Can we observe the QCD phase transition-generated gravitational waves through pulsar timing arrays?

TL;DR

This study uses numerical simulations to explore gravitational waves generated during the QCD phase transition, suggesting they could be detected by pulsar timing arrays like NANOGrav, especially considering turbulence spectra and helicity effects.

Contribution

It provides new insights into the spectral properties of QCD transition-induced gravitational waves, highlighting the impact of turbulence type and helicity on detectability.

Findings

GWs from QCD transition may be observable by pulsar timing arrays.

Shallower spectra increase low-frequency GW power, aiding detection.

Helicity significantly reduces GW energy at higher frequencies.

Abstract

We perform numerical simulations of gravitational waves (GWs) induced by hydrodynamic and hydromagnetic turbulent sources that might have been present at cosmological quantum chromodynamic (QCD) phase transitions. For turbulent energies of about 4% of the radiation energy density, the typical scale of such motions may have been a sizable fraction of the Hubble scale at that time. The resulting GWs are found to have an energy fraction of about $10^{-9}$ of the critical energy density in the nHz range today and may already have been observed by the NANOGrav collaboration. This is further made possible by our findings of shallower spectra proportional to the square root of the frequency for nonhelical hydromagnetic turbulence. This implies more power at low frequencies than for the steeper spectra previously anticipated. The behavior toward higher frequencies depends strongly on the nature of the turbulence. For vortical hydrodynamic and hydromagnetic turbulence, there is a sharp drop of spectral GW energy by up to five orders of magnitude in the presence of helicity, and somewhat less in the absence of helicity. For acoustic hydrodynamic turbulence, the sharp drop is replaced by a power law decay, albeit with a rather steep slope. Our study supports earlier findings of a quadratic scaling of the GW energy with the magnetic energy of the turbulence and inverse quadratic scaling with the peak frequency, which leads to larger GW energies under QCD conditions.