Observations of galaxy clusters both in the radio and X-ray bands probe a direct link between cluster mergers and giant radio halos , suggesting that these sources can be used as probes of the cluster merging rate with cosmic time .
However , while all giant radio halos are found in merging clusters not every merging cluster host a giant radio halo .
In this paper we carry out an explorative study that combines the observed fractions of merging clusters and radio halos with the merging rate predicted by cosmological simulations and attempt to infer constraints on merger properties of clusters that appear disturbed in X-rays and of clusters that host radio halos .
We use classical morphological parameters to identify merging systems and analyze the currently largest ( mass-selected M _ { 500 } \gtrsim 6 \times 10 ^ { 14 } M _ { \odot } and 0.2 \leq z \leq 0.33 ) sample of galaxy clusters with radio and X-ray data ; we extract this sample from the Planck Sunyaev-Zeldovich cluster catalogue .
We found that the fraction of merging clusters in this sample is f _ { m } \sim 62 - 67 \% while that of clusters with radio halos is f _ { RH } \sim 44 - 51 \% .
We assume that the morphological disturbance measured in the X-rays is driven by the merger with the largest mass ratio , \xi ( \xi = M _ { i } / M _ { 1 } < 1 with M _ { i } and M _ { 1 } being the progenitor masses ) , that is still ongoing in the cluster at the epoch of observation .
Results from theoretical studies allow to derive the fraction of mergers with mass ratio above a minimum threshold ( those with \xi \raise 1.29 pt \hbox { $ > $ \kern - 7.5 pt \raise - 4.73 pt \hbox { $ \sim$ } } \xi _ { min } ) in our sample , under the assumption of a timescale \tau _ { m } for the duration of merger-induced disturbance .
The comparison of the theoretical merger fraction with the observed one allows to constrain a region in the ( \xi _ { min } , \tau _ { m } ) plane .
We find that under the assumption of \tau _ { m } \sim 2 - 3 Gyr , as constrained by simulations , the observed merger fraction matches the theoretical one for \xi _ { min } \sim 0.1 - 0.18 .
This is consistent with optical and near-IR observations of galaxy clusters in the sample that constrain \xi _ { min } \simeq 0.14 - 0.16 through weak lensing analysis or study of the velocity distribution of galaxies in the clusters .
The fact that radio halos are found only in a fraction of merging galaxy clusters may suggest that merger events generating radio halos are characterized by larger mass ratio ; this seems supported by optical/near-IR observations of RH clusters in the sample that indeed allow to constrain \xi _ { min } \sim 0.2 - 0.25 .
Alternatively , radio halos may be generated in all mergers but their lifetime is shorter ( by \sim f _ { RH } / f _ { m } ) than the timescale of the merger-induced disturbance .
We stress that this is an explorative study , however it suggests that follow up studies using the forthcoming radio surveys and adequate numerical simulations have the potential to derive quantitative constraints on the link between cluster merging rate and radio halos at different cosmic epochs and for different cluster masses .