Equations of State (EOS)

The FUKA solvers support both piecewise polytropic and tabulated EOS in generating ID for Neutron Stars. For both cases, a file is required which includes either the tabulated EOS or describes the piecewise polytrope, as described below.

Piecewise Polytropic Equations of State

The file format for storing a piecewise polytrope is quite basic. All lines starting with a # or are blank are ignored.
Most importantly, the order of parameters is strictly defined

#h4 pwpolytrope
num_pieces: 4
rhomin: 1.e-19
rhomax: 1.0
ktab0: 3.99873692e-8
Ptab0: 0
 
gamma_tab
1.35692395 2.909 2.246 2.144
 
rho_tab
0.0 8.87824e+14 5.01187234e+14 1.0e+15
 
#units can be:
#geometrised
#cgs
#cgs_cgs_over_c2
units: cgs_cgs_over_c2

in the first block, the number of pieces, the value range of the density, as well as K_0 (constant factor at the initial boundary and P0 (pressure at the initial boundary) must be defined in this order
secondly the values of the polytropic exponent for each piece is defined in a single row
thirdly the values of the density are defined for each piece within a single row
finally the units must be specified for the input values

Tabulated Equations of State

The format for tabulated EOS' that are currently supported is the well known format used by the LORENE spectral solver.
Details on the format of the table can be found here

EOS Framework

The backend that handles the EOS is constructed in two parts

1. EOS Management

The construction and evaluation of the EOS is handled by a standalone version of the Margherita EOS framework developed by Elias R. Most For code details see $HOME_KADATH/include/EOS/standalone/

2. EOS Interface

To interface between KADATH and Margherita, a user-defined module was written by Samuel Tootle and L. Jens Papenfort allowing the use of Margherita within KADATH's System_of_equations framework. For details see $HOME_KADATH/include/EOS/EOS.hh.

To initialize Margherita, the following parameters need to be set within the config file

{"eostype",EOSTYPE}, // Options are currently: Cold_PWPoly, Cold_Table
{"eosfile",EOSFILE}, // Polytrope or Tabulated EOS file
{"h_cut",HCUT}, // value to cut the specific enthalpy (0 is default)
{"interpolation_pts", INTERP_PTS} // number of points to use for interpolating the table

Regarding the eos_file, if no path is specified, e.g. eos_file togashi.lorene, the EOS framework will only search the $HOME_KADATH/eos/ directory for the EOS file specified. In the event you want to specify an EOS not located in the default directory, a path must be included. For example, to read an EOS from the current directory, one would need to write eos_file ./togashi.lorene.