Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar global oscillation eigenfunctions and eigenfrequencies. If the Lorentz force is added to the equilibrium equation of motion, stellar eigenmodes can couple. In quasi-degenerate perturbation theory, this coupling, also known as the direct effect, can be quantified by the general matrix element. We present the analytical expression of the matrix element for a superposition of subsurface zonal toroidal magnetic field configurations. The matrix element is important for forward calculations of perturbed solar and stellar eigenfunctions and frequency perturbations. The results presented here will help to ascertain solar and stellar large-scale subsurface magnetic fields, and their geometric configuration, strength, and their change over the course of activity cycles.
We investigate the oscillation spectrum of rotating Newtonian neutron stars endowed with purely toroidal magnetic fields, using a time evolution code to evolve linear perturbations in the Cowling approximation. The background star is generated by numerically solving the MHD equilibrium equations and may be nonspherical by virtue of both rotation and magnetic effects; hence our perturbations and background are fully consistent. Whilst the background field is purely toroidal, the perturbed field is mixed poloidal-toroidal. From Fourier analysis of the perturbations we are able to identify a numb…
We calculate non-axisymmetric oscillations of uniformly rotating polytropes magnetized with a purely toroidal magnetic field, taking account of the effects of the deformation due to the magnetic field. As for rotation, we consider only the effects of Coriolis force on the oscillation modes, ignoring those of the centrifugal force, that is, of the rotational deformation of the star. Since separation of variables is not possible for the oscillation of rotating magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We calculate magnetically …
Solar oscillation frequencies change with the level of magnetic activity. Localizing subsurface magnetic field concentrations in the Sun with helioseismology will help us to understand the solar dynamo. Because the magnetic fields are not considered in standard solar models, adding them to the basic equations of stellar structure changes the eigenfunctions and eigenfrequencies. We use quasi-degenerate perturbation theory to calculate the effect of toroidal magnetic fields on solar oscillation mean multiplet frequencies for six field configurations. In our calculations, we consider both the dir…
We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength $B_{\rm{S}}\sim10^{16}$ G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd pa…
We present Hall equilibrium solutions for neutron stars crusts containing toroidal and poloidal magnetic field. Some simple cases are solved analytically while more complicated configurations are found numerically through a Gauss-Seidel elliptic partial differential equation solver.
We study $m=1$ oscillations and instabilities of magnetised neutron stars, by numerical time-evolution of linear perturbations of the system. The background stars are stationary equilibrium configurations with purely toroidal magnetic fields. We find that an $m=1$ instability of toroidal magnetic fields, already known from local analyses, may also be found in our relatively low-resolution global study. We present quantitative results for the instability growth rate and its suppression by rotation. The instability is discussed as a possible trigger mechanism for Soft Gamma Repeater (SGR) flares…
We present 3D MHD simulations of purely toroidal and mixed poloidal-toroidal magnetic field configurations to study the behavior of the Tayler instability. For the first time the simultaneous action of rotation and magnetic diffusion are taken into account and the effects of a poloidal field on the dynamic evolution of unstable toroidal magnetic fields is included. In the absence of diffusion, fast rotation (rotation rate compared to Alfvén frequency) is able to suppress the instability when the rotation and magnetic axes are aligned and when the radial field strength gradient p < 1.5. When di…
Two well known turbulent dynamo and MHD oscillation mechanisms are critically examined and fundamental difficulties are presented. Following new ideas on the genesis of the solar cycle and activity phenomena are presented. Inevitability of most likely existence of a combined steady poloidal and toroidal magnetic field structure in the solar interior. Owing to suitable steady poloidal field structure, Alfven wave perturbations of long periods (~ 22 yrs) that excite in the solar core travel first to the poles in both the hemispheres and later reach the equator. While traveling towards the surfac…
A new method for reconstruction of coronal magnetic fields as force-free fields (FFFs) is presented. Our method employs poloidal and toroidal functions to describe divergence-free magnetic fields. This magnetic field representation naturally enables us to implement the boundary conditions at the photospheric boundary, i.e., the normal magnetic field and the normal current density there, in a straightforward manner. At the upper boundary of the corona, a source-surface condition can be employed, which accommodates magnetic flux imbalance at the bottom boundary. Although our iteration algorithm …
Using the energy variational method of magneto-solid-mechanical theory of a perfectly conducting elastic medium threaded by magnetic field, the frequency spectrum of Lorentz-force-driven global torsional nodeless vibrations of a neutron star with Ferraro's form of axisymmetric poloidal nonhomogeneous internal and dipole-like external magnetic field is obtained and compared with that for this toroidal Alfvén mode in a neutron star with homogeneous internal and dipolar external magnetic field. The relevance of considered asteroseismic models to quasi-periodic oscillations of the X-ray flux durin…
We study coupled axial and polar axisymmetric oscillations of a neutron star endowed with a strong magnetic field, having both poloidal and toroidal components. The toroidal component of the magnetic field is driving the coupling between the polar and axial oscillations. The star is composed of a fluid core as well as a solid crust. Using a two dimensional general relativistic simulation and a magnetic field B = 10^16 G, we study the change in the polar and axial spectrum caused by the coupling. We find that the axial spectrum suffers a dramatic change in its nature, losing its continuum chara…
Normal modes of oscillation of the Sun are useful probes of the solar interior. In this work, we use the even-order splitting coefficients to study the evolution of magnetic fields in the convection zone over solar cycle 23, assuming that the frequency splitting is only due to rotation and a large scale magnetic field. We find that the data are best fit by a combination of a poloidal field and a double-peaked near-surface toroidal field. The toroidal fields are centered at r=0.999R_solar and r=0.996R_solar and are confined to the near-surface layers. The poloidal field is a dipole field. The p…
We investigate non-axisymmetric low frequency modes of a rotating and magnetized neutron star, assuming that the star is threaded by a dipole magnetic field whose strength at the stellar surface, $B_0$, is less than $\sim 10^{12}$G, and whose magnetic axis is aligned with the rotation axis. For modal analysis, we use a neutron star model composed of a fluid ocean, a solid crust, and a fluid core, where we treat the core as being non-magnetic assuming that the magnetic pressure is much smaller than the gas pressure in the core. Here, we are interested in low frequency modes of a rotating and ma…
In this work, we have studied oscillations in the crust of a neutron star which magnetic field has both dipolar and toroidal components, the former extends from the stellar interior to the outer space and the later is confined inside the star radius. Our study is based on the solutions we have got for perturbations in the star fluid, confined to the crust thickness. Our results are compared to the frequencies observed in the Soft Gamma Repeaters signals.
Aims. We construct a new analytical model of a solar coronal loop that is embedded in a gravitationally stratified and magnetically confined atmosphere. On the basis of this analytical model, we devise a numerical model of solar coronal loops. We adopt it to perform the numerical simulations of its vertical kink oscillations excited by an external driver. Methods. Our model of the solar atmosphere is constructed by adopting a realistic temperature distribution and specifying the curved magnetic field lines that constitute a coronal loop. This loop is described by 2D, ideal magnetohydro- dynami…
We present solutions for Hall equilibria applicable to neutron star crusts. Such magnetic configurations satisfy a Grad-Shafranov-type equation, which is solved analytically and numerically. The solutions presented cover a variety of configurations, from purely poloidal fields connected to an external dipole to poloidal-toroidal fields connected to an external vacuum field, or fully confined within the star. We find that a dipole external field should be supported by a uniformly rotating electron fluid. The energy of the toroidal magnetic field is generally found to be a few percent of the tot…
Quasi-biennial oscillations (QBO) are frequently observed in the solar activity indices. However, no clear physical mechanism for the observed variations has been suggested so far. Here we study the stability of magnetic Rossby waves in the solar tachocline using the shallow water magnetohydrodynamic approximation. Our analysis shows that the combination of typical differential rotation and a toroidal magnetic field with a strength > 10^5 G triggers the instability of the m=1 magnetic Rossby wave harmonic with a period of 2 years. This harmonic is antisymmetric with respect to the equator and …
Annual oscillations have been detected in many indices of solar activity during many cycles. Recent multi spacecraft observations of coronal bright points revealed slow retrograde toroidal phase drift (with the speed of 3 m/s of 1 yr oscillations, which naturally suggested their connection with Rossby-type waves in the interior. We have studied from a theoretical point of view the dynamics of global magneto-Kelvin and magneto-Rossby waves in the solar tachocline with toroidal magnetic field. Using spherical coordinates, the dispersion relations of the waves and latitudinal structure of solutio…
Observations of magnetic clouds, within interplanetary coronal mass ejections (ICMEs), are often well described by flux rope models. Most of these assume either a cylindrical or toroidal geometry. In some cases, these models are also capable of accounting for non-axisymmetric crosssections but they generally all assume axial invariance. It can be expected that any ICME, and its flux rope, will be deformed along its axis due to influences such as the solar wind. In this work, we aim to develop a writhed analytical magnetic flux rope model which would allow us to analytically describe a flux rop…
The ultra-strong magnetic field of magnetars modifies the neutrino cross section due to the parity violation of the weak interaction and can induce asymmetric propagation of neutrinos. Such an anisotropic neutrino radiation transfers not only the linear momentum of a neutron star but also the angular momentum, if a strong toroidal field is embedded inside the stellar interior. As such, the hidden toroidal field implied by recent observations potentially affects the rotational spin evolution of new-born magnetars. We analytically solve the transport equation for neutrinos and evaluate the degre…
We study magneto-elastic oscillations of highly magnetized neutron stars (magnetars) which have been proposed as an explanation for the quasi-periodic oscillations (QPOs) appearing in the decaying tail of the giant flares of soft gamma-ray repeaters (SGRs). We extend previous studies by investigating various magnetic field configurations, computing the Alfvén spectrum in each case and performing magneto-elastic simulations for a selected number of models. By identifying the observed frequencies of 28 Hz (SGR 1900+14) and 30 Hz (SGR 1806-20) with the fundamental Alfvén QPOs, we estimate the req…
Observations of long-term north-south asymmetry in solar activity demand the equator-symmetric (quadrupolar) mode be present in the solar magnetic field in line with the dominant antisymmetric (dipolar) mode. This paper proposes treating the sunspot area as a proxy for subsurface toroidal magnetic flux to infer the quadrupolar mode of the solar dynamo from sunspot data. Toroidal pseudo-fluxes (PF) in the northern and southern hemispheres are defined as a signed sunspot area with plus or minus sign prescribed to them in accord with the Hale's sunspot polarity rules. Statistical correlation anal…
Strong magnetic fields play an important role in powering the emission of neutron stars. Nevertheless a full understanding of the interior configuration of the field remains elusive. In this work, we present General Relativistic MagnetoHydroDynamics simulations of the magnetic field evolution in neutron stars lasting 500 ms (5 Alfven crossing times) and up to resolutions of 0.231 km using Athena++. We explore two different initial conditions, one with purely poloidal magnetic field and the other with a dominant toroidal component, and study the poloidal and toroidal field energies, the growth …
