Toroidal magnetic field of a superfluid neutron star in a postnewtonian approximation

The effect of proton superconductivity on the generation of a toroidal magnetic field inside a neutron star is examined. It is shown that including the entrainment of superconducting protons by superfluid neutrons does not change the previously obtained results. Proton superconductivity does influence the structure of the generated magnetic field since, over a time on the order of 10⁴–10⁵ years, the magnetic field increases linearly with time and can exceed the first critical field for proton superconductivity. The distribution of the stationary toroidal magnetic field inside a neutron star is also found.     

NuSTAR observations of the X-ray pulsar LMC X-4: A constraint on the magnetic field and tomography of the system in the fluorescent iron line

We present the results of the spectral and timing analysis of the X-ray pulsar LMC X-4 based on data from the NuSTAR observatory in the broad X-ray energy range 3–79 keV. Along with a detailed analysis of the source’s averaged spectrum, high-precision spectra corresponding to different phases of the neutron star spin cycle have been obtained for the first time. The Comptonization model is shown to describe best the source’s spectrum, and the evolution of its parameters as a function of the pulse phase has been traced. For all spectra (the averaged and phase-resolved ones) in the energy range 5–55 keV we have searched for the cyclotron absorption line. The derived upper limit on the optical depth of the cyclotron line τ ~ 0.15 (3σ) points to the absence of this feature in the given energy range, which provides a constraint on the magnetic field of the neutron star: B <3 × 10¹¹ or >6.5 × 10¹² G. The latter constraint is consistent with the magnetic field estimate obtained by analyzing the pulsar’s power spectrum, B ? 3 × 10¹³ G. Based on our analysis of the phase-resolved spectra, we have determined the delay between the emission peaks and the equivalent width of the fluorescent iron line. This delay depends on the orbital phase and is apparently associated with the travel time of photons between the emitting regions in the vicinity of the neutron star and the region where the flux is reflected (presumably in the inflowing stream or at the place of interaction between the stream and the outer edge of the accretion disk).     

General properties of magnetic CP stars

We present the review of our previous studies related to observational evidence of the fossil field hypothesis of formation and evolution of magnetic and non-magnetic chemically peculiar stars. Analysis of the observed data shows that these stars acquire their main properties in the process of gravitational collapse. In the non-stationary Hayashi phase, a magnetic field becomes weakened and its configuration complicated, but the fossil field global orientation remains. After a non-stationary phase, relaxation of young star’s tangled field takes place and by the time of joining ZAMS (Zero Age Main Sequence) it is generally restored to a dipole structure. Stability of dipole structures allows them to remain unchanged up to the end of their life on the Main Sequence which is 10⁹ years at most.     

Dynamics of the flows accreting onto a magnetized neutron star

We investigate the unsteady column accretion of material at a rate \(10^{15} g s^{ - 1} \leqslant \dot M \leqslant 10^{16} g s^{ - 1}\) onto the surface of a magnetized neutron star using a modified first-order Godunov method with splitting. We study the dynamics of the formation and evolution of a shock in an accretion column near the surface of a star with a magnetic field 5×10¹¹≤B≤10¹³ G. An effective transformation of the accretion flow energy into cyclotron radiation is shown to be possible for unsteady accretion with a collisionless shock whose front executes damped oscillations. The collisionless deceleration of the accreting material admits the conservation of a fraction of the heavy nuclei that have not been destroyed in spallation reactions. The fraction of the CNO nuclei that reach the stellar atmosphere is shown to depend on the magnetic field strength of the star.     

New results of magnetic field measurements for BP Tau

We present measurements of the longitudinal magnetic field component B _‖ of the young star BP Tau in the He I 5876 emission line formation region, i.e., in the accretion flow near the stellar surface. The values obtained (?1.7 kG and ?1.0 kG in 2000 and 2001, respectively) agree with the results of similar measurements by other authors. At the same time, we show that the previously obtained field strength at the magnetic pole, B _p, and the inclination of the magnetic axis to the rotation axis, β, are untrustworthy. In our opinion, based on the B _‖ measurements available to date, it is not possible to conclude whether the star’s magnetic field is a dipole one or has a more complex configuration and to solve the question of whether this field is stationary. However, we argue that at least in the He I 5876 line formation region, the star’s magnetic field is not stationary and can be restructured in a time of the order of several hours. Nonstationary small-scale magnetic fields of active regions on the stellar surface and/or magnetospheric field line reconnection due to the twisting of these field lines as the star rotates could be responsible for the short-term magnetic field variability. It seems highly likely that there are no strictly periodic variations in brightness and emission line profiles in BP Tau due to the irregular restructuring of the star’s magnetic field.     

Heat blanketing envelopes and thermal radiation of strongly magnetized neutron stars

Strong (B?10⁹ G) and superstrong (B?10¹⁴ G) magnetic fields profoundly affect many thermodynamic and kinetic characteristics of dense plasmas in neutron star envelopes. In particular, they produce strongly anisotropic thermal conductivity in the neutron star crust and modify the equation of state and radiative opacities in the atmosphere, which are major ingredients of the cooling theory and spectral atmosphere models. As a result, both the radiation spectrum and the thermal luminosity of a neutron star can be affected by the magnetic field. We briefly review these effects and demonstrate the influence of magnetic field strength on the thermal structure of an isolated neutron star, putting emphasis on the differences brought about by the superstrong fields and high temperatures of magnetars. For the latter objects, it is important to take proper account of a combined effect of the magnetic field on thermal conduction and neutrino emission at densities ρ?10¹⁰ g?cm^?3. We show that the neutrino emission puts a B-dependent upper limit on the effective surface temperature of a cooling neutron star.     

Obliquity and magnetic dipole radiation from collapsing,rotating, magnetized stars

We consider in this paper the evolution of a collapsing (or exploding), uniformly rotating, uniformly magnetized spheroidal star with non-aligned rotational and magnetic axes. Analytical expressions were obtained for the change in angle (obliquity) between the two axes (based on the frozen field condition), and the energy loss via magnetic, dipole radiation. Numerical estimates with typical data show that the obliquity increases (asymptotically to /2) with the collapse from white dwarf to neutron star, and the energy loss could be as much as 4×10³⁹ ergs, about twice the amount emitted when the two axes are aligned.     

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.      

Inefficient star formation: the combined effects of magnetic fields and radiative feedback

We investigate the effects of magnetic fields and radiative protostellar feedback on the star formation process using self-gravitating radiation magnetohydrodynamical calculations. We present results from a series of calculations of the collapse of  50 M_⊙  molecular clouds with various magnetic field strengths and with and without radiative transfer. We find that both magnetic fields and radiation have a dramatic impact on star formation, though the two effects are in many ways complementary. Magnetic fields primarily provide support on large scales to low-density gas, whereas radiation is found to strongly suppress small-scale fragmentation by increasing the temperature in the high-density material near the protostars. With strong magnetic fields and radiative feedback, the net result is an inefficient star formation process with a star formation rate of  ≲10  per cent per free-fall time that approaches the observed rate, although we have only been able to follow the calculations for 1/3 of a free-fall time beyond the onset of star formation.     

Ohm’s law for plasma in general relativity and Cowling’s theorem

The general-relativistic Ohm’s law for a two-component plasma which includes the gravitomagnetic force terms even in the case of quasi-neutrality has been derived. The equations that describe the electromagnetic processes in a plasma surrounding a neutron star are obtained by using the general relativistic form of Maxwell equations in a geometry of slow rotating gravitational object. In addition to the general-relativistic effect first discussed by Khanna and Camenzind (Astron. Astrophys. 307:665, 1996) we predict a mechanism of the generation of azimuthal current under the general relativistic effect of dragging of inertial frames on radial current in a plasma around neutron star. The azimuthal current being proportional to the angular velocity ω of the dragging of inertial frames can give valuable contribution on the evolution of the stellar magnetic field if ω exceeds 2.7×10¹⁷(n/σ) s⁻¹ (n is the number density of the charged particles, σ is the conductivity of plasma). Thus in general relativity a rotating neutron star, embedded in plasma, can in principle generate axial-symmetric magnetic fields even in axisymmetry. However, classical Cowling’s antidynamo theorem, according to which a stationary axial-symmetric magnetic field can not be sustained against ohmic diffusion, has to be hold in the general-relativistic case for the typical plasma being responsible for the rotating neutron star.     

Scenarios for the formation of binary and millisecond pulsars – A critical assessment

The evolution of high-and low-mass X-ray binaries (HMXB and LMXB) into different types of binary radio pulsars, the ‘high-mass binary pulsars’(HMBP) and ‘low-mass binary pulsars’ (LMBP) is discussed. The HMXB evolve either into Thorne-Zytkow objects or into short-period binaries consisting of a helium star plus a neutron star (or a black hole), resembling Cygnus X-3. The latter systems evolve (with or without a second common-envelope phase) into close binary pulsars, in which the companion of the pulsar may be a massive white dwarf, a neutron star or a black hole ( some final systems may also consist of two black holes). A considerable fraction of the systems may also be disrupted in the second supernova explosion. We discuss the possible reasons why the observed numbers of double neutron stars and of systems like Cyg X-3 are several orders of magnitude lower than theoretically predicted. It is argued that the observed systems form the tip of an iceberg of much larger populations of unobserved systems, some of which may become observable in the future. As to the LMBP, we consider in some detail the origins of systems with orbital periods in the range 1–20 days. We show that to explain their existence, losses of orbital angular momentum (e.g., by magnetic braking) and in a number of cases: also of mass, have to be taken into account. The masses of the low-mass white dwarf companions in these systems can be predicted accurately. We notice a clear correlation between spin period and orbital period for these systems, as well as a clear correlation between pulsar magnetic field strength and orbital period. These relations strongly suggest that increased amounts of mass accreted by the neutron stars lead to increased decay of their magnetic fields: we suggest a simple way to understand the observed value of the ‘bottom’ field strengths of a few times 10⁸ G. Furthermore, we find that the LMBP-systems in which the pulsar has a strong magnetic field (> 10¹¹ G) have an about two orders of magnitude larger birth rate (i.e., about 4 × 10^-4 yr^-1 in the Galaxy) than the systems with millisecond pulsars (which have B < 10⁹ G). Using the observational fact that neutron stars receive a velocity kick of ∼450 km/s at birth, we find that some 90% of the potential progenitor systems of the strong-field LMBP must have been disrupted in the Supernovae in which their neutron stars were formed. Hence, the formation rate of the progenitors of the strong-field LMBP is of the same order as the galactic supernova rate (4 × 10^-3 yr^-1). This implies that a large fraction of all Supernovae take place in binaries with a close low-mass (< 2.3 M⊙) companion.     

Magnetic survey of emission line B‐type stars with FORS 1 at the VLT

We report the results of our search for magnetic fields in a sample of 16 field Be stars, the binary emission‐line B‐type star υ Sgr, and in a sample of fourteen members of the open young cluster NGC3766 in the Carina spiral arm. The sample of cluster members includes Be stars, normal B‐type stars and He‐strong/He‐weak stars. Nine Be stars have been studied with magnetic field time series obtained over ∼1 hour to get an insight into the temporal behaviour and the correlation of magnetic field properties with dynamical phenomena taking place in Be star atmospheres. The spectropolarimetric data were obtained at the European Southern Observatory with the multi‐mode instrument FORS1 installed at the 8m Kueyen telescope. We detect weak photospheric magnetic fields in four field Be stars, HD 62367, μ Cen, o Aqr, and ε Tuc. The strongest longitudinal magnetic field, 〈B_z〉 = 117 ± 38 G, was detected in the Be star HD 62367. Among the Be stars studied with time series, one Be star, λ Eri, displays cyclic variability of the magnetic field with a period of 21.12 min. The binary star υ Sgr, in the initial rapid phase of mass exchange between the two components with strong emission lines in the visible spectrum, is a magnetic variable star, probably on a timescale of a few months. The maximum longitudinal magnetic field 〈B_z〉 = –102 ± 10 G at MJD 54333.018 was measured using hydrogen lines. The cluster NGC3766 seems to be extremely interesting, where we find evidence for the presence of a magnetic field in seven early B‐type stars out of the observed fourteen cluster members (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star – II. Solution of the induction equations

We have solved numerically the general relativistic induction equations in the interior background space–time of a slowly rotating magnetized neutron star. The analytic form of these equations was discussed recently (Paper I), where corrections due to both the space–time curvature and the dragging of reference frames were shown to be present. Through a number of calculations we have investigated the evolution of the magnetic field with different rates of stellar rotation, different inclination angles between the magnetic moment and the rotation axis, as well as different values of the electrical conductivity. All of these calculations have been performed for a constant-temperature relativistic polytropic star and make use of a consistent solution of the initial-value problem which avoids the use of artificial analytic functions. Our results show that there exist general relativistic effects introduced by the rotation of the space–time which tend to decrease the decay rate of the magnetic field. The rotation-induced corrections are however generally hidden by the high electrical conductivity of the neutron star matter, and when realistic values for the electrical conductivity are considered, these corrections become negligible even for the fastest known pulsar.     

Features of magnetic field structures in chemically peculiar stars. IV

We present results of modeling of the sample of magnetic stars. We have obtained such important for magnetic star physics parameters as the mean surface magnetic field B_s, the magnetic field at magnetic poles—B_p, the dipole inclination to the rotation equatorial plane α, and the distance to monopoles from the center of the star Δa. We present some information onmagnetic star physics that helps to understand the derived results better.     

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star – I. Formulation of the equations

We present analytic solutions of Maxwell equations in the internal and external background space–time of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat space–time solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections resulting from the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections resulting from both the space–time curvature and the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.     

Evolution of the number of accreting white dwarfs with shell nuclear burning and the SNe Ia rate

We analyze the time evolution of the number of accreting white dwarfs with surface shell hydrogen burning in semidetached and detached binaries. We consider the case where continuous star formation with a constant rate takes place in a stellar system over 10¹⁰ Gyr and the case of a starburst in which the same mass of stars is formed over 10⁹ Gyr. The evolution of the number of white dwarfs is compared with the evolution of the rate of events that are usually considered as SNe Ia and/or accretion-induced collapses, i.e., the accumulation of a Chandrasekhar mass by white dwarfs or the merger of white dwarf pairs with a total mass greater than or equal to the Chandrasekhar one. In stellar systems with a starburst, the supersoft X-ray sources observed at t = 10¹⁰ yr are most likely not the progenitors of SNe Ia. The same is true for a significant fraction of the sources in systems with a constant star formation rate. In both cases, the merger of white dwarfs is the dominant mechanism of SNe Ia. In symbiotic binaries, accreting CO dwarfs do not accumulate enough mass for an SNe Ia explosion, while ONeMg dwarfs finish their evolution by an accretion-induce collapse with the formation of a neutron star.     

On the differential rotation of the polar caps of neutron stars

The model of a magnetized rotating neutron star with an electric current in the region of its fluid polar magnetic caps is considered. The presence of an electric current leads to differential rotation of the magnetic caps. The rotation structure is determined by the electric current density distribution over the surface. In the simplest axisymmetric configuration, the current flows in one direction near the polar cap center and in the opposite direction in the outer ring (the total current is zero for the neutron star charge conservation). In this case, two rings with opposite directions of rotation appear on the neutron star surface, with the inner ring always lagging behind the star’s main rotation. The differential rotation velocity is directly proportional to the electric current density gradient along the polar cap radius. At a width of the region of change in the electric current from 1 to 10² cm and a period ～1 s and a magnetic field B ～ 10¹² G typical of radio pulsars, the linear differential rotation velocity is ～10^?2–10^?4 cm s^?1 (corresponding to a revolution time of ～0.1–10 yr).     

Magnetic star-disk interaction in classical T Tauri systems

We simulate the impact of a dipolar stellar magnetic field rooted in a classical T Tauri star on the accretion disk and the halo above using a 2.5D finite difference code. The gas is assumed resistive, and inside the disk accretion is driven by a Shakura-Sunyaev-type eddy viscosity. The rotational shear between the star and the Keplerian disk causes the magnetic field to be wound up and stretched outwards, away from the star. Part of the field lines open and an outflow is launched. Direct disk disruption by the Lorentz force only occurs for sufficient field strength. For our model system with a solar-mass central star, an accretion rate of 10^-7M⊙/a, and a viscosity parameter α_SS=0.01, a field strength of 1 kG, measured at the poles on the surface of the star, was found insufficient for disk disruption.     

HARPS spectropolarimetry of Herbig Ae/Be stars

Our knowledge of the presence and the strength of magnetic fields in intermediate‐mass pre‐main‐sequence stars remains very poor. We present new magnetic field measurements in six Herbig Ae/Be stars observed with HARPS in spectropolarimetric mode. We downloaded from the European Southern Observatory (ESO) archive the publically available HARPS spectra for six Herbig Ae/Be stars. Wavelength shifts between right‐ and left‐hand side circularly polarised spectra were interpreted in terms of a longitudinal magnetic field 〈B_z〉, using the moment technique introduced by Mathys. The application of the moment technique to the HARPS spectra allowed us in addition to study the presence of the crossover effect and quadratic magnetic fields. Our search for longitudinal magnetic fields resulted in first detections of weak magnetic fields in the Herbig Ae/Be stars HD 58647 and HD 98922. Further, we confirm the previous tentative detection of a weak magnetic field in HD 104237 by Donati et al. and confirm the previous detection of a magnetic field in the Herbig Ae star HD 190073. Surprisingly, the measured longitudinal magnetic field of HD 190073, 〈B_z〉 = 91 ± 18 G at a significance level of 5σ is not in agreement with the measurement results of Alecian et al. (2013), 〈B_z〉 = –10 ± 20 G, who applied the LSD method to exactly the same data. No crossover effect was detected for any star in the sample. Only for HD 98922 the crossover effect was found tobe close to 3σ with a measured value of –4228 ± 1443 km s^–1 G. A quadratic magnetic field of the order of 10 kG was detected in HD 98922, and of ∼3.5 kG in HD 104237. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)