Black Hole-neutron Star Binaries Research Articles

Black hole-neutron star mergers in Einstein-scalar-Gauss-Bonnet gravity

Gravitational wave observations of black hole-neutron star binaries, particularly those where the black hole has a lower mass compared to other observed systems, have the potential to place strong constraints on modifications to general relativity that arise at small curvature length scales. Here we study the dynamics of black hole-neutron star mergers in shift-symmetric Einstein-scalar-Gauss-Bonnet gravity, a representative example of such a theory, by numerically evolving the full equations of motion. We consider quasi-circular binaries with different mass-ratios that are consistent with recent gravitational wave observations, including cases with and without tidal disruption of the star, and quantify the impact of varying the coupling controlling deviations from general relativity on the gravitational wave signal and scalar radiation. We find that the main effect on the late inspiral is the accelerated frequency evolution compared to general relativity, and that—even considering Gauss-Bonnet coupling values approaching those where the theory breaks down—the impact on the merger gravitational wave signal is mild, predominately manifesting as a small change in the amplitude of the ringdown. We compare our results to current post-Newtonian calculations and find consistency throughout the inspiral. Published by the American Physical Society 2024

Signatures of low-mass black hole–neutron star mergers

ABSTRACT The recent observation of the GW230529 event indicates that black hole–neutron star binaries can contain low-mass black holes. Since lower mass systems are more favourable for tidal disruption, such events are promising candidates for multimessenger observations. In this study, we employ five finite-temperature, composition-dependent matter equations of state and present results from ten 3D general relativistic hydrodynamic simulations for the mass ratios $q = 2.6$ and 5. Two of these simulations target the chirp mass and effective spin parameter of the GW230529 event, while the remaining eight contain slightly higher mass black holes, including both spinning ($a_{\mathrm{ BH}} = 0.7$) and non-spinning ($a_{\mathrm{ BH}} = 0$) models. We discuss the impact of the equation of state, spin, and mass ratio on black hole–neutron star mergers by examining both gravitational-wave and ejected matter properties. For the low-mass ratio model we do not see fast-moving ejecta for the softest equation of state model, but the stiffer model produces on the order of $10^{-6}\,\mathrm{ M}_\odot$ of fast-moving ejecta, expected to contribute to an electromagnetic counterpart. Notably, the high-mass ratio model produces nearly the same amount of total dynamical ejecta, but yields 52 times more fast-moving ejecta than the low-mass ratio system. In addition, we observe that the black-hole spin tends to decrease the amount of fast-moving ejecta while increasing significantly the total ejected mass. Finally, we note that the disc mass tends to increase as the neutron star compactness decreases.

Black hole-neutron star mergers with massive neutron stars in numerical relativity

We study the merger of black hole-neutron star (BH-NS) binaries in numerical relativity, focusing on the properties of the remnant disk and the ejecta, varying the mass of compactness of the NS and the mass and spin of the BH. We find that within the precision of our numerical simulations, the remnant disk mass and ejecta mass normalized by the NS baryon mass (M^rem and M^eje, respectively), and the cutoff frequency fcut normalized by the initial total gravitational mass of the system at infinite separation approximately agree among the models with the same NS compactness CNS=MNS/RNS, mass ratio Q=MBH/MNS, and dimensionless BH spin χBH irrespective of the NS mass MNS in the range of 1.092−1.691M⊙. This result shows that the merger outcome depends sensitively on Q, χBH, and CNS but only weakly on MNS. This justifies the approach of studying the dependence of NS tidal disruptions on the NS compactness by fixing the NS mass but changing the EOS. We further perform simulations with massive NSs of MNS=1.8M⊙, and compare our results of M^rem and M^eje with those given by existing fitting formulas to test their robustness for more compact NSs. We find that the fitting formulas obtained in the previous studies are accurate within the numerical errors assumed, while our results also suggest that further improvement is possible by systematically performing more precise numerical simulations. Published by the American Physical Society 2024

Relativistic Roche problem for stars in precessing orbits around a spinning black hole

Tidal disruptions of stars on the equatorial plane orbiting Kerr black holes have been widely studied. However, thus far, there have been fewer studies of stars in inclined precessing orbits around a Kerr black hole. In this paper, we use the tensor virial equations to show the presence of possible resonances in these systems for typical physical parameters of black hole–neutron star binaries in close orbits or of a white dwarf/an ordinary star orbiting a supermassive black hole. This suggests the presence of a new instability before the tidal disruption limit is encountered in such systems. Published by the American Physical Society 2024

Multi-messenger prospects for black hole – neutron star mergers in the O4 and O5 runs

The existence of merging black hole-neutron star (BHNS) binaries has been ascertained through the observation of their gravitational wave (GW) signals. However, to date, no definitive electromagnetic (EM) emission has been confidently associated with these mergers. Such an association could help unravel crucial information on these systems, for example, their BH spin distribution, the equation of state (EoS) of the neutron star and the rate of heavy element production. We modeled the multi-messenger (MM) emission from BHNS mergers detectable during the fourth (O4) and fifth (O5) observing runs of the LIGO-Virgo-KAGRA (LVK) GW detector network in order to provide detailed predictions that can help enhance the effectiveness of observational efforts and extract the highest possible scientific information from such remarkable events. Our methodology is based on a population synthesis approach, which includes the modeling of the signal-to-noise ratio of the GW signal in the detectors, the GW-inferred sky localization of the source, the kilonova (KN) optical and near-infrared light curves, the relativistic jet gamma-ray burst (GRB) prompt emission peak photon flux, and the GRB afterglow light curves in the radio, optical, and X-ray bands. The resulting prospects for BHNS MM detections during O4 are not promising, with an LVK GW detection rate of 15.0−8.8+15.4 yr−1, but joint MM rates of ∼10−1 yr−1 for the KN and ∼10−2 yr−1 for the jet-related emission. In O5, we found an overall increase in expected detection rates by around an order of magnitude, owing to both the enhanced sensitivity of the GW detector network and the coming online of future EM facilities. Considering variations in the NS EoS and BH spin distribution, we find that the detection rates can increase further by up to a factor of several tens. Finally, we discuss direct searches for the GRB radio afterglow with large field-of-view instruments during O5 and beyond as a new possible follow-up strategy in the context of ever-dimming prospects for KN detection due to the recession of the GW horizon.

A Channel to Form Fast-spinning Black Hole–Neutron Star Binary Mergers as Multimessenger Sources. II. Accretion-induced Spin-up

In this work, we investigate an alternative channel for the formation of fast-spinning black hole–neutron star (BHNS) binaries, in which super-Eddington accretion is expected to occur in accreting BHs during the stable mass transfer phase within BH-stripped helium (BH–He-rich) star binary systems. We evolve intensive MESA grids of close-orbit BH–He-rich star systems to systematically explore the projected aligned spins of BHs in BHNS binaries, as well as the impact of different accretion limits on the tidal disruption probability and electromagnetic (EM) signature of BHNS mergers. Most of the BHs in BHNS mergers cannot be effectively spun up through accretion if the accretion rate is limited to ≲10ṀEdd , where ṀEdd is the standard Eddington accretion limit. In order to reach high spins (e.g., χ BH ≳ 0.5), the BHs are required to be born less massive (e.g., ≲3.0 M ⊙) in binary systems with initial periods of ≲0.2–0.3 days and accrete material at ∼100ṀEdd . However, even under this high accretion limit, ≳6 M ⊙ BHs are typically challenging to significantly spin up and generate detectable associated EM signals. Our population simulations suggest that different accretion limits have a slight impact on the ratio of tidal disruption events. However, as the accretion limit increases, the EM counterparts from the cosmological BHNS population can become bright overall.

From ZAMS to merger: Detailed binary evolution models of coalescing neutron star – black hole systems at solar metallicity

Neutron star – black hole (NSBH) merger events bring us new opportunities to constrain theories of stellar and binary evolution and understand the nature of compact objects. In this work, we investigated the formation of merging NSBH binaries at solar metallicity by performing a binary population synthesis study of merging NSBH binaries with the newly developed code POSYDON. The latter incorporates extensive grids of detailed single and binary evolution models, covering the entire evolution of a double compact object progenitor. We explored the evolution of NSBHs originating from different formation channels, which in some cases differ from earlier studies performed with rapid binary population synthesis codes. In this paper, we present the population properties of merging NSBH systems and their progenitors such as component masses, orbital features, and BH spins, and we detail our investigation of the model uncertainties in our treatment of common envelope (CE) evolution and the core-collapse process. We find that at solar metallicity, under the default model assumptions, most of the merging NSBHs have BH masses in the range of 3 − 11 M⊙ and chirp masses within 1.5 − 4 M⊙. Independently of our model variations, the BH always forms first with dimensionless spin parameter ≲0.2, which is correlated to the initial binary orbital period. Some BHs can subsequently spin up moderately (χBH ≲ 0.4) due to mass transfer, which we assume to be Eddington limited. Binaries that experience CE evolution rarely demonstrate large tilt angles. Conversely, approximately 40% of the binaries that undergo only stable mass transfer without CE evolution contain an anti-aligned BH. Finally, accounting for uncertainties in both the population modeling and the NS equation of state, we find that 0 − 18.6% of NSBH mergers may be accompanied by an electromagnetic counterpart.

Rapid Localization of Gravitational Wave Sources from Compact Binary Coalescences Using Deep Learning

The mergers of neutron star–neutron star and neutron star–black hole binaries (NSBHs) are the most promising gravitational wave (GW) events with electromagnetic (EM) counterparts. The rapid detection, localization, and simultaneous multimessenger follow-up of these sources are of primary importance in the upcoming science runs of the LIGO-Virgo-KAGRA Collaboration. While prompt EM counterparts during binary mergers can last less than 2 s, the timescales of existing localization methods that use Bayesian techniques, vary from seconds to days. In this paper, we propose the first deep learning–based approach for rapid and accurate sky localization of all types of binary coalescences, including neutron star–neutron star and NSBHs for the first time. Specifically, we train and test a normalizing flow model on matched-filtering output from GW searches to obtain sky direction posteriors in around 1 s using a single P100 GPU, which is several orders of magnitude faster than full Bayesian techniques.

Eccentric catastrophes & what to do with them

Analytic modeling of gravitational waves (GWs) from inspiraling eccentric binaries poses an interesting mathematical challenge. When constructing analytic waveforms in the frequency domain, one has to contend with the fact that the phase of the Fourier integral in non-monotonic, resulting in a breakdown of the standard stationary phase approximation (SPA). In this work, we study this breakdown within the context of catastrophe theory. We find that the SPA holds in the context of eccentric Keplerian orbits when the Fourier frequency satisfies , where are integer multiples of the apocenter/pericenter frequencies, respectively. For values outside of this interval, the phase undergoes a fold catastrophe, giving rise to an Airy function approximation of the Fourier integral. Using these two different approximations, we generate a matched asymptotic expansion that approximates generic Fourier integrals of Keplerian motion for bound orbits across all frequency values. This asymptotic expansion is purely analytic and closed-form. We discuss several applications of this investigation and the resulting approximation, specifically: (1) the development and improvement of effective fly-by waveforms for binary black holes, (2) the transition from burst emission in the high eccentricity limit to wave-like emission in the quasi-circular limit, which results in an analogy between eccentric GW bursts and Bose–Einstein condensates, and (3) the calculation of f-mode amplitudes in eccentric binary neutron stars and black hole-neutron star binaries in terms of complex Hansen coefficients. The techniques and approximations developed herein are generic, and will be useful for future studies of GWs from eccentric binaries within the context of post-Newtonian theory.

Electromagnetic Precursors to Black Hole–Neutron Star Gravitational Wave Events: Flares and Reconnection-powered Fast Radio Transients from the Late Inspiral

The presence of magnetic fields in the late inspiral of black hole–neutron star binaries could lead to potentially detectable electromagnetic precursor transients. Using general-relativistic force-free electrodynamics simulations, we investigate premerger interactions of the common magnetosphere of black hole–neutron star systems. We demonstrate that these systems can feature copious electromagnetic flaring activity, which we find depends on the magnetic field orientation but not on black hole spin. Due to interactions with the surrounding magnetosphere, these flares could lead to fast-radio-burst-like transients and X-ray emission, with as an upper bound on the luminosity, where B * is the magnetic field strength on the surface of the neutron star.

Nucleosynthesis in outflows of compact objects and detection prospects of associated kilonovae

ABSTRACT We perform a comparative analysis of nucleosynthesis yields from binary neutron star (BNS) mergers, black hole-neutron star (BHNS) mergers, and core-collapse supernovae (CCSNe) with the goal of determining which are the most dominant sources of r-process enrichment observed in stars. We find that BNS and BHNS binaries may eject similar mass distributions of robust r-process nuclei post-merger (up to third peak and actinides, A ∼ 200−240), after accounting for the volumetric event rates. Magnetorotational (MR) CCSNe likely undergo a weak r-process (up to A ∼ 140) and contribute to the production of light element primary process (LEPP) nuclei, whereas typical thermal, neutrino-driven CCSNe only synthesize up to first r-process peak nuclei (A ∼ 80−90). We also find that the upper limit to the rate of MR CCSNe is $\lesssim 1~{{\ \rm per\ cent}}$ the rate of typical thermal CCSNe; if the rate was higher, then weak r-process nuclei would be overproduced. Although the largest uncertainty is from the volumetric event rate, the prospects are encouraging for confirming these rates in the next few years with upcoming surveys. Using a simple model to estimate the resulting kilonova light curve from mergers and our set of fiducial merger parameters, we predict that ∼7 BNS and ∼2 BHNS events will be detectable per year by the Vera C. Rubin Observatory (LSST), with prior gravitational wave (GW) triggers.

Constraints on Undetected Long-period Binaries in the Known Pulsar Population

Although neutron star–black hole binaries have been identified through mergers detected in gravitational waves, a pulsar–black hole binary has yet to be detected. While short-period binaries are detectable due to a clear signal in the pulsar’s timing residuals, effects from a long-period binary could be masked by other timing effects, allowing them to go undetected. In particular, a long-period binary measured over a small subset of its orbital period could manifest via time derivatives of the spin frequency incompatible with isolated pulsar properties. We assess the possibility of pulsars having unknown companions in long-period binaries and put constraints on the range of binary properties that may remain undetected in current data, but that may be detectable with further observations. We find that for 35% of canonical pulsars with published higher-order derivatives, the precision of measurements is not enough to confidently reject binarity (period ≳2 kyr), and that a black hole binary companion could not be ruled out for a sample of pulsars without published constraints if the period is >1 kyr. While we find no convincing cases in the literature, we put more stringent limits on orbital period and longitude of periastron for the few pulsars with published higher-order frequency derivatives (n ≥ 3). We discuss the detectability of candidates and find that a sample pulsar in a 100 yr orbit could be detectable within 5–10 yr.

Rapid population synthesis of black hole high-mass X-ray binaries: implications for binary stellar evolution

ABSTRACT We conduct binary population synthesis to investigate the formation of wind-fed high-mass X-ray binaries containing black holes (BH-HMXBs). We evolve multiple populations of high-mass binary stars and consider BH-HMXB formation rates, masses, spins, and separations. We find that systems similar to Cygnus X-1 likely form after stable Case A mass transfer (MT) from the main-sequence progenitors of BHs, provided such MT is characterized by low accretion efficiency, β ≲ 0.1, with modest orbital angular momentum losses from the non-accreted material. Additionally, efficient BH-HMXB formation relies on a new simple treatment for Case A MT that allows donors to retain larger core masses compared to traditional rapid population-synthesis assumptions. At solar metallicity, our Preferred model yields $\mathcal {O}(1)$ observable BH-HMXBs in the Galaxy today, consistent with observations. In this simulation, 8 per cent of BH-HMXBs go on to merge as binary black holes or neutron star-black hole binaries within a Hubble time; however, none of the merging binaries have BH-HMXB progenitors with properties similar to Cygnus X-1. With our preferred settings for core mass growth, mass transfer efficiency, and angular momentum loss, accounting for an evolving metallicity, and integrating over the metallicity-specific star formation history of the Universe, we find that BH-HMXBs may have contributed ≈2–5 BBH merger signals to detections reported in the third gravitational-wave transient catalogue of the LIGO–Virgo–KAGRA Collaboration. We also suggest MT efficiency should be higher during stable Case B MT than during Case A MT.

Compact Binary Merger Rate in Dark-matter Spikes

Today, the existence of supermassive black holes (SMBHs) in the center of galactic halos is almost confirmed. An extremely dense region referred to as dark-matter spike is expected to form around central SMBHs as they grow and evolve adiabatically. In this work, we calculate the merger rate of compact binaries in dark-matter spikes while considering halo models with spherical and ellipsoidal collapses. Our findings exhibit that ellipsoidal-collapse dark-matter halo models can potentially yield the enhancement of the merger rate of compact binaries. Finally, our results confirm that the merger rate of primordial black hole binaries is consistent with the results estimated by the LIGO-Virgo detectors, while such results cannot be realized for binary neutron stars and primordial black hole-neutron star binaries.

Population of Merging Compact Binaries Inferred Using Gravitational Waves through GWTC-3

We report on the population properties of compact binary mergers inferred from gravitational-wave observations of these systems during the first three LIGO-Virgo observing runs. The Gravitational-Wave Transient Catalog 3 (GWTC-3) contains signals consistent with three classes of binary mergers: binary black hole, binary neutron star, and neutron star–black hole mergers. We infer the binary neutron star merger rate to be between 10 and 1700 Gpc−3 yr−1 and the neutron star–black hole merger rate to be between 7.8 and 140 Gpc−3 yr−1, assuming a constant rate density in the comoving frame and taking the union of 90% credible intervals for methods used in this work. We infer the binary black hole merger rate, allowing for evolution with redshift, to be between 17.9 and 44 Gpc−3 yr−1 at a fiducial redshift (z=0.2). The rate of binary black hole mergers is observed to increase with redshift at a rate proportional to (1+z)κ with κ=2.9−1.8+1.7 for z≲1. Using both binary neutron star and neutron star–black hole binaries, we obtain a broad, relatively flat neutron star mass distribution extending from 1.2−0.2+0.1 to 2.0−0.3+0.3M⊙. We confidently determine that the merger rate as a function of mass sharply declines after the expected maximum neutron star mass, but cannot yet confirm or rule out the existence of a lower mass gap between neutron stars and black holes. We also find the binary black hole mass distribution has localized over- and underdensities relative to a power-law distribution, with peaks emerging at chirp masses of 8.3−0.5+0.3 and 27.9−1.8+1.9M⊙. While we continue to find that the mass distribution of a binary’s more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above approximately 60M⊙, which would indicate the presence of a upper mass gap. Observed black hole spins are small, with half of spin magnitudes below χi≈0.25. While the majority of spins are preferentially aligned with the orbital angular momentum, we infer evidence of antialigned spins among the binary population. We observe an increase in spin magnitude for systems with more unequal-mass ratio. We also observe evidence of misalignment of spins relative to the orbital angular momentum.22 MoreReceived 4 February 2022Revised 28 October 2022Accepted 19 December 2022DOI:https://doi.org/10.1103/PhysRevX.13.011048Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGravitational wave sourcesGravitational wavesTechniquesGravitational wave detectionGravitation, Cosmology & Astrophysics

Multimessenger emission from tidal waves in neutron star oceans

ABSTRACT Neutron stars in astrophysical binary systems represent exciting sources for multimessenger astrophysics. A potential source of electromagnetic transients from compact binary systems is the neutron star ocean, the external fluid layer encasing a neutron star. We present a groundwork study into tidal waves in neutron star oceans and their consequences. Specifically, we investigate how oscillation modes in neutron star oceans can be tidally excited during compact binary inspirals and parabolic encounters. We find that neutron star oceans can sustain tidal waves with frequencies between 0.01 and 20 Hz. Our results suggest that tidally resonant neutron star ocean waves may serve as a never-before studied source of precursor electromagnetic emission prior to neutron star–black hole and binary neutron star mergers. If accompanied by electromagnetic flares, tidally resonant neutron star ocean waves, whose energy budget can reach 1046 erg, may serve as early warning signs (≳1 min before merger) for compact binary mergers. Similarly, excited ocean tidal waves will coincide with neutron star parabolic encounters. Depending on the neutron star ocean model and a flare emission scenario, tidally resonant ocean flares may be detectable by Fermi and Nuclear Spectroscopic Telescope Array (NuSTAR) out to ≳100 Mpc with detection rates as high as ∼7 yr−1 for binary neutron stars and ∼0.6 yr−1 for neutron star–black hole binaries. Observations of emission from neutron star ocean tidal waves along with gravitational waves will provide insight into the equation of state at the neutron star surface, the composition of neutron star oceans and crusts, and neutron star geophysics.

Fractions of Compact Object Binaries in Star Clusters: Theoretical Predictions

The binary population in field stars and star clusters contributes to the formation of gravitational wave (GW) sources. However, the fraction of compact-object binaries (CBs), which is an important feature parameter of binary populations, is still difficult to measure and very uncertain. This paper predicts the fractions of important CBs and semi-compact object binaries (SCBs) making use of an advanced stellar population synthesis technique. A comparison with the result of N-body simulation is also presented. It is found that most CBs are formed within about 500 Myr after the starburst. The fractions of CBs and SCBs are demonstrated to correlate with stellar metallicity. The higher the metallicity becomes, the smaller the fraction of black hole binaries (BHBs), neutron star binaries (NSBs) and SCBs. This suggests that the GW sources of BHBs and NSBs are more likely to form in metal-poor environments. However, the fraction of black hole-neutron star binaries is shown to be larger for metal-rich populations on average.

Mechanisms for high spin in black-hole neutron-star binaries and kilonova emission: inheritance and accretion

ABSTRACT A black-hole neutron-star binary merger can lead to an electromagnetic counterpart called a kilonova if the neutron star is disrupted prior to merger. The observability of a kilonova depends on the amount of neutron star ejecta, which is sensitive to the aligned component of the black hole spin. We explore the dependence of the ejected mass on two main mechanisms that provide high black hole spin in isolated stellar binaries. When the black hole inherits a high spin from a Wolf–Rayet star that was born with least $\sim 10{{\ \rm per\ cent}}$ of its breakup spin under weak stellar core-envelope coupling, relevant for all formation pathways, the median of the ejected mass is ≳10−2 M⊙. Though only possible for certain formation pathways, similar ejected mass results when the black hole accretes $\gtrsim 20{{\ \rm per\ cent}}$ of its companion’s envelope to gain a high spin. Together, these signatures suggest that a population analysis of black-hole neutron-star binary mergers with observed kilonovae may help distinguish between mechanisms for spin and possible formation pathways. We show that these kilonovae will be difficult to detect with current capabilities, but that future facilities, such as the Vera Rubin Observatory, can do so even if the aligned dimensionless spin of the black hole is as low as ∼0.2. Our model predicts kilonovae as bright as Mi ∼ −14.5 for an aligned black hole spin of ∼0.9 and mass ratio Q = 3.6.

Forecasting the Detection Capabilities of Third-generation Gravitational-wave Detectors Using GWFAST

We introduce GWFAST, a novel Fisher-matrix code for gravitational-wave studies, tuned toward third-generation gravitational-wave detectors such as Einstein Telescope (ET) and Cosmic Explorer (CE). We use it to perform a comprehensive study of the capabilities of ET alone, and of a network made by ET and two CE detectors, as well as to provide forecasts for the forthcoming O4 run of the LIGO-Virgo-KAGRA (LVK) collaboration. We consider binary neutron stars, binary black holes, and neutron star–black hole binaries, and compute basic metrics such as the distribution of signal-to-noise ratio (S/N), the accuracy in the reconstruction of various parameters (including distance, sky localization, masses, spins, and, for neutron stars, tidal deformabilities), and the redshift distribution of the detections for different thresholds in S/N and different levels of accuracy in localization and distance measurement. We examine the expected distribution and properties of golden events, with especially large values of the S/N. We also pay special attention to the dependence of the results on astrophysical uncertainties and on various technical details (such as choice of waveforms, or the threshold in S/N), and we compare with other Fisher codes in the literature. In the companion paper Iacovelli et al., we discuss the technical aspects of the code. Together with this paper, we publicly release the code GWFAST, (https://github.com/CosmoStatGW/gwfast) and the library WF4Py (https://github.com/CosmoStatGW/WF4Py) implementing state-of-the-art gravitational-wave waveforms in pure Python.

Measurability of neutron star tidal deformability from merging neutron star-black hole binaries

The neutron star-black hole binary (NSBH) system has been considered one of the promising detection candidates for ground-based gravitational-wave (GW) detectors such as LIGO and Virgo. The tidal effects of neutron stars (NSs) are imprinted on the GW signals emitted from NSBHs as well as binary neutron stars. In this work, we study how accurately the parameter $\lambda_{\rm NS}$ can be measured in GW parameter estimation for NSBH signals. We set the parameter range for the NSBH sources to $[4M_{\odot}, 10M_{\odot}]$ for the black hole mass, $[1M_{\odot}, 2M_{\odot}]$ for the NS mass, and $[-0.9, 0.9]$ for the dimensionless black hole spin. For realistic populations of sources distributed in different parameter spaces, we calculate the measurement errors of $\lambda_{\rm NS}$ ($\sigma_{\lambda_{\rm NS}}$) using the Fisher matrix method. In particular, we perform a single-detector analysis using the advanced LIGO and the Cosmic Explorer detectors and a multi-detector analysis using the 2G (advanced LIGO-Hanford, advanced LIGO-Livingstone, advanced Virgo, and KAGRA) and the 3G (Einstein Telescope and Cosmic Explorer) networks. We show the distribution of $\sigma_{\lambda_{\rm NS}}$ for the population of sources as a one-dimensional probability density function. Our result shows that the probability density function curves are similar in shape between advanced LIGO and Cosmic Explorer, but Cosmic Explorer can achieve $\sim 15$ times better accuracy overall in the measurement of $\lambda_{\rm NS}$. In the case of the network detectors, the probability density functions are maximum at $\sigma_{\lambda_{\rm NS}} \sim 130$ and $\sim 4$ for the 2G and the 3G networks, respectively, and the 3G network can achieve $\sim 10$ times better accuracy overall.