Analytical representations of unified equations of state of neutron star matter

Introduction

The equation of state (EOS) of dense matter is a crucial input for the neutron-star structure calculations. Under standard conditions neutron-star matter is strongly degenerate, and therefore the matter pressure is temperature independent; exceptions are the outermost (a few meters thick) envelopes, newly-born neutron stars, and the envelopes of exploding X-ray bursters. At density rho > 108 g cm-3 the EOS is not affected by the magnetic field even as strong as 1014 G and by the temperature T<109 K. Therefore, except for a thin outer envelope, the EOS of neutron-star matter has a one-parameter character. In order to determine the neutron-star structure up to the maximum allowable mass, one has to know the EOS up to a few times 1015 g cm-3.

A "unified EOS" is obtained in the many-body calculations based on a single effective nuclear Hamiltonian, and is valid in all regions of the neutron star interior. For unified EOSs the transitions between the outer crust and the inner crust, and between the inner crust and the core are obtained as a result of many-body calculation. Alas, up to now only a few models of unified EOSs have been constructed. All other EOSs consist of crust and core segments obtained using different physical models. The crust-core interface has there no physical meaning and both segments are joined using an ad hoc matching procedure.

Analytical representations of the EOSs have two important advantages over the tabulated ones. First, there is no ambiguity of interpolation and the derivatives can be precisely calculated. Second, these representations can be constructed fulfilling exactly the thermodynamic relations. In this way, analytical EOSs can allow for a very high precision of neutron star structure calculation in the 2D and 3D cases.

We have derived analytical representations for six unified EOSs: BSk19, BSk20, BSk21 [1,2,3], and BSk22, BSk24, BSk25, BSk26 [4,5]. Here we present computer subroutines in Fortran that realize these representations.

References

  1. J. M. Pearson, S. Goriely, & N. Chamel: Properties of the outer crust of neutron stars from Hartree-Fock-Bogoliubov mass models, Phys. Rev. C 83, 065810 (2011)
  2. J. M. Pearson, N. Chamel, S. Goriely, & C. Ducoin: Inner crust of neutron stars with mass-fitted Skyrme functionals, Phys. Rev. C 85, 065803 (2012) [arXiv:1206.0205]
  3. A. Y. Potekhin, A. F. Fantina, N. Chamel, J. M. Pearson, & S. Goriely: Analytical representations of unified equations of state for neutron-star matter, Astron. Astrophys. 560, A48 (2013) [arXiv:1310.0049]
  4. S. Goriely, N. Chamel, & J. M. Pearson: Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XIII. The 2012 atomic mass evaluation and the symmetry coefficient, Phys. Rev. C 88, 024308 (2013)
  5. J. M. Pearson, N. Chamel, A. Y. Potekhin, A. F. Fantina, C. Ducoin, A.K. Dutta, & S. Goriely: Unified equations of state for cold nonaccreting neutron stars with Brussels-Montreal functionals. I. Role of symmetry energy, Mon. Not. R. Astr. Soc. 481, 2994 (2018); Erratum (2019, Mon. Not. R. Astr. Soc. 486, 768) is taken into account in this PDF file.

Basic references
Please cite while using the present fits in a publication

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EOS fitting subroutines

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Page created on July 20, 2012 by Alexander Potekhin.
Last update: 26.06.2019.