Rotating protoneutron stars: Spin evolution, maximum mass, and I-Love-Q relations

Abstract

Shortly after its birth in a gravitational collapse, a protoneutron star enters in a phase of quasistationary evolution characterized by large gradients of the thermodynamical variables and intense neutrino emission. In a few tens of seconds, the gradients smooth out while the star contracts and cools down, until it becomes a neutron star. In this paper we study this phase of the protoneutron star life including rotation, and employing finite-temperature equations of state. We model the evolution of the rotation rate, and determine the relevant quantities characterizing the star. Our results show that an isolated neutron star cannot reach, at the end of the evolution, the maximum values of mass and rotation rate allowed by the zero-temperature equation of state. Moreover, a mature neutron star evolved in isolation cannot rotate too rapidly, even if it is born from a protoneutron star rotating at the mass-shedding limit. We also show that the I-Love-Q relations are violated in the first second of life, but they are satisfied as soon as the entropy gradients smooth out.

From macro to micro: universal properties of neutron stars

“…The main result point out that the EoS independence relies on the assumption that the star is modeled by isodensity contours which are self-similar ellipsoids, with large variations of the eccentricity being able to destroy the universality. This idea has also been corroborated by a different study carried out on hot proto-neutron stars, showing that the I-Love-Q lose their validity when entropy gradients are active inside the star, which reflect in considerable changes of the ellipticity of the isodensity contours [19].…”

“…Although some finite-temperature EoS have been considered [5,6], they have been treated as barotropic, assuming a uniform temperature of T = 10 9 K. Such configurations yield a good picture of the star only 1 minute after the supernova explosion. This scenario has been extended in [19], in which newly-born neutron stars were stud-…”

“…Confirmed in [10], these relations have been deeply analysed to assess their domain of validity, considering highly dynamical binaries close the coalescence [11], strong magnetic fields [12], fast rotating objects, [13,14,15,16,17,18], and newly-born proto-neutron stars [19]. Moreover, similar universal relations have been discovered for higher order multipole moments [13,17,16,18,20], tidal coefficients of NS binaries [21], other physical quantities [11,22,23], and in different classes of theories, alternative to GR [24,25,26,27,28,29].…”

“…From macro to micro Andrea Maselli Figure 9: Ellipticity of the isodensity contours normalised to the star rotation rate, as function of the equatorial radius, at different times of the star evolution after the bounce (taken from [19]). …”

Critical mass, moment of inertia and universal relations of rapidly rotating neutron stars with exotic matter

“…Finally in Fig 8, we show the variation of the normalised moment of inertia for the rest mass sequences I, II, III and IV of Fig 2b. Fixed rest mass sequence has also been used by Martinon et al 51 to study quasistationary evolution of I-Love-Q universal relations for a particular EoS. In Fig 8a, we note I/M R 2 changes appreciably with EoS for supra-massive sequences, however is practically independent of EoS for normal sequence (1.92M solar rest mass).…”