Meissner Effect for “Color” Superconducting Quark Matter

The behavior of the magnetic field inside the superconducting quark matter core of a neutron star is investigated in the framework of the Ginzburg-Landau theory. We take into account the simultaneous coupling of the diquark condensate field to the usual magnetic and to the gluomagnetic gauge fields. We solve the problem for three different physical situations: a semi-infinite region with a planar boundary, a spherical region, and a cylindrical region. We show that Meissner currents near the quark core boundary effectively screen the external static magnetic field.     

Dynamics of tilted spherical star and stability of non-tilted congruence

This paper aims to study the dynamics of spherical star having anisotropic pressure, heat dissipation and shear viscosity with radial four-velocity. We formulate the field equations, equations of motion and equations for the Weyl tensor to study the inhomogeneity factor of the tilted congruence. An evolution equation for the shear is established to explore the stability of the non-tilted congruence. We conclude that the non-tilted congruence is stable for shear-free case.     

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.     

Maximum mass of magnetic white dwarfs

We revisit the problem of the maximum masses of magnetized white dwarfs(WDs).The impact of a strong magnetic field on the structure equations is addressed.The pressures become anisotropic due to the presence of the magnetic field and split into parallel and perpendicular components.We first construct stable solutions of the Tolman-Oppenheimer-Volkoff equations for parallel pressures and find that physical solutions vanish for the perpendicular pressure when B(?) 10~(13) G.This fact establishes an upper bound for a magnetic field and the stability of the configurations in the(quasi) spherical approximation.Our findings also indicate that it is not possible to obtain stable magnetized WDs with super-Chandrasekhar masses because the values of the magnetic field needed for them are higher than this bound.To proceed into the anisotropic regime,we can apply results for structure equations appropriate for a cylindrical metric with anisotropic pressures that were derived in our previous work.From the solutions of the structure equations in cylindrical symmetry we have confirmed the same bound for B ~ 10~(13) G,since beyond this value no physical solutions are possible.Our tentative conclusion is that massive WDs with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist.     

An Exact Anisotropic Quark Star Model

We present an exact analytical solution of the gravitational field equations describing a static spherically symmetric anisotropic quark matter distribution. The radial pressure inside the star is assumed to obey a linear equation of state, while the tangential pressure is a complicated function of the radial coordinate. In order to obtain the general solution of the field equations a particular density profile inside the star is also assumed. The anisotropic pressure distribution leads to an increase in the maximum radius and mass of the quark star, which in the present model is around three solar masses.     

Relativistic models of magnetars: structure and deformations

We find numerical solutions of the coupled system of Einstein–Maxwell equations with a linear approach, in which the magnetic field acts as a perturbation of a spherical neutron star. In our study, magnetic fields having both poloidal and toroidal components are considered, and higher order multipoles are also included. We evaluate the deformations induced by different field configurations, paying special attention to those for which the star has a prolate shape. We also explore the dependence of the stellar deformation on the particular choice of the equation of state and on the mass of the star. Our results show that, for neutron stars with mass   M = 1.4 M_⊙  and surface magnetic fields of the order of 10¹⁵ G, a quadrupole ellipticity of the order of 10⁻⁶ to 10⁻⁵ should be expected. Low-mass neutron stars are in principle subject to larger deformations (quadrupole ellipticities up to 10⁻³ in the most extreme case). The effect of quadrupolar magnetic fields is comparable to that of dipolar components. A magnetic field permeating the whole star is normally needed to obtain negative quadrupole ellipticities, while fields confined to the crust typically produce positive quadrupole ellipticities.     

The effect of magnetic fields on star cluster formation

We examine the effect of magnetic fields on star cluster formation by performing simulations following the self-gravitating collapse of a turbulent molecular cloud to form stars in ideal magnetohydrodynamics. The collapse of the cloud is computed for global mass-to-flux ratios of  ∞, 20, 10, 5  and 3, i.e. using both weak and strong magnetic fields. Whilst even at very low strengths the magnetic field is able to significantly influence the star formation process, for magnetic fields with plasma  β < 1  the results are substantially different to the hydrodynamic case. In these cases we find large-scale magnetically supported voids imprinted in the cloud structure; anisotropic turbulent motions and column density striations aligned with the magnetic field lines, both of which have recently been observed in the Taurus molecular cloud. We also find strongly suppressed accretion in the magnetized runs, leading to up to a 75 per cent reduction in the amount of mass converted into stars over the course of the calculations and a more quiescent mode of star formation. There is also some indication that the relative formation efficiency of brown dwarfs is lower in the strongly magnetized runs due to a reduction in the importance of protostellar ejections.     

Effects of external magnetic field on the outflows of an accretion disc

The aim of this work is to study the effects of an external magnetic field generated by a magnetized compact star on the outflows of its accretion disc. For this purpose, we solve a set of magneto-hydrodynamic (MHD) equations for an accretion disc in spherical coordinates to consider the disc structure along the θ-direction. We also consider the magnetic field of a compact star beyond its surface as a dipolar field, producing a toroidal magnetic field inside the disc. We convert the equations to a set of ordinary differential equations (ODEs) as a function of the θ only by applying self-similar assumptions in the radial direction. Then, this set of equations is solved under symmetrical boundary conditions in the equatorial plane to obtain the velocity field. The results are considered in the gas-pressure-dominated (GPD) region and radiation-pressure-dominated (RPD) region as well. The dipolar field of the compact stars can significantly enhance the speed of outflows. It also can change the structure of the disc. The results of this work would be useful in the study of X-ray binaries, the origin of ultra-relativistic outflows, and jet formation around the compact stars.     

Accretion magnetar in the close binary system 4U 2206+54

The magneto-rotational evolution of a neutron star in the massive binary system 4U 2206+54 is discussed in light of the recent discovery of its 5555 s rotational period and its average rate of spin-down. We show that this behavior of the neutron star means that its magnetic field exceeds the quantum mechanical critical limit and it is an accretion magnetar. The system’s evolution is explained by wind driven mass transfer without formation of an accretion disk. The constant character of the x-ray source indicates a steady rate of accretion and raises anew the question of the stability of the boundary of the magnetosphere of a star undergoing spherical accretion. A solution to this problem is also a key to determining the mechanism for the slowing down of the star’s rotation.     

Tenma observation of the X-ray pulsar 4U1626-67

Energy-dependent pulse profiles from the X-ray pulsar 4U1626-67, observed with Tenma in May 1983, were studied using an anisotropic radiation transfer model in an accretion column on a strongly magnetized neutron star. The result indicates that the strength of the magnetic field is about 8×10¹² G at the surface of the neutron star.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Star formation rate and magnetic fields in spiral galaxies

We have constructed a dynamo model for the magnetic field in spiral galaxies that takes into account the differences in star formation rates in different galaxies. The difficulty in constructing the model is that the star formation rate does not enter directly into the equations of magnetohydrodynamics, which include only the root-mean-square velocity of the interstellar gas, its density, and the half-thickness of the ionized gas disk. We propose a parametrization of these quantities that relates them to the star formation rate and investigate our model in terms of the so-called no-z approximation, which neglects the details of the magnetic field structure in a direction perpendicular to the galactic disk. The influence of the star formation rate on the galactic dynamo is a threshold one. This influence is small at moderate star formation rates and significant only at very high star formation rates. If the starburst intensity reaches some critical level (exceeding that in the Milky Way by an order of magnitude), then the large-scale magnetic field is destroyed and it is restored only after completion of the starburst. We provide a list of galaxies that exhibit a fairly high star formation rate and that can be interesting to study their magnetic fields.     

Star formation and galactic dynamo model with helicity fluxes

We propose a possible scenario of large-scale magnetic field evolution for galaxies with star formation. An important point affecting the results of our calculations is a parametrization of dynamo-governing quantities. In comparison with previous works, we have reconsidered the views of how star formation affects the stationary magnetic field strength, viscosity, and other parameters important for galactic dynamos. The calculations have been performed by taking into account the magnetic helicity fluxes, which introduce an additional nonlinearity into the model and change the regime of galactic dynamo action. We have confirmed the previously suggested idea that for weak star formation its influence on the magnetic field strength is minor and the relationship between them clearly manifests itself only when the star formation rate reaches a certain threshold value. In this case, on the one hand, the threshold lowers-this effect manifests itself at a star formation surface density greater than that in the Milky Way by a factor of 5. On the other hand, intense star formation can cause both a monotonic decay of the large-scale magnetic field and its oscillations near some value.     

The direction of propagation of the solar dynamo wave

We propose a solution to one of the oldest problems in the solar-dynamo theory: explaining the equatorward drift of magnetic activity in the solar cycle. The well-known suggestion that the dynamo waves propagate along the surfaces of constant angular velocity is shown to be restricted to an isotropic medium. Allowance for the rotation-induced anisotropy in turbulent diffusion leads to an equatorward deviation of the wave phase velocity from the isorotational surface. Estimates for the dynamo waves are illustrated with two-dimensional numerical models in a spherical geometry. The model with anisotropic diffusion also shows an equatorward drift of the toroidal magnetic field when the rotation is radially uniform.     

Equilibrium configuration of the magnetosphere of a star loaded with accreted magnetized mass

Equilibrium configuration of the magnetosphere of a star loaded by the gravitationally accreted plasma having its own magnetic field is investigated. Axisymmetry around the star’s magnetic axis is assumed for simplicity. It is seen that two distinct configurations appear for the cases of parallel and antiparallel magnetic field of the accreted plasma with respect to the star’s magnetic moment. If the external field is antiparallel to the star’s magnetic moment, the stellar magnetosphere is confined within a spherical region surrounded by the external field with a separatric surface between them. This is an extension of the case of the spherical accretion of non-magnetic plasma dealt with thus far in connection with the mass accretion by the degenerate stars in X-ray binaries. It is noticed that the mass slides down along the field lines to the point closest to the star and is stratified hydrostatically in equilibrium to form a disk in the equatorial plane. The mass loading compresses the sphere as a whole in this case. If, on the other hand, the external field is parallel to the star’s magnetic moment, there appears a ring of magnetic neutral point in the equatorial plane. Polar field is open and extends to infinity while the low-latitude field is closed and faces the external field of opposite polarity across the neutral point. The increase of the loaded mass in this case causes a shrink of the closed field region, and the open polar flux is increased. Therefore, the transition between equilibria with small and large amount of the loaded mass requires the reconnection of magnetic lines of force, and the reconnection of the flux through the magnetic neutral ring is proposed as the mechanism of the steady or the intermittent mass leakage like the ones postulated for some X-ray bursters. Visiting Scientist supported by the Japan Society for the Promotion of Sciences.     

Amplification of primordial magnetic fields by anisotropic gravitational collapse

If a magnetic field is frozen into a plasma that undergoes spherical compression, then the magnetic field B varies with the plasma density ρ according to   B ∝ρ^2/3  . In the gravitational collapse of cosmological density perturbations, however, quasi-spherical evolution is very unlikely. In anisotropic collapses the magnetic field can be a much steeper function of gas density than in the isotropic case. We investigate the distribution of amplifications in realistic gravitational collapses from Gaussian initial fluctuations using the Zel'dovich approximation. Representing our results using a relation of the form   B ∝ρ^α  , we show that the median value of α can be much larger than the value  α= 2/3  resulting from spherical collapse, even if there is no initial correlation between magnetic field and principal collapse directions. These analytic arguments go some way towards understanding the results of numerical simulations.     

The sixth frequency of roAp star HR 1217

The frequency of the sixth mode observed in HR 1217 cannot currently be understood in the light of the asymptotic theory for high-frequency acoustic modes, valid for adiabatic pulsations in spherically symmetric stars. Deviations from spherical symmetry will change the frequency of the observed oscillations away from the frequencies predicted by the asymptotic theory. Among other things, the presence of a magnetic field in the star will introduce such deviations from spherical symmetry. In the present work we inspect the effect of the magnetic field on the oscillations of HR 1217. Although we model HR 1217 in a rather simplified manner, we believe, as argued in the text, that the essence of the conclusions would not be modified if a more sophisticated model were to be used instead. The results show that the frequency of the sixth mode observed in HR 1217 might be understood if the effect of the magnetic field on the frequencies of the oscillations is fully taken into account. Moreover, we interpret the sixth frequency as a mode of even degree, and explain the absence from the observations of an intermediate l =1 , m =0 mode as the result of large energy losses associated with the coupling of the latter with Alfvénic waves, in the strongly magnetized outer layers of the star. Finally, we show how, in the light of this explanation, the frequency of the sixth mode might be used in order to put constraints on the parameters characterizing the star.     

Structure of the Magnetic Field of a Neutron Star

The magnetic field distribution in the superfluid, spherical, hadronic core of a rotating neutron star, which consists of vortex and vortex-free zones, is investigated. Due to the effect of entrainment of superconducting protons by rotating superfluid neutrons, a nonuniform magnetic field, the average value of which is constant, is formed in the vortex zone of the neutron star, directed parallel to the star's axis of rotation. It is shown that at the stellar surface, near the equatorial plane, there is a vortex-free zone of macroscopic size in which there is no magnetic field. The magnetic field near the boundaries of the vortex-free zone falls off exponentially with depth into the interior of this zone. This result essentially alters earlier concepts about the magnetic field distribution in the superfluid hadronic core of a neutron star. Outside the hadronic core the magnetic field has a dipole character with a magnetic moment on the order of 10³⁰ g×cm³.     

The physics of strong magnetic fields in neutron stars

In this paper we present a new result, namely that the primal magnetic field of the collapsed core during a supernova explosion will, as a result of the conservation of magnetic flux, receive a massive boost to more than 90 times its original value by the Pauli paramagnetization of the highly degenerate relativistic electron gas just after the formation of the neutron star. Thus, the observed super-strong magnetic field of neutron stars may originate from the induced Pauli paramagnetization of the highly degenerate relativistic electron gas in the interior of the neutron star. We therefore have an apparently natural explanation for the surface magnetic field of a neutron star.     

Magnetic braking in magnetic binary stars

The role of an external magnetic field in the magnetic braking of a star with a dipolar field is investigated. In a magnetic cataclysmic variable system (i.e. the primary compact star has a strong magnetic field), the field external to the braking star (a late-type main-sequence star with a dynamo-generated field) originates from the compact star. A closed field region — the system dead zone — is formed within the binary system, and it does not take part in magnetic braking. The overall braking rate depends on the extent of this region and of the open flux, and is dependent on centrifugal effects. In the case of two interacting dipoles, the dipole orientations relative to the spin axes and to each other are found to be important, leading to different amounts of open flux and therefore of magnetic braking, owing to different centrifugal effects on closed field regions. However, in circumstances consistent with observations and dynamo theory, the white dwarf's field reduces the magnetic braking of the secondary significantly, a finding qualitatively similar to the results previously obtained for two anti-aligned dipoles perpendicular to the orbital plane. In the cases where the two dipole axes are not perpendicular to the orbital plane, but are inclined in the plane that links them, the 'cut-off' in magnetic braking is less abrupt, and this effect is more obvious as the inclinations increase. Only in the extreme cases when the two dipole axes are aligned in the orbital plane does the braking increase with white dwarf field strength. We conclude that detailed evolutionary modelling of AM Herculis systems needs to take account of the inclination effect.