# Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817

## Abstract

In this study, 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 Λ _{1}/Λ _{2} = q ^{6}. 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$$+420\atop{-138}$$ for a uniform component mass prior, ˜Λ = 245$$+453\atop{-151}$$ for a component mass prior informed by radio observations of Galactic double neutron stars, and ˜Λ = 233$$+448\atop{-144}$$ 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 ≤ $$\hat{R}$$ ≤ 13.2 km , with a mean value of <$$\hat{R}$$> = 10.8 km . Finally, 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.

- Authors:

- Syracuse Univ., NY (United States)
- Stony Brook Univ., NY (United States)
- Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States)
- Syracuse Univ., NY (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE; National Science Foundation (NSF)

- OSTI Identifier:
- 1484643

- Alternate Identifier(s):
- OSTI ID: 1467957

- Report Number(s):
- LA-UR-18-23911

Journal ID: ISSN 0031-9007; PRLTAO

- Grant/Contract Number:
- 89233218CNA000001; FG02-87ER40317

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 121; Journal Issue: 9; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS

### Citation Formats

```
De, Soumi, Finstad, Daniel, Lattimer, James, Brown, Duncan A., Berger, Edo, and Biwer, Christopher Michael. Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817. United States: N. p., 2018.
Web. doi:10.1103/PhysRevLett.121.091102.
```

```
De, Soumi, Finstad, Daniel, Lattimer, James, Brown, Duncan A., Berger, Edo, & Biwer, Christopher Michael. Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817. United States. doi:10.1103/PhysRevLett.121.091102.
```

```
De, Soumi, Finstad, Daniel, Lattimer, James, Brown, Duncan A., Berger, Edo, and Biwer, Christopher Michael. Wed .
"Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817". United States. doi:10.1103/PhysRevLett.121.091102. https://www.osti.gov/servlets/purl/1484643.
```

```
@article{osti_1484643,
```

title = {Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817},

author = {De, Soumi and Finstad, Daniel and Lattimer, James and Brown, Duncan A. and Berger, Edo and Biwer, Christopher Michael},

abstractNote = {In this study, 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$+420\atop{-138}$ for a uniform component mass prior, ˜Λ = 245$+453\atop{-151}$ for a component mass prior informed by radio observations of Galactic double neutron stars, and ˜Λ = 233$+448\atop{-144}$ 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 ≤ $\hat{R}$ ≤ 13.2 km , with a mean value of <$\hat{R}$> = 10.8 km . Finally, 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.},

doi = {10.1103/PhysRevLett.121.091102},

journal = {Physical Review Letters},

number = 9,

volume = 121,

place = {United States},

year = {2018},

month = {8}

}

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#### Figures / Tables:

*m*) that are shown as points colored by their radii

*R*. Dashed curves are lower bounds to Λ formore »

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*