恒星磁场的解析极大似然估计
Analytical maximum likelihood estimation of stellar magnetic fields
摘要：
恒星辐射的偏振光谱编码了关于恒星大气状况和渗透其中的磁场的宝贵信息。在本文中，我们给出了明确的表达式来估计磁场矢量和它的相关误差，从观察到的斯托克斯参数。我们研究太阳的情况下，观察到特定的强度，然后恒星的情况下，我们收到的偏振通量。在这第二种情况下，我们集中在一个缓慢的转子与偶极磁场几何形状的情况下的显式表达式。此外，我们还给出了明确的公式来检索磁场矢量从LSD的配置文件，而不假设平均值的LSD人工谱线。这些公式是在假定谱线可以在弱场区描述的条件下，用极大似然方法得到的。误差通过厄米矩阵恢复。对估计量的偏差进行了深入分析。
英文摘要：
The polarised spectrum of stellar radiation encodes valuable information on the conditions of stellar atmospheres and the magnetic fields that permeate them. In this paper, we give explicit expressions to estimate the magnetic field vector and its associated error from the observed Stokes parameters. We study the solar case where specific intensities are observed and then the stellar case, where we receive the polarised flux. In this second case, we concentrate on the explicit expression for the case of a slow rotator with a dipolar magnetic field geometry. Moreover, we also give explicit formulae to retrieve the magnetic field vector from the LSD profiles without assuming mean values for the LSD artificial spectral line. The formulae have been obtained assuming that the spectral lines can be described in the weak field regime and using a maximum likelihood approach. The errors are recovered by means of the hermitian matrix. The bias of the estimators are analysed in depth.
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