Magnetic fields of Ap stars as a result of the Tayler instability

Ap star magnetism is often attributed to fossil magnetic fields which have not changed much since the pre‐main‐sequence epoch of the stars. Stable magnetic field configurations are known which could persist probably for the entire mainsequence life of the star, but they may not show the complexity and diversity exhibited by the Ap stars observed. We suggest that the Ap star magnetism is not a result of stable configurations, but is the result of an instability based on strong toroidal magnetic fields buried in the stars. The highly nonaxisymmetric remainders of the instability are reminiscent of the diversity of fields seen on Ap stars. The strengths of these remnant magnetic fields are actually between a few per cent up to considerable fractions of the internal toroidal field; this means field strengths of the order of kGauss being compatible with what is observed. The magnetic fields emerge at the surface rather quickly; rough estimates deliver time‐scales of the order of a few years. Since rotation stabilizes the instability, normal A stars may still host considerable, invisible toroidal magnetic fields (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic survey of emission line B‐type stars with FORS 1 at the VLT

We report the results of our search for magnetic fields in a sample of 16 field Be stars, the binary emission‐line B‐type star υ Sgr, and in a sample of fourteen members of the open young cluster NGC3766 in the Carina spiral arm. The sample of cluster members includes Be stars, normal B‐type stars and He‐strong/He‐weak stars. Nine Be stars have been studied with magnetic field time series obtained over ∼1 hour to get an insight into the temporal behaviour and the correlation of magnetic field properties with dynamical phenomena taking place in Be star atmospheres. The spectropolarimetric data were obtained at the European Southern Observatory with the multi‐mode instrument FORS1 installed at the 8m Kueyen telescope. We detect weak photospheric magnetic fields in four field Be stars, HD 62367, μ Cen, o Aqr, and ε Tuc. The strongest longitudinal magnetic field, 〈B_z〉 = 117 ± 38 G, was detected in the Be star HD 62367. Among the Be stars studied with time series, one Be star, λ Eri, displays cyclic variability of the magnetic field with a period of 21.12 min. The binary star υ Sgr, in the initial rapid phase of mass exchange between the two components with strong emission lines in the visible spectrum, is a magnetic variable star, probably on a timescale of a few months. The maximum longitudinal magnetic field 〈B_z〉 = –102 ± 10 G at MJD 54333.018 was measured using hydrogen lines. The cluster NGC3766 seems to be extremely interesting, where we find evidence for the presence of a magnetic field in seven early B‐type stars out of the observed fourteen cluster members (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamo-generated magnetic fields at the surface of a massive star

Spruit has shown that an astrophysical dynamo can operate in the non-convective material of a differentially rotating star as a result of a particular instability in the magnetic field (the Tayler instability). By assuming that the dynamo operates in a state of marginal instability, Spruit has obtained formulae which predict the equilibrium strengths of azimuthal and radial field components in terms of local physical quantities. Here, we apply Spruit's formulae to our previously published models of rotating massive stars in order to estimate Tayler dynamo field strengths. There are no free parameters in Spruit's formulae. In our models of 10- and  50-M_⊙  stars on the zero-age main sequence, we find internal azimuthal fields of up to 1 MG, and internal radial components of a few kG. Evolved models contain weaker fields. In order to obtain estimates of the field strength at the stellar surface, we examine the conditions under which the Tayler dynamo fields are subject to magnetic buoyancy. We find that conditions for Tayler instability overlap with those for buoyancy at intermediate to high magnetic latitudes. This suggests that fields emerge at the surface of a massive star between magnetic latitudes of about 45° and the poles. We attempt to estimate the strength of the field which emerges at the surface of a massive star. Although these estimates are very rough, we find that the surface field strengths overlap with values which have been reported recently for line-of-sight fields in several O and B stars.     

On the incidence of magnetic fields in slowly pulsating B, β Cephei and B-type emission-line stars

We have obtained 40 high-resolution circular spectropolarimetric measurements of 12 slowly pulsating B (SPB) stars, eight β Cephei stars and two Be stars with the Echelle Spectropolarimetric Device for the Observation of Stars at CFHT (ESPaDOnS) and Narval spectropolarimeters. The aim of these observations is to evaluate recent claims of a high incidence of magnetic field detections in stars of these types obtained using low-resolution spectropolarimetry by Hubrig et al. The precision achieved is generally comparable to or superior to that obtained by Hubrig et al., although our new observations are distinguished by their resolution of metallic and He line profiles, and their consequent sensitivity to magnetic fields of zero net longitudinal component. In the SPB stars, we confirm the detection of magnetic field in one star (16 Peg), but find no evidence of the presence of fields in the remaining 11. In the β Cep stars, we detect a field in  ξ¹  CMa, but not in any of the remaining seven stars. Finally, neither of the two B-type emission-line stars shows any evidence of magnetic field. Based on our results, we conclude that fields are not common in SPB, β Cep and B-type emission-line stars, consistent with the general rarity of fields in the broader population of main sequence B-type stars. A relatively small, systematic underestimation of the error bars associated with the UV Focal Reducer and Low Dispersion Spectrograph for the Very Large Telescope (FORS1) longitudinal field measurements of Hubrig et al. could in large part explain the discrepancy between their results and those presented here.     

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.     

On non-axisymmetric magnetic equilibria in stars

In previous work, stable approximately axisymmetric equilibrium configurations for magnetic stars were found by numerical simulation. Here, I investigate the conditions under which more complex, non-axisymmetric configurations can form. I present numerical simulations of the formation of stable equilibria from turbulent initial conditions and demonstrate the existence of non-axisymmetric equilibria consisting of twisted flux tubes lying horizontally below the surface of the star, meandering around the star in random patterns. Whether such a non-axisymmetric equilibrium or a simple axisymmetric equilibrium forms depends on the radial profile of the strength of the initial magnetic field. The results could explain observations of non-dipolar fields on stars such as the B0.2 main-sequence star τ Sco or the pulsar 1E 1207.4-5209. The secular evolution of these equilibria due to Ohmic and buoyancy processes is also examined.     

The first magnetic maps of a pre-main-sequence binary star system – HD 155555

We present the first maps of the surface magnetic fields of a pre-main-sequence binary system. Spectropolarimetric observations of the young, 18 Myr, HD 155555 (V824 Ara, G5IV+K0IV) system were obtained at the Anglo-Australian Telescope in 2004 and 2007. Both data sets are analysed using a new binary Zeeman–Doppler imaging (ZDI) code. This allows us to simultaneously model the contribution of each component to the observed circularly polarized spectra. Stellar brightness maps are also produced for HD 155555 and compared to previous Doppler images.
Our radial magnetic maps reveal a complex surface magnetic topology with mixed polarities at all latitudes. We find rings of azimuthal field on both stars, most of which are found to be non-axisymmetric with the stellar rotational axis. We also examine the field strength and the relative fraction of magnetic energy stored in the radial and azimuthal field components at both epochs. A marked weakening of the field strength of the secondary star is observed between the 2004 and 2007 epochs. This is accompanied by an apparent shift in the location of magnetic energy from the azimuthal to radial field. We suggest that this could be indicative of a magnetic activity cycle. We use the radial magnetic maps to extrapolate the coronal field (by assuming a potential field) for each star individually – at present ignoring any possible interaction. The secondary star is found to exhibit an extreme tilt (≈75°) of its large-scale magnetic field to that of its rotation axis for both epochs. The field complexity that is apparent in the surface maps persists out to a significant fraction of the binary separation. Any interaction between the fields of the two stars is therefore likely to be complex also. Modelling this would require a full binary field extrapolation.     

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.     

Dynamo action in the presence of an imposed magnetic field

Dynamo action within the cores of Ap stars may offer intriguing possibilities for understanding the persistent magnetic fields observed on the surfaces of these stars. Deep within the cores of Ap stars, the coupling of convection with rotation likely yields magnetic dynamo action, generating strong magnetic fields. However, the surface fields of the magnetic Ap stars are generally thought to be of primordial origin. Recent numerical models suggest that a primordial field in the radiative envelope may possess a highly twisted toroidal shape. We have used detailed 3-D simulations to study the interaction of such a twisted magnetic field in the radiative envelope with the core-dynamo operating in the interior of a 2 solar mass A-type star. The resulting dynamo action is much more vigorous than in the absence of such a fossil field, yielding magnetic field strengths (of order 100 kG) much higher than their equipartition values relative to the convective velocities. We examine the generation of these fields, as well as the growth of large-scale magnetic structure that results from imposing a fossil magnetic field. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the first generation of stars

We argue that the first stars may have spanned the conventional mass range rather than be identified with the very massive objects  (∼100–10³ M_⊙)  favoured by numerical simulations. Specifically, we find that magnetic field generation processes acting in the first protostellar systems suffice to produce fields that exceed the threshold for magneto-rotational instability (MRI) to operate, and thereby allow the MRI dynamo to generate equipartition-amplitude magnetic fields on protostellar mass scales below  ∼50 M_⊙  . Such fields allow primordial star formation to occur at essentially any metallicity by regulating angular momentum transfer, fragmentation, accretion and feedback in much the same way as occurs in conventional molecular clouds.     

Surface magnetic fields on two accreting T Tauri stars: CV Cha and CR Cha

We have produced brightness and magnetic field maps of the surfaces of CV Cha and CR Cha: two actively accreting G- and K-type T Tauri stars in the Chamaeleon I star-forming cloud with ages of 3–5 Myr. Our magnetic field maps show evidence for strong, complex multipolar fields similar to those obtained for young rapidly rotating main-sequence stars. Brightness maps indicate the presence of dark polar caps and low-latitude spots – these brightness maps are very similar to those obtained for other pre-main-sequence and rapidly rotating main-sequence stars.
Only two other classical T Tauri stars have been studied using similar techniques so far: V2129 Oph and BP Tau. CV Cha and CR Cha show magnetic field patterns that are significantly more complex than those recovered for BP Tau, a fully convective T Tauri star.
We discuss possible reasons for this difference and suggest that the complexity of the stellar magnetic field is related to the convection zone; with more complex fields being found in T Tauri stars with radiative cores (V2129 Oph, CV Cha and CR Cha). However, it is clearly necessary to conduct magnetic field studies of T Tauri star systems, exploring a wide range of stellar parameters in order to establish how they affect magnetic field generation, and thus how these magnetic fields are likely to affect the evolution of T Tauri star systems as they approach the main sequence.     

The exceptional Herbig Ae star HD 101412: The first detection of resolved magnetically split lines and the presence of chemical spots in a Herbig star

In our previous search for magnetic fields in Herbig Ae stars, we pointed out that HD 101412 possesses the strongest magnetic field among the Herbig Ae stars and hence is of special interest for follow‐up studies of magnetism among young pre‐main‐sequence stars. We obtained high‐resolution, high signal‐to‐noise UVES and a few lower quality HARPS spectra revealing the presence of resolved magnetically split lines. HD 101412 is the first Herbig Ae star for which the rotational Doppler effect was found to be small in comparison to the magnetic splitting and several spectral lines observed in unpolarized light at high dispersion are resolved into magnetically split components. The measured mean magnetic field modulus varies from 2.5 to 3.5kG, while the mean quadratic field was found to vary in the range of 3.5 to 4.8 kG. To determine the period of variations, we used radial velocity, equivalent width, line width, and line asymmetry measurements of variable spectral lines of several elements, as well as magnetic field measurements. The period determination was done using the Lomb‐Scargle method. The most pronounced variability was detected for spectral lines of He I and the iron peak elements, whereas the spectral lines of CNO elements are only slightly variable. From spectral variations and magnetic field measurements we derived a potential rotation period P_rot = 13.86 d, which has to be proven in future studies with a larger number of observations. It is the first time that the presence of element spots is detected on the surface of a Herbig Ae/Be star. Our previous study of Herbig Ae stars revealed a trend towards stronger magnetic fields for younger Herbig Ae stars, confirmed by statistical tests. This is in contrast to a few other (non‐statistical) studies claiming that magnetic Herbig Ae stars are progenitors of the magnetic Ap stars. New developments in MHD theory show that the measured magnetic field strengths are compatible with a current‐driven instability of toroidal fields generated by differential rotation in the stellar interior. This explanation for magnetic intermediate‐mass stars could be an alternative to a frozen‐in fossil field (© 2010 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)     

Evolution of magnetic fields in stars across the upper main sequence: II. Observed distribution of the magnetic field geometry

We re‐discuss the evolutionary state of upper main sequence magnetic stars using a sample of Ap and Bp stars with accurate Hipparcos parallaxes and definitely determined longitudinal magnetic fields. We confirm our previous results obtained from the study of Ap and Bp stars with accurate measurements of the mean magnetic field modulus and mean quadratic magnetic fields that magnetic stars of mass M < 3 M_⊙ are concentrated towards the centre of the main‐sequence band. In contrast, stars with masses M > 3 M_⊙ seem to be concentrated closer to the ZAMS. The study of a few known members of nearby open clusters with accurate Hipparcos parallaxes confirms these conclusions. Stronger magnetic fields tend to be found in hotter, younger and more massive stars, as well as in stars with shorter rotation periods. The longest rotation periods are found only in stars which spent already more than 40% of their main sequence life, in the mass domain between 1.8 and 3 M_⊙ and with log g values ranging from 3.80 to 4.13. No evidence is found for any loss of angular momentum during the main‐sequence life. The magnetic flux remains constant over the stellar life time on the main sequence. An excess of stars with large obliquities β is detected in both higher and lower mass stars. It is quite possible that the angle β becomes close to 0. in slower rotating stars of mass M > 3 M_⊙ too, analog to the behaviour of angles β in slowly rotating stars of M < 3 M_⊙. The obliquity angle distribution as inferred from the distribution of r ‐values appears random at the time magnetic stars become observable on the H‐R diagram. After quite a short time spent on the main sequence, the obliquity angle β tends to reach values close to either 90. or 0. for M < 3 M_⊙. The evolution of the obliquity angle β seems to be somewhat different for low and high mass stars. While we find a strong hint for an increase of β with the elapsed time on the main sequence for stars with M > 3 M_⊙, no similar trend is found for stars with M < 3 M_⊙. However, the predominance of high values of β at advanced ages in these stars is notable. As the physics governing the processes taking place in magnetised atmospheres remains poorly understood, magnetic field properties have to be considered in the framework of dynamo or fossil field theories. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Studies of accretion flows around rotating black holes – I. Particle dynamics in a pseudo-Kerr potential

We study the formation of the absorption features, called the cyclotron–annihilation lines, in the γ-spectra of the neutron stars (pulsars), owing to the fundamental quantum-electrodynamic effect of the one–photon pair creation in magnetized vacuum. As a result, we substantiate a new method for the determination of the neutron star magnetic fields B based on measuring the interval between the main annihilation and the first cyclotron–annihilation absorption lines. It is found that these lines may be easily resolved, and, consequently, the method is surely applicable if the following conditions are satisfied. (i) A γ-source has to be compact enough and located near a star, but not close to its magnetic poles. For instance, it may be a disc in the plane of a star magnetic equator with latitudinal angular width less than     and radial extent up to 25 per cent of the star radius. (ii) The source is to produce detectable γ-radiation at large angles ≳60° to the local magnetic field. Being situated in a closed field line region and having a broad radiation pattern, such a source is not what is usually considered in the context of the polar cap and outer gap models of the pulsar γ-emission dealing with open field lines only. (iii) Magnetic field strength must lie in a certain narrow interval with the centre at  ∼(3–4) × 10¹²  G. Its width depends on the star orientation and disc radial extend and in the most favourable case is about 20–30 per cent of its lower boundary. Finally, the influence of the star rotation on this method employment is considered and new possibilities arising from forthcoming polarization observations are briefly discussed.     

Catalogue of averaged stellar effective magnetic fields – II. Re-discussion of chemically peculiar A and B stars

This paper presents a catalogue and the method of determining averaged quadratic effective magnetic fields  〈 B _e〉  for 1212 main-sequence and giant stars, and 11 white dwarf stars. The catalogue includes stars that are members of several open clusters. We have compiled measurements of the longitudinal magnetic field for those stars, which were scattered in the existing literature. A new parameter, magnetization (MA), has been defined, and we present values of MA for stars of various spectral classes. Our sample includes a subset of 610 chemically peculiar early-type stars. We confirm the conclusion of our previous study that the number distribution of all chemically peculiar stars versus the averaged magnetic field strength is described by a decreasing exponential function. Relations of this type also hold for stars of all the analysed subclasses of chemical peculiarity. Magnetization tends to correlate with the effective temperature only at high MA, for He-weak and He-rich stars.     

Type I and two-gap superconductivity in neutron star magnetism

Neutron star inner cores with several charged baryonic components are likely to be analogues of the two-gap superconductor which is of current interest in condensed-matter physics. Consequently, type I superconductivity is less probable than type II but may nevertheless be present in some intervals of matter density. The intermediate-state structure formed at finite magnetic flux densities after the superconducting transitions is subject to buoyancy, frictional and neutron vortex interaction forces. These are estimated and it is shown that the most important frictional force is that produced by the stable stratification of neutron star matter, the irreversible process being diffusion in the normal, finite magnetic flux density, parts of the structure. The length-scale of the structure, in directions perpendicular to the local magnetic field is of crucial importance. For small scales, the flux comoves with the neutron vortices, as do the proton vortices of a type II superconductor. But for much larger length-scales, flux movement tends to that expected for normal charged Fermi systems.     

Magnetic and spin evolution of neutron stars in close binaries

The evolution of neutron stars in close binary systems with a low-mass companion is considered, assuming the magnetic field to be confined within the solid crust. We adopt the standard scenario for the evolution in a close binary system, in which the neutron star passes through four evolutionary phases ('isolated pulsar'–'propeller'– accretion from the wind of a companion – accretion resulting from Roche-lobe overflow). Calculations have been performed for a great variety of parameters characterizing the properties of both the neutron star and the low-mass companion. We find that neutron stars with more or less standard magnetic field and spin period that are processed in low-mass binaries can evolve to low-field rapidly rotating pulsars. Even if the main-sequence life of a companion is as long as 10¹⁰ yr, the neutron star can maintain a relatively strong magnetic field to the end of the accretion phase. The model that is considered can account well for the origin of millisecond pulsars.     

Spectroscopic study of the weak magnetic star HD220825-κPsc

The star HD220825 is studied as part of a program to investigate the chemical abundance of CP stars with weak magnetic fields. Its magnetic field is found to be Be < 100 G. The chemical abundance appears to correspond to that of CP stars with high magnetic fields. The present results and other data imply that the magnetic field has little effect on the degree of anomaly in the chemical abundance, although it undoubtedly has an effect. The rotation speed of the star is 37.5 km/s, substantially lower than for normal stars with the same temperature. The weak magnetic field raises difficulties for the hypothesis that the loss of angular momentum involves the magnetic field. __________ Translated from Astrofizika, Vol. 49, No. 4, pp. 585–594 (November 2006).     

Measurements of mean longitudinal magnetic fields in the Of?p stars HD 108 and HD 191612

Using polarimetric spectra obtained with the SOFIN spectrograph installed at the Nordic Optical Telescope, we detect a longitudinal magnetic field 〈B_z〉 = –168±35 G in the Of?p star HD 108. This result is in agreement with the longitudinal magnetic field measurement of the order of –150 G recently reported by the MiMeS team. The measurement of the longitudinal magnetic field in the Of?p star HD 191612 results in 〈B_z〉 = +450±153 G. The only previously published magnetic field measurement for this star showed a negative longitudinal magnetic field 〈B_z〉 = –220±38 G, indicating a change of polarity over ∼100 days. Further, we report the detection of distinct Zeeman features in the narrow Ca II and Na I doublet lines for both Of?p stars, hinting at the possible presence of material around these stars. The origin of these features is not yet clear and more work is needed to investigate how magnetic fields interact with stellar wind dynamics (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)