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

Abstract

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 $m_1$-$m_2$-$χ_{\rm eff}$-$e_0$, where the nuetron 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 $-0.2 \leq χ_{\rm eff} \leq0 .2$, 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 ($λ$) 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 ($Δθ$) for the chirp mass ($M_c$), symmetric mass ratio ($η$), effective spin ($χ_{\rm eff}$), and effective tidal deformability ($\tildeλ$), and obtain generalized distributions of the biases. The distribution of biases in $M_c, η$, and $χ_{\rm eff}$ 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 $\tildeλ$ 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.

Figures (11)

• Figure 1: Bayesian parmeter estimation results calculated with various SNRs. The contours indicate 39, 86, and 99$\%$ confidence regions. Injection values are $(m_1,m_2, [M_c,\eta],\chi_{\rm eff},\tilde{\lambda},\delta \tilde{\lambda })=(2M_\odot,1M_\odot,[1.21673 M_\odot,0.22222],0.05,237,101)$ marked in orange. PDFs for $\delta\tilde{\Lambda}$ are shown in the bottom-right, separately.
• Figure 2: Comparison between the FM (black) and Bayesian parameter estimation (gray). All parameters are successfully recovered overall, but those are biased at low SNRs.
• Figure 3: Bayesian PDFs biased due to eccentricity. The true value is marked in red. We assume $\rho=300$.
• Figure 4: Comparison of systematic biases between the FCV and the Bayesian parameter estimation methods. The bias is normalized by the bias value of FCV at $e_0=0.024$ ($\Delta \theta^{\rm FCV}_{e_0=0.024}$).
• Figure 5: Distribution of the fractional biases $\Delta \theta/\sigma_{\theta}$ for the $10^4$ Monte Carlo signals. For the measurement error $\sigma_{\theta}$, we assume $\rho=300$.