Signal-to-noise Ratio Analytic Formulae of the Inspiral Binary Black Holes in TianQin

Abstract

Binary black holes are one of the important sources for the TianQin gravitational wave project. Our research has revealed that, for TianQin, the signal-to-noise ratio of inspiral binary black holes can be computed analytically. This finding is expected to greatly simplify the estimation of detection capabilities for binary black holes. In this paper, we demonstrated the signal-to-noise ratio relationships from stellar-mass black holes to massive black holes. With the all-sky average condition, the signal-to-noise ratio for most binary black hole signals can be determined with a relative error of $\lesssim 10\%$, with notable deviations only for chirp masses near $1000M_{\odot }$. In contrast, the signal-to-noise ratio without the average includes an additional term, which we refer to as the response factor. Although this term is not easily calculated analytically, we provide a straightforward estimation method with an error margin of $1\sigma$ within 2\%.

16 pages, 6 figures, comments welcome

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Cited by in corpus (2)

• Archival Inference for Eccentric Stellar-Mass Binary Black Holes in Space-Based Gravitational Wave Observations
• Evaluating statistical significance for massive black hole binary mergers with space-based gravitational wave detectors