Detecting a gravitational-wave background with next-generation space interferometers

TL;DR

This work develops a generalized optimal‑filter framework for detecting stochastic gravitational‑wave backgrounds with next‑generation space interferometers and quantifies sensitivity to both isotropic and anisotropic GWBs in the 0.1–10 Hz band. By deriving cross‑correlation SNR expressions and filters for isotropic skies and extending to anisotropic components via spherical‑harmonic motifs, the authors assess mission designs (BBO/DECIGO/FP‑DECIGO/Ultimate DECIGO) and demonstrate substantial gains from cross‑correlation over self‑correlation. They show that astrophysical foregrounds, especially at low frequencies, can limit detectability but that foreground subtraction and favorable designs can reach $h^2\Omega_{\rm gw}$ levels near $10^{-16}$–$10^{-15}$, potentially approaching inflationary GWBs. Anisotropy measurements, including dipole signals from the Solar System's motion, are much more challenging and generally require larger isotropic backgrounds. Overall, the paper provides a rigorous, practical framework and quantitative projections to guide pre‑conceptual designs of space interferometers for stochastic GWB science.

Abstract

Future missions of gravitational-wave astronomy will be operated by space-based interferometers, covering very wide range of frequency. Search for stochastic gravitational-wave backgrounds (GWBs) is one of the main targets for such missions, and we here discuss the prospects for direct measurement of isotropic and anisotropic components of (primordial) GWBs around the frequency 0.1-10 Hz. After extending the theoretical basis for correlation analysis, we evaluate the sensitivity and the signal-to-noise ratio for the proposed future space interferometer missions, like Big-Bang Observer (BBO), Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO) and recently proposed Fabry-Perot type DECIGO. The astrophysical foregrounds which are expected at low frequency may be a big obstacle and significantly reduce the signal-to-noise ratio of GWBs. As a result, minimum detectable amplitude may reach h^2 \ogw = 10^{-15} \sim 10^{-16}, as long as foreground point sources are properly subtracted. Based on correlation analysis, we also discuss measurement of anisotropies of GWBs. As an example, the sensitivity level required for detecting the dipole moment of GWB induced by the proper motion of our local system is closely examined.

Figures (6)

• Figure 1: A typical orbital configuration for a future space interferometer. One of the three interferometers on the ecliptic orbit consists of six spacecrafts, and the six probes form a hexagonal space-interferometer.
• Figure 2: Spectral amplitude sensitivity $h_{\mathrm{eff}}$ for several space-based interferometers Larson:1999we. Solid curves show the sensitivity for self-correlation analysis for LISA, TDI-DECIGO/BBO, FP-DECIGO and ultimate DECIGO (Table \ref{['table: instrument parameter']}). So-called $X$-variable Armstrong:1999 of TDIs is used for the self-correlation analysis, and the transfer function of FP-DECIGO can be found in, e.g., Schilling:1997id. The dashed curves show the sensitivity for cross-correlation analysis, assuming the hexagonal spacecraft configuration. Oscillation of the sensitivity curves at high frequency band comes from overlap reduction function. Dotted lines show $h^2 {\Omega_{\mathrm{gw}}} = 10^{-10}, 10^{-12}, \cdots, 10^{-18}$. In these plots, we have taken $\overline{\mathrm{SNR}}=5$, $\Delta f=f/10$, and $T_{\rm obs}=1$ year.
• Figure 3: Dependence of low-frequency cutoff $f_{\rm cut}$ on the minimum detectable value $\Omega_{\rm gw}$ in the case of flat spectra, $\Omega_{\rm gw}\propto f^0$. The resultant values $\Omega_{\rm gw}^{\rm cutoff}$ are plotted by normalizing them to $\Omega_{\rm gw}$ without cutoff. Observational band (available frequency band) is the same as shown in Fig. \ref{['fig:h_eff for omega_GW']}.
• Figure 4: Left: optimal filter functions for isotropic GWB with various amplitudes ${\Omega_{\mathrm{gw}}}$ in the case of TDI-DECIGO. In plotting the functions, all the filters are normalized to have maximum magnitude equal to unity. Right: signal-to-noise ratio (SNR) as function of $h^2 {\Omega_{\mathrm{gw}}}$ with and without the low-frequency cutoff. Dashed curves shows the SNR with the cutoff frequency $f_{\mathrm{cut}}=0.2$ Hz. Respective dotted thin lines depict the SNR based on the weak-signal approximation (\ref{['eq:SNR_weak']}).
• Figure 5: Effective strain amplitude $h_{\mathrm{eff}}$ for TDI-DECIGO/BBO ( left) and FP-DECIGO ( right). In plotting the sensitivity curves for TDI-DECIGO/BBO, we specifically consider the cross-correlation between the TDI $X$-variables extracted from the nearest spacecrafts in the star-like configuration. In both cases, the interferometers are most sensitive to lower even multipoles of $\ell=0,2,4$. Because of the hexagonal form, the detectors are also sensitive to lower odd multipoles $\ell=1, 3, 5$. The sensitivity to higher multipoles $\ell \ge 6$ is very poor and this fact is especially evident in the low frequency band.