Cooling of neutron stars with strong toroidal magnetic fields

We present models of temperature distribution in the crust of a neutron star in the presence of a strong toroidal component superposed to the poloidal component of the magnetic field. The presence of such a toroidal field hinders heat flow toward the surface in a large part of the crust. As a result, the neutron star surface presents two warm regions surrounded by extended cold regions and has a thermal luminosity much lower than in the case the magnetic field is purely poloidal. We apply these models to calculate the thermal evolution of such neutron stars and show that the lowered photon luminosity naturally extends their life-time as detectable thermal X-ray sources. Work partially supported by UNAM-DGAPA grant #IN119306.     

Axisymmetric stars with both poloidal and toroidal magnetic fields

Chandrasekhar and Prendergast have established a result which has been assumed to imply that axisymmetric stars with an internal toroidal magnetic field should have zero external poloidal field. By considering mildly singular functions, the range of solutions is increased, and models can then be constructed which have toroidal and poloidal fields in the interior and a non-zero, external, poloidal field. Both the magnetic field and its associated current are continuous everywhere.     

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.     

Some observational results on long-time variability of stars with magnetic fields

Ziel dieser Arbeit ist die Zusammenfassung von langzeitigen Phänomenen magnetischer Sterne, die am Potsdamer Observatorium erhalten wurden. Die betrachteten magnetischen Sterne sind γ Equ, HD 9996, 53 Cam, 52 Her und v Cep. Viele Ergebnisse wurden schon publiziert; hier sollen die Resultate zusammengefaßt und durch neue Details vervollständigt werden.     

Statistics of magnetic fields for OB stars

Based on an analysis of the catalog of magnetic fields, we have investigated the statistical properties of the mean magnetic fields for OB stars. We show that the mean effective magnetic field B of a star can be used as a statistically significant characteristic of its magnetic field. No correlation has been found between the mean magnetic field strength B and projected rotational velocity of OB stars, which is consistent with the hypothesis about a fossil origin of the magnetic field. We have constructed the magnetic field distribution function for B stars, F(B), that has a power-law dependence on B with an exponent of ≈−1.82. We have found a sharp decrease in the function F(B) for B ⩽ 400 G that may be related to rapid dissipation of weak stellar surface magnetic fields.     

Generation of a toroidal magnetic field in rotating neutron stars

The electromagnetic properties of neutron stars (pulsars) are studied. It is shown that taking the presence of two angular rotation velocities of the components of neutron stars and the first corrections to the general theory of relativity into account in the equations of hydrodynamic equilibrium for the plasma and in Maxwell’s equations leads to the generation of toroidal magnetic fields in the depths of a neutron star. __________ Translated from Astrofizika, Vol. 49, No. 1, pp. 97–101 (February 2006).     

Evidence for weak magnetic fields in early-type emission stars

We report the results of our study of magnetic fields in a sample of 15 Be stars using spectropolarimetric data obtained at the European Southern Observatory with the multi-mode instrument FORS 1 installed at the 8m Kueyen telescope. We detect weak photospheric magnetic fields in four stars, HD56014, HD148184, HD155806, and HD181615. We note that for HD181615 the evolutionary status is not obvious due to the fact that it is a binary system currently observed in the initial rapid phase of mass exchange between the two components. Further, we notify the possible presence of distinct circular polarisation features in the circumstellar components of Ca II H&K in three stars, HD58011, HD117357, and HD181615, hinting at a probable presence of magnetic fields in the circumstellar mass loss disks of these stars. We emphasize the need for future spectropolarimetric observations of Be stars with detected magnetic fields to study the temporal evolution of their magnetic fields and the correlation of magnetic field properties with dynamical phenomena taking place in the gaseous circumstellar disks of these stars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A search for magnetic fields in cool sdB stars

Hot cluster horizontal branch (HB) stars and field subdwarf B (sdB) stars are core helium burning stars that exhibit abundance anomalies that are believed to be due to atomic diffusion. Diffusion can be effective in these stars because they are slowly rotating. In particular, the slow rotation of the hot HB stars (T_eff > 11000 K), which show abundance anomalies, contrasts with the fast rotation of the cool HB stars, where the observed abundances are consistent with those of red giants belonging to the same cluster. The reason why sdB stars and hot HB stars are rotating slowly is unknown. In order to assess the possible role of magnetic fields on abundances and rotation, we investigated the occurrence of such fields in sdB stars with T_eff < 30 000 K, whose temperatures overlap with those of the hot HB stars. We conclude that large‐scale organised magnetic fields of kG order are not generally present in these stars but at the achieved accuracy, the possibility that they have fields of a few hundred Gauss remains open. We report the marginal detection of such a field in SB 290; further observations are needed to confirm it (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equilibrium structure of polytropes with toroidal magnetic fields

Structure equations for the equilibrium of the gaseous polytropes with toroidal magnetic fields are solved numerically for two values of polytropic indexn-1.5 and 3, using a variant of Stoeckly's method. In addition to the structure parameters frequencies of the characteristic modes of oscillation are calculated. The results are considerably different from the values obtained by Anand for weak toroidal fields.     

Additional polarised standards in the fields of known bright standard stars

We present the results based on broad-band (VRI) polarimetric observations of a number of stars that are present towards the fields of already known bright polarised standard stars namely BD+59^° 389, HD 19820, and HD 25443. These three relatively bright stars were observed continuously for various observing programs using ARIES Imaging Polarimeter (AIMPOL) attached with 1-m Sampurnanand Telescope (ST) since 2006 to correct for any polarisation position angle offset. Since AIMPOL is an imaging polarimeter with a field-of-view of ～8 arcmin diameter, we could get polarisation measurements of a number of relatively faint stars that are present within the field-of-view of the AIMPOL towards the above three bright polarised standards. Based on these compiled observations for a relatively long duration, we could examine the constancy of the degree of polarisation and position angles of them. With the help of some statistical tests, five stars in the field of BD+59^° 389 and two stars in the field of HD 19820 have been identified as stars that could be used as additional polarised standard stars. Since these additional stars are relatively fainter than the known polarised standards, they could be observed with bigger aperture telescopes (like 2-m) without them getting saturated.     

Helmholtz instability in stratified shear flows with magnetic fields

The stability characteristics of a Helmholtz velocity profile in a stratified Boussinesq fluid in the presence of a rigid boundary is studied. A jump in the magnetic field is introduced at a level different from the velocity discontinuity. New unstable modes in addition to the Kelvin-Helmholtz mode are found. The wavelengths of these unstable modes are close to the wavelengths of internal Alfvén gravity waves in the atmosphere.     

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.     

Lithium in chemically peculiar CP stars with magnetic fields

The problem of lithium in chemically peculiar Ap-CP stars has been the subject of debate for many years. The main reason for this is a lack of spectral observations of Ap stars in the neighborhood of the lithium resonance doublet Li I 6708 Å. An international cooperation project on “Lithium in cool CP stars with magnetic fields” was started in 1996. Systematic observations of CP stars in spectral regions of the 6708 Å and 6103 Å lines at the ZTSh (CrAO), CAT (ESO), Feros (ESO), and the 74″ telescope of the Mount Stromlo Observatory (Australia) have been used to analyze spectra of several CP stars studied by the way the 6708 Å lithium line varies with the stars’ rotational phase. Monitoring of the spectra of the oscillating CP stars (group I) HD 83368, HD 60435, and HD 3980, for which significant Doppler shifts of the Li I 6708 Å line are observed led to the discovery of “lithium spots” on the surface of these stars whose positions are related to the magnetic field structure. Models of the surfaces of these stars with the special program “ROTATE” based on the profiles of the Li I 6708 Å line are used to estimate the size of the spots, their positions on the stars’ surface, and the lithium abundances in these spots. A detailed analysis and modelling of the spectra of slowly rotating oscillating CP stars with strong, invariant lithium 6708 Å emission, including blending with lines of the rare earth elements, reveals an enhanced lithium abundance, with the abundance determined from the lithium 6103 Å line being higher than that determined from the 6708 Å line for all the stars. This may indicate vertical stratification of lithium in the atmospheres of CP stars with an anomalous isotopic composition (⁶Li/⁷Li = 0.2–0.5). HD 101065, an ultraslow rotator (vsini ≈ 1.5) visible from the poles and with powerful oscillations which cause pulsating line broadening in its spectrum, is unique among these stars. The amount of lithium in the atmosphere of HD 101065 logN(Li) = 3.1 on a scale of logN(H) = 12.0 and the isotope ratio ⁶Li/⁷Li ≈ 0.3. The high estimates of ⁶Li/⁷Li may be explained by the production of lithium in spallation reactions and the preservation of surface ⁶Li and ⁷Li by strong magnetic fields in the upper layers of the atmosphere near the magnetic poles. __________ Translated from Astrofizika, Vol. 50, No. 3, pp. 463–492 (August 2007).     

Stability of toroidal magnetic fields in the solar tachocline and beneath

Stability of toroidal magnetic field in a stellar radiation zone is considered for the cases of uniform and differential rotation. In the rigidly rotating radiative core shortly below the tachocline, the critical magnetic field for instability is about 600 G. The unstable disturbances for slightly supercritical fields have short radial scales ∼1 Mm. Radial mixing produced by the instability is estimated to conclude that the internal field of the sun can exceed the critical value of 600 G only marginally. Otherwise, the mixing is too strong and not compatible with the observed lithium abundance. Analysis of joint instability of differential rotation and toroidal field leads to the conclusion that axisymmetric models of the laminar solar tachocline are stable to nonaxisymmetric disturbances. The question of whether sun-like stars can posses tachoclines is addressed with positive answer for stars with rotation periods shorter than about two months. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Tayler instability of toroidal magnetic fields in a columnar gallium experiment

The nonaxisymmetric Tayler instability of toroidal magnetic fields due to axial electric currents is studied for conducting incompressible fluids between two coaxial cylinders without endplates. The inner cylinder is considered as so thin that the limit of R_in → 0 can be computed. The magnetic Prandtl number is varied over many orders of magnitudes but the azimuthal mode number of the perturbations is fixed to m = 1. In the linear approximation the critical magnetic field amplitudes and the growth rates of the instability are determined for both resting and rotating cylinders. Without rotation the critical Hartmann numbers do not depend on the magnetic Prandtl number but this is not true for the corresponding growth rates. For given product of viscosity and magnetic diffusivity the growth rates for small and large magnetic Prandtl number are much smaller than those for Pm = 1. For gallium under the influence of a magnetic field at the outer cylinder of 1 kG the resulting growth time is 5 s. The minimum electric current through a container of 10 cm diameter to excite the instability is 3.20 kA. For a rotating container both the critical magnetic field and the related growth times are larger than for the resting column (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)