Are stellar-mass black-hole binaries too quiet for LISA?

TL;DR

The paper evaluates the detectability of stellar-mass black-hole binaries with LISA and finds that a realistic template-bank search demands a higher SNR threshold, ρ_thr ≈ 15, than previously assumed. This steep threshold implies a strong suppression of multiband detections since event counts scale as ρ_thr^{-3}, potentially yielding zero forewarnings within a 10-year mission. However, incorporating prior information from ground-based detections via archival searches can dramatically reduce the threshold to about ρ_thr ≈ 9, producing a few detectable events. The results underscore the need for long mission durations and careful high-frequency performance, and suggest that some signals may only be recoverable through archival analyses or alternative data-analysis strategies; extending the mass range to higher BH masses could increase the multiband yield to a small number of detections.

Abstract

The progenitors of the high-mass black-hole mergers observed by LIGO and Virgo are potential LISA sources and promising candidates for multiband GW observations. In this letter, we consider the minimum signal-to-noise ratio these sources must have to be detected by LISA. Our revised threshold of $ρ_{\rm thr}\sim 15$ is higher than previous estimates, which significantly reduces the expected number of events. We also point out the importance of the detector performance at high-frequencies and the duration of the LISA mission, which both influence the event rate substantially.

Figures (3)

• Figure 1: The threshold SNR as a function of template bank size. Solid vertical lines indicate the bank sizes for stellar origin black hole (SOBH) binaries with component masses in the range $(5$ - $50)\,M_{\odot}$; these are split into those which merge in $<10\,\mathrm{yrs}$ (fast chirping) and $>10\,\mathrm{yrs}$ (slow chirping). The thresholds are $\rho_{\rm thr}\mathchar"5218\, 15$ and $\mathchar"5218\, 14$ respectively (see Table. \ref{['tab:rhothresh-vs-mass']}). For comparison, two other classes of GW are also indicated. Binary BHs in LIGO/Virgo can be detected with single-detector SNRs as low as $\mathchar"5218\,8$ using banks containing $\mathchar"5218\,4\times10^{5}$ templates (2017arXiv170501845D; this number does not include the time-of-arrival parameter; including this enlarges the effective size of the bank by a factor of $\mathchar"5218\,10^{3}$, the number of cycles in a typical template). At the other extreme, EMRIs in LISA have $\rho_{\rm thr}\gtrsim16$ and would require very large template banks 2017PhRvD..96d4005C. As discussed in the text, we do not propose to actually use such huge template banks in practical searches; these are estimates of the numbers required by a hypothetical, optimal search and provide lower bounds on the threshold for a practical, possibly suboptimal search.
• Figure 2: Number of stellar-mass BH binaries jointly detectable by the LISA space mission and ground-based interferometers as a function of the threshold SNR. Blue (red) curves assume a LISA mission duration $T_{\rm obs}=4\,$yr (10 yr). We only consider binaries merging within $T_{\rm wait}=10\,$yr. For each set of parameters, the shaded areas captures the current uncertainties in the local BH merger rate; in particular, we set $\mathcal{R}=97 \,{\rm Gpc}^{-3} {\rm yr}^{-1}$ ($32 \,{\rm Gpc}^{-3} {\rm yr}^{-1}$) for the upper (lower) line in each set. Vertical solid lines mark the SNR thresholds estimated in this letter for both forewarnings ($\rho_{\rm thr}\mathchar"5218\, 15$, c.f. Fig. \ref{['checkTwait']}) and targeted archival searches ($\rho_{\rm thr}\mathchar"5218\, 9$).
• Figure 3: Number of stellar-mass BH binaries merging within $T_{\rm wait}$ observable by LISA with $\rho \geq 15$. Blue (red) curves assume a LISA mission duration $T_{\rm obs}=4\,$yr (10 yr). For each set of parameters, the shaded areas captures the current uncertainties in the local BH merger rate; in particular, we set $\mathcal{R}=97 \,{\rm Gpc}^{-3} {\rm yr}^{-1}$ ($32 \,{\rm Gpc}^{-3} {\rm yr}^{-1}$) for the upper (lower) line in each set. The vertical line marks $T_{\rm wait}=10$yr, as used in Fig. \ref{['impactSNRthr']}.