Constraining B in the ICM from Statistic s o f Giant Radio Halos

1. Constraining B in the ICM from Statistics of GiantRadio Halos R. Cassano1,2, G. Brunetti2 & G. Setti1,2 1) Astronomy Department of University of Bologna, Italy 2) Istitute of Radioastronomy of Bologna –INAF, Italy International Conference: "The Origin and the Evolution of Cosmic Magnetism ", 29 Aug-2 Sep 2005, CNR Area della Ricerca, Bologna-Italy

2. Giant Radio Halos in Galaxy Clusters andCorrelations with Cluster Mergers A 2163 Size~1.9 h70-1 Mpc, z=0.2030 P1.4 Ghz~[1.84±0.03]1025 Watt/Hz LX~[2.34 ±0.15]1044 erg/s (0.1-2.4keV) TX~[13.29±0.64]keV Mv~5 · 1015 M⊙ The 1.4 Ghz Syn. Radio power of Radio Halos increases with the cluster mass. The probability to find Radio Halos increases with cluster mass (Giovannini et al., 1999) The Diffusion Problem: diffuse non-thermal emission on Mpc scale Tdiff (~1010 yr) >> Tv (~108 yr) One possibility is: in situ acceleration by turbulence (e.g. Brunetti et al. 2001, 2004; Petrosian 2001; Fujita et al.2003)

3. Goal investigate the Merger-Radio Halo connection in the framework of in situ acceleration model (modelling the statistical properties of Giant Radio Halos ) Brief summary of the statistical magneto-turbulent model(Cassano & Brunetti 2005, MNRAS 357, 1313; C&B ) The MHD turbulence (we focus onmagnetosonic waves) in the ICM is supposed to be injected during cluster mergers. The energetic of the this waves is estimated from the PdV work done by the infalling subclusters in passing through the main : Et~t<>ICMvi2Vt, whereVt is the stripping volume,vi is the velocity between the two colliding clusters and t is a parameter. Relativistic electrons (REs) in the ICM are continuously injected by AGN, shocks and/or galactic winds. Using a Fokker-Planck approach we calculate the evolution of the REs by taking into account all the relevant physical processes (energy losses and acceleration processes) . We calculate the synchrotron and Inverse Compton emission spectra from the electron spectra at each redshift. Cluster formation (mergers) Press & Schechter (1974)  semi-analytical theory of cluster formation. Montecarlo generation of a large number of merger trees in order to have a large synthetic population of galaxy clusters.

4. Main Results of the C&B Model 1) The typical observed radio, LR[1040 - 10 41] erg s- 1andhard-X ray, L HX[10 42 - 10 44] erg s -1luminosities can be obtained in M~1015M⊙ clusters during merger events, provided that a fraction of the cluster thermal energy (of the order of 3-5 % ) is channelled into MS waves and that the energy injected into relativisticelectrons during the cluster life is at least a few 10-4times the present energy of the thermal pool. 2)The expected probability to form radio halos at z<0.2 is 30-40 % in the more massive galaxy cluster (M2·1015M⊙) and a few % in less massive ones. This is in good agreement with observations (Giovannini et al. 1999).

5. What is the role of the magneticfield ? The role of the magnetic field has not been investigated so far in the framework of particle acceleration models. We try to obtain some constraints on B: from energetic request in turbulence from the observed radio-X rays correlations

6. Limits on B from energetic request (Cassano, Brunetti, Setti, in prep.) Radio Halos in the synthetic cluster population are identified with those objects with a synchrotron cut-off b  300 MHz in a region of 1 Mpc h50-1 size. The cut-off frequency can be expressed (for rs RH): Assuming: B=Bo·(M/Mo)b In order to reduce the energetic request in MS waves the magnetic field in the central Mpc of galaxy clusters should be B>>0.1μG. For a Coma-like cluster B>> 0.2 μG.

7. Model expectations for PR-Mv & PR-T correlation In the case of giant Radio Halos (RH≥500/h50 kpc)the merger which mainly contribute to the injection of turbulence in the ICM are those withrs≥ RH, for these mergers the model predicts a correlation : where T M 2/3 (virial scaling) or 0.56 We can assume that: •ne(the number density of relativistic electrons) is independent from the cluster's mass; • B=Bo·(M/Mo)b, the magnetic field strength depend on the cluster's mass. The expected slopes of the PR-M correlations is thus given by: 1,2 = log(P1/P2) = f(B,b) log(M1/M2) which can be directly compared with the observed values and which can be used to constrainB and b.

8. Observed PR-Mv & PR-T correlations P1.4-Mv P1.4-T Radio power-virial mass relation P1.4GHz Mv Combining [PR- LX]with [LX- Mv] : =2.84±0.35 ; Radio power temperature correlation P1.4GHz T, best-fit value:T=6.4±1.64 T

9. Constraints from observed correlations to the parameters <B> and b : BT2(Dolag et al 2002) Combining the limit obtained from the PR-Mv & PR-T correlations we obtain the allowed region in the plane (<B>,b). The observed correlations can be matched by the model for a range of values for B and b. In particular if we would reproduce the observed correlations  0.2 G B 3.5 G 0.2 In the marked regions of the plane (B,b) the model can reproduce : 1)the observed probability at z≤0.2 2)observed radio-X-ray correlations

10. The Luminosity Functions of giant Radio Halos Giventhe PM (the probability to form radio halos with cluster's mass) and the nPS (M,z) (Press & Schechter mass funcion): ● we estimate the radio halo mass functions: ●... and thus the RHLF is given by: were (dP1.4/dM) is taken from the observed correlations [P1.4-Mv] z We predict the presence of a low radio power cut-off due to the decrease of the efficiency of the particles acceleration in the case of less massive galaxy clusters. 0.0 z 0.6

11. The Number Counts of giant Radio Halos Given the RHLFs (dNH(z)/dL dV) the Number Counts of giant RHs are given by: where dV/dz is the comoving volumeelement in the CDM cosmology. We calculate the number of expected RHs above a given radio fluxat 1.4 Ghz from a full sky coverage up to z≤0.2.The colors indicate calculations obtained assuming allthe allowed physical configurations. The black points indicate the present radio data(from the statistical analysis of Giovannini et al. 1999) whosenormalization has been corrected for incompleteness deriving fro their sky-coverage (~ 2sr). z=02 The Number Counts of giant RHs at z≤0.2, at f> 30 mJy are in excellent agreement with observations. A bulk of RHs at lower fluxes is expected to be discovered with future radio observations ( LOFAR, LWA).

12. Conclusions Prediction for the statistic of giant radio halos Particle acceleration model may reproduce for the same choice of the physical parameters: the observed probability to form giant radio halos at z0.2; the observed PR-Mv & PR-T correlations for giant radio halos; the observed Number Counts of giant radio halos at z 0.2. Constraints on B from statistics of radio halos: The B intensity in the central 1 Mpc of a Coma-like cluster: minimum value of ~ 0.2-0.3 G in order to reduce the energetic request in turbulence; values of 0.5-3.5 G from the comparison between the observed and expecteed radio-X rays correlations for giant radio halos.

13. masses calculated from the -model fit: =4.34±1.1

14. Magnetic field in the Coma cluster Statistic of radio halos: 0.2 G  B3.7 G ( cental Mpc) if BT2(Dolag et al 2002) than 1.7 G  B 3 G two-fase model (Brunetti et al 2001): B~1-1.5 G IC method (Fusco-Femiano 2001): BIC~0.15 G (volume average magnetic field) Equipartition magnetic field (Giovannini et al. 1993): Beq~0.4 G Rotation mesures (Kim et al 1990, Feretti et al. 1995): BRM~2-6 G

15. Energy budget in fluid turbulence during cluster formation The energy budget injected in fluid turbulence during cluster formation is well below the thermal energy.In particular the turbulent energy is found to be~ 15 %of the thermalenergy. Finally the energy injected in turbulence calculated with our approach is found to roughly scale with the thermal energy of the cluster.