Self-similar pressure oscillations in neutron star envelopes as probes of neutron star structure

We study eigenmodes of acoustic oscillations of high multipolarity l ∼ 100–1000 and high frequency (∼100 kHz), localized in neutron star envelopes. We show that the oscillation problem is self-similar. Once the oscillation spectrum is calculated for a given equation of state (EOS) in the envelope and given stellar mass M and radius R , it can be rescaled to a star with any M and R (but the same EOS in the envelope). For l ≳ 300, the modes can be subdivided into the outer and inner ones. The outer modes are mainly localized in the outer envelope. The inner modes are mostly localized near the neutron drip point, being associated with the softening of the EOS after the neutron drip. We calculate oscillation spectra for the EOSs of cold-catalyzed and accreted matter and show that the spectra of the inner modes are essentially different. A detection and identification of high-frequency pressure modes would allow one to infer M and R and determine also the EOS in the envelope (accreted or ground state) providing a new, potentially powerful method to explore the main parameters and internal structure of neutron stars.     

Oscillations of rapidly rotating stratified neutron stars

We use time evolutions of the linear perturbation equations to study the oscillations of rapidly rotating neutrons stars. Our models account for the buoyancy due to composition gradients and we study, for the first time, the nature of the resultant g modes in a fast spinning star. We provide detailed comparisons of non-stratified and stratified models. This leads to an improved understanding of the relationship between the inertial modes of a non-stratified star and the g modes of a stratified system. In particular, we demonstrate that each g mode becomes rotation dominated, i.e. approaches a particular inertial mode, as the rotation rate of the star is increased. We also discuss issues relating to the gravitational wave driven instability of the various classes of oscillation modes.     

Almost analytic models of ultramagnetized neutron star envelopes

Recent ROSAT measurements show that the X-ray emission from isolated neutron stars is modulated at the stellar rotation period. To interpret these measurements, one needs precise calculations of the heat transfer through the thin insulating envelopes of neutron stars. We present nearly analytic models of the thermal structure of the envelopes of ultramagnetized neutron stars. Specifically, we examine the limit in which only the ground Landau level is filled. We use the models to estimate the amplitude of modulation expected from non-uniformities in the surface temperatures of strongly magnetized neutron stars. In addition, we estimate cooling rates for stars with fields B  ∼ 10¹⁵ − 10¹⁶ G, which are relevant to models that invoke 'magnetars' to account for soft γ-ray emission from some repeating sources.     

On the dynamics of superfluid neutron star cores

We discuss the nature of the various modes of pulsation of superfluid neutron stars using comparatively simple Newtonian models and the Cowling approximation. The matter in these stars is described in terms of a two-fluid model, where one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars, and the other fluid represents a conglomerate of all other constituents (crust nuclei, protons, electrons, etc.). In our model, we incorporate the non-dissipative interaction known as the entrainment effect, whereby the momentum of one constituent (e.g. the neutrons) carries along part of the mass of the other constituent. We show that there is no independent set of pulsating g-modes in a non-rotating superfluid neutron star core, even though the linearized superfluid equations contain a well-defined (and real-valued) analogue to the so-called Brunt–Väisälä frequency. Instead, what we find are two sets of spheroidal perturbations whose nature is predominately acoustic. In addition, an analysis of the zero-frequency subspace (i.e. the space of time-independent perturbations) reveals two sets of degenerate spheroidal perturbations, which we interpret to be the missing g-modes, and two sets of toroidal perturbations. We anticipate that the degeneracy of all these zero-frequency modes will be broken by the Coriolis force in the case of rotating stars. To illustrate this we consider the toroidal pulsation modes of a slowly rotating superfluid star. This analysis shows that the superfluid equations support a new class of r-modes, in addition to those familiar from, for example, geophysical fluid dynamics. Finally, the role of the entrainment effect on the superfluid mode frequencies is shown explicitly via solutions to dispersion relations that follow from a 'local' analysis of the linearized superfluid equations.     

Multidimensional thermal structure of magnetized neutron star envelopes

Recently launched X-ray telescopes have discovered several candidate isolated neutron stars. The thermal radiation from these objects may potentially constrain our understanding of nuclear physics in a realm inaccessible to terrestrial experiments. To translate the observed fluxes from neutron stars into constraints, one needs precise calculations of the heat transfer through the thin insulating envelopes of neutron stars. We describe models of the thermal structure of the envelopes of neutron stars with magnetic fields up to 10¹⁴ G. Unlike earlier work, we infer the properties of envelope models in two dimensions and precisely account for the quantization of the electron phase-space. Both dipole and uniformly magnetized envelopes are considered.     

Resonant cyclotron scattering and Comptonization in neutron star magnetospheres

Resonant cyclotron scattering of the surface radiation in the magnetospheres of neutron stars may considerably modify the emergent spectra and impede efforts to constrain neutron star properties. Resonant cyclotron scattering by a non-relativistic warm plasma in an inhomogeneous magnetic field has a number of unusual characteristics. (i) In the limit of high resonant optical depth, the cyclotron resonant layer is half opaque , in sharp contrast to the case of non-resonant scattering. (ii) The transmitted flux is on average Compton up-scattered by  ∼1 + 2β_T  , where  β_T  is the typical thermal velocity in units of the velocity of light; the reflected flux has on average the initial frequency. (iii) For both the transmitted and reflected fluxes, the dispersion of intensity decreases with increasing optical depth. (iv) The emergent spectrum is appreciably non-Planckian while narrow spectral features produced at the surface may be erased.
We derive semi-analytically modification of the surface Planckian emission due to multiple scattering between the resonant layers and apply the model to the anomalous X-ray pulsar 1E  1048.1 − 5937  . Our simple model fits just as well as the 'canonical' magnetar spectra model of a blackbody plus power law.     

Minimal models of cooling neutron stars with accreted envelopes

We study the 'minimal' cooling scenario of superfluid neutron stars with nucleon cores, where the direct Urca process is forbidden and enhanced cooling is produced by neutrino emission due to the Cooper pairing of neutrons. Extending our recent previous work, we include the effects of surface accreted envelopes of light elements. We employ the phenomenological density-dependent critical temperatures   T _cp(ρ)  and   T _cnt(ρ)  of singlet-state proton and triplet-state neutron pairing in a stellar core, as well as the critical temperature   T _cns(ρ)  of singlet-state neutron pairing in a stellar crust. We show that the presence of accreted envelopes simplifies the interpretation of observations of thermal radiation from isolated neutron stars in the scenario of our recent previous work and widens the class of models for nucleon superfluidity in neutron star interiors consistent with the observations.     

The magnetosphere of oscillating neutron stars in general relativity

Just as a rotating magnetized neutron star has material pulled away from its surface to populate a magnetosphere, a similar process can occur as a result of neutron-star pulsations rather than rotation. This is of interest in connection with the overall study of neutron star oscillation modes but with a particular focus on the situation for magnetars. Following a previous Newtonian analysis of the production of a force-free magnetosphere in this way Timokhin et al., we present here a corresponding general-relativistic analysis. We give a derivation of the general relativistic Maxwell equations for small-amplitude arbitrary oscillations of a non-rotating neutron star with a generic magnetic field and show that these can be solved analytically under the assumption of low current density in the magnetosphere. We apply our formalism to toroidal oscillations of a neutron star with a dipole magnetic field and find that the low current density approximation is valid for at least half of the oscillation modes, similarly to the Newtonian case. Using an improved formula for the determination of the last closed field line, we calculate the energy losses resulting from toroidal stellar oscillations for all of the modes for which the size of the polar cap is small. We find that general relativistic effects lead to shrinking of the size of the polar cap and an increase in the energy density of the outflowing plasma. These effects act in opposite directions but the net result is that the energy loss from the neutron star is significantly smaller than suggested by the Newtonian treatment.     

Thermal relaxation in young neutron stars

The internal properties of the neutron star crust can be probed by observing the epoch of thermal relaxation. After the supernova explosion, powerful neutrino emission quickly cools the stellar core, while the crust stays hot. The cooling wave then propagates through the crust, as a result of its finite thermal conductivity. When the cooling wave reaches the surface (age 10–100 yr) , the effective temperature drops sharply from 250 eV to 30 or 100 eV, depending on the cooling model. The crust relaxation time is sensitive to the (poorly known) microscopic properties of matter of subnuclear density, such as the heat capacity, thermal conductivity, and superfluidity of free neutrons. We calculate the cooling models with the new values of the electron thermal conductivity in the inner crust, based on a realistic treatment of the shapes of atomic nuclei. Superfluid effects may shorten the relaxation time by a factor of 4. The comparison of theoretical cooling curves with observations provides a potentially powerful method of studying the properties of the neutron superfluid and highly unusual atomic nuclei in the inner crust.     

Atmospheres and spectra of strongly magnetized neutron stars

We construct atmosphere models for strongly magnetized neutron stars with surface fields     and effective temperatures     . The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars, including radio pulsars, soft gamma-ray repeaters, and anomalous X-ray pulsars. In our models, the atmosphere is composed of pure hydrogen or helium and is assumed to be fully ionized. The radiative opacities include free–free absorption and scattering by both electrons and ions computed for the two photon polarization modes in the magnetized electron–ion plasma. Since the radiation emerges from deep layers in the atmosphere with     , plasma effects can significantly modify the photon opacities by changing the properties of the polarization modes. In the case where the magnetic field and the surface normal are parallel, we solve the full, angle-dependent, coupled radiative transfer equations for both polarization modes. We also construct atmosphere models for general field orientations based on the diffusion approximation of the transport equations and compare the results with models based on full radiative transport. In general, the emergent thermal radiation exhibits significant deviation from blackbody, with harder spectra at high energies. The spectra also show a broad feature     around the ion cyclotron resonance     , where Z and A are the atomic charge and atomic mass of the ion, respectively; this feature is particularly pronounced when     . Detection of the resonance feature would provide a direct measurement of the surface magnetic fields on magnetars.