The Sun’s Magnetic Power Spectra over Two Solar Cycles. I. Calibration between SDO/HMI and SOHO/MDI Magnetograms

Abstract

Abstract The Sun’s magnetic field is strongly structured over a broad range of scales. Magnetic spatial power spectral analysis provides a powerful tool for understanding the various scales of magnetic fields and their interactions with plasma motions. We aim to investigate the power spectra using spherical harmonic decomposition of high-resolution Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI) and Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (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 cotemporal 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 the spherical harmonic. The calibration factor satisfies r ( l ) = − 0.021 l 0.64 + 2 ( 5 < l ≤ 539 ) . 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 three orders of magnitude. Moreover, magnetic power spectra from SOHO/MDI and SDO/HMI maps show peaks/knees at l ≈ 120, 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.