Polarization of gravitational waves from helical MHD turbulent sources

TL;DR

This study uses numerical simulations to analyze how helical magnetohydrodynamic turbulence in the early universe influences gravitational wave polarization, amplitude, and spectrum, with implications for detection by future space-based observatories.

Contribution

It provides the first detailed analysis of gravitational wave polarization from helical MHD turbulence, highlighting how magnetic helicity affects GW spectra and polarization, and assesses detectability prospects.

Findings

Driven magnetic fields produce more efficient GWs than initial magnetic fields.

The GW polarization degree peaks at the spectral peak and depends on magnetic helicity.

Detectability of the GW signal depends on the turbulence energy density and the observational network.

Abstract

We use direct numerical simulations of decaying primordial hydromagnetic turbulence with helicity to compute the resulting gravitational wave (GW) production and its degree of circular polarization. We find a clear dependence of the polarization of the resulting GWs on the fractional helicity of the turbulent source and we show that driven magnetic fields produce GWs more efficiently than magnetic fields that are initially present, leading to larger spectral amplitudes. The helicity does not have a huge impact on the maximum spectral amplitude in any of the two types of turbulence considered. However, the GW spectrum at wave numbers away from the peak becomes smaller for larger values of the magnetic fractional helicity. The degree of circular polarization approaches zero at frequencies below the peak, and reaches its maximum at the peak. At higher frequencies, it stays finite if the magnetic field is initially present, and it approaches zero if it is driven. We predict that the spectral peak of the GW signal can be detected by LISA if the turbulent energy density is at least $\sim 3\%$ of the radiation energy density, and the characteristic scale is a hundredth of the horizon at the electroweak scale. We show that the resulting GW polarization is unlikely to be detectable by the anisotropies induced by our proper motion in the dipole response function of LISA. Such signals can, however, be detectable by cross-correlating data from the LISA-Taiji network for turbulent energy densities of $\sim 5\%$, and fractional helicity of 0.5 to 1. Second-generation space-based GW detectors, such as BBO and DECIGO, would allow for the detection of a larger range of the GW spectrum and smaller amplitudes of the magnetic field.