# Finite-temperature Equation of State Tables¶

There are several classes designed to provide a consistent interface to several EOS tables intended for core-collapse supernovae and neutron-star mergers. The abstract base class is eos_sn_base. The child classes correspond to different EOS table formats:

eos_sn_ls - The Lattimer-Swesty EOS tables from Jim’s webpage ([Lattimer91])

eos_sn_stos - The H. Shen et al. EOS tables ([Shen98] and [Shen98b])

eos_sn_sht - The G. Shen et al. EOS tables ([Shen10a], [Shen10b], [Shen11])

eos_sn_hfsl - The M. Hempel et al. EOS tables ([Hempel10] and [Hempel12])

eos_sn_oo - The Lattimer-Swesty and H. Shen et al. tables reformatted by O’Connor and Ott ([OConnor10])

The O2scl distribution does not contain the tables themselves, as they are quite large and most are freely available. O2scl includes code which parses these tables and puts them in tensor_grid3 objects for analysis by the user.

The EOSs are stored in a set of tensor_grid3 objects on grids with baryon density in \(\mathrm{fm}^{-3}\), electron fraction (unitless) and temperature in \(\mathrm{MeV}\). The choice of baryon density is preferred to that of ‘rest mass density’ (commonly denoted \(\rho\)) because the rest mass density has no unambiguous definition. This is especially the case if dense matter contains deconfined quark matter. On the other hand, baryon number is conserved (to a very good approximation).

The electron fraction is also a natural variable to use when tabulating, because charge is also conserved and the electron has one unit of charge but no baryon number. The electron fraction is also a sensible choice because of its central role in the relevant weak interaction physics. This is also the choice made in [Lattimer91]. Some tables are tabulated for constant “proton fraction”, which in this case includes all protons whether or not they are inside nuclei. Because all baryonic matter in these EOS tables is made up of neutrons and protons and because there are no muons, one can assume that the electron fraction is equal to the proton fraction. The total proton fraction is always larger than the number fraction of free protons.

Not all tabulated EOSs contain all of the data, in which case the
associated tensor_grid3 object may be empty. For
example, EOSs which do not contain the leptonic contributions do not
provide `eos_sn_base::E`

, `eos_sn_base::F`

,
`eos_sn_base::S`

, and `o2scl::eos_sn_base::P`

. In
these case, the grid is set for these objects but the data is set to
zero. To compute these from the data after loading the EOS table, use
`o2scl::eos_sn_base::compute_eg()`

.

Also, some EOS tables tabulate the ‘mass fraction’ of the various particles, but this is a slight misnomer. What is actually tabulated is ‘baryon number fraction’, i.e. the fraction of baryons which are in particles of type \(i\). These fractions \(X_i\) are defined by

where \(A_i\) is the number of baryons in particle \(i\)
and \(n_i\) is the number of particles per unit volume.
In the case of the representative heavy nucleus, the
baryon number fraction is \(X_h = A n_h n_B^{-1}\) where
\(A\) is the baryon number of the representative heavy
nucleus in `o2scl::eos_sn_base::A`

.

The functions named `load()`

in the children classes load
the entire EOS into memory. Memory allocation is automatically
performed, but not deallocated until `free()`

or the destructor is
called.

After loading, you can interpolate the EOS by using
:cpp_func:`o2scl:tensor_grid3::interp_linear()` directly. For example,
the following returns the mass number at an arbitrary
baryon density, electron fraction, and temperature
assuming the table is stored in `skm.dat`

:

```
ls_eos ls;
ls.load("skm.dat");
double nb=0.01, Ye=0.2, T=10.0;
cout << ls.A.interp_linear(nb,Ye,T) << endl;
```

This function performs linear interpolation, however, some of the grids are logarithmic, so linear interpolation on a logarithmic grid leads to power-laws in between grid points. Note also that some grids are not purely linear or purely logarithmic, but a mixture between the two.

All of these classes are experimental.