Modeling the Longitudinal Asymmetry in Sunspot Emergence -- the Role of the Wilson Depression

TL;DR

This paper investigates how the Wilson depression influences the observed east-west asymmetry in sunspot emergence, revealing that the Wilson effect significantly impacts sunspot visibility beyond simple geometrical foreshortening.

Contribution

It introduces a model incorporating the Wilson depression to explain sunspot appearance asymmetries and estimates the mean depth of the tau=1 layer in sunspot umbrae.

Findings

Wilson depression depth estimated between 500 and 1500 km.

Wilson effect significantly affects sunspot visibility.

Model aligns with observed sunspot longitude distributions.

Abstract

The distributions of sunspot longitude at first appearance and at disappearance display an east-west asymmetry that results from a reduction in visibility as one moves from disk centre to the limb. To first order, this is explicable in terms of simple geometrical foreshortening. However, the centre-to-limb visibility variation is much larger than that predicted by foreshortening. Sunspot visibility is also known to be affected by the Wilson effect: the apparent dish shape of the sunspot photosphere caused by the temperature-dependent variation of the geometrical position of the tau=1 layer. In this article we investigate the role of the Wilson effect on the sunspot appearance distributions, deducing a mean depth for the umbral tau=1 layer of 500 to 1500 km. This is based on the comparison of observations of sunspot longitude distribution and Monte Carlo simulations of sunspot appearance using different models for spot growth rate, growth time and depth of Wilson depression.