BBO and the Neutron-Star-Binary Subtraction Problem

TL;DR

The paper tackles whether the Big Bang Observer can subtract the neutron-star binary foreground to reveal an inflationary GW background in the 0.1–1 Hz band. It develops a self-consistent subtraction framework that determines the resolvable boundary in redshift and angles, then propagates confusion noise from unresolved sources into the total noise and iterates to a fixed point for the unsubtracted fraction F. It quantifies how waveform errors, eccentricity, spins, and high-order PN terms affect subtraction, and analyzes the SNR and computing-power constraints on detecting NS binaries. The results indicate that the baseline BBO sensitivity should permit effective subtraction under realistic merger rates, while significant degradation would demand more sophisticated pipelines and perhaps even alternative waveform families; the framework provides a practical path to assess mission viability and guide future data-analysis development.

Abstract

The Big Bang Observer (BBO) is a proposed space-based gravitational-wave (GW) mission designed primarily to search for an inflation-generated GW background in the frequency range 0.1-1 Hz. The major astrophysical foreground in this range is gravitational radiation from inspiraling compact binaries. This foreground is expected to be much larger than the inflation-generated background, so to accomplish its main goal, BBO must be sensitive enough to identify and subtract out practically all such binaries in the observable universe. It is somewhat subtle to decide whether BBO's current baseline design is sufficiently sensitive for this task, since, at least initially, the dominant noise source impeding identification of any one binary is confusion noise from all the others. Here we present a self-consistent scheme for deciding whether BBO's baseline design is indeed adequate for subtracting out the binary foreground. We conclude that the current baseline should be sufficient. However if BBO's instrumental sensitivity were degraded by a factor 2-4, it could no longer perform its main mission. It is impossible to perfectly subtract out each of the binary inspiral waveforms, so an important question is how to deal with the "residual" errors in the post-subtraction data stream. We sketch a strategy of "projecting out" these residual errors, at the cost of some effective bandwidth. We also provide estimates of the sizes of various post-Newtonian effects in the inspiral waveforms that must be accounted for in the BBO analysis.

Figures (8)

• Figure 1: The Big-Bang Observer (BBO) consists of four LISA-like triangular constellations orbiting the Sun at $1\,$AU. The GW background is measured by cross-correlating the outputs of the two overlapping constellations.
• Figure 2: Shows the amplitude of the instrumental noise, $\sqrt{f S_{\rm h}^{\rm inst}(f)}$, compared to the amplitude of the (pre-subtraction) NS binary foreground (plotted for $\dot n_0 = 10^{-7}\,{\rm Mpc}^{-3}{\rm yr}^{-1}$) and the sought-for cosmic GW background (plotted for $\Omega_{\rm GW}(f) = 10^{-15}$). Clearly, to reveal a cosmic GW background at this level, the NS foreground must be subtracted off, with fractional residual of $\lesssim 10^{-2.5}$.
• Figure 3: The total number of NS-NS mergers closer than redshift $z$, The results here are normalized to a 3-yr observation period and $\dot n_0= 10^{-7} {\rm Mpc}^{-3}{\rm yr}^{-1}$.
• Figure 4: Figure plots $S_{\rm h}^{\rm NSm, >z}/S_{\rm h}^{\rm NSm}$ vs. $z$, i.e., it plots the fractional contribution of NS-NS binaries beyond redshift $z$ to the total NS-NS foreground noise.
• Figure 5: Shows the function $F(F_{\rm G})-F_{\rm G}$ for three merger rates: $\dot{n}_0=\{10^{-8},\,10^{-7},\,10^{-6}\}\,{\rm yr}^{-1}{\rm Mpc}^{-3}$. All curves are for "standard/2" sensitivity and detection threshold $\rho_{\rm th}=30$.