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1.
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 Ep / E , it is found that the stability condition is a ( E / U ) < Ep / 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.  相似文献   

2.
We study the effect of the magnetic field geometry on the oscillation spectra of strongly magnetized stars. We construct a configuration of magnetic field where a toroidal component is added to the standard poloidal one. We consider a star with a type I superconductor core so that both components of the magnetic field are expelled from the core and confined in the crust. Our results show that the toroidal contribution does not influence significantly the torsional oscillations of the crust. On the contrary, the confinement of the magnetic field in the crust drastically affects the torsional oscillation spectrum. A comparison with estimations for the magnetic field strength, from observations, excludes the possibility that magnetars will have a magnetic field solely confined in the crust, that is, our results suggest that the magnetic field in whatever geometry has to permeate the whole star.  相似文献   

3.
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.  相似文献   

4.
The effect of rotation and a general magnetic field on the luminosity, radius, and effective temperature of the upper Main-Sequence stars has been investigated using a perturbation analysis. The magnetic field profile prevailing inside the star is assumed to have both poloidal and toroidal components. The case of constant as well as differential rotation is admitted. Model calculations indicate that these stellar parameters modify considerably as a result of coupling between rotation and the magnetic field.  相似文献   

5.
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.  相似文献   

6.
The magnetic and thermal evolution of neutron stars is a very complex process with many non-linear interactions. For a decent understanding of neutron star physics, these evolutions cannot be considered isolated. A brief overview is presented, which describes the main magneto–thermal interactions that determine the fate of both isolated neutron stars and accreting ones. Special attention is devoted to the interplay of thermal and magnetic evolution at the polar cap of radio pulsars. There, a strong meridional temperature gradient is maintained over the lifetime of radio pulsars. It may be strong enough to drive thermoelectric magnetic field creation which perpetuate a toroidal magnetic field around the polar cap rim. Such a local field component may amplify and curve the poloidal surface field at the cap, forming a strong and small scale magnetic field as required for the radio emission of pulsars.  相似文献   

7.
First-order perturbation theory results for the changes in pulsation frequencies of a Cowling model star containing a magnetic field with both poloidal and toroidal components are presented. A toroidal field large enough to stabilize the poloidal field may reverse the sign of the frequency change caused by a purely poloidal field for some modes, including the fundamental radial mode.  相似文献   

8.
Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?1022Mx) and smaller elements ranging down to flux fibres (? 1018Mx). Some implications of similar features in other stars are discussed.  相似文献   

9.
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)  相似文献   

10.
Neutron stars contain persistent, ordered magnetic fields that are the strongest known in the Universe. However, their magnetic fluxes are similar to those in magnetic A and B stars and white dwarfs, suggesting that flux conservation during gravitational collapse may play an important role in establishing the field, although it might also be modified substantially by early convection, differential rotation, and magnetic instabilities. The equilibrium field configuration, established within hours (at most) of the formation of the star, is likely to be roughly axisymmetric, involving both poloidal and toroidal components. The stable stratification of the neutron star matter (due to its radial composition gradient) probably plays a crucial role in holding this magnetic structure inside the star. The field can evolve on long time scales by processes that overcome the stable stratification, such as weak interactions changing the relative abundances and ambipolar diffusion of charged particles with respect to neutrons. These processes become more effective for stronger magnetic fields, thus naturally explaining the magnetic energy dissipation expected in magnetars, at the same time as the longer-lived, weaker fields in classical and millisecond pulsars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

11.
Natural, low-frequency, hydromagnetic oscillations of an isolated, nonrotating neutron star, which are localized in the peripheral crust, the structure of which is determined by the electron-nuclear plasma (the Ae phase), are studied. The plasma medium of the outer crust is treated as a homogeneous, infinitely conducting, incompressible continuum, the motions of which are determined by the equations of magnetohydrodynamics. In the approximation of a constant magnetic field inside the crust (the magnetic field outside the star is assumed to have a dipole structure), the spectrum of normal poloidal and toroidal hydromagnetic oscillations, due to presumed residual fluctuations of flow and their associated fluctuations in magnetic field strength, is calculated. Numerical estimates given for the periods of MHD oscillations fall in the range of periods of radio pulsar emission, indicating a close connection between the residual hydromagnetic oscillations and the electromagnetic activity of neutron stars. Translated from Astrofizika, Vol. 40, No. 1, pp. 77–86, January–March, 1997.  相似文献   

12.
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.  相似文献   

13.
We suggest a model based on the representation of the stellar magnetic field as a superposition of a finite number of poloidal and toroidal free decay modes to describe the dynamo action in fully convective stars. For the adopted law of stellar differential rotation, we determined the dynamo number in exceeding which the generation of a cyclically varying magnetic field is possible in stars without a radiative core and derived an expression for the period of the cycle. The dynamo cycles in fully convective stars and in stars with thin convective envelopes are shown to differ qualitatively: first, the distributions of spots in latitude during the cycle are different for these two types of stars and, second, the model predicts a great weakening of the spot formation in fully convective stars at certain phases of the cycle. To compare the theory with observations, we have analyzed the historical light curve for the weak-line T Tauri star V410 Tau and found that its long-term activity is not a well-defined cycle with a definite period—its activity is more likely quasi-cyclic with a characteristic time of ～4 yr and with a chaotic component superimposed. we have also concluded that a redistribution of spots in longitude is responsible for the secular brightness variations in the star. This does not allow the results of photometric observations to be directly compared with predictions of ourmodel, in which, for simplicity, we assumed a symmetry in longitude and investigated the temporal evolution of the spot distribution in latitude. Therefore, we discuss the questions of what and how observations can be compared with predictions of the dynamo theory.  相似文献   

14.
The generation of magnetic fields by a battery, operating in an ion–electron plasma around a Kerr black hole, is studied in the 3+1 split of the Kerr metric. It is found that the gravitomagnetic contributions to the electron partial pressure are able to drive currents. The strength of the equilibrium magnetic field should be higher than for the classical Biermann battery, which is found to operate in this relativistic context as well, since the gravitomagnetic driving terms can less easily be quenched than the classical ones. In axisymmetry the battery can induce only toroidal magnetic fields. Once a toroidal magnetic field is present, however, the coupling of gravitomagnetic and electromagnetic fields generates a poloidal magnetic field even in axisymmetry. A rotating black hole, embedded in plasma, will therefore always generate toroidal and poloidal magnetic fields.  相似文献   

15.
We use the so-called complex plane iterative technique (CIT) to the computation of polytropic stars distorted by rotation (either rigid or differential) and magnetic fields (both toroidal and poloidal). We give emphasis on computing(i) critically rotating configurations, and (ii) configurations that – dueto the counterbalancing of the effects of rotation and poloidal magnetic field with the effects of toroidal magnetic field – obtain an almost spherical shape. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

16.
We derive general equations for axisymmetric Newtonian magnetohydrodynamics and use these as the basis of a code for calculating equilibrium configurations of rotating magnetized neutron stars in a stationary state. We investigate the field configurations that result from our formalism, which include purely poloidal, purely toroidal and mixed fields. For the mixed-field formalism, the toroidal component appears to be bounded at less than 7 per cent. We calculate distortions induced both by magnetic fields and by rotation. From our non-linear work, we are able to look at the realm of validity of perturbative work: we find for our results that perturbative-regime formulae for magnetic distortions agree to within 10 per cent of the non-linear results if the ellipticity is less than 0.15 or the average field strength is less than 1017 G. We also consider how magnetized equilibrium structures vary for different polytropic indices.  相似文献   

17.
In the context of white dwarf asteroseismology, we investigate the vibrational properties of a non-convective solid star with an axisymmetric purely toroidal intrinsic magnetic field of two different shapes. Focus is laid on the regime of node-free global Lorentz-force-driven vibrations about the symmetry axis at which material displacements have one and the same form as those for nodeless spheroidal and torsional vibrations restored by Hooke’s force of elastic shear stresses. Particular attention is given to the even-parity poloidal Alfvén modes whose frequency spectra are computed in analytic form, showing how the purely toroidal magnetic fields completely buried beneath the star surface can manifest itself in seismic vibrations of non-magnetic white dwarfs. The spectral formulae obtained are discussed in juxtaposition with those for Alfvén modes in the solid star model with the poloidal, homogeneous internal and dipolar external, magnetic field whose inferences are relevant to Alfvén vibrations in magnetic white dwarfs.  相似文献   

18.
We find general relativistic solutions of equilibrium magnetic field configurations in magnetars, extending previous results of Colaiuda et al. Our method is based on the solution of the relativistic Grad–Shafranov equation, to which Maxwell's equations can be reduced. We obtain equilibrium solutions with the toroidal magnetic field component confined into a finite region inside the star, and the poloidal component extending to the exterior. These so-called twisted torus configurations have been found to be the final outcome of dynamical simulations in the framework of Newtonian gravity, and appear to be more stable than other configurations. The solutions include higher-order multipoles, which are coupled to the dominant dipolar field. We use arguments of minimal energy to constrain the ratio of the toroidal to the poloidal field.  相似文献   

19.
In this paper, we present new spectropolarimetric observations of the planet-hosting star τ Bootis, using ESPaDOnS and Narval spectropolarimeters at Canada–France–Hawaii Telescope and Telescope Bernard Lyot, respectively.
We detected the magnetic field of the star at three epochs in 2008. It has a weak magnetic field of only a few gauss, oscillating between a predominant toroidal component in January and a dominant poloidal component in June and July. A magnetic polarity reversal was observed relative to the magnetic topology in 2007 June. This is the second such reversal observed in 2 years on this star, suggesting that τ Boo has a magnetic cycle of about 2 years. This is the first detection of a magnetic cycle for a star other than the Sun. The role of the close-in massive planet in the short activity cycle of the star is questioned.
τ Boo has a strong differential rotation, a common trend for stars with shallow convective envelope. At latitude 40°, the surface layer of the star rotates in 3.31 d, equal to the orbital period. Synchronization suggests that the tidal effects induced by the planet may be strong enough to force at least the thin convective envelope into corotation.
τ Boo shows variability in the Ca  ii H & K and Hα throughout the night and on a night-to-night time-scale. We do not detect enhancement in the activity of the star that may be related to the conjunction of the planet. Further data are needed to conclude about the activity enhancement due to the planet.  相似文献   

20.
It is thought that the large-scale solar-cycle magnetic field is generated in a thin region at the interface of the radiative core (RC) and solar convection zone (SCZ). We show that the bulk of the SCZ virogoursly generates a small-scale turbulent magnetic field. Rotation, while not essential, increases the generation rate of this field.Thus, fully convective stars should have significant turbulent magnetic fields generated in their lower convection zones. In these stars the absence of a radiative core, i.e., the absence of a region of weak buoyancy, precludes the generation of a large-scale magnetic field, and as a consequence the angular momentum loss is reduced. This is, in our opinion, the explanation for the rapid rotation of the M-dwarfs in the Hyades cluster.Adopting the Utrecht's group terminology, we argue that the residual chromospheric emission should have three distinctive components: the basal emission, the emission due to the large-scale field, and the emission due to the turbulent field, with the last component being particularly strong for low mass stars.In the conventional dynamo equations, the dynamo frequencies and the propagation of the dynamo wave towards the equator are based on the highly questionable assumption of a constant . Furthermore, meridional motions, a necessary consequence of the interaction of rotation with convection, are ignored. In this context we discuss Stenflo's results about the global wave pattern decomposition of the solar magnetic field and conclude that it cannot be interpreted in the framework of the conventional dynamo equations.We discuss solar dynamo theories and argue that the surface layers could be essential for the generation of the poloidal field. If this is the case an -effect would not be needed at the RC-SCZ interface (where the toroidal field is generated). The two central problems facing solar dynamo theories may the transport of the surface poloidal field to the RC-SCZ interface and the uncertainty about the contributions to the global magnetic field by the small-scale magnetic features.Visitor, National Solar Observatory, National Optical Astronomy Observatories.The National Optical Astronomy Observatories are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.  相似文献   

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