Gravitational waves from supermassive black hole binaries in ultraluminous infrared galaxies

Gravitational waves (GWs) in the nano-hertz band are great tools for understanding the cosmological evolution of supermassive black holes (SMBHs) in galactic nuclei. We consider SMBH binaries in high-z ultra-luminous infrared galaxies (ULIRGs) as sources of a stochastic GW background (GWB). ULIRGs are likely associated with gas-rich galaxy mergers containing SMBHs that possibly occur at most once in the life of galaxies, unlike multiple dry mergers at low redshift. Adopting a well-established sample of ULIRGs, we study the properties of the GWB due to coalescing binary SMBHs in these galaxies. Since the ULIRG population peaks at z>1.5, the amplitude of the GWB is not affected even if BH mergers are delayed by as long as ∼ 10 Gyrs. Despite the rarity of the high-z ULIRGs, we find a tension with the upper limits from Pulsar Timing Array (PTA) experiments. This result suggests that if a fraction fm,gal of ULIRGs are associated with SMBH binaries, then no more than 20fm,gal(λEdd/0.3)5/3(tlife/30 Myr) % of the binary SMBHs in ULIRGs can merge within a Hubble time, for plausible values of the Eddington ratio of ULIRGs (λEdd) and their lifetime (tlife).