Overview of the observations

The radio burst on 2015 April 16 around 11:57 UT was simultaneously observed by one of the largest decameter arrays, the LOw Frequency ARray (LOFAR)25 and by the URAN-226 (Ukrainian Radio interferometer of National Academy of Sciences). The latter provides corroborating observations at other frequencies, polarization information, and valuable cross-calibration for the LOFAR observations between 30 and 32 MHz.

The dynamic spectrum (radio flux in the frequency-time plane; Fig. 1) shows two main burst components, each characterized by a rapid decrease in frequency with time; the first burst passes through 20 MHz at \( \simeq \)11:57:00 UT and is followed a few seconds later by another burst which passes through 20 MHz at \( \simeq \)11:57:04 UT. The first burst is radiation at the fundamental plasma frequency, while the second burst is harmonic emission from the same electron beam forming a so-called type IIIb-type III pair27,28 (for example, at 11:57:00 UT the emission in the first burst is concentrated at frequencies around 20 MHz while the emission in the second burst is concentrated around 40 MHz.)

Fig. 1 Sun-integrated dynamic spectrum of the solar radio burst. a The Type III-IIIb solar radio burst observed on 2015 April 16 with both LOw Frequency ARray (LOFAR)25 and Ukrainian Radio interferometer of National Academy of Sciences (URAN-2)26. b The expanded view of a 3-s interval shows finely-structured Type IIIb striae at frequencies between 32 and 36 MHz that have frequency widths of only 0.1–0.3 MHz Full size image

The Type III burst in this event is rather typical;19,28 for example, the peak flux density between 32 and 40 MHz is 100–200 solar flux units (sfu) (1 sfu = 10−22 J s−1 m−2 Hz−1), and it has circular polarizations of ~15% and <5% for the fundamental and harmonic components, respectively. The rapid downward drift of frequency with time is a defining characteristic of solar Type III bursts;19 it results from the rapidly decreasing ambient density (and hence decreasing plasma frequency away from the Sun) as the emitting electron beam propagates upward through the decreasing density of the solar atmosphere. Since the plasma frequency \(f \propto {n^{1/2}}\), it follows that \((1/f){\rm{d}}f/{\rm{d}}t = (1/2n){\rm{d}}n/{\rm{d}}t = (1/2)({\rm{dln}} \, (n)/{\rm{d}}r)({\rm{d}}r/{\rm{d}}t) = v/2L\), where \(L = ({\rm{dln}}(n)/{\rm{d}}r)^{ - 1}\) is the density scale height and v = dr/dt is the vertical component of the velocity of the exciting electron beam. Using the Newkirk29 density model of the solar corona as a typical model, the characteristic density scale height is \(L \simeq 0.3{R_ \odot } \simeq 2 \times {10^{10}}\) cm at a level in the atmosphere corresponding to plasma frequencies around 32 MHz. Therefore, the observed frequency drift rate \({\rm{d}}f/{\rm{d}}t \simeq 7\) MHz s−1 at the f = 32 MHz point in the fundamental frequency burst component corresponds to \(v = (2L/f)({\rm{d}}f/{\rm{d}}t) \simeq {10^{10}}{\rm{cm}}\,{{\rm{s}}^{ - {\rm{1}}}} \simeq c/3\), where c is the speed of light. The speed c/3 is a typical speed for the ~ 30 keV electrons that excite Type III bursts19,30.

The expanded view in Fig. 1 shows that the fundamental component of the burst consists of multiple fine-structured striae; such fine structure is the characteristic signature of Type IIIb bursts24 (the number of striae increases with decreasing frequency, so that below ~30 MHz, the frequency structure of the burst looks quasi-continuous). These fine frequency structures are believed to be due to small-scale density fluctuations4,28,31,32 that modulate the resulting radio emission; they have full width at half-maximum (FWHM) durations around 1 s at a given frequency (Fig. 1). The presence of these fine striae in the fundamental component of the burst provides an estimate of the characteristic size of the emitting volume (intrinsic emission source size), which can then (see below) be compared to the source sizes obtained from direct imaging in order to evaluate the effects of radio wave propagation on the observed source size. Specifically, the individual striae (see the zoomed-in dynamic spectrum in Fig. 1) have FWHM frequency widths Δf ~ 0.3 MHz. Although the relationship between Δf and the size of the radio emitting source is model dependent5, and in particular depends on the angle between the direction of beam propagation and the direction of the density gradient, an order-of-magnitude estimation based on the plasma emission mechanism suggests that the limited frequency range corresponds to a vertical extent \(\Delta r \simeq 2L(\Delta f/f) \simeq 4 \times {10^8}\) cm. We note this would be the size of a density inhomogeneity leading to an enhanced level of Langmuir waves, while the electron beam generating the Langmuir waves is extended over a much larger distance4,31. Such a characteristic size of the fundamental emitting source extends over an angle \(\theta \simeq 0.1\) arcmin at the Sun and hence subtends a very small solid angle (\(\Omega \simeq {10^{ - 2}}\) arcmin2) on the sky. The harmonic emission is likely to form over a much larger region in physical space33, a feature that is also evident from the dynamic spectra—the fundamental component has clear striae, but the harmonic is rather smooth.

Imaging

LOFAR imaging observations were made using 24-core Low Band Antenna stations with tied-array beam forming25,34,35,36,37, an observing mode that provides images with sub-second time resolution and unprecedented frequency resolution in order to resolve the individual striae in the Type IIIb burst. The array of 127 tied-array beams cover the sky out to \(\sim 2{R_ \odot }\) with a mosaic beam spacing of ~ 0.1 degrees. We note that tied-array mosaic imaging is different from the traditional method of producing images from interferometric visibilities. The LOFAR core size of \(D \simeq 3.5\) km provides an angular resolution \(\lambda /D \simeq 9\) arcmin at 32 MHz (wavelength λ = 9.4 m) and the dirty beam FWHM area A LOFAR was \( \simeq 110\) arcmin2 at the time of the observation. The flux was calibrated against the Crab nebula both before and after the burst observations; in addition, the Sun-integrated flux was compared with URAN-2 data, which showed agreement within a factor of ~ 2. The temporal modulation of the URAN-2 flux also demonstrated excellent agreement with the observed fine frequency structures, excluding instrumental effects.

The imaging of the radio emission was performed with time resolution \( \simeq \)50 ms, during which radio waves propagate a distance of only ~ 1.5 × 109 cm \( \simeq 0.3\) arcmin, allowing us to accurately track variations in both the location and the areal extent of the source on sub-second timescales. For each 12 kHz-wide frequency channel we fitted an elliptical Gaussian to the LOFAR images. The ellipse centroid position (which is determined to an accuracy significantly better than the angular resolution of a single beam measurement38) and the FWHM area of each source were estimated for all frequency channels during the radio burst (Fig. 2). Figure 3 shows the size and centroid positions (with uncertainties) of both fundamental (F) and harmonic (H) images for a typical stria near 32 MHz; the FWHM areas are A F ~ 400 arcmin2 for the fundamental and A H ~ 600 arcmin2 for the harmonic. The accuracy of determining the source position and area is variable, depending on the emission flux (Methods section), and near the burst peak they can be as high as ± 0.1 arcmin for the position and ± 5 arcmin2 for the area (see Fig. 4). The areas and area uncertainties are well above the LOFAR resolution limit and hence the radio sources are reliably resolved (Methods section). The radio source sizes corrected for the LOFAR beam, \({A^{\{ {\rm{F}},{\rm{H}}\} }} - {A_{{\rm{LOFAR}}}}\), are both four orders of magnitude larger than the emission region size \(\Omega \sim {10^{ - 2}}\) arcmin2 as determined above from considerations of the fine frequency width of individual burst striae.

Fig. 2 Radio images of the fine structure components of the burst. Superimposed images of the Extreme Ultra-Violet (EUV) and radio emission at the selected 32.5 MHz frequency (Fig. 1). Green: Observations from the Solar Dynamics Observatory/Atmospheric Imaging Assembly43 171 Å at 2015 April 16 11:57 UT; Red: radio fundamental plasma frequency (F) component at 11:56:57.5 UT; Blue: second-harmonic (H) radio component at 11:57:01 UT. The centroid positions of the F- and H-components are marked with white and black crosses, respectively. The full width at half-maximum (FWHM) ellipses are made using two-dimensional Gaussian fits to the data. The white dots show the phased array beam locations and the oval shows the half-maximum synthesized LOw Frequency ARray (LOFAR) beam. See also Supplementary Movie 1 Full size image

Fig. 3 Centroid locations of the fundamental (F; red) and harmonic (H; blue) sources for 32.5 MHz as a function of time, determined using a two-dimensional Gaussian fit to each observed source. Darker colors correspond to later times, as shown in the color scale in the insert. Straight-line fits to the positions of each centroid are shown by the arrows. The time elapsed is measured as time after the flux peak; 11:56:57.6 UT for fundamental and 11:57:01 UT for harmonic (Fig. 4). The full solar disk shows clearly that the F source is displaced radially outwards. The error bars represent one standard deviation of uncertainty. The uncertainties of the source position were determined by the 2D Gaussian fit (see Methods) Full size image

Fig. 4 Time variations of flux, radial distance from the solar disk center, and areal extent, for the selected stria in the 32.5 MHz frequency channel. a time histories of the F and H-components of the radio flux density in solar flux units (sfu) b Radial distances of the F and H sources versus time; c Areas of the F- and H-source areas versus time. Linear fits (red and blue lines, for the F and H sources, respectively) to the radial positions \(r = {r_0} + (dr/dt)(t - {t_0})\) and areas \(A = {A_0} + (dA/dt)(t - {t_0})\) were applied in the time ranges shown by the dark and light gray patches, respectively. The error bars represent one standard deviation of uncertainty. The uncertainties of the source size and position were determined by the 2D Gaussian fit (Methods section) Full size image

Figure 3 shows the temporal evolution of the centroid location, and the areal extent, of the fundamental and harmonic sources (both observed at a frequency of 32.5 MHz, so that the H-radiation is produced in a region with a density one-fourth that of the region emitting the fundamental—and a few seconds later, when the emission at the fundamental frequency has drifted downward to 16.25 MHz). The centroid of the fundamental frequency radiation moves in a direction roughly parallel to the local solar radius (i.e., north-west in the plane-of-image; see full-disk image in Fig. 3), whereas the centroid of the source of harmonic radiation moves in a roughly transverse direction. The motion of F and H sources due to frequency drift between 38 and 32 MHz caused by electron transport is shown in Fig. 5. Figure 4 shows the time evolution of the radial centroid positions and areas in the X–Y plane, for both F and H components (Fig. 3). The areal expansion of both F and H components is most pronounced during the decay of the burst. This is consistent with various wave scattering models6,10,11, although these models predict different motions and growth rates of the source, depending on the assumed emission and scattering anisotropies39. Therefore, we focus on times during the decay and estimate the radial velocity in the X-Y plane and areal expansion rate by fitting linear expressions \(r(x,y) = {r_0} + ({\rm{d}}r/{\rm{d}}t)(t - {t_0}),A = {A_0} + ({\rm{d}}A/{\rm{d}}t)(t - {t_0})\) during the time intervals shown by the shaded regions in Fig. 4. The centroid of the F-emission moves radially outward at an average speed \(dr/dt \simeq 1.8\,{\rm{arcmin}}\,{{\rm{s}}^{ - 1}} \simeq c/4\), while its area A F grows from ~ 420 arcmin2 to ~ 530 arcmin2 within ~ 0.6 sec, an average areal expansion rate \({\rm{d}}{A^{\rm{F}}}/{\rm{d}}t \simeq 180\) arcmin2 s−1. On the other hand, the centroid of the harmonic component shows negligible radial motion, while its area A H grows from ~ 600 arcmin2 to ~ 760 arcmin2 over ~ 3 s. The average areal expansion rate is \(d{A^{\rm{H}}}/dt \simeq 50\) arcmin2 s−1, about one-fourth the areal expansion rate for the fundamental component.

Fig. 5 Motion of the sources. Gray arrows show the projected motion of the burst component in frequency as the burst drifts in frequency given by the color bar. Centroid positions as a function of time for fundamental (red) and harmonic (blue) components with time after the peak at each frequency (Fig. 4). The error bars represent one standard deviation of uncertainty. The uncertainties of the position determined by the 2D Gaussian fit (Methods section) are given by the red and blue crosses Full size image

We repeated this analysis for 48 well-observed striae in frequency channels between 32 and 38 MHz (Fig. 6). We excluded frequencies below 32 MHz where the striae start to overlap and images above 38 MHz due to low signal-to-noise ratio. Figure 6 shows that for all well-resolved striae, the rate of areal expansion of the fundamental source is ~(2–4) times greater than the expansion rate for the harmonic source.

Fig. 6 Statistical properties of the source areal expansion factors. a Flux along the spine of the Type IIIb burst as a function of frequency. Peaks colored in red indicate selected fine temporal stria. b Expansion rate dA/dt for all frequency channels with well-observed striae (those indicated by red in the top panel); the red and blue lines show the 1-MHz average values for fundamental and harmonic radiation, respectively. c ratio of the expansion rates \((d{A^{\rm{F}}}/dt)/(d{A^{\rm{H}}}/dt)\) as a function of frequency, averaged over the 1 MHz frequency bins. The error bars represent one standard deviation of uncertainty Full size image

Individual striae start at different times within the Type IIIb burst (Fig. 1). Each stria also initially appears at a different location on the solar disk within a broad envelope of the Type IIIb burst (Methods section). However, nearly all stria sources move radially while the harmonic component at the same frequency behaves in a completely different manner. This allows us to exclude refraction effects in the Earth’s ionosphere as an explanation for the observed motion of the fundamental stria component. Further, the very similar expansion rates inferred from observations in 235 different frequency channels, at 48 different striae spread over 2 s (larger than ~ 1 s duration of a stria) allow us to infer with a high degree of confidence that observed regions of fundamental radiation expand faster than regions of harmonic radiation. As we argue next, this result is not supported by any reasonable variation in the intrinsic source sizes in existing models2, but is consistent with propagation-scattering effects.

An intrinsic variation of source size with time at a given frequency requires that the emitting source grows in time as larger and larger iso-density surfaces start to emit17. However, in order to produce the observed striae, which are very narrow in frequency and large in imaged sources, such a model would require two essential features. Firstly, the emitting region is distributed over a thin but large (and changing) volume, all at the same plasma frequency and thus density; any density inhomogeneities would have to be always parallel to iso-frequency surfaces, and secondly, the positions of the stria, which originate at different locations, have nearly identical centroid motions. Moreover, in such a scenario, the expansion rate is related to the structure of the iso-density surface and it is challenging to explain why the expansion has a similar rate at all frequencies, or equivalently why all the iso-density surfaces, which are spread over a height range \(\sim 0.2{R_ \odot }\), expand at nearly identical rates. Finally, such a model does not explain why the centroids of the fundamental and harmonic components behave differently. Therefore, we reach the rather inescapable conclusions that the emitting sources most probably have sizes comparable to the inhomogeneity scale; they are randomly located within the corona and are responsible for the individual striae; and that the observed extent of the radio burst is primarily determined not by the size of the emitting region but rather by wave propagation effects in the surrounding atmosphere.

Radio wave propagation