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Analytical EoSs of Neutron Star Matter

These analytical representations are designed for older equations of state FPS, SLy4, and APR.
For newer equations of state BSk19-20-21-22-24-25, see this http URL.

For other EOSs, see this collection of links.


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. While the EoS of the neutron-star crust (rho < (1-2)*1014 g cm-3) is rather well known [1], the EoS of the liquid stellar core remains uncertain (e.g., [2]).

The EoS of the crust depends on the crust formation scenario. Two limiting cases are: cold catalyzed matter being at the ground state at a fixed baryon density, and the accreted crust formed via compression from the thermonuclear ashes of the X-ray bursts in the outer envelopes of accreting neutron stars. The EoS of the liquid core does not depend on the formation scenario.

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. Here we consider two unified EoSs: FPS [3] and SLy [4].

EoSs are usually given in the form of tables. Therefore, in order to use them, one has to employ interpolation between the tabulated points. Interpolation implies ambiguity: the interpolation procedure is not unique. This introduces ambiguities in the calculated parameters of the neutron star models. Moreover, interpolation should be done respecting exact thermodynamic relations. This turned out to be a particularly serious problem in the high-precision 2D calculations of models of rapidly rotating neutron stars. In the 3D calculations of the stationary configurations of a close binary neutron-star system one needs derivatives of pressure with respect to the enthalpy, and tabulated non-polytropic EoSs are not useful in this respect.

In view of the deficiencies and ambiguities inherent in the tabulated EoSs, which are particularly serious in the case of matched EoSs, it is of great interest to derive analytical representations of the EoSs. They 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 of the unified FPS and SLy EoSs. They are described and discussed in the paper (Haensel & Potekhin, 2004) listed below. Here we present computer subroutines in Fortran and C++ that realize these representations.

In addition, the Fortran subroutines also present analogous fits for a nonunified EoS, composed of the SLy4 EoS in the crust and the APR A18+δv+UIX* EoS [5] in the core.


Basic references

to be cited while using in a publication the results or subroutines presented at this Web site:

Other most relevant references:
  1. P. Haensel (2001). "Neutron Star Crusts," in Physics of Neutron Star Interiors, ed. D. Blaschke, N. K. Glendenning, A. Sedrakian, Lecture Notes in Physics, 578 (Heidelberg: Springer), 127 [PDF file (535 K)]
  2. P. Haensel (2003). "Equation of State of Dense Matter and Maximum Mass of Neutron Stars," in Final Stages of Stellar Evolution, ed. C. Motch, J.-M. Hameury, EAS Publications Ser., 7 (Les Ulis: EDP), 249 (arXiv:astro-ph/0301073)
  3. V.R. Pandharipande, D.G. Ravenhall (1989). "Hot Nuclear Matter," in Nuclear Matter and Heavy Ion Collisions, NATO ADS Ser., B205, ed. M. Soyeur, H. Flocard, B. Tamain, M. Porneuf (New York: Plenum), 103
  4. F. Douchin, P. Haensel (2001). "A unified equation of state of dense matter and neutron star structure," Astron. Astrophys. 380, 151 [gzipped PostScript file (262 K)]
  5. A. Akmal, V. R. Pandharipande, D. G. Ravenhall (1998). "Equation of state of nucleon matter and neutron star structure," Phys. Rev. C 58, 1804 (arXiv:nucl-th/9804027)

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EoS tables and fitting subroutines

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Page created on April 5, 2004, last updated on November 22, 2017 by Alexander Potekhin.