The presence of a correlation between the radio power and the X-ray luminosity is well known (Liang et al. 2000; Esslin & Röttgering 2002). CBS06 also obtained the correlation between the X-ray luminosity in the 0.1-0.2 keV energy band and the radio power at 1.4 GHz for their sample of 17 RHs
Successively the existence of this correlation has been confirmed also for clusters belonging to the larger sample of the GRHS (e.g. Brunetti et al. 2009). However, one of the most important results obtained by means of the P1.4− LX diagram with the GRHS clusters is the discovery of the radio bimodality of galaxy clusters (e.g. Brunetti et al. 2007, 2009). RH clusters indeed trace the P1.4 − LX correlation, while clusters without extended radio emission populate the region of the upper limits, lying about an order of magnitude below the correlation (Fig. 4.6).
It is worth noticing that the discovery of such bimodal behaviour was made possi-
Figure 4.6: Left panel: distribution of GMRT galaxy clusters (blue) and of RH clus- ters from literature (filled blach simbols) in the P1.4− [0.1 − 2.4]kev luminosity plane.
Empty circles mark RHs from the GMRT sample, arrows mark upper limits for GMRT clusters with no evidence of Mpc-scale radio emision. The solid line gives the best fit of the distribution of RHs. Right panel: distribution of RHs (GMRT+literature) in the
P1.4−bolometric X-ray luminosity plane. The solid line gives the best fit of the distribu-
ble by the fact that firm upper limits on the diffuse emission of cluster without RH have been established. Fig. 4.6 essentially shows that clusters with similar redshift and LX have a clear bimodal distribution. This is a very crucial issue for the under- standing of the origin and evolution of RHs, indeed clusters with similar thermal properties (X-ray luminosity, mass..) are expected to have similar probability to host RHs. In this case the observed difference on the non-thermal properties should be understood in terms of different evolutionary stages.
The RH-merger connection, suggested by e.g. V08, may explain the separation be- tween RH and “radio quiet” clusters in term of different dynamical status. Apart from the detailed mechanisms that origin RHs, the evolutionary cycle can be sum- marized as follows:
(1) galaxy clusters host RHs for a period of time, in connection with merger events, and populate the P1.4− LX correlation;
(2) then, when clusters become dynamically relaxed, the synchrotron emission is gradually suppressed and clusters fall into the region of the upper limits. In this framework, the empty region is expected to be populated by (a) “intermedi- ate” systems at late merging phase where synchrotron emission is being suppressed, or (b) by very young systems at the beginning of the merging phase, where syn- chrotron emission is increasing. Hence, assuming that RHs are transient phenomena connected with the cluster merging phase, the emptiness of the region between RHs and upper limits in the P1.4− LX diagram becomes a tool to constrain the time- scale of the evolution (amplification and suppression) of the synchrotron emission in galaxy clusters. The significant lack of clusters in the intermediate region sug- gests that this time-scale is much shorter than both the cluster life-time and the RH life-time (which is the time clusters spend on the correlation). Brunetti et al. (2007) found that the life-time of RHs is τRH ≈ 1 Gyr (in agreement with theoretical models, see Sec. 3.2) and the time-scale for the suppression (or ampli- fication) of synchrotron emission from the level of RHs to that of radio quiet (or vice versa) is τ ≈ 90Myr. Monte Carlo analysis of the distribution of clusters in the P1.4− LX plane shows that the time interval that clusters spend in the empty region is τevol ≈200 Myr with the probability that τevol being as large as 1 Gyr≤ 1% (Brunetti et al. 2009). This statistical analysis provides more quantitative support to the previous results.
The evolution of the radio properties of galaxy clusters in the P1.4 − LX diagram reflects the evolution of relativistic particles and magnetic field in the ICM. The tight constraints on the time-scale of this evolution provides crucial information on the physics of the particle acceleration and magnetic field amplification.
If we consider the secondary electron model, we can explain the clusters radio bi- modality by assuming that the passage of mergers shock through the ICM may increase the protons energy density enhancing the rate of production of secondary electrons and the resulting cluster-scale synchrotron emission. However, protons
have very long life-time and the production rate of secondary electrons would re- main basically unchanged during cosmic time, moreover, this mechanism doesn’t predict the suppression of the synchrotron emission when clusters turn back to the relaxed phase. Therefore, in the context of secondary electron models, RHs are ex- pected to be long-living and common phenomena and there is no reason to expect a radio bimodality2.
A possible explanation of the bimodality is that cluster mergers amplify the cluster magnetic field in the ICM enhancing the synchrotron emission on Mpc scales. To explain a suppression ≥ 10 of the synchrotron emission from the RH phase to the radio quiet one (Fig. 4.6) the ratio between the magnetic field in RHs, B + δB and that in clusters with upper limit, B, must be:
B + δB B !α−1 1 + (BCM B/B)2 1 + (BCM B/(B + δB))2 ≥10 (4.2)
In the case B + δB BCM B secondary models must admit that the energy density of the magnetic field in radio quiet clusters is ≥ 100 times smaller than that in RHs, and even larger if B + δB BCM B. Even if, theoretically, it is possible to admit that the magnetic field is amplified by turbulence during mergers and later dissipated, this scenario is not supported by present observations. Faraday rotation measurements (e.g. Carilli & Taylor 2002) and more recent studies of polarization (Bonafede et al. 2011) indeed don’t show any statistical difference between the energy density of the large scale magnetic field in radio quiet clusters and clusters hosting RHs. Furthermore, even if the magnetic field is amplified by cluster mergers, the dissipation of this magnetic field through the decay of cluster-MHD turbulence is expected to take too long time (≈a few Gyr, Subramanian et al. 2006). Such a time is inconsistent (larger than) with the time-scale of the suppression of the synchrotron emission inferred from the P1.4− LX diagram analysis.
Present data suggest that the magnetic field does not play a fundamental role in the evolution of non-thermal properties in galaxy clusters, therefore relativistic elec- trons must drive the generation and suppression of RHs.
As discussed in Sec. 3.2, cluster mergers inject turbulence on large scale in the ICM and, as soon as turbulence reaches small, resonant, scales, particles are accelerate and generate synchrotron emission at GHz frequencies. The cascading of turbu- lence from large to small scales is expected to take ≈ 100 Myr, during this time the clusters move from the region of the upper limits to the P1.4− LX correlation and should appear dynamically disturbed. At the end of the merging phase turbu- lence starts to dissipate, the synchrotron power is suppressed and the synchrotron emission at higher frequencies falls below the detection limit of radio observations. Clusters move back to the region of the upper limits and appear as relaxed systems in the X-rays.
2Although some attempts have been made assuming that spatial diffusion of CR plays a role, decreasing the level of synchrotron emission in relaxed clusters (Enßlin et al. 2011)
Figure 4.7: X-ray luminosity (0.1-2.4 keV) versus z for the total sample of clusters (XBACs+REFLEX+eBCS) used by Cassano et al. (2008). Open black circles are clusters belonging to the GRHS. Open red circles indicate the clusters with known giant RHs. The lines give the lower limit to the cluster X-ray luminosities calculated by adopting three different approaches (Cassano et al. 2008).