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We study the relation between the mean effective surface temperature $\overline{T}_\mathrm{s}$and the internal temperature $T_\mathrm{b}$for magnetic neutron stars, assuming that the magnetic field near the surface has a small-scale structure. The heavy-element (iron) and light-element (accreted) heat-blanketing envelopes are considered, and the results are compared with the case of a dipole magnetic field. We argue that the difference in the $T_\mathrm{b}(\overline{T}_\mathrm{s})$-relation for different magnetic configurations is always much smaller than the possible difference caused by variations of the chemical composition in the envelope.

Analytical representations are derived for two equations of state (EOSs) of neutron-star matter: FPS and SLy. Each of these EOSs is unified, that is, it describes the crust and the core of a neutron star using the same physical model. Two versions of the EOS parametrization are considered. In the first one, pressure and mass density are given as functions of the baryon density. In the second version, pressure, mass density, and baryon density are given as functions of the pseudo-enthalpy, which makes this representation particularly useful for 2-D calculations of stationary rotating configurations of neutron stars.

We calculate the thermal structure and quiescent thermal luminosity of accreting neutron stars (warmed by deep crustal heating in accreted matter) in soft X-ray transients (SXTs). We consider neutron stars with nucleon and hyperon cores and with accreted envelopes. It is assumed that an envelope has an outer helium layer (of variable depth) and deeper layers of heavier elements, either with iron or with much heavier nuclei (of atomic weight $A\gtrsim100$) on the top [CITE]. The relation between the internal and surface stellar temperatures is obtained and fitted by simple expressions. The quiescent luminosity of the hottest (low-mass) and coldest (high-mass) neutron stars is calculated, together with the ranges of its possible variations due to variable thickness of the helium layer. The results are compared with observations of SXTs, particularly, containing the coldest (SAX J1808.4-3658) and the hottest (Aql X-1) neutron stars. The observations of SAX J1808.4-3658in a quiescent state on March 24, 2001 [CITE] can be explained only if this SXT contains a massive neutron star with a nucleon/hyperon core; a hyperon core with a not too low fraction of electrons is preferable. Future observations may discriminate between the various models of hyperon/nucleon dense matter. The thermal emission of SAX J1808.4-3658is also sensitive to the models of plasma ionization in the outermost surface layers and can serve for testing such models.

The thermal structure of neutron stars with magnetized envelopes is studied using modern physics input. The relation between the internal ($T_\mathrm{int}$) and local surface temperatures is calculated and fitted by analytic expressions for magnetic field strengths Bfrom 0 to 1016G and arbitrary inclination of the field lines to the surface. The luminosity of a neutron star with dipole magnetic field is calculated and fitted as a function of B, $T_\mathrm{int}$, stellar mass and radius. In addition, we simulate cooling of neutron stars with magnetized envelopes. In particular, we analyse ultramagnetized envelopes of magnetars and also the effects of the magnetic field of the Vela pulsar on the determination of critical temperatures of neutron and proton superfluids in its core.

Topical problems in the physics of and basic facts about neutron stars are reviewed. The observational manifestations of neutron stars, their core and envelope structure, magnetic fields, thermal evolution, and masses and radii are briefly discussed, along with the underlying microphysics.

Recent observations show that the thermal X-ray spectra of many isolated neutron stars are featureless and in some cases (e.g., RX J1856.5-3754) well fit by a blackbody. Such a perfect blackbody spectrum is puzzling since radiative transport through typical neutron star atmospheres causes noticeable deviation from blackbody. Previous studies have shown that in a strong magnetic field, the outermost layer of the neutron star may be in a condensed solid or liquid form because of the greatly enhanced cohesive energy of the condensed matter. The critical temperature of condensation increases with the magnetic field strength and can be as high as 106 K (for Fe surface at B ~ 1013 G or H surface at B ~ a few x 1014 G). Thus the thermal radiation can directly emerge from the degenerate metallic condensed surface without going through a gaseous atmosphere. Here we calculate the emission properties (spectrum and polarization) of the condensed Fe and H surfaces of magnetic neutron stars in the regimes in which such condensation may be possible. For a smooth condensed surface, the overall emission is reduced from the blackbody by less than a factor of 2. The spectrum exhibits modest deviation from blackbody across a wide energy range and shows mild absorption features associated with the ion cyclotron frequency and the electron plasma frequency in the condensed matter. The roughness of the solid condensate (in the Fe case) tends to decrease the reflectivity of the surface and make the emission spectrum even closer to blackbody. We discuss the implications of our results for observations of dim, isolated neutron stars and magnetars.

The polarizability tensor of a strongly magnetized plasma and the polarization vectors and opacities of normal electromagnetic waves are studied for conditions typical of neutron star atmospheres, taking account of partial ionization effects. Vacuum polarization is also included, and a new set of fitting formulae are used that are accurate for wide range of field strengths. The full account of the coupling of the quantum mechanical structure of the atoms to their center-of-mass motion across the magnetic field is shown to be crucial for the correct evaluation of the polarization properties and opacities of the plasma. The self-consistent treatment of the polarizability and absorption coefficients proves to be necessary if the ionization degree of the plasma is low, which can occur in the atmospheres of cool or ultramagnetized neutron stars. Atmosphere models and spectra are presented to illustrate the importance of such self-consistent treatment.

The equation of state and radiative opacities of partially ionized, strongly magnetized hydrogen plasmas, presented in a previous paper for the magnetic field strengths, 8 x 1011 G [?] B [?] 3 x 1013 G, are extended to the field strengths, 3 x 1013 G [?] B [?] 1015 G, relevant for magnetars. The first- and second-order thermodynamic functions and radiative opacities are calculated and tabulated for 5 x 105 K [?] T [?] 4 x 107 K in a wide range of densities. We show that bound-free transitions give an important contribution to the opacities in the considered range of B in the outer neutron star atmosphere layers. Unlike the case of weaker fields, bound-bound transitions are unimportant.

We construct partially ionized hydrogen atmosphere models for magnetized neutron stars in radiative equilibrium with surface fields B = 1012-5 x 1014 G and effective temperatures Teff ~ a few x 105-106 K. These models are based on the latest equation of state and opacity results for magnetized, partially ionized hydrogen plasmas that take into account various magnetic and dense medium effects. The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars. For the models with B = 1012-1013 G, the spectral features due to neutral atoms lie at extreme UV and very soft X-ray energy bands and therefore are difficult to observe. However, the continuum flux is also different from the fully ionized case, especially at lower energies. For the superstrong field models (B [?] 1014 G), we show that the vacuum polarization effect not only suppresses the proton cyclotron line as shown previously, but also suppresses spectral features due to bound species; therefore, spectral lines or features in thermal radiation are more difficult to observe when the neutron star magnetic field is [?]1014 G.

We study the thermal structure of neutron stars with magnetized envelopes composed of accreted material, using updated thermal conductivities of plasmas in quantizing magnetic fields, as well as the equation of state and radiative opacities for partially ionized hydrogen in strong magnetic fields. The relation between the internal and local surface temperatures is calculated and fitted by an analytic function of the internal temperature, magnetic field strength, angle between the field lines and the normal to the surface, surface gravity, and the mass of the accreted material. The luminosity of a neutron star with a dipole magnetic field is calculated for various values of the accreted mass, internal temperature, and magnetic field strength. Using these results, we simulate cooling of superfluid neutron stars with magnetized accreted envelopes. We consider slow and fast cooling regimes, paying special attention to very slow cooling of low-mass, superfluid neutron stars. In the latter case, the cooling is strongly affected by the combined effect of magnetized accreted envelopes and neutron superfluidity in the stellar crust. Our results are important for the interpretation of observations of the isolated neutron stars hottest for their age, such as RX J0822-43 and PSR B1055-52.

We present an equation of state and radiative opacities for a strongly magnetized hydrogen plasma at magnetic fields B, temperatures T, and densities r typical for atmospheres of isolated neutron stars. The first- and second-order thermodynamic functions, monochromatic radiative opacities, and Rosseland mean opacities are calculated and tabulated, taking account of partial ionization, for 8 x 1011 G [?] B [?] 3 x 1013 G, 2 x 105 K [?] T [?] 107 K, and a wide range of r. We show that bound-bound and bound-free transitions give an important contribution to the opacities at T [?] (1-5) x 106 K in the considered range of B in the outer neutron star atmosphere layers, which may substantially modify the X-ray spectrum of a typical magnetized neutron star. In addition, we reevaluate opacities due to free-free transitions, taking into account the motion of both interacting particles, electron and proton, in a strong magnetic field. Compared to the previous neutron star atmosphere models, the free-free absorption is strongly suppressed at photon frequencies below the proton cyclotron frequency. The latter result holds for any field strength, which prompts a revision of existing theoretical models of X-ray spectra of magnetar atmospheres.

Multidimensional cosmologies allow for variations of fundamental physical constants over the course of cosmological evolution, and different versions of the theories predict different time dependences. In particular, such variations could manifest themselves as changes of the proton-to-electron mass ratio ? = mp/meover the period of ~1010yr since the moment of formation of high-redshift QSO spectra. Here we analyze a new high-resolution spectrum of the z= 2.81080 molecular hydrogen absorption system toward the QSO PKS 0528-250 to derive a new observational constraint to the time-averaged variation rate of the proton-to-electron mass ratio. We find | /? |<1.5×10?14yr-1, which is much tighter than previously measured limits.

Multidimensional cosmologies allow for variations of fundamental physical constants over the course of cosmological evolution, and different versions of the theories predict different time dependences. In particular, such variations could manifest themselves as changes of the proton-to-electron mass ratio m = mp/me over the period of ~1010 yr since the moment of formation of high-redshift QSO spectra. Here we analyze a new high-resolution spectrum of the z = 2.81080 molecular hydrogen absorption system toward the QSO PKS 0528-250 to derive a new observational constraint to the time-averaged variation rate of the proton-to-electron mass ratio. We find | {\ucpmathaccent{{\mu}}{"705F}} ${&ucpmathaccent;{{μ}}{"705F}}$ ${&ucpmathaccent;{{μ}}{"705F}}$ ${&ucpmathaccent;{{μ}}{"705F}}$ /m |<1.5x10 [?]14 yr-1, which is much tighter than previously measured limits.

The strong magnetic fields (B ~ 1012-1013 G) characteristic of neutron stars make all the properties of an atom strongly dependent on the transverse component K[?] of its generalized momentum. In particular, the photoionization process is modified substantially: (1) threshold energies are decreased as compared with those for an atom at rest, (2) cross section values are changed significantly, and (3) selection rules valid for atoms at rest are violated by the motion so that new photoionization channels become allowed. To calculate the photoionization cross sections, we employ, for the first time, exact numerical treatment of both initial and final atomic states. This enables us to take into account the quasi-bound (autoionizing) atomic states as well as coupling of different ionization channels. We extend the previous consideration, restricted to the so-called centered states corresponding to relatively small values of K[?], to arbitrary states of atomic motion. We fold the cross sections with the thermal distribution of atoms over K ${&bmi; K}$ . For typical temperatures of neutron star atmospheres, the averaged cross sections differ substantially from those of atoms at rest. In particular, the photoionization edges are strongly broadened by the thermal motion of atoms; this "magnetic broadening" exceeds the usual Doppler broadening by orders of magnitude. The decentered states of the atoms give rise to the low-energy component of the photoionization cross section. This new component grows significantly with increasing temperature above 105.5 K and decreasing density below 1 g cm-3, i.e., for the conditions expected in atmospheres of middle-aged neutron stars.

The early 21st century is witnessing a breakthrough in the study of the thermal radiation of neutron stars. Observations with modern space telescopes have provided a wealth of valuable information, which, when properly interpreted, can elucidate the physics of superdense matter in the interior of these stars. This interpretation is underlain by the theory of formation of the neutron star thermal spectra, which is in turn based on plasma physics and on the understanding of radiative processes in stellar photospheres. In this paper, the current status of the theory is reviewed, with particular emphasis on neutron stars with strong magnetic fields. In addition to the conventional deep (semi-infinite) atmospheres, radiative condensed surfaces of neutron stars and ‘thin’ (finite) atmospheres are considered.

Aims.We constrain the mass-to-radius ratio of isolated neutron stars by performing a spin-phase resolved X-ray spectroscopic analysis.

Topical problems in the physics of and basic facts about neutron stars are reviewed. The observational manifestations of neutron stars, their core and envelope structure, magnetic fields, thermal evolution, and masses and radii are briefly discussed, along with the underlying microphysics.

Context.In the X-ray spectra of most X-ray dim isolated neutron stars (XDINSs), absorption features with equivalent widths (EWs) of 50–200 eV are observed. These features are usually connected with the proton cyclotron line, but their nature is not yet well known.

Some X-ray dim isolated neutron stars (XDINS) and central compact objects in supernova remnants (CCO) contain absorption features in their thermal soft X-ray spectra. It has been hypothesized that this absorption may relate to periodic peaks in free-free absorption opacities, caused by either Landau quantization of electron motion in magnetic fields B$\la$1011G or analogous quantization of ion motion in magnetic fields B>1013G. Here, I review the physics behind cyclotron quantum harmonics in free-free photoabsorption, discuss different approximations for their calculation, and explain why the ion cyclotron harmonics (beyond the fundamental) cannot be observed.

Some X-ray dim isolated neutron stars (XDINS) and central compact objects in supernova remnants (CCO) contain absorption features in their thermal soft X-ray spectra. It has been hypothesized that this absorption may relate to periodic peaks in free-free absorption opacities, caused by either Landau quantization of electron motion in magnetic fields B$\la$1011G or analogous quantization of ion motion in magnetic fields B>1013G. Here, I review the physics behind cyclotron quantum harmonics in free-free photoabsorption, discuss different approximations for their calculation, and explain why the ion cyclotron harmonics (beyond the fundamental) cannot be observed.