Binary Supermassive Black Holes Orbiting Dark Matter Solitons: From the Dual AGN in UGC4211 to NanoHertz Gravitational Waves

We explore the orbital implications of the Supermassive Black Hole (SMBH) binary in UGC4211, for the frequency spectrum of stochastic gravitational wave background (SGWB) being measured with pulsar timing arrays. The SMBH binary in UGC4211 has a projected separation of \(\sim 230\) pc and relative velocity of \(\sim 150\) km/s along the line of sight. It orbits a common disk of gas and stars, with a total dynamical mass of \(\sim 10^9 M_\odot\) which is several times larger than the combined SMBHs plus the observed gas and stars. This can be explained by a massive soliton of wave dark matter present within the orbit of two SMBHs. Such a scenario is encouraging as during galaxy merger, the two precursor galactic solitons are expected to combine to generate a new soliton and hence the two initial SMBHs become efficiently bound. Generalizing this scenario to the cosmological population of SMBH binaries, we show that the SGWB spectrum produced by their late-stage inspiraling is modified preferentially at low frequency by the presence of the soliton. Finally we discuss future prospects for this proof-of-concept study, by fitting this scenario to the 15-year NANOGrav data.