# Impact of correlated magnetic noise on the detection of stochastic gravitational waves: Estimation based on a simple analytical model

## TL;DR

This paper presents an analytical model to estimate how correlated magnetic noise from Schumann resonances affects the detection of stochastic gravitational waves, highlighting the importance of detector geometry and implications for upcoming detectors.

## Contribution

It introduces a simple analytical model that estimates the impact of correlated magnetic noise on stochastic GW detection, considering detector geometry and matching recent measurements.

## Key findings

- Model reproduces observed global magnetic correlations.
- Correlated noise impact varies with detector pair geometry.
- Certain detector pairs are less affected by magnetic noise.

## Abstract

After the first direct detection of gravitational waves (GW), detection of stochastic background of GWs is an important next step, and the first GW event suggests that it is within the reach of the second-generation ground-based GW detectors. Such a GW signal is typically tiny, and can be detected by cross-correlating the data from two spatially separated detectors if the detector noise is uncorrelated. It has been advocated, however, that the global magnetic fields in the Earth-ionosphere cavity produce the environmental disturbances at low-frequency bands, known as Schumann resonances, which potentially couple with GW detectors. In this paper, we present a simple analytical model to estimate its impact on the detection of stochastic GWs. The model crucially depends on the geometry of the detector pair through the directional coupling, and we investigate the basic properties of the correlated magnetic noise based on the analytic expressions. The model reproduces the major trend of the recently measured global correlation between the GW detectors via magnetometer. The estimated values of the impact of correlated noise also match those obtained from the measurement. Finally, we give an implication to the detection of stochastic GWs including upcoming detectors, KAGRA and LIGO India. The model suggests that LIGO Hanford-Virgo and Virgo-KAGRA pairs are possibly less sensitive to the correlated noise, and can achieve a better sensitivity to the stochastic GW signal in the most pessimistic case.