Power law relating 10.7 cm flux to sunspot number

TL;DR

This study develops polynomial and power law models to relate 10.7 cm solar radio flux to sunspot numbers, using Bayesian analysis to identify the most plausible model for estimating historical solar activity.

Contribution

It introduces a Bayesian approach to compare models relating radio flux and sunspot number, identifying the power law as the most plausible for historical data estimation.

Findings

Power law model is most plausible for flux-sunspot relation.

Bayesian analysis effectively discriminates between models.

Model normalization impacts parameter uncertainty.

Abstract

To investigate the relation between observations of the 10.7 cm flux and the international sunspot number so that a physical unit may be ascribed to historical records, both polynomial and power law models are developed giving the radio flux as a function of sunspot number and vice versa. Bayesian data analysis is used to estimate the model parameters and to discriminate between the models. The effect on the parameter uncertainty and on the relative evidence of normalizing the measure of fit is investigated. The power law giving flux as a function of sunspot number is found to be the most plausible model and may be used to estimate the radio flux from historical sunspot observations.