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  • Review Article
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Gravitational-wave and X-ray probes of the neutron star equation of state

Nature Reviews Physics volume 4, pages 237–246 (2022)Cite this article

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Abstract

The physics of neutron stars is a remarkable combination of Einstein’s theory of general relativity and nuclear physics. Their interiors harbour extreme matter that cannot be probed in the laboratory. At such high densities and pressures, their cores may consist predominantly of exotic matter, such as free quarks or hyperons. Observations from the Laser Interferometer Gravitational-Wave Observatory (LIGO) and other gravitational-wave interferometers and X-ray observations from the Neutron Star Interior Composition Explorer (NICER) are beginning to provide information about neutron star cores and, therefore, about the mechanisms that make such objects possible. In this Review, we discuss what has been learned so far about the physics of neutron stars from gravitational-wave and X-ray observations. We focus on what has been observed with certainty and what should be observable in the near future, emphasizing the physical understanding that these new observations will bring.

Key points

  • The processes at play inside neutron stars are a combination of general relativity, quantum mechanics, particle physics and nuclear physics effects that cannot be replicated in the lab.

  • Gravitational-wave observations of binary neutron star mergers are beginning to provide information about the equation of state of supranuclear matter through constraints on the tidal deformability of neutron stars.

  • The X-rays emitted by hotspots on the surface of certain pulsars are starting to provide information about nuclear physics through constraints on the radius of neutron stars.

  • Future observations of gravitational waves and X-rays from LIGO, Virgo, Kamioka Gravitational Wave Detector (KAGRA) and the Neutron Star Interior Composition Explorer will provide unprecedented insights into the physics of neutron stars.

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Fig. 1: Schematic of the structure of a neutron star and its internal structure.
Fig. 2: Schematic representation of equations of state.
Fig. 3: Gravitational waveform from the last few cycles of a compact binary inspiral.
Fig. 4: Posterior for M and R of each component (blue and orange) of the binary system that generated GW170817.
Fig. 5: Posterior distribution of M and R of neutron stars derived from NICER observations.

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Acknowledgements

The authors thank K. Chatziioannou and J. Noronha-Hostler for carefully reading the manuscript and giving us valuable comments. N.Y. acknowledges support from National Science Foundation (NSF) grant AST award no. 2009268 and the Simons Foundation. M.C.M. acknowledges support from NASA ADAP grant 80NSSC21K0649. N.Y. and M.C.M. performed part of their work on this paper at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611. K.Y. acknowledges support from NSF grant PHY-1806776, NASA grant 80NSSC20K0523, a Sloan Foundation Research Fellowship and the Owens Family Foundation.

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Authors and Affiliations

  1. Illinois Center for Advanced Studies of the Universe, Department of Physics, University of Illinois Urbana-Champaign, Urbana, IL, USA

    Nicolás Yunes

  2. Department of Astronomy and Joint Space-Science Institute, University of Maryland, College Park, MD, USA

    M. Coleman Miller

  3. Department of Physics, University of Virginia, Charlottesville, VA, USA

    Kent Yagi

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Glossary

Supranuclear densities

Densities above nuclear saturation 2.7 × 1014 g cm−3.

Speed of sound

cs = (dp/dε)1/2, that is, the square root of the derivative of the pressure p with respect to the energy density ε.

Primary stable branch

First stable range of masses and radii in the mass–radius diagram of neutron stars where the mass increases as the central density increases.

Magnetic braking

Decrease in rotational angular momentum of a star because of the interaction of the star’s magnetic field with ejected ionized material that escapes the star and is transported along the magnetic field lines.

High-Lorentz-factor electrons

The Lorentz factor of electrons is \(\Gamma ={(1-{v}^{2}/{c}^{2})}^{-1/2}\), where v is the electron velocity and c is the speed of light. A high Lorentz factor, Γ ≫ 1, corresponds to electron velocities close to the speed of light.

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Yunes, N., Miller, M.C. & Yagi, K. Gravitational-wave and X-ray probes of the neutron star equation of state. Nat Rev Phys 4, 237–246 (2022). https://doi.org/10.1038/s42254-022-00420-y

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