Hello Chia-Hui,
I have a problem about the gallery example of binary neutron star (https://einsteintoolkit.org/gallery/bns/index.html).
Is it possible to evolve and output some parameters like entropy , temperature and electron fraction ? Is so , how should I modify the parameter file (NsNsToHMNS.par) ?
Unfortunately the gallery example is not set up to do that. It uses a simple gamma-law equation of state that does not support entropy, temperature or electron fraction.
The closest thing that exists to temperature is the specific internal energy that appears in the equation of state and you could try and separate it into a "cold" piece due to eg Fermi energy and a thermal piece.
There are right now no public examples in the Einstein Toolkit on how to evolve a BNS using a finite temperature EOS that would support entropy and electron fraction.
If you wanted to do so, you would have to modify the parfile to use a tabulated equation of state to a tabulated EOS:
GRHydro::GRHydro_eos_table = nuc_eos
set options for the root finding required for the hot eos, eg.
GRHydro::GRHydro_eos_hot_eps_fix = yes
as well as specifying temperature and electron fraction for the hot atmosphere in the
grhydro::grhydro_hot_atmo_temp grhydro::grhydro_hot_atmo_Y_e
parameters and range of allowed electron fractions in grhydro_y_e_min/max.
You will have to tell HydroBase that initial date for temperature, entropy and y_e are provided by setting the respective HydroBase::initial_XXX parameters and setting the HydroBase::XXX_evolution_method parameters to "GRHdyro". Obviously you will have to provide initial data. LORENE provides some datasets for tabulated EOS (ftp://octane.obspm.fr/BinaryNS/GR/Realistic/ though none matches a cold slice of a finite difference EOS and given a cold, beta-equilibrium slice one could use its tabulated EOS capability to create ID) that may serve though I have never used them myself. You will also have to extend the Meudon_BNS_ID reader in Cactus to support the extra variables (and likely use LORENE2 instead of LORENE).
You can find tabulated EOS on the stellarcollapse.org website https://stellarcollapse.org/microphysics which can be used with GRHydro. Please see that site for references to acknowledge when using them.
Note that without a neutrino radiation code like ZelmaniLeak or ZelmaniM1 (both on stellarcollapse.org https://stellarcollapse.org/Zelmani) the electron fraction is simply advected along. Setting up the neutrino codes is not something I have experience in.
Also please note that I have not myself evolved BNS using a finite temperature EOS in Cactus and that the description above is a best effort based on my reading of param.ccl.
Yours, Roland