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A new detection method for ultra-low frequency gravitational waves (GWs) witha frequency much lower than the observational range of pulsar timing arrays(PTAs) was suggested in Yonemaru et al. (2016). In the PTA analysis, ultra-lowfrequency GWs ($\lesssim 10^{-10}$ Hz) which evolve just linearly during theobservation time span are absorbed by the pulsar spin-down rates since bothhave the same effect on the pulse arrival time. Therefore, such GWs cannot bedetected by the conventional method of PTAs. However, the bias on the observedspin-down rates depends on relative direction of a pulsar and GW source andshows a quadrupole pattern in the sky. Thus, if we divide the pulsars accordingto the position in the sky and see the difference in the statistics of thespin-down rates, ultra-low frequency GWs from a single source can be detected.In this paper, we evaluate the potential of this method by Monte-Carlosimulations and estimate the sensitivity, considering only the "Earth term"while the "pulsar term" acts like random noise for GW frequencies$10^{-13}-10^{-10}$ Hz. We find that with 3,000 milli-second pulsars, which areexpected to be discovered by a future survey with the Square Kilometre Array,GWs with the derivative of amplitude of about $3 \times 10^{-19}~\rm{s}^{-1}$can in principle be detected. Implications for possible supermassive binaryblack holes in Sgr${}^*$ and M87 are also given.

Sensitivity of new detection method for ultra-low frequency gravitational waves with pulsar spin-down rate statistics