Author: Hamish Reid and Eduard Kontar
Astronomy and Astrophysics Group, University of Glasgow.
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Solar flares accelerate particles that then produce radio emission as they move through the corona. Type III radio bursts are commonly observed signatures of electron beams propagating along magnetic field that extends into interplanetary space. Seen less often are radio U-bursts and J-bursts, signatures of electron beams propagating along magnetic loops confined to the corona [1,2]. It is not clear why we do not commonly see U-bursts or J-bursts. To answer this question, we need to understand the properties of the accelerated electrons and the magnetic loops they travel along.
We used Low Frequency Array (LOFAR) imaging spectroscopy  to analyse two solar radio J-bursts and one U-burst from a storm of bursts that occurred shortly after a large flare at 12:00 UT on 6 May 2015. The dynamic spectrum of all three bursts is shown in Figure 1. The inverted U or J shape arises from an electron beam travelling up the ascending leg of a magnetic loop and through a decreasing plasma density, corresponding to a decrease in the radio frequency of the burst with time. But unlike the more common Type III bursts, in the U and J-bursts the electrons then travel back down the descending leg of the magnetic loop, through an increasing plasma density, corresponding to an increase in the radio frequency of the burst with time. An inverted J shape is made instead of an inverted U shape if the beam stops emitting radio waves at the apex of the loop.
Low Frequency Array (LOFAR) observations have a substantially improved frequency coverage for imaging than past observations, combined with sub-second time resolution. We do not see large numbers of J- and U-bursts, especially at high frequencies. What is new with LOFAR is, for the first time, to be able to REALLY observe (image) the magnetic loop, with many frequencies. Below 100 MHz we previously had a maximum of three frequencies, which is not great for deducing plasma properties.
Figure 2 shows an image of the U-burst between 75 and 40 MHz at the times of peak intensity, so the higher frequency contours were earlier in time than the lower frequency ones. The bursts allow a large part of the magnetic loop to be visible at altitudes not dense enough for EUV or X-ray imaging. This U-burst showed faint radio emission originating from the descending leg of the magnetic loop. A fit to the radio centroids finds a loop with an altitude of approximately 1 solar radius and a length around 1.5 solar radii from the bottom to the apex of the loop. Starting heights for the radio emission were between 0.6 – 0.8 solar radii. The magnetic loop model was combined with the frequency evolution in time to estimate exciter velocities between 0.13c and 0.23c, all without requiring the common assumption of a coronal density model or emission mechanism. We also estimated a density model of the magnetic loop. It had a much smaller density gradient than the standard density models of the quiet Sun, although there are uncertainties in the radio positions because of scattering effects of the light from the source to the observer .
Occurrence of U-bursts
Why are U-bursts and J-bursts not observed more often than their type III counterparts? For an electron beam to generate radio emission, it must become unstable and generate Langmuir waves during propagation. The Langmuir wave instability time must be shorter than the propagation time or no Langmuir waves will be generated. We used the results above to construct a graph of instability time versus propagation time, shown in Figure 3.
As the electron beam travels through the solar atmosphere, the bump-in-tail instability can cause Langmuir waves to be generated. This requires an instability distance [5,6] which is independent of initial beam density. If the magnetic loop is too small then the electron beam will not become unstable and no radio emission will be generated.
Once the electron beam is unstable to Langmuir waves, the instability time must be short. This timescale is proportional to the square root of the background electron density and inversely proportional to the electron beam density [7,8]. So higher initial beam densities correspond to shorter instability times (i.e. smaller timescales). However, the low magnitude of the density gradient in closed loops (J-, U- bursts) keeps the background density high and causes instability times to be longer than for open loops (type III bursts).
The fine spectral and temporal resolution of the LOFAR images between 75 and 40 MHz indicated a loop-shaped structure extending from the flaring active region in which an X-ray source was present . Using this enhanced resolution, we extracted properties of both the accelerated electron population and the background plasma they travelled through.
We found that U-bursts or J-bursts are only produced from a restricted range of accelerated beam and background plasma parameters, resulting in type III bursts being more frequently observed. The large instability distances required before Langmuir waves are produced by some electron beams, and the small magnitude of the background density gradients, makes closed loops less fertile for producing radio emission than loops that extend into interplanetary space.
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