Analytic I-Love-C relations for realistic neutron stars

摘要

Recent observations of neutron stars with radio, x rays, and gravitational waves have begun to constrain the equation of state for nuclear matter beyond the nuclear saturation density. To one's surprise, there exist approximate universal relations connecting certain bulk properties of neutron stars that are insensitive to the underlying equation of state and having important applications on probing fundamental physics including nuclear and gravitational physics. To date, analytic works on universal relations for realistic neutron stars are lacking, which may lead to a better understanding of the origin of the universality. Here, we focus on the universal relations between the compactness (C), the moment of inertia (I), and the tidal deformability (related to the Love number) and derive analytic, approximate I-Love-C relations. To achieve this, we construct slowly rotating and tidally deformed neutron star solutions analytically starting from an extended Tolman VII model that accurately describes nonrotating realistic neutron stars, which allows us to extract the moment of inertia and the tidal deformability on top of the compactness. We solve the field equations analytically by expanding them about the Newtonian limit and keeping up to sixth order in the stellar compactness. Based on these analytic solutions, we can mathematically demonstrate the O(10) equationof- state variation in the I-C and Love-C relations and the O(1) variation in the I-Love relation that have previously been found numerically. Our new analytic relations agree more accurately with numerical results for realistic neutron stars (especially the I-C and Love-C ones) than the analytic relations for constant-density stars derived in previous work. Based on these analytic findings, we attribute a possible origin of the universality for the I-C and Love-C relations to the fact that the energy density of realistic neutron stars can be approximated as a quadratic function, as is the case for the Tolma