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To allow interpretation of synoptic polarimetric measurements of Be stars, Clarke & McGale (1986) have explored the behaviour of a stochastic model whereby small localized scattering clouds, or globules, appear at speci c positions de ned by stellar polar coordinates, and at various distances from the star for a range of viewing angles according to the stellar inclination The pseudo-data distributions in the q u-plane showed that globules ejected randomly in stellar azimuth and latitude do not translate to a random data density distribution in the q u-plane It was proposed that real data might be compared with the simulations to infer the basic geometries and astrophysical processes giving rise to any recorded polarization uctuations The problem of inferring mass loss distributions in time and polar angle have been explored by Brown & Wood (1992) to see how these might be obtained from observed polarimetric and absorption line strength variations They considered the numerical application of analytic inversions to both simulated and the real data associated with Ori Using a Monte Carlo radiative transfer code, Wood, Bjorkman, Whitney, et al (1996a) have investigated the effects of multiple scattering within axisymmetric circumstellar envelopes Contrary to immediate expectation, they found that multiple scattering tends to increase the expected polarization, as the scattering predominantly arises within the optically thick parts of the disc; the orientation of the scattering planes for these multiply scattered photons is biased towards a common direction, that being the plane of the disc In the absence of any absorptive opacity, which would reduce the number of multiple scatterings, resultant polarization levels of order 3 4% are expected in circumstellar discs The exercise was also undertaken by considering the stellar source to have nite angular extent Rather than their being a depolarization effect as appears in single-scattering calculations, an enhancement of polarization also occurs This happens because more photons enter the disc from a nite star than from the more highly attenuated point source; these additional photons are multiply scattered, raising the polarization for a nite star above that for a point-source star If multiple scattering occurs in any stellar system, caution must be taken in applying single-scattering, or point-source approximations, to place constraints on circumstellar geometries by polarimetry Multiple scattering can have a dramatic effect on the predicted polarization levels, possibly producing a 90 ip of the position angle The computational scheme above has been extended by Wood, Bjorkman, Whitney, et al (1996b) to include absorptive opacity According to the level of this parameter, the resultant olarization reduces to become similar to the levels predicted by schemes involving single scattering with attenuation An important consequence of this relates to wavelengths around an ionization edge such as the Balmer jump Much larger changes in p are predicted relative to single-scattering plus attenuation approximations This arises because just shortward of the jump, the absorptive opacity is large and the polarization approaches the level associated with single-scattering plus attenuation; just longward of the jump, where the absorptive opacity a small, multiple scattering is dominant and the polarization is larger than.

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the single-scattering plus attenuation prediction For these reasons, the combined effects of multiple scattering, plus absorptive opacity, provides much larger polarization discontinuities at the Balmer jump than previous predictions For geometrically thick equatorial disc-like geometries, a position angle ip of 90 can occur shortward of the Balmer jump as the large hydrogen opacity absorbs the multiply scattered photons in the disc, the polarization dominated by singly scattered photons from the polar regions producing negative values of Q Using a Monte Carlo radiative transfer code in respect of spectropolarimetric data, Wood, Bjorkman & Bjorkman (1997) investigated possible geometries for Tau It turned out that the observations could be mimicked by either a geometrically thin disc, with a half-opening angle of 2 5, or a thick disc with a half-opening angle of 56 Key to determining which option should be preferred is the prediction for the thin disc model to produce a polarization ip at 12 m, so that it is orthogonal relative to what is recorded in the visible spectrum As for interpretations and modelling of p ( ) and the intrinsic polarizations associated with the emission lines themselves, McLean (1979) discussed the issues with physical insight The paper demonstrates that all axisymmetric, quasi-optically thin Be star envelopes have approximately the same form of p ( ) in the continuum and that the behaviour is controlled by the average properties of the envelope The size of the oscillation of the position angle across the emission lines, as well as depending on the optical depths of the envelope, is shown to be proportional to cos i A numerical model for the behaviour of Cas was presented by Poeckert & Marlborough (1978a) by assuming a density distribution in a rotating, expanding envelope, with the hydrogen level populations determined appropriately at points through the envelope The Balmer line intensities and polarimetric pro les were then determined by integrating the equation of radiative transfer along the lines of sight, and so including stellar disc occultation effects in the process The exercise was successful in predicting the observed behaviour across the H line An investigation of the physical factors that control the behaviour of p ( ) and ( ) across emission line pro les has been made by Wood, Brown & Fox (1993) based on Thomson scattering in an optically thin circumstellar cloud which is subject to bulk motions in the form of a rotating and/or expanding disc The value of p is asymmetric about the line centre and stronger in the red wing unless there is no disc expansion Changes in across the line occur through the symmetry breaking effects of stellar occultation of the scattering material, and the combination of rotation and expansion of the disc A symmetric p pro le indicates envelope rotation, while pro les which show stronger p in the red wing indicate expansion of a scattering region The ratio of p in the red and blue wings should lead to information on the ratios of expansion to rotation velocities In a later paper, Wood & Brown (1994a) developed the model by considering the star to act as a monochromatic source for scattering by a rotating and expanding isc, the assumption being reasonably realistic, the line broadening being dominated by the scattering rather than in its origins By assuming certain parametric forms for the disc velocity and density distributions, analytic expressions were obtained for the wavelength dependence of the scattered pro les in terms of the veloc-.

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to shell-line absorption For the observed stars, various strategies were explored to separate the intrinsic stellar polarization from any subsequent interstellar component, these involving information provided by eld stars, the temporal behaviour of p, the application of Serkowski s law to the colour measurements, and the spectral behaviour of p across the Balmer emission lines Further attention to the emission line polarization of Cas was given by Poeckert & Marlborough (1977) who obtained a more detailed record of the behaviour across the H line, the most important feature being a near sinusoidal variation in the position angle across the emission When plotted in the Stokes parameter plane, the wavelength scan provided a locus in the form of a loop A model was presented based on a rotating disc, with he absorption along the line of sight dependent on both line and continuum absorption As a result of Doppler shifts, in the blue wing, the radiation is coming from further within the stellar envelope on the receding side, with the converse for the light of the red wing The strength of the effect depends on the inclination of the rotation axis, and a value of i 45 matched the behaviour of Cas The sense of position angle change from C/0/ ,. Draw ISSN In .NET Using Barcode generation for .Related: EAN 128 Generator Java , Print ISBN .NET , Creating Code 39 Java

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Polarimetric Principles and Instruments in Visual Studio .NET Draw Code 3/9 n Visual Studio .NET Polarimetric Principles and Instruments. UPCA In .NET Framework Using Barcode creation for .Generally the reference axis of the polarimeter is described with respect to equatorial coordinates, i e the duciary of the instrument is such that, when is zero, the polarizer s transmission axis runs N/S, and aligned with Declination Thus, it can be seen that the variation of intensity produced by a rotating polarizer modulator omprises a mean level, on which a modulation is superimposed, with amplitude dependent on the degree of polarization, and with the phase dependent on the direction of vibration of the incoming light Essentially, there are three unknowns requiring quanti cation In fact, the actual signal, Sk ( ), involves additional parameters to describe it, and should be written as Sk ( ) D 1 Gk ( )T(t) I C Q cos 2 C U sin 2 , 2 (84).Related: Print ISBN Word , UPC-A Generation Java , .NET WinForms EAN-13 Generator

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