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Radio and X-ray observations of galaxy clusters probe a direct link betweencluster mergers and giant radio halos (RH), suggesting that these sources canbe used as probes of the cluster merging rate with cosmic time. In this paperwe carry out an explorative study that combines the observed fractions ofmerging clusters (fm) and RH (fRH) with the merging rate predicted bycosmological simulations and attempt to infer constraints on merger propertiesof clusters that appear disturbed in X-rays and of clusters with RH. We usemorphological parameters to identify merging systems and analyze the currentlylargest sample of clusters with radio and X-ray data (M500>6d14 Msun, and0.2<z<0.33, from the Planck SZ cluster catalogue). We found that in this samplefm~62-67% while fRH~44-51%. The comparison of the theoretical f_m with theobserved one allows to constrain the combination (xi_m,tau_m), where xi_m andtau_m are the minimum merger mass ratio and the timescale of merger-induceddisturbance. Assuming tau_m~ 2-3 Gyr, as constrained by simulations, we findthat the observed f_m matches the theoretical one for xi_m~0.1-0.18. This isconsistent with optical and near-IR observations of clusters in the sample(xi_m~0.14-0.16). The fact that RH are found only in a fraction of mergingclusters may suggest that merger events generating RH are characterized bylarger mass ratio; this seems supported by optical/near-IR observations of RHclusters in the sample (xi_min~0.2-0.25). Alternatively, RH may be generated inall mergers but their lifetime is shorter than \tau_m (by ~ fRH/fm). This is anexplorative study, however it suggests that follow up studies using theforthcoming radio surveys and adequate numerical simulations have the potentialto derive quantitative constraints on the link between cluster merging rate andRH at different cosmic epochs and for different cluster masses.

Can giant radio halos probe the merging rate of galaxy clusters?