A numerical method to determine the electromagnetic field of the pulsar magnetosphere with inclined magnetic moment

A numerical method to determine the electromagnetic field of a steadily rotating magnetosphere with an inclined magnetic moment under a given boundary condition on an arbitrary shaped boundary surface is presented. The region may include the light cylinder. The present method, together with a companion method giving particle motion and creation, makes an iterative scheme to obtain a global model of the pulsar magnetosphere. A key problem for explaining the particle acceleration in pulsars is to solve field-aligned electric field in an accelerating region bounded by an ideal-MHD region. The present method is fit to connect a solution for the non-ideal-MHD region with another solution for the ideal-MHD region on a boundary surface whose location should also be solved (i.e., a floating boundary). The integration scheme is based on the boundary element method and it has great advantage as compared with other methods like the finite difference method and the Fourier transformation method.     

New pulsar rotation measures and the Galactic magnetic field

We measured a sample of 150 pulsar rotation measures (RMs) using the 20-cm receiver of the Parkes 64-m radio telescope. 46 of the pulsars in our sample have not had their RM values previously published, whereas 104 pulsar RMs have been revised. We used a novel quadratic fitting algorithm to obtain an accurate RM from the calibrated polarization profiles recorded across 256 MHz of receiver bandwidth. The new data are used in conjunction with previously known dispersion measures and the NE2001 electron-density model to study models of the direction and magnitude of the Galactic magnetic field.     

Vortex lines in neutron star superfluids and decay of pulsar magnetic fields

We adopt that in the interior of neutron stars both the proton and neutron superfluids are in the vortex state. Thus, in the superconducting core the magnetic field is expected to be organized in the form of quantized fluxoids. It is shown that fluxoids are buoyant. This gives rise to a rapid (5×10⁴ yr) expulsion of the magnetic field out of the superconducting core to the subcrustal region, and a subsequent decay within the outer crust. The effect considered may be the physical reason why the characteristic decay-time of pulsar magnetic fields (10⁶ yr) corresponds to the ohmic dissipation time within the neutron star crust. The intersection of two types of vortex lines with each other and its possible consequence for pulsars is briefly discussed.     

The decay of the large-scale solar magnetic field

In the absence of new bipolar sources of flux, the large-scale magnetic field at the solar photosphere decays due to differential rotation, meridional flow, and supergranular diffusion. The rotational shear quickly winds up the nonaxisymmetric components of the field, increasing their latitudinal gradients and thus the rates of diffusive mixing of their flux. This process is particularly effective at mid latitudes, where the rotational shear is largest, so that eventually low- and high-latitude remnants of the initial, nonaxisymmetric field pattern survive. In this paper I solve analytically the transport equation describing the evolution of the large-scale photospheric field, to study its time-asymptotic behavior. The solutions are rigidly rotating, uniformly decaying distributions of flux, wound up by differential rotation and localized near either the equator or the poles. A balance between azimuthal transport of flux by the rotational shear and meridional transport by the diffusion gives rise to the rigidly rotating field patterns. The time-scale on which this balance is achieved, and also on which the nonaxisymmetric flux decays away, is the geometric mean of the short time-scale for shearing by differential rotation and the long time-scale for dispersal by supergranular diffusion. A poleward meridional flow alters this balance on its own, intermediate time-scale, accelerating the decay of the nonaxisymmetric flux at low latitudes. Such a flow also hastens the relaxation of the axisymmetric field to a modified dipolar configuration.     

The decay of the mean solar magnetic field

We have analyzed the effects that differential rotation and a hypothetical meridional flow would have on the evolution of the Sun's mean line-of-sight magnetic field as seen from Earth. By winding the large-scale field into strips of alternating positive and negative polarity, differential rotation causes the mean-field amplitude to decay and the mean-field rotation period to acquire the value corresponding to the latitude of the surviving unwound magnetic flux. For a latitudinally broad two-sector initial field such as a horizontal dipole, the decay is rapid for about 5 rotations and slow with a t ^–1/2 dependence thereafter. If a poleward meridional flow is present, it will accelerate the decay by carrying the residual flux to high latitudes where the line-of-sight components are small. The resulting decay is exponential with an e-folding time of 0.75 yr (10 rotations) for an assumed 15 m s^–1 peak meridional flow speed.E.O. Hulburt Center for Space Research.Laboratory for Computational Physics.     

Has the crab pulsar magnetic field grown after its birth?

We investigate the evolution of rotation period and spindown age of a pulsar whose surface magnetic field undergoes a phase of growth. Application of these results to the Crab pulsar strongly indicates that its parameters cannot be accounted for by the field growth theories.     

The scale and strength of the galactic magnetic field according to the pulsar data

In accordance with the data on the Faraday rotation, angular coordinates, and dispersion measurements and distances of 38 pulsars, the strengthB=2.1±1.1 G and directionl=99°±24°,b0° of the large-scale galactic magnetic field and the mean electron density in the galactic discN _e=0.03±0.01 cm^–3 are determined. A comparison with the results of a study of the measures of rotation of extragalactic radio sources enabled us to estimate the characteristic half-width of the distribution of the electron density on the Z-coordinate (h400 ps). The characteristic size of galactic magnetic field flucturations is shown to be =100–150 ps.     

A synthesized method for determining the azimuth of solar transverse magnetic field

The analyses have been made with the emphasis on four existing criteria for calibrating the azimuth of the photospheric transverse magnetic field measured with a heliomagnetograph. The results indicate that the potential criterion, Krall's criterion, i.e. B_t · B_z < 0 and Wu-Ai's criterion, i.e.

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, are applicable to different cases, and the criterion based on the assumption about azimuth continuity of the transverse field is unreliable for the magnetograms with discrete data. On the basis of these analyses, a synthesized method for determining the azimuth of the transverse magnetic field on solar photosphere has been suggested in this paper. The main points of the method are as follows:

The transverse magnetic field observed with a heliomagnetograph could be calibrated, respectively, by means of potential criterion and Krall's criterion, and two different results could be obtained. By comparing the both results with one another, we can find that the azimuth distributions of transverse field are the same in some areas, which are named as areas with certain transverse field (CA), and different in other areas, which are named as areas with uncertain transverse field(UA). In order to determine the transverse field in UA, we introduce an assumption that the values of (the factor of force-free magnetic field) at neighbouring points are close. According to this assumption, the distribution of in UA could be determined through extrapolating from the CA, and hence the azimuth distribution of the transverse field in UA could be determined as well.

An observational example shown in this paper preliminarily demonstrates the availability of the synthesized method.     

Field-aligned electric field caused by the decay of force-free magnetic field and particle acceleration

Numerical simulation for the dynamics of a coronal filamentary magnetic loop has been made under the assumption that the field is initially force-free and an electric resistivity suddenly increases at a given moment due to an appearance of ion sound waves, which can be excited due to a high current density if a characteristic radius r ₀ of the magnetic loop is about 3 km or less in a magnetic field B ₀ of 1000 G. During the resistive decay of the magnetic field a strong field-aligned electric field is created and maintained for a sufficient time to acceleratie both electrons and protons to a high energy, which is proportional to B ₀/r ₀ and can be 100 MeV if r ₀ = 10 km and B ₀ = 1000 G. If the coronal magnetic tube is composed of many such filamentary loops, the total number of accelerated electrons is consistent with the observations.     

A method of evolving synoptic maps of the solar magnetic field

The evolution of magnetic flux at the solar surface is widely modeled by the flux transport equation. This describes the distribution of flux from instant to instant over the whole surface but does not describe how the synoptic map for one Carrington rotation evolves into the synoptic map for the next rotation. We derive the correct synoptic evolution equation, show that a simple version yields extremely accurate predictions of synoptic maps and discuss the implications for previous studies of the evolution of surface magnetic structures. We also note that the procedure yields a method of reconstructing an approximate map of the flux over the whole surface at any instant.     

A diagnostic method for probing the possible twist of magnetic field lines in sunspots

In order to study the three-dimensional structure of sunspot magnetic fields it is necessary to determine whether the field lines are twisted, i.e., if the azimuthal angle of transverse field changes with depth. For this purpose we propose the following method. At a fixed point in a spot, and in a certain wavelength interval of a magnetic-sensitive spectral line, one may measure the two Stokes parameters Q and U and then calculate the azimuthal angle of the polarization plane. If the wavelength interval of observation is moved successively from the line center to a wing, one may draw the azimuth diagram by the method proposed by Makita (1986) and refined by us (Ye Shi-hui and Jin Jie-hai, 1987). According to our theoretical calculations, described in this paper, if sunspot field lines are sufficiently strongly twisted, the curve on this diagram contains loop structures. If the twist is rather weak, the curve is approximately semi-circular. From the direction in which the curve winds (clockwise or counterclockwise) one may infer whether the magnetic field is twisting in one direction or in the opposite. In the case of no twist at all, the curve is comparatively simple and similar to a parabola.When the sensitivity of observational data is high enough, our method can also be applied to regions of weak magnetic fields outside sunspots.This work has been supported by the National Natural Science Foundation of China under grant No. 9187006-01.     

The alignment of the Crab pulsar magnetic axis

The magnetic distortion is estimated for neutron stars in which the matter in the interior consists of superfluid neutrons and superconducting protons. For type II proton superconductivity, the arrangement of magnetic flux in a two-dimensional lattice of quantized fluxoids and the kinetic energy of the supercurrent carriers cause some components of the spatially averaged stress tensor for field and superconductor to be several orders of magnitude greater than the components of the Max-well stress tensor for a uniform distribution of the same magnetic flux. It is shown that for the Crab pulsar PSR 0531+21, which is considered to have the greater part of its mass in the form of superfluid neutrons and superconducting protons, the magnetic distortion is almost certainly more important than the clastic energy of the outer shell in determining the departure of the inertia tensor from its spherically symmetric form. With the assumption that internal and external magnetic fields have the same symmetry axis, the external field dipole moment of the Crab pulsar is predicted to be approximately perpendicular to the spin direction, in agreement with a number of published interpretations of observational data.     

A short review of the pulsar magnetic inclination angles (II)

The pulsar magnetic inclination angle is a key parameter for pulsar physics. It influences the observable properties of pulsars, such as the pulse beam width, braking index, polarization, and emission geometry. In this study, we give a brief overview of the current state of knowledge and research on this parameter and its implications for the internal physics of pulsars. We use the observed pulsar data of magnetic inclination angle and braking index to constrain the star's number of precession cycles, $\xi$, which reflects the interaction between superfluid neutrons and other particles inside a neutron star (NS). We apply the method proposed by Cheng et al. (Cheng, Q., Zhang, S. N., Zheng, X. P., & Fan, X. L., 2019, Phys. Rev. D, 99, 083011) to analyze the data of PSR J2013 + 3845 and obtain the constraints for $\xi$ ranging from $2.393\times 10^5$ to $1.268\times 10^6$. And further analysis suggests that the internal magnetic field structure of PSR J2013 + 3845 is likely dominated by toroidal components. This study may help us understand the process of internal viscous dissipation and the related evolution of the inclination angles of pulsars, and may have important implications for the study of continuous gravitational wave emissions from NS.     

A possible diagnostic method for magnetic field and velocity gradients in sunspots

We present a diagnostic method for detecting magnetic field gradients and velocity gradients in sunspots through the analysis of Stokes parameters profiles in magnetoactive lines. On one hand, the method is based on the concept of response functions for the Stokes profiles introduced by Landi Degl'Innocenti and Landi Degl'Innocenti (1977); on the other hand, it takes advantage of the diagnostic content of the residuals between observed Stokes profiles and best-fit Unno-profiles. The analysis of synthesis profiles obtained for the line 6302.502 FeI forming in the Sunspot Sunspot Model (Avrett, 1981) suggests that the method could actually be promising, at least if the dependence of the magnetic field vector on optical depth is sufficiently simple.     

Axion decay in a strong magnetic field and radio fluxes from magnetic white dwarfs

Radio emission of isolated magnetic white dwarfs due to invisible axions decay in a strong magnetic field is estimated. It is possible to reach theoretical limits on the abundance and coupling of cosmic axions provided that radiofluxes would be observed at the level 1 Jy.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Implications of mean field accretion disc theory for vorticity and magnetic field growth

In addition to the scalar Shakura–Sunyaev α _ss turbulent viscosity transport term used in simple analytic accretion disc modelling, a pseudo-scalar transport term also arises. The essence of this term can be captured even in simple models for which vertical averaging is interpreted as integration over a half-thickness and each hemisphere is separately studied. The additional term highlights a complementarity between mean field magnetic dynamo theory and accretion disc theory treated as a mean field theory. Such pseudo-scalar terms have been studied, and can lead to large-scale magnetic field and vorticity growth. Here it is shown that vorticity can grow even in the simplest azimuthal and half-height integrated disc model, for which mean quantities depend only on radius. The simplest vorticity growth solutions seem to have scales and vortex survival times consistent with those required for facilitating planet formation. In addition, it is shown that, when the magnetic back-reaction is included to lowest order, the pseudo-scalar driving the magnetic field growth and that driving the vorticity growth will behave differently with respect to shearing and non-shearing flows: the former pseudo‐scalar can more easily reverse sign in the two cases.