# The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition

## TL;DR

This paper analytically models the gravitational wave spectrum from turbulence and magnetic fields generated during a first-order phase transition, accounting for prolonged source activity and initial stirring effects, leading to more realistic predictions.

## Contribution

It introduces a comprehensive analytical framework that includes the sustained source activity and initial stirring phase, refining previous models of gravitational wave production from phase transitions.

## Key findings

- The gravitational wave spectrum's peak frequency remains similar to previous models.
- The amplitude of the gravitational wave signal is reduced with a more realistic turbulence spectrum.
- The predicted signal could be detected by LISA for a strong electroweak phase transition.

## Abstract

We analytically derive the spectrum of gravitational waves due to magneto-hydrodynamical turbulence generated by bubble collisions in a first-order phase transition. In contrast to previous studies, we take into account the fact that turbulence and magnetic fields act as sources of gravitational waves for many Hubble times after the phase transition is completed. This modifies the gravitational wave spectrum at large scales. We also model the initial stirring phase preceding the Kolmogorov cascade, while earlier works assume that the Kolmogorov spectrum sets in instantaneously. The continuity in time of the source is relevant for a correct determination of the peak position of the gravitational wave spectrum. We discuss how the results depend on assumptions about the unequal-time correlation of the source and motivate a realistic choice for it. Our treatment gives a similar peak frequency as previous analyses but the amplitude of the signal is reduced due to the use of a more realistic power spectrum for the magneto-hydrodynamical turbulence. For a strongly first-order electroweak phase transition, the signal is observable with the space interferometer LISA.