The low-high-low trend of type III radio burst starting frequencies and solar flare hard X-rays

Aims. Using simultaneous X-ray and radio observations from solar flares, we investigate the link between the type III radio burst starting frequency and hard X-ray spectral index. For a proportion of events the relation derived between the starting height (frequency) of type III radio bursts and the electron beam velocity spectral index (deduced from X-rays) is used to infer the spatial properties (height and size) of the electron beam acceleration region. Both quantities can be related to the distance travelled before an electron beam becomes unstable to Langmuir waves. Methods. To obtain a list of suitable events we considered the RHESSI catalogue of X-ray flares and the Phoenix 2 catalogue of type III radio bursts. From the 200 events that showed both type III and X-ray signatures, we selected 30 events which had simultaneous emission in both wavelengths, good signal to noise in the X-ray domain and >20 s duration. Results. We find that >50% of the selected events show a good correlation between the starting frequencies of the groups of type III bursts and the hard X-ray spectral indices. A low-high-low trend for the starting frequency of type III bursts is frequently observed. Assuming a background electron density model and the thick target approximation for X-ray observations, this leads to a correlation between starting heights of the type III emission and the beam electron spectral index. Using this correlation we infer the altitude and vertical extents of the flare acceleration regions. We find heights from 183 Mm down to 25 Mm while the sizes range from 13 Mm to 2 Mm. These values agree with previous work that places an extended flare acceleration region high in the corona. We also analyse the assumptions that are required to obtain our estimates and explore possible extensions to our assumed model. We discuss these results with respect to the acceleration heights and sizes derived from X-ray observations alone