Gravitational flexion, its measurement and its application to galaxy clusters

宇宙结构的引力透镜效应是绘制暗物质空间分布和总量的首选方法之一。为此目的，通常使用引力潮汐场，即所谓的引力切变，它可以从引力透镜物体背景中遥远星系图像的椭圆变形中测量。这种测量的角分辨率限于大约半弧分的角尺度。然而，为了检验冷暗物质的假设，人们希望在更小的尺度上探测暗物质的分布，潮汐场的导数可以组合成单重或三重旋转对称的量，从而保证了获得这种测量结果。本申请旨在扩展和完成先前授予的项目，该项目旨在首次以可靠和无偏差的方式测量屈曲的两个分量。最初设想的工作方案由于在工作过程中发现和解决的相当大的困难而推迟，我们现在能够测量真实模拟的星系图像的弯曲。在该项目的下一个（第四）年，我们在这里申请资金，迄今为止开发的测量方法将扩展到观测数据，并用于校准星系图像中固有弯曲的统计分布。最后，弯曲将首次与剪切一起用于重建至少一个星系团的物质分布。

Gravitational lensing by cosmic structures is one of the preferred methods for mapping the spatial distribution and the total amount of dark matter. For this purpose, the gravitational tidal field is routinely being used, the so-called gravitational shear, which can be measured from the elliptical distortions of the images of distant galaxies in the background of the gravitationally lensing objects. The angular resolution of such measurements is limited to angular scales of approximately half an arc minute. It would be desirable, however, to probe the distribution of dark matter also on smaller scales in order to test the hypothesis of cold dark matter.Access to such measurements is promised by the derivatives of the tidal field which can be combined to form quantities of single or three-fold rotational symmetry. They are called the F and G flexions, both of which have two components.The present application is meant to extend and conclude a previously granted project aiming at measuring for the first time both components of the flexions in a reliable and unbiased way. The work programme originally foreseen was delayed by considerable difficulties, which were uncovered and solved in the course of the work.We are now in a position to measure the flexions of realistically simulated galaxy images. During the further (fourth) year of the project, for which we apply for funding here, the measurement method developed so far will be extended to observational data and used for calibrating the statistical distribution of intrinsic flexions in galaxy images. Finally, the flexion will be used for the first time jointly with the shear to reconstruct the matter distribution of at least one galaxy cluster.