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expected net polarization, while at high inclination, the polarization is reduced by occultation Their analysis was also applied to the variation of polarization from binary systems in which the scattering material consists of a rotating onedimensional plume between the stars, superposed on an axisymmetric disc They showed that the inclination of the system and the radial structure of the plume can be deduced for suf ciently high inclinations (i > 60 ) The extent to which the method can be generalized to an arbitrarily distributed two-dimensional scattering region was considered via Fourier analysis It was found that the inclination of the system is largely insensitive to the density distribution when the distribution function is of a simple power-law form The question was also raised that for some stars, the polar mass loss will have a greater ionization fraction than the equatorial region, such that the pole might be the dominant source for free electrons In the third paper of this series, Fox (1991) considered the effects of occultation and nite sized-source depolarization, concluding that the net polarization has a complicated inclination dependence, and that the simple result of it being p / sin2 i, obtained by Brown & McLean (1977), does not hold For Be stars with high intrinsic polarizations, the circumstellar envelope must be concentrated either towards equatorial or polar regions, and that a substantial optical depth is required with > 005 The possible variability of the observed polarization from an obliquely rotating envelope has been investigated by Fox (1992), such a scenario having been mooted by others as being an alternative interpretation to diagnoses involving binary motion, but with lack of spectroscopic evidence to add weight to such duplicity The results of the exercise were not too sanguine as it was evident that effects due to rotation about a body axis and binary orbital motion are indistinguishable It was also found that the physical geometry of the obliquely rotating envelope could ot be inferred When the light source is considered to have nite extent, discrimination between envelope geometries emerges to some degree as a result of the occultation of parts of the envelope by the extended source Further modelling by Fox (1993a) has emphasized the effect that an extended light source has on the resulting polarization by scattering in circumstellar envelopes If the underlying star is non-spherical, as a result of its large rotational velocity say, its photosphere will also generate a net polarization, adding to that which is produced by scattering within the extended atmosphere This situation has been modelled by Fox (1993a) who found that, in general, the predicted polarization was a factor of 2 3 times larger than what is observed for Be star systems It was also noted that the theoretical models for Be star envelopes had not yet reached a level of sophistication to estimate by polarimetry the number density of free electrons throughout the circumstellar envelope The origin of stellar winds in Be stars may be in uenced by magnetic elds and Fox (1993b) has considered this additional parameter in polarimetric models From his analysis, the range of observed values of p can be explained if the stars possess small magnetic elds of B0 < 100 G Observed increases in p during the onset of a shell phase is indicative of an increased magnetic eld.

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The polarimetry of close binary systems has been modelled by Buerger & Collins II (1970) by considering the distortions on the distribution of scattering material by axial rotation and gravitational interactions The method allows calculation of intrinsic polarization in and out of eclipse Predictions are for polarization variations of several tenths of a per cent By investigating the effects of Thomson scattering in optically thin stellar envelopes, Brown, McLean & Emslie (1978) established the fundamental polarimetric behaviour associated with binary systems with co-rotating steady state electron clouds This paper is frequently cited, and the model will be referred to here as the BMcLE model The form of the variation, as plotted in the q u-plane, is dependent on the inclination, i, of the system and may be expressed in terms of the fundamental period and its rst harmonic It was demonstrated how the formulation may be formally inverted to provide a systematic diagnostic for inferring the characteristics of a binary and its envelope This seminal work has provided the basis of studies of a variety of binary types Simmons (1983) later extended the BMcLE model by considering arbitrary scattering mechanisms other than Thomson scattering, with the results illustrated by Mie scattering An alternative approach to modelling of the effects of scattering material in binary systems has been made by Dolan (1984) using regularized Monte Carlo calculations Aspin, Simmons & Brown (1981) performed an analysis of the required accuracy of q, u measurements to allow their variation to provide useful estimates of i The procedure comprised evaluation of the con dence interval of i for a model involving single Thomson scattering in a co-rotating envelope which ields an acceptable 2 t to simulated data when optimized over the free parameters involved in the model The required accuracy of polarimetric observations was found to be significantly higher for low values of inclination A later paper by Simmons, Aspin & Brown (1982) showed that tting the canonical model to binary star data will tend to yield values of inclination greater than the true value The statistical bias is most pronounced for data with higher noise values when the inferred value, and the formal linear error, have no bearing on the actual value As the noise increases, the inferred inclination approaches 90 Errors for inclination which are established by formal techniques are seriously over optimistic, except for data with high signal-tonoise ratios It was also demonstrated by Brown, Aspin, Simmons, et al (1982) that if the binary orbits are eccentric, third harmonics are generated in the polarimetric variation, making a clear diagnosis of noisy data more problematic The polarimetric behaviour of binary systems embedded in electron shells of various geometries has been explored by Manset & Bastien (2000) It was shown that the polarimetric variations should be more apparent for systems with the low inclination, a high optical depth, a at envelope, a small cavity, or an orbit that brings the stars close to the inner edge of the cavity They also demonstrated that the BMcLE model remains powerful in nding orbital inclinations & 45 for a variety of distribution forms for optically thin Thomson scattering clouds; the atness of the.

NET Control to generate, create barcode image in isual Studio NET applicationsenvelope, the size of any central cavity and the size of the orbit have no signi cant in uence on the inclination deduced by the BMcLE model Returning to the BMcLE model, the polarimetric effect of Thomsom scattering by material between a pair of stars can be considered by applying the simple approach as ummarized in (934) and (935), i e q D e q 0 C q 1 cos(2 t) C q 2 cos(4 t) , and u D e u 1 sin(2 t) C u 2 sin(4 t) (111) (112)Related: EAN-13 Generating VBNET , Intelligent Mail Generating C# , Intelligent Mail Generating NET WinForms.

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