Diffractive lensing of nano-Hertz gravitational waves emitted from supermassive binary black holes by intervening galaxies

Pulsar timing array (PTA) experiments are expected to detect nano-Hertz gravitational waves (GWs) emitted from individual inspiralling supermassive binary black holes (SMBBHs). The GW signals from a small fraction of these SMBBHs may be diffractively lensed by intervening galaxies. In this paper, we investigate the diffractive lensing effects on the continuous GW signals from the lensed SMBBHs and estimate the detectable number of such signals by PTAs, such as the Chinese PTA (CPTA) and the Square Kilometer Array (SKA) PTA. We find that the amplitude of the lensed GW signals may be only amplified by a factor of $\sim 1.01-1.14$ ($16\%-84\%$ range) and the phase of the signals may shift somewhat due to the lensing, significantly different from those strongly lensed high frequency GW signals from compact binary mergers in the geometric optics. We estimate that $\sim 0.01\%$ of all detected nano-Hertz GW signals from individual SMBBHs by future PTA experiments are lensed by foreground galaxies (i.e., up to $\sim 106$ for CPTA and up to $\sim 289$ for SKA-PTA). However, the lensed nano-Hertz GW signals are difficult to be distinguished from those without lensing by the PTA observations only. We further discuss the possibility about the identification of the lensed nano-Hertz GW signals from SMBBHs via the electromagnetic detection of their host galaxies or active galactic nuclei.