Astron. Astrophys. 323, 415-428 (1997)

1. Introduction

It is well known that the cooling of a neutron star (NS) is strongly affected by the relationship between the internal temperature of the star, , and its effective surface temperature . Throughout this paper, denotes the temperature at the outer boundary of the isothermal internal region. The - relationship is determined by equation of state (EOS) and thermal conductivity of matter in the outer NS envelope. For non-magnetized NSs with envelopes composed of iron, this relationship has been thoroughly studied in a classical article of Gudmundsson et al. (1983, hereafter GPE). Several papers (Hernquist 1984, 1985, Van Riper 1988, 1991, Schaaf 1988, 1990) have considered strongly magnetized NS envelopes.

In this article, we will reconsider thermal transport in non-magnetized envelopes of NSs and extend the results of the preceding authors in two respects.

First, we analyze matter composed not only of iron, but of light elements as well. The light elements can be provided by an accretion from a supernova remnant (e.g., Chevalier 1989, 1996, Brown & Weingartner 1994), from interstellar medium (e.g., Miralda-Escudé et al. 1990, Blaes et al. 1992, Nelson et al. 1993, Morley 1996), from a distant binary component, or by comets. Freshly accreted matter burns then into heavier elements (He, C, O, Fe) while sinking within the NS. Recent multiwavelength observations of the Geminga pulsar (1E 0630+17.8) suggest a possible H or He cyclotron feature in its spectrum (Bignami et al. 1996). If confirmed, it may be a direct observational evidence of the presence of the light elements in the pulsar atmosphere. Chemical composition affects the EOS and thermal conduction, and, therefore, the thermal structure and cooling of a NS. As a reference case, we reconsider the outer NS envelopes composed of iron.

Second, we implement new, advanced theoretical data on EOS and thermal conductivity of dense matter. Specifically, we employ the Opacity Library (OPAL) radiative opacities for H, He, and C, improved considerably with respect to the Los-Alamos opacities used in the previous studies. In the outermost NS layers, we also implement the modern OPAL EOS for Fe and the Saumon-Chabrier EOS for H and He. We use improved thermal conductivities of degenerate electrons. For solidified matter, we employ the thermal conductivity due to the electron-phonon scattering obtained with the inclusion of the Debye-Waller factor. For liquid matter, we recalculate and implement the thermal conductivity due to Coulomb electron-ion and electron-electron collisions. The electron-ion scattering is described with the exact (non-Born) Coulomb cross sections and with the ion structure factors calculated when taking into account the response of the electron background. The new physics input allows us to extend the results of previous studies to colder NSs, with down to 50 000 K.

The physics input is described in Sec. 2. In Sec. 3, we calculate the - relationships for non-accreted and partly accreted NSs and analyze the sensitivity of the results to the uncertainty in our knowledge of the electron thermal conductivity. In addition, we simulate the cooling of NSs with standard and enhanced neutrino energy losses. We show that the cooling of a NS with the accreted envelope can be quite different from the cooling of a non-accreted NS. This can change the conclusions on the internal structure of NSs deduced from comparison of theoretical cooling curves with observations of NS thermal radiation. Useful analytical formulae for the physics input are given in the Appendix.

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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