Rotational periods and other parameters of magnetars

The rotational periods P, period derivatives dP/dt, and magnetic fields B in the region where the emission of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) is generated are calculated using a model that associates the emission of these objects with the existence of drift waves at the periphery of the magnetosphere of a neutron star. The values obtained for these parameters are P = 11?737 ms, dP/dt = 3.7 × 10^?16?5.5 × 10^?12, and log B (G) = 2.63?6.25. We find a dependence between the X-ray luminosity of AXPs and SGRs, L _x, and the rate at which they lose rotational energy, dE/dt, which is similar to the L _x(dE/dt) dependence for radio pulsars with detected X-ray emission. Within the errors, AXPs/SGRs and radio pulsars with short periods (P < 0.1 s) display the same slopes for their log(dP/dt)-log P relations and for the dependence of the efficiency of their transformation of rotational energy into radiation on their periods. A dipole model is used to calculate the surface magnetic fields of the neutron stars in AXPs and SGRs, which turn out to be, on average, comparable to the surface fields of normal radio pulsars (〈log B _s (G)〉 = 11.90).     

The magnetic field of the pulsating subdwarf Balloon 090100001

We have analyzed polarization observations of the subdwarf Bal 09, which is one of a group of hybrid sdB stars that display simultaneously both short- and long-period pulsations. Certain properties previously unknown for subdwarfs have been established for Bal 09, such as variations of the pulsation amplitude of the main oscillation mode, rotational splitting of multiplets, and variations of this splitting. Information about the stellar magnetic field must be considered if we wish to explain these properties. New observational data enabling estimation of the longitudinal magnetic field of Bal 09 have been obtained on the main stellar spectrograph of the 6-m telescope of the Special Astrophysical Observatory. Studies of the longitudinal component of the magnetic field 〈B _z 〉 were carried out using a regression analysis. This method simultaneously yields estimates of the uncertainty in 〈B _z 〉. Test measurements of 〈B _z 〉 were carried out using the same method. For the star HD 158974, which has zero total magnetic field, the estimated longitudinal magnetic field is 〈B _z 〉 = −4 ± 5 G. The standard magnetic field for the Ap star α ²CVn was measured to be −363 ± 17 G, in very good agreement with measurements in the literature. The estimated longitudinal magnetic field for Bal 09 is 34 ± 63G—appreciably lower than values established earlier for six subdwarfs, ≈1.5 kG. The results of the regression analysis for both individual spectral subranges and for intervals containing characteristic spectral features did not indicate reliable detections of a magnetic field exceeding the uncertainties in 〈B _z 〉. The uncertainty in 〈B _z 〉, which was 60–80 G for the entire spectral range and 140–200 G for selected spectral intervals, leads to an estimated upper limit on the longitudinal magnetic field 〈B _z 〉 for Bal 09. This estimate for 〈B _z 〉 can place observational constraints on theoretical explanations for the amplitude variations of the pulsations, rotational splitting of multiplets, and possible variations of the internal structure of the star.     

A new model of a magnetar

A new model is put forward to explain the observed features of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs). It is shown that drift waves can be excited in the magnetosphere of a neutron star with a rotational period of P～0.1 s, surface magnetic field B_s～10¹² G, and angle between the rotational axis and magnetic moment β<10°. These waves lead to the formation of radiation pulses with a period of P_dr～10 s. The rate of loss of rotational energy by such a star (～10³⁷ erg/s) is sufficient to produce the observed increase in the period \((\dot P \sim 10^{ - 10} )\), the X-ray luminosities of AXPs and SGRs (～10³⁴–10³⁶ erg/s), and an injection of relativistic particles into the surrounding supernova remnant. A modulation of the constant component of the radiation with a period of P～0.1 s is predicted. In order for SGRs to produce gamma-ray bursts, an additional source of energy must be invoked. Radio pulsars with periods of P_obs>5 s can be described by the proposed model; in this case, their rotational periods are considerably less than P_obs and the observed pulses are due to the drift waves.     

The geometry of radio pulsar magnetospheres

Data on the profiles and polarization of the 10- and 20-cm emission of radio pulsars are used to calculate the angle β between the rotational axis of the neutron star and its magnetic moment. It is shown that, for these calculations, it is sufficient to use catalog values of the pulse width at the 10% level W ₁₀, since the broadening of the observed pulses due to the transition to the full width W ₀ and narrowing of the pulses associated with the emission of radiation along tangents to the field lines approximately cancel each other out. The angles β ₁ are calculated for 283 pulsars at 20 cm and 132 pulsars at 10 cm, assuming that the line of sight passes through the center of the emission cone. The mean values of these angles are small and similar for the two wavelengths (〈β ₁〉 = 18° at λ = 10 cm and 〈β ₁〉 = 14° at λ = 20 cm). The angle β ₂ is estimated for several dozen pulsars for the case when the orientation of the angle to the line of sight is arbitrary. The mean value of β ₂ at 10 cm is found to be 〈β ₂〉 = 33.9° if the maximum derivative of the polarization position angle C is positive and 〈β ₂〉 = 52.1° ifC < 0. We find at 20 cm 〈β ₂〉 = 33.9° ifC > 0 and 〈β2〉 = 54.1° ifC < 0. The values at the two wavelengths are equal within the errors, and close to the β ₂ value obtained earlier at 30 cm (〈β ₂〉 = 36.4° if C >0 and 〈β2〉 = 49.1° if C < 0). The mean 〈β ₂〉 for the entire set of data can be taken to be 43.5°. The period dependence of the pulse width W(P) √ P ^−0.25 differs from the relation that is usually used in the polar-cap model, W(P) √ P ^−0.5. This difference could be associated with the rate of development of plasma instabilities near the surface of the neutron star (in the region where high-frequency radiation is generated). The role of the quadrupole component of the magnetic field is not important here. There is no dependence of the angle β on the pulsar age (z distance, luminosity L, or characteristic age τ = P/(2dP/dt)) for the studied sample.     

Evolution of the velocity ellipsoids in the thin disk of the Galaxy and the radial migration of stars

Data from the revised Geneva-Copenhagen catalog are used to study the influence of radial migration of stars on the age dependences of parameters of the velocity ellipsoids for nearby stars in the thin disk of the Galaxy, assuming that the mean radii of the stellar orbits remain constant. It is demonstrated that precisely the radial migration of stars, together with the negative metallicity gradient in the thin disk, are responsible for the observed negative correlation between the metallicities and angular momenta of nearby stars, while the angular momenta of stars that were born at the same Galactocentric distances do not depend on either age or metallicity. The velocity components of the Sun relative to the Local Standard of Rest derived using data for stars born at the solar Galactocentric distance are (U _⊙, V _⊙, W _⊙) _LSR = (5.1 ± 0.4, 7.9 ± 0.5, 7.7 ± 0.2) km/s. The two coordinates of the apex of the solar motion remain equal to 〈l _⊙〉 = 70° ± 7° and 〈b _⊙〉 = 41° ± 2°, within the errors. The indices for the power-law age dependences of them ajor, middle, and minor semi-axes become 0.26±0.04, 0.32±0.03, and 0.07±0.03, respectively. As a result, with age, the velocity ellipsoid for thin-disk stars born at the solar Galactocentric distance increases only in the plane of the disk, remaining virtually constant in the perpendicular direction. Its shape remains far from equilibrium, and the direction of the major axis does not change with age: the ellipsoid vertex deviation remains constant and equal to zero within the errors (〈L〉 = 0.7° ± 0.6°, 〈B〉 = 1.9° ± 1.1°). Such a small increase in the velocity dispersion perpendicular to the Galactic plane with age can probably be explained by “heating” of the stellar system purely by spiral density waves, without a contribution from giant molecular clouds.     

Period clustering of anomalous X-ray pulsars

The question of why the observed periods of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) cluster in the range 2–12 s is discussed. The possibility that AXPs and SGRs are the descendants of high-mass X-ray binaries that have disintegrated in core-collapse supernova explosions is investigated. The spin periods of neutron stars in high-mass X-ray binaries evolve towards the equilibrium period, which is a few seconds, on average. After the explosion of its massive companion, the neutron star becomes embedded in a dense gaseous envelope, and accretion from this envelope leads to the formation of a residual magnetically levitating disk. It is shown that the expected mass of the disk in this case is 10^?7–10^?8 M_⊙, which is sufficient to support accretion at the rate 10¹⁴–10¹⁵ g/s over a few thousand years. During this period, the star manifests itself as an isolated X-ray pulsar with a number of parameters similar to those of AXPs and SGRs. The periods of such pulsars can cluster if the lifetime of the residual disk does not exceed the spin-down timescale of the neutron star.     

The estimation of dispersion behavior in discrete fractured networks of andesite in Lan-Yu Island,Taiwan

This study was based on the discrete fracture model to investigate the influence of fracture parameters on the solute transport in the fractured rocks of andesite in Lan-Yu island, Taiwan. In the simulation cases, the centers of fractures, fracture lengths and apertures were assumed to have Poisson’s distribution, negative exponential distribution and lognormal distribution, respectively. With the above assumptions, constructing the discrete fracture model became practicable. Using the mass-balance equation with specified boundary conditions, the flow field in the rock was solved. Then particles were released under the flow field. Monte Carlo method was used assuming that the amount of particles was proportional to the flow rates to get the particle accumulated percentage breakthrough curve and to estimate the dispersion coefficient. On the basis of the discrete fracture model, it was possible to evaluate the property of dispersion behavior of andesite in Lan-Yu Island with flow and transport mechanism. Properties of the dispersion behavior such as the relation between distance and traveling-time (ln〈r ²〉 and ln 〈t〉), anisotropic behavior, and the overall dispersion coefficient in a fracture network were characterized: the slope value of ln〈r ²〉 and ln〈t〉 was 1.64 an indication of non-Fickian dispersion, the particles dispersion along the flow (D11) was bigger than that perpendicular to the flow (D22), and the dispersion coefficient by this study was 0.91 m comparing the value 1 m from Sauty’s method.     

Drift loss cone instability in the ring current and plasma sheet

The drift loss cone instability, propagating nearly transverse to the ambient magnetic field, is studied in the ring current plasma taking into account the relative driftU between electrons and protons due to density gradients. The growth rates attain maxima and then decrease as the wave number parallel to the magnetic fieldk _II increases. The peak values of the growth rates, maximised with respect tok _II, are enhanced by the increase in number density, electron temperature and loss cone index, and by the decrease in β_t, the ratio of the proton thermal pressure to magnetic field pressure. The unstable frequencies fall in the range of 5 to 30Ω_p with the growth rate γ ≥Ω_p. In the ring current region betweenL=4 and 5, the instability will generate a strong turbulence in the frequency range between 5–500 Hz which can produce fluctuating electric fields 0. 5–5 mV/m and magnetic field 0.8–80mγ. This instability can also occur on the auroral field lines, which connect to the region of intense earthward plasma flow in the distant magnetotail and produce a broad band electrostatic noise.     

The age-metallicity relation in the thin disk of the galaxy

HST trigonometric distances, photometric metallicities, isochronic ages from the second revised version of the Geneva-Copenhagen survey, and uniform spectroscopic Fe and Mg abundances from our master catalog are used to construct and analyze the age-metallicity and age-relative Mg abundance relations for stars of the thin disk. The influences of selection effects are discussed in detail. It is demonstrated that the radial migration of stars does not lead to appreciable distortions in the age dependence of the metallicity. During the first several billion years of the formation of the thin disk, the interstellarmaterial in this disk was, on average, fairly rich in heavy elements (〈[Fe/H]〉 ≈ −0.2) and poorly mixed. However, the metallicity dispersion continuously decreased with age, from σ _[Fe/H] ≈ 0.22 to ≈0.13. All this time, the mean relative abundance of Mg was somewhat higher than the solar value (〈[Mg/Fe]〉 ≈ 0.1). Roughly four to five billion years ago, the mean metallicity began to systematically increase, while retaining the same dispersion; the mean relative Mg abundance began to decrease immediately following this. The number of stars in this subsystem increased sharply at the same time. These properties suggest that the star-formation rate was low in the initial stage of formation of the thin disk, but abruptly increased about four to five billion years ago.     

Structural and magnetic properties of Co2Al4Si5O18 and Mn2Al4Si5O18 cordierite

The crystal structures, lattice dynamics and magnetic properties of synthetic Co-cordierite, Co₂Al₄Si₅O₁₈, and Mn-cordierite, Mn₂Al₄Si₅O₁₈ have been studied by neutron powder diffraction, infrared spectroscopy and magnetisation measurements. Due to different synthesis conditions, the Co-cordierite used here crystallised in the hexagonal α-cordierite structure with a disordered Si/Al distribution in the framework, while for the Mn-cordierite the orthorhombic β-structure has been determined. The experimentally determined paramagnetic moments, _exp (Mn) = 5.47(6) _B and _exp (Co) = 3.88(4) _B , are in good agreement with theoretical predictions for octahedrally coordinated Mn²⁺ and Co²⁺, respectively. In both compounds there is no magnetic long-range order down to at least 1.5 K. However, the onset of an anti-ferromagnetic short-range correlation of magnetic moments along [001] has been observed for Mn-cordierite by magnetisation and neutron diffraction measurements. This short-range magnetic correlation becomes evident from diffuse scattering observed at 2 K. The diffuse scattering has been interpreted in terms of a Blech-Averbach function. Received: 30 June 1998 / Revised, accepted: 3 March 1999     

A preliminary study on the magnetic signatures of modern soil in Central Asia

In this study, magnetic techniques were used to characterize the surface soil from different geomorphologies (i.e., sand desert, oasis, Gobi, and dry lake) in Central Asia. Results demonstrate that the main magnetic minerals in the surface soil are magnetite, maghaemite and haematite with some paramagnetic materials. Cross plots of M _rs/M _s versus B _cr/B _c and χ_fd% versus χ_arm/saturation isothermal remanent magnetization (SIRM) indicate that the main magnetic grain sizes in surface soil are pseudo single domain (PSD) and multidomain (MD). The samples from West China (i.e., Tarim basin and Junggar basin) are dominated by magnetic minerals with larger grain size, while those from North China (i.e., Alxa plateau, Erdos plateau, and Mongolia plateau) are dominated by fine magnetic minerals. The similarity in magnetic mineral constitutions between the Chinese loess and the surface soils from Central Asia implies that the loess originated from a vast area of arid, semi-arid regions of Central Asia. The low value of concentration-dependent magnetic parameters indicates that the low concentration of magnetic minerals in the surface soils from Central Asia and the magnetic enhancement from the pedogenic take place in both the loess and the paleosols, although the progress is stronger in the latter. Translated from Quaternary Sciences, 2006, 26(6): 937–946 [译自: 第四纪研究]     

A theoretical investigation of the relative stabilities of Fe-free clinozoisite and orthozoisite

 The relative stabilities of orthozoisite, Ca₂Al₃[O|OH|Si₂O₇|SiO₄], space group Pnma, and the monoclinic polymorph, clinozoisite, space group P2₁/m, have been investigated using calculations based on density functional theory. It is found that orthozoisite is more stable than clinozoisite by about 1 kJ mol⁻¹ at zero pressure in the athermal limit. The bulk moduli of the two polymorphs have been calculated to be B_ortho=117.5(1.7) GPa and B_clino=136(4) GPa. Received: 20 March 2000 / Accepted: 26 February 2001     

Ion acoustic instability of HPT particles,FAC density,anomalous resistivity and parallel electric field in the auroral region

During the magnetic storm of 21st March 1990, the DE-1 spacecraft encountered the auroral region at high invariant latitude at altitudes ranging from a few thousand kilometers in the ionosphere to many earth radii in the magnetosphere. The magnetic field perturbations interpretable as field aligned current (FAC) layers and the electrostatic turbulence possibly due to electrostatic ion acoustic instability driven by these currents are shown. The critical drift velocity of Hot Plasma Torus (HPT) electrons and the growth rate of ion acoustic wave as a function of electron to ion temperature ratio (T _e/T_i) for low and high current densities and energy of HPT electrons are found out. The intense FAC destabilizes the ion acoustic wave and the resultant electrostatic turbulence creates an anomalous resistivity. The current driven resistivity produces parallel electric field and high power dissipation. The anomalous resistivityη, potential difference along the auroral field lines V_t|, intensity of electric field turbulenceE _t| and power produced per unit volumeP are computed. It is found that the change in westward magnetic perturbation increasesJ _t|, η, V_t|, E_t| andP. Hence HPT electrons are heated and accelerated due to power dissipation during magnetically active periods in the auroral region. Concerning, applications, such HPT electrons can be used in particle accelerators like electron ring accelerator, smokatron etc.     

Possible scenarios for the formation of Ap/Bp stars

Possible paths for the formation of Ap/Bp stars—massive main-sequence stars with strong magnetic fields—are analyzed based on modern theories for the evolution of single and binary stars. Assuming that the strong magnetic fields of these stars are the main reason for their comparatively slow axial rotation and the observed anomalies in the chemical compositions of their atmospheres, possible origins for these high magnetic fields are considered. Analysis of several possible scenarios for the formation of these stars leads to the conclusion that their surface magnetic fields are probably generated in the convective envelopes of the precursor stars. These precursors may be young, single stars with masses 1.5–3 M _⊙ that formed at the peripheries of forming star clusters and ended their accretion at the Hayashi boundary, or alternatively close binaries whose components have convective envelopes, whose merger leads to the formation of an Ap/Bp star. Arguments are presented supporting the view that the merger of close binaries is the main channel for the formation of Ap/Bp stars, and a detailed analysis of this scenario is presented. The initial major axes of the merging binary systems must be in the range 6–12 R _⊙, and the masses of their components in the range 0.7–1.5 M _⊙. When the merging components possess developed convective envelopes and fairly strong initial magnetic fields, these can generate powerful magnetic fields “inherited” by the products of the merger—Ap/Bp stars. The reason the components of the close binaries merge is a loss of angular momentum via the magnetic stellar winds of the components.     

Texture development and elastic stresses in magnesiowűstite at high pressure

Cubic magnesiowűstite has been deformed in a diamond anvil cell at room temperature. We present results for (Mg_0.4Fe_0.6)O, (Mg_0.25Fe_0.75)O, and (Mg_0.1Fe_0.9)O up to 37, 16, and 18 GPa, respectively. The diffraction images, obtained with the radial diffraction technique, are analyzed using both single peak intensities and a Rietveld method. For all samples, we observe a [100] fiber texture but the texture strength decreases with increasing iron content. This texture pattern is consistent with {110}〈1-10〉 slip. The images were also analyzed for stress, elastic strains, and elastic anisotropy. In general, the stress measured in magnesiowűstite samples is lower than previously measured on MgO. The elastic anisotropy deduced from the X-ray measurements shows a broad agreement with models based on measurements with other techniques.     

The radio emission of anomalous pulsars

Previously developed methods for estimating the angle β between the spin axis of a neutron star and its magnetic moment together with observational data for anomalous X-ray pulsars (AXPs) indicate that these objects are nearly aligned rotators, and that the drift model can be applied to them. The magnetospheres of aligned rotators are appreciably more extended than in pulsars with large values of β. With such extents for the magnetosphere, the conditions for the generation of transverse waves via the cyclotron instability are satisfied. The expected spectrum of the resulting radiation is very steep (its spectral index is α > 3), consistent with the observed radio spectra of known AXPs (α > 2). A large magnetosphere also favors the appearance of appreciable pitch angles for relativistic electrons, and therefore the generation of synchrotron emission. The maximum of this emission falls in the microwave range. This mechanism provides appreciable fluxes at frequencies of tens of gigahertz and can explain the observed enhanced AXP radiation in this range.     

The appearance of a radio-pulsar magnetosphere from a vacuum with a strong magnetic field. Accumulation of particles

The motion of electrons and positrons in the vacuum magnetosphere of a neutron star with a surface magnetic field of B ≈ 10¹² G is considered. Particles created in the magnetosphere or falling into it from outside are virtually instantaneously accelerated to Lorentz factors γ ≈ 10⁸. After crossing the force-free surface, where the projection of the electric field onto the magnetic field vanishes, a particle begins to undergo ultra-relativistic oscillations. The particle experiences a regular drift along the force-free surface simultaneous with this oscillatory motion.     

TEM characterization of dislocations and slip systems in stishovite deformed at 14 GPa, 1,300°C in the multianvil apparatus

Transmission electron microscopy (TEM) has been used to investigate deformation microstructures of synthetic stishovite specimens deformed at 14 GPa, 1,300°C. Geometrical characteristics of numerous dislocations have been characterized by dislocation contrast and stereographic analyses in order to identify the easy slip systems of stishovite. TEM data allowed us to characterize the following slip systems: 〈100〉{001}, 〈100〉{010}, 〈100〉{021}, [001]{100}, [001]{110}, [001]{210} and Observation of sub-grain boundaries and scalloped edge dislocations suggest that climb has been activated in the specimens.