On the non-thermal energy content of cosmic structures
aa r X i v : . [ a s t r o - ph . C O ] N ov Article
ON THE NON-THERMAL ENERGY CONTENT OFCOSMIC STRUCTURES
Franco Vazza , Denis Wittor ,Marcus Brüggen , Claudio Gheller Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany; ETHZ-CSCS, Via Trevano 131, CH-6900 Lugano, Switzerland * Correspondence: [email protected] Editor: nameVersion April 9, 2018 submitted to Entropy; Typeset by L A TEX using class file mdpi.cls
Abstract:
1) Background: the budget of non-thermal energy in galaxy clusters is not wellconstrained, owing to the observational and theoretical difficulties in studying these diluted plasmason large scales. 2) Method: we use recent cosmological simulations with complex physics in orderto connect the emergence of non-thermal energy to the underlying evolution of gas and dark matter.3) Results: the impact of non-thermal energy (e.g. cosmic rays, magnetic fields and turbulentmotions) is found to increase in the outer region of galaxy clusters. Within numerical and theoreticaluncertainties, turbulent motions dominate the budget of non-thermal energy in most of the cosmicvolume. 4) Conclusion: assessing the distribution non-thermal energy in galaxy clusters is crucialto perform high-precision cosmology in the future. Constraining the level of non-thermal energy incluster outskirts will improve our understanding of the acceleration of relativistic particles and ofthe origin of extragalactic magnetic fields.
Keywords:
Galaxy clusters; cosmic rays; magnetic fields; turbulence.
1. Introduction
Galaxy clusters are the largest reservoir in the Universe of, both, thermal and non-thermal (NT)energy. They sit atop of the matter hierarchy of the Universe and are still forming nowadays, throughthe continuous accretion of matter [e.g. 1,2]. Each accretion episode converts a fraction of the infallkinetic energy into gas thermal energy [e.g. 3,4], and is accompanied by the injection of turbulentmotions across a wide range of scales [e.g. 5–9].Mergers can inject an amount of NT energy of the order of the infall kinetic energy, and thusthey can give us a view onto out-of-equilibrium plasma conditions, where relativistic particles can beaccelerated [10,11] and give rise to observed diffuse radio emission [e.g. 12,13]. Moreover, a the NTpressure support may yield signifiant deviations from the mass estimates based on the hypothesisof virial theorem and hydrostatic equilibrium, which are inferred from X-ray analysis[e.g. 14–17].Galaxy clusters are predicted to behave as closed boxes that retain all dark and gaseous matteraccreted onto their deep gravitational wells. Therefore, observed departures of their baryon fractionfrom the cosmic average can inform us about the relevance of non-gravitational processes, from NTprocesses to the integrated effect of galaxy feedback within them [e.g. 18–20].Also the mass growth rate of clusters, their abundance at a given cosmic epoch and the slopeof observed scaling relations between X-ray luminosity, the average temperature and total masscan constrain the cosmological parameters complementary to the analysis of the CMB [e.g. 21,22].Therefore, galaxy clusters can be used as “high-precision” cosmological tools provided that weachieve a satisfactory understanding of the complex interplay between thermal and NT effects.
Submitted to
Entropy
Entropy
This will be important both for a calibration of cluster scaling relations within the standard Λ CDMmodel (which future missions like EUCLID , will probe via gravitational lensing), as well as forthe cosmological use of the information encoded in the intergalactic medium, that locks-in ∼ .Since the NT components should have a broader energy profile compared to the thermal gasdistribution, and are also subject to longer dynamical timescales, they offer the chance to probe theconditions of rarefied cosmic plasma prior to the formation of large-scale structures.For example, cosmic rays (CR) protons injected by shocks are long-lived in clusters as they aresubject to negligible energy losses and stay confined inside clusters for cosmological timescales [23,24]. Upper limits on the presence of CRs in clusters at low redshift [25–27] have the potential to probethe acceleration efficiency of cosmic shocks across the entire lifetime of clusters, and also to constrainthe acceleration efficiency of shocks in environments too faint to be directly observable [e.g. 28,29].Also magnetic fields in the ICM are subject to very long dissipation timescales. While thedynamical activity in the innermost cluster regions is probably strong enough to boost a small-scaledynamo [e.g. 30–33], in cluster outskirts and in filaments the dynamo amplification should be muchless efficient. Therefore, the dynamical memory of the seed magnetic fields should be still presentnowadays in cluster outskirts [34] and might be detectable by incoming radio telescopes [35].In this contribution, we use state-of-the art cosmological simulations of large-scale structures toassess the spatial distribution of NT energy in the local Universe. Our findings are compared to thescarce observational constraints at the scale of galaxy clusters (Sec. 2.1) , as well as on the scale oflarge cosmic volumes (Sec 2.2). Our discussion and conclusions are given in Sec. 3.
2. Results
We first focus on the high-resolution view of one massive ( ≈ · M ⊙ ) galaxy cluster.We chose this object because its mass its similar to the one of the Coma cluster, for which manyobservational constraints are available.In detail, we used the grid code ENZO [36] and employed 5 levels of adaptive mesh refinement(AMR) to selectively increase the dynamical resolution in most of the cluster volume, i.e. ∼
80% ofthe viral volume is refined up to the maximum resolution of ∆ x = z ≤
1. Our AMRscheme is aggressive in order to allow the largest possible dynamical range in the gas flows, whichis crucial to allow the growth of a small-scale dynamo [e.g. 37]: we refined all cells which are ≥ ≥ et al. [39] and Wittor etal. (this volume).All our runs followed magneto-hydrodynamics (MHD) using the Dedner Cleaning method of ENZO [e.g. 36,40]. We simulated two extreme scenarios for the seeding of magnetic fields: a) inthe primordial scenario (used in the non-radiative setup) we started the simulation from a uniformmagnetic field seeds of B = − G (comoving) at z =
30, which is at the level of upper limits allowedfrom the analysis of the Cosmic Microwave Background (i.e. B ≤ − et al. astrophysical scenario (combined with the radiative setup,including gas equilibrium cooling and thermal/magnetic feedback from active galactic nuclei) weinjected magnetic dipoles storing 1% of the AGN feedback energy, starting from z =
4. The thermal Entropy
Figure 1.
Projected energy maps for our simulated clusters at z =
0, including the thermal energy(top left) the turbulent energy (top right), the magnetic energy (lower left) and the CR-proton energy(lower right). The size of each image is 8.192 Mpc. For clarity the white contours of the projectedthermal energy are reported in each panel. ersion April 9, 2018 submitted to
Entropy feedback is released in bursts of E agn = erg thermal energy for events (corresponding to a powerof W agn ≈ · erg/s) , with energy deposited in a couple of over-pressurised outflows at randomopposite directions from the halo centre (along one random direction along the coordinate axes). Inprevious works we showed that this simplified approach to include the large-scale effects of AGNin clusters can reasonably well reproduce the innermost thermodynamical profiles of clusters andcluster scaling relations [29,43]. Where the magnetisation from AGN is not present, we initialise aprimordial magnetic field to B = − G (comoving) at z = et al.
39, seealso Wittor et al. this volume). This is a reasonable approximation, under the following assumptions:a) the CRs are frozen into the gas because their spatial diffusion relative to the thermal gas is negligibleon our resolution scale ( ∆ x ); b) they represent a passive fluid with limited influence on the gasdynamics, which is justified by the low, ∼
1% energy budget, allowed by γ -ray upper limits [27]and also based on our previous work using a self-consistent 2-fluid model for CRs [29,44].In post-processing, we used 240 high-resolution ENZO ’s snapshots from z = z = ≈ · tracers using the OPEN-MP code Crater [39]. Each tracer samples ≈ M ⊙ of gas mass, and is monitored in order to model the injection and re-acceleration of CRs,based on an on-the-fly shock finder. CRs are assumed to be injected only by quasi-parallel shocks(angle ≤ ◦ between the shock normal and the upstream magnetic field), based on recent resultsfrom particle-in-cell simulations [45]. For these shocks, the acceleration efficiency as function of Machnumber follows from the best acceleration efficiency model found in Vazza et al. [29], which can fulfilthe constraints posed by the FERMI satellite [27]. This model is a rescaled version of the modelsuggested by [46], where the acceleration efficiency is rescaled down ∼ × area centred on thecluster centre at z = E thermal = k B ∆ x ρ T / ( µ m p ) , where ρ is the gas density within eachcell, T is the temperature and µ = k B and m p are the Boltzmannconstant and the proton mass, respectively). The turbulent energy is E turb = ρδ v ∆ x , where δ v is the residual velocity after filtering out velocity structures on scales L ≥
300 kpc. This scale ischosen for consistency with our previous works [e.g. 6] and is meant to filter out the typical scaleof subgroups accreting into clusters of this size. However, the choice of this scale is not unique, asduring major merger events the outer scale of turbulent motions can increase, and more complexfiltering techniques should be used [47]. In the following, we will also discuss the case in which nolarge-scale motions are filtered out from the turbulent kinetic energy budget, in order to bracket thereal level of turbulence in the ICM. The magnetic energy is computed as E mag = B ∆ x / ( π ) , where B is the magnetic field strength in each cell. Finally, the CR-proton energy in the cell is computedas E cr = ∑ i e cr,i , where e cr,i is the CR-energy measured by each tracer particle ending up in thecell; e cr,i is the result of the injection and the reacceleration of CRs by shocks, and of the adiabaticcompression/expansion experienced by each tracer, neglecting energy losses via Coulomb/hadroniccollisions [see 39, for details].Our maps show that the thermal gas energy clearly dominates over all other NT energy forms(Fig 1) across the entire cluster volume. All energy forms roughly follows the gas density profile ofthe cluster. However, the perturbed dynamical state of the cluster (which underwent a major mergerat z ∼ ersion April 9, 2018 submitted to Entropy levels in the first panel), while the magnetic energy density has a more extended distribution goingout towards the filaments.To better quantify the relative contribution of the different kinds of energies, we show in Figure2 the radial profiles of the ratios between each NT energy component and the thermal energy of theICM. The ratios are computed between enclosed energies inside the radius (e.g. ∑ ≤ i ≤ R i E thermal ( R i ) ,where E thermal ( R i ) is the total thermal energy of all cells in each radial shell with radius R i andthickness ∆ R = • the turbulent kinetic energy ranges from the case in which all velocity components larger than L ≥
300 kpc are filtered out (lower line), to the upper limit in which all the kinetic energyresolved in the cells is assumed to be turbulent. While our previous studies suggest that thetypical outer scale of turbulent motions is of the order of L ∼ −
300 kpc, in the presence oflarge-scale accretion this scale can increase. Hence the hatched region here is meant to bracketthe plausible range of ICM turbulence. The turbulent energy support increases with radius,because the driving from infall motions in the outskirts is increasingly supersonic, due to theradial drop in the ICM temperature. • The magnetic energy ranges from the primordial seed field model (trend increasing with radius)to the trend of the AGN seeding (trend decreasing with radius). In the AGN scenario themagnetic energy drops quickly with radius, as the overall activity by AGN is unable tosignificantly magnetise large volumes outside of clusters . Both these scenarios are probablyunderestimating the magnetic energy in the cluster centre, because the finite Reynolds numberachieved in our run ( R e ≤ R e ∼ N , where N is the 1-dimensional size of thehigh-resolution domain of the simulations, in number of cells, e.g. Kritsuk et al.
48) likely causesa delayed start of the small-scale dynamo amplification, compared to reality[e.g. 37]. Limited tothe single case of the Coma cluster, our primordial seeding run seems to be in better agreementwith the observational results of Faraday Rotation [e.g. 49,50], which suggests a distribution ofmagnetic energy that scales with the gas thermal energy, and a significant magnetisation in theoutskirts (even if limited to a single narrow sector of Coma, e.g. Bonafede et al. • The cosmic-ray energy goes from the upper limit obtained with out post-processing modellingof tracers [39] to zero in case no CR-protons are accelerated by shocks within the cluster. Theincreasing trend with radius of the CR-energy follows from the sharp increase of the accelerationefficiency as a function of Mach number, which rapidly increase towards cluster outskirts [e.g.38].For comparison, we also show the upper and lower limits available for the different quantitiesby observations. For the turbulent motions, we show here the upper limits derived by Churazov et al. [51] from the analysis of X-ray fluctuations in the innermost region of the Coma cluster, which are atthe level of E turb / E thermal ∼ E mag / E thermal ∼ −
2% obtained through the modelling of Faraday Rotation in the Coma cluster by Bonafede et al. [49]and Bonafede et al. [50]. Finally, the ratio of CRs to the thermal gas energy has an upper limit basedon the non-detection of hadronic γ -ray emission by Ackermann et al. [27], of the order of ∼ − E NT = E turb + E mag + E cr ) becomes more relevant at large radii,as it ranges from E NT ∼ E thermal in the cluster core to E NT ∼ E thermal at the cluster virial radius( ∼ It shall be noted that also the underlying distribution of the thermal is slightly modified in the astrophysical seedingscenarios, due to the balance of cooling and feedback, which results into a denser cluster core.ersion April 9, 2018 submitted to
Entropy
Coma-like cluster at z=0
100 1000radius [kpc]0.00010.00100.01000.10001.0000 E ne r g y r a t i o s E TURB /E THERMAL E MAG /E THERMAL E CR /E THERMAL observations:X-rayRadioGamma
Figure 2.
Radial profile of the ratios between NT energies and the thermal energy of the ICM for asimulated galaxy clusters at z = an outside-in fashion and is first mediated by outer accretion shocks, and later by the progressivedissipation of turbulent energy into gas heating (and possibly magnetic field amplification). In allcases the trend of NT energy is dominated by turbulence. In general, the lower bound given by oursmall-scale filtering should be considered probably the most realistic estimate of turbulence in theICM in the central regions, while in cluster outskirts the presence of shock waves and infall motionsmakes this estimate more uncertain.For the other two NT components (cosmic rays and magnetic fields) the simulated trend suggeststhat their pressure contribution is small enough to consider them negligible for the dynamicalevolution of the ICM. However, in the case of CR-energy this is the result of having assumed anacceleration efficiency of CR-protons which fulfils the comparison with FERMI limits, which areotherwise exceeded [29,39]. This shows that despite the scarcity of direct observations of NT energyin the ICM, upper limits from observations are helpful not only to limit the NT energy budget ofgalaxy clusters nowadays, but also the underlying efficiency of processes responsible for the injectionof NT energy in past epochs. Using a second set of simulations, we generalise the previous results for the entire cosmicvolume. We must resort to simulations with a lower resolution, which cover a 50 Mpc volume with512 cells for a fixed spatial resolution of 97 kpc, and 512 dark matter particles. In this case, instead ofusing a tracer approach to model cosmic rays we use our direct simulation using a 2-fluid method weimplemented in ENZO [29,44]. However, this 2-fluid method does not work with the MHD solver in
ENZO , and therefore we must combine independent resimulations of the same volume alternativelyobtained including either CRs or magnetic fields. This approximated approach is valid as long asthe two NT energies are small compared to the thermal energy and can therefore be viewed as twopassive fields which do not affect the gas dynamics. Based on available constraints (see below) thisassumption is probably reasonable. We will come back to this point in Sec.3.The runs modelling cosmic rays have been produced with a 2-fluid model originally developedin
ENZO [29,44], which allow us to simulate at run-time the injection, the advection, the pressurefeedback and the energy losses of CR-protons. The CRs are assumed to follow the ultra-relativistic ersion April 9, 2018 submitted to
Entropy equation of state ( Γ cr = ∼ B = − Gcomoving at z = n / h n i , where h n i is the cosmic mean gas density) at z =
0. For the NT energies we considered the turbulentenergy, the CR-proton energy and the magnetic energy. Figure 3 shows the distribution of these NTenergy forms normalised to the thermal energy within the same density bins. Given the very largeuncertainties in each of these quantities, we show through the various hatched regions in Fig. 3 therange of uncertainties due to, both, numerical (e.g. resolution effects) and physical (e.g. accelerationefficiency of CRs, magnetic field seeds etc.) effects.In detail, we show: • the turbulent kinetic energy is estimated as in the previous case via small-scale filtering (lowerlimit), or assuming that the entire post-shock kinetic energy is channeled into turbulence. Thissecond option is particularly significant in the rarefied warm-hot intergalactic medium (WHIM)outside cluster, where our coarse resolution might underestimate vorticity injected by strongaccretion shocks [32] . Again, the turbulent kinetic energy budget increases towards lowerdensities, becoming nearly supersonic at the scale of the linear structures of the Universe (e.g.filaments). At the over density probed through CIV absorption lines in the WHIM, the limits onshear motions at high-z are ∼
10 % percent of the thermal energy [52], which is at the level ofour highest estimate of turbulence. For the cluster cores, the turbulent support is instead in linewith present upper limits from X-ray analysis by XMM-Newton observations [53,54], consistentwith our estimate at higher resolution in the previous Section. • The magnetic energy is here measured by combining runs including only primordial seedingat high redshift, or with the additional seeding by AGN at run-time. Outside of clusters theuncertainties are very big because the fields are in the range 10 − G ≤ B ≤ − dependingon the seeding model. Even more significantly than in the previous Section, our simulatedmagnetic fields are found to be smaller than what has been observed through Faraday Rotation[e.g. 49,50,55], due to the lack of resolution that prevents the formation of a small-scale dynamo.However, in the high density range of our distribution the magnetic energy can be significant,owing to the assumed fixed thermal/magnetic energy per event, which can have a higherimpact on low mass systems compared to the previous analysis of the Coma-like cluster. • The cosmic-ray energy is limited by the requirement of staying within the γ -ray limits by FERMI[27]. While the uncertainties in the acceleration function produce a large uncertainty in the CRenergy budget within clusters (owing to the fact that the acceleration efficiency of weak, M ≤
M ≫
10) and the acceleration efficiency is expected to be ∼ − ersion April 9, 2018 submitted to Entropy
Figure 3.
Distribution of NT energies as a function of cosmic environment for a 50 Mpc volume at z =
0, normalised to the thermal energy within each density bin. The additional arrows show theavailable observational constraints for each energy field (see text for discussion). made difficult by the choice of an appropriate filtering scale, and also by the fact that the MHD pictureof this environment may eventually break down for very diluted plasmas.
3. Discussion & Conclusions
In this contribution we attempted to bracket the distribution of all major components of NT energy in galaxy clusters and in large-scale structures in general: turbulent kinetic energy, magnetic energyand cosmic-ray energy.Our simulations suggest that, everywhere in the cosmic volume, the NT energy from turbulentmotions is dominant over other kinds of NT energies. The kinetic pressure support from turbulentmotions increases moving away from clusters and approaches the thermal budget at the scale ofthe linear structures of the Universe. This is expected, because infall kinetic energy approachesthe complete virialisation only at high over-densities, while in the more rarefied Universe turbulentmotions, shocks and the additional role played by galactic outflows can cause larger departures fromvirialisation and channel a larger energy into NT components. Consistent with observations, theother two NT components (CR-energy and magnetic energy) are measured to reach the level of afew percent of the thermal energy budget in clusters. While the first is highly uncertain due tothe (unknown) acceleration efficiency of CRs by weak shocks, the distribution of magnetic energyis anchored to observations of Faraday Rotation in cluster cores. However, uncertainties in theefficiencies of dynamo amplification as well as on the origin of seed magnetic fields makes ourpredictions outside of clusters extremely uncertain. This makes any future observational attemptsto detect these components appealing, because new detections (or even robust upper limits) havethe potential of restricting the present range of uncertainties. In particular, detecting the continuumor polarised emission from shock-accelerated electrons in the WHIM will offer the chance of ersion April 9, 2018 submitted to
Entropy understanding, both, the origin of extragalactic magnetic fields and the physics of structure formationshocks [e.g. 35,57].Finally, a few important caveats to our analysis must be considered. First, our simulated CRs areassumed to be frozen into the gas via coupling to the tangled magnetic fields lines. This is a soundenough approximation for the ≥
10 kpc scales considered here, but on long dynamical timescales theeffect of CR diffusion might further smooth the distribution of CRs. Additionally, if CRs can stream atsuper-Alfvenic speed [an interesting yet very debated scenario, e.g. 58] then the distribution derivedin our approximation might be subject to further smoothing in the radial direction. Moreover, in ourwork we assumed that CRs and magnetic fields do not directly interact, while more detailed workon CR-driven magnetic field instabilities suggest that this is not the case in small-scale features of theICM [e.g. 59]. Finally, we also neglect the possible re-acceleration of CR-protons by turbulence [e.g.8]. In the future, constraining the level of non-thermal energy in galaxy clusters (and especially ingalaxy cluster outskirts) is crucial to perform high-precision cosmology. The expected NT budget ingalaxy clusters is already constrained to be rather low. X-ray and SZ analysis have shown that theNT pressure support is in general ≤
20% within R in most clusters [e.g. 16,17,60–63]. Numericalsimulations are important to predict the realistic 3-dimensional distribution of NT pressure and itsdependence on the host cluster properties, such has total mass, formation epoch and dynamical state.To conclude, future cosmological simulations including all relevant NT components will havethe potential to facilitate entering into an epoch of high-precision cosmology, and will also help futureobservations to become a physical probe of elusive processes in the very rarefied cosmic plasmas. Acknowledgments:
The computations described in this work were performed using the
ENZO code(http://enzo-project.org), which is the product of a collaborative effort of scientists at many universities andnational laboratories. We gratefully acknowledge the
ENZO development group for providing extremely helpfuland well-maintained on-line documentation and tutorials. The simulations were partially performed at the NICof the Forschungszentrum Jülich, under allocations no. 9016 and 10755 (F.V. and D. W.) and no. 9059 (M. B.), andon Piz Daint (ETHZ-CSCS, Lugano) under allocation s585. FV acknowledges financial support from the grantVA 876-3/1 by the Deutsche 153 Forschungsgemeinschaft (DFG). DW acknowledges support through grants SFB676 and BR 2026/17 of the DFG. F.V. and M.B. acknowledge partial financial support from the FOR1254 ResearchUnit of the German Science Foundation (DFG).
Author Contributions:
F. V. and D. W. performed the simulations used in this work; F. V. and M. B. wrote thiscontribution; C. G. contributed to the development of the numerical tools necessary to analyse the data.
Conflicts of Interest:
The authors declare no conflict of interest.
Bibliography
1. Mantz, A.; Allen, S.W.; Rapetti, D.; Ebeling, H. The observed growth of massive galaxy clusters - I.Statistical methods and cosmological constraints.
MNRAS , , 1759–1772, [0909.3098].2. Kravtsov, A.V.; Borgani, S. Formation of Galaxy Clusters. Annual Review of Astronomy and Astrophysics , , 353–409, [arXiv:astro-ph.CO/1205.5556].3. Ryu, D.; Kang, H.; Hallman, E.; Jones, T.W. ApJ , , 599–610, [arXiv:astro-ph/0305164].4. Brüggen, M.; Bykov, A.; Ryu, D.; Röttgering, H. Magnetic Fields, Relativistic Particles, and Shock Wavesin Cluster Outskirts. Science & Space Review , pp. 71–+, [arXiv:astro-ph.HE/1107.5223].5. Subramanian, K.; Shukurov, A.; Haugen, N.E.L. Evolving turbulence and magnetic fields in galaxyclusters.
MNRAS , , 1437–1454, [arXiv:astro-ph/0505144].6. Vazza, F.; Brunetti, G.; Gheller, C.; Brunino, R.; Brüggen, M. Massive and refined. II. The statisticalproperties of turbulent motions in massive galaxy clusters with high spatial resolution. A&A , , A17+, [arXiv:astro-ph.CO/1010.5950].7. Miniati, F. The Matryoshka Run: A Eulerian Refinement Strategy to Study the Statistics of Turbulence inVirialized Cosmic Structures. ApJ , , 21, [1310.2951].8. Brunetti, G.; Jones, T.W. Cosmic Rays in Galaxy Clusters and Their Nonthermal Emission. InternationalJournal of Modern Physics D , , 1430007–98, [1401.7519]. ersion April 9, 2018 submitted to Entropy
10 of 12
9. Brüggen, M.; Vazza, F. Turbulence in the Intracluster Medium. Magnetic Fields in Diffuse Media;Lazarian, A.; de Gouveia Dal Pino, E.M.; Melioli, C., Eds., 2015, Vol. 407,
Astrophysics and Space ScienceLibrary , p. 599.10. Bykov, A.M.; Dolag, K.; Durret, F. Cosmological Shock Waves.
Science & Space Review , , 119–140,[0801.0995].11. Dolag, K.; Bykov, A.M.; Diaferio, A. Non-Thermal Processes in Cosmological Simulations. Science &Space Review , , 311–335, [0801.1048].12. Ferrari, C.; Govoni, F.; Schindler, S.; Bykov, A.M.; Rephaeli, Y. Observations of Extended Radio Emissionin Clusters. Science & Space Review , , 93–118, [0801.0985].13. Feretti, L.; Giovannini, G.; Govoni, F.; Murgia, M. Clusters of galaxies: observational properties of thediffuse radio emission. The Astronomy and Astrophysics Review , , 54, [arXiv:astro-ph.CO/1205.1919].14. Rasia, E.; Tormen, G.; Moscardini, L. A dynamical model for the distribution of dark matter and gas ingalaxy clusters. MNRAS , , 237–252, [astro-ph/0309405].15. Lau, E.T.; Kravtsov, A.V.; Nagai, D. Residual Gas Motions in the Intracluster Medium andBias in Hydrostatic Measurements of Mass Profiles of Clusters. ApJ , , 1129–1138,[arXiv:astro-ph.CO/0903.4895].16. Zhang, Y.Y.; Okabe, N.; Finoguenov, A.; Smith, G.P.; Piffaretti, R.; Valdarnini, R.; Babul, A.; Evrard, A.E.;Mazzotta, P.; Sanderson, A.J.R.; Marrone, D.P. LoCuSS: A Comparison of Cluster Mass Measurementsfrom XMM-Newton and Subaru Testing Deviation from Hydrostatic Equilibrium and Non-thermalPressure Support. ApJ , , 1033–1043, [arXiv:astro-ph.CO/1001.0780].17. Eckert, D.; Molendi, S.; Vazza, F.; Ettori, S.; Paltani, S. The X-ray/SZ view of the virial region. I.Thermodynamic properties. A&A , , A22, [arXiv:astro-ph.CO/1301.0617].18. Ettori, S.; Dolag, K.; Borgani, S.; Murante, G. The baryon fraction in hydrodynamical simulations ofgalaxy clusters. MNRAS , , 1021–1030, [astro-ph/0509024].19. Battaglia, N.; Bond, J.R.; Pfrommer, C.; Sievers, J.L. On the Cluster Physics of Sunyaev-Zel’dovich andX-Ray Surveys. I. The Influence of Feedback, Non-thermal Pressure, and Cluster Shapes on Y-M ScalingRelations. ApJ , , 74, [arXiv:astro-ph.CO/1109.3709].20. Eckert, D.; Ettori, S.; Molendi, S.; Vazza, F.; Paltani, S. The X-ray/SZ view of the virial region. II. Gas massfraction. A&A , , A23, [1301.0624].21. Voit, G.M. Tracing cosmic evolution with clusters of galaxies. Reviews of Modern Physics , , 207–258,[astro-ph/0410173].22. Vikhlinin, A.; Kravtsov, A.V.; Burenin, R.A.; Ebeling, H.; Forman, W.R.; Hornstrup, A.; Jones, C.; Murray,S.S.; Nagai, D.; Quintana, H.; Voevodkin, A. Chandra Cluster Cosmology Project III: CosmologicalParameter Constraints. ApJ , , 1060–1074, [0812.2720].23. Berezinsky, V.S.; Blasi, P.; Ptuskin, V.S. Clusters of Galaxies as Storage Room for Cosmic Rays. ApJ , , 529–+, [arXiv:astro-ph/9609048].24. Völk, H.J.; Atoyan, A.M. Clusters of galaxies: magnetic fields and nonthermal emission. AstroparticlePhysics , , 73–82, [arXiv:astro-ph/9812458].25. Reimer, O.; Pohl, M.; Sreekumar, P.; Mattox, J.R. EGRET Upper Limits on the High-Energy Gamma-RayEmission of Galaxy Clusters. ApJ , , 155–164, [arXiv:astro-ph/0301362].26. Brunetti, G.; Venturi, T.; Dallacasa, D.; Cassano, R.; Dolag, K.; Giacintucci, S.; Setti, G. Cosmic Rays andRadio Halos in Galaxy Clusters: New Constraints from Radio Observations. ApJ Letters , , L5–L8,[arXiv:0710.0801].27. Ackermann, M.; Ajello, M.; Albert, A.; Allafort, A.; Atwood, W.B.; Baldini, L.; Ballet, J.; Barbiellini, G.;Bastieri, D.; Bechtol, K.; Bellazzini, R.; Bloom, E.D.; Bonamente, E.; Bottacini, E.; Brandt, T.J.; Bregeon, J.;Brigida, M.; Bruel, P.; Buehler, R.; Buson, S.; Caliandro, G.A.; Cameron, R.A.; Caraveo, P.A.; Cavazzuti, E.;Chaves, R.C.G.; Chiang, J.; Chiaro, G.; Ciprini, S.; Claus, R.; Cohen-Tanugi, J.; Conrad, J.; D’Ammando,F.; de Angelis, A.; de Palma, F.; Dermer, C.D.; Digel, S.W.; Drell, P.S.; Drlica-Wagner, A.; Favuzzi, C.;Franckowiak, A.; Funk, S.; Fusco, P.; Gargano, F.; Gasparrini, D.; Germani, S.; Giglietto, N.; Giordano, F.;Giroletti, M.; Godfrey, G.; Gomez-Vargas, G.A.; Grenier, I.A.; Guiriec, S.; Gustafsson, M.; Hadasch, D.;Hayashida, M.; Hewitt, J.; Hughes, R.E.; Jeltema, T.E.; Jóhannesson, G.; Johnson, A.S.; Kamae, T.; Kataoka,J.; Knödlseder, J.; Kuss, M.; Lande, J.; Larsson, S.; Latronico, L.; Llena Garde, M.; Longo, F.; Loparco, F.;Lovellette, M.N.; Lubrano, P.; Mayer, M.; Mazziotta, M.N.; McEnery, J.E.; Michelson, P.F.; Mitthumsiri, W.; ersion April 9, 2018 submitted to Entropy
11 of 12
Mizuno, T.; Monzani, M.E.; Morselli, A.; Moskalenko, I.V.; Murgia, S.; Nemmen, R.; Nuss, E.; Ohsugi, T.;Orienti, M.; Orlando, E.; Ormes, J.F.; Perkins, J.S.; Pesce-Rollins, M.; Piron, F.; Pivato, G.; Rainò, S.; Rando,R.; Razzano, M.; Razzaque, S.; Reimer, A.; Reimer, O.; Ruan, J.; Sánchez-Conde, M.; Schulz, A.; Sgrò, C.;Siskind, E.J.; Spandre, G.; Spinelli, P.; Storm, E.; Strong, A.W.; Suson, D.J.; Takahashi, H.; Thayer, J.G.;Thayer, J.B.; Thompson, D.J.; Tibaldo, L.; Tinivella, M.; Torres, D.F.; Troja, E.; Uchiyama, Y.; Usher, T.L.;Vandenbroucke, J.; Vianello, G.; Vitale, V.; Winer, B.L.; Wood, K.S.; Zimmer, S.; Fermi-LAT Collaboration.;Pinzke, A.; Pfrommer, C. Search for Cosmic-Ray-induced Gamma-Ray Emission in Galaxy Clusters.
ApJ , , 18, [arXiv:astro-ph.HE/1308.5654].28. Vazza, F.; Eckert, D.; Brüggen, M.; Huber, B. Electron and proton acceleration efficiency by merger shocksin galaxy clusters. MNRAS , , 2198–2211, [arXiv:astro-ph.HE/1505.02782].29. Vazza, F.; Brüggen, M.; Wittor, D.; Gheller, C.; Eckert, D.; Stubbe, M. Constraining the efficiency of cosmicray acceleration by cluster shocks. MNRAS , , 70–83, [1603.02688].30. Dolag, K.; Bartelmann, M.; Lesch, H. SPH simulations of magnetic fields in galaxy clusters. A&A , , 351–363.31. Schekochihin, A.A.; Cowley, S.C.; Taylor, S.F.; Maron, J.L.; McWilliams, J.C. Simulations of the Small-ScaleTurbulent Dynamo. ApJ , , 276–307, [astro-ph/0312046].32. Ryu, D.; Kang, H.; Cho, J.; Das, S. Turbulence and Magnetic Fields in the Large-Scale Structure of theUniverse. Science , , 909–, [0805.2466].33. Cho, J. Origin of Magnetic Field in the Intracluster Medium: Primordial or Astrophysical? ApJ , , 133, [1410.1893].34. Vazza, F.; Brüggen, M.; Gheller, C.; Wang, P. On the amplification of magnetic fields in cosmic filamentsand galaxy clusters. MNRAS , , 3706–3722, [1409.2640].35. Vazza, F.; Ferrari, C.; Brüggen, M.; Bonafede, A.; Gheller, C.; Wang, P. Forecasts for the detection of themagnetised cosmic web from cosmological simulations. A&A , , A119, [1503.08983].36. The Enzo Collaboration.; Bryan, G.L.; Norman, M.L.; O’Shea, B.W.; Abel, T.; Wise, J.H.; Turk, M.J.;Reynolds, D.R.; Collins, D.C.; Wang, P.; Skillman, S.W.; Smith, B.; Harkness, R.P.; Bordner, J.; Kim, J.h.;Kuhlen, M.; Xu, H.; Goldbaum, N.; Hummels, C.; Kritsuk, A.G.; Tasker, E.; Skory, S.; Simpson, C.M.;Hahn, O.; Oishi, J.S.; So, G.C.; Zhao, F.; Cen, R.; Li, Y. Enzo: An Adaptive Mesh Refinement Code forAstrophysics. ArXiv e-prints , [arXiv:astro-ph.IM/1307.2265].37. Beresnyak, A.; Miniati, F. Turbulent Amplification and Structure of the Intracluster Magnetic Field.
ApJ , , 127, [1507.00342].38. Vazza, F.; Brunetti, G.; Gheller, C.; Brunino, R. Massive and refined: A sample of large galaxy clusterssimulated at high resolution. I: Thermal gas and properties of shock waves. New Astronomy , , 695–711, [arXiv:astro-ph.CO/1003.5658].39. Wittor, D.; Vazza, F.; Brüggen, M. Testing cosmic-ray acceleration with radio relics: a high-resolutionstudy using MHD and tracers. ArXiv e-prints , [arXiv:astro-ph.HE/1610.05305].40. Wang, P.; Abel, T.; Kaehler, R. Adaptive mesh fluid simulations on GPU.
New Astronomy , , 581–589,[arXiv:astro-ph.CO/0910.5547].41. Subramanian, K. The origin, evolution and signatures of primordial magnetic fields. ArXiv e-prints ,[1504.02311].42. Planck Collaboration.; Ade, P.A.R.; Aghanim, N.; Arnaud, M.; Arroja, F.; Ashdown, M.; Aumont, J.;Baccigalupi, C.; Ballardini, M.; Banday, A.J.; et al.. Planck 2015 results. XIX. Constraints on primordialmagnetic fields.
A&A , , A19, [1502.01594].43. Vazza, F.; Brüggen, M.; Gheller, C. Thermal and non-thermal traces of AGN feedback: results fromcosmological AMR simulations. MNRAS , , 2366–2388, [arXiv:astro-ph.CO/1210.3541].44. Vazza, F.; Brüggen, M.; Gheller, C.; Brunetti, G. Modelling injection and feedback of cosmicrays in grid-based cosmological simulations: effects on cluster outskirts. MNRAS , p. 2518,[arXiv:astro-ph.CO/1201.3362].45. Caprioli, D.; Spitkovsky, A. Simulations of Ion Acceleration at Non-relativistic Shocks. I. AccelerationEfficiency.
ApJ , , 91, [arXiv:astro-ph.HE/1310.2943].46. Kang, H.; Ryu, D. Diffusive Shock Acceleration at Cosmological Shock Waves. ApJ , , 95,[arXiv:astro-ph.HE/1212.3246]. ersion April 9, 2018 submitted to Entropy
12 of 12
47. Vazza, F.; Roediger, E.; Brueggen, M. Turbulence in the ICM from mergers, cool-core sloshingand jets: results from a new multi-scale filtering approach.
ArXiv e-prints 1202.5882 ,[arXiv:astro-ph.CO/1202.5882].48. Kritsuk, A.G.; Norman, M.L.; Padoan, P. Adaptive Mesh Refinement for Supersonic Molecular CloudTurbulence.