# EOSs

Sequences of neutron star crust equations-of-state spanning a conservative range of the slope of the symmetry energy L were generated using the compressible liquid drop model, the results of which are outlined in this paper. We make them available here. These EOSs will be updated within the next two weeks (from 01/08/13) with newer versions which correct some small flaws in the current batch, such as acausality in a few EOSs at the highest densities. We anticipate replacing with a set of EOSs using inherently causal RMF models, together with consistent crusts, shortly.

There are two sequences which span L=25 to L=115 MeV. The first keeps the magnitude of the symmetry energy at saturation density fixed at J=35 MeV (the ‘J35′ sequence), while the second adjusts J for each value of L so that the equation of state of pure neutron matter is consistent with low density theoretical calculations (the `PNM’ sequence).

The EoSs are joined at low densities to the BPS EoS to describe the outer crust. The tables are headed by the number of points in the table and the value of L. Then the EoS is listed in order of decreasing density; each row contains the mass-energy density (in units of g/cc), the pressure (in dynes cm^-2) and the baryon number density (in cm^-3).

We also tabulate the crust composition in separate files “results_crust_composition_…”. Quantities listed in each row are, from left to right (see paper for more details; Debye screening lengths are estimates from the formula used in, e.g., Heiselberg, Pethick and Staubo PRL70, 1993):

- Baryon number density (fm^-3)
- The nuclear geometry (S – sphere, C – cylinder, SL – slab, CH – cylindrical hole, SH – spherical hole)
- volume fraction of charged component of crust
- nuclear mass number A
- nuclear charge number Z
- density fraction of dripped neutrons
- radius of Wigner-Seitz cell (fm)
- radius of clustered matter/bubbles (fm)
- local baryon density of charged component (fm^-3)
- local baryon density of dripped neutrons (fm^-3)
- local proton fraction of charged component
- average proton fraction of matter
- energy density of matter (without rest mass) (MeV fm^-3)
- pressure of matter (MeV fm^-3)
- neutron chemical potential (MeV)
- proton chemical potential (MeV)
- Debye screening length (electron) (fm)
- Debye screening length (clustered protons) (fm)
- Debye screening length (assuming uniform density) (fm)
- Debye screening length (total clustered) (fm)
- Debye screening length (total assuming uniform density) (fm)

And finally we also tabulate some useful, mostly thermodynamic, quantities in the files “results_thermodynamic_…”. From left to right, we have:

- Baryon number density (fm^-3)
- The nuclear geometry (S – sphere, C – cylinder, SL – slab, CH – cylindrical hole, SH – spherical hole)
- volume fraction of charged component of crust, v
- volume fraction of nucleus/pasta shape, u, (which is the same as the previous quantity except for the bubble phases, in which case it is 1-v)
- Energy density contribution of the charged nuclear matter (e.g. the spherical nuclei) (MeV fm^-3)
- Energy density contribution of neutron gas (MeV fm^-3)
- Total energy density of matter (minus rest mass) (MeV fm^-3)
- Pressure of the charged nuclear matter = pressure of neutron gas (MeV fm^-3)
- Pressure of electrons (MeV fm^-3)
- Total pressure (MeV fm^-3)
- Neutron chemical potential (MeV)
- Proton chemical potential (MeV)
- Energy density contribution of nuclear surface (MeV fm^-3)
- Energy density contribution of nuclear curvature (MeV fm^-3)
- Sum of the above two contributions (MeV fm^-3)
- Surface and curvature contributions as fraction of total energy density
- Effective surface tension (MeV fm^-2)
- Effective curvature tension (MeV fm^-1)

The surface quantities tabulated in the last six columns of these files are defined here.

The following links take you to:

(1) The crust equation of state tables (matched to the BPS EoS at lower, outer crust, densities)

(3) The corresponding tables for the thermodynamic quantities

(4) Full neutron star EOSs in which the crust EOSs smoothly continue on to core EOSs constructed using the same model for the nuclear matter EOS with the same values of J and L. The nuclear matter EOS is used to construct the core EOSs right up to the highest densities in the core; the softer EOSs (L<70 MeV) give maximum masses below 2 solar masses.

(5) As above, but with the addition of two polytropic EOSs at high densities in the core (explained and used in this paper; the polytropes are constructed in a similar way to this paper). These EOSs all give maximum masses above 2 solar masses without significantly changing the radius of the stars compared with the pure nuclear matter EOSs above. These sequences of EOSs allow exploration of neutron star properties for all values of the slope of the symmetry energy while still fulfilling the observational requirement that the neutron stars have masses above 2 solar masses. Note that for L<50MeV, these polytropes violate causality at the very highest densities; by the end of Jan 2013 these will be replaced by a new set of EOSs which correct this flaw.

(6) tarred packages containing the various tables listed above.

Any questions/comments/suggestions are welcome!