Yukun Luo1,2, Jie Jiang1,2, Ruihui Wang1,2
1. School of Space and Earth Science, Beihang University, Beijing 102206, China
2. Key Laboratory of Space Environment Monitoring and Information Processing of MIIT, Beijing, China
Solar magnetic fields, as the main source of solar activity, include two prominent components: active regions (ARs) and magnetic network (NW). The investigation of their interaction and temporal variation with the solar cycle can help to understand the evolution of magnetic fields, dynamic processes with flow fields, and their impact on the solar atmosphere. The cycle dependence of AR is well-studied, but there is an ongoing debate about the cycle dependence of NW due to the small spatial scales[1].
Previous attempts to determine the variation of NW with the solar cycle use different proxies, yielding divergent results. The magnetic power spectrum obtained from magnetograms is a useful tool to directly investigate properties of NW. With the availability of high-resolution synoptic magnetograms from SOHO/MDI and SDO/HMI spanning three consecutive solar cycle minima, we can derive power spectra that enable us to investigate properties of NW across multiple solar cycles.
As the first step in investigating NW properties varying over multiple solar cycles, we have developed a scale-dependent calibration method for MDI and HMI magnetograms to ensure a consistent analysis (see Ref. [2]). With the calibration, most contemporaneous MDI and HMI magnetograms show consistent power spectra from about 8 Mm to the global scales. In the calibrated power spectra, there are peaks or knees corresponding to AR or NW. As an example, Figure 1 presents the power spectrum derived from the CR 1960 synoptic map. The peak at l=30 (146 Mm) is identified as representing the size of the AR and the knee around l=155 (28 Mm) corresponds to the NW size. More examples and identification methods can be found in Ref. [3]. Among the total power spectra derived from 355 synoptic maps spanning CR1911 to CR2265, NW was identified in the power spectra of 254 maps.
Figure 1| Magnetic power spectrum derived from the CR1960 synoptic magnetogram. Identified AR size and NW size are marked by the vertical gray dashed line. The red dashed line is the fitting one of power spectrum between AR size and NW size.
The identified typical NW sizes are shown in the left panel of Figure 2, ranging from 26 Mm to 41 Mm. The scale range is broad and nearly homogeneous in any phase of the solar cycle, implying that the NW sizes have no significant cycle phase dependence or cycle dependence. Meanwhile, this emphasizes that NW is also identifiable during the active phase, not only during the solar minimum. Besides the cycle dependence of NW sizes, the variation of NW power could also be investigated. The ratio between NW power and total power varies slightly from 19.3% to 22.1% with anti-correlation with the solar cycle (see the right panel of Figure 2). Taking account for the small amplitude of ratio variation, we can quantify that the ratio remains approximately 20% throughout all phases of the solar cycle.
Figure 2| Left: NW sizes identified in magnetic power spectra during solar cycles 23, 24 and part of 25. Right: the variation of the ratio between NW power and total power with the solar cycle. The data are smoothed using a smoothing window of 2 year.
In Figure 1, the power spectrum relating the AR size to the NW size exhibits a consistent power index, indicating that the cascade from AR power to NW power is universal. Based on the identified AR sizes and NW sizes, we calculate the power-law indices of the magnetic power spectra for 191 CRs. Figure 3 displays the scatter plot between indices and the monthly smoothed total sunspot number (SSN). The power-law indices have a linear relationship with the logarithm of SSN. This relationship provides a way to evaluate the power-law index with a given SSN and shows that the solar activity modulates the power-law index: stronger activity results in a smaller index. During the solar active phase of cycle 23, the power-law indices are universally smaller than those in cycle 24. However, all power-law indices are larger than -1.5, suggested by the theory about magnetohydrodynamic turbulence power spectra[4]. This indicates that the presence of energy injection in network scales, except from ARs.
Figure 3| Power-law indices of the spectrum relating the AR size to the NW size versus SSN. The red line is the fitting line.
In summary, we have presented the magnetic power spectra of the Sun, spanning scales from approximately 8 Mm to global dimensions over three orders of magnitude, derived from continuous synoptic magnetograms from SOHO/MDI and SDO/HMI since Cycle 23. From these spectra, we have measured both the AR and NW sizes, and investigated their cycle-dependent properties and relationships[2,3]. These properties provide new constraints for high-resolution simulations of the global magnetic field at the solar surface.
References:
[1] Bellot Rubio, L., & Orozco Suárez, D. 2019, LRSP, 16, 1
[2] Luo, Y., Jiang, J., & Wang, R. 2023, ApJ, 954, 199
[3] Luo, Y., Jiang, J., & Wang, R. 2024, ApJ, 970, 76
[4] Kraichnan, R. H. 1965, PhFl, 8, 1385