相对论膨胀介质中的线膨胀不透明度
Line Expansion Opacity in Relativistically Expanding Media
摘要：
超新星和中子星合并的喷出物中重原子元素的谱线即使在元素丰度很小的情况下也能对喷出物物质的不透明度作出重要贡献。在有利的条件下，由谱线和介质的膨胀引起的线膨胀不透明度可以比电子散射的不透明度大几个数量级。本文在狭义相对论的框架下，导出了膨胀介质中线膨胀不透明度及其Rosseland平均的计算公式，它可以看作是牛顿近似下的推广。通过与牛顿公式的比较，探讨了相对论效应对不透明度的影响，并利用重原子元素的谱线对新公式进行了检验。我们还推导出一些近似公式的Rosseland平均线膨胀不透明度，易于使用的数值计算工作，同时仍然保持足够高的精度相对于精确的解决方案。本文导出的公式可望在涉及相对论或亚相对论展开的相对论天体物理现象如中子星合并、超新星和伽马射线暴等辐射问题中有重要的应用。
英文摘要：
Spectral lines of heavy atomic elements in the ejecta of supernovae and neutron star mergers can have important contribution to the opacity of the ejecta matter even when the abundance of the elements is very small. Under favorable conditions, the line expansion opacity arising from spectral lines and the expansion of the medium can be orders of magnitude larger than the opacity of electron scattering. In this paper we derive the formulae for evaluating the line expansion opacity and its Rosseland mean in an expanding medium in the framework of special relativity, which can be considered as a generalization of the previous work in the Newtonian approximation. Then we compare the derived relativistic formulae to the Newtonian ones to explore the relativistic effect on the opacity, and test the new formulae with the spectral lines of some heavy atomic elements. We also derive some approximation formulae for the Rosseland mean of the line expansion opacity that are easy to use in numerical works while still maintaining a high enough accuracy relative to exact solutions. The formulae derived in this paper are expected to have important applications in radiative problems related to relativistic astrophysical phenomena such as neutron star mergers, supernovae, and gamma-ray bursts where relativistic or subrelativistic expansions are involved.
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