arXiv subjects

Hee-Suk Cho

Publications and source records attributed to Hee-Suk Cho.

16 recordsLinked to original sources

arXiv2025

Systematic bias due to eccentricity in parameter estimation for merging binary neutron stars : Spinning case

In our previous work [Phys. Rev. D {\bf 105}. 124022 (2022)], we studied the impact of eccentricity on gravitational-wave parameter estimation for a nonspinning binary neutron star (BNS) system. We here extend the work to a more realistic case by including the spin parameter in the system. As in the previous work, we employ the analytic Fisher-Cutler-Vallisneri method to calculate the systematic bias that can be produced by using noneccentric waveforms in parameter estimation, and we verify the reliability of the method by comparing it with numerical Bayesian parameter estimation results. We generate $10^4$ BNS sources randomly distributed in the parameter space $m_1$-$m_2$-$\chi_{\rm eff}$-$e_0$, where the neutron star mass is in the range of $1 M_\odot \leq m_{1,2}\leq 2M_\odot (m_2 \leq m_1)$, the effective spin is $-0.2 \leq \chi_{\rm eff} \leq0 .2$, and the eccentricity (at the reference frequency 10 Hz) is $0 \leq e_0 \leq 0.024$. For the true value of the tidal deformability ($\lambda$) of neutron stars, we assume the equation of state model APR4. For all gravitational-wave signals emitted from the sources, we calculate the systematic biases ($\Delta \theta$) for the chirp mass ($M_c$), symmetric mass ratio ($\eta$), effective spin ($\chi_{\rm eff}$), and effective tidal deformability ($\tilde{\lambda}$), and obtain generalized distributions of the biases. The distribution of biases in $M_c, \eta$, and $\chi_{\rm eff}$ shows narrow bands that increase or decrease quadratically with increasing $e_0$, indicating a weak dependence of biases on the three parameters. On the other hand, the biases of $\tilde{\lambda}$ are widely distributed depending on the values of the mass and spin parameters at a given $e_0$. We investigate the implications of biased parameters for the inference of neutron star properties by performing Bayesian parameter estimation for specific cases.

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arXiv2025

Impact of Higher-order Tidal Corrections on the Measurement Accuracy of Neutron Star Tidal Deformability

Gravitational waves emitted by binary neutron stars (BNS) provide information about the internal structure of neutron stars (NSs), helping to verify dense matter equations of state. We investigate how the measurement accuracy of NS's tidal deformability can be improved by incorporating the higher-order post-Newtonian (pN) tidal corrections up to 7.5 pN. We assume an aligned-spin BNS system and adopt TaylorF2, which is the most commonly used pN waveform model. To calculate the measurement error, we use a semi-analytic method, Fisher Matrix, which is much faster than performing parameter estimation simulations. We employ Universal Relation to remove additional parameters that appear in higher-order corrections beyond 6 pN. We find that the effect of tidal corrections shows no behavior of convergence with increasing pN orders. Assuming a fiducial binary NS system whose physical parameters are compatible with GW170817, we find that the measurement error of tidal deformability ($\tilde{\lambda}$) decreases linearly as the effective spin ($\chi_{\rm eff}$) increases and the tidal deformability can be better measured for stiffer equation of states.

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arXiv2022

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 $λ_{\rm NS}$ 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 $λ_{\rm NS}$ ($σ_{λ_{\rm NS}}$) 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 $σ_{λ_{\rm NS}}$ 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 $λ_{\rm NS}$. In the case of the network detectors, the probability density functions are maximum at $σ_{λ_{\rm NS}} \sim 130$ and $\sim 4$ for the 2G and the 3G networks, respectively, and the 3G network can achieve $\sim 10$ times better accuracy overall.

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arXiv2022

Systematic bias due to eccentricity in parameter estimation for merging binary neutron stars

We study the impact of eccentricity on gravitational-wave parameter estimation for binary neutron star systems. For signals with small eccentricity injected into the advanced LIGO sensitivity, we perform Bayesian parameter estimation using the circular waveform model and show how the recovered parameters can be biased from their true values, focusing on the intrinsic parameters the chirp mass ($M_c$), the symmetric mass ratio ($η$), and the tidal deformability ($\tildeλ$). By comparing the results between the Bayesian and the analytic Fisher-Cutler-Vallisneri (FCV) methods, we obtain the valid criteria for the FCV approach. Employing the FCV method and using the realistic population of binary neutron star sources distributed in the $m_1$-$m_2$-$e_0$ space, where $e_0$ indicates the eccentricity at 10Hz, we calculate the measurement errors ($σ_θ$) and the systematic biases ($Δθ/σ_θ$) and obtain their generalized distributions in the range of $0 \leq e_0 \leq 0.025$. We find that for all of the three parameters, the biases increase with increasing $e_0$, and this increase is faster for larger $e_0$. The bias is mainly dependent on the value of $e_0$ and weakly dependent on the component masses, and thus the distribution shows a narrow band in the $e_0$-$Δθ/σ_θ$ plane. We present various posterior examples to illustrate our new findings, such as the bimodality of posteriors. In particular, we give a specific injection-recovery example to demonstrate the importance of including eccentricity in parameter estimation to avoid incorrect predictions of the neutron star equation of state.

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arXiv2022

Improvement of the parameter measurement accuracy by the third-generation gravitational wave detector Einstein Telescope

The Einstein Telescope (ET) has been proposed as one of the third-generation gravitational wave (GW) detectors. The sensitivity of ET would be a factor of 10 better than the second-generation GW detector, Advanced LIGO (aLIGO); thus, the GW source parameters could be measured with much better accuracy. In this work, we show how the precision in parameter estimation can be improved between aLIGO and ET by comparing the measurement errors. We apply the TaylorF2 waveform model defined in the frequency domain to the Fisher matrix method which is a semi-analytic approach for estimating GW parameter measurement errors. We adopt as our sources low-mass binary black holes with the total masses of $M\leq 16 M_{\odot} $ and the effective spins of $-0.9 \leq χ_{\rm eff} \leq 0.9$ and calculate the measurement errors of the mass and the spin parameters using $10^4$ Monte-Carlo samples randomly distributed in our mass and spin parameter space. We find that for the same sources ET can achieve $\sim 14$ times better signal-to-noise ratio than aLIGO and the error ratios ($σ_{λ, \rm ET}/σ_{λ, \rm aLIGO}$) for the chirp-mass, symmetric mass ratio, and effective spin parameters can be lower than $7\%$ for all binaries. We also consider the equal-mass binary neutron stars with the component masses of 1, 1.4, and 2 $M_{\odot}$ and find that the error ratios for the mass and the spin parameters can be lower than $1.5 \%$. In particular, the measurement error of the tidal deformability $\tildeΛ$ can also be significantly reduced by ET, with the error ratio of $3.6 - 6.1 \%$.

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arXiv2019

Measurement of Tidal Deformability in the Gravitational Wave Parameter Estimation for Nonspinning Binary Neutron Star Mergers

One of the main targets for ground-based gravitational wave (GW) detectors such as Advanced LIGO (Laser Interferometer Gravitational wave Observatory) and Virgo is coalescences of neutron star (NS) binaries. Even though a NS's macroscopic properties such as mass and radius have been obtained from electro-magnetic wave observations, its internal structure has been studied mainly by using theoretical approaches. However, with the advent of Advanced LIGO and Virgo, the tidal deformability of a NS, which depends on the internal structure of the NS, has been recently obtained from GW observations. Therefore, reducing the measurement error of tidal deformability as small as possible in the GW parameter estimation is important. In this study, we introduce a post-Newtonian (PN) gravitational waveform model in which the tidal deformability contribution appears from 5 PN order, and we use the Fisher matrix (FM) method to calculate parameter measurement errors. Because the FM is computed semi-analytically using the wave function, the measurement errors can be obtained much faster than those of practical parameter estimations based on Markov Chain Monte Carlo method. We investigate the measurement errors for mass and tidal deformability by applying the FM to the nonspinning TaylorF2 waveform model. We show that if the tidal deformability corrections are considered up to the 6 PN order, the measurement error for the dimensionless tidal deformability can be reduced to about $75 \%$ compared to that obtained by considering only the 5 PN order correction.

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arXiv2017

Gravitational Wave Searches for Aligned-Spin Binary Neutron Stars Using Nonspinning Templates

We study gravitational wave searches for merging binary neutron stars (NSs). We use nonspinning template waveforms towards the signals emitted from aligned-spin NS-NS binaries, in which the spins of the NSs are aligned with the orbital angular momentum. We use the TaylorF2 waveform model, which can generate inspiral waveforms emitted from aligned-spin compact binaries. We employ the single effective spin parameter $χ_{\rm eff}$ to represent the effect of two component spins ($χ_1, χ_2$) on the wave function. For a target system, we choose a binary consisting of the same component masses of $1.4 M_{\odot}$ and consider the spins up to $χ_i= 0.4$, We investigate fitting factors of the nonspinning templates to evaluate their efficiency in gravitational wave searches for the aligned-spin NS-NS binaries. We find that the templates can achieve the fitting factors exceeding $0.97$ only for the signals in the range of $-0.2 \lesssim χ_{\rm eff} \lesssim 0$. Therefore, we demonstrate the necessity of using aligned-spin templates not to lose the signals outside that range. We also show how much the recovered total mass can be biased from the true value depending on the spin of the signal.

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arXiv2017

Systematic Bias Due to Nonspinning Template Waveforms in the Gravitational Wave Parameter Estimation for Aligned-Spin Binary Black Holes

We study the parameter estimation of gravitational waves for aligned-spin binary black hole (BBH) signals and assess the impact of bias that can be produced by using nonspinning template waveforms. We employ simple methods to calculate the statistical uncertainty from an overlap distribution. For the fiducial waveform model, we use a phenomenological model, which is designed to generate the gravitational waveforms emitted from merging BBH systems. We show that the mass parameters recovered by nonspinning waveform templates can be significantly biased from the true values of aligned-spin signals. By comparing the systematic bias with the statistical uncertainty, we examine the validity of nonspinning templates for the parameter estimation of aligned-spin BBHs.

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arXiv2016

Efficiency of nonspinning templates in gravitational wave searches for aligned-spin binary black holes

We study the efficiency of nonspinning waveform templates in gravitational wave searches for aligned-spin binary black holes (BBHs). We use PhenomD, which is the most recent phenomenological waveform model designed to generate the full inspiral-merger-ringdown waveforms emitted from BBHs with the spins aligned with the orbital angular momentum. Here, we treat the effect of aligned-spins with a single spin parameter $χ$. We consider the BBH signals with moderately small spins in the range of $-0.4\leq χ\leq 0.4$. Using nonspinning templates, we calculate fitting factors of the aligned-spin signals in a wide mass range up to $\sim 100 M_{\odot}$. We find that the signals with negative spins can have higher fitting factors than those with positive spins. If $χ= 0.3$, only the highly asymmetric-mass signals can have the fitting factors exceeding the threshold of 0.965, while the fitting factors for all of the signals can be larger than the threshold if $χ= -0.3$. We demonstrate that the discrepancy between the regions of a positive and a negative spins is due to the physical boundary ($η\leq 0.25$) of the template parameter space. We also show that the recovered mass parameters can be significantly biased from the true parameters. We examine the impact of the systematic bias on the parameter estimation by comparing the bias with the statistical error.

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arXiv2016

Accuracy in Measuring the Neutron Star Mass in Gravitational Wave Parameter Estimation for Black Hole-Neutron Star Binaries

Recently, two gravitational wave (GW) signals, named as GW150914 and GW151226, have been detected by the two LIGO detectors. Although both signals were identified as originating from merging black hole (BH) binaries, GWs from systems containing neutron stars (NSs) are also expected to be detected in the near future by the Advanced detector network. In this work, we assess the accuracy in measuring the NS mass ($M_{ns}$) for the GWs from BH-NS binaries adopting the Advanced LIGO sensitivity with a signal-to-noise ratio of 10. By using the Fisher matrix method, we calculate the measurement errors ($σ$) in $M_{ns}$ assuming the NS mass of $1 \leq M_{ns}/M_{\odot} \leq 2$ and low mass BHs with the range of $4 \leq M_{bh}/M_{\odot} \leq 10$. We used the TaylorF2 waveform model where the spins are aligned with the orbital angular momentum, but here we only consider the BH spins. We find that the fractional errors ($σ/M_{ns} \times 100$) are in the range of $10\% - 50\%$ in our mass region for a given dimensionless BH spin as $χ_{bh} = 0$. The errors tend to increase as the BH spin increases, and this tendency is stronger for higher NS masses (or higher total masses). In particular, for the highest mass NSs ($M_{ns}=2~M_{\odot}$), the errors $σ$ can be larger than the true value of $M_{ns}$ if the dimensionless BH spin exceeds $\sim 0.6$.

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arXiv2015

Parameter estimation using a complete signal and inspiral templates for low mass binary black holes with Advanced LIGO sensitivity

We study the validity of inspiral templates in gravitational wave data analysis with Advanced LIGO sensitivity for low mass binary black holes with total masses of $M \leq 30 Msun$. We mainly focus on the nonspinning system. As our complete inspiral-merger-ringdown waveform model ($IMR$), we assume the phenomenological model, "PhenomA", and define our inspiral template model ($Imerg$) by taking the inspiral part into account from $IMR$ up to the merger frequency (fmerg). We first calculate the {\it true} statistical uncertainties using $IMR$ signals and $IMR$ templates. Next, using $IMR$ signals and $Imerg$ templates, we calculate fitting factors and systematic biases, and compare the biases with the {\it true} statistical uncertainties. We find that the valid criteria of the bank of $Imerg$ templates are obtained as $Mcrit \sim 24 Msun$ for detection (if $M>Mcrit$, the fitting factor is smaller than $0.97$), and $Mcrit \sim 26 Msun$ for parameter estimation (if $M>Mcrit$, the systematic bias is larger than the {\it true} statistical uncertainty where the signal to noise ratio is $20$), respectively. In order to see the dependence on the cutoff frequency of the inspiral waveforms, we define another inspiral model $Iisco$ which is terminated at the innermost-stable-circular-orbit frequency ($fisco<fmerg$). We find that the valid criteria of the bank of $Iisco$ templates are obtained as $Mcrit \sim 15 Msun$ and $\sim 17 Msun$ for detection and parameter estimation, respectively. We investigate the statistical uncertainties for the inspiral template models considering various signal to noise ratios, and compare those to the {\it true} statistical uncertainties. We also consider the aligned-spinning system with fixed mass ratio ($m_1/m_2=3$) and spin ($χ=0.5$) by employing the recent phenomenological model, "PhenomC".

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arXiv2015

Testing the validity of the phenomenological gravitational waveform models for nonspinning binary black hole searches at low masses

The phenomenological gravitational waveform models, which we refer to as PhenomA, PhenomB and PhenomC, generate full inspiral-merger-ringdown waveforms of coalescing binary back holes (BBHs). These models are defined in the Fourier domain, thus can be used for fast matched filtering in the gravitational wave search. PhenomA has been developed for nonspinning BBH waveforms, while PhenomB and PhenomC were designed to model the waveforms of BBH systems with nonprecessing (aligned) spins, but can also be used for nonspinning systems. In this work, we study the validity of the phenomenological models for nonspinning BBH searches at low masses, $m_{1,2}\geq 4 Msun$ and $m_1+m_2\equiv M \leq 30 Msun$, with Advanced LIGO. As our complete signal waveform model, we adopt EOBNRv2 that is a time-domain inspiral-merger-ringdown waveform model. To investigate the search efficiency of the phenomenological template models, we calculate fitting factors by exploring overlap surfaces. We find that only PhenomC is valid to obtain the fitting factors better than 0.97 in the mass range of $M<15 Msun$. Above $15 Msun$, PhenomA is most efficient in symmetric mass region, PhenomB is most efficient in highly asymmetric mass region, and PhenomC is most efficient in the intermediate region. Specifically, we propose an effective phenomenological template family that can be constructed by employing the phenomenological models in four subregions individually. We find that fitting factors of the effective templates are better than 0.97 in our entire mass region and mostly greater than 0.99.

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arXiv2014

Application of the effective Fisher matrix to the frequency domain inspiral waveforms

The Fisher matrix (FM) has been generally used to predict the accuracy of the gravitational wave parameter estimation. Although a limitation of the FM has been well known, it is still mainly used due to its very low computational cost compared to the Monte Carlo simulations. Recently, Rodriguez et al. [Phys. Rev. D 88, 084013 (2013)] performed Markov chain Monte Carlo (MCMC) simulations for nonspinning binary systems with total masses $M \leq 20 M_{\odot}$, they found systematic differences between the predictions from FM and MCMC for $M>10 M_{\odot}$. On the other hand, an effective Fisher matrix (eFM) was recently introduced by Cho et al. [Phys. Rev. D 87, 24004 (2013)]. The eFM is a semi-analytic approach to the standard FM, in which the partial derivative is taken by a quadratic fitting function to the local overlap surface. In this work, we apply the eFM method to several nonspinning binary systems and find that the error bounds in eFM are qualitatively in good agreement with the MCMC results of Rodriguez et al. in all mass regions. In particular, we provide concrete examples showing an importance of taking into account the template-dependent frequency cutoff of the inspiral waveforms.

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arXiv2014

Parameter Estimation of Gravitational Waves from Nonprecessing BH-NS Inspirals with higher harmonics: Comparing MCMC posteriors to an Effective Fisher Matrix

Using the \texttt{lalinference} Markov-chain Monte Carlo parameter estimation code, we examine two distinct nonprecessing black hole-neutron star (BH-NS) binaries with and without higher-order harmonics. Our simulations suggest that higher harmonics provide a minimal amount of additional information, principally about source geometry. Higher harmonics do provide disproportionately more information than expected from the signal power. Our results compare favorably to the "effective Fisher matrix" approach. Extrapolating using analytic scalings, we expect higher harmonics will provide little new information about nonprecessing BH-NS binaries at the signal amplitudes expected for the first few detections. Any study of subdominant degrees of freedom in gravitational wave astronomy can adopt the tools presented here ($V/V_{\rm prior}$ and $D_{KL}$) to assess whether new physics is accessible (e.g., modifications of gravity; spin-orbit misalignment) and if so precisely what information those new parameters provide. For astrophysicists, we provide a concrete illustration of how well parameters of a BH-NS binary can be measured, relevant to the astrophysical interpretation of coincident EM and GW events (e.g., short GRBs). For our fiducial initial-detector example, the individual masses can be determined to lie between $7.11-11.48 M_\odot$ and $1.77-1.276M_\odot$ at greater than 99% confidence, accounting for unknown BH spin. Assuming comparable control over waveform systematics, future measurements of BH-NS binaries can constrain the BH and perhaps NS mass distributions.

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arXiv2013

Validity of the Effective Fisher matrix for parameter estimation analysis: Comparing to the analytic Fisher matrix

The effective Fisher matrix method recently introduced by Cho et al. is a semi-analytic approach to the Fisher matrix, in which a local overlap surface is fitted by using a quadratic fitting function. Mathematically, the effective Fisher matrix should be consistent with the analytic one at the infinitesimal fitting scale. In this work, using the frequency-domain waveform (TaylorF2), we give brief comparison results between the effective and analytic Fisher matrices for several non-spinning binaries consisting of binary neutron stars with masses of (1.4, 1.4)M_sun, black hole-neutron star of (1.4, 10)M_sun, and binary black holes of (5, 5) and (10, 10)M_sun for a fixed signal to noise ratio (SNR=20) and show a good consistency between two methods. We also give a comparison result for an aligned-spin black hole-neutron star binary with a black hole spin of χ=1, where we define new mass parameters (Mc, η^-1, χ^7/2) to find good fitting functions to the overlap surface. The effective Fisher matrix can also be computed by using the time-domain waveforms which are generally more accurate than frequency-domain waveform. We show comparison results between the frequency-domain and time-domain waveforms (TaylorT4) for both the non-spinning aligned-spin binaries.

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arXiv2012

Gravitational waves from BH-NS binaries: Effective Fisher matrices and parameter estimation using higher harmonics

Inspiralling black hole-neutron star (BH-NS) binaries emit a complicated gravitational wave signature, produced by multiple harmonics sourced by their strong local gravitational field and further modulated by the orbital plane's precession. Some features of this complex signal are easily accessible to ground-based interferometers (e.g., the rate of change of frequency); others less so (e.g., the polarization content); and others unavailable (e.g., features of the signal out of band). For this reason, an ambiguity function (a diagnostic of dissimilarity) between two such signals varies on many parameter scales and ranges. In this paper, we present a method for computing an approximate, effective Fisher matrix from variations in the ambiguity function on physically pertinent scales which depend on the relevant signal to noise ratio. As a concrete example, we explore how higher harmonics improve parameter measurement accuracy. As previous studies suggest, for our fiducial BH-NS binaries and for plausible signal amplitudes, we see that higher harmonics at best marginally improve our ability to measure parameters. For non-precessing binaries, these Fisher matrices separate into intrinsic (mass, spin) and extrinsic (geometrical) parameters; higher harmonics principally improve our knowledge about the line of sight. For the precessing binaries, the extra information provided by higher harmonics is distributed across several parameters. We provide concrete estimates for measurement accuracy, using coordinates adapted to the precession cone in the detector's sensitive band.

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