The frequency ratio and time delay of fundamental and harmonic components in solar radio bursts by X. Chen et al

Solar radio bursts generated through the plasma emission mechanism produce radiation near the local plasma frequency (fundamental emission, hereafter, F) and double the plasma frequency (harmonic, hereafter, H). While the theoretical ratio of these two frequencies is close to 2, simultaneous observations give ratios ranging from 1.6 to 2, suggesting either a ratio different from 2, a delay of the F emission, or both.

Observations suggest that a delayed F component leads to the derived H/F frequency ratio to be less than 2, as illustrated in Figure 1. The time delay between F and H components can be explained by a combination of different group velocities and scattering effects, with the latter forming a larger contribution. As the F component is emitted at the local plasma frequency, it undergoes a stronger scattering effect than the H component, which lengthens the propagation path of the F emission and leads to a delayed F band.

Figure 1. A physical scenario of two dynamic spectra showing the time delay between the observed and intrinsic F components of the normal type III burst (left panel) and the type III burst with striae structures (right panel).

Figure 2. LOFAR observations and correlation results for type III (a, b) and type J (c, d) bursts.

The type III and type J bursts that present striae in both F and H components are well observed by LOFAR, seen in Figure 2. The short-lived and narrow frequency-band fine structures observed at the same time at F and H frequencies give a frequency ratio of 1.66 and 1.73, similar to previous observations. In order to determine the frequency ratio and delay time simultaneously, we implement the correlation of striae in F and H components. The fine structures are crucial to this method because striae in the F components have their counterparts in the H components and can be well correlated, allowing clear determination of the frequency ratio and delay time. Frequency-time cross-correlations suggest a frequency ratio of 1.99 and 1.95 with a time delay between the F and H emissions of 1.00 and 1.67 s, respectively for type III and type J bursts.

The observed radio source properties at metre and longer wavelengths are strongly affected by the propagation effects, eg. scattering, refraction and absorption, while scattering dominates (Kontar et al. 2019, Kuznetsov et al. 2020, Chen et al. 2020, Musset et al. 2021). We quantitatively estimate the delay times caused by the different group velocities and propagation effects through ray-tracing simulations of radio wave propagation (Kontar et al. 2019). If we adopt the same characteristic parameters as in the ray tracing simulations that successfully reproduced the observed properties of the same type IIIb burst analysed in Chen et al. (2020), the simulated delay time is very close to the observed delay, supporting to resolve the long-standing question of why different frequency ratios are often observed.

The delay time is dependent on the anisotropic turbulent conditions that vary between events. Using these simulations we are able to, for the first time, provide quantitative estimates of the delay time of the F emissions caused by radio-wave propagation effects at multiple frequencies, which should be considered in future studies.

Based on the recent paper by Xingyao Chen, Eduard P. Kontar, Daniel L. Clarkson and Nicolina Chrysaphi, The frequency ratio and time delay of solar radio emissions with fundamental and harmonic components, MNRAS 520, 3117–3126 (2023), DOI:


Kontar, E. P., Chen, X., Chrysaphi, N., et al., 2019, ApJ, 884, 122

Kuznetsov, A. A., Chrysaphi, N., Kontar, E. P., Motorina G., 2020, ApJ, 898,94

Chen, X., Kontar, E. P., Chrysaphi, N., et al., 2020, ApJ, 905, 43

Musset, S., Maksimovic, M., Kontar, E., et al., 2021, A&A, 656, A34