Hard X-ray (HXR) flares and type III radio bursts are produced by electron beams accelerated during solar flares. Most statistical studies on the relation of the two emissions have focused on coronal type III bursts, which occasionally show a close temporal and spatial association with HXR flares, thereby suggesting a common acceleration site. Mild correlations have been identified when comparing the peak radio flux directly to the peak HXR count rates in associated events, partly due to the distinct emission mechanisms and media. In contrast, systematic studies on the relation between HXRs and interplanetary (IP) type III bursts remain scarce. Leveraging the Solar Orbiter mission's unique capability for simultaneous HXR and radio observations, this study aims to establish a quantitative diagnostic link between the energy content and spectral properties of the electron beams that precipitate to produce HXRs at the Sun and those that escape to generate type III bursts in space. The Spectrometer/Telescope for Imaging X-rays (STIX) and the Radio and Plasma Waves instrument (RPW) on board Solar Orbiter are well suited for such a study. We analyzed 38 events from September 2021 to May 2023 with a clear temporal association between HXR bursts and type III bursts. For each event, we performed HXR spectroscopy at the time of the associated HXR peak to derive the spectral index (δ) and nonthermal power of the HXR-emitting electrons. From the RPW dynamic spectra, we measured the type III peak radio flux and fit the time profiles to extract the frequency drift of the burst's front, peak, and back velocities, which were then converted to exciter velocities. The type III radio peak flux exhibits a strong anticorrelation with the HXR spectral index, δ, and a significant positive correlation with the nonthermal electron power. Furthermore, the analysis of radio exciter velocities shows that the front velocity correlates with both the hardness and power of the HXR-emitting electrons. The peak and back velocities only describe weak relationships. The energy of radio-emitting electron beams estimated from radio observations (∼ 10^ 22 –10²4 erg) is smaller than the energy derived from HXR-emitting electrons (∼ 10^ 25 –10²9 erg). However, the two are still correlated. Our results support a common electron accelerator for flares with a temporal association between HXRs and radio, as expected. The peak radio flux correlates with the spectral hardness and energy of escaping electron beams; whereas the front velocity shows a weaker, but still significant correlation with high-energy electron power. Although their energies are correlated, radio-emitting electrons carry only a minor fraction (łesssim 10^ -3) of the energy contained in HXR-emitting electrons. We find that this difference might be linked to electron escape conditions in acceleration regions.
Paipa-Leon et al. (Wed,) studied this question.