  Many galaxy clusters host Megaparsec-scale radio halos, generated by
ultrarelativistic electrons in the magnetized intracluster medium. Correlations
between the power of radio halos and the thermal properties of the hosting
clusters were established in the last decade, including the connection between
the presence of a halo and cluster mergers. The X-ray luminosity and redshift
limited Extended GMRT Radio Halo Survey provides a rich and unique dataset for
statistical studies of the halos. We uniformly analyze the radio and X-ray data
for the GMRT cluster sample, and use the new Planck SZ catalog, to revisit the
correlations between the power of halos and the thermal properties of galaxy
clusters. We find that the radio power of halos at 1.4 GHz scales with the
cluster X-ray (0.1--2.4 keV) luminosity computed within R_500 as P_1.4
L_500^2.0. Our bigger and more homogenous sample confirms that the X-ray
luminous (L_500 > 5x10^44 erg/s) clusters branch into two populations --- radio
halos lie on the correlation, while clusters with upper limits to radio-halo
emission are well below that correlation. This bimodality remains if we excise
cool cores from the X-ray luminosities. Correlating with Planck data, we find
that P_1.4 scales with the cluster integrated SZ signal within R_500 as P_1.4
Y_500^2.1, in line with previous findings. However, contrary to previous
studies that were limited by incompleteness and small sample size, we find that
the "SZ-luminous" Y_500 > 6x10^-5 Mpc^2 clusters show a bimodal behavior
similar to that in the radio-X-ray diagram. Bimodality of both correlations can
be traced to clusters dynamics, with radio halos found exclusively in merging
clusters. These results confirm the key role of mergers for the origin of giant
radio halos, suggesting that they trigger the relativistic particle
acceleration.
