Sensitivity of spin-aligned searches for neutron star-black hole systems using future detectors

Current searches for gravitational waves from compact-binary objects are primarily designed to detect the dominant gravitational-wave mode and assume that the binary components have spins which are aligned with the orbital angular momentum. These choices lead to observational biases in the observed distribution of sources. Sources with significant spin-orbit precession or unequal-mass-ratios, which have non-negligible contributions from subdominant gravitational-wave modes, may be missed; in particular, this may significantly suppress or bias the observed neutron star–black hole (NSBH) population. We simulate a fiducial population of NSBH mergers and determine the impact of using searches that only account for the dominant-mode and aligned spin. We compare the impact for the Advanced LIGO design, $\mathrm{A}+$, LIGO Voyager, and Cosmic Explorer observatories. We find that for a fiducial population where the spin distribution is isotropic in orientation and uniform in magnitude, we will miss $\sim 25\%$ of sources with mass-ratio $q>6$ and up to $\sim 60\%$ of highly precessing sources $({\chi }_p>0.5)$, after accounting for the approximate increase in background. In practice, the true observational bias can be even larger due to strict signal-consistency tests applied in searches. The observation of low spin, unequal-mass-ratio sources by Advanced LIGO design and Advanced Virgo may in part be due to these selection effects. The development of a search sensitive to high mass-ratio, precessing sources may allow the detection of new binaries whose spin properties would provide key insights into the formation and astrophysics of compact objects.

Figure 1

The angular momentum vectors for a precessing binary. The inclination angle $i$ is defined as the angle between the orbital angular momentum $\mathbf{L}$ and the line of sight to the observer $\mathbf{N}$. The angle between $\mathbf{J}$ and $\mathbf{N}$ is denoted as ${\theta }_{JN}$. Due to spin-orbit coupling, $\mathbf{L}$ and $\mathbf{S}$ will precess around the approximately fixed $\mathbf{J}$.

Figure 2

A comparison of the noise amplitude spectral density (ASD) of each detector configuration used in this study. Aligned-spin template banks are generated for each noise curve using the appropriate $f_{\mathrm{low}}$.

Figure 3

Cumulative distribution of the FFs for different classes of signals obtained using a dominant mode, aligned-spin template bank using the Advanced LIGO design noise curve. The blue curve confirms the expected number of signals recovered with high FFs above the average minimum match ($<1\%$). We find long tails of poor FFs for signals with precession or HMs. Also, note precession effects dominate the FFs.

Figure 4

Average fitting factors for a population of simulated NSBH signals distributed across the ($m_1^{\det },m_2^{\det }$) space obtained using a dominant mode, aligned-spin template bank and assuming the Advanced LIGO design sensitivity. We show the FFs for four different class of signals—nonprecessing dominant mode only(top left), nonprecessing with HMs (top right), precessing dominant mode only (bottom left) and precessing with HMs (bottom right). We observe a reduction in FFs (fractional loss in observable SNR) up to 8% for signals with HMs, and up to 20% for precessing sources. Notice the precession effects dominate the FF distribution over HMs.

Figure 5

The average FFs as a function of ($q,{\theta }_{JN}$) at $f_{\mathrm{ref}}=100\mathrm{Hz}$, for a simulated population of signals containing HMs (left) and precession with only the dominant mode (right). We observe larger losses in FFs for precessing signals than for signals with HMs. We notice a trend of decreasing FFs when the source orientation changes from face-on/off to edge-on or when the mass-ratio increases.

Figure 6

The average FFs as a function of effective precession and source orientation $({\chi }_p,{\theta }_{JN})$, for precessing signals without HMs (left) and with HMs (right). Due to the dominance of the precessing effects, there is no significant difference between the two subplots. The FFs decrease as the effective precession increases and the source becomes closer to edge-on, up to an average loss of $\sim 20–30\%$ in SNR.

Figure 7

FF distribution for precessing sources with HMs as a function of $(m_1^{\det },m_2^{\det })$ for different detector configurations. We can see that the results are not strongly dependent on the noise curve.

Figure 8

The fraction of detectable precessing sources (with HMs) at a fixed SNR threshold (SRF) $m_1^{\det }-m_2^{\det }$ for different detector configurations. We observe a similar trend as the FF distribution in Fig. 7; the SRF decreases as the mass-ratio increases and there is no significant change in sensitivity across various detector configurations. We observe a loss of up to 40% for precessing sources (13% for nonprecessing sources) with higher modes included.

Figure 9

The fraction of precessing sources with HMs detected at a fixed false alarm rate relative to an idealized HM (upper left), dominant-mode precessing (upper right), or higher-mode precessing (lower) search as a function of the detector frame component masses $(m_1^{\det },m_2^{\det })$. We approximate the increase in background for the reference ideal searches by taking the relevant thresholds from [45, 46] at a fixed FAR (as shown in Table 3). Regions with values $\ge 1$ indicate better sensitivity of a dominant mode, aligned-spin search relative to a search including additional effects, whereas, regions with modified $\mathrm{SRF}<1$ indicate lower relative sensitivity. We observe that a dominant mode, aligned spin search has better sensitivity than the naive idealized nonprecessing search that includes HMs due to the increase in background; however the HM search will have higher sensitivity to edge-on sources. In the regions with $q>6$, precessing searches will detect up to $\sim 20\%$ more signals for our fiducial signal population.

Figure 10

Relative sensitivity of an aligned-spin search with respect to an idealized precessing search with HMs as a function of $(q,{\chi }_P)$ (left) and $({\chi }_P,{\mathrm{\Theta }}_{JN})$ (right). Small mass-ratio $q\le 5$ systems which are highly precessing will be missed by a dominant mode, aligned spin searches. For high mass-ratios $q>6$, there will be a significant loss in sensitivity (up to 60%) even for moderately precessing systems.

Figure 11

Distribution of match (overlap maximized over time and phase) between the two polarizations $m(h_{+},h_{\times })$ for a simulated population of precessing signals with higher modes across the two-dimensional surface $({\chi }_P,{\theta }_{JN})$. The values correspond to the fractional loss in SNR measured using a single polarization matched filter statistic; regions with significantly lower values may require a generic statistic.