# Cross correlation and time-lag between cosmic ray intensity and solar activity during solar cycles 21, 22 and 23

## TL;DR

This study analyzes the relationship between cosmic ray intensity and solar activity indicators over three solar cycles using cross-correlation, revealing significant negative correlations and specific time lags between variables.

## Contribution

It provides a systematic analysis of the time-lagged relationships between cosmic rays and solar activity indicators across multiple solar cycles using cross-correlation.

## Key findings

- Maximum negative correlation of 0.85 with sunspot number
- Time lag of approximately 181 days for sunspot correlation
- Time lag of approximately 156 days for flare index

## Abstract

In the present paper a systematic study is carried out to validate the similarity or degree of relationship between daily terrestrial cosmic rays intensity and three characteristics of about evolution of solar corona, like a number of sunspots and flare index observed in the solar corona and to Ap index for regular magnetic field variation caused by regular solar radiation changes. The study is made in a range including three solar cycles starting with the cycle 21 (year 1976) and ending on cycle 23 (year 2008). The technique used in this case will be the use of the cross-correlation technique to establish patterns and dependence on the behavior of both variables. This study focused on the time lag calculation for these variables and found a maximum of negative correlation over $CC_1\approx 0.85$, $CC_2\approx 0.75$ and $CC_3\approx 0.63$ with an estimation of 181, 156 and 2 days of deviation between maximum/minimum of peaks for the intensity of cosmic rays related with sunspot number, flare index and Ap index regression, respectively.