Strongly Lensed Supermassive Black Hole Binaries as Nanohertz Gravitational-Wave Sources

Supermassive black hole binary systems (SMBHBs) should be the most powerful sources of gravitational waves (GWs) in the Universe. Once Pulsar Timing Arrays (PTAs) detect the stochastic GW background from their cosmic merger history, searching for individually resolvable binaries will take on new importance. Since these individual SMBHBs are expected to be rare, here we explore how strong gravitational lensing can act as a tool for increasing their detection prospects by magnifying fainter sources and bringing them into view. Unlike for electromagnetic waves, when the geometric optics limit is nearly always valid, for GWs the wave-diffraction-interference effects can become important when the wavelength of the GWs is larger than the Schwarzchild radius of the lens, i.e. $M_{\rm lens} \sim 10^8\,(\frac{f}{mHz})^{-1}\,M_\odot$. For the GW frequency range explored in this work, the geometric optics limit holds. We investigate GW signals from SMBHBs that might be detectable with current and future PTAs under the assumption that quasars serve as bright beacons that signal a recent merger. Using the black hole mass function derived from quasars and a physically motivated magnification distribution, we expect to detect a few strongly lensed binary systems out to $z \approx 2$. Additionally, for a range of fixed magnifications $2 \leq \mu \leq 100$, strong lensing adds up to $\sim$30 more detectable binaries for PTAs. Finally, we investigate the possibility of observing both time-delayed electromagnetic signals and GW signals from these strongly lensed binary systems -- that will provide us with unprecedented multimessenger insights into their orbital evolution.