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The dissertation deals with modeling of stellar oscillations in close binary systems. This topic is импортант not only in for the study of binary stars, but also for asteroseismo-logy.
One of the key problems of asetroseismology is the “mode identification” of stellar oscillations. Mode identification is the process of associating an oscillation frequency measured from photometric or spectroscopic observations with a spherical harmonic of degree and order which describes the spatial characteristics of the mode. The main obstacle for this crucial step between the collection and interpretation of data is the symmetry inherent to the patterns of oscillations that makes the periodic changes in the brightness and the radial velocities of surface elements cancel each other out, resulting in diminishing of observed amplitudes. Low sensitivity of both photometry and spectroscopy to high degree modes ( and in photometric and spectroscopic observations, respectively), is one of the consequences of this phenomenon, making the detection and identification of oscillations a difficult task.
A method for mode identification by grid-fitting spherical harmonics to photometric light curves of pulsating stars inside eclipsing binary systems is developed in the dissertation. The eclipse of the pulsating star by its binary companion has visible effects on the observed properties of the oscillations because the eclipse spoils the symmetry of oscillation pattern, producing a modulation of frequency, amplitude and phase unique for each mode that can be recognized and fitted. Fitting, however, requires a model of a binary system with pulsating components.
The only existing implementation of the method of fitting spherical harmonics to light curves uses a very simple model of the binary, with ideally spherical stars in circular orbits, and does not account for any of the proximity effects. Moreover, the oscillations are represented as sinusoidal perturbations of an arbitrary surface brightness distribution. This dissertation uses a much more detailed model, based on Roche geometry that includes all the important proximity effects. Modeling of stellar oscillations is improved by representing them as direct perturbations of local tempe-
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rature and gravitational potential and including the effects of tidal distortion and rotation on the frequencies and spatial properties of the modes.
The scientific goal of the dissertation is to develop a reliable method – the method of fitting spherical harmonics – for mode identification on pulsating stars in close binary systems, in order to enable asteroseismological studies of their interiors.
The basic assumption is that a close binary system can be represented using the Roche model, which is based on the approximation of total central condensation. In other words, it is assumed that the contribution of outer layers of the star to its total mass can be neglected. With this approximation, it is possible to treat the gravitational interaction of the components as the interaction of point masses.
Within the Roche model, the shape of the star is determined by the Roche potential that corresponds to the superposition of the gravitational and the centrifugal force. The temperature distribution across the surface is determined by the von Zeipel law that defines the dependence of flux on the effective gravitational acceleration.
Stellar oscillations are then modeled as perturbations of the local values of the Roche potential and temperature. It is assumed that the oscillations are adiabatic, of small amplitudes, and that they can be represented using spherical harmonics. It is also assumed that the symmetry axis of the oscillations will coincide with the dominant geometrical axis (usually with the rotation axis, or in the case of tidally distorted stars, with the line connecting the centers of the components).
The proposed method of mode identification on pulsating components of close binary systems is implemented as a part of the modeling program Infinity. Infinity is based on the Roche model and accounts for all the phenomena that influence the formation of light and radial velocity curves, from limb darkening and surface temperature distribution caused by departures from spherical shape, to the reflection effect, irregularities in surface brightness and the presence of the accretion disc. Stellar oscillations can be modeled on one or both components of the system.
The method is verified by means of tests using synthetic data. In other words, the results of fitting are compared to the stellar and orbital parameters that were used to generate
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the synthetic light curves, or the fake “observations”. The tests encompass both favorable and unfavorable configurations (total and partial eclipses, approximately spherical and tidally distorted stars, modes of low and high degrees and so forth). The results are finally compared to the results of a similar technique of mode identification – the method of eclipse mapping.
From the obtained results, we can conclude that the proposed method of mode identification is reliable (i.e. provides correct identification) for approximately spherical stars in detached binary systems. The results for tidally distorted stars are encouraging, but show that before an attempt is made to apply the method on real observation of that nature, it will be necessary to include the simultaneous fitting of frequency, amplitude and phase for each trial mode into the procedure of mode identification, and to try to solve the problem of ambiguous identifications. This will be the focus of my future work. |
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