Radio continuum tails in ram pressure-stripped spiral galaxies: Experimenting with a semi-empirical model in Abell 2255

Context. Wide-field radio continuum observations of galaxy clusters are revealing an increasing number of spiral galaxies hosting tens of kiloparsec-length radio tails produced by the displacement of nonthermal interstellar medium (ISM) by ram pressure. Aims. We present a semi-empirical model for the multifrequency radio continuum emission from ram-pressure-stripped tails based on the pure synchrotron cooling of a radio plasma moving along the stripping direction with a uniform velocity. Methods. We combine LOFAR and uGMRT observations at 144 and 400 MHz to study the flux density and spectral index profiles of the radio tails of seven galaxies in Abell 2255, and use the model to reproduce the flux density and spectral index profiles, and infer the stripped radio plasma velocity. Results. For five out of these seven galaxies, we observe a monotonic decrease in both flux density and spectral index up to 30 kpc from their stellar disk. Our model reproduces the observed trends with a projected radio plasma bulk velocity of between 160 and 430 km s-1. This result represents the first indirect measurement of the stripped, nonthermal ISM velocity. The observed spectral index trends indicate that the synchrotron cooling is faster than the adiabatic expansion losses, suggesting that the stripped radio plasma can survive for a few tens of million years outside of the stellar disk. This provides a lower limit on the lifetime of the stripped ISM outside of the disk. As a proof of concept, we use the best-fit velocities to constrain the 3D velocity of the galaxies in the cluster to be in the range of 300-1300 km s-1. We estimate the ram pressure affecting these galaxies to be between 0.1 and 2.9×10-11 erg cm-3, and measure the inclination between their stellar disk and the ram pressure wind.