# Magnetic Power Spectra of Emerging Active Regions

## TL;DR

This study analyzes the magnetic energy spectra of emerging active regions on the Sun, revealing simultaneous energy growth across scales and challenging the idea that inverse cascades dominate active region formation.

## Contribution

It provides new insights into the scale-dependent energy dynamics during active region emergence, emphasizing the role of large-scale structure emergence over inverse cascades.

## Key findings

- Rapid steepening of the magnetic power spectrum at emergence onset
- Energy increases at all scales, with larger scales dominating growth
- Both direct and inverse cascades are observed, but large-scale emergence is primary

## Abstract

Magnetic field data provided by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory were utilized to explore the changes in the magnetic energy of four active regions (ARs) during their emergence. We found that at the very early stage of the magnetic flux emergence, an abrupt steepening of the magnetic power spectrum takes place leading to rapid increase of the absolute value of the negative spectra power index $\alpha$ in $E(k)$ $\sim$ $k^{\alpha}$. As the emergence proceeds, the energy increases at all scales simultaneously implying that elements of all sizes do appear in the photosphere. Meanwhile, the energy gain at scales larger than $\approx$10 Mm prevails as compared to that at smaller scales. Both direct (i.e., fragmentation of large structures into smaller ones) and inverse (i.e., merging of small magnetic features into larger elements) cascades are readily observed during the emergence. However, in the case of inverse cascade, the total energy gained at large scales exceeds the energy loss at smaller scales assuming simultaneous appearance of large-scale magnetic entities from beneath the photosphere. We conclude that most of the time the energy may grow at all scales. We also cannot support the point of view regarding the dominant role of the inverse cascade in the formation of an AR. Although the coalescence of small magnetic elements into larger pores and sunspots is observed, our analysis shows that the prevailed energy contribution to an AR comes from emergence of large-scale structures.