Thermal emission and magnetic beaming in the radio and X-ray mode-switching PSR B0943+10

PSR B0943+10 is a mode-switching radio pulsar characterized by two emission modes with different radio and X-ray properties. Previous studies, based on simple combinations of blackbody and power law models, showed that its X-ray flux can be decomposed in a pulsed thermal plus an unpulsed non-thermal components. However, if PSR B0943+10 is a nearly aligned rotator seen pole-on, as suggested by the radio data, it is difficult to reproduce the high observed pulsed fraction unless magnetic beaming is included. In this work we reanalyze all the available X-ray observations of PSR B0943+10 with simultaneous radio coverage, modeling its thermal emission with polar caps covered by a magnetized hydrogen atmosphere or with a condensed iron surface. The condensed surface model provides good fits to the spectra of both pulsar modes, but, similarly to the blackbody, it can not reproduce the observed pulse profiles, unless an additional power law with an ad hoc modulation is added. Instead, the pulse profiles and phase-resolved spectra are well described using the hydrogen atmosphere model to describe the polar cap emission, plus an unpulsed power law. For the X-ray brighter state (Q-mode) we obtain a best fit with a temperature kT~0.09 keV, an emitting radius R~260 m, a magnetic field consistent with the value of the dipole field of 4x10^12 G inferred from the timing parameters, and a small angle between the magnetic and spin axis, $\xi$=5. The corresponding parameters for the X-ray fainter state (B-mode) are kT~0.08 keV and R~170 m.Comment: 16 pages, 10 figures, accepted for publication in Ap

Neutron Stars—Cooling and Transport

Observations of thermal radiation from neutron stars can potentially provide information about the states of supranuclear matter in the interiors of these stars with the aid of the theory of neutron-star thermal evolution. We review the basics of this theory for isolated neutron stars with strong magnetic fields, including most relevant thermodynamic and kinetic properties in the stellar core, crust, and blanketing envelopes.The work of A.P. on the effects of strong magnetic fields on blanketing envelopes (Sect. 5.2 and Appendix B) has been supported by the Russian Science Foundation (grant 14-12-00316)

Thermal structure and cooling of superfluid neutron stars with accreted magnetized envelopes

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 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 interpretation of observations of isolated neutron stars hottest for their age, such as RX J0822-43 and PSR B1055-52.Comment: 15 pages, 12 figures, 2 tables. Corrected title only (v2

Atmospheres and Spectra of Strongly Magnetized Neutron Stars -- III. Partially Ionized Hydrogen Models

We construct partially ionized hydrogen atmosphere models for magnetized neutron stars in radiative equilibrium with surface fields B=10^12-5 \times 10^14 G and effective temperatures T_eff \sim a few \times 10^5-10^6 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=10^12-10^13 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\ga 10^14 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 \ga 10^14 G.Comment: 12 pages, 10 figures; ApJ, accepted (v599: Dec 20, 2003

Equation of state of classical Coulomb plasma mixtures

We develop analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasma mixtures. In the regime of strong Coulomb coupling, we use our previously developed analytic approximations for the free energy of one-component plasmas with rigid and polarizable electron background and apply the linear mixing rule (LMR). Other thermodynamic functions are obtained through analytic derivation of this free energy. In order to obtain an analytic approximation for the intermediate coupling and transition to the Debye-Hueckel limit, we perform hypernetted-chain calculations of the free energy, internal energy, and pressure for mixtures of different ion species and introduce a correction to the LMR, which allows a smooth transition from strong to weak Coulomb coupling in agreement with the numerical results.Comment: 6 pages, 7 figures; Phys. Rev. E. In v.2 after proofreading, minor typos are fixe

Statistical equilibrium and ion cyclotron absorption/emission in strongly magnetized plasmas

We calculate the transition rates between proton Landau levels due to non-radiative and radiative Coulomb collisions in an electron-proton plasma with strong magnetic field B. Both electron-proton collisions and proton-proton collisions are considered. The roles of the first-order cyclotron absorption and second-order free-free absorption and scattering in determining the line strength and shape as well as the continuum are analysed in detail. We solve the statistical balance equation for the populations of proton Landau levels. For temperatures \sim 10^6-10^7 K, the deviations of the proton populations from LTE are appreciable at density \rho < 0.1 B_{14}^{3.5} g cm^{-3}, where B_{14}=B/(10^{14} G). We present general formulae for the plasma emissivity and absorption coefficents under a wide range of physical conditions. Our results are useful for studying the possibility and the conditions of proton/ion cyclotron line formation in the near vicinity of highly magnetized neutron stars.Comment: 17 pages, 8 figures, MNRAS, accepte

Equation of state and opacities for hydrogen atmospheres of magnetars

The equation of state and radiative opacities of partially ionized, strongly magnetized hydrogen plasmas, presented in a previous paper [ApJ 585, 955 (2003), astro-ph/0212062] for the magnetic field strengths 8.e11 G < B < 3.e13 G, are extended to the field strengths 3.e13 G < B < 1.e15 G, relevant for magnetars. The first- and second-order thermodynamic functions and radiative opacities are calculated and tabulated for 5.e5 < T < 4.e7 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.Comment: 7 pages, 6 figures, LaTeX using emulateapj.cls (included). Accepted by Ap

Neutron Stars—Thermal Emitters

Confronting theoretical models with observations of thermal radiation emitted by neutron stars is one of the most important ways to understand the properties of both, superdense matter in the interiors of the neutron stars and dense magnetized plasmas in their outer layers. Here we review the theory of thermal emission from the surface layers of strongly magnetized neutron stars, and the main properties of the observational data. In particular, we focus on the nearby sources for which a clear thermal component has been detected, without being contaminated by other emission processes (magnetosphere, accretion, nebulae). We also discuss the applications of the modern theoretical models of the formation of spectra of strongly magnetized neutron stars to the observed thermally emitting objects.The work of A.P. has been partly supported by the RFBR (grant 14-02-00868) and by the Program “Leading Scientific Schools of RF” (grant NSh 294.2014.2)

Photoionization of hydrogen in atmospheres of magnetic neutron stars

The strong magnetic fields (B ~ 10^{12} - 10^{13} G) characteristic of neutron stars make all the properties of an atom strongly dependent on the transverse component K_\perp of its generalized momentum. In particular, the photoionization process is modified substantially: (i) threshold energies are decreased as compared with those for an atom at rest, (ii) cross section values are changed significantly, and (iii) 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, for the first time, employ 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_\perp, to arbitrary states of atomic motion. We fold the cross sections with the thermal distribution of atoms over 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 10^{5.5} K and decreasing density below 1 g/cm^3, i.e., for the conditions expected in atmospheres of middle-aged neutron stars.Comment: 19 pages including 8 figures, LaTeX (using aas2pp4.sty and epsf.sty). Accepted for publication in ApJ. PostScript available also at http://www.ioffe.rssi.ru/dtastrop.htm

Radiation from condensed surface of magnetic neutron stars

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 10^6 K (for Fe surface at B \sim 10^{13} G or H surface at B \sim a few times 10^{14} 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 where 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.Comment: 12 pages, 11 figures. ApJ, accepted (final version; eq.(3) corrected