尘埃色温与光谱指数之间的简并性。多重卡方极小问题
The degeneracy between the dust colour temperature and the spectral index. The problem of multiple chi^2 minima
摘要：
由于Herschel和Planck卫星任务，人们对解释星际云的亚毫米尘埃光谱有着浓厚的兴趣。已经做了大量的工作来理解光谱指数beta_Obs和色温T_C之间的依赖关系，这部分是由噪声引起的。（T_C，beta_Obs）置信区域是细长的香蕉形结构。我们研究了在什么条件下，这些表现出异常的，强烈的非高斯行为，可能会影响所观察到的（T_C，β_Obs）关系的解释。我们检验了修正的黑体光谱和用辐射转移模型计算的100 - 850 μ m波段的对流云光谱。我们进行了改进的黑体拟合，并检查了chi^2（T_，beta_Obs）函数的结构。我们展示了当信噪比较低时，chi ^2在（T_C，beta_Obs）平面上具有多个局部极小值的情况。数据点权重的微小变化可能导致解决方案跳到完全不同的值。特别是，噪声可以导致具有低色温和高光谱指数的单独的解决方案群体的出现。这些异常是由噪声引起的，但显示多个卡方面积最小值的趋势取决于模型和所分析的波长。与假设的单一修正黑体光谱的偏差并不重要。局部极小值的存在意味着从卡方最小化得到的结果取决于优化的起点，并且可能对应于非全局极小值。（T_C，beta_Obs）分布可能被少数具有不切实际的低色温和高光谱指数的解决方案污染。必须应用适当的加权，以避免β_Obs（T_C）关系的确定受到这些测量的不当影响。
英文摘要：
Because of the Herschel and Planck satellite missions, there is strong interest in the interpretation the sub-millimetre dust spectra from interstellar clouds. Much work has been done to understand the dependence between the spectral index beta_Obs and the colour temperature T_C that is partly caused by the noise. The (T_C, beta_Obs) confidence regions are elongated, banana-shaped structures. We studied under which conditions these exhibit anomalous, strongly non-Gaussian behaviour that could affect the interpretation of the observed (T_C, beta_Obs) relations. We examined modified black body spectra and spectra calculated from radiative transfer models of filamentary clouds at wavelengths 100um-850um. We performed modified black body fits and examined the structure of the chi^2(T_, beta_Obs) function. We show cases where, when the signal-to-noise ratio is low, the chi^2 has multiple local minima in the (T_C, beta_Obs) plane. A small change in the weighting of the data points can cause the solution to jump to completely different values. In particular, noise can lead to the appearance of a separate population of solutions with low colour temperatures and high spectral indices. The anomalies are caused by the noise but the tendency to show multiple chi^2 minima depends on the model and the wavelengths analysed. Deviations from the assumed single modified black body spectrum are not important. The presence of local minima implies that the results obtained from the chi^2 minimisation depend on the starting point of the optimisation and may correspond to non-global minima. The (T_C,beta_Obs) distributions may be contaminated by a few solutions with unrealistically low colour temperatures and high spectral indices. Proper weighting must be applied to avoid the determination of the beta_Obs(T_C) relation to be unduly affected by these measurements.
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