Electron-positron plasma generation in a magnetar magnetosphere

We consider the electron—positron plasma generation processes in the magnetospheres of magnetars—neutron stars with strong surface magnetic fields, B ? 10¹⁴–10¹⁵ G. We show that the photon splitting in a magnetic field, which is effective at large field strengths, does not lead to the suppression of plasma multiplication, but manifests itself in a high polarization of γ-ray photons. A high magnetic field strength does not give rise to the second generation of particles produced by synchrotron photons. However, the density of the first-generation particles produced by curvature photons in the magnetospheres of magnetars can exceed the density of the same particles in the magnetospheres of ordinary radio pulsars. The plasma generation inefficiency can be attributed only to slow magnetar rotation, which causes the energy range of the produced particles to narrow. We have found a boundary in the \(P - \dot P\) diagram that defines the plasma generation threshold in a magnetar magnetosphere.     

Evolution of neutron star magnetic fields

This paper reviews the current status of the theoretical models of the evolution of the magnetic fields of neutron stars other than magnetars. It appears that the magnetic fields of neutron stars decay significantly only if they are in binary systems. Three major physical models for this, namely spindown-induced flux expulsion, ohmic evolution of crustal field and diamagnetic screening of the field by accreted plasma, are reviewed.     

Heating and cooling of magnetars with accreted envelopes

We study the thermal structure and evolution of magnetars as cooling neutron stars with a phenomenological heat source in an internal layer. We focus on the effect of magnetized (   B ≳ 10¹⁴  G) non-accreted and accreted outermost envelopes composed of different elements, from iron to hydrogen or helium. We discuss a combined effect of thermal conduction and neutrino emission in the outer neutron star crust and calculate the cooling of magnetars with a dipole magnetic field for various locations of the heat layer, heat rates and magnetic field strengths. Combined effects of strong magnetic fields and light-element composition simplify the interpretation of magnetars in our model: these effects allow one to interpret observations assuming less extreme (therefore, more realistic) heating. Massive magnetars, with fast neutrino cooling in their cores, can have higher thermal surface luminosity.     

Newborn magnetars as sources of gravitational radiation: constraints from high energy observations of magnetar candidates

Two classes of high-energy sources, the Soft Gamma Repeaters and the Anomalous X-ray Pulsars are believed to contain slowly spinning “magnetars,” i.e. neutron stars the emission of which derives from the release of energy from their extremely strong magnetic fields (>10¹⁵ G). The enormous energy liberated in the 2004 December 27 giant flare from SGR 1806-20 (～5×10⁴⁶ erg), together with the likely recurrence time of such events, points to an internal magnetic field strength of ≥10¹⁶ G. Such strong fields are expected to be generated by a coherent α?Ω dynamo in the early seconds after the Neutron Star (NS) formation, if its spin period is of a few milliseconds at most. A substantial deformation of the NS is caused by such fields and, provided the deformation axis is offset from the spin axis, a newborn millisecond-spinning magnetar would thus radiate for a few days a strong gravitational wave signal the frequency of which (～0.5–2 kHz range) decreases in time. This signal could be detected with Advanced LIGO-class detectors up to the distance of the Virgo cluster, where ≥1 yr^?1 magnetars are expected to form. Recent X-ray observations revealed that SNRs around magnetar candidates do not appear to have received a larger energy input than in standard SNRs (see Vink and Kuiper, Mon. Not. Roy. Astron. Soc. 319, L14 (2006)). This is at variance with what would be expected if the spin energy of the young, millisecond NS were radiated away as electromagnetic radiation and/or relativistic particle winds. In fact, such energy would be transferred quickly and efficiently to the expanding gas shell. This may thus suggest that magnetars did not form with the expected very fast initial spin. We show here that these findings can be reconciled with the idea of magnetars being formed with fast spins, if most of their initial spin energy is radiated through GWs. In particular, we find that this occurs for essentially the same parameter range that would make such objects detectable by Advanced LIGO-class detectors up to the Virgo Cluster. If our argument holds for at least a fraction of newly formed magnetars, then these objects constitute a promising new class of gravitational wave emitters.     

Strong magnetic field helical Čerenkov effect with some astrophysica implications

It is at very strong magnetic fields that the helical Čerenkov effect, originating from the electron guiding center for an electron in helical motion in a magnetic field which is superimposed on a dielectric medium, resembles most closely the ordinary Čerenkov effect. In the absence of extremely strong magnetic fields in the laboratory, we turn our attention to the neutron stars (pulsar) and supernovae which can have magnetic fields whose values can easily be in the range of 10⁵ — 10⁹ T. The medium in which these magnetic fields reside is likely to be an ionized medium; that is, a plasma, which, as usual, may be assumed to be dominated by electrons. Here we wish to argue that in such a strong magnetic field dominated medium, at least on a classical level, radiation process associated with the helical Čerenkov radiation could be rather important.     

Evolution of superhigh magnetic fields of magnetars

In this paper, we consider the effect of Landau levels on the decay of superhigh magnetic fields of magnetars. Applying ³ P ₂ anisotropic neutron superfluid theory yield a second-order differential equation for a superhigh magnetic field B and its evolutionary timescale t. The superhigh magnetic fields may evolve on timescales ∼(10⁶–10⁷) yrs for common magnetars. According to our model, the activity of a magnetar may originate from instability caused by the high electron Fermi energy.     

One-photon and two-photon annihilation of positronium in strong magnetic fields

In the presence of a strong magnetic field (such as those believed to be characteristic of neutron stars:B-10¹² Gauss) positronium may annihilate through the emission of a single photon, the magnetic field providing the photon momentum. We report on calculations of the one-photon and two-photon annihilation rates for the ground state of positronium, for magnetic fields in the range (1–44)×10¹² Gauss, and give, in the two-photon case, the minimum energy half-width of the emission line due to the momentum contributions from the magnetic field. We find that unless neutron stars have magnetic fields in excess of 10¹³ Gauss, it is unlikely that the one-photon process will be observable.Research supported in part by the National Research Council of Canada.     

Are There Magnetars in High-mass X-Ray Binaries?

Magnetars form a special population of neutron stars with strong magnetic fields and long spin periods.About 30 magnetars and magnetar candidates known currentl...     

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.     

High Magnetic Field Pulsars and Magnetars: A Unified Picture

We propose a unified picture of high magnetic field radio pulsars and magnetars by arguing that they are all rotating high-field neutron stars but that their magnetic axes have different orientations with respect to their rotation axes. In strong magnetic fields where photon splitting suppresses pair creation near the surface, the high-field pulsars can have active inner accelerators while the anomalous X-ray pulsars cannot. This can account for the very different observed emission characteristics of the anomalous X-ray pulsar 1E 2259+586 and the high-field radio pulsar PSR J1814-1744. A predicted consequence of this picture is that radio pulsars having surface magnetic fields greater than about 2x1014 G should not exist.     

Are the magnetic fields of millisecond pulsars ∼108 G?

It is generally assumed that the magnetic fields of millisecond pulsars (MSPs) are ～10⁸ G. We argue that this may not be true and the fields may be appreciably greater. We present six evidences for this: (1) The ～10⁸G field estimate is based on magnetic dipole emission losses which is shown to be questionable; (2) The MSPs in low mass X-ray binaries (LMXBs) are claimed to have <10¹¹ G on the basis of a Rayleygh-Taylor instability accretion argument. We show that the accretion argument is questionable and the upper limit 10¹¹ G may be much higher; (3) Low magnetic field neutron stars have difficulty being produced in LMXBs; (4) MSPs may still be accreting indicating a much higher magnetic field; (5) The data that predict ～10⁸ G for MSPs also predict ages on the order of, and greater than, ten billion years, which is much greater than normal pulsars. If the predicted ages are wrong, most likely the predicted ～10⁸ G fields of MSPs are wrong; (6) When magnetic fields are measured directly with cyclotron lines in X-ray binaries, fields ?10⁸ G are indicated. Other scenarios should be investigated. One such scenario is the following. Over 85% of MSPs are confirmed members of a binary. It is possible that all MSPs are in large separation binaries having magnetic fields >10⁸ G with their magnetic dipole emission being balanced by low level accretion from their companions.     

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.     

Rotating superdense configurations: pulsars and their astrophysical manifestations

This paper is a discussion of some results from papers by followers of V. A. Ambartsumyan, whose fundamental articles serve as the beginning of research on superdense stars: white dwarfs and neutron stars. Solutions of the Einstein equations are given for the case of axial symmetry and are used to determine the integral parameters of rotating neutron stars and white dwarfs. A theory of magnetic field generation in neutron stars has been developed and is consistent with the existence of high, nonuniform magnetic fields on the order of 10¹⁴ G in pulsars. A theory has been proposed for the dynamics of neutron vortices and used to explain the observed relaxation of the angular velocity of pulsars following glitches.     

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.     

The spin evolution of nascent neutron stars

The loss of angular momentum owing to unstable r-modes in hot young neutron stars has been proposed as a mechanism for achieving the spin rates inferred for young pulsars. One factor that could have a significant effect on the action of the r-mode instability is fallback of supernova remnant material. The associated accretion torque could potentially counteract any gravitational-wave-induced spin-down, and accretion heating could affect the viscous damping rates and hence the instability. We discuss the effects of various external agents on the r-mode instability scenario within a simple model of supernova fallback on to a hot young magnetized neutron star. We find that the outcome depends strongly on the strength of the magnetic field of the star. Our model is capable of generating spin rates for young neutron stars that accord well with initial spin rates inferred from pulsar observations. The combined action of r-mode instability and fallback appears to cause the spin rates of neutron stars born with very different spin rates to converge, on a time-scale of approximately 1 year. The results suggest that stars with magnetic fields ≤10¹³ G could emit a detectable gravitational wave signal for perhaps several years after the supernova event. Stars with higher fields (magnetars) are unlikely to emit a detectable gravitational wave signal via the r-mode instability. The model also suggests that the r-mode instability could be extremely effective in preventing young neutron stars from going dynamically unstable to the bar-mode.     

Gravitational collapse of magnetic neutron stars

Pulsars are presently believed to be rotating neutron stars with frozen-in magnetic fields. Because of the high density of neutron stars, general relativistic effects are important since they effect both the structure and stability of such stars. Besides this, the magnetic field outside the star is also affected. Instead of falling of asr ^(2+l) as in flat space, it is shown that each magnetic multipole varies as a hypergeometric function of radius. A closed form of these hypergeometric functions is given in terms of Legendre functions of the second kind. If the mass of a neutron star exceeds about 2.4m , the star becomes unstable and coliapses. For a quasistatically collapsing body, it is shown that the magnetic field seen by a distant observer vanishes as the radius approaches the gravitational radius.This work was supported in part by the Air Force Office of Scientific Research, Office of Aerospace Research under AFOSR Grant 70-1866.     

Progenitors with enhanced rotation and the origin of magnetars

Among the dozen known magnetar candidates, there are no binary objects. Given that the fraction of binary neutron stars is estimated to be about 3–10 per cent, it is reasonable to address the question of solitarity of magnetars, to estimate theoretically the fraction of binary objects among them, and to identify the most probable companions. We present population synthesis calculations of massive binary systems. In this study, we adopt the hypothesis that magnetic field of a magnetar is generated at the protoneutron star stage due to a dynamo mechanism, so rapid rotation of the core of a progenitor star is essential. Our goal is to estimate the number of neutron stars originated from progenitors with enhanced rotation. In our calculations, the fraction of neutron stars originating from such progenitors is about 8–9 per cent. This should be considered as an upper limit to the fraction of magnetars, as some of the progenitors can lose momentum. Most of these objects are isolated due to coalescences of components prior to neutron star formation, or due to system disruption after the second supernova explosion. The fraction of such neutron stars in surviving binaries is about 1 per cent or lower. Their most numerous companions are black holes.     

Magnetic field decay of magnetars in supernova remnants

In this paper, we modify our previous research carefully, and derive a new expression of electron energy density in superhigh magnetic fields. Based on our improved model, we re-compute the electron capture rates and the magnetic fields’ evolutionary timescales t of magnetars. According to the calculated results, the superhigh magnetic fields may evolve on timescales ～(10⁶?10⁷) yrs for common magnetars, and the maximum timescale of the field decay, t≈2.9507×10⁶ yrs, corresponding to an initial internal magnetic field B ₀=3.0×10¹⁵ G and an initial inner temperature T ₀=2.6×10⁸ K. Motivated by the results of the neutron star-supernova remnant (SNR) association of Zhang and Xie (2011), we calculate the maximum B ₀ of magnetar progenitors, B _max～(2.0×10¹⁴?2.93×10¹⁵) G when T ₀=2.6×10⁸ K. When T ₀～2.75×10⁸?1.75×10⁸ K, the maximum B ₀ will also be in the range of ～10¹⁴?10¹⁵ G, not exceeding the upper limit of magnetic field of a magnetar under our magnetar model. We also investigate the relationship between the spin-down ages of magnetars and the ages of their SNRs, and explain why all AXPs associated with SNRs look older than their real ages, whereas all SGRs associated with SNRs appear younger than they are.     

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.     

The birthrate of magnetars

Magnetars, neutron stars with ultrastrong magnetic fields  ( B ∼ 10¹⁴−10¹⁵G)  , manifest their exotic nature in the form of soft gamma-ray repeaters and anomalous X-ray pulsars. This study estimates the birthrate of magnetars to be ∼0.22 per century with a Galactic population comprising ∼17 objects. A population synthesis was carried out based on the five anomalous X-ray pulsars detected in the ROSAT All Sky Survey by comparing their number to that of massive OB stars in a well-defined volume. Additionally, the group of seven X-ray dim isolated neutron stars detected in the same survey were found to have a birthrate of ∼2 per century with a Galactic population of ∼22 000 objects.