Generalized model-independent characterization of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe
Generalized model-independent characterization of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe
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DOI：
10.1093/mnras/stz2717
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发表时间：
2018-12
影响因子：
4.8
通讯作者：
J. Wagner;Sven Meyer
中科院分区：
文献类型：
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作者：
J. Wagner;Sven Meyer
我们从Ia型超新星中确定宇宙膨胀率，以建立一个基于数据的距离测量，该测量不需要对宇宙的组成进行假设，即关于弗里德曼宇宙学模型的特定参数化。尺度由哈勃常数H0决定，是引力透镜形式论中唯一的自由宇宙学参数。我们研究了从万神殿样本中确定透镜距离比D的准确度和精度。将D及其不确定性插入给定H0的透镜方程中，特别是一对多图像之间的时间延迟方程，可以确定透镜特性，特别是透镜势的差异（Δϕ），而无需指定宇宙学模型。我们将亮度距离扩展为解析正交基，通过全局最优χ2参数估计确定基函数的最大似然权重，并通过蒙特卡罗模拟推导置信界限。为典型的强透镜z = 0.5和1.0之间的配置,Δϕ可以确定相对不精确的1.7%,假设不精确的时间延迟和红移镜头的1%。只有一个小,可容忍的精度损失,model-independent镜头描述在本文开发的系列可以普遍下降的具体弗里德曼模型确定基于数据的距离D的比率。此外，对于任何天体物理应用，本文提出的方法提供了z≤2.3的距离测量，这在任何均匀的、各向同性的宇宙中都是有效的，广义相对论作为引力理论。
We determine the cosmic expansion rate from supernovae of type Ia to set up a data-based distance measure that does not make assumptions about the constituents of the universe, i.e. about a specific parametrization of a Friedmann cosmological model. The scale, determined by the Hubble constant H0, is the only free cosmological parameter left in the gravitational lensing formalism. We investigate to which accuracy and precision the lensing distance ratio D is determined from the Pantheon sample. Inserting D and its uncertainty into the lensing equations for given H0, especially the time-delay equation between a pair of multiple images, allows to determine lens properties, especially differences in the lensing potential (Δϕ), without specifying a cosmological model. We expand the luminosity distances into an analytic orthonormal basis, determine the maximum-likelihood weights for the basis functions by a globally optimal χ2-parameter estimation, and derive confidence bounds by Monte Carlo simulations. For typical strong lensing configurations between z = 0.5 and 1.0, Δϕ can be determined with a relative imprecision of 1.7 per cent, assuming imprecisions of the time delay and the redshift of the lens on the order of 1 per cent. With only a small, tolerable loss in precision, the model-independent lens characterisation developed in this paper series can be generalised by dropping the specific Friedmann model to determine D in favour of a data-based distance ratio. Moreover, for any astrophysical application, the approach presented here, provides distance measures for z ≤ 2.3 that are valid in any homogeneous, isotropic universe with general relativity as theory of gravity.