We study for the first time the low-frequency ($sim$150 MHz) radio brightness distribution of Arp~299 at subarcsecond resolution, tracing in both compact and extended emission regions the local spectral energy distribution (SED) in order to characterize the dominant emission and absorption processes. We analysed the spatially resolved emission of Arp 299 revealed by 150 MHz international baseline Low-Frequency Array (LOFAR) and 1.4, 5.0, and 8.4 GHz Very Large Array (VLA) observations. We present the first subarcsecond (0.4$sim$100~pc) image of the whole Arp~299 system at 150~MHz. The high surface brightness sensitivity of our LOFAR observations ($sim$100 $mu$Jy/beam) allowed us to detect all of the nuclear components detected at higher frequencies, as well as the extended steep-spectrum emission surrounding the nuclei. We obtained spatially resolved, two-point spectral index maps for the whole galaxy: the compact nuclei show relatively flat spectra, while the extended, diffuse component shows a steep spectrum. We fitted the radio SED of the nuclear regions using two different models: a continuous free-free medium model and a clumpy model. The continuous model can explain the SED of the nuclei assuming a population of relativistic electrons subjected to synchrotron, bremsstrahlung, and ionization losses. The clumpy model fits assuming relativistic electrons with negligible energy losses, and thermal fractions that are more typical of star-forming galaxies than those required for the continuous model. Our results confirm the usefulness of combining spatially resolved radio imaging at both MHz and GHz frequencies to characterize in detail the radio emission properties of LIRGs from the central 100 pc out to the kiloparsec galaxy-wide scales.
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