Simulating large-scale structure formation with magnetic fields

0.66 MB·English

by  Klaus Dolag

Astron.Nachr./ANxxx(xxxx)x,xxx–xxx
Simulating large-scale structure formation with magnetic fields
KLAUS DOLAG
Max-Planck-Institutfu¨rAstrophysik,P.O.Box1317,D-85741Garching,Germany
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Abstract. Inthepast,differentworksbasedonnumericalsimulationshavebeenpresentedtoexplainmagneticfields(MFs)
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inthelargescalestructureandwithingalaxyclusters.Inthisreview,Iwillsummarizethemainfindingsobtainedbydifferent
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authorsand-evenifmanydetailsarestillunclear-Iwilltrytoconstructaconsistentpictureofourinterpretationoflarge-

1 scalemagneticfieldsbasedonnumericaleffort.Iwillalsosketchhowthisisrelatedtoourunderstandingofradioemission
v andsummarizesomeargumentswhereourtheoreticalunderstandinghastobeimprovedtomatchtheobservations.
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Keywords:cosmology:large-scalestructure–cosmology:theory–magnetohydrodynamics(MHD)
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(cid:13)c0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
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1. Introduction 2. PossibleoriginsofMFs withinthe LSS
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p
InthefollowingIwilldescribethethreemainclassesofmod-
- There are several different approaches to study the build-
o up of MFs in the intergalactic medium. Many papers elsfortheoriginofcosmologicalMFwithintheLSS.
tr consider MHD simulations of cloud-wind interaction (see In the first one, MFs are assumed to be produced ‘lo-
s Gregorietal. 2000 and references therein) or are simulat- cally’atrelativelylowredshifts(z ∼2−3)bygalactic(e.g.
a
: ing the rise of relic radio bubbles (see Jones&DeYoung Vo¨lk&Atoyan2000)orAGNejecta(e.g.Furlanetto&Loeb
v
2005,Reynoldsetal.2005andreferencesherein).Suchwork 2001). One of the main argumentsin favor of this model is
i
X is usually focused more on the relevance of the local MFs thatthehighmetallicityobservedintheICMsuggestsasig-
r within these processes, whereas in this review I will con- nificantenrichmentdrivenbygalacticwindsorAGNsinthe
a centrate more on the discussion of MHD simulationswhich past.WindsandjetsshouldcarryMFstogetherwiththepro-
aim at understandingthe build-up of the cluster MF and its cessed matter. While it has been shown that windsfrom or-
possibleorigin.Sofar,firmevidenceforthepresenceofex- dinary galaxies give rise to MFs which are far weaker than
tendedMFshasbeenfoundonlyingalaxyclusters.Forrecent thoseobservedingalaxyclusters,MFsproducedbytheejecta
reviews see Carilli&Taylor (2002) and Govoni&Feretti of starburst galaxiescan be as large as 0.1µG. Clearly, this
(2004). Recently there are observational claims of a detec- classofmodelspredictsthatMFsaremainlyconcentratedin
tion of substantial MFs also within the large scale structure galaxyclusters.Notethat,ifthemagneticpollutionhappens
(LSS), see contribution by Kronberg.The origin of the MF early enough (around z ∼ 3), these fields will not only be
in galaxy clusters is still under debate. The variety of pos- amplified by the adiabatic compression of the proto-cluster
sible contributorsrangesfrom primordialfields, battery and region,butalsobyshearflows,turbulentmotions,andmerg-
dynamofieldsoverallclassesofastrophysicalobjectswhich ingeventsduringtheformationofgalaxyclusters.
contributewiththeirejecta.Thelaterpossibilityissupported Inthesecondclassofmodels,theMFseedsareassumed
bytheobservationofthemetalenrichmentoftheintracluster to be produced at higher redshifts, before galaxy clusters
medium(ICM),whichhastobeoriginatedasejectaofastro- formgravitationallyboundsystems.Althoughthestrengthof
physicalobjects.Inaddition,the MFsproducedbyall these the seed field isexpectedto be considerablysmaller than in
contributorswillbecompressedandamplifiedbytheprocess the previous scenario, the adiabatic compression of the gas
ofstructureformation.Theexactamountofthisamplification andtheshearflowsdrivenbytheaccretionofstructurescan
andthe resultingMFfilling factorwilldependonplaceand giverisetoaconsiderableamplificationoftheMFs.Several
timeatwhichthecontributeristhoughttobemostefficient. mechanismshavebeenproposedtoexplaintheoriginofMF
seedsathighredshift.Someofthemaresimilartothosedis-
Correspondenceto:[email protected] cussed above, differing only in the time at which the mag-
3 LOCALAMPLIFICATIONOFMFS
Fig.2.ThegasvelocityfieldinaslicethroughthecentralMpcof
a cluster simulation after subtracting the global mean bulk veloc-
Fig.1.ExampleofMF(y-component)withinanevolvingKHinsta- ityofthecluster.TheleftpanelshowsarunwiththeoriginalSPH
viscosity,therightpanel foralow-viscosityscheme.Theunderly-
bility(inlay)anditstimeevolution.TakenfromBirketal.(1999).
ing color maps represent the ratio of turbulent kinetic energy and
totalkineticenergycontent of particles,inferredaftersubstracting
netic pollutionisassumedtotakeplace.Inthepresentclass thelocalmeanvelocity,asdescribedinDolagetal.(2005)
of models the MF seeds are supposed to be expelled by an
early population of dwarf starburst galaxies or by AGN at
fields produced by the battery process to the MFs observed
aredshiftbetween4and6(Kronberg,Lesch&Hopp1999),
today.Attemptsto constructsuch modelsbased on combin-
allowing them to magnetize a large fraction of the volume.
ingnumericalandanalyticalcomputationshavenotbeenre-
Alternative models invoke processes that took place in the
portedtosuccessfulreproducetheobservedscalingrelations
early universe. Indeed, the ubiquity of MFs in the universe
ofMFsingalaxyclusterssofar.
suggeststhattheymayhaveacosmologicalorigin.Ingeneral,
all ‘high-z models’ predict MF seeds filling the entire vol-
umeoftheuniverse.However,theassumedcoherencelength 3. Local amplificationofMFs
of the field crucially depends on the details of the models.
Whilescenariosbasedonphasetransitionsgiverisetocoher- AverybasicprocessofamplificationforMFsisrelatedtothe
encelengthswhicharesosmallthatthecorrespondingfields Kelvin-Helmholtz (KH) instabilities driven by shear flows,
haveprobablybeendissipated,MFsgeneratedatneutrinoor whicharecommonwithinthedynamicsofthestructurefor-
photondecouplinghavemuchhigherchancestosurviveun- mation process. Birk,Wiechen&Otto (1999) performed a
til the present time. Another (speculative) possibility is that detailed study of such an amplification within the environ-
theseedfieldwasproducedduringinflation.Inthiscase,the ment of galactic outflows (see Fig. 1) in starburst galaxies
coherence length can be as large as the Hubble radius. See where the KH timescale should be ≈ 4×105 years. Using
Grasso&Rubinstein(2001)forarecentreview. aCartesianresistiveMHDcodetheyfoundthattheobtained
The thirdscenarioassumes thatthe MFseeds were pro- amplificationfactorfortheMFmainlydependsontheinitial
ducedbytheso-calledBiermannbatteryeffect(Kulsrudetal. ratioofmagnetictokineticenergyandonlymildlydepends
1997,Ryu,Kang&Biermann 1998). The idea here is that ontheassumedresistivity.Theyreachedtheconclusionthat
mergershocksrelatedtothehierarchicalstructureformation such a processcouldindeed explainthe significantlyhigher
processgiverisetosmallthermionicelectriccurrentswhich, MFobservedinthestarburstgalaxyhalocomparedtowhatis
inturn,maygenerateMFs.Thebatteryprocesshastheattrac- expectedfromtheMFsobservedwithingalacticdisks.When
tivefeatureofbeingindependentofunknownphysicsathigh appliedtoaclustercoreenvironment,theKHtimescaleturns
redshift.Itsdrawbackisthat,duetothelargeconductivityof outtobe107 years,makingitaninterestingprocessforfur-
the IGM, it can give rise to at most verytiny MFs, of order theramplifyingweakMFs.
10−21 G.Onethereforeneedstoinvokeasubsequentturbu- In recent high-resolution smoothed particle hydrody-
lentdynamotoboostthefieldstrengthtotheobservedlevel. namic (SPH) simulations of galaxy clusters within a cos-
Suchaturbulentamplification,however,cannotbesimulated mological environment, using a novel scheme to treat ar-
numerically yet, making it quite difficult to predict how it tificial viscosity within the Gadget2 code (Springel 2005),
wouldproceedinarealisticenvironment.Itisclearthatone Dolagetal. (2005) demonstrated how such shear flows,
expects the level of turbulence to be strongly dependenton which are quite common in the process of cosmic structure
the environment, and that it should mostly appear in high- formation,drivefluidinstabilitiesandincreasetheturbulence
densityregionslikecollapsedobjects.Whileenergeticevents levelwithintheICMtoasignificantlevel(seeFig.2).Itwas
such as mergersof galaxy clusters can be easily considered alsoshownthattheartificialviscosityusedinstandardSPH
to drive the required levels of turbulence, this is harder to simulationsmightsignificantlysuppresssuchfluidinstabili-
understandinrelativelyquietregionslikefilaments.Lacking ties.
a theoreticalunderstandingof the turbulentamplification, it In earlier work, extensive MHD simulations of single
is thereforenotstraightforwardto relate theveryweak seed merging events performed using the Eulerian code ZEUS
4 THEQUESTFORRADIORELICS
1.50
1.40
1.30
11..1200Spectral Index
1.00
0.90
0.80
0. 0 0.2 0.4 0.6 0.8 1.0
R (Mpc)
Fig.4. Inthe leftpanel weshow thesimulatedA3667 X-ray sur-
facebrightnessandradiodata.ContoursrepresenttheX-raysurface
brightness.Thegrayscalerepresentsthesyntheticradioemissionat
1.4GHz.Theimageis3.15×3.85Mpc.Dashedanddottedlines
refertothelocationoftheradiospectral index(α1.4)profilesdis-
4.9
playedintherightpanel.TakenfromRoettigeretal.(1999).
AdetaileddiscussionoftheamplificationofMFinacluster
environment,usingvarioussimulationsofdriventurbulence,
can be found in Subramanian,Shukurov&Haugen (2005),
whereitis shownthatreasonablestrengthandlengthscales
forgalaxyclusterscanbeobtainedbyturbulentprocesses.
Fig.3. The evolution of (logarithm of) gas density (left column), 4. The quest forradio relics
gastemperature(centralcolumn),and(logarithmof)magneticpres-
sure (right column) in two-dimensional slices taken through the By extending such merger simulations to reproduce
clustercoreintheplaneofthemerger.Eachrowreferstodifferent the observed X-ray properties of A3667 and adding a
epochs:t=0(i.e.thetimeofcorecoincidence),t=1.3,t=3.4, model for in situ re-acceleration of relativistic particles,
andt=5.0Gyrs,fromtoptodown.Eachpanelis3.75×3.75Mpc. Roettiger,Burns&Stone (1999) were able to reproducethe
TakenfromRoettigeretal.(1999). mainfeaturesoftheextendedperipheralradioemission(the
so-called radio relics) observed in A3667. In their models
they injected relativistic electrons with a power-law spec-
(Stone&Norman1992a,b) demonstratedthe MFamplifica- trum,wherethepower-lawindexγ =3/(r−1)+1isrelated
tioninsuchmergerevents(Roettiger,Stone&Burns1999). to the gas compressionrate r at the shock. They also relate
Inparticulartheyfoundthatfirst,thefieldbecomesquitefil- theageoftheradioplasmata tothedistanced = κvsta,us-
amentaryasaresultofstretchingandcompressioncausedby ingaweak-field/high-diffusionlimitκ=1.Havingeffective
shocksandbulkflowsduringinfall,butonlyaminimalam- shock velocities vs ≈ 700−1000km/s and aging the syn-
plificationoccurs.Second,field amplificationis morerapid, chrotronspectrumusingtheformalismbyMyers&Spangler
particularlyinlocalizedregions,asthebulkflowisreplaced (1985)theyhavebeenabletoreproducetheobserveddistri-
by turbulentmotions(e.g., eddies), see Fig 3. The total MF butionofspectralindexforaMFof≈ 0.6µGattheposition
energy is found to increase by nearly a factor of three with oftheradiorelic,seeFig.4.Sincesuchconfigurationsseem
respecttoanon-mergingcluster.Inlocalizedregions(associ- to be quite common in galaxy clusters, naturally the ques-
atedwithhighvorticity),themagneticenergycanincreaseby tionarises,whynotallclustersshowsuchaperipheralradio
afactorof20ormore.Apowerspectrumanalysisofthemag- emission.Onepossibleexplanationisthatsuchshockstruc-
neticenergyshowedthattheamplificationislargelyconfined turesarerelativelyshortlivedcomparedtothemergerevent
toscalescomparabletoorsmallerthantheclustercores:this itself. Also, it is necessary to have the presence of a large-
indicatesthatthecoredimensionsdefinetheinjectionscale. scale MF. It could further be that only massive clusters can
It is worth to notice that, due to the lack of resolution, the provideenoughMFandstrongenoughmergereventstotrig-
previous results can be considered a lower limit on the to- gersuchaperipheralemission.
talamplification.Furthermore,itisquitelikelythatagalaxy To overcome this problem, Enßlin&Bru¨ggen (2002)
clusterundergoesmorethanonesuchaneventduringitsfor- proposedthatsuchradiorelicscouldbemadebypre-existing
mationprocess,andthatalsotheaccretionofsmallerhaloes fossil radio plasma illuminated via shock waves initiated
injects turbulent motions within the ICM: consequently the by merger events. In their work they evolved the electron
MFamplificationwithingalaxyclusterswillbeevenhigher. spectrum for the tracer particles, representing the fossil ra-
5 SHOCKSINCOSMOLOGICALSIMULATIONS
Fig.5. Evolution of the gas density (top) and MF energy density
(bottom) for a shock interacting with fossil radio plasma. Taken
fromEnßlin&Bru¨ggen(2002).
Fig.6.Theprojected’potential’radioluminositiesfor1.13Gyrold
radio plasma, where PB/Pgas = 0.01. For comparison the bolo-
dioplasma,followingEnßlin&Gopal-Krishna(2001)which metric surface X-ray luminosity is given. The total bolometric X-
takeintoaccountsynchrotron,inverseComptonandadiabatic rayluminosityoftheclusteris2×1044ergs−1 andtheemission-
energy losses and gains. Their simulation, using the ZEUS weightedtemperatureis3keV.TakenfromHoeftetal.(2004).
code,followstheevolutionofasphereoftracerparticleshit
byashockfront(seeFig.5).Suchaconfigurationnicelyre-
In such a scenario, the MF is strongly correlated with the
produces the filamentary radio emission and toroidal struc-
large-scale structure (see Fig. 7). This means that in such a
tures,asobservedinmanycases.Thesesimulationsalsopre-
case, the MF within the filamentary structure couldbe even
dict the MFs to be mostly aligned with the direction of the
slightly higher than its equipartitionvalue withoutviolating
filaments,assuggestedbyobservationaldata.
the (weak) upper limits of rotation measure of quasars, as
This idea was investigatedin a more realistic modelling
pointedoutbyRyuetal.(1998).Itisworthtopointoutthat
by Hoeft,Bru¨ggen&Yepes (2004), using an SPH Gadget
theargumentsfortheturbulentdynamoaction,whichcould
(Springel,Yoshida&White 2001) simulation of a merging
amplify the battery seed fields up to µG level, as presented
galaxy cluster within a cosmological environment. Such a
in Kulsrudetal. (1997), refer explicitly to regions about to
simulation showed that the probability for a shock wave to
collapseintogalaxies.Ithasstilltobeproventhatsuchargu-
flare theradioplasmaishighlysuppressedin thecentralre-
mentsholdwithinproto-clustersorevencosmologicalstruc-
gions of galaxy clusters compared to the peripheral ones,
tures,likesheetsandfilaments.Ingeneral,thetimeevolution
where they found illuminated structures up to Mpc in size
oftheMFaspredictedbythesesimulationssaturatesaround
(see Fig. 6). Thereasonforthisis thatfirstatthe centerthe
z ≈ 3(Kulsrudetal.1997)andleadstoarelativelyuniform
radioplasmaagesmuchfasterduetoitshigherpressure(and
MFstrengthonscalesoftensofMpcwithintheLSSaround
the lossescomingintogetherwith the higherMF),andsec-
galaxyclusters(seeFig.7).Notethatsofarthereisnocom-
ond that the compression ratio of the shock wave is much
parison of synthetic rotation measurements obtained by the
higherinthelow-densityperipheralregions.Itisworthtono-
MFs predicted by up-scaling the battery fields, with obser-
ticethatanecessaryconditiontoformsuchrelicsisthatthe
vationson scales of galaxy clusters. This might be partially
initialstateofthefossilradioplasmaischaracterizedbyara-
motivatedbythelackofresolutioninsimulatedclusters.
tioofP /P whichisaslowas1percenttoallowshocks
B gas
to revive ≈ 1-Gyr old radio ghosts. It is also important to In addition these shocks act as place for acceleration
of cosmic rays (CR) which then will be accreted into the
mentionthatHoeftetal.(2004)findhighprobabilityofradio
LSS, specially within galaxy clusters. Using the COSMOR
emissionoutsideoftheshocks,relatedtodrainedgasflows,
(Miniati 2001) code, Miniatietal. (2001) followed primary
inducedbythemergerevents,whichtransportmaterialfrom
ionsandelectrons(injectedandacceleratedbydiffusecosmic
the outskirtstowards the higher density regions.Thereby in
shocks) and secondaryelectronsand positrons(producedin
somecasestheadiabaticcompressionseemstobeenoughto
p-pinelasticcollisionsofCRionswiththermalICMnuclei)
revivethefossilradioplasma.
withinacosmologicalsimulation.Undertheassumptionthat
theMFproducedbythebatteryeffectreflectsafairrepresen-
5. Shocks incosmologicalsimulations tationofthetruedistributionofrelativeMFstrengthswithin
theLSS,theywereabletopredictthecentralradioemission
Cosmologicalshocks,mainlytheaccretionshocksoncosmo- (radiohalos)-mainlyproducedbysecondaryCRs-aswellas
logical objects like galaxy clusters and filaments, are much theperipheralradioemission(radiorelics)-mainlyproduced
more frequentthan the ones producedby individualmerger by primary CRs - in a self-consistent treatment (see Fig.
events. They also can produce MFs by the so-called Bier- 9):theresultingmorphology,polarizationandspectralindex
mannbatteryeffect(Kulsrudetal.1997;Ryuetal.1998)on match the observed properties. However, one has to notice
which a subsequent turbulent may operate (see section 2). thattheextrapolationofthesesimulations(ongroupscale)to
6 COSMOLOGICALMHDSIMULATIONS
Fig.7. A two-dimensional cut through a cosmological box simu-
lated by Miniatietal. (2001), and following the evolution of bat- Fig.8. Slice through the centre of the simulated box, hosting a
teryfields.Shownis(thelogarithmof)theup-scaledMFstrengthin
massivegalaxycluster.Thesimulation,madeusingtheAMRcode
Gausstakenatz=0.TakenfromSigl,Miniati&Enssßlin(2004).
FLASH,followstheevolutionofaweakmagneticseedfield.Shown
isthelogarithmof theMFstrengthinGauss, asmeasured atz =
theobserveddata(i.e.onmassiveclusterscale)mightnotbe 0.5.TakenfromBru¨ggenetal.(2005).
straightforward(seeFig.13).Itisfurtherworthtonoticethat
evenwithaprotoninjectionratioR of10−2(whichisde-
e/p This result is now confirmed to hold over several orders of
rivedfromobservations,seeTab.5inMiniatietal.2001),the
magnitude in a collection of observational data existing in
predictedluminositiesfortheprimaryemissionisstillsignif-
the literature (see Fig 12). ExtendingGadget2to follow the
icantlyhigherthanforthesecondaryone(seeFig.13),which
full set of ideal MHD equations, Dolagetal. (2004, 2005)
seemsnottobeconfirmedbytheobservations.Althoughthe
performedseveralrealizationsofacosmologicalvolumecon-
resultsforthesecondarymodelareinagreementwithprevi-
firmingthepreviousfindingsevenatmuchhigherresolution.
ousworkonmassivegalaxyclusters(Dolag&Enßlin2000),
Recently,Bru¨ggenetal.(2005)performedasimulationofthe
wenoticethatgenerallyinthesecondarymodelradiohaloes
formationofasinglegalaxyclusterinacosmologicalframe-
are predicted for every cluster, which is in contradiction to
work,usingapassiveMHDsolverimplementedintoFLASH.
theobservations(seeFig.13).
Therebytheynicely confirmedallpreviousresultsbased on
theSPHcodes,usingtheiradaptivemeshrefinement(AMR)
6. CosmologicalMHDsimulations simulationcode(seeFig.8).
Another interesting quantity to look at is the slope α of
Using GrapeMSPH (Dolag,Bartelmann&Lesch 1999) and theMFpowerspectrum(∝k−α,withkbeingthewavevec-
assuming that a small initial magnetic seed field exists tor).WithingalaxyclustersαispredictedbytheSPHsimu-
before structure formation (see section 2), the first self- lations(Dolagetal.2002,Rordorf,Grasso&Dolag2004)to
consistent simulations which follow the MF amplifica- beslightlylower,butstillverycloseto11/3,whichistheex-
tion during the formation of galaxy clusters with cos- pected value for a Kolmogorov-like spectrum (in 3D). The
mological environment have been performed (Dolagetal. AMR simulation by Bru¨ggenetal. (2005) nearly perfectly
1999,Dolag,Bartelmann&Lesch 2002). These runs were matchestheKolmogorovslope.Fig.14showsacollectionof
abletodemonstratethatthecontributiontotheamplification predictedandobservedslopesfortheMFspectrum.Notethat
ofMFsbyshearflows(andbyitsinducedturbulence)issig- thiscanonlybeacrudecomparison,duetothelimitationsin
nificant(seeFig.10).Thereforeforthefirsttimeaconsistent both observationsand simulations. But in generalthe range
picture of the MF in galaxy clusters could be constructed: ofslopespredictedbythesimulationsseemstobeconsistent
the amplification predicted by the simulations was capable withtheslopesinferredfromobservationsofrealclusters.It
tolinkthepredictedstrengthoftheseedMFs(seesection2 isworth to noticethatthe numericalresultssuggestthatthe
andreferencestherein)athighredshift(z ≈3andhigher)to spreadoftheslopesmightreflectthedynamicalstageofthe
the today observedMF strength in galaxy clusters. Further- system,indicatedbythe inlay,showingthe two massaccre-
morethesimulationspredictedthatthefinalstructureofthe tionhistories.Herethesmoothlyaccretingclustersshowthe
MFingalaxyclusterreflectstheprocessofstructureforma- smallestslope(indicatingthelackoflarge-scalepower).On
tion,andnomemoryontheinitialMFconfigurationsurvives: thecontrary,theclustershavingaquiteviolenthistory,with
thisrelaxestheconstraintsonmodelsforseedMFs. Ingen- severalmajormergersindicatedbythesmallarrows,showa
eral such modelspredicta MF profile similar to the density verysteepspectra.Twoofthemhappenedinthelast3Gyrs,
profile. Thereby the predicted rotation measure (RM) pro- therebyinducinganexcessofpoweronlargescales.
file agrees with the observed one (see Fig. 11). Dolagetal. Further support for strong MF amplification during the
(2001)foundaquasilinearcorrelationbetweentwoobserv- processofstructureformationcomesfromtheapplicationof
ables,namelytheX-raysurfacebrightnessandtheRMr.m.s.. the Zel’dovichapproximationto follow the MHD equations
7 CONCLUSIVEREMARKS
Saturation
Shear + Turbulence
Fig.9. Synchrotron power at 1.4 GHz from secondary electrons + Major Merger
(left panel) and primary electrons (right panel). Note that the val- Shear
uesfortheluminositiesforprimaryelectronsshouldbescaledwith
theelectrontoprotoninjectionratioR .TakenfromMiniatietal.
e/p
(2001).
Fig.10.TheMFstrengthasafunctionofbaryonicoverdensity.The
during the gravitationalcollapse (Bruni,Maartens&Tsagas long-dashedlineshowstheexpectationforapurelyadiabaticevo-
2003; King&Coles 2005). Such works showed super- lution,thesolidlinegivesthemeanfieldstrengthatagivenover-
adiabatic amplificationdue to theanisotropyofthe collapse densitywithinacosmologicalsimulation(Dolagetal.2005).While
oftheLSSwithinthecolddarkmatterparadigm. thelatterisclosetotheadiabaticvalueinunderdenseregions,there
AnovelaspectofincludingMFpressureintoLSSsimu- isasignificantinductiveamplificationinclustersduetoshearflows
lation-evenifinasimplifiedway-isinvestigatedinanon- andturbulence,subjecthowevertosaturationintheclustercores.At
goingproject(seethecontributionbyGazzola),whichaims anygivendensity,alargefractionofparticlesremainsclosetothe
atidentifyingthepointforwhichsuchnonthermalpressure adiabaticexpectation,asshownbythedottedline,whichgivesthe
supportstartstosignificantlymodifythestructureformation. medianofthedistributionateachdensity.
7. Conclusiveremarks ingtheregionsfilledwithhighMFsshowninFigs.7and8.
Itis clearthatthe highMF regionsfor the batteryfieldsare
It seems that within the last years a probably con- predictedtobemuchmoreextended,leadingtoaflatprofile
sistent picture of MFs arises from numerical works aroundthe formingstructure, whereas for the turbulentam-
and observations. Supported by simulations of individual plifiedMFs the clusters showa muchmorepeakedMF dis-
events/environmentslike shear flows, shock/bubble interac- tribution.Partofthisdifferenceoriginatesfromthephysical
tionsor turbulence/mergingevents,a super-adiabaticampli- modelbehind,asthecosmologicalshocksaremuchstronger
fication of MF is predicted. It is worth to notice that this outside the clusters than inside. Somewhat more unclear is
common finding is obtained by using a variety of different whatthecontributionofthedifferentnumericalresolutionsof
codes, based on different numerical schemes. Further sup- these simulationsto these discrepanciesis. Calibratingsuch
portfor such super-adiabaticamplificationscomesfroman- simulationsusingtheMFmeasuredonlyinthehigh-density
alytical estimates of anisotropic collapse making use of the regionsofgalaxyclustersmakesitcrucialtoperformamore
Zel’dovichapproximation.When applied in fully consistent detailedcomparisonwithallavailableobservations.Notethat
cosmological simulations, various observational aspects are extrapolating the predictions of the simulations into lower
reproduced(see Figs. 11 and 12) and the resulting MF am- densityregions,wherenostrongobservationalconstraintsex-
plificationreachesalevelsufficienttolinkmodelspredicting ist,willevenamplifythedifferencesinthepredictionsforthe
seed MFs at high redshift with the MFs observed in galaxy MFstructurebetweenthedifferentsimulations.
clusterstoday.Itisimportanttomentionthatallsimulations Moreover,onehastokeepinmindthatdependingonthe
show that this effect increases when the resolution is im- ICMresistivitytheMFcouldbesufferingdecay,whichsofar
proved, and therefore all the numbers have to be taken as isneglectedinallthesimulationsdiscussedbefore.Further-
lowerlimitsofpossibleamplification. more a clear lack of the present simulations is that they do
Note that on the other hand there are significant differ- notincludethecreationofMFbyallthefeedbackprocesses
ences for the predictionsof the MF structures coming from happeningwithinLSS(likeradiobubblesinflatedbyAGNs,
differentmodelsofseedMFs.Inparticulartherearemaindif- galactic winds, etc.): this might alter the MF prediction if
ferences between the up-scaled, cosmological battery fields theircontributionturnsouttobesignificant.Alsoallthesim-
(Miniatietal. 2001; Sigletal. 2004) and the MF predicted ulationsdonesofarneglectradiativelosses:ifincluded,this
fromhigh-resolutionsimulationsofgalaxyclustersusingei- wouldleadtoasignificantincreaseofthedensityinthecen-
ther AMR (Bru¨ggenetal. 2005) or SPH (Dolagetal. 1999, tral part of clusters and thereby to a further MF amplifica-
2002,2005).Inthelattercaseitispossibletofollowtheam- tion in these regions. Finally, there is an increasing number
plification of seed fields within the turbulent ICM in more of argumentssuggesting that instabilities and turbulence on
detail.Agoodvisualimpressioncanbeobtainedbycompar- very small scales can amplify the MFs in a relatively short
7 CONCLUSIVEREMARKS
+ 8 rad/m2
Fig.11.ComparisonofRMsfromthesimulationwithobservations Fig.12. Correlation of rotation measurements withX-ray surface
for Abell clusters, as a function of distance to the closest cluster. brightness for different galaxy clusters. Thedatapoints areobser-
Smoothlinesrepresentthemedianvaluesof|RM|producedbysim- vationscollectedfromtheliterature.Thecolorsrepresentthevirial
ulatedclusterswithmassesabove5×1014M⊙and3×1014M⊙. clustertemperaturetakenfromliterature.Thisisanupdatedversion
The broken line represents the median of combined data taken ofthecorrelationpresentedinDolagetal.(2001).
from the independent samples presented in Kimetal. (1991) and
Clarkeetal.(2001).Wealsoincludedata(diamonds) forthethree
that there is also no indication from observations that clus-
elongatedsourcesobservedinA119(Ferettietal.1999),andforthe
tersshowingradioemissioncontainhigherMFsthantheones
elongatedsourceobservedintheComacluster(Ferettietal.1995).
withoutobservableextended,diffuseradioemission.Onthe
contrary,the clusterA2142hasaMFstrengthsimilar tothe
timescalereachingtheobservedµGlevel.Howeveritisstill Coma cluster (see Fig. 12), but the upper limit on its radio
unclear how such very small scale fields can be ordered on emissionisatleasttwoordersofmagnitudebelowthevalue
large(uptohundredsofkpc)scalesasobserved. expected from the correlation (see Fig. 13). Note that both
clusters are merging systems characterized by the presence
Concerning Radio haloes and relics the picture is only
of two central cD galaxies. This indicates that there should
partially consistent ( for a more detailed discussion of pri-
befurtherprocessesinvolvedoradditionalconditionstoful-
maryandsecondarymodelsseeBrunetti2004andreferences
filltoproduceradioemission.Itisworthtonoticethatrecent
therein).Radiorelicsseemtobemostlikelyrelatedtostrong
models, based on turbulent acceleration, seem to overcome
shocksproducedbymajormergingeventsandthereforepro-
this problem (see Kuo,Hwang&Ip 2003; Brunetti&Blasi
ducedbydirectre-accelerationofCRs,theso-calledprimary
2005;Cassano&Brunetti2005andreferencestherein).Note
models. Although some of the observed features like mor-
thatCassano&Brunetti(2005)predictedtheprobabilityfor
phology, polarization and position with respect to the clus-
agalaxyclustertoshowgiantradiohalotobeanincreasing
ter centre can be resonablywell reproduced,there mightbe
functionofclustermassandreproducedtheobservedfraction
still some puzzles to solve. On one hand, direct accelera-
of≈30%formassivegalaxyclusters.
tion of CRs in shocks seems to overestimate the abundance
and maybethe luminosityof radio relics; on the other hand There is a big challenge for the next generation of cos-
simulations which illuminate fossil radio plasma can pro- mologicalMHD simulations. Simulations are quite close to
duce reasonable relics only starting from a small range of havingtheresolutionnecessarytoproperlydescribetheMF
parameter settings. A similar situation arises for modelling components down to the observed scales, but on the other
the central radio emission of galaxy clusters by secondary handthismeanstoresolvegalaxiesinsidethesimulationsas
models.Ononehand,thetotalluminosityseemstoberepro- well.Notethatfollowingthedynamicsofsuchstructuresfor
duced using reasonable assumptions and also the steep ob- which the MF might dominate the evolution, is a real chal-
servedcorrelationbetweenclustertemperature/massandra- lenge within LSS simulations. However, we expect that - if
diopowerseemstobereproducedquitewell.Butsuchmod- succeeding in overcomingthese limitations - the dynamical
els suffer from two drawbacks. The first one is that in the impactoftheMFonregionslikethecoolingflowsatthecen-
framework of such models every massive cluster produces tresofgalaxyclusterswillbesignificantandwillcontribute
a powerfulradio halo, butthis is notconfirmedby observa- tosolvetheseoutstandingpuzzles.
tions (see Fig. 13). The other problems is that the detailed
Acknowledgements. Thisworkhasbenefitdfromresearchfunding
radiopropertiesarenotreproduced.Firstly,theprofileofra-
fromtheEuropeanCommunity’ssixthFrameworkProgrammeun-
dio emission in most cases is too steep, so that these mod-
der the HPC-EUROPA project (RII3-CT-2003-506079) and under
els cannotreproducethe size of the observedradio halos in RadioNet(R113-CT-2003-5058187).IwanttothanktheINAF-IRA
almost all cases. Secondly,the observedspectralsteepening inBolognaandtheAstronomyDepartmentinTriestefortheirhospi-
(e.g.Giacintuccietal.2005)alsocannotbereproduced.Note tality.ManythankstoS.BorganiandL.Moscardiniforstimulating
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