Aspin, Colin
(1981)
On the interpretation of polarimetric observations of close binary stars.
PhD thesis, University of Glasgow.
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Abstract
Over the last few years the problem of determining orbital and physical parameters of close binaries has become paramount in interpreting the complex nature of these systems. Photometry and spectroscopy have in many cases combined to give reasonably accurate values of such parameters as the binary inclination and orbital eccentricity. In some cases however the two methods have provided conflicting values of the inclination i, for example, and it remains to obtain independent estimates to confirm or not the previous values. The development of techniques to interpret the variable linear polarization observed in certain binaries has proceeded hand in hand with the improvement of observational techniques and the continuing discovery of new 'polarimetric binaries'. A relatively simple model was presented by Brown,McLean and Emslie (1978) whereby the variation inpolarization of the light from binaries is caused by the orbital motion of a scattering region situated within the system and corotating with it. This scattering region is assumed optically thin and under the corotation assumption to be in a circular orbit about the primary star. The behaviour of the polarization is phase locked to the orbital period of the system and variation occurs, in the general case at both the first and second harmonic of that period (i.e. at the period itself and half that period). If the scattering region is of a form symmetric about the orbital plane of the system then the polarization has a second harmonic structure only (i.e. it varies a half the binary period) and produces a double looped ellipse figure in the Q,U plane. In this thesis we extend this simple, and hence 'canonical' model to enable an optimum set of JONILP.6.0 parameters to be obtained in the presence of noisy data. The optimum inclination iopt is found when the χ2 statistic is minimized and an eror or uncertainty in this value is estimated by forming a Relative Confidence Interval at a particular (i.e. chosen) significance level. This model optimization technique is then applied to Cygnus X1 data with the result that the uncertainty in iopt is significantly larger than previous estimates. (cf. Chapter 2) thorough statistical and numerical analysis of the determination of inclinations by this method is undertaken in Chapter 3 and Chapter It where we establish the severe nature of the bias of the inclination estimator in the canonical model and show that a high degree of accuracy is needed in polarimetric measurements before reasonable (i.e. + 5°) Confidence Intervals on i are established. In Chapter 5 we reanalyse the available data for seven binaries (Algol, AO Cas, HD47129, On E (B and U filter data), u Her, U Sge and V444 Cygni) and shag that the previous confidence in the values of the inclination i estimated from such analyses was misleading and that by the optimization technique of Chapter 2 a wide range of inclinations would equally well fit the data at the significance level chosen (10% sig.). We also discuss in this Chapter the determination of other parameters from polarimetric observations (namely the number of scatterers inthe scattering region, the scatterer (i.e. electron) density and in the case of systems with gas streams the mass transfer rate between the two stars). Chapters 6and 7 deal with the generalization of the model to take into account the effect of orbital eccentricity of the scattering region and a calculation of the expected polarization from an accretion disk ar wake respectively. Chapter 8 again generalizes the canonical model ,this time to enable analysis of data taken at ungenial phase intervals. In the previous optimization of Chapter 2 the model was developed to produce best fit values of the free parameters from equally spaced observations. This new general analysis now allows the analysis of sections of data, not covering the complete phase range. This would Allow treatment of perhaps outofeclipse data only for eclipsing binaries or a sequential analysis of data sectioned into small groups from complete data set and hence giving a more flexible range of possible ways of treating the data. This new optimization technique is applied to the data mentioned above in three different ways (i.e. all the data, outofeclipse data and sectioned data) in Chapter 9. Chapter 10 consists of the application of the various optimization techniques outlined in the previous Chapters to the B,U and G filter of HD50896 provided by McLean (1980). Throughout this thesis we have frequently noted that the analyses and techniques developed herein will only be fully testable when new data taken in the way outlined in Chapter 8, has been squired. The data used in the Chapters mentioned above are from binary systems that do not correspond entirely to the type we would generally expect to analyse with the canonical model. New data of such systems would poove the ultimate test for the procedures related in this thesis.
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