Prominence: A discriminator of gravitational wave signals
The concept of prominence is familiar to signal engineers, topographers and mountaineers. We introduce Prominence $\cal P$ as a discriminator of gravitational wave (GW) signals. We treat black hole and neutron star binaries as astrophysical background sources, and show how $\cal P$ can be used to distinguish between GW spectra produced by first-order phase transitions, domain walls and cosmic strings, and combinations thereof. Prominence can also be used to discriminate between these and off-piste sources of GWs. The uncertainty in the measured energy density in GWs at Pulsar Timing Arrays needs to be at the sub-percent to percent level for $\cal{P}$ to achieve discrimination at 3$σ$. LISA and ET data are expected to have sufficiently small uncertainties that Prominence can play a central role in their analysis. We define and apply a $χ^2$ statistic based on an inner product in signal space to show that sources indistinguishable at $2σ$ using the signal-to-noise ratio can be distinguished using $\mathcal{P}$ with significances above and in some cases far above $3σ$.