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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]
[click here to go straight to the Fortran programs]

conductivity codes have been updated in September 2019.


The Fortran programs supplied here are generalizations of the program for quick evaluation in strongly degenerate magnetized electron-ion plasma ("short version" of the magnetic conductivity code). The generalization consists in taking into account the finite size of the ion (or the nuclear form factor) and the switching-off the Umklapp electron-phonon scattering events at very low temperture/high density. Both these modifications are described in the Appendix of Gnedin et al. (2001) (Ref.[16] on the main page).

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 rnuc). The characteristic dimensionless parameter that determines importance of the finite size of the ion is the ratio of rnuc to the ion-sphere radius ai:

In the outer envelope (where all neutrons are confined within nuclei), the ordinary nuclear-physics formula
rnuc=1.15A1/3 fm
is employed. In this case, xnuc<<1 and the finite ion-size effects are not very important.

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

rnuc=1.83Z1/3 fm.
In this case, xnuc is not negligible. Allowance for the finite nuclear size strongly changes the electrical and thermal conductivities near the bottom of the inner crust, as demonstrated in Ref.[16].

The key subroutine of condegin19 is CONDEGIN, whose input parameters are temperature T, number density of ions ni, 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 Zimp (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 rnuc. 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 xnuc 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 Zimp. 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):
first code condegin19.f  condegsc19.f condegsc19.f  condBSk.f condBSk.f

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Page design and maintenance: Alexander Potekhin
Page created in 2000; last updated on 12.09.19.
The codes presented on this page have been last updated on 12.09.19.