies witha spectral index of Γ ≃ −2.2 in the TeV regime. Thisimplies that the CR pressure is enhanced by an addi-tional factor of almost two. Using our simulated flux weobtained an upper limit on the CR-to-thermal pressureaveraged across the entire cluster volume of 〈XCR〉 < 8%and < 4% for the cluster core region. This corresponds toan upper limit on the CR energy of ECR/Eth < 13% and< 6.5%, respectively. We note that this is the first workwhere results from cosmological simulations and obser-vational data analysis are combined. This demonstratesthe need for cosmological simulations in order to morereliably predict CR spectra which provides a safeguardagainst too simplified and optimistic models which thenlead to limits that are too tight.

The upper limits resulting from the data analysis are

a factor of ≃ 2 larger than our conservative model pre-diction for the CR induced γ-ray emission and hence inagreement with our cosmological cluster simulations. Fu-ture more sensitive measurements will be able to putinteresting constraints on the maximum shock acceler-ation efficiency. Using minimum γ-ray flux arguments,we show that improving the sensitivity of this observa-tion by a factor of about seven will enable us to finallycritically test the hadronic model for the Perseus radiomini halo: a non-detection of γ-ray emission at this levelimplies cosmic rays fluxes that are too small to produceenough electrons through hadronic interactions with theambient gas protons to explain the observed synchrotronemission.

As DM dominates the cluster mass, significant γ-rayemission resulting from its annihilation is also expected.With the assumed particle physics model, one of the mostoptimistic allowed scenarios (Sanchez-Conde et al. 2007)with the neutralino as DM particle, the boost factor forthe typically expected DM annihilation induced emis-sion is constrained to < 104. Note that for this estima-tion we neglected possible contributions from InternalBremsstrahlung, Sommerfeld enhancement as well as en-hancement factors due to substructures.

The upper limits obtained for the NGC 1275 emissionare consistent with the recent detection by the Fermi-LAT satellite. In this case a one-zone SSC model forthe entire emission is implausible, since the large sepa-ration in frequency between the two peaks would requireextremely large values of the Doppler factor for the jet(Tavecchio & Ghisellini 2008). The most direct way toovercome this problem is to assume two emission regions,as in the spine-layer model (Ghisellini et al. 2005) whichexplains the radio galaxy emission.

While no galaxy cluster has been detected in γ-rays upto now, our estimations indicate that Perseus is amongthe most promising clusters to be detected by IACTs.Using the newly inaugurated MAGIC second telescopeand operating the telescopes in stereo mode (Colin et al.2009), a total observation time of about 150 hours maygive us a chance to detect the CR induced γ-ray emissionor to definitively probe the validity of the hadronic modelof radio (mini-)halos. As the emission of NGC 1275dominates the accessible energy range of the Fermi-LATsatellite, it could potentially hinder the satellite from de-tecting the CR as well as the DM induced γ-ray emis-sion in this cluster. Similar problems might arise in otherclusters. Therefore, the IACTs will play a crucial role inthe quest for γ-ray emission from galaxy clusters.

We would like to thank the anonymous referee forvaluable comments. We would like to thank VolkerSpringel for the important work on cosmic ray imple-mentation into the GADGET code and comments on thepaper. We would also like to thank Yoel Rephaeli for theuseful comments on the paper and Eugene Churazov forproviding us XMM-Newton X-ray contours. We wouldlike to thank the Instituto de Astrofisica de Canariasfor the excellent working conditions at the Observatoriodel Roque de los Muchachos in La Palma. The supportof the German BMBF and MPG, the Italian INFNand Spanish MICINN is gratefully acknowledged. Thiswork was also supported by ETH Research Grant TH


34/043, by the Polish MNiSzW Grant N N203 390834,by the YIP of the Helmholtz Gemeinschaft, and bygrant DO02-353 of the the Bulgarian National Science

Fund.

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