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

TL;DR

This paper derives analytical formulas for the signal-to-noise ratio of inspiral binary black holes in TianQin, simplifying detection capability estimations across a range of black hole masses with high accuracy.

Contribution

It introduces an analytical approach to compute the SNR for binary black holes in TianQin, including an estimation method for the response factor with minimal error.

Findings

Analytical SNR formulas applicable from stellar-mass to massive black holes.

High accuracy (within 10%) for most binary black hole signals using all-sky average.

Response factor estimation method with 1σ error within 2%.

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 $\lesssim10\%$, with notable deviations only for chirp masses near $1000~M_\odot$. 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\%.