Can a slowly rotating neutron star be a radio pulsar?

It is shown that the radius of curvature of magnetic field lines in the polar region of a rotating magnetized neutron star can be significantly less than the usual radius of curvature of the dipole magnetic field. The magnetic field in the polar cap is distorted by toroidal electric currents flowing in the neutron star crust. These currents close up the magnetospheric currents driven by the electron–positron plasma generation process in the pulsar magnetosphere. Owing to the decrease in the radius of curvature, electron–positron plasma generation becomes possible even for slowly rotating neutron stars, with   PB ^−2/3₁₂ < 10 s  , where P is the period of star rotation and   B ₁₂= B /10¹² G  is the magnitude of the magnetic field on the star surface.     

Axisymmetric magnetic fields in stars: relative strengths of poloidal and toroidal components

In this third paper in a series on stable magnetic equilibria in stars, I look at the stability of axisymmetric field configurations and, in particular, the relative strengths of the toroidal and poloidal components. Both toroidal and poloidal fields are unstable on their own, and stability is achieved by adding the two together in some ratio. I use Tayler's stability conditions for toroidal fields and other analytic tools to predict the range of stable ratios and then check these predictions by running numerical simulations. If the energy in the poloidal component as a fraction of the total magnetic energy is written as E_p / E , it is found that the stability condition is a ( E / U ) < E_p / E ≲ 0.8 where E /U is the ratio of magnetic to gravitational energy in the star and a is some dimensionless factor whose value is of order 10 in a main-sequence star and of order 10³ in a neutron star. In other words, whilst the poloidal component cannot be significantly stronger than the toroidal, the toroidal field can be very much stronger than the poloidal–given that in realistic stars we expect E / U < 10⁻⁶. The implications of this result are discussed in various contexts such as the emission of gravitational waves by neutron stars, free precession and a 'hidden' energy source for magnetars.     

Emergence of magnetic field due to spin-polarized baryon matter in neutron stars

A model of the ferromagnetic origin of magnetic fields of neutron stars is considered. In this model, the magnetic phase transition occurs inside the core of neutron stars soon after formation. However, owing to the high electrical conductivity the core magnetic field is initially fully screened. We study how this magnetic field emerges for an outside observer. After some time, the induced field that screens the ferromagnetic field decays enough to uncover a detectable fraction of the ferromagnetic field. We calculate the time-scale of decay of the screening field and study how it depends on the size of the ferromagnetic core. We find that the same fractional decay of the screening field occurs earlier for larger cores. We conjecture that weak fields of millisecond pulsars, B ∼10⁸–10⁹ G, could be identified with ferromagnetic fields of unshielded fraction ε ∼10⁻⁴–10⁻³ resulting from the decay of screening fields by a factor 1− ε in ∼10⁸ yr since their birth.     

Low-frequency gravitational waves from cosmological compact binaries

We consider gravitational waves emitted by various populations of compact binaries at cosmological distances. We use population synthesis models to characterize the properties of double neutron stars, double black holes and double white dwarf binaries, and white dwarf–neutron star, white dwarf–black hole and black hole–neutron star systems.
We use the observationally determined cosmic star formation history to reconstruct the redshift distribution of these sources and their merging rate evolution.
The gravitational signals emitted by each source during its early spiralling in phase add randomly to produce a stochastic background in the low-frequency band with spectral strain amplitude between ~10⁻¹⁸ and ~5×10⁻¹⁷ Hz^−1/2 at frequencies in the interval ~5×10⁻⁶–5×10⁻⁵ Hz.
The overall signal, which at frequencies above 10⁻⁴ Hz is largely dominated by double white dwarf systems, might be detectable with LISA in the frequency range 1–10 mHz and acts like a confusion-limited noise component, which might limit the LISA sensitivity at frequencies above 1 mHz.     

Continuous frequency spectrum of the global hydromagnetic oscillations of a magnetically confined mountain on an accreting neutron star

We compute the continuous part of the ideal-magnetohydrodynamic (ideal-MHD) frequency spectrum of a polar mountain produced by magnetic burial on an accreting neutron star. Applying the formalism developed by Hellsten & Spies, extended to include gravity, we solve the singular eigenvalue problem subject to line-tying boundary conditions. This spectrum divides into an Alfvén part and a cusp part. The eigenfunctions are chirped and anharmonic with an exponential envelope, and the eigenfrequencies cover the whole spectrum above a minimum ω_low. For equilibria with accreted mass  1.2 × 10⁻⁶≲ M _a/M_⊙≲ 1.7 × 10⁻⁴  and surface magnetic fields  10¹¹≲ B _*/G ≲ 10¹³, ω_low  is approximately independent of   B _*  , and increases with M _a. The results are consistent with the Alfvén spectrum excited in numerical simulations with the zeus-mp solver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than ∼100 Hz. The implications for gravitational-wave searches for low-mass X-ray binaries are considered briefly.     

Burial of the polar magnetic field of an accreting neutron star – II. Hydromagnetic stability of axisymmetric equilibria

The theory of polar magnetic burial in accreting neutron stars predicts that a mountain of accreted material accumulates at the magnetic poles of the star, and that, as the mountain spreads equatorward, it is confined by, and compresses, the equatorial magnetic field. Here, we extend previous, axisymmetric, Grad–Shafranov calculations of the hydromagnetic structure of a magnetic mountain up to accreted masses as high as   M _a= 6 × 10⁻⁴ M_⊙  , by importing the output from previous calculations (which were limited by numerical problems and the formation of closed bubbles to   M _a < 10⁻⁴ M_⊙  ) into the time-dependent, ideal-magnetohydrodynamic code zeus-3d and loading additional mass on to the star dynamically. The rise of buoyant magnetic bubbles through the accreted layer is observed in these experiments. We also investigate the stability of the resulting hydromagnetic equilibria by perturbing them in zeus-3d . Surprisingly, it is observed that the equilibria are marginally stable for all   M _a≤ 6 × 10⁻⁴ M_⊙  ; the mountain oscillates persistently when perturbed, in a combination of Alfvén and acoustic modes, without appreciable damping or growth, and is therefore not disrupted (apart from a transient Parker instability initially, which expels <1 per cent of the mass and magnetic flux).     

The evolution of low-metallicity asymptotic giant branch stars and the formation of carbon-enhanced metal-poor stars

We investigate the behaviour of asymptotic giant branch (AGB) stars between metallicities   Z = 10⁻⁴  and 10⁻⁸. We determine which stars undergo an episode of flash-driven mixing, where protons are ingested into the intershell convection zone, as they enter the thermally pulsing AGB phase and which undergo third dredge-up. We find that flash-driven mixing does not occur above a metallicity of   Z = 10⁻⁵  for any mass of star and that stars above  2 M_⊙  do not experience this phenomenon at any metallicity. We find carbon ingestion (CI), the mixing of carbon into the tail of hydrogen-burning region, occurs in the mass range  2 M_⊙  to around  4 M_⊙  . We suggest that CI may be a weak version of the flash-driven mechanism. We also investigate the effects of convective overshooting on the behaviour of these objects. Our models struggle to explain the frequency of Carbon-Enhanced Metal-Poor (CEMP) stars that have both significant carbon and nitrogen enhancement. Carbon can be enhanced through flash-driven mixing, CI or just third dredge-up. Nitrogen can be enhanced through hot bottom burning and the occurrence of hot dredge-up also converts carbon into nitrogen. The C/N ratio may be a good indicator of the mass of the primary AGB stars.     

Hot stars in old stellar populations: a continuing need for intermediate ages

We present numerical investigations into the formation of massive stars from turbulent cores of density structure  ρ∝ r ^−1.5  . The results of five hydrodynamical simulations are described, following the collapse of the core, fragmentation and the formation of small clusters of protostars. We generate two different initial turbulent velocity fields corresponding to power-law spectra   P ∝ k ⁻⁴  and   P ∝ k ^−3.5  , and we apply two different initial core radii. Calculations are included for both completely isothermal collapse, and a non-isothermal equation of state above a critical density  (10⁻¹⁴ g cm⁻³)  . Our calculations reveal the preference of fragmentation over monolithic star formation in turbulent cores. Fragmentation was prevalent in all the isothermal cases. Although disc fragmentation was largely suppressed in the non-isothermal runs due to the small dynamic range between the initial density and the critical density, our results show that some fragmentation still persisted. This is inconsistent with previous suggestions that turbulent cores result in the formation of a single massive star. We conclude that turbulence cannot be measured as an isotropic pressure term.     

Magnetic fields and rotation in white dwarfs and neutron stars

Recent spectropolarimetric observations of Ap and Bp stars with improved sensitivity have suggested that most Ap and Bp stars are magnetic with dipolar fields of at least a few hundred gauss. These new estimates suggest that the range of magnetic fluxes found for the majority of magnetic white dwarfs is similar to that of main-sequence Ap–Bp stars, thus strengthening the empirical evidence for an evolutionary link between magnetism on the main sequence and magnetism in white dwarfs. We draw parallels between the magnetic white dwarfs and the magnetic neutron stars and argue that the observed range of magnetic fields in isolated neutron stars  ( B_p ∼ 10¹¹–10¹⁵ G)  could also be explained if their mainly O-type progenitors have effective dipolar fields in the range of a few gauss to a few kilogauss, assuming approximate magnetic flux conservation with the upper limit being consistent with the recent measurement of a field of   B_p ∼ 1100 G  for θ Orion C.
In the magnetic field–rotation diagram, the magnetic white dwarfs can be divided into three groups of different origin: a significant group of strongly magnetized slow rotators  ( P _rot∼ 50 –100 yr)  that have originated from single-star evolution, a group of strongly magnetized fast rotators  ( P _rot∼ 700 s)  , typified by EUVE J0317–853, that have originated from a merger, and a group of modest rotators ( P _rot∼ hours–days) of mixed origin (single-star and CV-type binary evolution). We propose that the neutron stars may similarly divide into distinct classes at birth , and suggest that the magnetars may be the counterparts of the slowly rotating high-field magnetic white dwarfs.     

Resistive relaxation of a magnetically confined mountain on an accreting neutron star

Three-dimensional numerical magnetohydrodynamic (MHD) simulations are performed to investigate how a magnetically confined mountain on an accreting neutron star relaxes resistively. No evidence is found for non-ideal MHD instabilities on a short time-scale, such as the resistive ballooning mode or the tearing mode. Instead, the mountain relaxes gradually as matter is transported across magnetic surfaces on the diffusion time-scale, which evaluates to  τ_I∼ 10⁵–10⁸ yr  (depending on the conductivity of the neutron star crust) for an accreted mass of   M _a= 1.2 × 10⁻⁴ M_⊙  . The magnetic dipole moment simultaneously re-emerges as the screening currents dissipate over  τ_I  . For non-axisymmetric mountains, ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane. Ideal-MHD oscillations on the Alfvén time-scale, which can be excited by external influences, such as variations in the accretion torque, compress the magnetic field and hence decrease  τ_I  by one order of magnitude relative to its standard value (as computed for the static configuration). The implications of long-lived mountains for gravitational wave emission from low-mass X-ray binaries are briefly explored.     

The bottom magnetic field and magnetosphere evolution of neutron star in low-mass X-ray binary

The accretion-induced neutron star (NS) magnetic field evolution is studied through considering the accretion flow to drag the field lines aside and dilute the polar-field strength, and as a result the equatorial field strength increases, which is buried inside the crust on account of the accretion-induced global compression of star crust. The main conclusions of model are as follows: (i) the polar field decays with increase in the accreted mass; (ii) the bottom magnetic field strength of about 10⁸ G can occur when the NS magnetosphere radius approaches the star radius, and it depends on the accretion rate as     ; and (iii) the NS magnetosphere radius decreases with accretion until it reaches the star radius, and its evolution is little influenced by the initial field and the accretion rate after accreting  ∼0.01 M_⊙  , which implies that the magnetosphere radii of NSs in low-mass X-ray binaries would be homogeneous if they accreted the comparable masses. As an extension, the physical effects of the possible strong magnetic zone in the X-ray NSs and recycled pulsars are discussed. Moreover, the strong magnetic fields in the binary pulsars PSR 1831−00 and PSR 1718−19 after accreting about  0.5 M_⊙  in the binary-accretion phase,  8.7 × 10¹⁰  and  1.28 × 10¹² G  , respectively, can be explained through considering the incomplete frozen flow in the polar zone. As an expectation of the model, the existence of the low magnetic field  (∼3 × 10⁷ G)  NSs or millisecond pulsars is suggested.     

Magnetic and spin evolution of neutron stars in close binaries

The evolution of neutron stars in close binary systems with a low-mass companion is considered, assuming the magnetic field to be confined within the solid crust. We adopt the standard scenario for the evolution in a close binary system, in which the neutron star passes through four evolutionary phases ('isolated pulsar'–'propeller'– accretion from the wind of a companion – accretion resulting from Roche-lobe overflow). Calculations have been performed for a great variety of parameters characterizing the properties of both the neutron star and the low-mass companion. We find that neutron stars with more or less standard magnetic field and spin period that are processed in low-mass binaries can evolve to low-field rapidly rotating pulsars. Even if the main-sequence life of a companion is as long as 10¹⁰ yr, the neutron star can maintain a relatively strong magnetic field to the end of the accretion phase. The model that is considered can account well for the origin of millisecond pulsars.     

Radiative transitions of the helium atom in highly magnetized neutron star atmospheres

Recent observations of thermally emitting isolated neutron stars revealed spectral features that could be interpreted as radiative transitions of He in a magnetized neutron star atmosphere. We present Hartree–Fock calculations of the polarization-dependent photoionization cross-sections of the He atom in strong magnetic fields ranging from 10¹² to 10¹⁴ G. Convenient fitting formulae for the cross-sections are given along with the related oscillator strengths for various bound–bound transitions. The effects of finite nucleus mass on the radiative absorption cross-sections are examined using perturbation theory.     

The violent past of Cygnus X-2

Cygnus X-2 appears to be the descendant of an intermediate-mass X-ray binary (IMXB). Using Mazzitelli's stellar code we compute detailed evolutionary sequences for the system and find that its prehistory is sensitive to stellar input parameters, in particular the amount of core overshooting during the main-sequence phase. With standard assumptions for convective overshooting a case B mass transfer starting with a 3.5-M_⊙ donor star is the most likely evolutionary solution for Cygnus X-2. This makes the currently observed state rather short-lived, of order 3 Myr, and requires a formation rate > 10⁻⁷–10⁻⁶ yr⁻¹ of such systems in the Galaxy. Our calculations show that neutron star IMXBs with initially more massive donors (≳4 M_⊙) encounter a delayed dynamical instability; they are unlikely to survive this rapid mass transfer phase. We determine limits for the age and initial parameters of Cygnus X-2 and calculate possible dynamical orbits of the system in a realistic Galactic potential, given its observed radial velocity. We find trajectories which are consistent with a progenitor binary on a circular orbit in the Galactic plane inside the solar circle that received a kick velocity ≤200 km s⁻¹ at the birth of the neutron star. The simulations suggest that about 7 per cent of IMXBs receiving an arbitrary kick velocity from a standard kick velocity spectrum would end up in an orbit similar to Cygnus X-2, while about 10 per cent of them reach yet larger Galactocentric distances.     

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.     

What is the nature of RX J0720.4–3125?

RX J0720.4–3125 has recently been identified as a pulsating soft X-ray source in the ROSAT all-sky survey with a period of 8.391 s. Its spectrum is well characterized by a blackbody with a temperature of 8 × 10⁵ K. We propose that the radiation from this object is thermal emission from a cooling neutron star. For this blackbody temperature we can obtain a robust estimate of the object's age of ∼ 3 × 10⁵ yr, yielding a polar field ∼ 10¹⁴ G for magnetic dipole spin-down and a value of P compatible with current observations.     

Boundary layer on the surface of a neutron star

In an attempt to model the accretion on to a neutron star in low-mass X-ray binaries, we present 2D hydrodynamical models of the gas flow in close vicinity of the stellar surface. First, we consider a gas pressure-dominated case, assuming that the star is non-rotating. For the stellar mass we take   M _star= 1.4 × 10⁻² M_⊙  and for the gas temperature   T = 5 × 10⁶ K  . Our results are qualitatively different in the case of a realistic neutron star mass and a realistic gas temperature of T ≃ 10⁸ K, when the radiation pressure dominates. We show that to get the stationary solution in a latter case, the star most probably has to rotate with the considerable velocity.     

Star formation triggered by supernova explosions in young galaxies

We study the evolution of supernova remnants in a low-metallicity medium   Z /Z_⊙= 10⁻⁴ to 10⁻²  in the early universe, using one-dimensional hydrodynamics with non-equilibrium chemistry. Once a post-shock layer is able to cool radiatively, a dense shell forms behind the shock. If this shell becomes gravitationally unstable and fragments into pieces, next-generation stars are expected to form from these fragments. To explore the possibility of this triggered star formation, we apply a linear perturbation analysis of an expanding shell to our results and constrain the parameter range of ambient density, explosion energy and metallicity where fragmentation of the shell occurs. For the explosion energy of  10⁵¹ erg (10⁵² erg)  , the shell fragmentation occurs for ambient densities higher than  ≳10² cm⁻³ (10 cm⁻³  ), respectively. This condition depends little on the metallicity in the ranges we examined. We find that the mode of star formation triggered occurs only in massive  (≳10⁸ M_⊙)  haloes.     

The micro-glitch in PSR B1821−24: a case for a strange pulsar?

The single glitch observed in PSR B1821−24, a millisecond pulsar in M28, is unusual on two counts. First, the magnitude of this glitch is at least an order of magnitude smaller  (Δν/ν∼ 10⁻¹¹)  than the smallest glitch observed to date. Secondly, all other glitching pulsars have strong magnetic fields with   B ≳ 10¹¹ G  and are young, whereas PSR B1821−24 is an old recycled pulsar with a field strength of  2.25 × 10⁹ G  . We have earlier suggested that some of the recycled pulsars could actually be strange quark stars. In this work, we argue that the crustal properties of such a strange pulsar are just right to give rise to a glitch of this magnitude, explaining the scarcity of larger glitches in millisecond pulsars.     

The strong magnetic fields of the X-ray pulsars Hercules X-1 and 4U 1626–67 and their evolutionary scenarios

We consider the magnetic and spin evolution of the X-ray binary pulsars Her X-1 and 4U 1626–67, assuming that their magnetic fields are of crustal origin. We adopt the standard evolutionary model which implies that the neutron star passes through several phases in a binary system ('isolated pulsar' – propeller – wind accretion – Roche lobe overflow). In the framework of the model under consideration, the strong magnetic fields of relatively old pulsars like Her X-1 and 4U 1626–67 can naturally be understood if, at their birth, they had a sufficiently strong magnetic field, ∼3 × 10¹³ G, comparable to the maximal field observed in radio pulsars.