Tomography of stellar non‐radial pulsations

The stellar surface imaging technique is used for studying stellar non‐radial pulsations on the basis of inversions of time series of variable line profiles without making assumptions on the specific shape of the pulsations. The inversion results in an image of the stellar surface in which sectoral and tesseral modes can be distinguished in many cases and the pulsational degree and the azimuthal order can be determined. The capability of the technique is studied with simulated data. Then, the surface imaging technique is applied to high‐resolution spectra of the rapidly rotating Beta Cep‐type star ω¹ Sco, which shows strong line‐profile variations. Stellar surface imaging is concluded to be a useful technique for pulsation‐mode identification. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multimode stellar pulsations

We apply the two time method to weakly anharmonic (nonlinear) stellar pulsations. The problem contains two small parameters: -the ratio of the dynamical and the thermal timescale and -the measure of the anharmonicity in the oscillator equation. The 0(⁰) system is solved up to 0() by the use of an asymptotic perturbation method. This solution is then used within the framework of the two time method to obtain the slow evolution of the amplitudes and entropy. Both monomode and double-mode pulsations are treated in a non-resonance case.Work supported by the National Science Foundation (AST79-20024).     

A composite stellar model of geostrophic flows I

This paper has been presented the geometric study and solutions of the electromagnetogeostrophic flows, and spatially the geometry of magnetic and current lines are discussed.     

On the oscillations of a composite stellar model with a weak magnetic field

The unrestricted second-order virial tensor formalism has been used to calculate the characteristic frequencies of linear adiabatic oscillations of a composite stellar model having an isothermal core and a polytropic envelope in presence of a weak poloidal magnetic field. The frequencies of the transverse shear mode and the nonradial pulsation mode for both a radiative and a convective envelope (corresponding to polytropic index 3 and 1.5, respectively) alongwith that of the toroidal mode for the radiative envelope get increased in presence of the magnetic field. However, the frequency of the toroidal mode for the convective envelope registers a decrease in presence of the field. The corrections to the various frequencies decrease with increasing values of the parameter characterizing the lowering of the core temperature in presence of the magnetic field.     

Adiabatic pulsations and convective instability of rotating gaseous masses

Third order virial equations have been used to investigate the oscillations and the stability of the sequence of differentially rotating, compressible Maclaurin spheroids in the presence of toroidal magnetic fields. It is shown that the neutral point occurring at eccentricitye=0.731 13, which is the analogue of the first point of bifurcation along the Dedekind sequence, remains unaffected by the presence of differential rotation or a toroidal magnetic field. The point of onset of dynamical instability corresponding to the third harmonic deformations does, however, depend upon the magnetic field. It is shifted to values higher thane=0.966 96, the value that obtains in the case of uniform rotation; and a sufficiently large magnetic field can suppress this point. Complete frequency spectra (‘Kelvin’ modes belonging to the harmonicsl=3 and compressible modes belonging tol=1) are obtained in two cases of interest: when the equilibrium state is one of equipartition, and when toroidal magnetic and velocity fields (vanishing at the surface) are present in a configuration rotating with a constant angular velocity.     

Contributing factors to flux changes in nonradial stellar pulsations

The linearized analytic representation of observed flux changes due to nonradial pulsations is examined under conditions applicable to a variety of pulsating star types. Histograms are presented as a function ofl, documenting the relative importance of local temperature, geometry, pressure, and limb-darkening variations, which are all contributing factors to the predicted flux changes. The most favourable situation for light and colour data to assist in mode discrimination for lowl requires, amongst other things, that the geometry-related factor be significant. This is noted to occur only if theQ value of the pulsation is not grossly different from theQ value of a radial fundamental pulsation. Published light and colour data for Cephei, 53 Persei, Scuti, rapidly oscillating Ap, Cepheid, and ZZ Ceti variables are compared with model predictions on an amplitude ratio versus phase difference plane . With the notable exception of the rapidly oscillating Ap stars, these comparisons suggest consistency of the nonradial flux change model with other known constraints on the different variable star groups.     

A composite stellar model of magnetofluid continuum via anholonomic descriptions

A theoretical analysis based on the equations of magnetofluid-dynamics is undertaken, in order to completely classify the geometry of the motion admitted by this pattern.     

Adiabatic pulsations and convective instability of uniformly rotating gaseous masses

Third-order virial equations are used to investigate the oscillations and the stability of the sequence of uniformly rotating compressible Maclaurin spheroids, referred to in an inertial frame. It is seen that in the case of the oscillations belonging to the third harmonics, the frequency spectrum of the Maclaurin sequence referred to in an inertial frame is distinct from the spectrum of the Maclaurin sequence considered stationary in a rotating frame of reference. Considering the Maclaurin sequence in an inertial frame, the neutral point and the point of onset of dynamical instability (corresponding to the third harmonic deformations) are isolated. They occur for the values of the eccentricitye=0.73113 and 0.96696, respectively. The neutral point is the analogue of the first point of bifurcation along the Dedekind sequence of ellipsoids and is distinct from the neutral point (e=0.89926) along the Maclaurin sequence considered stationary in a rotating frame; this latter point is the analogue of the first point of bifurcation along the Jacobian sequence. Both the Maclaurin sequences in an inertial frame and in a rotating frame become, however, dynamically unstable for the same eccentricitye=0.96696.     

Baade-Wesselink and related techniques for mode discrimination in nonradial stellar pulsations

Linearized nonradial expressions for light, colour and radial velocity changes are employed to examine the Baade-Wesselink method as applied to the problem of nonradial mode identification in variable stars. It is demonstrated that the usual assumption of a single-valued relation between surface brightness changes and colour variations fails for spherical harmonics withl>1. A Baade-Wesselink expression taking this into account is then given. Using test models for different variable star regimes it is shown that discrimination betweenl=0, 1, and 2 is currently feasible provided adequate attention is paid to pressure effects and to the procedure used to obtain radial velocity data. For higherl, mode discrimination, while possible in principle, is constrained by the stringent requirements on radial velocity measurements and by cases of confusion with lowerl. A review of related but less observationally demanding possible mode discriminators is given. This demonstrates that techniques based on amplitude and phase information in light and colour data may provide reliable discrimination betweenl=0, 1, and 2 when pressure effects are allowed for. For these techniques discrimination of higherl is limited by inadequate model atmosphere limbdarkening information and by confusion with lowerl.     

Demonstration of photon-noise limit in stellar radial velocities

We have measured apparent fluctuations in stellar radial velocities with the ELODIE fiber-fed crossed-dispersion spectrograph and the 193-cm telescope of Observatoire de Haute-Provence. Within one given night, the fluctuations consist of two terms which may be sorted out. The first comes from imperfect scrambling of the stellar beam; the second arises from photon noise and agrees closely with our published calculations. So far, scrambler noise dominates for bright stars, but a perfect scrambler could be built by combining adatative optics and a single-mode fiber. The photon-noise results confirm that extrasolar planetary searching by the radial-velocity technique may be implemented with relatively small telescopes for a large number of stars. Consequences for the detection of astrophysical noise are discussed.     

Reduced normal form as minimal models for nonlinear radial pulsations

We prove that the time behaviour of the currently adopted deterministicradial stellar pulsation equations is always equivalent, in a sense to be defined, to the time behaviour of a low dimensional parametric differential equation (Reduced Normal Form Family). The algebraic construction of this equation is explicitly given. All simple models so far discussed in the literature are members of this family.     

A two-component model of a spherical stellar system

As a generalization of the King's widely-used model for a spherical stellar system containing stars of identical masses, a two-component model of an equilibrium stellar system consisting of stars of two different masses is built proceeding from a proper generalization of the distribution function. In such a system, the principle of thermal equilibrium, generally speaking, does not hold, i.e. equipartition of mean kinetic energy between light and heavy stars is absent.The radial distribution of partial density and velocity dispersion for each of the components and of the total density and velocity dispersion is obtained. The profiles of both the total density and velocity dispersion differ considerably from those given by the King's one-component model, especially in the centre of the system. In particular, the velocity dispersion of stars may there have a non-monotonous behaviour. The possibility of applying the many-component model for the explanation of the recently discovered luminosity cusps in the central regions of some elliptical galaxies is briefly discussed.