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Ambiguities in gravitational lens models: the density field from the source position transformation

机译：引力透镜模型中的歧义：来自源位置变换的密度场

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Strong gravitational lensing is regarded as the most precise technique to measure the mass in the inner region of galaxies or galaxy clusters. In particular, the mass within one Einstein radius can be determined with an accuracy of the order of a few percent or better, depending on the image configuration. For other radii, however, degeneracies exist between galaxy density profiles, precluding an accurate determination of the enclosed mass. The source position transformation (SPT), which includes the well-known mass-sheet transformation (MST) as a special case, describes this degeneracy of the lensing observables in a more general way. In this paper we explore properties of an SPT, removing the MST to leading order, that is we consider degeneracies which have not been described before. The deflection field hbox{$hat(cheta)$} resulting from an SPT is not curl-free in general, and thus not a deflection that can be obtained from a lensing mass distribution. Starting from a variational principle, we construct lensing potentials that give rise to a deflection field hbox{$tilde$} , which differs from hbox{$hat$} by less than an observationally motivated upper limit. The corresponding mass distributions from these “valid” SPTs are studied: their radial profiles are modified relative to the original mass distribution in a significant and non-trivial way, and originally axi-symmetric mass distributions can obtain a finite ellipticity. These results indicate a significant effect of the SPT on quantitative analyses of lens systems. We show that the mass inside the Einstein radius of the original mass distribution is conserved by the SPT; hence, as is the case for the MST, the SPT does not affect the mass determination at the Einstein radius. Furthermore, we analyse a degeneracy between two lens models, empirically found previously, and show that this degeneracy can be interpreted as being due to an SPT. Thus, degeneracies between lensing mass distributions are not just a theoretical possibility, but do arise in actual lens modeling.
机译：强引力透镜被认为是测量星系或星系团内部区域质量的最精确技术。尤其是，可以根据图像配置，以几个百分点或更高的精度确定一个爱因斯坦半径内的质量。但是，对于其他半径，在银河系密度分布图之间存在简并性，因此无法精确确定封闭质量。源位置变换（SPT）作为特殊情况包括众所周知的质量表变换（MST），它以更一般的方式描述了镜头可观察物的这种退化。在本文中，我们探索了SPT的属性，将MST删除为领先顺序，也就是说，我们考虑了以前未描述的简并性。由SPT产生的偏转场 hbox {$ ahat（ vc theta）$}通常不是无卷曲的，因此也不是可以从透镜质量分布获得的偏转。从变分原理开始，我们构造出引起偏转场 hbox {$ atilde $}的透镜势，该偏转场与 hbox {$ ahat $}的差异小于观察得出的上限。研究了来自这些“有效” SPT的相应质量分布：它们的径向轮廓相对于原始质量分布以显着且非平凡的方式进行了修改，并且原始轴对称质量分布可以得到有限的椭圆率。这些结果表明，SPT对镜头系统的定量分析具有重大影响。我们表明，SPT守恒了原始质量分布的爱因斯坦半径内的质量;因此，与MST一样，SPT不会影响爱因斯坦半径处的质量确定。此外，我们分析了先前凭经验发现的两个透镜模型之间的简并性，并表明该简并性可以解释为是由于SPT引起的。因此，镜片质量分布之间的退化不仅是理论上的可能性，而且在实际的镜片建模中也会出现。

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