Supermassive Binary Black Hole Evolution can be traced by a small SKA Pulsar Timing Array

Supermassive black holes are commonly found in the center of galaxies and evolve with their hosts. The supermassive binary black holes (SMBBH) are thus expected to exist in close galaxy pairs, however, none has been unequivocally detected. The square kilometre array (SKA) is a multi-purpose radio telescope with a collecting area approaching 1 million square metres, with great potential for detecting nanohertz gravitational waves (GWs). In this paper, we quantify the GW detectability by SKA for a realistic SMBBH population using pulsar timing array (PTA) technique and quantify its impact on revealing SMBBH evolution with redshift for the first time. With only $\sim20$ pulsars, much smaller a requirement than in previous work, the SKA PTA is expected to obtain detection within about 5 years of operation and to achieve a detection rate of more than 100 SMBBHs/yr after about 10 years. Although beyond the scope of this paper, we must acknowledge that the presence of persistent red noise will reduce the number of expected detections here. It is thus imperative to understand and mitigate red noise in the PTA data. The GW signatures from a few well-known SMBBH candidates, such as OJ 287, 3C 66B, NGC 5548 and Ark 120, will be detected given the currently best-known parameters of each system. Within 30 years of operation, about 60 individual SMBBHs detection with $z<0.05$ and more than $10^4$ with $z<1$ are expected. The detection rate drops precipitately beyond $z=1$. The substantial number of expected detections and their discernible evolution with redshift by SKA PTA will make SKA a significant tool for studying SMBBHs.