Neutron Star Structure Parameter Space

We understand simple systems of Standard Model particles at almost any scale, but the physics of the complex condensed matter system of a neutron star is far less well understood. 

A new study, however, argues that the end product of the analysis of that complex condensed matter system, called its "Equation of State" can be summarized well with just three observable properties of neutron stars. Observation basically confine this parameter space to the portion of the area surrounded by the thick solid black line near the center of the chart below that is not ruled out on other grounds shown. The paper summarizes the evidence supporting these bounds on neutron star parameters.

Numerous models of neutron star (NS) equation of state (EoS) exist based on different superdense-matter physics approaches. Nevertheless, some NS properties show universal (EoS-independent) relations. Here, we propose a novel class of such universalities. Despite different physics inputs, a wide class of realistic nucleonic, hyperonic, and hybrid EoS models can be accurately described using only three parameters. For a given EoS, these are the mass and radius of the maximum-mass NS (or pressure and density in its center) and the radius of a half-maximum-mass star. With such a parametrization, we build universal analytic expressions for mass-radius and pressure-density relations. They form a semi-analytic mapping from the mass-radius relation to the EoS in NS cores (the so-called inverse Oppenheimer-Volkoff mapping). This mapping simplifies the process of inferring the EoS from observations of NS masses and radii. Applying it to current NS observations we set new limits on the high end of the EoS.

Dmitry D. Ofengeim, Peter S. Shternin, Tsvi Piran, "A three-parameter characterization of neutron stars' mass-radius relation and equation of state" arXiv:2404.17647 (April 26, 2024). The body text clarifies that:

One of the most intriguing problems of modern physics is to unveil the mystery of the neutron star (NS) equation of state (EoS, pressure P − density ρ relation). One of the few ways to study it is to measure NS masses M andradii R. As the star is in hydrostatic equilibrium, its EoS determines the M − R relation. Inverting this relation, we can find the EoS. Non-rotating NS hydrostatics is described by the Tolman-Oppenheimer-Volkoff (TOV) equations. The Oppenheimer-Volkoff (OV) mapping from the P − ρ to M − R is a bijection, i.e., there exists inverse OV mapping (IOVM). Thus unambiguous finding of EoS from M and R observations is, in principle, possible. Additionally, a maximum-mass NS (MMNS) exists regardless of the EoS model used. The MMNS characteristics, such as mass Mtov, radius Rtov, pressure Ptov, density ρtov in the center, etc., are specific for a given EoS. 

While the true NS EoS is unique, there are hundreds of various theoretical EoS models present in the literature. Each yields its own M −R, M — central ρ and P relations and, in particular, its own Mtov, Rtov, ρtov, and Ptov. Nevertheless, it has been known for a long time that some relations between various NS properties are universal across the EoS manifold. Some of these relations, like the I-Love-Q relation, originate from a unifying ability of relativistic gravity and are very accurate for almost all existing models of EoS. Others are less precise and exist due to some common features of a subclass of EoSs, which are considered to be “realistic”.

The one-dimensional 68% credible intervals for the key parameters of the approximations (1)— (4) are[:]

M(tov) = 2.28+0.05 −0.06 M⊙, 

R(tov) = 11.2+0.4 −0.3 km, 

R(1/2) = 12.0+0.4 −0.3 km, 

ρ(tov) = 7.7+0.6 −0.3 ρ0, and 

P(tov) = 3.5+1.0 −0.4 ρ0c2.

The boundaries on the maximum neutron star mass are known with roughly ± 2% precision, and the maximum and half-maximum mass neutron star radii are known with roughly ± 4% precision.