Detection for Intermediate-mass Binary Black Holes in Population III Star Clusters with TianQin

Context. Population III star clusters are predicted to form in unenriched dark matter halos. Direct N-body simulation of Pop III clusters implies the possible formation and merger of intermediate-mass binary black holes (IMBBHs). The gravitational wave signals could be detected by space-borne gravitational wave detectors like TianQin. Aims. This study evaluates the potential of TianQin in detecting IMBBHs from Pop III star clusters, focusing on key factors such as the detection horizon, detection number, and Fisher uncertainty. Methods. A Monte Carlo simulation is employed to derive IMBBH sources, utilizing the IMRPhenomD waveform model to simulate catalogs of observable IMBBH mergers. The mass and redshift distributions are derived from direct N-body simulations of IMBBHs in Population III star clusters. Detection numbers are determined by calculating the signal-to-noise ratios (SNR) of the simulated signals and applying thresholds for detection. Fisher uncertainty is obtained through Fisher information matrix analysis. Results. The findings suggest that TianQin could achieve detection numbers within 5 years ranging from 1 in the most pessimistic scenario to 253 in the most optimistic scenario. Furthermore, TianQin can precisely constrain the IMBBH mass with a relative uncertainty of $10^{-6}$, coalescence time $t_c$ within 1 second, and sky location $\bar{\Omega}_S$ within 1 $\rm{deg}^2$. However, the luminosity distance $D_L$ and inclination angle $\iota$ exhibit substantial degeneracies, limiting their precise estimation.