The effect of the energy functional on the pasta-phase properties of catalysed neutron stars

Thi, Hoa Dinh; Fantina, Anthea; Gulminelli, F.

doi:10.1140/epja/s10050-021-00605-6

Cited by 17 publications

(9 citation statements)

References 65 publications

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“…However, in realistic models of crust the filling factor for spherical nuclei is u 0.2 and spherical Wigner-Seitz cell seems a reasonable approximation, but we don't check the latter statement straightforwardly. We also warn that we neglect the curvature corrections to the surface tension, which shown to be important for thermodynamically determined boundaries of the pasta layers (e.g., [29]), however, we don't expect that it can affect our results qualitatively. the proton charge density inside nucleus, ρ e = −uρ pi is the electron charge density (the cell is electrically neutral).…”

Section: Discussion Results and Conclusionmentioning

confidence: 91%

Stability of Spherical Nuclei in the Inner Crust of Neutron Stars

Chugunov

2022

Particles

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Neutron stars are the densest objects in the Universe. In this paper, we consider the so-called inner crust—the layer where neutron-excess nuclei are immersed in the degenerate gas of electrons and a sea of quasi-free neutrons. It was generally believed that spherical nuclei become unstable with respect to quadrupole deformations at high densities, and here, we consider this instability. Within the perturbative approach, we show that spherical nuclei with equilibrium number density are, in fact, stable with respect to infinitesimal quadrupole deformation. This is due to the background of degenerate electrons and associated electrostatic potential, which maintain stability of spherical nuclei. However, if the number of atomic nuclei per unit volume is much less than the equilibrium value, instability can arise. To avoid confusion, we stress that our results are limited to infinitesimal deformations and do not guarantee strict thermodynamic stability of spherical nuclei. In particular, they do not exclude that substantially non-spherical nuclei (so-called pasta phase) represent a thermodynamic equilibrium state of the densest layers of the neutron star crust. Rather, our results point out that spherical nuclei can be metastable even if they are not energetically favourable, and the timescale of transformation of spherical nuclei to the pasta phases should be estimated subsequently.

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Section: Discussion Results and Conclusionmentioning

confidence: 91%

Stability of Spherical Nuclei in the Inner Crust of Neutron Stars

Chugunov

2022

Particles

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“…To compare our results with previous works, in Figure 3, we demonstrate the transverse shear modulus, normalized to the Coulomb energy density in the non-deformed state w 0 C (see Equation (11) for ε = ε p = 0) as a function of filling factor u. The solid line represents our final expression (16), while the long-dashed line is for Equation (17) ignoring the change in the cross-section shape. The latter agrees well with the fit provided in Ref.…”

Section: Resultsmentioning

confidence: 84%

“…Thus, to illustrate our results in physical units (see Figure 4), we use a rather wide n b region; following [19], we applied the SLy4 nucleon interaction model for numerical estimates. As in Figure 3, the solid line represents our final expression (16), while the long-dashed line is for Equation (17), which ignores the change in the cross-section shape. Short dashes correspond to the fit provided in Ref.…”

Section: Resultsmentioning

confidence: 99%

The Elasticity of the Neutron Star Mantle: The Improved Compressible Liquid Drop Model for Cylindrical Phases

Chugunov

2023

Universe

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Neutron stars are the densest objects in the Universe. They have a microscopically homogeneous core and heterogeneous crust. In particular, there may be a specific layer inside neutron stars, the mantle, which consists of substantially non-spherical nuclei immersed in a background of relativistic degenerate electrons and quasi-free neutrons. In this paper, we reconsider the transverse shear modulus for cylindrical phases of the mantle within the framework of the compressible liquid drop model. We demonstrate that transverse shearing affects the shape of nuclear clusters: their cross-section becomes elliptical. This effect reduces the respective elastic constant. Using a simple model, we perform all derivations analytically and obtain the expression for the transverse shear modulus, which can be useful for astrophysical applications.

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“…In order to describe the nuclear energetics, we employed a compressible liquid-drop (CLD) model approach, as in Carreau et al (2019), Carreau et al (2020a), Dinh Thi et al (2021a), and Dinh Thi et al (2021b, which describes the ion as a cluster of nucleons in a leptodermous expansion. Considering the inner crust in the liquid phase, the collective degrees of freedom are translational, meaning that F i in Eq.…”

Section: Model Of the Inner Crust At Finite Temperaturementioning

confidence: 99%

“…In this paper, we carry out a study of the effect of the inclusion of translational degrees of freedom on the equation of state and the composition of matter in the liquid phase in the density regime relevant to the inner crust of the (proto-)NS. We employed the formalism of Carreau et al (2019), Carreau et al (2020a), Dinh Thi et al (2021a), Dinh Thi et al (2021b), and Grams et al (2022a that, although not as microscopic as a full density functional treatment, was recently shown to provide results in good agreement with extended Thomas-Fermi calculations both at zero (Grams et al 2022b) and finite temperature (Carreau et al 2020a). This approach is extended here to include the possible presence of proton drip and to compute the exact numerical calculation of the Fermi integrals beyond the Sommerfeld approximation previously used in Carreau et al (2020a).…”

Section: Introductionmentioning

confidence: 99%

The proto-neutron star inner crust in the liquid phase

Thi

Fantina

Gulminelli

2023

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Context. The crust of a neutron star is known to melt at a temperature that increases with increasing matter density, up to about 1010 K. At such high temperatures and beyond, the crustal ions are put into collective motion and the associated entropy contribution can affect both the thermodynamic properties and the composition of matter. Aims. We studied the importance of this effect in different thermodynamic conditions relevant to the inner crust of the proto-neutron star, both at beta equilibrium and in the fixed-proton-fraction regime. Methods. To this aim, we solved the hydrodynamic equations for an ion moving in an incompressible, irrotational, and non-viscous fluid, with different boundary conditions, thus leading to different prescriptions for the ion effective mass. We then employed a compressible liquid-drop approach in the one-component plasma approximation, including the renormalisation of the ion mass to account for the influence of the surrounding medium. Results. We show that the cluster size is determined by the competition between the ion centre-of-mass motion and the interface properties, namely the Coulomb, surface, and curvature energies. In particular, including the translational free energy in the minimisation procedure can significantly reduce the optimal number of nucleons in the clusters and lead to an early dissolution of clusters in dense beta-equilibrated matter. On the other hand, we find that the impact of translational motion is reduced in scenarios where the proton fraction is assumed constant and is almost negligible on the inner-crust equation of state. Conclusions. Our results show that the translational degrees of freedom affect the equilibrium composition of beta-equilibrated matter and the density and pressure of the crust-core transition in a non-negligible way, highlighting the importance of its inclusion when modelling the finite-temperature inner crust of the (proto-)neutron star.

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The effect of the energy functional on the pasta-phase properties of catalysed neutron stars

Cited by 17 publications

References 65 publications

Stability of Spherical Nuclei in the Inner Crust of Neutron Stars

Stability of Spherical Nuclei in the Inner Crust of Neutron Stars

The Elasticity of the Neutron Star Mantle: The Improved Compressible Liquid Drop Model for Cylindrical Phases

The proto-neutron star inner crust in the liquid phase

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