To appear in “MAGNETIC FIELDS IN THE UNIVERSE II: From Laboratory and Stars to the Primordial Universe

THE EVOLUTION OF CLUSTER MAGNETIC FIELDS PROBED BY THE

SKA

M. Huarte-Espinosa,1 P. Alexander,1 R. Bolton,1 J. Geisbuesch,1 and M. Krause2

RESUMEN

El SKA sera una herramienta sin paralelo para estudiar los campos magneticos, y de hecho, uno de susproyectos cientıficos prioritarios es el origen y la evolucion del “Magnetismo Cosmico’. Como parte de losEstudios Europeos de Diseno del SKA (SKADS) estamos desarrollando simulaciones del cielo y de variosexperimentos asociados con su instrumentacion para estudiar la evolucion de estos campos magneticos. Enparticular, consideramos detalladamente como pueden observarse los campos magneticos en cumulos de galaxias(cumulos) en corrimientos al rojo altos, usando la rotacion de Faraday con fuentes de radio ubicadas detras de loscumulos. En esta presentacion describimos los modelos y observaciones de los campos magneticos en los cumulosen el contexto del SKA. Mostramos como sera posible estudiar con este telescopio los campos magneticos encumulos a altos corrimientos al rojo. Ademas discutimos nuestras simulaciones numericas (3DMHD) de cumulosmagnetizados, en los que existe retroalimentacion de Nucleos Activos de Galaxias (NAG) proveniente de fuentesde radio de tipo FR II. Implementamos la estructura magnetica inicial de este cumulo con un espectro espacial,con diferentes ındices espectrales, y fases generadas al azar. Usamos las propiedades fısicas observadas envarios cumulos para simular el plasma del medio inter-galactico de nuestro cumulo. Finalmente, discutimosbrevemente la capacidad del SKA de observar razgos de actividad de NAG en los cumulos.

ABSTRACT

The Square Kilometer Array (SKA) will provide an unparalleled tool to study magnetic fields, and indeedone of the “Key Science Cases” for the SKA is the origin and evolution of cosmic magnetism. As part ofthe European SKA Design Study (SKADS) we are developing sky simulations and associated instrumentalsimulations of various experiments to probe the evolution of magnetic fields. In particular we are consideringin detail how cluster magnetic fields can be probed to high redshift using Faraday rotation against backgroundsources as the probe. In this presentation, modelling and observations of the magnetic fields in galaxy clustersare described in the context of the SKA. We show how it will be possible with the SKA to study evolution ofthe field in clusters out to high redshift. We also discuss our work on 3D MHD simulations of a magnetisedgalaxy cluster, when we have AGN feedback from a powerful FR II radio source. The initial magnetic structureof this cluster has a spatial spectrum with a range of spectral index and randomly generated phases; the intra-cluster medium plasma is implemented with physical properties resembling those observed in many clusters.We discuss briefly the ability of the SKA to observe any signature of past AGN activity in clusters.

Key Words: Magnetic fields — MHD — Galaxies: clusters — Galaxies: jets — (galaxies: intergalactic medium)

1. INTRODUCTION

Magnetic fields of Mpc scale have been ob-served to permeate the the intra-cluster medium(ICM) inside galaxy clusters (clusters from now on).X-ray observations show that the ICM consist of hotplasma emitting Bremsstrahlung radiation with tem-peratures ranging from 107 to 108K, and a β dens-ity profile extending to ∼ 2 Mpc distances (Sarazin1988). This gas, with masses of the order of 1013 to

1Astrophysics Group, Cavendish Laboratory, Cam-bridge CB3 0HE, UK (mh475@mrao.cam.ac.uk,pa@mrao.cam.ac.uk, rosie@mrao.cam.ac.uk, jo-ern@mrao.cam.ac.uk)

2Max-Planck-Institut fuer Extraterrestrische Physik,Garching, Germany (M.Krause@mpe.mpg.de)

1014 M⊙, is the dominant baryonic component inclusters. Observations in radio frequencies have beenused to study the magnetic fields in clusters (seeFeretti & Giovannini 2007 and referenced therein).These studies reveal non-thermal synchrotron struc-tures embedded inside the clusters, which are di-vided in either halos or radio galaxies. The formerare usually found in the cores of clusters, showinglow surface brightnesses and are usually unpolar-ised. On the contrary, radio galaxies are extendedand highly polarised sources, associated with activegalactic nuclei (AGN) and quasars, which producejets giving rise to sources which can extend beyondthe core radius. The Coma cluster presents good

1

2 HUARTE-ESPINOSA, ALEXANDER, SKADS, & KRAUSE

examples of all these radio sources (Feretti & Gio-vannini 2007).

The polarised radiation from radio galaxies, em-bedded in clusters or behind them (backgroundsources), have been used to reveal yet another con-stituent of the cluster magnetic fields (CMFs). Thisis done by observing Faraday Rotation (e.g., seeClarke et al. 2001; Carilli & Taylor 2002; Govoniet al. 2006), where the plane of polarisation of theradio emission rotates as it goes through a magnet-ised medium. The degree of rotation is characterisedby the Rotation Measure (RM). These investigationshave found that, in general, the CMFs have coher-ence lengths of ∼ 5 − 10 kpc and intensities of theorder of 1−10 µ G decreasing with the distance fromthe core of the cluster. RM observations also show acorrelation between the RM and the cooling flow ratein cool core clusters (Taylor et al. 2002). Moreover,RM data enables modelling and characterisation ofthe CMFs with spatial power spectra of the mag-netic field fluctuations (Murgia et al. 2004; Vogt &Enßlin 2005). It is this component of the CMFs thatwe study in this letter.

Radio telescopes such as the VLA have been usedto study the CMFs. However, a detailed analysisof the structure and origin of these, requires morepowerful radio telescopes such as the Square Kilo-metre Array (SKA), which will provide an improve-ment of approximately two orders of magnitude insensitivity over existing telescopes.

2. PROBING THE STRUCTURE OF CLUSTERMAGNETIC FIELDS

We have been implementing a Faraday screen tosimulate the effects of a set of magnetised clustersat high redshift, on the radiation from backgroundradio sources. The clusters are implemented with aβ density profile, with a mean core radius of 100 kpc,and a radial RM distribution based on local universedata.

Figure 1 shows the different stages of one of theseFaraday screens. The colour scale in each of the im-ages shows the RM associated with it. The Faradaydepth from cosmological clusters is simulated first,illustrated in figure 1a. The clusters are resolvedin this image. Figure 1b exhibits the simulated re-covered SKA sampling of the screen above it, assum-ing a 100 − hour observation. Figure 1c depicts thesmoothened version of the SKA sampling above it(b). Statistical analysis, on the number of clustersand their magnetic fields as a function of redshift,are done with these screens.

We have also investigated random field structuresusing techniques similar to Murgia et al. (2004).

a

b

c

Fig. 1. Simulated Faraday screens. (a) FaradayDepth from Cosmological Clusters. (b) Recovered SKAsampling assuming a 100 − hour of observation. (c)Smoothed SKA sampling.

3D numerical cubes, simulating the ICM of a singlecluster with a β density profile and a turbulent mag-netic distribution, are produced. The latter is im-plemented with a random vector potential follow-

REVMEXAA(SC) DEMO DOCUMENT 3

ing a given spatial power spectrum. Polarised radioemission is then simulated to pass through this en-vironment with a range of lines of sight, to studythe correlation between its RM and the structure ofthe ambient magnetic fields, i.e., the index of themagnetic power spectrum. The top panel in fig-ure 2 shows two of these cubes with power spectraindexes 2 and 4 (left and right, respectively). Beloweach of these cubes, the figure shows their associ-ated RM screens. It is evident that the structurein the magnetic fields, i.e., the scales at which theyare important, translates into structure in the RMscreens. We have been using these magnetic cubesto investigate radio sources feedback on the CMFs,as we shall explain in the following section.

3. RADIO SOURCE FEEDBACK ON CLUSTERMAGNETIC FIELDS

The combination of high resolution X-ray and ra-dio observations of clusters, reveal huge X-ray cav-ities filled with radio emitting structures (Fabian etal. 2000). This is evidence of the well known com-plex energy interchange taking place in the cores ofclusters, between the ICM gas and the central radiogalaxies (see Begelman 2004; Ruszkowski 2007 forreviews). These galaxies obtain a great deal of en-ergy from the neighbouring ICM gas via accretion.An substantial fraction of the energy is then injectedback in kinetic form, as collimated ambipolar and re-lativistic outflows, or jets. A strong magnetohydro-dynamical (MHD) shock is then produced ahead ofan ellipsoidal cavity, the cocoon. The latter pushesaway the ICM gas in its way and deposits hot plasmaand magnetic fields into the ambient.

Once the injection ceases, the cocoon becomeshot under-dense magnetised bubbles that rise buoy-antly into the ICM, interchanging energy with it.The stability and morphology of these bubbles, andthe mixing of their plasma with that in the sur-rounding gas, strongly depend on the topology of thebubble and the ICM magnetic fields (see Ruszkowskiet al. 2007 and references therein). The evolutionof the bubbles is also influenced by the dynamicalimportance, or intensity, of the CMFs. This is char-acterised by the ratio of the ICM’s thermal pressureover its magnetic pressure; the plasma β. The lateris typically observed to be above unity (Blanton etal. 2003). CMFs seem to suppress hydrodynamicalinstabilities from the bubbles. On the other hand,the rising bubbles form kpc scale convective flows,like those simulated by Basson & Alexander (2003),give place to wakes behind the bubbles. Magneticwakes of this nature seem to amplify and deform the

topology of the neighbouring CMFs (Ruszkowski etal. 2007). Presumably the AGN jets, not only thebubbles, will have effects here as well.

To investigate this, we perform 3D MHD sim-ulations of a magnetised jet injected into magnet-ised stratified atmospheres. We solve the equationof ideal MHD using the Flash code (Fryxell et al.2000), which is a third order interpolation parallelcode with an adaptive grid. We use a 3D cube withedge lengths of 0.5 Mpc and a mesh with 64×64×64zones. This grid is adjusted to refine adaptively upto scales of 0.98 kpc, necessary for the injection ofthe jet.

Our initial conditions are the following: an iso-thermal gas with γ = 5/3, a temperature of 108 Kand a King density distribution (King 1972):

ρ(r) =1 × 10−23

1 + (r/100kpc)2kg m−3. (1)

where r is the radial distance from the centre of thecluster (the centre of one of the faces of our cubicdomain). Equation (1) simulates the ICM gas withan embedded dark matter halo, which we implementin hydrostatic equilibrium with the ICM’s thermalpressure. The ICM initial magnetic distribution istaken form the cubes described in §2; with a tur-bulent magnetic distributions. At every numericalzone we adjust the magnetic fields intensities so thatβ = 10, i.e.:

B(r) = B0

√

2 µ0 (0.1)P (r)

γ − 1r, (2)

where µ0 is the vacuum permeability, P (r) is theICM’s thermal pressure (as a function of the radialdistance from the cluster’s centre), and B0 is a factorcharacterised by a spatial spectrum and randomlygenerated phases. The index of the power spectrumof the magnetic distribution is a parameter we in-tend to vary in our simulations. Figure 3 shows theplane z = 0 of the initial magnetic distribution inour cluster. The colour scale exhibits Bz while thearrows depict the magnetic vectors corresponding tothe xy plane. The random phases of the fields areevident.

We then continue to the jet phase of the simu-lation. Using the (ghost) zones at the centre of oneof the faces of the numerical domain (the one cor-responding to the centre of the cluster), we injecta nearly-relativistic collimated jet. This outflow isunder-dense with respect to the initial central dens-ity of the cluster by a factor of 103 and is in pressureequilibrium with the initial central ambient medium.

4 HUARTE-ESPINOSA, ALEXANDER, SKADS, & KRAUSE

Fig. 2. (Top) Simulated magnetic cubes generated with random vector potentials with two different spatial powerspectra. (Bottom) RM structure corresponding to the magnetic distributions of the top panel. The structure in themagnetic fields translates into structure in the RM screens.

Fig. 3. The initial magnetic structure of our simulatedICM showing the xy plane in the middle of our numericaldomain, with sides of length 500 kpc. The cluster’s centreis located at the middle of the left boundary of the plane.The colour scale shows Bz and the arrows depict themagnetic vectors corresponding to the xy plane.

Moreover, the jet has a radius of 3 kpc and a velo-city of a third of the speed of light, hence simulatingan FR II radio source, with a bulk kinetic powerof 1.38 × 1045 erg s−1, over 10 Myrs. We discuss ourpreliminary results concerning this simulations in thefollowing section.

Once the injection finishes, the simulation passesto the remnant phase. The jet’s relic thenevolves passively under the influence of gravitational,thermal and magnetic forces, in order to reach anequilibrium state. We expect to find magnetisedbuoyant bubbles and magnetic wakes behind them,having important effects on the neighbouring CMFs,as was found by Ruszkowski et al. (2007).

4. DISCUSSION AND CONCLUSIONS

The solenoidal nature of the magnetic fields intro-duces an important problem in numerical MHD sim-ulations. This is because numerical analysis workswith finite domains, with boundaries, and thus themagnetic lines cannot be continuous there. This isone of the problems we have been facing. Moreover,

REVMEXAA(SC) DEMO DOCUMENT 5

Fig. 4. The jet injected into the magnetised ICM show-ing the xy plane of a zoom to the centre of our simulatedcluster. Each side is 100 kpc long. The colour scale showsBz and the arrows, the magnetic vectors correspondingto the xy plane. The jet was injected at the middle ofthe left boundary of the plane, where ordering of theneighbouring magnetic fields is evident. The semicircu-lar (radius

∼< 25 kpc) magnetic structures with smaller

coherence length are the jet’s cocoon and strong MHDshock, the former inside the latter.

the state of the magnetic field lines present at theboundary between the cocoon and the ICM is notclear. These lines ought to be continuous there butthe physical conditions are very different on each sideof the boundary. This is a delicate numerical MHDproblem (e.g., see Ruszkowski et al. 2007). As we in-ject the jet into the magnetised ICM, we do not havecontrol over these “cocoon magnetic fields”. We canimplement the magnetic boundary conditions at thebase of the jet though, which is an interesting para-meter we have been experimenting with.

Our simulations are now giving us some inform-ation about the jet phase (see §3). The cocoon andthe MHD strong shock are shown in figure 4 nearthe middle of the left side. These are semicircular(radius

∼

< 25 kpc) magnetic structures with smallercoherence length than the magnetic fields away fromthem; the CMFs. Figure 4 also shows that after in-jecting the jet for 2.5 Myrs, the magnetic fields inthe vicinity of the cocoon are ordered, and close toits contact discontinuity the fields get amplified by afactor of the order of 100.

Our preliminary results are interesting and we arenow working in order to solve our numerical prob-lems and get the full 3DMHD simulations of relativ-istic jets, and their remnants, propagating in mag-

netised galaxy cluster atmospheres.

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