A higher probability of detecting lensed supermassive black hole binaries by LISA

Gravitational lensing of gravitational waves (GWs) is a powerful probe of the matter distribution in the universe. Here we revisit the wave-optics effects induced by dark matter (DM) haloes on the GW signals of merging massive black hole binaries (MBHBs), and we study the possibility of discerning these effects using the Laser Interferometer Space Antenna (LISA). In particular, we include the haloes in the low-mass range of 10(5)-10(8) M-circle dot since they are the most numerous according to the cold DM model. We simulate the lensed signals corresponding to a wide range of impact parameters, and we find distinguishable deviation from the standard best-fitting GW templates even when the impact parameter is as large y similar or equal to 50. Consequently, we estimate that over (0.1-1.6) per cent of the MBHBs in the mass range of 10(5)(.0)-10(6.5) M-circle dot and the redshift range of 4 - 10 should show detectable wave-optics effects. This probability is one order of magnitude higher than that derived in previous works. The uncertainty comes mainly from the mass function of the DM haloes. Not detecting any signal during the LISA mission would imply that DM haloes with 10(5)-10(8) M-circle dot are less numerous than what the cold DM model predicts.

Automated summary

Gravitational lensing of gravitational waves is a powerful tool to study the matter distribution in the universe. This study revisits the wave-optics effects induced by dark matter haloes on the gravitational wave signals of merging massive black hole binaries, and investigates the possibility of detecting these effects using the Laser Interferometer Space Antenna (LISA). The results show that the effects of dark matter haloes on the gravitational wave signals can be distinguished even for large impact parameters, suggesting a higher probability of detecting wave-optics effects than previous studies.