Optimizing signal recycling for detecting a stochastic gravitational-wave background

Signal recycling is applied in laser interferometers such as the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) to increase their sensitivity to gravitational waves. In this study, signal recycling configurations for detecting a stochastic gravitational wave background are optimized based on aLIGO parameters. Optimal transmission of the signal recycling mirror (SRM) and detuning phase of the signal recycling cavity (SRC) under a fixed laser power and low-frequency cutoff are calculated. Based on the optimal configurations, the compatibility with a binary neutron star (BNS) search is discussed. Then, different laser powers and low-frequency cutoffs are considered. Two models for the dimensionless energy density of gravitational waves $\Omega_{gw}(f) = \Omega_{\alpha} (f/f_{ref})^{\alpha}$, the flat model $\alpha = 0$ and the $\alpha = 2/3$ model, are studied. For a stochastic background search, it is found that an interferometer using signal recycling has a better sensitivity than an interferometer not using it. The optimal stochastic search configurations are typically found when both the SRM transmission and the SRC detuning phase are low. In this region, the BNS range mostly lies between 160 and 180 Mpc. When a lower laser power is used (reducing radiation pressure at low frequencies), the optimal SRC detuning phase increases, the optimal SRM transmission increases and the optimal sensitivity improves. A reduced low-frequency cutoff gives a better sensitivity limit. For both models of $\Omega_{gw}$, a typical optimal sensitivity limit on the order of $10^{-10}$ is achieved at a reference frequency of $f_{ref} = 25$ Hz.