Foreground and internal free-free absorption in particle-accelerating colliding-wind binaries : Insights from the radio emission of WR 147

Radio emission from massive binary systems is generally of composite nature, showing both a thermal emission component from the winds and a non-thermal component from relativistic electrons accelerated in the colliding-wind region. Understanding the processes ruling their radio spectrum is essential to investigate the role of these objects in the production of non-thermal particle populations in our galaxy. Our objective is to explore how the processes at work in particle-accelerating colliding-wind binaries (PACWBs) alter their spectral energy distribution, following a simple phenomenological description. We focus mainly on the role of free-free absorption (FFA) at low frequencies. Our intention is to use WR 147 as a test case, before tentatively extrapolating to a more generic behaviour. We processed recent Karl G. Jansky Very Large Array data, optimised for spectral analysis, combined with older measurements published in the literature at other frequencies. We analysed the radio spectrum considering both a more classical foreground free-free absorption (f-FFA) model and, for the first time, an internal free--free absorption (i-FFA) model. Our results show that the f-FFA model does not reproduce the spectral energy distribution of WR 147 at low frequencies. The i-FFA model is more efficient in providing a more complete description of the SED down to 610 MHz. This model is the only one to account for a change in the spectral index at low frequencies without any exponential drop in flux, as predicted by the f-FFA model. In addition, the upper limit at 150 MHz shows that two turnovers occur in the radio spectrum of WR 147, suggesting the effect of both i-FFA and f-FFA is seen in two regions of the spectrum. (abridged)