Hydrodynamic and hydromagnetic stability

modes often occur in multiplets with closely spaced periods (with a typical separation of 1%). In some cases this separation can clearly not be due to rotational splitting, which would yield much larger spacings, as was pointed out by De Cat and Aerts (2002). In this letter we propose that such frequency splitt ings are due to the presence of a magnetic field. If this hypothesis is correct, then the splitting of frequencies can be used to e stimate the field strength in the interior of SPB stars.

https://www.aanda.org/articles/aa/pdf/2005/47/aahg282.pdf

Probing the internal magnetic field of slowly pulsating B-stars through g modes

Reviews the observational evidence for rotation and magnetic fields in stars and discusses the effects of these perturbations on stellar structure and whether the resultant configurations are stable. The authors consider how rotation and magnetism affect the life history of a star from its formation through the main-sequence phases to its post-main-sequence evolution. Theoretical results are compared with observation and some of the many unsolved problems are emphasised. Binary stars or the Sun are not discussed in any detail.

https://iopscience.iop.org/article/10.1088/0034-4885/44/8/001/pdf

Stellar rotation and magnetic stars

The observation by Claverie et al.1. of fine structure in the peaks in the power spectrum of low-degree 5-min solar oscillations has been interpreted as being a result of rotational splitting. Claverie et al.1 claim that their measurements imply that an appropriately weighted average Ω of the interior angular velocity Ω(r) of the Sun is about twice the value of Ω at the surface. At first sight their claim looks doubtful, because all 2l + 1 components of the set of modes of degree l appear in the spectrum, whereas only l + 1 of them should be detectable. However, Isaak2 has recently speculated that the additional components are produced by an intense rotating magnetic core, such as had been postulated by Dicke3,4 to account for the 12.2-day periodic component in the Princeton oblateness data5–9. Isaak2 pointed out that the mean period 2π/Ω≃15 days of the solar interior that was inferred from the Birmingham data1 is consistent with a central core rotating with the 12.2-day period and an outer envelope rotating with the photosphere. Moreover, his rough estimate of a few megagauss for the r.m.s. magnetic field that is required to support his conjecture is within about a factor 10 of that required by Dicke3. Thence he concluded that the Birmingham data1 provide the first clear empirical evidence for an intense internal solar magnetic field. Here I examine this evidence in more detail, and show that the conclusion is premature. If the magnetic core does exist, the 5-min oscillations provide no clear evidence that it is rotating rapidly. Furthermore, unless one accepts a contrived magnetic-field configuration, an explanation for the 2l + 1 components of the multiplets is still lacking.

Evidence for an oblique magnetic solar rotator

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 Alfv\'en 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 during the ultra powerful outbursts of SGR 1806-20 and SGR 1900+14 is discussed.

Frequency spectrum of toroidal Alfv\'en mode in a neutron star with Ferraro's form of nonhomogeneous poloidal magnetic field

The effect of a weak magnetic field on the adiabatic radial and non-radial oscillations of a stellar configuration is studied by means of a perturbation method. Special attention is devoted to the perturbation of the oscillation frequencies resulting from the change of the boundary conditions caused by the magnetic field. This change is related to the fact that the introduction of a magnetic field removes the singularity at the surface of the equilibrium configuration. The perturbation method is applied to Ferraro's model and the influence of a magnetic field on the frequencies of the different types of oscillation modes is discussed.

Stellar oscillations and magnetic field perturbations of the boundary conditions

The behavior ofp-modes of high degree and high order in the homogeneous compressilbe model is examined. The second-order differential equation of Pekeris is used to construct asymptotic expansions near the centre and near the surface, which are singular points, and near the turning point of that equation. An equation for the frequencies is obtained by requiring the continuity of the asymptotic solutions and of their first derivatives. Numerical applications are considered.

Asymptotic expansions for acoustical modes of the homogeneous compressible model

An asymptotic representation is developed for high order unstable gravity modes in a star which are associated with a convective zone enclosed between two radiative layers. In the domain which contains both turning points of the differential equation, the solutions are represented by a single asymptotic expansion in terms of Weber functions.

J Denis

Papers

Stellar oscillations and magnetic field perturbations of the boundary conditions

Asymptotic expansions for acoustical modes of the homogeneous compressible model

An asymptotic representation of unstable gravity modes in stars