旋转恒星磁偶极子Stokes剖面的解析计算
Analytical calculation of Stokes profiles of rotating stellar magnetic dipole
摘要：
由于著名的塞曼多普勒成像，对旋转恒星在不同相位出现的偏振的观测开辟了绘制恒星表面磁场的可能性。当磁场足够弱时，恒星上每一点的圆偏振和线偏振分布分别正比于未扰动强度分布的一阶和二阶导数。我们表明，弱场近似（弱线的情况下，线偏振）可以推广到旋转的恒星，包括多普勒效应的情况下，并考虑到恒星表面上的集成。斯托克斯轮廓被写作为一个线性组合的波长相关的条款表示为系列的展开厄米多项式。这些项包含表面积分磁场和速度分量。这些量的直接数值评估限于旋转速度不大于8倍的多普勒宽度的本地吸收配置文件。此外，我们证明，在一个旋转的恒星，圆偏振通量取决于导数的强度通量相对于波长，也对自己的配置文件。同样，线性偏振取决于轮廓及其相对于波长的一阶和二阶导数。我们将一般表达式推广到旋转偶极子。
英文摘要：
The observation of the polarization emerging from a rotating star at different phases opens up the possibility to map the magnetic field in the stellar surface thanks to the well-known Zeeman Doppler Imaging. When the magnetic field is sufficiently weak, the circular and linear polarization profiles locally in each point of the star are proportional to the first and second derivatives of the unperturbed intensity profile, respectively. We show that the weak-field approximation (for weak lines in the case of linear polarization) can be generalized to the case of a rotating star including the Doppler effect and taking into account the integration on the stellar surface. The Stokes profiles are written as a linear combination of wavelength-dependent terms expressed as series expansions in terms of Hermite polynomials. These terms contain the surface integrated magnetic field and velocity components. The direct numerical evaluation of these quantities is limited to rotation velocities not larger than 8 times the Doppler width of the local absorption profiles. Additionally, we demonstrate that, in a rotating star, the circular polarization flux depends on the derivative of the intensity flux with respect to the wavelength and also on the profile itself. Likewise, the linear polarization depends on the profile and on its first and second derivative with respect to the wavelength. We particularize the general expressions to a rotating dipole.
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