Neutron Star Observations: Prognosis for Equation of State Constraints

TL;DR

This paper assesses how current and forthcoming observations of neutron stars—across electromagnetic, neutrino, and gravitational-wave channels—can constrain the dense-matter equation of state, focusing on the maximum mass and typical radius as primary indicators. It blends general-relativistic structure theory with a survey of observational probes (mass measurements, radius proxies from thermal emission and bursts, crustal phenomena, cooling behavior, QPOs, and gravitational waves from mergers) and links these to the symmetry energy and its density dependence near nuclear saturation. Key contributions include quantifying relativistic bounds on mass, radius, and central density; detailing crustal constraints from glitches and seismology; analyzing cooling sensitivities to composition and superfluidity; and outlining how gravitational waves and proto-neutron-star neutrinos can reveal high-density EOS features, including potential differences between normal and self-bound (strange-quark) stars. The work emphasizes that multiple, complementary observables are necessary to narrow the EOS, with laboratory data (mass measurements, neutron skins, giant resonances, and heavy-ion collisions) providing essential terrestrial constraints that sharpen astrophysical inferences.

Abstract

We investigate how current and proposed observations of neutron stars can lead to an understanding of the state of their interiors and the key unknowns: the typical neutron star radius and the neutron star maximum mass. A theoretical analysis of neutron star structure, including general relativistic limits to mass, compactness, and spin rates is made. We consider observations made not only with photons, ranging from radio waves to X-rays, but also those involving neutrinos and gravity waves. We detail how precision determinations of structural properties would lead to significant restrictions on the poorly understood equation of state near and beyond the equilibrium density of nuclear matter.

Figures (19)

• Figure 1: The maximum mass - central density relation predicted by causality coupled with the Tolman VII and Tolman IV analytic GR solutions are compared with structure integration results for a variety of EOSs. NR refers to non-relativistic potential EOSs, R refers to relativistic field-theoretical EOSs, and Exotica refers to EOSs with considerable softening at high density due to kaon condensation or strange quark matter deconfinement. A possible redshift measurement of $z=0.35$ is also shown. Figure taken from. Ref. LP05.
• Figure 2: Mass-radius trajectories for typical EOSs (see LP01 for notation) are shown as black curves. Green curves (SQM1, SQM3) are self-bound quark stars. Orange lines are contours of radiation radius, $R_\infty=R/\sqrt{1-2GM/Rc^2}$. The dark blue region is excluded by the GR constraint $R>2GM/c^2$, the light blue region is excluded by the finite pressure constraint $R>(9/4)GM/c^2$, and the green region is excluded by causality, $R>2.9GM/c^2$. The light green region shows the region $R>R_{max}$ excluded by the 716 Hz pulsar J1748-2446ad Hessels06 using Eq. (\ref{['pmin1']}). The upper red dashed curve is the corresponding rotational limit for the 1122 Hz X-ray source XTE J1739-285 Kaaret06; the lower blue dashed curve is the rogorous causal limit using the coefficient 0.74 ms in Eq. (\ref{['pmin1']}).
• Figure 3: Measured and estimated masses of neutron stars in radio binary pulsars (gold, silver and blue regions) and in x-ray accreting binaries (green). For each region, simple averages are shown as dotted lines; weighted averages are shown as dashed lines. The labels (a) = Clark02 through (C) = Nice99 are references cited in the bibliography. For the stars with references z-C, a lower limit to the pulsar mass of 1 M$_\odot$ was assumed.
• Figure 4: Empirical demonstration of the constancy $Rp_*^{-1/4}$, for 1 M$_\odot$ (upper panel) and 1.4 M$_\odot$ (lower panel) stars. For each mass, 3 fiducial number densities are selected. Figure and EOS labels are from reference LP01.
• Figure 5: Contours of enthalpy ${\cal H}_t$, transition density $n_t/n_s$, and pressure $p_t$ are displayed as functions of $S_v$ and the logarithmic derivative of $E_{sym}$ at $n_s$ for the simple model described by Eq. (\ref{['vs']}).