# The frequency ratio and time delay of solar radio emissions with fundamental and harmonic components

**Authors:** Xingyao Chen, Eduard P. Kontar, Daniel L. Clarkson, Nicolina Chrysaphi  
**arXiv:** [2301.11299](https://arxiv.org/abs/2301.11299)  
**Date:** 2023-01-26  
**Summary page:** https://www.summarizepaper.com/en/paper/2301.11299v1/

## Key points

- Solar radio bursts are generated through the plasma emission mechanism
- Fundamental and harmonic emissions are produced near local plasma frequency
- Theoretical ratio of these two frequencies is close to 2, but observations have given ratios ranging from 1.6 to 2
- Xingyao Chen and colleagues conducted high-frequency, high-time-resolution imaging spectroscopy of type III and type J bursts with fine structures for both the fundamental and harmonic components using LOFAR between 30 and 80 MHz
- Short-lived and narrow frequency-band fine structures were observed simultaneously at fundamental and harmonic frequencies that gave a frequency ratio of 1.66 and 1.73, similar to previous observations
- Frequency-time cross-correlations suggested 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 for each event respectively
- Simultaneous frequency ratio measurements different from two were caused by the delay of the fundamental emission due to anisotropic radio-wave scattering
- Levels of anisotropy and density fluctuations reproducing the delay of fundamental emissions were consistent with those required to simulate source size and duration
- Using simulations for radio-wave propagation effects at multiple frequencies allowed for quantitative estimates of the delay time of fundamental emissions for future studies
- This study provides new insights into solar radio bursts' behavior generated through plasma emission mechanisms by addressing a long-standing question about their observed frequency ratios differing from theory's predictions
- The findings suggest that delays in fundamental emissions are caused by anisotropic radio-wave scattering rather than differences in ratios or other factors
- These results provide a foundation for future studies to better understand the physics of solar radio bursts and their impact on space weather

## Summary

Solar radio bursts are generated through the plasma emission mechanism, producing radiation near the local plasma frequency (fundamental emission) and double the plasma frequency (harmonic). The theoretical ratio of these two frequencies is close to 2, but simultaneous observations have given ratios ranging from 1.6 to 2, suggesting a different ratio, a delay of the fundamental emission, or both. To address this long-standing question, Xingyao Chen and colleagues conducted high-frequency, high-time-resolution imaging spectroscopy of type III and type J bursts with fine structures for both the fundamental and harmonic components using LOFAR between 30 and 80 MHz. The researchers observed short-lived and narrow frequency-band fine structures simultaneously at fundamental and harmonic frequencies that gave a frequency ratio of 1.66 and 1.73, similar to previous observations. However, frequency-time cross-correlations suggested 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 for each event respectively. Therefore, simultaneous frequency ratio measurements different from two were caused by the delay of the fundamental emission. Among the processes causing fundamental emission delays, anisotropic radio-wave scattering was found to be dominant in this study. Moreover, simulations showed that levels of anisotropy and density fluctuations reproducing the delay of fundamental emissions were consistent with those required to simulate source size and duration. Using these simulations for radio-wave propagation effects at multiple frequencies allowed for quantitative estimates of the delay time of fundamental emissions for future studies – something that has not been done before in this field. In conclusion, this study provides new insights into solar radio bursts' behavior generated through plasma emission mechanisms by addressing a long-standing question about their observed frequency ratios differing from theory's predictions. The findings suggest that delays in fundamental emissions are caused by anisotropic radio-wave scattering rather than differences in ratios or other factors. These results provide a foundation for future studies to better understand the physics of solar radio bursts and their impact on space weather.