An analytical model of turbulence in Parker spiral geometry and associated magnetic field line lengths

TL;DR

This paper develops the first analytical model of heliospheric magnetic fields incorporating dominant 2D turbulence, revealing how turbulence affects magnetic field line spreading and lengths, with implications for solar energetic particle propagation.

Contribution

It introduces a novel analytical model of the turbulent heliospheric magnetic field with dominant 2D turbulence, extending field line length estimates and spatial spread at 1 au.

Findings

Turbulence causes magnetic field lines to spread over 60° at 1 au.

Field line lengths are extended up to 1.6 au, longer than the nominal Parker spiral.

Small source regions map to intermittent longitudes and latitudes, explaining particle dropouts.

Abstract

Understanding the magnetic connections from the Sun to interplanetary space is crucial for linking in situ particle observations with the solar source regions of the particles. A simple connection along the large-scale Parker spiral magnetic field is made complex by the turbulent random-walk of field lines. In this paper, we present the first analytical model of heliospheric magnetic fields where the dominant 2D component of the turbulence is transverse to the Parker spiral. The 2D wave field is supplemented with a minor wave field component that has asymptotically slab geometry at small and large heliocentric distances. We show that turbulence spreads field lines from a small source region at the Sun to a 60$^\circ$ heliolongitudinal and -latitudinal range at 1~au, with standard deviation of the angular spread of the field lines $14^\circ$. Small source regions map to an intermittent range of longitudes and latitudes at 1~au, consistent with dropouts in solar energetic particle intensities. The lengths of the field lines are significantly extended from the nominal Parker spiral length of 1.17~au up to 1.6~au, with field lines from sources at and behind the west limb considerably longer than those closer to the solar disk centre. We discuss the implications of our findings on understanding charged particle propagation, and the importance of understanding the turbulence properties close to the Sun.