Precession as a probe of the neutron star interior

Strong evidence that some neutron stars precess (nutate) with long periods (∼1 yr) challenges our current understanding of the neutron star interior. I describe how neutron star precession can be used to constrain the state of the interior in a new way. I argue that the standard picture of the outer core, in which superfluid neutrons coexist with type II, superconducting protons, requires revision. One possible resolution is that the protons are not type II, but type I. Another possibility is that the neutrons are normal in the outer core. I conclude with a brief discussion of the implications for detectable gravitational wave emission from millisecond pulsars. Much of the work described here was supported by the National Science Foundation under Grant AST-00098728.     

Fast rotation of neutron stars and equation of state of dense matter

Fast rotation of compact stars (at sub-millisecond period) and, in particular, their stability, are sensitive to the equation of state (EOS) of dense matter. Recent observations of XTE J1739-285 suggest that it contains a neutron star rotating at 1122 Hz. At such rotational frequency the effects of rotation on star’s structure are significant. We study the interplay of fast rotation, EOS, and gravitational mass of a sub-millisecond pulsar. We discuss the EOS dependence of spin-up to a sub-millisecond period, via mass accretion from a disk in a low-mass X-ray binary.     

Equation of state constraints from neutron stars

Recent measurements of thermal radiation from neutron stars have suggested a rather broad range of radiation radii ( ). Sources in M13 and Omega Cen imply R _∞∼12–14 km, but X7 in 47 Tuc implies R _∞∼16–20 km and RX J1856-3754 R _∞>17 km. If these measurements are all correct, only a limited selection of EOS’s could be consistent with them, but a broad range of neutron star masses (up to 2 M_⊙) would also be necessary. The surviving equations of state are incompatible with significant softening above nuclear saturation densities, such as would occur with Boson condensates, a low-density quark-hadron transition, or hyperons. Other potential constraints, such as from QPO’s, radio pulsar mass and moment of inertia measurements, and neutron star cooling, are compared. US DOE Grant DE-FG02-87ER-40317.     

Impact of neutron star oscillations on the accelerating electric field in the polar cap of pulsar

Pulsar “standard model”, that considers a pulsar as a rotating magnetized conducting sphere surrounded by plasma, is generalized to the case of oscillating star. We developed an algorithm for calculation of the Goldreich-Julian charge density for this case. We consider distortion of the accelerating zone in the polar cap of pulsar by neutron star oscillations. It is shown that for oscillation modes with high harmonic numbers (l,m) changes in the Goldreich-Julian charge density caused by pulsations of neutron star could lead to significant altering of an accelerating electric field in the polar cap of pulsar. In the moderately optimistic scenario, that assumes excitation of the neutron star oscillations by glitches, it could be possible to detect altering of the pulsar radioemission due to modulation of the accelerating field. This work was partially supported by RFBR grant 04-02-16720, and by the grants N.Sh.-5218.2006.2 and RNP-2.1.1.5940.     

Two-fluid models of superfluid neutron star cores

Both relativistic and non-relativistic two-fluid models of neutron star cores are constructed, using the constrained variational formalism developed by Brandon Carter and co-workers. We consider a mixture of superfluid neutrons and superconducting protons at zero temperature, taking into account mutual entrainment effects. Leptons, which affect the interior composition of the neutron star and contribute to the pressure, are also included. We provide the analytic expression of the Lagrangian density of the system, the so-called master function, from which the dynamical equations can be obtained. All the microscopic parameters of the models are calculated consistently using the non-relativistic nuclear energy density functional theory. For comparison, we have also considered relativistic mean field models. The correspondence between relativistic and non-relativistic hydrodynamical models is discussed in the framework of the recently developed 4D covariant formalism of Newtonian multifluid hydrodynamics. We have shown that entrainment effects can be interpreted in terms of dynamical effective masses that are larger in the relativistic case than in the Newtonian case. With the nuclear models considered in this work, we have found that the neutron relativistic effective mass is even greater than the bare neutron mass in the liquid core of neutron stars.     

An algorithm for solving the pulsar equation

We present an algorithm of finding numerical solutions of pulsar equation. The problem of finding the solutions was reduced to finding expansion coefficients of the source term of the equation in a base of orthogonal functions defined on the unit interval by minimizing a multi-variable mismatch function defined on the light cylinder. We applied the algorithm to Scharlemann and Wagoner boundary conditions by which a smooth solution is reconstructed that by construction passes successfully the Gruzinov’s test of the source function exponent.      

Internal heating and thermal emission from old neutron stars

The equilibrium composition of neutron star matter is achieved through weak interactions (direct and inverse beta decays), which proceed on relatively long time scales. If the density of a matter element is perturbed, it will relax to the new chemical equilibrium through non-equilibrium reactions, which produce entropy that is partly released through neutrino emission, while a similar fraction heats the matter and is eventually radiated as thermal photons. We examined two possible mechanisms causing such density perturbations: (1) the reduction in centrifugal force caused by spin-down (particularly in millisecond pulsars), leading to rotochemical heating, and (2) a hypothetical time-variation of the gravitational constant, as predicted by some theories of gravity and current cosmological models, leading to gravitochemical heating. If only slow weak interactions are allowed in the neutron star (modified Urca reactions, with or without Cooper pairing), rotochemical heating can account for the observed ultraviolet emission from the closest millisecond pulsar, PSR J0437-4715, which also provides a constraint on |dG/dt| of the same order as the best available in the literature. This work made use of NASA’s Astrophysics Data System Service, and received financial support from FONDECYT through regular grants 1020840 and 1060644.     

Mountains on neutron stars

The aim of this work is to compare a neutron star with an accreted crust and one with a non-accreted crust, and estimate which one is potentially a better source of gravitational waves (i.e. can sustain a larger “mountain”). To do this we present a new formalism, and find that a non-accreted crust can sustain a slightly larger “mountain”. We also discuss the importance of relativistic effects.      

The complex X-ray spectrum of the isolated neutron star RBS1223

We present a first analysis of a deep X-ray spectrum of the isolated neutron star RBS1223 obtained with XMM-Newton. Spectral data from four new monitoring observations in 2005/2006 were combined with archival observations obtained in 2003 and 2004 to form a spin-phase averaged spectrum containing 290 000 EPIC-pn photons. This spectrum shows higher complexity than its predecessors, and can be parameterised with two Gaussian absorption lines superimposed on a blackbody. The line centers, E ₂≃2E ₁, could be regarded as supporting the cyclotron interpretation of the absorption features in a field B∼4×10¹³ G. The flux ratio of those lines does not support this interpretation. Hence, either feature might be of truly atomic origin.      

The strongest cosmic magnets: soft gamma-ray repeaters and anomalous X-ray pulsars

Two classes of X-ray pulsars, the anomalous X-ray pulsars and the soft gamma-ray repeaters, have been recognized in the last decade as the most promising candidates for being magnetars: isolated neutron stars powered by magnetic energy. I review the observational properties of these objects, focussing on the most recent results, and their interpretation in the magnetar model. Alternative explanations, in particular those based on accretion from residual disks, are also considered. The possible relations between these sources and other classes of neutron stars and astrophysical objects are also discussed.     

Slow glitches in the pulsar B1822-09

The pulsar B1822-09 (J1825-0935) experienced a series of five unusual, slow glitches over the 1995–2004 interval. The results of further study of this unusual glitch phenomenon are presented. It is also reported the detection a new glitch of typical signature that occurred in the pulsar period in 2006 January.      

A numerical survey of neutron star crustal density profiles

An accurate numerical survey of the density profiles corresponding to the crusts of neutron stars for representative equation of state models is presented. This will find application in calculations of thermal and magnetic evolution of neutron stars.     

A microscopic equation of state for protoneutron stars

We study the structure of protoneutron stars within the finite-temperature Brueckner–Bethe–Goldstone many-body theory. If nucleons, hyperons, and leptons are present in the stellar core, we find that neutrino trapping stiffens considerably the equation of state, because hyperon onsets are shifted to larger baryon density. However, the value of the critical mass turns out to be smaller than the “canonical” value 1.44M _⊙. We find that the inclusion of a hadron-quark phase transition increases the critical mass and stabilizes it at about 1.5–1.6M _⊙.      

First-principles point-defect calculations for solid neutron star matter

Formation enthalpies are calculated for a number of point-defect structures in solid neutron star matter at densities above the neutron-drip threshold. The enthalpies obtained show that an amorphous heterogeneous solid phase is formed at temperatures in a glass transition region, and is likely to persist as the star cools. Its structural differences from the homogeneous body-centred cubic lattice previously assumed make it necessary to reconsider predictions of neutron-star magnetic field evolution, and severely limit the role of conventional superfluid neutron vortex pinning in the interpretation of pulsar glitch phenomena.     

Simulations of glitches in isolated pulsars

Many radio pulsars exhibit glitches wherein the star's spin rate increases fractionally by ∼10⁻¹⁰–10⁻⁶. Glitches are ascribed to variable coupling between the neutron star crust and its superfluid interior. With the aim of distinguishing among different theoretical explanations for the glitch phenomenon, we study the response of a neutron star to two types of perturbations to the vortex array that exists in the superfluid interior: (1) thermal motion of vortices pinned to inner crust nuclei, initiated by sudden heating of the crust, (e.g., a starquake), and (2) mechanical motion of vortices (e.g., from crust cracking by superfluid stresses). Both mechanisms produce acceptable fits to glitch observations in four pulsars, with the exception of the 1989 glitch in the Crab pulsar, which is best fitted by the thermal excitation model. The two models make different predictions for the generation of internal heat and subsequent enhancement of surface emission. The mechanical glitch model predicts a negligible temperature increase. For a pure and highly conductive crust, the thermal glitch model predicts a surface temperature increase of as much as ∼2 per cent, occurring several weeks after the glitch. If the thermal conductivity of the crust is lowered by a high concentration of impurities, however, the surface temperature increases by ∼10 per cent about a decade after a thermal glitch. A thermal glitch in an impure crust is consistent with the surface emission limits following the 2000 January glitch in the Vela pulsar. Future surface emission measurements coordinated with radio observations will constrain glitch mechanisms and the conductivity of the crust.     

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.     

Towards self-consistent models of isolated neutron stars

We propose a self–consistent model to explain all observational properties reported so far on the isolated neutron star (INS) RX J0720-3125 with the aim of giving a step forward towards our understanding of INSs. For a given magnetic field structure, which is mostly confined to the crust and outer layers, we obtain theoretical models and spectra which account for the broadband spectral energy distribution (including the apparent optical excess), the X-ray pulsations, and for the spectral feature seen in the soft X-ray spectrum of RX J0720-3125 around 0.3 keV. By fitting our models to existing archival X-ray data from 6 different XMM–Newton observations and available optical data, we show that the observed properties are fully consistent with a normal neutron star, with a proper radius of about 12 km, a temperature at the magnetic pole of about 100 eV, and a magnetic field strength of 2–3×10¹³ G. Moreover, we are able to reproduce the observed long–term spectral evolution in terms of free precession which induces changes in the orientation angles of about 40 degrees with a periodicity of 7 years. In addition to the evidence of internal toroidal components, we also find strong evidence of non–dipolar magnetic fields, since all spectral properties are better reproduced with models with strong quadrupolar components.