Joint observations of space-based gravitational-wave detectors: Source localization and implications for parity-violating gravity

Space-based gravitational-wave (GW) detectors, including LISA, Taiji and TianQin, are able to detect mHz GW signals produced by mergers of supermassive black hole binaries, which opens a new window for GW astronomy. In this article, we numerically estimate the potential capabilities of the future networks of multiple space-based detectors using Bayesian analysis. We modify the public package bilby and employ the sampler pymultinest to analyze the simulated data of the space-based detector networks, and investigate their abilities for source localization and testing the parity symmetry of gravity. In comparison with the case of an individual detector, we find detector networks can significantly improve the source localization. While for constraining the parity symmetry of gravity, we find that detector networks and an individual detector follow the similar constraints on the parity-violating energy scale $M_{\mathrm{PV}}$. Similar analysis can be applied to other potential observations of various space-based GW detectors.

Figure 1

Noise power spectra of three space-based GW detectors. Blue, green, and red lines represent LISA, Taiji and TianQin, respectively. Taiji and LISA have smaller noise in the low frequency band, while TianQin is more sensitive to the relatively higher frequencies.

Figure 2

Configuration of space-based GW detectors. The upper panel is the LISA-Taiji network configuration [7], in which LISA and Taiji take heliocentric orbits and are separated by an angle of 40°. The lower panel is TianQin’s orbit configuration in the heliocentric-ecliptic coordinate system [2]. The ecliptic plane is spanned by $x$ and $y$ axes. The $x$ axis points toward the direction of the vernal equinox. $\beta$ is the longitude of the perihelion. The normal of TianQin’s detector plane points to the reference source RX $\mathrm{J}0806.3+1527$ whose coordinates in the ecliptic frame is $({\theta }_s,{\varphi }_s)$.

Figure 3

$|h_{+}(f)|$ of GWs from different sources. Blue, orange and green lines are generated from SMBHBs with component masses of $5\times {10}^5$, $5\times {10}^6$, and $5\times {10}^7{M}_{\odot }$, respectively. Here, we use the waveform template imrphenomxhm.

Figure 4

Posterior distributions generated with a single LISA observation. The yellow solid lines are injected values, and the blue dashed lines are 5% and 95% percentiles.

Figure 5

Posterior distributions generated with LISA and Taiji joint observation. The yellow lines are injected values, and blue dashed lines are 5% and 95% percentiles.

Figure 6

The 90% credible contours of posterior distribution of $({\theta }_e,{\varphi }_e)$ for GW sources in three directions. Results of different detector networks are plotted in a different color. For each panel, the true location is indicated by a red star. 90% credible areas for the case with ${\theta }_e=30°$ are 0.54, 0.034, and $0.20{\mathrm{deg}}^2$ for LISA, $\mathrm{LISA}+\mathrm{Taiji}$ network, and $\mathrm{LISA}+\mathrm{TianQin}$ network, respectively. For the case with ${\theta }_e=60°$, they are 160.3, 0.035 and $0.22{\mathrm{deg}}^2$, respectively. For the case with ${\theta }_e=90°$, they are 0.11, 0.019 and $0.079{\mathrm{deg}}^2$, respectively.

Figure 7

The upper panels show the violin plots for effective PV parameters $A$ and $B$ and the lower panels show the distribution of $M_{\mathrm{PV}}$ derived from different cases. Note that 90% percentiles are plotted in dashed lines. For velocity birefringence, 90% percentiles correspond to 3.20, 4.53, and 3.24 eV for LISA, $\mathrm{LISA}+\mathrm{Taiji}$ network, $\mathrm{LISA}+\mathrm{TianQin}$ network, respectively. While for amplitude birefringence, 90% percentiles are $1.85\times {10}^{-15}$, $1.70\times {10}^{-15}$, and $1.82\times {10}^{-15}\mathrm{eV}$, respectively.