Gravitational waves from strong first-order phase transitions

We study gravitational wave production at strong first order phase transitions, with large-scale, long-running simulations of a system with a scalar order parameter and a relativistic fluid. One transition proceeds by detonations with asymptotic wall speed $v_\text{w}=0.92$ and transition strength $α_n=0.67$, and the other by deflagrations, with a nominal asymptotic wall speed $v_\text{w}=0.44$ and transition strength $α_n=0.5$. We investigate in detail the power spectra of velocity and shear stress and - for the first time in a phase transition simulation - their time decorrelation, which is essential for the understanding of gravitational wave production. In the detonation, the decorrelation speed is larger than the sound speed over a wide range of wavenumbers in the inertial range, supporting a visual impression of a flow dominated by supersonic shocks. Vortical modes do not contribute greatly to the produced gravitational wave power spectra even in the deflagration, where they dominate over a range of wavenumbers. In both cases, we observe dissipation of kinetic energy by acoustic turbulence, and in the case of the detonation an accompanying growth in the integral scale of the flow. The gravitational wave power approaches a constant with a power law in time, from which can be derived a gravitational wave production efficiency. For both cases this is approximately $\tildeΩ^\infty_\text{gw} \simeq 0.017$, even though they have quite different kinetic energy densities. The corresponding fractional density in gravitational radiation today, normalised by the square of the mean bubble spacing in Hubble units, for flows which decay in much less than a Hubble time, is $Ω_{\text{gw},0}/(H_\text{n} R_*)^2=(4.8\pm1.1)\times 10^{-8}$ for the detonation, and $Ω_{\text{gw},0}/(H_\text{n} R_*)^2=(1.3\pm0.2)\times 10^{-8}$ for the deflagration.