Overconstrained gravitational lens models and the Hubble constant

Overconstrained gravitational lens models and the Hubble constant
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过度约束的引力透镜模型和哈勃常数

DOI:
10.1093/mnras/staa344
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发表时间:
2020
影响因子:
4.8
通讯作者:
Kochanek, C S
Kochanek, C S
中科院分区:
物理与天体物理2区
文献类型:
--
作者:
Kochanek, C S

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众所周知,从引力透镜时间延迟测量H 0的尺度为H 0 <$1 − κE,其中κ E是爱因斯坦半径RE处的平均收敛,但除了延迟之外,所有可用的透镜数据都没有直接约束κE。由透镜数据约束的径向质量分布的性质为RE和无量纲量ε =REα“(RE)/(1 − κE),其中α”(RE)是在RE处偏转轮廓的二阶导数。自由度太少的透镜模型,如密度为ρ r-n的幂律模型,在ε和κE之间有一对一的对应关系(对于幂律模型,ε = 2(n-2)和κE=(3-n)/2 =(2-ε)/4)。这意味着具有很少参数的高度约束的透镜模型很快导致非常精确但不准确的κ E估计,因此H 0。基于一个广泛的合理的暗物质晕模型的实验,这是不可能的,任何目前的估计h 0从引力透镜时间延迟是更准确的,无论报告的精度。
It is well known that measurements ofH0from gravitational lens time delays scale asH0∝ 1 − κE, where κEis the mean convergence at the Einstein radiusREbut that all available lens data other than the delays provide no direct constraints on κE. The properties of the radial mass distribution constrained by lens data areREand the dimensionless quantity ξ =REα″(RE)/(1 − κE), where α″(RE) is the second derivative of the deflection profile atRE. Lens models with too few degrees of freedom, like power-law models with densities ρ ∝r−n, have a one-to-one correspondence between ξ and κE(for a power-law model, ξ = 2(n− 2) and κE= (3 −n)/2 = (2 − ξ)/4). This means that highly constrained lens models with few parameters quickly lead to very precise but inaccurate estimates of κEand henceH0. Based on experiments with a broad range of plausible dark matter halo models, it is unlikely that any current estimates ofH0from gravitational lens time delays are more accurate than, regardless of the reported precision.
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