Solar Kinetic Energy and Cross Helicity Spectra

TL;DR

This paper introduces a formalism for calculating solar kinetic energy and cross helicity spectra, applying a two-scale approach to analyze active regions and the quiet Sun, revealing spectral similarities and differences.

Contribution

It develops a unified formalism for kinetic and magnetic spectra and applies a two-scale method to analyze cross helicity in solar active regions.

Findings

Magnetic helicity is close to maximal at certain wavenumbers.

Cross helicity spectra are within 10% of maximum possible value.

Active regions show steep cross helicity spectra, quiet Sun spectra are small.

Abstract

We develop a formalism that treats the calculation of solar kinetic energy and cross helicity spectra in an equal manner to that of magnetic energy and helicity spectra. The magnetic helicity spectrum is shown to be equal to the vertical part of the current helicity spectrum divided by the square of the wavenumber. For the cross helicity, we apply the recently developed two-scale approach globally over an entire active region to account for the sign change between the two polarities. Using vector magnetograms and Dopplergrams of NOAA 11158 and 12266, we show that kinetic and magnetic energy spectra have similar slopes at intermediate wavenumbers, where the contribution from the granulation velocity has been removed. At wavenumbers around 0.3 Mm$^{-1}$, the magnetic helicity is found to be close to its maximal value. The cross helicity spectra are found to be within about 10% of the maximum possible value. Using the two-scale method for NOAA 12266, the global cross helicity spectrum is found to be particularly steep, similarly to what has previously been found in theoretical models of spot generation. In the quiet Sun, by comparison, the cross helicity spectrum is found to be small.