Early-type Stars in .NET framework

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13 Early-type Stars
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131 Introduction
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The origins of polarimetric interest in early-type stars relate to the theory of radiative transfer in their atmospheres through the work of Chandrasekhar, particularly his iconic paper of 1946 (see Chandrasekhar, 1946)For pure scattering, it was suggested that p may be as large as 12% at the limb of the stellar disc A method for theoretically investigating the polarization of radiation from stellar atmospheres has also been presented by Harrington (1970) The high values of limb polarization predicted by Chandrasekhar were later reassessed by Ruci ski (1970), and he n put forward arguments to suggest that any polarization would be much smaller The problem of solving the behaviour of polarized radiation arising in a planeparallel non-gray atmosphere from Thomson scattering by free electrons was also investigated by Collins (1970) By performing the calculations in respect of earlytype stars, it was shown that almost no net polarization is to be expected in the visible part of the spectrum A similar outcome was arrived at by Loskutov (1987) who also drew attention to the fact that the polarization direction should ip along a projected stellar radius At the limb, the vibration is tangential to the disc The magnitude decreases across the disc, becoming zero within a short distance along the radius, but then reappearing again, with the vibration parallel to the stellar radius, before reducing again to zero at the centre of the disc Such signatures were shown to be more pronounced with increasing temperature, becoming marked at stellar temperatures >10 000 K Many early-type stars have high v sin i values, with possible associated global distortions as a result of the fast rotation Harrington & Collins (1968) demonstrated that the presence of gravity darkening, limb darkening and rotational distortion will affect the symmetry of early-type stars such that the electron scattering should produce detectable polarizations under suitable conditions, or geometries Some simple rotationally distorted stellar geometries with electron scattering atmospheres have been explored by Cassinelli & Haisch (1974) suggesting that overall polarizations of 2 to 6% might be exhibited Later, Haisch & Cassinelli (1976) examined the potential of electron scattering using equations of transfer, modi ed by an absorptive opacity, in extended, distorted atmospheres of early-type stars The
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Stellar Polarimetry David Clarke Copyright 2010 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 978-3-527-40895-5
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Stellar P larimetry
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explored models, with rotational asymmetry, provided a net polarization, but highly attened discs were required to obtain values of p D 1%, or higher The p ( ) variations produced by the models matched the observed behaviour of Be stars between the Balmer and Paschen edges This basic category of early-type star will be discussed rst
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132 Be Stars
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Be stars are loosely de ned simply because their Balmer lines are in emission, or have been at some time They may be divided into three main groups, i e (1) Classical rapidly rotating near main sequence B stars, (2) B spectral types associated within star-forming regions with the emission line character indicating an early age, (3) B[e] stars noted for the presence of forbidden lines, as well as HI emission, in their spectra, accompanied by a strong IR continuum excess, this latter feature also seen in Herbig Be stars Clear differences in the behaviours of the various stellar categories are revealed when the polarimetry is assessed in terms of correlation with photometry For example, Yudin (2000) has shown that classical Be stars can exhibit optical polarizations from very low values up to 2%, with little photometric colour excess, E(V L), whereas for Herbig Ae/Be (HAEBE) stars, p can have similar or higher values which are correlated with the colour excess The polarization associated with Be stars originates from scattering by free electrons, while that from Ae/Be stars may carry a component from dust scattering, the dust also giving rise to a thermal emission providing the colour excess In a comprehensive survey of classical Be stars, Yudin (2001) has examined the statistical behaviour of 627 stars He found that the distributions of p are signi cantly different according to spectral subgroups In contrast with stars categorized as B5!B95, the distribution of those in the range B0!B2 does not peak at p values around zero The same study examines correlations of p with v sin i and infrared excess, with an overall conclusion that the circumstellar envelopes for the majority of Be stars are optically thin discs with a range of the half-opening angles given by 10 < < 40 The rst suggestion that stars of B spectral type exhibiting emission in the Balmer lines carry intrinsic polarization appears at the end of a general stellar survey by Hall & Mikesell (1950) A comment is made there in respect of Tau, a wellknown Be shell star, on the unexpected high value of p for its small colour excess
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