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The multi-scaled solar magnetic field consists of two major components: active regions (ARs) and magnetic network. Unraveling the cycle-dependent properties and interrelations of these components is crucial for understanding the evolution of the solar magnetic field. In this study, we investigate these components using magnetic power spectra derived from high-resolution and continuous synoptic magnetograms since cycle 23 onwards. Our results show that the size of the magnetic network ranges from 26 Mm to 41 Mm without dependence on the solar cycle. The power of the network field ($P_{NW}$) accounts for approximately 20\% of the total power during any phase of solar cycles. In contrast to the AR power ($P_{AR}$), $P_{NW}$ displays a weaker cycle dependence, as described by the relationship $P_{NW}$ $\approx$ 0.6* $P_{AR}$ + 40. The power-law index between AR sizes and magnetic network sizes presents a strong anti-correlation with the activity level. Additionally, our study indicates that in the absence of sunspots on the solar disc, the magnetic power spectra remain time-independent, consistently exhibiting similarity in both shape and power. This study introduces a new method to investigate the properties of the magnetic network and provides magnetic power spectra for high-resolution simulations of the solar magnetic field at the surface at various phases of solar cycles., Comment: 13 pages, 11 figures, accepted for publication in ApJ

Solar active regions (ARs) determine solar polar fields and cause solar cycle variability within the framework of the Babcock-Leighton (BL) dynamo. The contribution of an AR to the polar field is measured by its dipole field, which results from flux emergence and subsequent flux transport over the solar surface. The dipole fields contributed by an AR before and after the flux transport are referred to as the initial and final dipole fields, respectively. For a better understanding and prediction of solar cycles, in this paper, we provide a database including AR's initial and final dipole fields and the corresponding results of their bipolar magnetic region (BMR) approximation from 1996 onwards. We also identify the repeated ARs and provide the optimized transport parameters. Based on our database, we find that although the commonly used BMR approximation performs well for the initial dipole field, it exhibits a significant deviation for the final dipole field. To accurately assess an AR's contribution to the polar field, the final dipole field with its real configuration should be applied. Despite the notable contributions of a few rogue ARs, approximately the top 500 ARs ordered by their final dipole fields are necessary to derive the polar field at the cycle minimum. While flux transport may increase or decrease the dipole field for an individual AR, its collective impact over all ARs in a cycle is a reduction in their total dipole field., Comment: 14 pages, 8 figures, Submitted to ApJ

The Sun's magnetic field is strongly structured over a broad range of scales. The magnetic spatial power spectral analysis provides a powerful tool to understand the various scales of magnetic fields and their interaction with plasma motion. We aim to investigate the power spectra using spherical harmonic decomposition of high-resolution SOHO/MDI and SDO/HMI synoptic magnetograms covering three consecutive solar cycle minima in a series of papers. As the first of the series, we calibrate and analyze the power spectra based on co-temporal SDO/HMI and SOHO/MDI data in this paper. For the first time, we find that the calibration factor $r$ between SOHO/MDI and SDO/HMI varies with the spatial scale $l$ of the magnetic field, where $l$ is the degree of a spherical harmonics. The calibration factor satisfies $r(l)=\sqrt{-0.021 l^{0.64}+2} \quad(5<\mathrm{l}\leq539)$. With the calibration function, most contemporaneous SOHO/MDI and SDO/HMI magnetograms show consistent power spectra from about 8 Mm to the global scales over about 3 orders of magnitudes. Moreover, magnetic power spectra from SOHO/MDI and SDO/HMI maps show peaks/knees at $l\approx120$ corresponding to the typical supergranular scale (about 35 Mm) constrained from direct velocimetric measurements. This study paves the way for investigating the solar-cycle dependence of supergranulation and magnetic power spectra in subsequent studies., Comment: Accepted for publication in the Astrophysical Journal. 15 pages, 7 figures, 2 tables

Recent studies indicate that a small number of rogue solar active regions (ARs) may have a significant impact on the end-of-cycle polar field and the long-term behavior of solar activity. The impact of individual ARs can be qualified based on their magnetic field distribution. This motivates us to build a live homogeneous AR database in a series of papers. As the first of the series, we develop a method to automatically detect ARs from 1996 onwards based on SOHO/MDI and SDO/HMI synoptic magnetograms. The method shows its advantages in excluding decayed ARs and unipolar regions and being compatible with any available synoptic magnetograms. The identified AR flux and area are calibrated based on the co-temporal SDO/HMI and SOHO/MDI data. The homogeneity and reliability of the database are further verified by comparing it with other relevant databases. We find that ARs with weaker flux have a weaker cycle dependence. Stronger ARs show the weaker cycle 24 compared with cycle 23. Several basic parameters, namely, location, area, and flux of negative and positive polarities of identified ARs are provided in the paper. This paves the way for AR's new parameters quantifying the impact on the long-term behavior of solar activity to be presented in the subsequent paper of the series. The constantly updated database covering more than two full solar cycles will be beneficial for the understanding and prediction of the solar cycle. The database and the detection codes are accessible online., Comment: Accepted for publication in the Astrophysical Journal Supplement Series. 14 pages, 8 figures, 3 tables