星系团强透镜模拟的贝叶斯方法
A Bayesian approach to strong lensing modelling of galaxy clusters
摘要：
在本文中，我们描述了强透镜星系团的参数化建模过程，并使用贝叶斯证据定量地对模型进行排序。我们使用公开的马尔可夫链蒙特卡罗（MCMC）采样器（Bayesys），使我们能够避免局部极小值的似然函数。为了说明MCMC技术的力量，我们模拟了三个星系团，每个星系团由一个星系团规模的晕和一组扰动的星系规模的subhalos。我们光线跟踪三个光束通过每个模型产生一个目录的多个图像，然后使用MCMC采样器恢复模型参数在三个不同的透镜配置。我们发现，对于典型的哈勃太空望远镜（HST）质量的成像数据，在爱因斯坦半径的总质量恢复与1-5%的误差根据所考虑的透镜配置。然而，我们发现，当星系团中心没有多重像出现时，星系团的质量与星系团的质量呈强烈的简并关系。星系的质量通常以20%的误差恢复，这主要是由于截止半径的限制很差。最后，我们描述了如何使用贝叶斯证据对模型进行定量排名。我们证实了强透镜效应以这种方式约束星系团中心区域质量分布的能力。最终，这种方法应用于具有非常大量的多个图像的强透镜簇，可以提供对宇宙学的独特几何约束。本文中使用的MCMC采样器的实现已经在公开可用的Lensool软件包的框架内完成。
英文摘要：
In this paper, we describe a procedure for modelling strong lensing galaxy clusters with parametric methods, and to rank models quantitatively using the Bayesian evidence. We use a publicly available Markov chain Monte-Carlo (MCMC) sampler ('Bayesys'), allowing us to avoid local minima in the likelihood functions. To illustrate the power of the MCMC technique, we simulate three clusters of galaxies, each composed of a cluster-scale halo and a set of perturbing galaxy-scale subhalos. We ray-trace three light beams through each model to produce a catalogue of multiple images, and then use the MCMC sampler to recover the model parameters in the three different lensing configurations. We find that, for typical Hubble Space Telescope (HST)-quality imaging data, the total mass in the Einstein radius is recovered with ~1-5% error according to the considered lensing configuration. However, we find that the mass of the galaxies is strongly degenerated with the cluster mass when no multiple images appear in the cluster centre. The mass of the galaxies is generally recovered with a 20% error, largely due to the poorly constrained cut-off radius. Finally, we describe how to rank models quantitatively using the Bayesian evidence. We confirm the ability of strong lensing to constrain the mass profile in the central region of galaxy clusters in this way. Ultimately, such a method applied to strong lensing clusters with a very large number of multiple images may provide unique geometrical constraints on cosmology. The implementation of the MCMC sampler used in this paper has been done within the framework of the Lenstool software package, which is publicly available.
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