Conductivities in the inner crust of a neutron star Quick evaluation of electrical and thermal conductivities of degenerate fully ionized plasmas without magnetic field
Department of Theoretical Astrophysics	[Conductivity Main page] [Neutron Star Group]

We provide here three programs: condegin19, condegsc19, condBSk.

In the first of them, we assume that the charge distribution of an ion is steplike (that is, uniform within the radius r_nuc). The characteristic dimensionless parameter that determines importance of the finite size of the ion is the ratio of r_nuc to the ion-sphere radius a_i:

In the inner crust (where dripped neutrons are present), we use an interpolation formula by Itoh & Kohyama (1983, ApJ 275, 858):

The key subroutine of condegin19 is CONDEGIN, whose input parameters are temperature T, number density of ions n_i, magnetic field B, ion charge number Z, ion mass number A, the number of neutrons per nucleus (in a Wigner-Seitz cell) A', and the effective impurity charge Z_imp (which is the square root of the usual impurity parameter Q). In general, A' may be greater than A because of the presence of dripped neutrons. The output parameters are the longitudinal, transverse, and off-diagonal components of the electrical and thermal conductivity tensors. All dimensional input and output parameters of CONDEGIN are in relativistic units. The conversion from/to conventional units is exemplified in the auxiliary MAIN program.

The other two codes, condegsc19 and condBSk, take into account that the proton charge profile in a nucleus is not steplike, but goes from a finite value to zero continuously near r_nuc. In "condegsc19", we use the charge profile parametrization worked out by Oyamatsu (1993, Nucl. Phys. A 561, 431). The corresponding nuclear shape parameters, as well as Z, A, and A', are interpolated as functions of baryon density throughout the neutron-star crust. This interpolation (named the smooth composition model by Kaminker et al. (1999)) is performed in the subroutine OYAFORM. The parameter x_nuc and an auxiliary parameter x'_nuc, which enter the fit for the effective Coulomb logarithm, are expressed through the nuclear shape parameters as explained in Appendix A of Ref.[16]. Accordingly, the key subroutine CONDEGsc has smaller number of free input arguments than CONDEGIN described above: the input parameters of CONDEGsc are log₁₀(T [K]), log₁₀(rho [g/cc]), B₁₂=B/10¹² G, and Z_imp. The output parameters are the longitudinal, transverse, and off-diagonal components of the electrical and thermal conductivity tensors in CGS units.

CONDBSK is analogous to CONDEGsc, but instead of Oyamatsu's profiles we use the nuclear form factors worked out recently in a series of works by N.Chamel and coauthors. A detailed paper on the used parametrizations, realized in subroutines FRACRUST and NUCPAR of the latter code, is in preparation.

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Fortran codes to download (at a choice):

condegin19.f

condegsc19.f

condBSk.f