Dense Matter in Compact Stars: Theoretical Developments and Observational Constraints

Hempel

2013

A&A

Context. The Jacobi virial equation is a very powerful tool for exploring several aspects of the stellar internal structure and evolution. In a previous paper we have shown that the function αβ GR /Λ 0.9 (R) is constant (≈0.4) for pre main-sequence stars (PMS), white dwarfs (WD) and for some neutron star (NS) models, where α GR and β GR are the form-factors of the gravitational potential energy and of the moment of inertia. Aims. To investigate the structural evolution of another type of celestial bodies, we extend these calculations to gaseous planets. We also analyse the cases for which this function is not conserved during some stellar evolutionary phases. Concerning NS, we study the influence of the equation of state (EOS) on this function and refine the exponent of the auxiliary function Λ(R). We also present a macroscopic criterion of stability for these stars. Methods. Non-stop calculations from the PMS to the white dwarf cooling sequences were performed with the MESA code. The covered mass range was 0.1-1.7 M . We used the same code to compute models for gaseous planets with masses between 0.1-50 M J . Neutron star models were computed using two codes. The first one is a modified version of the NSCool/TOV subroutines. The second code is a plain TOV solver that allows one to use seven previously described EOS. The relativistic moment of inertia and gravitational potential energy were computed through a fourth-order Runge-Kutta method. Results. By analysing the internal structure of gaseous planets we show that the function αβ GR /Λ 0.8 (R) ≡ Γ(M, EOS) is conserved for all models during the whole planetary evolution and is independent of the planet mass. For the PMS to the white dwarf cooling sequences, we have found a connection between the strong variations of Γ(M, EOS) during the intermediary evolutionary phases and the specific nuclear power. A threshold for the specific nuclear power was found. Below this limit this function is invariant (≈0.4) for these models, i.e., at the initial and final stages (PMS and WD). For NS, we showed that the function Γ(M, EOS) is also invariant (≈0.4) and is independent of the EOS and of the stellar mass. Therefore, we confirm that regardless of the final products of the stellar evolution, NS or WD, they recover the initial value of Γ(M, EOS) ≈ 0.4 acquired at the PMS. Finally, we have introduced a macroscopic stability criterion for NS models based on the properties of the relativistic product αβ GR .

“…The first is a modified version of the NSCool/TOV subroutines (Page & Reddy 2006;. We computed neutron star models adopting the non-relativistic EOS by Akmal et al (1998, hereafter APR).…”

Section: Neutron Star Modelsmentioning

confidence: 99%

The internal structure of neutron stars and white dwarfs, and the Jacobi virial equation. II.

Hempel

2013

A&A

“…The neutron star models were computed with the spherically symmetric neutron star cooling code NSCool/TOV (Page & Reddy 2006;. The four differential equations -in the general relativistic framework -for the internal structure of neutron stars (mass, gravitational energy, hydrostatic equilibrium, and baryon number) were solved by a fourth order Runge-Kutta method.…”

Section: Neutron Star Modelsmentioning

confidence: 99%

The internal structure of neutron stars and white dwarfs, and the Jacobi virial equation

2012

A&A

Aims. The internal structure constants k j and the radius of gyration are useful tools for investigating the apsidal motion and tidal evolution of close binaries and planetary systems. These parameters are available for various evolutionary phases but they are scarce for the late stages of stellar evolution. To cover this gap, we present here the calculations of the apsidal-motion constants, the fractional radius of gyration, and the gravitational potential energy for two grids of cooling evolutionary sequences of white dwarfs and for neutron star models. Methods. The cooling sequences of white dwarfs were computed with LPCODE. An additional alternative to the white dwarf models was also adopted with the MESA code which allows non-stop calculations from the pre main-sequence (PMS) up to the white dwarf cooling sequences. Neutron star models were acquired from the NSCool/TOV subroutines. The apsidal-motion constants, the moment of inertia, and the gravitational potential energy were computed with a fourth-order Runge-Kutta method. Results. The parameters are made available for four cooling sequences of white dwarfs (DA and DB types): 0.52, 0.57, 0.837 and 1.0 M and for neutron star models covering a mass range from 1.0 up to 2.183 M , in 0.1 mass step. We show that, contrary to previously established opinion, the product of the form-factors β and α, which are related to the moment of inertia, and gravitational potential energy, is not constant during some evolutionary phases. Regardless of the final products of stellar evolution (white dwarfs, neutron stars and perhaps black holes), we found that they recover the initial value of product αβ at the pre main-sequence phase (≈0.4). These results may have important consequences for the investigation of the Jacobi virial equation.

“…The NS models were computed using the NSCool/TOV subroutines (Page & Reddy 2006;Page et al 2006, see Figs. 1 and 2).…”

Section: Testing the Invariance Of γ(M Eos) For Neutronmentioning

confidence: 99%

Neutron, quark, and proto-neutron stars at the onset of formation of black-holes: the memory effect

2014

A&A

Context. In previous papers it was shown that the function Γ(M, EOS) ≡ αβ GR /Λ 0.8 (R) is invariant (≈0.40) for pre main-sequence stars (PMS), white dwarfs (WD), and for neutron stars (NS) computed with equations of state using relativistic mean-field nucleon interactions. The form-factors α GR and β GR are related to the relativistic gravitational potential energy and the moment of inertia and are a key to handling the Jacobi virial equation, which is a powerful tool for investigating the stellar internal structure and evolution. We also found that Γ(M, EOS) is invariant for gaseous planets. Moreover, a macroscopic criterion of stability for NS was derived. Aims. To test if the invariance of Γ(M, EOS) also holds for an equation of state (EOS) in the non-relativistic framework, we compute NS models by adopting four different EOS prescriptions. We also computed models for hybrid and pure quark stars to extend the range of validity of the Γ(M, EOS) memory effect. To complete the three known final scenarios for stellar evolution, we follow the core-collapse supernova until the onset of formation of a black hole. Methods. Calculations from the PMS up to the WD stages were performed using the MESA code. Neutron, hybrid, and pure quark star models were computed using a modified version of the NSCool/TOV subroutines. The core-collapse supernova simulation was carried out using the code AGILE-IDSA. The relativistic moment of inertia and gravitational potential energy were computed through a fourth-order Runge-Kutta method. Results. We confirm that the function Γ(M, EOS) is invariant for PMS, WD, NS, hybrid, and pure quark stars and is independent of the mass and of the EOS (relativistic and non-relativistic frameworks). We show that our macroscopic criterion of stability is also valid for all mentioned compact stars. In a core-collapse supernova simulation, the PMS value of Γ(M, EOS) is recovered at the onset of formation of a black hole. Therefore, we conclude that, regardless of the final products of the stellar evolution, white dwarfs, neutron/hybrid/quark stars or proto-neutron star at the onset of formation of a black hole, they present a memory effect and recover the fossil value of Γ(M, EOS) ≈ 0.40, acquired during the PMS. Finally, we have shown the invariance of Γ(M, EOS) for earth-like planets as well.