FeaturesΒΆ

The library contains different types of one-parametric EOS that can be accessed through a generic interface. It is quite simple to add custom EOS without modifying the library.

The interface provides the following functions:

  • \(P(\rho)\)

  • \(\epsilon(\rho)\)

  • \(c_s(\rho)\)

  • \(h(\rho)\)

  • \(Y_e(\rho)\) (optionally)

  • \(T(\rho)\) (optionally)

In addition, the global minimum \(h_0>0\) of the enthalpy over the valid range is given for each EOS.

Providing the electron fraction and temperature as function of mass density is mainly intendend for constructing initial data that is later evolved with the full EOS including thermal and composition effects. For example, \(Y_e(\rho)\) could correspond to beta-equilibrium. Specifying a non-zero temperature a function of mass density may seem strange, but might be useful to emulate a temperature gradient that happens to be aligned with the density gradient.

We decided to not restrict the framework to isentropic EOS (but provide methods to querry this important EOS property). However, the temperature and electron fraction profiles are not completely unrestricted. The framework requires that

\[\frac{\mathrm{d} P}{\mathrm{d} \rho} \ge 0\]

This is required for use in initial data. For hydrostatic equilibrium in a gravitational field, the pressure gradient is nonzero. If the pressure were allowed to also decrease with density, the density at given pressure becomes multi-valued and the intial data ambiguous.

In order to support constructing initial data, the interface also provides functions in terms of pseudo enthalpy

  • \(g(\rho)\)

  • \(\rho(g)\)

  • \(P(g)\)

  • \(c_s(g)\)

  • \(h(g)\)

  • \(Y_e(g)\) (optionally)

  • \(T(g)\) (optionally)

Here, the pseudo enthalpy is defined as

\[g(P) = \exp\left(\int_0^P \frac{dP'}{\rho(P')h(P')}\right) \qquad \rightarrow g(0)=1\]

which relies on the requirement that pressure never decreases with mass density. Note that if the EOS is isentropic, then \(g=h\) up to a constant factor.

The pseudo enthalpy is useful for initial data, because under certain conditions hydrostatic equilibrium reduces to an invariant algebraic expression involving spacetime metric and pseudo enthalpy. Within a stationary neutron star, \(g\) is continuous, in contrast to mass density, which can have discontinuities.

The pseudo enthalpy is anyway useful for parametrizing an EOS because, even if the EOS has phase transitions, \(P(g)\) is always continuous as well as invertible. Conversely, \(g(\rho)\) can have plateaus and \(\rho(g)\) can have discontinuities. Internally, we use \(g\) as independent variable for barotropic EOS, and functions based on \(\rho\) internally evaluate \(g(\rho)\) first.