  Shocks arising in galaxy mergers could accelerate cosmic-ray (CR) ions to
TeV-PeV energies. While propagating in the intergalactic medium, these CRs can
produce high-energy neutrinos, electron-positron pairs and gamma-rays. In the
presence of intergalactic magnetic fields, the secondary pairs will radiate
observable emissions through synchrotron radiation and inverse Compton
scattering. In this paper, we demonstrate that these emissions can explain the
radio and X-ray fluxes of merging galaxies such as NGC 660 and NGC 3256. Using
our model in combination with the observations, we can constrain the gas mass,
shock velocity, magnetic field and the CR spectral index $s$ of these systems.
For NGC 660 a single-zone model with a spectral index $2.1\lesssim
s\lesssim2.2$ is able to reproduce simultaneously the radio and X-ray
observations, while a simple one-zone scenario with $s\sim2$ can describe the
radio and a large fraction of X-ray observations of NGC 3256. Our work provides
a useful approach for studying the dynamics and physical parameters of galaxy
mergers, which can play an important part in future multi-messenger studies of
similar and related extragalactic sources.
