Electron beam propagation and radio-wave scattering in the inner heliosphere using five spacecraft

Context. Solar energetic particles such as electrons can be accelerated to mildly relativistic velocities in the solar corona. These electrons travel through the turbulent corona, generating radio waves, which are then severely affected by scattering. Aims. The physical interpretation of the discrepancies between the actual and observed radio sources is still subject to debate. We used radio emission observed by an unprecedented total of five spacecraft to track the path of radio sources from the low corona to the inner heliosphere (15–75 R ⊙ or 0.07–0.35 au generated during a solar event on 4 December 2021. Methods. We used the Bayesian multilateration technique known as BELLA to track the apparent path of radio sources observed by Parker Solar Probe, STEREO A, Wind, Solar Orbiter, and Mars Express. To validate the accuracy of the tracked path, we used Nançay Radioheliograph interferometric imaging at 150 MHz, which was found to agree with the estimated footpoints predicted by BELLA. We further validated our results using ACE in situ measurements. Results. We find that the apparent radio sources followed the path of an Archimedean Parker spiral, with an associated solar wind velocity of approximately 493 km s −1 (consistent with the corresponding speed observed at 1 au at the relevant longitude), and connected to the solar surface at 75° longitude east. Finally, we made quantitative estimates of the scattering of radio waves, which we found to be in good agreement with contemporary models of scattering in which the radio waves primarily propagate along the local Parker spiral. Conclusions. This work shows conclusive evidence that the cause of the widely observed ‘higher-than-expected’ electron densities at interplanetary distances is due to radio-wave scattering, and provides a more detailed understanding of the propagation of radio waves emitted near the local plasma frequency in turbulent astrophysical plasmas.