The concept of prominence is familiar to signal engineers, topographers and mountaineers. We introduce Prominence $\mathcal{P}$ as a discriminator of gravitational wave (GW) signals. We treat black hole and neutron star binaries as astrophysical background sources, and show how $\mathcal{P}$ 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 subpercent to percent level for $\mathcal{P}$ to achieve discrimination at $3\sigma$. 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 ${\chi }^2$ statistic based on an inner product in signal space to show that sources indistinguishable at $2\sigma$ using the signal-to-noise ratio can be distinguished using $\mathcal{P}$ with significances above and in some cases far above $3\sigma$.

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• Cosmic strings & domain walls
• Gravitational waves
• Phase transitions
• Phenomenology