On the frequency of gravitational waves

TL;DR

The paper argues that the canonical expectation that gravitational waves inherit the source’s frequency is not universal, especially for cosmological, spatially extended but short-lived sources. Through a Gaussian-wave-packet model and a stochastic, homogeneous, isotropic short-lived source, it shows that the GW spectrum can reflect the source’s wavenumber distribution, with the peak set by the largest eddies, rather than by the largest eddy turnover frequency. This clarifies prior claims that turbulence-related GWs peak at the time-domain frequency and highlights the importance of the source’s space-time structure in interpreting stochastic GW backgrounds. The results bear on future searches for primordial GWs, stressing careful interpretation of spectral peaks in terms of spatial structure and epoch durations.

Abstract

We show that there are physically relevant situations where gravitational waves do not inherit the frequency spectrum of their source but its wavenumber spectrum.

Figures (2)

• Figure 1: The quantity $\sin^2((k-\omega_s)\Delta)/(k-\omega_s)^2$, $\Delta=(t_{\rm fin}-t_{\rm in})/2$, is shown as a function of $k-\omega_s$ for the values of $\Delta=$ 1 (black, solid) 0.3 (red dotted) and 10 (blue, dashed). For clarity the red (dotted) and black (solid) curves are displaced.
• Figure 2: The past light cone (on which gravitons propagate) of a detector at $x=0$ observing for a given time interval sweeps a portion of space in the temporally confined source (solid, red line). Therefore, the wave number of the source is registered as the frequency of the emitted GW observed at $x$. On the other hand, the detector observes the time evolution of a spatially confined source (dashed, blue line), and therefore sees its frequency.