Signal-to-noise ratio analytic formulae of the inspiral binary black holes in TianQin

Binary black holes (BBHs) are one of the important sources for the TianQin gravitational wave (GW) project. Our research has revealed that, for TianQin, the signal-to-noise ratio of inspiral BBHs can be computed analytically. This finding will help to quickly estimate the detectability of GWs from different types of BBHs. In addition, it provides us with the accumulation pattern of signal-to-noise ratios for BBH signals, which can be used for the identification of future signals and the construction of detection statistics. In this paper, we demonstrated the signal-to-noise ratio analytic formulae from stellar-mass black holes to massive black holes. With the all-sky average condition, the signal-to-noise ratio for most BBH signals can be determined with a relative error of , with notable deviations only for chirp masses near . Moreover, the signal-to-noise ratio without the average includes only an additional coefficient, which we refer to as the response factor. Although this term is not easily calculated analytically, we provide a straightforward calculation method with an error margin of 1σ within 2%.