Radio Halos in future surveys in the radio continuum
R. Cassano, G. Brunetti, Ray P. Norris, H. J. A. Roettgering, M. Johnston-Hollitt, M. Trasatti
aa r X i v : . [ a s t r o - ph . C O ] O c t Astronomy&Astrophysicsmanuscript no. cassano c (cid:13)
ESO 2018July 23, 2018
Radio Halos in future surveys in the radio continuum
R. Cassano ,⋆ , G. Brunetti , Ray P. Norris , H. J. A. R ¨ottgering , M. Johnston-Hollitt , M. Trasatti INAF - Istituto di Radioastronomia, via P. Gobetti 101,I-40129 Bologna, Italy School of Chemical & Physical Sciences, Victoria University of Wellington, Wellington 6140, New Zealand CSIRO Astronomy & Space Science, Epping, NSW 1710, Australia Leiden Observatory, Leiden University, Oort Gebouw, P.O. Box 9513, 2300 RA Leiden, The Netherlands Argelander-Institut f¨ur Astronomie, Auf dem H¨ugel 71, 53121 Bonn, GermanyPreprint online version: July 23, 2018
ABSTRACT
Aims.
Giant radio halos are Mpc-scale synchrotron sources detected in a significant fraction of massive and merging galaxy clusters.The statistical properties of radio halos can be used to discriminate among various models for the origin of non-thermal particles ingalaxy clusters. Therefore, theoretical predictions are important as new radio telescopes are about to begin to survey the sky at lowand high frequencies with unprecedented sensitivity.
Methods.
We carry out Monte Carlo simulations to model the formation and evolution of radio halos in a cosmological framework andextend previous calculations based on the hypothesis of turbulent-acceleration. We adopt a phenomenological approach by assumingthat radio halos are either generated in turbulent merging clusters, or are purely hadronic sources generated in more relaxed clusters,“o ff -state” halos. Results.
The models predict that the luminosity function of radio halos at high radio luminosities is dominated by the contribution ofhalos generated in turbulent clusters. The generation of these halos becomes less e ffi cient in less massive systems causing a flatteningof the luminosity function at lower radio luminosities, as also pointed out in previous studies. However, we find that potentially thiscan be more than compensated for by the intervening contribution of “o ff -state” halos that dominate at lower radio luminosities. Wederive the expected number of halos to explore the potential of the EMU + WODAN surveys that will be carried out with ASKAPand Aperitif, respectively, in the near future. By restricting to clusters at redshifts ≤ + WODANsurveys at 1.4 GHz have the potential to detect up to about 200 new radio halos, increasing their number by one order of magnitude.A fraction of these sources will be “o ff -state” halos that should be found at flux level f . ≤
10 mJy, presently accessible only todeep pointed observations. We also explore the synergy between surveys at di ff erent radio frequencies, the Tier 1 LOFAR surveyat 150 MHz and the EMU + WODAN surveys at 1.4 GHz. We predict a larger number of radio halos in the LOFAR survey due tothe high LOFAR sensitivity, but also due to the existence of halos with very steep spectrum that glow up preferentially at lowerfrequencies. These halos are only predicted in the framework of turbulent re-acceleration models and should not have counterparts inthe EMU + WODAN surveys, thus the combination of the two surveys will test theoretical models.
Key words.
Radiation mechanism: non–thermal - galaxies: clusters: general - radio continuum: general - X–rays: general
1. Introduction
Radio halos are di ff use Mpc–scale radio sources observed at thecenter of ∼
30% of massive galaxy clusters ( e.g.,
Ferrari et al.2008, Venturi 2011, Feretti et al. 2012 for recent reviews). Thesesources emit synchrotron radiation produced by GeV electronsdi ff using through µ G magnetic fields and provide the most im-portant evidence of non-thermal components in the intra-clustermedium (ICM).Clusters hosting radio halos always display evidence of veryrecent or ongoing merger events ( e.g.,
Buote 2001; Schuecker etal 2001; Govoni et al. 2004; Venturi et al. 2008; Cassano et al.2010a). The connection between radio halos and cluster mergerssuggests that the gravitational process of cluster formation pro-vides the energy to generate the non-thermal components in clus-
Send o ff print requests to : R.Cassano ⋆ e-mail: [email protected] ters through the acceleration of high-energy particles via shocksand turbulence (e.g., Sarazin 2004, Brunetti 2011a, for review).A scenario proposed to explain the origin of the synchrotronemitting electrons in radio halos assumes that seed relativisticelectrons in the ICM are re-accelerated by the interaction withmerger-driven MHD turbulence in merging galaxy clusters ( tur-bulent re-acceleration model, e.g., Brunetti et al. 2001; Petrosian2001). According to this scenario, the formation and evolution ofradio halos are tightly connected to the dynamics and evolutionof the hosting clusters. The occurrence of radio halos at any red-shift depends on the rate of cluster-cluster mergers and on thefraction of the merger energy channelled into MHD turbulenceand re-acceleration of high energy particles. This latter point de-pends on microphysics of the ICM and it is di ffi cult to estimate(see e.g., Brunetti & Lazarian 2011a).Despite model details, one of the most important expecta-tions of this scenario is the existence of a population of radiohalos with very steep radio spectra which will be mostly vis-
1. Cassano et al.: Radio Halos in future surveys in the radio continuum ible al low radio frequencies (Cassano et al. 2006; Brunetti etal. 2008). The existence of this population can be tested withthe upcoming surveys at low radio frequencies with the LowFrequency Array (LOFAR) , the Long Wavelength Array (LWA, e.g., Ellingson et al. 2009) and the Murchison Widefield Array(MWA, e.g.,
Tingay et al. 2012). Cassano et al. (2010b) haveshown that the LOFAR
Tier-1 “Large Area Survey” at 120-190MHz (R¨ottgering 2010), with an expected rms sensitivity of ∼ / beam, should detect about 350 giant radio halosup to redshift z ∼ .
8, and half of them should have very steepradio spectra (with α > ∼ . F ( ν ) ∝ ν − α ).An alternative scenario relies on the production of sec-ondary electrons. Inelastic collisions between cosmic ray pro-tons and target thermal protons in the ICM produce a popula-tion of secondary electrons that can generate di ff use synchrotronemission on galaxy cluster-scale ( e.g., Dennison 1980; Blasi &Colafrancesco 1999). Despite several observations pointed outthat pure secondary models have di ffi culties in explaining thespectral and morphological properties of several nearby giant ra-dio halos ( e.g., Brunetti et al. 2008; Donnert et al. 2010; Brown& Rudnick 2011; Jeltema & Profumo 2011, for additional con-straints based on γ -ray upper limits), synchrotron emission pro-duced by secondary electrons must be present in galaxy clus-ters. This comes from the theoretical argument that galaxy clus-ters are e ffi cient reservoirs of cosmic ray protons (acceleratedby structure formation shock waves, injected from radio galax-ies, or from supernova driven galactic winds) and consequentlythese protons accumulate with cluster life-time increasing theprobability to have proton-proton collisions (V¨olk et al 1996;Berezinsky et al 1997; Enßlin et al 1997).Recent Fermi-LAT and Cherenkov-telescopes observationshave placed upper limits on the ratio of non-thermal CRp tothermal energy densities at the level of ∼ few% in a number ofnearby clusters (Ackermann et al. 2010; Aleksi´c et al. 2012).Assuming these constraints, it has been suggested that duringcluster mergers the re-acceleration of secondary electrons bycompressible MHD turbulence can generate synchrotron radi-ation in good agreement with radio halos, while synchrotronemission ∼
10 times fainter is generated in dynamically relaxedclusters when turbulence is dissipated (Brunetti & Lazarian2011b). This theoretical conjecture is consistent with the ob-served radio bimodality in galaxy clusters ( e.g.,
Brunetti et al.2009; Cassano et al. 2010a), although it predicts a level of emis-sion (from pure secondaries) in relaxed clusters that is close theupper limits derived for these clusters from present radio obser-vations. More recently, Brown et al. (2011) claimed the detectionof radio emission from the stacking of SUMMS images of “o ff -state” (non-radio halo) clusters at a level ∼
10 times fainter thanthat of classical radio halos, potentially in line with the abovetheoretical picture.In about the next 10 years several revolutionary radio tele-scopes will survey the sky with unprecedented sensitivity andspatial resolution at very low (LOFAR, LWA, MWA) andGHz frequencies (ASKAP; Johnston et al. 2008 and Aperitif;Oosterloo, Verheijen, van Cappellen 2010). This gives the oppor-tunity to constrain the complex connection between cluster dy-namics and di ff use radio emission in galaxy clusters by means ofstatistical studies of adequately large cluster sample. The combi-nation of incoming surveys at low (LOFAR) and higher (e.g., theEMU survey with ASKAP) frequencies will add considerablevalue in the attempt to discriminate between di ff erent physicalorigins of giant radio halos in galaxy clusters and, in general, of http: // non-thermal cluster components. The first LOFAR observationat ∼
63 MHz of the giant radio halo in Abell 2256 shows thatthe radio spectrum extracted in the region of the halo steepens atlower frequencies. This unexpected result suggests that physicalscenario more complex than previously thought should be con-sidered to explain the formation of the radio halo in this cluster(van Weeren et al. 2012). In fact, di ff erent populations of rel-ativistic electrons may coexist in the volume of the radio haloif they originate from di ff erent acceleration mechanisms, or ifelectrons are accelerated in a non homogeneous turbulent regionwhere the e ffi ciency of particle acceleration change with spaceand time in the emitting volume (van Weeren et al. 2012).In this paper, we extend previous statistical modeling of gi-ant radio halos by combining a picture based on turbulent re-acceleration of relativistic electrons by MHD turbulence in clus-ter mergers with the process of continuous injection of secondaryelectrons via p-p collision in the ICM. This provide a novel ap-proach to interpret future data from surveys of galaxy clusters.This has not the aim to reproduce particular spectral featuressuch as those observed in Abell 2256, but its aim is to provide asimplified (but viable) description of the general observed prop-erties of the population of radio halos in galaxy clusters.In Sect. 2 we summarize the main ingredients used in themodel calculations, derive the occurrence of radio halos in clus-ters (Sect. 2.2) and the expected radio halo luminosity functions(Sect. 2.3). In Sect. 3 we discuss and model the contribution tothe di ff use cluster-scale synchrotron emission from secondaryelectrons. In Sect. 4 we describe the EMU and WODAN surveys,while in Sect. 5 we derive the expected number of radio halos at1.4 GHz and discuss the potential of the EMU and WODAN sur-veys. In Sect. 6 we discuss the potential of combining LOFARand EMU and WODAN surveys in addressing the physics of gi-ant radio halos. Our conclusions are given in Sect.7.A Λ CDM ( H o =
70 Km s − Mpc − , Ω m = . Ω Λ = .
7) cos-mology is adopted throughout the paper.
2. Statistical modelling of giant radio halos fromturbulent re-acceleration
Turbulence generated during cluster mergers may re-acceleraterelativistic particles and produce di ff use synchrotron emissionfrom Mpc regions in galaxy clusters ( e.g., Brunetti et al. 2008).Di ff use radio emission in the form of giant radio halos shouldbe generated in connection with massive mergers and fade awayas soon as turbulence is dissipated and the emitting electronscool due to radiative losses. Attempts for estimating the statisti-cal properties of giant radio halos in the context of this scenariohave been carried out in the past few years (Cassano & Brunetti2005; Cassano et al. 2006; Cassano et al. 2010b). These studiesallowed for a comparison with the presently observed statisti-cal properties of giant radio halos, while at the same time theyprovide predictions to test with future instruments.In these calculations we model the properties of the halosand their cosmic evolution by means of a Monte Carlo approach,taking into account the main processes that play a role in thisscenario: the rate of cluster-cluster mergers in the Universe andtheir mass ratios, and the fraction of the energy dissipated duringthese mergers that is channelled into MHD turbulence and accel-eration of high energy particles. We refer the reader to the papersquoted above for details, here for the sake of completeness webriefly report the essential steps of those calculations :
2. Cassano et al.: Radio Halos in future surveys in the radio continuum
Fig. 1.
Reference spectra of “turbulent” radio halos (solid lines)and “o ff -state” (hadronic) halos (dashed lines) in a massive( i.e., M v ∼ . × M ⊙ ; black lines) and less massive( i.e., M v ∼ M ⊙ ; red lines) cluster. Arrows indicate the posi-tion of the steepening frequency, ν s , in the two cases. The turbu-lent spectra are computed assuming in both cases a merger eventwith a sub-clump of mass ∆ M = × M ⊙ at z = . i) The formation and evolution of dark matter halos of galaxyclusters is computed by the extended Press & Schechter ap-proach (1974, hearafter PS; Lacey & Cole 1993), which isbased on the hierarchical theory of cluster formation. Giventhe present-day mass and temperature of the parent clusters,the cluster merger history ( merger trees ) is obtained by usingMonte Carlo simulations. ii)
The generation of the turbulence in the ICM is estimated foreach merger identified in the merger trees . Turbulence is as-sumed to be generated (and dissipated) within a timescale ofthe order of the cluster-cluster crossing time in that merger.Furthermore, it is assumed that the turbulence is generatedin the volume swept by the subcluster infalling into the maincluster. The injection rate of turbulent fast modes / waves, thatare used to calculate particle acceleration, is assumed to be afraction, η t , of the PdV work done by this subcluster. iii)
The resulting spectrum of MHD turbulence generated by thechain of mergers in any synthetic cluster and its evolutionwith cosmic time is computed by taking into account theinjection of waves and their damping, due to thermal andrelativistic particles, in a collisionless plasma. Accelerationof particles by this turbulence and their evolution is com-puted in connection with the evolution of synthetic clustersby solving Fokker-Planck equations and including all the rel-evant energy losses of particles. iv)
Synchrotron losses, particle acceleration and emissivity arecalculated assuming homogeneous models (see Cassano etal. 2006): radio halos are assumed to be homogeneousspheres of radius R H ∼ h − kpc, and volume-averagevalues of turbulent energy, acceleration rate and magnetic field are adopted. We assume a value of the magnetic fieldwhich scales with the virial mass of clusters, M v as < B > = B < M > (cid:16) M v < M > (cid:17) b , (1)where b >
0, and B < M > is the value of the rms magnetic fieldassociated with a cluster with mass < M > ≃ . × M ⊙ (see next Sect. and Sect. 3 in Cassano et al. 2006, for de-tails). This scaling is motivated by the results of cosmo-logical MHD simulations that found that the magnetic fieldscales with the temperature (and mass) of the simulated clus-ters ( e.g., Dolag et al. 2002) . Stochastic particle acceleration by MHD turbulence is a ratherine ffi cient process in the ICM that accelerates electrons at ener-gies m e c γ max ≤ several GeV, since at higher energies the radi-ation losses quench the acceleration process (see e.g., Brunetti2011b and references therein). In the case of a homogeneousmodel this implies a steepening of the synchrotron spectrum thata ff ects the capability to detect radio halos at frequencies sub-stantially larger than the frequency, ν s , where the steepening be-comes severe. The frequency ν s depends on the acceleration ef-ficiency , χ , and on < B > , as ν s ∝ < B > χ / ( < B > + B cmb ) ( e.g., Cassano et al. 2006, 2010b). Monte Carlo simulations ofcluster mergers that occur during the hierarchical process ofcluster formation (Sect. 2.1) allow for evaluating χ from the es-timated rate of turbulence-generation and the physical conditionin the ICM, and consequently to explore the dependence of ν s on cluster mass, redshift, and merger parameters in a statisticalsample of synthetic clusters.A reference example of spectra of “turbulent” radio halos asmodeled in the present paper is shown in Fig.1. A simplifiedapproach to estimate the occurrence of radio halos in surveysat di ff erent observing frequencies is to assume that only thosehalos with ν s ≥ ν o can be observable, ν o being the observingfrequency. Energy arguments imply that giant radio halos with ν s ≥ ν o ∼ e.g., Venturi 2011 and ref-erences therein, for a review). The fact that ∼ / ∼ GHzfrequencies has been used to constrain the parameters for thegeneration of turbulence in the modeling described in Sect. 2.1( η t ≈ . − .
3, Cassano & Brunetti 2005; Cassano et al 2008a).In Fig. 2, we plot the fraction of radio halos with ν s ≥ ff erential contribution to this fractionfrom radio halos with ν s in four frequency ranges (see figurecaption for details). This is obtained by assuming a reference setof model parameters, namely < B > = . µ G, b = . η t = . z = − . ν s ≥ Dolag et al. (2002) found a scaling B ∝ T , which would imply that B ∝ M . if the virial scaling M ∝ T / is assumed. 3. Cassano et al.: Radio Halos in future surveys in the radio continuum Fig. 2.
Fraction of clusters with radio halos with ν s ≥ − . . − . ν s in di ff erent frequencyranges are also shown : 1000 < ν s < < ν s < < ν s < ν > M v > − × M ⊙ ). On the other hand, the fraction of clus-ters hosting radio halos with ν s in the range 1-2 GHz (red andblue lines) reaches a maximum for clusters masses slightly be-low ∼ × M ⊙ , and then decreases for more massive systems.This behavior is due to the fact that in general, in our model, thefraction of clusters with radio halos increases with the clustermass, since more massive clusters are more turbulent, and thusare more likely to host a radio halo. The occurrence of haloswith relatively lower values of ν s ( ν s < ν s lower the valueof the mass up to which the occurrence of these halos increases,for larger masses their occurrence decrease since those clusterspreferentially form halos with larger values of ν s .Consequently we expect that very massive (and hot) clus-ters tend to generate giant radio halos with radio spectra flatter(higher values of ν s ) than those in less massive systems. A ten-dency to have halos with flatter spectra in more massive (hot)systems have been reported in literature (Feretti et al. 2004;Giovannini et al. 2009, Venturi et al. 2012, sub.). If confirmedthese findings would support our expectations.In addition, we find that giant radio halos with higher valuesof ν s become rarer with increasing redshift, mainly because ofthe inverse Compton losses that increase with redshift and limitthe maximum energy of the accelerated electrons. The luminosity functions of radio halos (RHLFs) with ν s ≥ ν ( i.e., the expected number of halos per comoving volume andradio power “observable” at frequency ν ) can be estimated by : dN H ( z ) dV dP ( ν ) = dN H ( z ) dM dV , dP ( ν ) dM , (2)where dN H ( z ) / dM dV is the theoretical mass function of radiohalos with ν s ≥ ν , that is obtained by combining Monte Carlo Fig. 3.
Radio halo luminosity function at ν o = . − .
2. The contributions fromhalos with ν s in di ff erent frequency ranges are also shown :1000 < ν s < < ν s < < ν s < ν > ξ =
3, see text for details) for EMU + WODAN surveyand for the NVSS (from left to right).
4. Cassano et al.: Radio Halos in future surveys in the radio continuum
Fig. 4.
Radio halo luminosity function at ν o = = − .
1, 0 . − .
2, 0 . − .
3, 0 . − . . − . . − . e.g., Cassano et al. 2006). dP ( ν ) / dM depends on (is proportional to) the unknownnumber of seeds electrons (or that of cosmic ray protons) in theICM. Following Cassano et al.(2006) we estimate dP ( ν ) / dM from the correlation observed for giant radio halos between the1.4 GHz radio power, P (1 . e.g., Govoni et al. 2001; Cassano et al. 2006). The observedcorrelation allows us to normalize the radio luminosity of gi-ant radio halos under the assumption that “all” radio halos with ν s > dP (1 . / dM depends on the set of parameters ( B < M > , b ),consequently the slope of the observed P (1 . − M correlation( P ∝ M α M with α M = . ± .
4) can be used to constrain modelparameters selecting an allowed region in the parameter space( B < M > , b ) (Cassano et al. 2006). In this paper we shall adopta reference set of model parameters, i.e., B < M > = . µ G and b = . η t = . α M ≈ . ν o = ν s > ν s in the frequency inter-val ∆ ν si , and then combined the di ff erent contributions from theconsidered intervals ∆ ν si : dN H ( z ) dV dP ( ν o ) = X i (cid:16) dN H ( z ) dM dV (cid:17) ∆ ν si (cid:16) dP ( ν o ) dM (cid:17) − ∆ ν si . (3)The relation between the monochromatic radio luminosity P ( ν o )of halos with a given ν s (with ν s ≥ ν ) and that of halos with ν s = . P ν s ( ν o , M v ) = P ν s ( ν s , M v ) (cid:18) ν s ν o (cid:19) α = P . (1 . , M v ) (cid:18) ν s ν o (cid:19) α , (4) allowing a prompt evaluation of ( dP ( ν o ) / dM ) ∆ ν si in Eq. 3.Taking P . ( ν , M v ) = P . (1 . , M v )(1 . /ν ) α , from Eq.4one has: P ν s ( ν o , M v ) = P . ( ν o , M v ) (cid:18) ν s (cid:19) α , (5) i.e., radio halos with synchrotron spectra that steepen at lowerfrequencies will also have smaller monochromatic radio powersat the observing frequency ν o .As a relevant example, in Fig.3 we report the expected RHLF at1.4 GHz (black lines) for z = . − . ff erentvalues of ν s (see caption).As already discussed in Cassano et al. (2006) and Cassano etal. (2010b), the shape of the RHLF flattens at lower radio pow-ers because of the expected decrease of the e ffi ciency of particleacceleration in the case of less massive clusters. We note thathalos with ν s > z of both the cluster mass function andthe fraction of galaxy clusters with radio halos (Fig. 2, see alsoCassano et al. 2006).
3. Secondary electrons
An additional contribution to the Mpc-scale synchrotron emis-sion from galaxy clusters comes from the process of continuousinjection of secondary electrons via p-p collisions in the ICM.A self-consistent modeling of the re-acceleration of primarycosmic rays and secondary electrons / positrons by compressibleMHD turbulence in the ICM has been developed in Brunetti &Lazarian (2011b). Implementing their formalism in our cosmo-logical Monte Carlo framework is challenging and out of themain focus of the present paper.Here we adopt a simplified approach based on two separate clus-ter radio-populations. We assume that presently observed radiohalos are mainly generated in merging clusters by particle ac-celeration by turbulence. In more relaxed clusters, turbulencecannot maintain a population of relativistic electrons emittingat the observing frequencies, ν o , and in these cases the domi-nant contribution to Mpc-scale radio emission is due to the gen-eration of secondary particles. As a first approximation we canassume that the level of the emission from secondary particlesin these clusters is stationary, i.e., it does not depend on clus-ter dynamics, since the primary protons accumulate in galaxyclusters over the cluster lifetime and continuously generate sec-ondaries (Blasi 2001) . Under our hypothesis the emission pro-duced by secondary particles can be constrained from the lim-its derived from deep radio observations of “radio quiet” galaxyclusters ( e.g., Brunetti et al. 2007, 2009). These limits are aboutone order of magnitude below the radio-X-ray luminosity cor-relation for classical giant radio halos (Fig. 5). More recently,Brown et al. (2011) have detected di ff use emission from “o ff -state” galaxy clusters by stacking SUMSS images of ∼
100 clus-ters. Potentially, this signal can be contributed by secondary par- We do not consider here possible modifications of the synchrotronemission in these clusters due to magnetic field amplification andcosmic-ray di ff usion ( e.g., Kushnir et al. 2009; Enßlin et al. 2011). 5. Cassano et al.: Radio Halos in future surveys in the radio continuum ticles in less turbulent systems. Motivated by these recent ob-servations, here we assume that clusters where turbulence is notenough to produce giant radio halos emitting at the observingfrequency ν ( i.e., with ν s < ν , see Sect.2) host di ff use radioemission powered by pure secondaries with a luminosity thatis similar to the upper limits in Fig. 5. Following Brown et al.(2011) we refer to these halos as to “o ff -state” radio halos.The massfunction of “o ff -state” halos is given by: dN secH ( z , ν o ) dV dM = (1 − f RH ( M , ν o )) × dN clM dV dM (6)where f RH ( M , ν o ) is the fraction of clusters of mass M with ra-dio halos due to turbulence re-acceleration (with ν s ≥ ν o ) and dN clM / dV dM is the cluster mass function. The luminosity func-tion of “o ff -state” halos is: dN secH ( z , ν o ) dV dP = dN secH ( z , ν o ) dV dM × dMdP , (7)We derive dM / dP from the expected relation between the ra-dio luminosity of “o ff -state” halos and the mass (or L X ) of thehost clusters. In their most simple formulation, secondary mod-els predict a correlation between the radio luminosity of halosand the cluster X-ray luminosity ( e.g., Kushnir, Katz & Waxman2009) that is slightly flatter than that of giant radio halos (seeBrunetti et al. 2009): P = A Xnorm L . X × B B + B cmb ≈ A Mnorm M . × B B + B cmb (8)where the second equivalence is obtained by assuming the M v − L X correlation (taken from Cassano et al. 2006). The normaliza-tion factors A Xnorm and A Mnorm are derived in order to be consistentwith the radio upper limits in the plane P . − L X obtained for“radio quiet” systems (Brunetti et al. 2007, 2009). Specifically,we adopt two di ff erent approaches and obtain two scalings (seeFig.5): a) in the first one we use the scaling of the magnetic fieldwith the cluster mass in Eq.1 with b = . B < M > = . µ G,and adopt P ≈ × Watt / Hz for L X = erg / sec (blue linein Fig.5); b) in the second one we consider a constant magneticfield B = µ G and a slightly higher normalization, P ≈ × Watt / Hz for L X = erg / sec (red line in Fig.5). The latter ap-proach maximizes the contribution from secondary electrons. Areference example of spectra of “o ff -state” (hadronic) halos inthe case a) is show in Fig.1.Apparently, the adopted scalings for secondaries are not fullyconsistent with non-detections of higher luminosity clusters,however some of these clusters are cool-core systems and theirluminosity is likely to be boosted (up to ∼ α = . α = . ff -state” halos, in the case a) (left panel) and b)(right panel). Under our assumptions, “o ff -state” halos dominatethe RHLF at lower radio luminosities where the RHLF due toturbulent radio halos flattens. Here we modify Kushnir et al. formalism to account also for thecase of weak magnetic fields.
Fig. 5.
Correlation between the radio halo luminosity at 1.4 GHzand the cluster X-ray luminosity. Clusters from the literature(filled circle) and clusters from the GMRT RH Survey (Venturiet al. 2008; open circles and black arrows) are reported. The redcrosses are obtained by staking the radio images of clusters fromthe SUMSS survey (Brown et al. 2011). On the same figure wealso report the two scalings adopted in the present paper for ha-los produced by secondary electrons: case a) (blue line) and caseb) (red line)(see text for details).
4. The EMU+WODAN Surveys
The Australian SKA Pathfinder (ASKAP) (Johnston et al. 2008)is a new radio telescope being built at the Murchison Radio-astronomy Observatory in Western Australia. It consists of 3612-metre antennas distributed over a region 6 km in diameter.ASKAP will have an instantaneous field of view of 30 deg ,enabling surveys of a scope that cannot be contemplated withcurrent-generation telescopes. The ASKAP array configurationbalances the need for high sensitivity to extended structures withthe need for high resolution. To achieve this, 30 antennas followa roughly Gaussian distribution with a scale of ∼
700 m, corre-sponding to a point spread function of ∼ ′′ , with a further sixantennas extending to a maximum baseline of 6 km, correspond-ing to a point spread function of ∼ ′′ . These short spacings ofASKAP deliver excellent sensitivity to low-surface brightnessemission, which is essential for studies of radio emission fromclusters.Science data processing will take place in an automatedpipeline processor in real time. The on-line imaging uses nei-ther natural nor uniform weighting, but instead uses an algo-rithm called preconditioning, which, together with multi-scaleclean, gives a similar sensitivity to uniform weighting at smallspatial scales, and a similar sensitivity to natural weighting atlarge spatial scales. So near-optimum sensitivity is obtained at allscales without needing to reweight the data. The ∼ µ Jy / beamrms continuum sensitivity in 12 hours is approximately con-stant for beam sizes from 10 to 30 arcsec, then increases to ∼ µ Jy / beam for a 90 arcsec beam and ∼ µ Jy / beam for a3 arcmin beam.
6. Cassano et al.: Radio Halos in future surveys in the radio continuum
Fig. 6.
Total RHLFs obtained by combining the contributions from “turbulent” radio halos and from (purely hadronic) “o ff -state”halos in the case a) ( left panel ) and b) ( right panel ) (see text for details). The RHLF are reported in di ff erent redshift interval:z = − .
1, 0 . − .
2, 0 . − .
3, 0 . − .
4, 0 . − . . − . µ Jy / beam rms) radio continuum survey of the en-tire Southern Sky, extending as far North as +
30 deg. EMU willcover roughly the same fraction (75%) of the sky as the bench-mark NVSS survey (Condon et al. 1998) , but will be 45 timesmore sensitive, and will have an angular resolution (10 arcsec)4.5 times better. Because of the excellent short-spacing uv cov-erage of ASKAP, EMU will also have higher sensitivity to ex-tended structures such as cluster haloes. APERTIF, the new Phased Array Feed (PAF) system that will beinstalled on the Westerbork Synthesis Radio Telescope (WSRT),will dramatically increase, at frequencies from 1.0 to 1.7 GHz,the instantaneous field of view of the WSRT and its observ-ing bandwidth ( e.g.,
Oosterloo et al 2010). Many beams can beformed simultaneously for each dish making it possible to imagean area of about 8 square degree on the sky, which is an increaseof about a factor 30 compared to the current WSRT. This entirefield of view will be imaged with 15 arcseconds spatial resolu-tion over a bandwidth of 300 MHz with a spectral resolution ofabout 4 km / s. The survey speed of APERTIF, and many of theother characteristics, will be very similar to ASKAP.The extremely large field of view of APERTIF would enablethe WODAN (Westerbork Observations of the Deep APERTIFNorthern-Sky) project ( e.g., R¨ottgering et al. 2011). This projecthas been proposed with the aim to chart the entire accessiblenorthern sky at 1400 MHz down to 10 µ Jy rms and about 1000deg down to 5 µ Jy. WODAN will be an important complementof the EMU project in the northern sky.
Fig. 7.
Integrated number of radio halos within a given redshiftexpected in the NVSS follow-up of the XBACS clusters (dashedline) compared with the observed values (black points) withinz = = f min ( z ) givenby Eq. 9 with ξ = ξ =
10 (long dashed line).
5. Number of radio halos in the EMU+WODANsurvey
It has been shown that results based on calculations carried outaccording to Sect.2 are consistent with the observed increase ofthe fraction of clusters with radio halos with the cluster mass (or
7. Cassano et al.: Radio Halos in future surveys in the radio continuum
Fig. 8.
Minimum flux (left panel) and power (right panel) of detectable radio halos at 1400 MHz obtained by Eq. 9 with ξ = ξ =
10 (dashed lines). Calculations are shown for the NVSS (rms = .
45 mJy, θ b =
45 arcsec; blackupper lines) and for EMU + WODAN (rms = µ Jy, θ b =
25 arcsec; red bottom lines).X-ray luminosity; Cassano et al. 2008a) and with the observednumber of nearby radio halos (Cassano et al. 2006). In particu-lar, Cassano et al. (2010b) showed that model expectations alsoproduce the flux distribution of giant radio halos observed inthe redshift ranges 0 . ≤ z ≤ . . ≤ z ≤ .
32 (derived from the
GMRT radio halo survey ; Venturi et al. 2007, 2008).The EMU + WODAN survey will explore the radio sky witha sensitivity ∼
10 times better than present surveys, making itpossible to test models in a totally unexplored range of radio haloluminosities and masses of the host systems. In this Section weshall derive the expected number of radio halos at 1400 MHz andexplore the potential of the upcoming EMU + WODAN survey.At this point it is important to estimate the minimum flux of aradio halo (integrated over a scale of ∼ i) a brightness-based criterion and ii) a flux-based criterion. i) The criterion based on a threshold in brightness guaranteesthat halos are detected in the images generated by the survey.From this threshold we derive the flux (luminosity, z) of ra-dio halos that can be detected by assuming a spatial distribu-tion of their brightness. The brightness profile of giant radiohalos is known to smoothly decrease with distance from thecluster center ( e.g.,
Murgia et al. 2009) implying that the outer-most, low brightness, regions of halos are very di ffi cult to detect.However what is important is the capability to detect at least,the brightest regions, of the radio halos. Radio halos emit abouthalf of their total radio flux within their half radius (Brunettiet al. 2007, Fig. 1). Following Cassano et al. (2010b) we esti-mate the minimum flux of a halo, f min ( z ), that can be detectedin the survey by requiring that the mean halo brightness withinhalf halo radius (0 . θ H ) is ξ times the noise level in the map, i.e., . f min / N b ≈ ξ F rms , where N b is the number of independentbeams within 0 . θ H and F rms is the rms noise per beam.This gives: f min ( z ) ≃ . × − ξ (cid:18) F rms µ Jy (cid:19)(cid:18)
100 arcsec θ b (cid:19)(cid:18) θ H ( z )arcsec (cid:19) [mJy] , (9) where θ H ( z ) is the angular size of radio halos at a given redshiftin arcseconds and θ b is the beam angular size of the survey inarcseconds. ii) A second possible approach to derive f min is to assume that thehalo is detectable when the integrated flux within 0 . θ H gives asignal to noise ratio ξ . This is: f min ( < . θ H ) ≃ ξ p N b × F rms , (10)From Eq. 10 it follows f min ( z ) ≃ . × − ξ (cid:18) F rms µ Jy (cid:19)(cid:18)
10 arcsec θ b (cid:19)(cid:18) θ H ( z )arcsec (cid:19) [mJy] , (11)In the following, for a better comparison with previous works(Cassano et al. 2010b), we will consider i) as our reference ap-proach, and will give some results also based on ii) .The number of radio halos with f lux ≥ f min ( z ) in the redshiftinterval, ∆ z = z − z , can be obtained by combining the RHLF( dN H ( z ) / dP ( ν o ) dV ) and f min ( z ): N ∆ z H = Z z = z z = z dz ′ ( dVdz ′ ) Z P min ( f ∗ min , z ′ ) dN H ( P ( ν o ) , z ′ ) dP ( ν o ) dV dP ( ν o ) (12)Estimating ξ and ξ is the more critical point in this proce-dure. Considering case i) , in Cassano et al. (2008a) we analysedVLA radio observations in D-array configuration of empty fieldswhere we injected fake radio halos in the (u,v) plane of the in-terferometric data; the injected radio halos were placed at z = ∼ ξ ∼ −
2. At redshift z > . ξ ∼ e.g., z =
8. Cassano et al.: Radio Halos in future surveys in the radio continuum detectable radio halos. Based on their findings (Fig. 3 in Brunettiet al. 2007) we adopt Eq. 11 with ξ ≃ z ≤ . ξ ∼ ξ ∼
10 givesa predicted number of radio halos consistent with that observedin the NVSS . In the following we will use Eq. 9 with ξ = ξ =
10 ina number of cases.Figure. 8 shows f min of giant radio halos as a functionof redshift (left panel), and the corresponding minimum ra-dio luminosity (right panel), obtained according to case i) and ii) . Calculations are shown for the NVSS (black upper lines)and for the EMU + WODAN survey (red lower lines). For theEMU + WODAN survey we assume rms = µ Jy and θ b = .In Fig. 9, ( left panel ) we show the all-sky number of radio halosexpected in the EMU + WODAN survey. We consider both giantradio halos that originate from turbulent re-acceleration in merg-ing clusters and “o ff -state” halos assuming the optimistic case b)in Sect. 3 (see caption for details). We consider the flux limitderived according to Eq. 9 with ξ = ξ =
10 (red lines).We note that “o ff -state” halos are expected to contribute signif-icantly (about 30%) to the total number of radio halos that areexpected in the EMU + WODAN survey. Their contribution islarger at lower redshift ( z < . + WODAN survey will detect up to 100-200 radio halos in the redshift range 0–0.6. This will increase thenumber of presently known giant radio halos by about one orderof magnitude. About 2 / . − . right panel ). The number ofradio halos expected in the EMU + WODAN surveys increasesby a factor ∼ ff -state” radiohalos that become detectable in low redshift ( z < .
2) clustersaccording to this prescription.Finally, in Fig.10 we report the all-sky number distributionof the radio halos detectable by EMU + WODAN as a function ofthe radio flux. “O ff -state” halos contribute potentially at smallerradio fluxes, f . <
10 mJy, i.e., at fluxes presently accessibleonly to deep pointed observations. To further highlight the poten-tial improvement that will be provided by EMU + WODAN withrespect to the present statistics of radio halos, in the same figurewe report the number of radio halos detected in the NVSS survey(by inspection of XBAC clusters up to redshift 0 .
2, Giovannini etal 1999) and in the GMRT RH Survey (Venturi et al. 2007, 2008;in the redshift range 0.2-0.32). For a sanity / consistency check,the number of radio halos in present surveys are also comparedwith model expectations derived for turbulent giant radio halosaccording to Eqs.9–12 and by taking into account the specifica-tion of these surveys. We note that case i) gives a more fair comparison becauseGiovannini et al. (1999) selected halos and candidate halos from theinspection of the NVSS images. We note that such noise level is of the same order of the confusionnoise expected in this configuration, however it can be reached aftersubtraction of uv components of the sources detected at more than 100 σ in the survey images obtained at the highest resolution. Fig. 10.
All-sky number distribution of radio halos within z < . . + WODAN surveys (blue lines). For comparison, in thesame figure, the expected distribution of radio halos in the red-shift range 0 . < z < .
2, compared with that observed inthe NVSS (black lines and symbols) and in the redshift range0 . < z < .
32 compared with that observed in the “GMRTRH Survey” (red lines and symbols) are also reported. The bluedashed line shows the distribution of turbulent generated halos.
6. Comparison between LOFAR and EMU surveys
The revolutionary radio telescope LOFAR will carry out surveysbetween 15 MHz and 210 MHz with unprecedented sensitivityand spatial resolution ( e.g.,
R¨ottgering et al. 2006), providing abreakthrough in the exploration of the Universe at the low radiofrequencies. In particular the
Tier 1 “Large Area” survey of thenorthern sky is planned to reach sensitivities ∼ / beam inthe frequency range 120-190 MHz. The combination of observ-ing frequency and sensitivity to di ff use emission of Tier 1 makethis survey the most sensitive survey in the pre-SKA era for theexploration of non-thermal radio emission from galaxy clustersand large scale structure.Based on the hypothesis that giant radio halos originate from tur-bulent re-acceleration in merging clusters, Cassano et al. (2010b)predict the discovery of about 400 giant radio halos at redshifts ≤ . Tier 1 survey data. This wouldincrease the statistics of these sources by a factor of ∼
20 withrespect to present day surveys. Remarkably about 1 / α > .
9, and consequently they would brightenonly at low frequencies, unaccessible to both present observa-tions and future observations with ASKAP and APERTIF.The surveys planned with the ASKAP array and with theAPERTIF onboard of WSRT will provide information comple-mentary to that coming from LOFAR. These surveys are plannedto reach a sensitivity similar to that of the
Tier 1 survey in thecase of extended emission with radio spectral index in the range
9. Cassano et al.: Radio Halos in future surveys in the radio continuum
Fig. 9.
Left Panel : expected integral number (all-sky) of radio halos as a function of redshift in EMU + WODAN.
Right Panel :expected number of RH (all-sky) in redshift intervals in EMU + WODAN. The reference set of model parameters ( b = . B < M > = . µ G, < M > = . × M ⊙ and η t = .
2) is assumed. In both panels black lines show the total number of halos (“turbulent” + “o ff -state” halos, solid) and of “turbulent” halos (dashed) obtained by considering Eq.9 with ξ = f min ( z ); while red upperlines show the total number of halos (“turbulent” + “o ff -state” halos) obtained by adopting Eq.11 with ξ =
10. Points show theintegral number of radio halos observed so far. α ∼ − .
2. Their synergy with LOFAR will add considerablevalue to discriminate between di ff erent physical origin of giantradio halos in galaxy clusters and, in general, to constrain theevolution of cluster non-thermal components.In this Section we shall focus on the comparison betweenexpectations for the statistics of radio halos in LOFAR andEMU + WODAN. LOFAR surveys and EMU will overlap byabout one steradiant, while WODAN will be looking at the samesky as LOFAR.Here we calculate the expected number of giant radio halos inthe LOFAR
Tier 1 survey following Cassano et al. (2010b). Weupgrade these calculations (i) by using merger trees from MonteCarlo simulations of cluster formation history with increasedstatistics with respect to what previously done ( i.e., increasednumber of trials), and (ii) by adopting a tighter grid to samplethe values of the steepening frequency of radio halos, ν s . In ad-dition, following Sect.3 we include the contribution to the halosstatistics at 120-190 MHz from “o ff -state” halos in more relaxedclusters. We adopt a spectral index α = + WODAN will observe di ff erent popula-tions of giant radio halos, because LOFAR will explore also thepopulation of halos with steepening frequency ν s ≤ ν s >
120 MHz (black solid lines) and that of halos with ν s > ff erent redshift ranges z = . − . = . − . ν s > + WODAN, are extrapolated at 120 MHz by assum-ing a spectral index α ≈ .
3. The di ff erence between the twoRHLF is maximized at higher redshift where the RHLF of high-frequency halos shows a dip at radio luminosities ≈ × Watt / Hz (at 120 MHz). It reflects the di ffi culty of generating high-frequency giant halos via turbulent re-acceleration in thepresence of stronger inverse Compton losses (higher z). Indeedthose high-frequency halos can be generated at higher redshiftonly by very massive merging events, which however preferen-tially produce halos with larger radio luminosities ( e.g., Eqs. 4–5). On the other hand, we find that radio halos emitting at lowerfrequencies can still be generated e ffi ciently at higher redshifts.Consequently the detection at low frequencies of a number ofradio halos with luminosities ∼ − W / Hz in excess ofthat of radio halos observed at higher frequencies with luminosi-ties ∼ × − × W / Hz would confirm our theoreticalexpectations; the sensitivities of the LOFAR
Tier 1 survey andof the planned EMU survey will be suitable to perform this test(Fig. 11).At lower luminosities both the high-frequency and low-frequency RHLF are dominated by the contribution of “o ff -state” halos. We note that the number density of these halos atlower frequencies is slightly smaller than that at higher frequen-cies (red curves are slightly higher than the black curves, Fig. 11)because at lower frequencies an increasing number of clusterscan generate giant radio halos via turbulent re-acceleration. Inother words, some of the clusters hosting low luminosity “o ff -state” (“secondary”) halos become “on-state” (turbulent) whenobserved at LOFAR frequencies, and migrate from low to highradio luminosities in the LOFAR luminosity function. Fig. 11shows that both LOFAR and EMU + WODAN will be able to de-tect “o ff -state” halos (assuming the optimistic case b) in Sect.3).Since LOFAR and WODAN will be looking at the same skywith the same sky coverage, here we report a comparison be-tween the expected number of radio halos in these two surveys.To derive the number of radio halos we follow the procedure inSect. 5, assuming a threshold value ξ ∼ left panel ) we show the integral numberof giant radio halos (in the LOFAR sky, i.e., in ∼
10. Cassano et al.: Radio Halos in future surveys in the radio continuum
LOFAR (black line) surveys, and in Fig. 12 ( right panel ) we re-port the number of radio halos in redshift intervals. The LOFAR
Tier 1 survey is expected to detect about 500 radio halos, ∼ i.e., ν s < GHz) atthe frequencies spanned by LOFAR. The di ff erence between thetwo surveys increases with redshift mainly due to the increas-ing number of low-frequency radio halos that are generated incluster mergers at higher redshifts.Giant radio halos with very steep spectrum (low-frequency ha-los) are only expected in the framework of the turbulent re-acceleration models ( e.g., Cassano et al. 2006; Brunetti et al.2008) thus unveiling a substantial population of these radiosources will promptly discriminate among di ff erent models pro-posed for the origin of di ff use radio emission in galaxy clusters.
7. Discussion and conclusions
In this paper we have presented results from Monte Carlo sim-ulations to model the formation and evolution of giant radio ha-los in the framework of the merger-induced particle accelerationscenario (see Sec. 2) and extended previous calculations by in-cluding the contribution of secondary electrons generating “o ff -state” halos in more relaxed galaxy clusters (Sect. 3). To com-bine these two mechanisms we follow a phenomenological ap-proach in which we assume that those clusters where turbulenceis not su ffi cient to generate radio halos emitting at the observ-ing frequency, ν o , host “o ff -state” halos generated only by theemission from secondary electrons. We assume that presentlyobserved giant radio halos are mainly driven by turbulent re-acceleration in merging clusters and constrain the level of the“o ff -state” halos using limits derived for “radio quiet” galaxyclusters (Brunetti et al. 2007; Brown et al. 2011). Under this as-sumption “o ff -state” halos are faint with luminosities typically ∼
10 times smaller than those of giant radio halos in turbu-lent / merging clusters. On the other hand, these “o ff -state” halosare expected to be more numerous than turbulent halos and thusthey may contribute significantly to the number of radio halos infuture radio surveys.The most important expectation of turbulent re-accelerationscenarios is that the synchrotron spectrum of radio halos shouldbecome gradually steeper above a frequency, ν s , that is de-termined by the competition between acceleration and energylosses and that is connected to the energetics of the mergerevents that generate the halos ( e.g., Fujita et al. 2003; Cassano& Brunetti 2005). Consequently, in this scenario the populationof radio halos is expected to be made of a complex mixture ofsources with di ff erent spectra, with massive (and hot) clustersthat have a tendency to generate halos with spectra flatter thanthose in less massive systems. Contrary to turbulent halos, “o ff -state” halos are expected with power-law spectra with fairly sim-ilar slopes. Consequently, surveying the sky at di ff erent radiofrequencies and with appropriate sensitivities allows to disen-tangle these two populations.In Sects. 2-3 we derive the expected radio halo luminos-ity functions (RHLF) at frequency ν o , that account for radiohalos originated from turbulent re-acceleration, with steepen-ing frequency ν s ≥ ν o , and “o ff -state” radio halos. As a rele-vant case we discuss the RHLF at ν o = . P ∼ few × − W / Hz, due to the decrease of the e ffi ciency ofturbulent acceleration in less massive systems, and by an upturnat lower radio luminosities due to the contribution of “o ff -state” halos. The flattening / dip is expected to become more prominentat higher redshift due to the increase of IC losses that quench theacceleration process especially in lower massive systems.Future radio surveys have the potential to constrain the for-mation and evolution of halos with cosmic time allowing fordetailed tests of models. Specifically, in Sect. 5 we derive theexpected number of radio halos in the EMU + WODAN survey.The EMU + WODAN surveys will probe the radio sky in the fre-quency range 1-2 GHz with a sensitivity 10 times better thanpresent surveys. They will allow comparison of model predic-tions and observations in a totally unexplored range of radiohalos luminosities and masses of the hosting clusters. A criti-cal point in our paper is to derive a meaningful estimate of thesensitivity of these surveys to radio halo emission at di ff erentredshifts. We explore two possible ways, one based on a bright-ness threshold of the radio emission and another one based ona threshold in flux density. Threshold values in both cases havebeen estimated from the injection of “fake” radio halos in ex-isting surveys (the GMRT RH Survey and the NVSS) under theassumption that the brightness distribution of presently knownhalos is representative. A better determination of the sensitiv-ity of EMU and WODAN will become available only whenASKAP and APERTIF on WSRT will start the commissioningphase. Despite the uncertainties on survey sensitivities, the ex-pected number of radio halos highlights the potential of the fu-ture EMU + WODAN surveys. By using a brightness based cri-terion for the detection of halos and assuming the expected sen-sitivity of EMU (Norris et al. 2011) and WODAN (R¨ottgeringet al. 2011), rms ∼ µ Jy / b, we predict that these surveys willpotentially discover up to 200 new giant radio halos at redshift z ≤ .
6. Most of these halos are predicted in the redshift range z ∼ . − .
4. This will increase the present number of known ra-dio halos by almost a factor 10. The number of halos expected inthese surveys further increases if a flux based threshold is usedto estimate the sensitivity of the surveys. In particular, accordingto this method, more radio halos can be discovered at z < . L X < ∼ × erg / s) andof “o ff -state” halos in more relaxed clusters. We derive also theflux distribution of expected radio halos, showing that “o ff -state”halos contribute at fluxes f . <
10 mJy that are presently acces-sible only to deep pointed observations; still no clear detectionof these halos has been obtained so far.The most important step in our understanding of the physicsof radio halos is expected from surveys at lower frequencies andfrom their combination with surveys at higher frequencies. InSect.6 we compare model expectations for the statistics of gi-ant radio halos at lower and higher frequencies. We upgradedprevious calculations used to derive the number of radio ha-los at lower frequencies, ν o ∼
120 MHz, (from Cassano etal. 2010b) i) by using Monte Carlo with improved statistics,and ii) by adopting a scenario based on two-populations of ha-los (as in Sect. 5, “o ff -state” and “turbulent” halos). These cal-culations allow us to explore the potential of the synergy be-tween surveys at lower and higher frequencies with LOFARand EMU / WODAN, respectively. According to the model basedon turbulent re-acceleration in galaxy clusters di ff erent popula-tion of giant radio halos should become visible at di ff erent fre-quencies. Based on our hypothesis of two-populations of halos,also the population of “o ff -state” halos changes with frequen-cies because more clusters generate radio halos via turbulent
11. Cassano et al.: Radio Halos in future surveys in the radio continuum
Fig. 11.
RHLF of halos with ν s ≥
120 MHz (black solid lines) and that of halos with ν s > ff erentredshift ranges z = . − . = . − . ff -state” halos to the LOFAR RHLF. The black and red arrows show the LOFAR andEMU + WODAN sensitivities, respectively, at the considered redshifts.
Fig. 12.
Left Panel : integral number of radio halos as a function of redshift in the WODAN (red line) and LOFAR (black line)surveys.
Right Panel ): RH distribution in redshift intervals in the WODAN (red line) and LOFAR (black line) surveys.re-acceleration at lower frequencies. We find that the LOFAR
Tier 1 survey will detect about 4 times more halos than theWODAN survey, thanks to its better sensitivity and to its lowerobserving frequency that allows the detection of turbulent ra-dio halos that become more frequent and luminous at lower fre-quencies. The majority of radio halos with very steep spectrum( i.e., lower values of ν s ) in the LOFAR Tier 1 survey are pre-dicted with luminosities P ∼ − W / Hz at 120 MHzand do not have counterparts detectable at higher frequencies.As a consequence, the RHLFs at 1.4 GHz exhibit a dip / flattening(at the luminosities P . ∼ − × (1400 / − . W / Hz ∼ few × − W / Hz at 1.4 GHz). The comparison betweenRHLFs at di ff erent frequencies is thus very important as it al-lows to promptly unveil the existence of di ff erent populations of radio halos. For instance, we have shown that comparing for ra-dio halos in the LOFAR and in the WODAN surveys will allow aprompt test of the existence of radio halos with extremely steepspectra.We predict that both the LOFAR and EMU + WODAN surveyswill have the potential to unveil “o ff -state” radio halos, openingthe possibility to study di ff use Mpc-scale emission also in morerelaxed systems. This is currently impossible with present radiosurveys, and will allow to better understand the e ff ect of clus-ter mergers on the evolution of non-thermal radio emission ingalaxy clusters.More generally, LOFAR and EMU + WODAN surveys will al-low to readily discriminate between a turbulent re-accelerationand a purely “hadronic” origin of radio halos. Indeed, if we as-
12. Cassano et al.: Radio Halos in future surveys in the radio continuum sume that turbulence does not play a role, and all halos are of“hadronic” origin, the luminosity function of “hadronic” halosin Fig.11 should be boosted up by at least one order of magni-tude to explain present number counts, implying a very largernumber of halos at lower luminosities. Although a quantitativecomparison between predictions derived by di ff erent authoursis di ffi cult because of the very di ff erent hypothesis on (poorlyconstrained) model parameters , we stress that the most impor-tant di ff erence between the two scenarios is in the spectral shapeof halos and in its consequences. Indeed, re-acceleration modelslead to the unique predictions of complex spectra, whereas in the“hadronic” models the spectra of secondary particles (and thusthe synchrotron spectra) are rather power-laws which extend inprinciple to very high energies (frequencies). The important con-sequences are that in re-acceleration models i) a still hidden pop-ulation of radio halos with very steep spectra is predicted to glowup at low radio frequencies ( e.g., Cassano et al. 2006; Brunettiet al. 2008; Cassano et al. 2010b) and ii) the shape of the lu-minosity function of giant radio halos depends on the observingfrequency (Fig.11); both predictions will be readily tested by fu-ture surveys at di ff erent frequencies. Our calculations provide a first step for interpreting future sur-veys at the light of models that combine turbulent re-accelerationof relativistic particles and the generation of secondary electronsin the ICM. The most important simplification in our approach isthat the evolution of magnetic field in the ICM does not accountfor the possible connection with the level of turbulence, yet themagnetic field is simply anchored to cluster mass at any red-shift. Present data do not show evidence for a direct connectionbetween the magnetic field and the cluster dynamics and turbu-lence (Govoni et al. 2010; Bonafede et al. 2011) thus for the aimof the present paper we prefer to keep the models as simple aspossible. In this paper, we have shown results based on a refer-ence set of model parameters ( < B > ,b and η t ). According toCassano et al. (2006) we expect that the general results given inthe present paper should be poorly dependent on the adopted pa-rameter values. The expected number of radio halos in a givensurvey is expected to change by a factor of about 2 when con-sidering di ff erent values of parameters (see also Figs.14 and 15in Cassano et al. 2006). Our two-population scenario for halosdoes not consider self-consistently the evolution of protons andof their secondaries in the ICM, rather we use a phenomenologi-cal approach based on the two “extreme situations” where halosoriginate from turbulence and pure hadronic collisions, respec-tively. Brunetti & Lazarian (2011) modeled the acceleration ofrelativistic protons and their secondaries in compressible MHDturbulence in a self-consistent way showing that radio halos be-come bright when turbulence is generated in the ICM and grad-ually evolve into fainter “o ff -state” halos when turbulence is dis-sipated. This complex evolution occurs in a time-scale shorterthan the life-time of halos and of the hosting clusters, thus ourapproach still provides a valuable way to model the basic statis-tical properties of halos (see discussion in Cassano et al. 2010b).As a final remark, in this paper we focussed only on the case ofMpc-sized radio halos. In reality, smaller halos could be gen-erated in dynamically disturbed and relaxed systems by sev- See, for example, the large discrepancies between Sutter & Ricker(2011) and Zandanel et al. (2012) which attempt to derive expectationsusing the “hadronic” model with di ff erent assumptions on the B-massscalings and cosmic ray dynamics. eral mechanisms, including turbulent re-acceleration in slosh-ing cores and in the region of AGN-driven bubbles (Cassano etal. 2008b; Mazzotta & Giacintucci 2008; ZuHone et al. 2012),reconnection regions (Lazarian & Brunetti 2011) and hadroniccollisions (Pfrommer & Enßlin 2004; Keshet & Loeb 2010). Allthese halos constitute an additional population of di ff use syn-chrotron source in galaxy cluster to investigate with future radiosurveys.Finally, it’s worth mentioning that there are a few radio halosfound in clusters with X-ray luminosity lower than that of typi-cal radio-halo clusters, that are over-luminous in radio (by aboutone order of magnitude) with respect to the radio-X-ray lumi-nosity correlation ( e.g., Giovannini et al. 2011 and ref. therein).These halos have radio luminosities similar to those of classi-cal radio halos and are hosted in clusters that are more com-mon than the very massive systems hosting classical radio halos.Consequently, their observed rarity suggests that they could beintrinsically rare. For this reason in our model we do not attemptto take into account these sources; future surveys (LOFAR,EMU / WODAN) are necessary to get a firm conclusion on theoccurrence of these sources in clusters.
Acknowledgements.
We thank the referee for useful comments. RC and GB ac-knowledge partial support by PRIN- INAF2009 and ASI-INAF I / / / References
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