Foreground and internal free-free absorption in particle-accelerating colliding-wind binaries

Context. Radio emission from massive binary systems is generally of composite nature, exhibiting 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 governing their radio spectrum is key to investigating the role of these objects in the production of non-thermal particle populations in our galaxy. Aims. Our objective is to explore how the processes at work in particle-accelerating colliding-wind binaries (PACWBs) alter their spectral energy distribution, based on a simple phenomenological description. We focus on the role of free–free absorption (FFA) at low frequencies. We use WR 147 as a test case, followed by a tentative extrapolation to more generic behaviour. Methods. We processed a set of recent Karl G. Jansky Very Large Array data, optimised for spectral analysis, combined with literature measurements at other frequencies. We analysed the radio spectrum, considering a more classical foreground free-free absorption (f-FFA) model along with the first application of an internal free-free absorption (i-FFA) model. Results. 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 spectral energy distribution 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. Conclusions. The radio spectrum at low frequencies for very long period systems might display some internally attenuated synchrotron emission, without necessarily being suppressed by a steep exponential cut-off. We propose a generic spectral energy distribution for FFA-affected radio spectra of colliding-wind massive binaries, where the overall spectral shape can be expressed in terms of the relative importance of f-FFA and i-FFA. We also comment on the observational consequences of this generic behaviour in the broader context of the full class of PACWBs.