## Abstract

We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform a Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that, for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars' dimensionless tidal deformabilities are determined by the binary's mass ratio q by Λ1/Λ2=q6. We investigate different choices of prior on the component masses of the neutron stars. We find that the tidal deformability and 90% credible interval is Λ=222-138+420 for a uniform component mass prior, Λ=245-151+453 for a component mass prior informed by radio observations of Galactic double neutron stars, and Λ=233-144+448 for a component mass prior informed by radio pulsars. We find a robust measurement of the common areal radius of the neutron stars across all mass priors of 8.9 13.2 km, with a mean value of =10.8 km. Our results are the first measurement of tidal deformability with a physical constraint on the star's equation of state and place the first lower bounds on the deformability and areal radii of neutron stars using gravitational waves.

Original language | English (US) |
---|---|

Article number | 091102 |

Journal | Physical Review Letters |

Volume | 121 |

Issue number | 9 |

DOIs | |

State | Published - Aug 29 2018 |

## ASJC Scopus subject areas

- Physics and Astronomy(all)

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*Physical Review Letters*,

*121*(9), [091102]. https://doi.org/10.1103/PhysRevLett.121.091102

**Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817.** / De, Soumi; Finstad, Daniel; Lattimer, James M. et al.

Research output: Contribution to journal › Article › peer-review

*Physical Review Letters*, vol. 121, no. 9, 091102. https://doi.org/10.1103/PhysRevLett.121.091102

**Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817**. In: Physical Review Letters. 2018 ; Vol. 121, No. 9.

}

TY - JOUR

T1 - Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817

AU - De, Soumi

AU - Finstad, Daniel

AU - Lattimer, James M.

AU - Brown, Duncan A.

AU - Berger, Edo

AU - Biwer, Christopher M.

N1 - Funding Information: We thank Stefan Ballmer, Swetha Bhagwat, Steven Reyes, Andrew Steiner, and Douglas Swesty for helpful discussions. We particularly thank Collin Capano and Alexander Nitz for contributing to the development of PyCBC Inference. This Letter was supported by NSF Grants No. PHY-1404395 (D.A.B., C.M.B.), No. PHY-1707954 (D.A.B., S.D.), No. PHY-1607169 (S.D.), No. AST-1559694 (D.F.), No. AST-1714498 (E.B.), and DOE Award No. DE-FG02-87ER40317 (J.M.L.). Computations were supported by Syracuse University and NSF Grant No. OAC-1541396. D.A.B., E.B., S.D., and J.M.L. thank the Kavli Institute for Theoretical Physics which is supported by the NSF Grant No. PHY-1748958. The gravitational-wave data used in this Letter was obtained from the LIGO Open Science Center. Funding Information: Using Bayesian parameter estimation, we have measured the tidal deformability and common radius of the neutron stars in GW170817. Table I summarizes our findings. To compare to Ref. [1] , which reports a 90% upper limit on Λ ˜ ≤ 800 under the assumption of a uniform prior on Λ ˜ , we integrate the posterior for Λ ˜ to obtain 90% upper limits on Λ ˜ . For the common EOS analyses, these are 485, 521, and 516 for the uniform, double neutron star, and Galactic neutron star component mass priors, respectively. We find that, in comparison to the unconstrained analysis, the common EOS assumption significantly reduces the median value and 90% confidence upper bound of Λ ˜ by about 28% and 19%, respectively, for all three mass priors. The difference between our common EOS results for the three mass priors is consistent with the physics of the gravitational waveform. At constant M , decreasing q causes the binary to inspiral more quickly [49] . At constant M and constant q , increasing Λ ˜ also causes the binary to inspiral more quickly, so there is a mild degeneracy between q and Λ ˜ . The uniform mass prior allows the largest range of mass ratios, so we can fit the data with a larger q and smaller Λ ˜ . The double neutron star mass prior allows the smallest range of mass ratios, and so, a larger Λ ˜ is required to fit the data, with the Galactic neutron star mass prior lying between these two cases. I 10.1103/PhysRevLett.121.091102.t1 TABLE I. Results from parameter estimation analyses using three different mass prior choices with the common EOS constraint and applying the causal minimum constraint to Λ ( m ) . We show 90% credible intervals for Λ ˜ , 90% credible intervals and systematic errors for R ^ , Bayes factors B comparing our common EOS to the unconstrained results, and the 90% upper limits on Λ ˜ . Mass prior Λ ˜ R ^ (km) B Λ ˜ 90 % Uniform 222 - 138 + 420 10.7 - 1.6 + 2.1 ± 0.2 369 < 485 Double neutron star 245 - 151 + 453 10.9 - 1.6 + 2.1 ± 0.2 125 < 521 Galactic neutron star 233 - 144 + 448 10.8 - 1.6 + 2.1 ± 0.2 612 < 516 Nevertheless, considering all analyses we performed with different mass prior choices, we find a relatively robust measurement of the common neutron star radius with a mean value ⟨ R ^ ⟩ = 10.8 km bounded above by R ^ < 13.2 km and below by R ^ > 8.9 km . Nuclear theory and experiment currently predict a somewhat smaller range by 2 km but with approximately the same centroid as our results [14,50] . A minimum radius 10.5–11 km is strongly supported by neutron matter theory [51–53] , the unitary gas [54] , and most nuclear experiments [14,50,55] . The only major nuclear experiment that could indicate radii much larger than 13 km is the PREX neutron skin measurement, but this has published error bars much larger than previous analyses based on antiproton data, charge radii of mirror nuclei, and dipole resonances. Our results are consistent with photospheric radius expansion measurements of x-ray binaries which obtain R ≈ 10 – 12 km [12,56,57] . Reference [58] found from an analysis of five neutron stars in quiescent low-mass x-ray binaries a common neutron star radius 9.4 ± 1.2 km , but systematic effects including uncertainties in interstellar absorption and the neutron stars’ atmospheric compositions are large. Other analyses have inferred 12 ± 0.7 [59] and 12.3 ± 1.8 km [60] for the radii of 1.4 M ⊙ quiescent sources. We have found that the relation q 7.48 < Λ 1 / Λ 2 < q 5.76 , in fact, completely bounds the uncertainty for the range of M relevant to GW170817, assuming m 2 > 1 M ⊙ [37] , and that no strong first-order phase transitions occur near the nuclear saturation density (i.e., the case in which m 1 is a hybrid star and m 2 is not). Analyses using this prescription, instead of the q 6 correlation, produce insignificant differences in our results [61] . Since models with the common EOS assumption are highly favored over those without this assumption, our results support the absence of a strong first-order phase transition in this mass range. In this Letter, we have shown that, for binary neutron star mergers consistent with observed double neutron star systems [38] , assuming a common EOS implies that Λ 1 / Λ 2 ≃ q 6 . We find evidence from GW170817 that favors the common EOS interpretation compared to uncorrelated deformabilities. Although previous studies have suggested that measurement of the tidal deformability is sensitive to the choice of mass prior [43] , we find that varying the mass priors does not significantly influence our conclusions, suggesting that our results are robust to the choice of mass prior. Our results support the conclusion that we find the first evidence for finite size effects using gravitational-wave observations. Recently, the LIGO/Virgo collaborations have placed new constraints on the radii of the neutron stars using GW170817 [62] . The most direct comparison is between our uniform mass prior result ( R ^ = 10.7 - 1.6 + 2.1 ± 0.2 ) and the LIGO/Virgo method that uses equation-of-state-insensitive relations [63,64] ( R 1 = 10.8 - 1.7 + 2.0 and R 2 = 10.7 - 1.5 + 2.1 km ). This result validates our approximation R 1 = R 2 used to motivate the prescription Λ 1 = q 6 Λ 2 , and Eqs. (3) , (5) . Our statistical errors are comparable to the error reported by LIGO/Virgo. Systematic errors from EOS physics of ± 0.2 km are added as conservative bounds to our statistical errors, broadening our measurement error, whereas Ref. [62] marginalized over these errors in the analysis. Reference [62] also investigates a method of directly measuring the parameters of the EOS which results in smaller measurement errors. Investigation of these differences between our analysis and the latter approach will be pursued in a future paper. Observations of future binary neutron star mergers will allow further constraints to be placed on the deformability and radius, especially if these binaries have chirp masses similar to GW170817 as radio observations suggest. As more observations improve our knowledge of the neutron star mass distribution, more precise mass-deformability correlations can be used to further constrain the star’s radius. We thank Stefan Ballmer, Swetha Bhagwat, Steven Reyes, Andrew Steiner, and Douglas Swesty for helpful discussions. We particularly thank Collin Capano and Alexander Nitz for contributing to the development of PyCBC Inference. This Letter was supported by NSF Grants No. PHY-1404395 (D. A. B., C. M. B.), No. PHY-1707954 (D. A. B., S. D.), No. PHY-1607169 (S. D.), No. AST-1559694 (D. F.), No. AST-1714498 (E. B.), and DOE Award No. DE-FG02-87ER40317 (J. M. L.). Computations were supported by Syracuse University and NSF Grant No. OAC-1541396. D. A. B., E. B., S. D., and J. M. L. thank the Kavli Institute for Theoretical Physics which is supported by the NSF Grant No. PHY-1748958. The gravitational-wave data used in this Letter was obtained from the LIGO Open Science Center. [1] 1 B. Abbott , Phys. Rev. Lett. 119 , 161101 ( 2017 ). PRLTAO 0031-9007 10.1103/PhysRevLett.119.161101 [2] 2 K. S. Thorne , in Three Hundred Years of Gravitation , edited by S. W. Hawking and W. Israel ( Cambridge University Press , Cambridge, England, 1987 ), Chap. 9, pp. 330–458 . [3] 3 J. S. Read , C. Markakis , M. 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PY - 2018/8/29

Y1 - 2018/8/29

N2 - We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform a Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that, for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars' dimensionless tidal deformabilities are determined by the binary's mass ratio q by Λ1/Λ2=q6. We investigate different choices of prior on the component masses of the neutron stars. We find that the tidal deformability and 90% credible interval is Λ=222-138+420 for a uniform component mass prior, Λ=245-151+453 for a component mass prior informed by radio observations of Galactic double neutron stars, and Λ=233-144+448 for a component mass prior informed by radio pulsars. We find a robust measurement of the common areal radius of the neutron stars across all mass priors of 8.9 13.2 km, with a mean value of =10.8 km. Our results are the first measurement of tidal deformability with a physical constraint on the star's equation of state and place the first lower bounds on the deformability and areal radii of neutron stars using gravitational waves.

AB - We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform a Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that, for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars' dimensionless tidal deformabilities are determined by the binary's mass ratio q by Λ1/Λ2=q6. We investigate different choices of prior on the component masses of the neutron stars. We find that the tidal deformability and 90% credible interval is Λ=222-138+420 for a uniform component mass prior, Λ=245-151+453 for a component mass prior informed by radio observations of Galactic double neutron stars, and Λ=233-144+448 for a component mass prior informed by radio pulsars. We find a robust measurement of the common areal radius of the neutron stars across all mass priors of 8.9 13.2 km, with a mean value of =10.8 km. Our results are the first measurement of tidal deformability with a physical constraint on the star's equation of state and place the first lower bounds on the deformability and areal radii of neutron stars using gravitational waves.

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U2 - 10.1103/PhysRevLett.121.091102

DO - 10.1103/PhysRevLett.121.091102

M3 - Article

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JF - Physical Review Letters

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