Cooling of pulsars

Cooling rates are calculated for superfluid neutron stars of about one solar mass and 10 km radius, with magnetic fields from zero to about 10 to the 14th power Gauss, when possible internal friction effects are neglected. The results show that most old pulsars are so cold that thermal ionization of surface atoms would be negligible. At an age of a million years and with canonical magnetic fields of 10 to the 12th power Gauss, the estimated stellar surface temperature is several thousand to a hundred thousand degrees. However, if we neglect magnetic fields and superfluid states of nucleons, the same surfaces would be about a million degrees

Polarization Evolution in A Strongly Magnetized Vacuum: QED Effect and Polarized X-ray Emission from Magnetized Neutron Stars

X-ray photons emitted from the surface or atmosphere of a magnetized neutron star is highly polarized. However, the observed polarization may be modified due to photon propagation through the star's magnetosphere. For photon frequencies much larger than the typical radio frequency, vacuum birefringence due to strong-field quantum electrodynamics dominates over the plasma effect. We study the evolution of photon polarization in the magnetized QED vacuum of a neutron star magnetosphere, paying particular attention to the propagation effect across the quasi-tangential (QT) point, where the photon momentum is nearly aligned with the magnetic field. In agreement with previous studies, we find that in most regions of the magnetosphere, the photon polarization modes are decoupled due to vacuum birefringence, and therefore a large net linear polarization can be expected when the radiation escapes the magnetosphere. However, we show that X-ray polarization may change significantly when the photon passes through the QT region. When averaging over a finite emission area, the net effect of QT propagation is to reduce the degree of linear polarization; the reduction factor depends on the photon energy, magnetic field strength, geometry, rotation phase and the emission area, and can be more than a factor of two. We derive the general conditions under which the QT propagation effect is important, and provide an easy-to-use prescription to account for the QT effect for most practical calculations of X-ray polarization signals from magnetic neutron stars. For a neutron star with a dipole magnetic field, the QT effect can be important for emission from the polar cap for certain magnetic field and energy ranges, and is negligible for emission from the entire stellar surface.Comment: 29 pages, 17 figures, accepted by MNRA

Constraining the Geometry of the Neutron Star RX J1856.5-3754

RX J1856.5-3754 is one of the brightest, nearby isolated neutron stars, and considerable observational resources have been devoted to its study. In previous work, we found that our latest models of a magnetic, hydrogen atmosphere matches well the entire spectrum, from X-rays to optical (with best-fitting neutron star radius R=14 km, gravitational redshift z_g~0.2, and magnetic field B~4x10^12 G). A remaining puzzle is the non-detection of rotational modulation of the X-ray emission, despite extensive searches. The situation changed recently with XMM-Newton observations that uncovered 7 s pulsations at the 1% level. By comparing the predictions of our model (which includes simple dipolar-like surface distributions of magnetic field and temperature) with the observed brightness variations, we are able to constrain the geometry of RX J1856.5-3754, with one angle < 6 deg and the other angle = 20-45 deg, though the solutions are not definitive given the observational and model uncertainties. These angles indicate a close alignment between the rotation and magnetic axes or between the rotation axis and the observer. We discuss our results in the context of RX J1856.5-3754 being a normal radio pulsar and a candidate for observation by future X-ray polarization missions such as Constellation-X or XEUS.Comment: 7 pages, 6 figures; MNRAS, accepte

Matter in Strong Magnetic Fields

The properties of matter are significantly modified by strong magnetic fields, $B>>2.35\times 10^9$ Gauss ($1 G =10^{-4} Tesla$), as are typically found on the surfaces of neutron stars. In such strong magnetic fields, the Coulomb force on an electron acts as a small perturbation compared to the magnetic force. The strong field condition can also be mimicked in laboratory semiconductors. Because of the strong magnetic confinement of electrons perpendicular to the field, atoms attain a much greater binding energy compared to the zero-field case, and various other bound states become possible, including molecular chains and three-dimensional condensed matter. This article reviews the electronic structure of atoms, molecules and bulk matter, as well as the thermodynamic properties of dense plasma, in strong magnetic fields, $10^9G << B < 10^{16}G$. The focus is on the basic physical pictures and approximate scaling relations, although various theoretical approaches and numerical results are also discussed. For the neutron star surface composed of light elements such as hydrogen or helium, the outermost layer constitutes a nondegenerate, partially ionized Coulomb plasma if $B<<10^{14}G$, and may be in the form of a condensed liquid if the magnetic field is stronger (and temperature $<10^6$ K). For the iron surface, the outermost layer of the neutron star can be in a gaseous or a condensed phase depending on the cohesive property of the iron condensate.Comment: 45 pages with 9 figures. Many small additions/changes. Accepted for publication in Rev. Mod. Phy

Comparison of microscopic calculations of solid neutron star matter

At the Urbana Workshop on "dense neutron matter" it was agreed that each group involved should check the many-body techniques so far employed on a test problem, outlined by H. A. Bethe. This paper reports the results using the t-matrix and variational approaches. Satisfactory agreement is obtained. Comparison with the results of other groups is discussed

t-matrix calculation of the ground-state energies of solid <SUP>3</SUP>He

The analysis of the Bethe-Goldstone equation for solid 3He is performed by removing the difficulties of symmetry encountered in a previously published version of the problem. Better agreement with experimental data is obtained. The new form of the Bethe-Goldstone two-body equation has special significance for problems related to fission and to solidification of neutron matter

t-Matrix calculation of ground state energy of solid He<SUP>3</SUP>

The results of recent extensive numerical computations of the ground state energy of solid He<SUP>3</SUP> in the t-matrix framework are summarized and compared with previous results. The improvements brought about by the exact numerical evaluation are emphasized