Nanohertz gravitational waves from a quasar-based supermassive black hole binary population model as dark sirens

Recently, several pulsar timing array (PTA) projects have detected evidence of the existence of a stochastic gravitational wave background (SGWB) in the nanohertz frequency band, providing confidence in detecting individual supermassive black hole binaries (SMBHBs) in the future. Nanohertz GWs emitted by inspiraling SMBHBs encode the luminosity distances of SMBHBs. They can serve as dark sirens to explore the cosmic expansion history via a statistical method to obtain the redshift information of GW sources' host galaxies using galaxy catalogs. The theoretical analysis of the dark siren method relies on the modeling of the population of SMBHBs. Using a population model consistent with the latest SGWB observations is essential, as the SGWB provides significant information about the distribution of SMBHBs. In this work, we employ a quasar-based model, which can self-consistently account for the SGWB amplitude, to estimate the population of SMBHBs. We constrain the Hubble constant using the mock GW data from different detection cases of PTAs in the future. Our results show that a PTA consisting of 100 pulsars with a white noise level of 20 ns could measure the Hubble constant with a precision close to $1\%$ over a 10-year observation period, and a PTA with 200 pulsars may achieve this goal over a 5-year observation period. The results indicate that modeling the SMBHB population significantly influences the analysis of dark sirens, and SMBHB dark sirens have the potential to be developed as a valuable cosmological probe.