Coriolis force acting on near-surface horizontal flows during simulations of flux emergence produces a tilt angle consistent with Joy’s law on the Sun

¹ The University of Newcastle, University Dr, Callaghan NSW 2308, Australia
² Max-Planck-Institut für Sonnensystemforschung, 37077 Göttingen, Germany
³ Institut für Astrophysik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany

^⋆ Corresponding author: hannah.schunker@newcastle.edu.au

Received: 25 February 2025
Accepted: 12 June 2025

Abstract

Context. Joy’s law describes the tilt of bipolar active regions on the Sun away from an east-west orientation, where the flux of the polarity concentrated at the prograde side tends to be closer to the equator than the polarity on the retrograde side. Joy’s law is attributed to the Coriolis force because of the observed increase in the tilt angle at higher latitudes. This tilt plays a crucial role in some solar dynamo models.

Aims. Our goal is to model the effects of the Coriolis force on a flux tube as it rises through the near-surface convection zone.

Methods. We used a three-dimensional Cartesian magnetohydrodynamic simulation of an untwisted flux tube ascending from a depth of 11 Mm. We modelled the Coriolis effect using the f-plane approximation, which only considers and acts on horizontal flows. On the Sun, Joy’s law is weak and is only evident as an average over many active regions. To achieve a measurable effect in a single simulation, we considered a rotation rate 110 times faster than that of the Sun.

Results. The simulation shows that the flux tube emerges at the surface with a tilt angle consistent with Joy’s law when scaled to the Sun’s slower rotation, and the tilt angle does not substantially change after emergence.

Conclusions. This shows that the Coriolis force acting on flows horizontal to the surface within the near-surface convection zone is consistent with Joy’s law.