Universal Relations for the Increase in the Mass and Radius of a Rotating Neutron Star

Abstract

Rotation causes an increase in a neutron star’s mass and equatorial radius. The mass and radius depend sensitively on the unknown equation of state (EOS) of cold, dense matter. However, the increases in mass and radius due to rotation are almost independent of the EOS. The EOS independence leads to the idea of neutron star universality. In this paper, we compute sequences of rotating neutron stars with constant central density. We use a collection of randomly generated EOSs to construct simple correction factors to the mass and radius computed from the equations of hydrostatic equilibrium for nonrotating neutron stars. The correction factors depend only on the nonrotating star’s mass and radius and are almost independent of the EOS. This makes it computationally inexpensive to include observations of rotating neutron stars in EOS inference codes. We also construct a mapping from the measured mass and radius of a rotating neutron star to a corresponding nonrotating star. The mapping makes it possible to construct a zero-spin mass–radius curve if the masses and radii of many neutron stars with different spins are measured. We show that the changes in polar and equatorial radii are symmetric, in that the polar radius shrinks at the same rate in which the equatorial radius grows. This symmetry is related to the observation that the equatorial compactness (the ratio of mass to radius) is almost constant on one of the constant-density sequences.

On the Maximum Mass and Oblateness of Rotating Neutron Stars with Generic Equations of State

“…We next employ our large set of rotating-star models to assess the validity of other quasi-universal relations, and we start by reporting a novel quasi-universal relation found for the surface oblateness, i.e., the ratio between the polar and equatorial proper radii, R p /R e , along the critical line. This ratio is obviously unity in the case of nonrotating stars and decreases as the angular momentum is increased, since the equatorial radius becomes larger and the quadrupolar deformation of the star increases (see also Frieben & Rezzolla 2012;Konstantinou & Morsink 2022;Gao et al 2023, for different but equally interesting relations). The result of our analysis in this case is presented in Figure 3, which is logically similar to Figure 2, but now for the ratio R p /R e .…”

“…Our incomplete knowledge of the EOS is partially compensated by a number of quasi-universal, i.e., essentially EOS-independent, relations that have been found among certain neutron-star quantities over the years, in terms of both isolated rotating and nonrotating stars (see, e.g., Yagi & Yunes 2013;Chakrabarti et al 2014;Doneva et al 2014;Haskell et al 2014;Pappas & Apostolatos 2014;Breu & Rezzolla 2016;Weih et al 2018;Konstantinou & Morsink 2022;Nath et al 2023) and the gravitational-wave signal from binary systems (see, e.g., Bauswein & Janka 2012;Read et al 2013;Bernuzzi et al 2014;Takami et al 2015;Rezzolla & Takami 2016;Bauswein et al 2019;Most et al 2019;Weih et al 2020;Gonzalez et al 2023); see Yagi & Yunes (2017) for a review. Clearly, the robustness of these quasi-universal relations depends on the number of EOSs that are employed in determining the relations.…”

“…Once the EOS ensemble has been generated, the corresponding models for rotating stars are constructed with the RNS code (Stergioulas & Friedman 1995). In particular, we solve for stationary and axisymmetric equilibrium solutions of uniformly rotating perfect fluids with varying central densities along sequences of constant angular momentum between J = 0 and J = J Kep , where J Kep is the Keplerian (or "mass-shedding") angular momentum and is a function of n c (see also Konstantinou & Morsink 2022;Jie et al 2023, for similar analyses with a much smaller set of EOSs). The set of stellar models having J = J Kep is also referred to as the Keplerian limit because along this sequence the angular velocity is the largest possible; any increase in the angular momentum at constant central density would lead to a shedding of mass at the equator.…”

Neutron stars in scalar torsion theories with non minimal coupling

“…We'll now use the universal relations established in [94] to estimate how rotation affects the mass of the NS. These relations offer formulas for the fractional increase in mass and radius of a rotating star, based on its rotational frequency and the properties of its non-rotating equivalent.…”

Confronting Strange Stars with Compact-Star Observations and New Physics

“…a new massive compact star with a mass of 2.35 ± 0.17 M was reported recently (PSR J0952-0607)[165]. It is one of the fastest-spinning pulsars with a spin period of 1.41 ms, and the rotation effects on the mass and radius cannot be ignored for this star[166]. 5 in the weak-field limit, a Yukawa term also appears in alternative theories of gravity such as f(R), the nonsymmetric gravitational theory, and modified gravity[6].…”