Approximate universal relations for neutron stars and quark stars

Abstract

Neutron stars and quark stars are ideal laboratories to study fundamental physics at supra nuclear densities and strong gravitational fields. Astrophysical observables, however, depend strongly on the star's internal structure, which is currently unknown due to uncertainties in the equation of state. Universal relations, however, exist among certain stellar observables that do not depend sensitively on the star's internal structure. One such set of relations is between the star's moment of inertia (I), its tidal Love number (Love) and its quadrupole moment (Q), the so-called I-Love-Q relations. Similar relations hold among the star's multipole moments, which resemble the well-known black hole no-hair theorems. Universal relations break degeneracies among astrophysical observables, leading to a variety of applications: (i) X-ray measurements of the nuclear matter equation of state, (ii) gravitational wave measurements of the intrinsic spin of inspiraling compact objects, and (iii) gravitational and astrophysical tests of General Relativity that are independent of the equation of state. We here review how the universal relations come about and all the applications that have been devised to date. Contents 3.2.

Studying strong phase transitions in neutron stars with gravitational waves

“…The different color maps correspond to different types of binaries with each EoS: 'HH" -two hadronic stars, "HQ" -one hadronic and one hybrid star, "QQ" -two hybrid stars. In all cases, purely hadronic binaries ("HH") have a radius bias of less than 500 m, which is consistent with the quoted systematic error in the EoS-insensitive relations [75,80]. This is most evident on the left panel for the purely hadronic DBHF EoS: all BNSs have a radius error of less than ∼ 0.4 km.…”

“…The second relation expresses the compactness of a star as a function of its tidal deformability C i (Λ i ) [74] and can be used to compute the radius through R i = m i /C i (Λ i ). An improved fit with more data has been presented in [80] results of which are utilized in the following. In summary, we use the GW data to measure the component masses and the effective tidal deformability.…”

Scalarization of neutron stars with realistic equations of state

“…Clearly, the compactness of the solutions is a major component in our understanding of the phenomenon of scalarization [10,11], and compactness features prominently in various model-independent relations [28,29]. In particular, we have confirmed and extended the results of the universal I-C relations [30,31,22].…”

Gravitational Wave Signatures of Crystalline Color Superconductors

“…Besides being directly related to gravitational-wave observations, the tidal deformability of compact stars has also been gaining a lot of attention because of the discovery of the universal I-Love-Q relations connecting the moment of inertia I, the tidal deformability λ (also called the Love number), and the spin-induced quadrupole moment Q [18,19] (see [20] for a review). In contrast to the massradius relation of compact stars, which depends sensitively on the EOS, the I-Love-Q relations are said to be universal because they are approximately EOS independent to about 1% level.…”