# On the saturation of acoustic mode frequencies at high solar activity

## TL;DR

This study analyzes solar acoustic mode frequencies over the solar cycle, revealing a saturation effect at high activity levels that challenges the assumption of a linear relationship, with implications for solar physics models.

## Contribution

It introduces the use of the Gompertz model to fit frequency data, demonstrating a statistically significant saturation level at high solar activity, which was previously unquantified.

## Key findings

- Evidence of saturation in acoustic mode frequencies at high solar activity.
- Estimated median saturation level of 400 sfu, 50% larger than previous measurements.
- Small but significant effect on frequency shifts during solar cycle extremes.

## Abstract

Acoustic mode frequencies obtained by applying spherical harmonic decomposition to HMI, MDI and GONG observations were analysed throughout the solar cycle. Evidence of a deviation from a linear relation with solar radio flux was found indicating a saturation effect at high solar activity. The Gompertz model, which is one of the most frequently used sigmoid functions to fit growth data, is used. It is shown that its fitting to MDI and GONG data are statistically significant and a median saturation of four-hundred sfu is estimated. This saturation level is 50% larger than any obtained in the last century, hence the small effect observed in the minimum-to-maximum frequency shift. However, as shown here, it should not be disregarded.