Gravity Echoes from Supermassive Black Hole Binaries

Abstract

Pulsar timing arrays record gravitational waves from supermassive black hole binaries at two spacetime points: an Earth term, measured when the wave passes the Earth, and a pulsar term, measured when the wave passed each pulsar at an earlier epoch. We show that a future $\mu$Hz-band detection of a nearby massive binary by a mission such as $\mu$Ares would turn PTA pulsar terms into targeted probes of binary evolution. In analogy with supernova light echoes, each pulsar term acts as a gravity echo: a dated snapshot of the binary at an earlier stage of its inspiral. Together, the $\mu$Hz Earth-term measurement and the nHz pulsar-term echoes provide a temporal baseline that neither detector could access alone. For a fiducial equal-mass binary with total mass $10^9\,M_\odot$ at 80~Mpc, we find a combined pulsar timing array echo signal-to-noise ratio of 33, with up to 24 pulsars individually resolving the signal among pulsars with 50-year baselines. The angular dependence of the single-pulsar echo sensitivity alone enables independent sky localization of the source to $\sim$10--100~deg$^2$, and the resolved pulsar-term frequencies directly measure the binary inspiral rate hundreds to thousands of years ago. With sufficient pulsar distance precision, a small set of anchor pulsars could additionally phase-connect the array and trace the post-Newtonian evolution coherently over kpc baselines. The source population required for gravity echoes is drawn from the same massive-end census responsible for the observed nanoHertz stochastic background.