arXiv 0711.49772007-11-30astro-phgr-qc

强引力透镜的误差研究

Study of errors in strong gravitational lensing

Thomas P. Kling, Simonetta Frittelli

备注：: accepted to ApJ
发表信息：: Astrophys.J.675:115-125,2008
DOI：: 10.1086/527368

摘要：

我们研究强引力透镜测定星系团质量的准确性，通过比较传统的方法与数值积分的完全相对论性零测地线方程在弱引力扰动的情况下罗伯逊-沃克度规。特别是，我们研究了球对称的，三维奇异等温球模型和Navarro等人（1997）的三维物质分布，这两个都是引力透镜研究中常用的。在这两种情况下，我们研究了两种不同的方法沿视线质量密度截断：硬截断和常规（无截断）。我们发现，在奇异等温球模型中，由薄透镜近似引入的总质量的相对误差小于0.3%，在Navarro等人（1997）的模型中小于2%.硬截断的去除在最好的情况下引入了相同数量级的额外误差，并且在最坏的情况下研究了更大的数量级。我们的研究结果确保了未来一代基于透镜研究的精密宇宙学实验将不需要去除薄透镜假设，但它们可能需要仔细处理截断。

英文摘要：

We examine the accuracy of strong gravitational lensing determinations of the mass of galaxy clusters by comparing the conventional approach with the numerical integration of the fully relativistic null geodesic equations in the case of weak gravitational perturbations on Robertson-Walker metrics. In particular, we study spherically-symmetric, three-dimensional singular isothermal sphere models and the three-dimensional matter distribution of Navarro et al. (1997), which are both commonly used in gravitational lensing studies. In both cases we study two different methods for mass-density truncation along the line of sight: hard truncation and conventional (no truncation). We find that the relative error introduced in the total mass by the thin lens approximation alone is less than 0.3% in the singular isothermal sphere model, and less than 2% in the model of Navarro et al. (1997). The removal of hard truncation introduces an additional error of the same order of magnitude in the best case, and up to an order of magnitude larger in the worst case studied. Our results ensure that the future generation of precision cosmology experiments based on lensing studies will not require the removal of the thin-lens assumption, but they may require a careful handling of truncation.

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