Neutron Star Group

Equation of State and Opacities for Hydrogen Atmospheres of Neutron Stars with Strong Magnetic Fields

Most of the typical neutron stars have surface magnetic fields B about 10¹¹-10¹³ Gauss, and some of the neutron stars (magnetars) have B about 10¹⁴-10¹⁵ Gauss. Such strong fields profoundly affect the outermost stellar layers.

First, the bottom density of a photosphere increases due to reduction of radiative opacities. Since the same magnetic field that reduces the opacities also suppresses the electron degeneracy, a typical neutron-star atmosphere remains non-degenerate in spite of this density increase. Consequently, at a given density, the pressure in the magnetized atmosphere is much lower than in non-magnetic one.

Second, the increase of the atomic binding energies tends to lower the ionization degree. Hence, there can be a significant amount of bound species in a highly magnetized atmosphere, even if it was negligibly small at the same temperature in the zero-field case.

Third, the quantum-mechanical effects of atomic and ionic thermal motion across the field influence the ionization equilibrium and equation of state. The motion lowers binding energies and affects abundances of atoms in different states. These factors, in turn, affect the ionization degree.

Here we present thermodynamic functions and Rosseland mean opacities for partially ionized hydrogen atmospheres in strong magnetic fields. The tables cover range of magnetic fields B from 3 × 10¹⁰ to 10¹⁵ Gauss, temperature T from ∼ 10⁵ to ∼ 10⁷ K, and astrophysical density parameter R [R=ρ/T₆³, where ρ is density in grams per cubic centimeter and T₆=T/10⁶ K] from a few × 10⁻⁸ to a few × 10³.

The data presented here have been obtained as a result of joint research by two theoretical astrophysics groups: at CRAL (Ecole Normale Superieure de Lyon) and at the Depatrment of Theoretical Astrophysics of the Ioffe Institute (St. Petersburg).

Here are the basic references to the thermodynamic model [1], the EOS and opacity calculation for ordinary neutron stars with B ∼ (10¹² - 10^13.5) G [2], similar calculation for magnetars with B ∼ (10^13.5 - 10¹⁵) G [3], and for moderately magnetized neutron stars with B ∼ (10^10.5 - 10¹²) G [4]:

1. A.Y. Potekhin, G. Chabrier, Yu.A. Shibanov (1999). Partially ionized hydrogen plasma in strong magnetic fields, Phys. Rev. E 60, 2193-2208 [astro-ph/9907006]
2. A.Y. Potekhin, G. Chabrier (2003). Equation of state and opacities for hydrogen atmospheres of neutron stars with strong magnetic fields, Astrophys. J. 585, 955-974 [astro-ph/0212062]
3. A.Y. Potekhin, G. Chabrier (2004). Equation of state and opacities for hydrogen atmospheres of magnetars, Astrophys. J., 600, 317 [astro-ph/0309310]
4. A.Y. Potekhin, G. Chabrier, and W.C.G. Ho (2014). Opacities and spectra of hydrogen atmospheres of moderately magnetized neutron stars, Astron. Astrophys., in press [arXiv:1409.7651]

• W.C.G. Ho, D. Lai, A.Y. Potekhin, G. Chabrier (2003). Atmospheres and spectra of strongly magnetized neutron stars - III. Partially ionized hydrogen models Astrophys. J. 599, 1293 [astro-ph/0309261]
• A.Y. Potekhin, D. Lai, G. Chabrier, W.C.G. Ho (2004). Electromagnetic polarization in partially ionized plasmas with strong magnetic fields and neutron star atmosphere models. Astrophys. J. 612, 1034-1043 [PDF file (456 K)] [astro-ph/0405383]
• W.C.G. Ho, A.Y. Potekhin, G. Chabrier (2008). Model X-ray spectra of magnetic neutron stars with hydrogen atmospheres. Astrophys. J. Suppl. Ser. 148, 102-109 [PDF file (879 K)] [arXiv:0802.2957]

• A.Y. Potekhin (2014). Atmospheres and radiating surfaces of neutron stars. Physics-Uspekhi 57 (8) [arXiv:1403.0074]

Page design and maintenance by Alexander Potekhin. Remarks are always welcome. Page created on May 30, 2002. last updated on October19, 2014.