Hierarchical Bayesian method for constraining the neutron star equation of state with an ensemble of binary neutron star postmerger remnants

Creators: Criswell, Alexander W.; Miller, Jesse; Woldemariam, Noah; Soultanis, Theodoros; Bauswein, Andreas; Chatziioannou, Katerina¹; Coughlin, Michael W.; Jones, Galin; Mandic, Vuk

1. California Institute of Technology

Abstract

Binary neutron star (BNS) postmerger gravitational-wave emission can occur in the aftermath of a BNS merger—provided the system avoids prompt collapse to a black hole—as a quasistable hypermassive remnant experiences quadrupolar oscillations and nonaxisymmetric deformations. The postmerger gravitational-wave spectrum possesses a characteristic peak frequency that has been shown to be dependent on the binary chirp mass and the neutron star equation of state (EOS), rendering postmerger gravitational waves a powerful tool for constraining neutron star composition. Unfortunately, the BNS postmerger signal is emitted at high (≳1.5 kHz) frequencies, where ground-based gravitational-wave detectors suffer from reduced sensitivity. It is therefore unlikely that postmerger signals will be detected with sufficient signal-to-noise ratio (SNR) until the advent of next-generation detectors. However, by employing empirical relations derived from numerical relativity simulations, we can combine information across an ensemble of BNS mergers, allowing us to obtain EOS constraints with many low-SNR signals. We present a hierarchical Bayesian method for deriving constraints on 𝑅_(1.6), the radius of a 1.6⁢ 𝑀_⊙ neutron star, through an ensemble analysis of binary neutron star mergers. We apply this method to simulations of the next two LIGO-Virgo-KAGRA observing runs, O4 and O5, as well as an extended four-year run at A+ sensitivity, demonstrating the potential of our approach to yield EOS information from the postmerger signal with current-generation detectors. The A+ four-year scenario is predicted to improve the constraint on 𝑅_(1.6) from the currently available multimessenger-based 95% credible interval (C.I.) uncertainty of 𝑅_(1.6) = 12.0⁢7^(+0.98)_(−0.77) to 𝑅_(1.6) = 11.9⁢1^(+0.80)_(−0.56) km, a 22% reduction of the 95% C.I. width.

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Acknowledgement

The authors would like to thank James Clark and Tim Dietrich for many helpful conversations about bayeswave and multimessenger considerations, respectively. This research makes use of the numpy [138], scipy [126], pandas [139], matplotlib [140] scientific computing packages, the bayeswave data analysis pipeline [102,104,141], and utilized computing resources provided by the Minnesota Supercomputing Institute at the University of Minnesota. The authors are grateful for computational resources provided by the LIGO Laboratory and supported by National Science Foundation Grants No. PHY-0757058 and No. PHY-0823459. This material is based upon work supported by NSF’s LIGO Laboratory which is a major facility fully funded by the National Science Foundation. A. W. C. and J. M. acknowledge support by the National Science Foundation Research Traineeship Program “Data Science in Multimessenger Astrophysics” under Grant No. 1922512. M. W. C. acknowledges support from the National Science Foundation with Grants No. PHY-2010970 and No. OAC-2117997. A. B. acknowledges support by the European Research Council under the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 759253, and support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project-ID 279384907—SFB 1245 and DFG—Project-ID 138713538—SFB 881 (“The Milky Way System,” subproject A10) and support by the State of Hesse within the Cluster Project ELEMENTS. The work of T. S. is supported by the State of Hesse within the Cluster Project ELEMENTS, and the Klaus Tschira Foundation. T. S. is Fellow of the International Max Planck Research School for Astronomy and Cosmic Physics at the University of Heidelberg (IMPRS-HD) and acknowledges financial support from IMPRS-HD. T. S. acknowledges support by the High Performance and Cloud Computing Group at the Zentrum für Datenverarbeitung of the University of Tübingen, the state of Baden-Württemberg through bwHPC, and the German Research Foundation (DFG) through Grant No. INST 37/935-1 FUGG. A. W. C. and J. M. contributed equally to this work.

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