Modeling sunspot and starspot decay by turbulent erosion

TL;DR

This paper develops an analytical and numerical model for sunspot and starspot decay through turbulent erosion, providing explicit decay rates and a parabolic decay law that align with observed data.

Contribution

It introduces a new analytical and numerical framework for modeling sunspot decay by turbulent erosion, improving quantitative predictions.

Findings

Derived explicit decay rate and lifetime formulas.

Established a parabolic decay law for sunspot area.

Validated model predictions against observational data.

Abstract

Disintegration of sunspots (and starspots) by fluxtube erosion, originally proposed by Simon and Leighton, is considered. A moving boundary problem is formulated for a nonlinear diffusion equation that describes the sunspot magnetic field profile. Explicit expressions for the sunspot decay rate and lifetime by turbulent erosion are derived analytically and verified numerically. A parabolic decay law for the sunspot area is obtained. For moderate sunspot magnetic field strengths, the predicted decay rate agrees with the results obtained by Petrovay and Moreno-Insertis. The new analytical and numerical solutions significantly improve the quantitative description of sunspot and starspot decay by turbulent erosion.