Correlation analysis of stochastic gravitational wave background around 0.1-1Hz

TL;DR

This work evaluates the feasibility of directly detecting a stochastic gravitational-wave background in the 0.1–1 Hz band via cross-correlation of orthogonal TDI channels from two star-like space-based detector units, focusing on an inflationary $\Omega_{GW}(f)$. It derives the optimal SNR and Fisher-matrix expressions for parameter estimation, and applies them to proposed BBO configurations, highlighting the benefits of central-frequency optimization to mitigate parameter degeneracies. Numerical forecasts show that a BBO-grand configuration could probe $\Omega_{GW}$ down to roughly $10^{-18}$ in a decade, provided foregrounds can be sufficiently mitigated. The study also emphasizes caveats, including foreground cleaning, noise correlations between channels, and the need for careful modeling of astrophysical foregrounds to realize the projected sensitivities.

Abstract

We discuss prospects for direct measurement of stochastic gravitational wave background around 0.1-1Hz with future space missions. It is assumed to use correlation analysis technique with the optimal TDI variables for two sets of LISA-type interferometers. The signal to noise for detection of the background and the estimation errors for its basic parameters (amplitude, spectral index) are evaluated for proposed missions.

Figures (7)

• Figure 1: Three vertices $(1,2,3)$ and three arms $(L_1,L_2,L_3)$ of the first unit (solid lines). Configuration of second unit (short-dashed lines) is obtained by $180^\circ$ rotation of the first one around its center. Labels for vertices and arms of the second ones are transported with this rotation.
• Figure 2: The optimal sensitivities for BBO-lite (thin solid curve), BBO-standard (solid curve) and BBO-grand (thick solid curve) configurations. The sensitivities for (A,E) modes (long-dashed curve) and T mode (short-dashed curve) are also given for BBO-standard configuration.
• Figure 3: The normalized overlap reduction function $\gamma(f)$ for a star-like constellation. These curves have a scaling parameter $f_*=c/(2\pi L)$ that is determined by the arm-length.
• Figure 4: Dependence of the signal to noise ratio on the lower cut-off frequency $f_{cut}$.
• Figure 5: Error ellipses ($2\sigma$; 86%CL) for two dimensional parameter estimation with different lower cut-off frequencies $f_{cut}$ (dashed curve: $f_{cut}=0$, solid curve: $f_{cut}=0.2$Hz, the dotted curve: $f_{cut}=0.3$Hz). The fisher matrix approach is used. The central frequency $F$ is set at $F=1$Hz that is slightly higher than the optimal sensitivity for measuring the background with above two BBO configurations. The true values of the spectrum $\Omega_{GW}(f)$ are $\Omega_{GW,F}=10^{-16}$ and $n=0$.