Systematic and statistical errors in a Bayesian approach to the estimation of the neutron-star equation of state using advanced gravitational wave detectors

Leslie Wade, Jolien D. E. Creighton, Evan Ochsner, Benjamin D. Lackey, Benjamin F. Farr, Tyson B. Littenberg, and Vivien Raymond

Phys. Rev. D 89, 103012 – Published 23 May 2014

Abstract

Advanced ground-based gravitational-wave detectors are capable of measuring tidal influences in binary neutron-star systems. In this work, we report on the statistical uncertainties in measuring tidal deformability with a full Bayesian parameter estimation implementation. We show how simultaneous measurements of chirp mass and tidal deformability can be used to constrain the neutron-star equation of state. We also study the effects of waveform modeling bias and individual instances of detector noise on these measurements. We notably find that systematic error between post-Newtonian waveform families can significantly bias the estimation of tidal parameters, thus motivating the continued development of waveform models that are more reliable at high frequencies.

Received 21 February 2014

DOI:https://doi.org/10.1103/PhysRevD.89.103012

Authors & Affiliations

Leslie Wade¹, Jolien D. E. Creighton¹, Evan Ochsner¹, Benjamin D. Lackey², Benjamin F. Farr³, Tyson B. Littenberg³, and Vivien Raymond⁴

¹Department of Physics, University of Wisconsin–Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201, USA
²Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
³Department of Physics and Astronomy, Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), 2145 Sheridan Road, Evanston, Illinois 60208, USA
⁴LIGO–California Institute of Technology, Pasadena, California 91125, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 89, Iss. 10 — 15 May 2014

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Marginalized one-dimensional (left and middle) and two-dimensional (right) posterior probability density functions for $\tilde{Λ}$ and $δ \tilde{Λ}$ of a $1.35 M_{⊙} : 1.35 M_{⊙}$ BNS system with $ρ_{net} = 32.4$ . The shaded regions in the one-dimensional PDFs enclose $2 σ$ (95%) confidence regions. The color bar in the two-dimensional PDF labels the (unnormalized) probability density. The injected values for $\tilde{Λ}$ and $δ \tilde{Λ}$ are consistent with the MPA1 EOS model [40] and are marked with straight dashed lines. These plots are PDFs smoothed with a Gaussian kernel density estimator. For these results, we injected into zero-noise (see Sec. 3c).
Reuse & Permissions
Figure 2
NS mass-radius plot for a sample of NS EOS models found in the literature [40] (top left). The $M_{c} - R_{c}$ plot (top right), where $R_{c}$ is defined in Sec. 4, depicts the same EOSs as the mass-radius plot now smeared out due to the extra degrees of freedom from not specifying individual masses and radii. We consider NSs with masses that range from $1 M_{⊙}$ to the maximum allowed mass for each EOS. The three horizontal, black lines are the $1 σ$ (68%) confidence regions of three recovered injections. The three bottom plots are zoomed-in to show these recovered injections more clearly. The injected values for $M_{c}$ and $R_{c}$ are consistent with the MPA1 EOS model and are marked with straight, dashed lines. For these results, we injected into zero-noise (see Sec. 3c).
Reuse & Permissions
Figure 3
Marginalized one-dimensional posterior probability density functions for $\tilde{Λ}$ of three BNS systems (labeled by the masses in the title) each with $ρ_{net} = 32.4$ . The injected $\tilde{Λ}$ values are consistent with the MPA1 EOS model [40] and are marked with straight, dashed lines. These plots are PDFs smoothed with a Gaussian kernel density estimator. To generate a single plot, we inject BNS signals modeled by each of the five PN waveform families derived in the Appendix. Though the waveform family for each signal is different, the injected waveform parameters are identical. The five PDFs, which are labeled by the injected waveform family, are all recovered using TaylorF2 waveform templates. The deviation of each peak away from the injected value is due to the systematic error in the PN waveform approximants. For these results, we injected into zero-noise (see Sec. 3c).
Reuse & Permissions
Figure 4
Marginalized one-dimensional posterior probability density functions for $\tilde{Λ}$ of three BNS systems (labeled by the masses in the title) each with $ρ_{net} = 32.4$ (bottom). The injected $\tilde{Λ}$ values are consistent with the MPA1 EOS model [40] and are marked with straight, dashed lines. These plots are PDFs smoothed with a Gaussian kernel density estimator. To generate a single plot, we inject the same BNS signal into ten different noise realizations. The deviation of each peak away from the injected value is due to the statistical error from the presence of random detector noise. Each PDF has an associated box-and-whisker representation (top), where the edges of each box mark the first and third quartile, the band inside each box is the median, and the end of the whiskers span the 90% confidence interval.
Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology