Testing general relativity with binary black holes: a study on the sensitivity requirements for future space-based detectors

Abstract

We study the sensitivity required for a future space-based detector to search for beyond general relativity effect in gravitational wave detection. To do this, we use the current design of TianQin, LISA, and $μ$Ares as starting points, and study how their key noise parameters should be improved to adequately detect some target signals, for which we choose a nonlinear ringdown mode, displacement memory, and a putative beyond general relativity signal, all from the merger of massive black hole binaries. We find that the required improvements are strongly dependent on the choice of the target signals and the population model of massive black hole binaries, and $4-9$ orders of magnitude improvement will be needed in the most demanding detection scenarios.

Figures (6)

• Figure 1: An illustration of the FBH model for a Schwarzschild black hole.
• Figure 2: The allowed values of $(S_a^{1/2}, S_x^{1/2})$ for a detection problem. In the plot, the target signal is the $(2,2,0) \times (2,2,0)$ ringdown mode, the reference detector is TianQin, and the injected source parameters are: $m_1 = 3\times 10^4 \mathrm{M_\odot}$, $m_2 = 2\times 10^4 \mathrm{M_\odot}$, $z=1$, $\iota = \pi/4$, and $\phi = 0$. See main text for more explanation.
• Figure 3: Signal of the $(2,2,0) \times (2,2,0)$ ringdown mode for all sources in the Q3nd super-sample. The sensitivity curves of the three reference detectors are also shown as a comparison.
• Figure 4: Distribution of optimal values of $(S_a^{1/2}, S_x^{1/2})$ for TianQin. The last row compares the major distribution regions and their centers for different population models. See main text for more explanation.
• Figure 5: Distribution of optimal values of $(S_a^{1/2}, S_x^{1/2})$ for LISA. The last row compares the major distribution regions and their centers for different population models. See main text for more explanation.