Uncovering the Dominant Spatial Scales of the Sun's Magnetic Field in Solar Cycle 24

TL;DR

This study identifies the dominant spatial scales of the Sun's magnetic field during solar cycle 24, revealing that large-scale structures are primarily captured by low harmonic degrees, which has implications for observations and modeling.

Contribution

The paper introduces a spherical-harmonic modal decomposition method to quantify the spatial resolution needed for capturing the Sun's magnetic field evolution.

Findings

Over 80% of magnetic field power is in low harmonic degrees (~145 Mm scale).

The effective harmonic degree decreases with height in the corona.

Sunspots have limited immediate influence on the global coronal magnetic field.

Abstract

The internal dynamics of the Sun generate magnetic and plasma structures in the photosphere and overlying atmosphere across a wide range of spatial scales. Identifying the critical spatial scale is essential for interpreting physical processes, selecting appropriate observations, optimizing numerical simulations and guiding future instrumentations and space missions. With the growing availability of high-resolution data, we investigate the spatial resolution required to capture the global evolution of the photospheric and atmospheric magnetic field during sunspot cycle 24. We address this problem using a quantitative spherical-harmonic-based modal decomposition. Full-disk photospheric magnetic fields are obtained from the Michelson Doppler Imager and the Helioseismic and Magnetic Imager. The corresponding global coronal field is derived using a newly developed potential field source surface extrapolation (PFSSE) model applied to observed magnetograms. Our analysis reveals two robust results. First, more than 80% of the total modal power is captured by low harmonic degrees corresponding to a spatial scale of approximately 145 Mm, which is significantly larger than individual sunspot dimensions. Second, the effective harmonic degree decreases with height in the corona, indicating that sunspots have little direct and immediate influence on the quasi-static global coronal field. It explains the PFSSE model's success in reproducing and predicting large-scale solar coronal structures, such as streamers and open-field variations, throughout the solar cycle. These results highlight the continued relevance of low-resolution magnetic maps from historical solar observations and contemporary stellar surveys, with direct implications for mission design and for characterizing magnetic environments relevant to exoplanetary systems.