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We have studied in detail the 0.15-15 GHz radio spectrum of the gamma-raybinary LS 5039 to look for a possible turnover and absorption mechanisms at lowfrequencies, and to constrain the physical properties of its emission. We haveanalysed two archival VLA monitorings, all the available archival GMRT data anda coordinated quasi-simultaneous observational campaign conducted in 2013 withGMRT and WSRT. The data show that the radio emission of LS 5039 is persistenton day, week and year timescales, with a variability $\lesssim 25~\%$ at allfrequencies, and no signature of orbital modulation. The obtained spectrareveal a power-law shape with a curvature below 5 GHz and a turnover at$\sim0.5$ GHz, which can be reproduced by a one-zone model with synchrotronself-absorption plus Razin effect. We obtain a coherent picture for a size ofthe emitting region of $\sim0.85~\mathrm{mas}$, setting a magnetic field of$B\sim20~\mathrm{mG}$, an electron density of $n_{\rm e}\sim4\times10^5~{\rmcm^{-3}}$ and a mass-loss rate of $\dot M\sim5\times10^{-8}~{\rm M_{\odot}yr^{-1}}$. These values imply a significant mixing of the stellar wind with therelativistic plasma outflow from the compact companion. At particular epochsthe Razin effect is negligible, implying changes in the injection and theelectron density or magnetic field. The Razin effect is reported for first timein a gamma-ray binary, giving further support to the young non-accreting pulsarscenario.

Physical properties of the gamma-ray binary LS 5039 through low and high frequency radio observations