# Scaling-laws of Radio Spike Bursts and Their Constraints on New Solar Radio Telescopes by Baolin Tan et al.

Previous statistical studies indicate that a solar eruption lasting several tens of minutes always contains several big pulses with timescales of minutes, and each big pulse is frequently composed of a group of pulses with timescales of seconds, and each pulse is still composed of many sub-pulses with timescales of sub-seconds. Actually, a violent solar eruption always contains a great number of sub-second radio bursts, which are called fast fine spectral structures (FFS). FFS includes spike bursts, dot bursts, and narrow-band type III bursts. In the microwave range, they are called small-scale microwave bursts (SMB) (Tan 2013). They have a very short lifetime, very narrow frequency band, and very high brightness temperature. They always occur in large groups and form various kinds of complex structures, such as QPPs, Zebra patterns, and other long-lasting pulses. Each SMB may represent an elementary energy release process, which can be regarded as the elementary burst (EB) in solar eruptions. Therefore, it becomes the basic requirement to identify clearly SMBs for the new generation of solar radio telescopes.

This work investigated the previous observational results of solar radio spike bursts, dot bursts, and narrowband type III bursts, including the previous publications (Gudel & Benz 1990, Rozhansky et al. 2008, etc.), and tried to obtain a modified scaling law of solar SMBs. Such a modified scaling law will be the theoretical basis to select reasonable parameters for designing the new generation of solar radio telescopes, and help us understand the nature of solar eruptions.

Figure 1 presents the statistical relationship between the averaged lifetime and frequency among solar radio spike bursts. The frequency range covers from 210 MHz to 7.0 GHz, and the lifetime ranges from 5 ms to 91 ms. It shows that the averaged lifetime of radio spike bursts is anti-correlated to the emission frequency, the correlation coefficient is -0.58. A fitted function is near a power-law function:

$\tau \approx 8.2 \times 10^3 f^{-0.84\pm0.15}$

is the averaged lifetime of SMB in units of ms, $f$ is the frequency in units of MHz.

Figure 1 – The relationship between the averaged lifetime and frequency among the solar radio spike bursts. Here, the crosses represent the results published in Gudel & Benz 1990 and Rozhansky et al. 2008 and the dashed line is obtained by least squared fitting method. The diamonds represent the results observed by the Chinese Solar Broadband Radio Spectrometers at Huairou (SBRS/Huairou) since 2006 (Wang et al. 2008, Tan 2013) and the solid line is obtained by least squared fitting method over the total sample.

Figure 2 presents the relationship between the averaged bandwidth and frequency among the solar radio spike bursts. The observing frequencies of the whole sample range from 305 MHz to 7.0 GHz. The narrowest bandwidth is 1.4 MHz at central frequency of 710 MHz, while the widest bandwidth is 115 MHz at 1250 MHz. We found that the higher the observing frequency, the wider the bandwidth of SMB. The statistical correlation coefficient between the bandwidth and the central frequency is 0.47 among the 166 samples, which is obviously positive correlation. A fitting function is also obtained:
$f_{bw}\approx 0.011 \times f^{0.99\pm0.018}\sim 1.1\% f$

Here, $f_{bw}$ is the averaged bandwidth of SMB in unit of MHz.

Figure 2 – The relationship between the averaged bandwidth and frequency among the solar radio spike bursts. Here, the crosses represent the results published in Gudel & Benz 1990 and Rozhansky et al. 2008. The diamonds represent the results observed by the Chinese Solar Broadband Radio Spectrometers at Huairou (SBRS/Huairou) since 2006 (Wang et al. 2008, Tan 2013) and the dot-dashed line is obtained by least squared fitting method over the total sample.

Because SMBs, including spike, dot, and narrow band type III bursts are the smallest eruptive units in solar eruptions, their scaling laws may provide a most important and fundamental basis for understanding the nature of solar eruptions and for the designing of the next generation solar radio telescopes.

Conclusions

Based on a recently published paper: Tan, Bao-lin, Cheng, Jun, Tan Cheng-ming, Kou, Hong-xiang, ChA&A, 2019, 43, 59-74, doi: 10.1016/j.chinastron.2019.02.005

References:

Guedel, M., Benz, A. O.: 1990, A&A, 231, 202

Rozhansky, I. V., Fleishman, G. D., Huang, G.-L.: 2008, ApJ, 681, 1688

Tan, B.L.: 2013, ApJ, 773, 165

Tan, B. L., Cheng, J., Tan, C. M., Kou, H. X.: 2019, ChA&A, 43, 59

Wang, S. J., Yan, Y. H., Liu, Y. Y., Fu, Q. J., Tan, B. L., Zhang, Y.: 2008, SoPh, 253, 133