On the relation between activity-related frequency shifts and the sunspot distribution over the solar cycle 23

TL;DR

This study models how sunspot properties influence solar acoustic frequency shifts over cycle 23, revealing a mix of stochastic and long-term effects and introducing a new observable to analyze short- and mid-term variations.

Contribution

Developed an empirical model linking sunspot characteristics to frequency shifts and proposed a new observable to separate short-term variations from long-term trends.

Findings

30% of frequency shifts are due to stochastic components.

70% of shifts are related to global long-term variations.

Frequency shifts correlate with sunspot area, especially on short timescales.

Abstract

The activity-related variations in the solar acoustic frequencies have been known for 30 years. However, the importance of the different contributions is still not well established. With this in mind, we developed an empirical model to estimate the spot-induced frequency shifts, which takes into account the sunspot properties, such as area and latitude. The comparison between the model frequency shifts obtained from the daily sunspot records and those observed suggests that the contribution from a stochastic component to the total frequency shifts is about 30%. The remaining 70% is related to a global, long-term variation. We also propose a new observable to investigate the short- and mid-term variations of the frequency shifts, which is insensitive to the long-term variations contained in the data. On the shortest time scales the variations in the frequency shifts are strongly correlated with the variations in the total area covered by sunspots. However, a significant loss of correlation is still found, which cannot be fully explained by ignoring the invisible side of the Sun when accounting for the total sunspot area. We also verify that the times when the frequency shifts and the sunspot areas do not vary in a similar way tend to coincide with the times of the maximum amplitude of the quasi-biennial variations found in the seismic data.